text:
\section{Introduction}

\subsection{Background}

In the classical theory of accretion discs the gas is assumed to rotate around a massive central object following coplanar, circular and approximately Keplerian orbits. Although this is the simplest solution for the motion of fluid elements placed in a Newtonian potential well, external forces can give rise to non-planar discs, composed of non-circular rings. In fact, the general solution allows for discs to be twisted or tilted, with their orbits presenting a smoothly varying eccentricity and/or inclination. The literature offers strong observational and theoretical evidence \citep[][and references therein]{bardeenpetterson1975,ogilvie2000,ogilvie2001,globalsimulations} to believe that under various conditions discs can become either warped or eccentric. In particular, the precession of deformed discs has been used to explain several phenomena in X-ray binaries \citep[e.g.][]{gerendboynton1976,whitehurst1988,sv1998,lai1999}.

Discs around black holes are warped if the spin axis of the central object and the angular momentum of the accreting matter are misaligned. The fluid elements in tilted orbits will be subject to Lense-Thirring (gravitomagnetic) precession which tends to twist and warp the disc \citep{bardeenpetterson1975}. The way a tilted ring communicates its inclination with respect to the equator of the black hole to its neighbouring rings depends on a balance between hydrodynamic and gravitomagnetic torques. Roughly speaking the warp propagation is diffusive if $\alpha>H/r$, and is wave-like if $\alpha<H/r$, where $\alpha$ is the \cite{ss73} viscosity parameter and $H/r$ is the angular semi-thickness of the disc. In a low-viscosity disc around a Kerr black hole, the warp has an oscillatory radial structure, as shown by \cite{ivanovillarionov1997} and discussed by \cite{lubowetal2002}. In several X-ray binaries, jets (which are thought to be aligned with the rotation axis of the black hole) are observed to be misaligned with respect to the binary rotation axis \citep[e.g. GRO J1655-40,][]{maccarone2002}. This is strong evidence for a warped disc around the compact object in the binary \citep{mtp2008}. Warping might also be induced by radiation pressure forces \citep{pringle1996}. Despite being more likely for discs around neutron star primaries \citep{ogilviedubus2001}, radiation-driven warping might also occur around black holes provided the disc extends to large enough radius, as in the case of GRS 1915+105 \citep{rauetal2003}.

Eccentric accretion discs are believed to exist in cataclysmic binaries of mass ratio $q\la 0.3$ \citep[e.g.][]{pattersonetal2005}. Eccentricity can result from an instability involving the orbiting gas and the tidal potential of the companion star. Discs may become eccentric if they are large enough to extend to the 3:1 resonance, the radius in the disc where its angular velocity equals three times that of the binary \citep{lubow1991a,lubow1991b}. The strongest observational evidence for eccentric discs is the detection, in the light curves of accreting binary systems, of long-period modulations known as superhumps, which can be explained by the action of tidal stresses on a precessing eccentric disc \citep{whitehurst1988}. Although this phenomenon is usually associated with cataclysmic variable stars, superhumps have been detected in an increasing number of black hole binaries \citep{donocharles1996,haswelletal2001,uemura2002,neiletal2007,zurita2008}. In fact, black hole binaries are likely to have mass ratios $q\la0.3$ and therefore to have eccentric discs during at least some stages of their outbursts. \cite{haswelletal2001} noted that the mechanism responsible for superhump luminosity variations differs in X-ray binaries and cataclysmic variables, but the underlying dynamics is the same.

Our goal is to describe the propagation of global eccentric and warped disturbances, under a variety of conditions, from the outer parts of the disc where they originate to the inner parts. In the outer parts of the disc, the motion is Keplerian and stationary or slowly precessing global deformations are supported. Since the Lense-Thirring precession frequency increases with decreasing $r$, tilted orbits at different radius will tend to precess at different rates, which tends to twist the disc. Hydrodynamic stresses counteract this effect, resulting in wavelike warp propagation from the outer disc to the inner region. Similarly, for eccentric discs a transition has to be made between the Keplerian region where eccentric instabilities are driven, and the inner region where general relativistic effects dominate the precession of elliptical orbits. It is this connection between different regions of the disc, with different characteristics, that we attempt to describe.

\subsection{Deformations as global modes}

Warped or eccentric disturbances of small amplitude can be thought of as linear perturbations of a circular and coplanar disc. In the simplest case of a vertically isothermal disc with unit ratio of specific heats, wave modes with a dependence in time and azimuth of the form $\exp{(\textrm{i}m\phi-\textrm{i}\omega t)}$, and local radial wavenumber $k$ obey \citep{okazakietal1987}

\begin{equation}
k^2=\frac{(\hat{\omega}^2-\kappa^2)(\hat{\omega}^2-n\Omega_z^2)}{\hat{\omega}^2c_\mathrm{s}^2},
\label{disprelation}
\end{equation}
where $\hat{\omega}=\omega-m\Omega$ is the Doppler-shifted wave frequency, integers $m$ and $n\geq0$ are the azimuthal and vertical mode numbers, respectively, and $c_\textrm{s}=\Omega_z H$ is the constant sound speed in the disc, with $H$ being the local vertical scaleheight. The symbols $\Omega$, $\kappa$ and $\Omega_z$ represent the angular velocity, epicyclic frequency and vertical frequency, respectively. Relativistic effects are included in the problem by using relativistic expressions for these characteristic frequencies. In the Kerr metric, valid for a rotating black hole, they read \citep{kato1990}

\begin{equation}
\Omega=(r^{3/2}+a)^{-1},
\label{relomega}
\end{equation}
\begin{equation}
\kappa=\Omega\sqrt{1-\frac{6}{r}+\frac{8a}{r^{3/2}}-\frac{3a^2}{r^2}},
\label{relkappa}
\end{equation}
\begin{equation}
\Omega_z=\Omega\sqrt{1-\frac{4a}{r^{3/2}}+\frac{3a^2}{r^2}},
\label{relomegaz}
\end{equation}
where $a$ is the dimensionless spin parameter of the black hole
($-1<a<1$), $r$ is the cylindrical radius in units of $GM/c^2$, and the frequencies are in units of $c^3/GM$, where $c$ is the speed of light, $G$ the gravitational constant and $M$ the mass of the black hole; in these units velocities are in units of $c$. The dispersion relation is local, i.e., it is different at each radius since the characteristic frequencies depend on $r$, and is valid only where the wavelength $\lambda=2\pi/k\ll r$.

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{loverhw.eps} \\
\vspace{-5mm}
\includegraphics[width=\linewidth]{loverhe.eps}
\end{center}
\caption{Local wavelength of (a) $(\omega,m,n)=(0,1,1)$ and (b) $(0,1,0)$ modes (stationary warp and eccentricity, respectively) in units of $H$ for several values of the black hole spin. The inner edge of the disc is taken to be the marginally stable orbit, where $\kappa=0$.}
\label{lambdah}
\end{figure}

Viewed as linear perturbations of a standard disc, warp and eccentricity correspond to low-frequency waves with azimuthal number $m=1$. As showed by \cite{kato1983,kato1989} these modes are global, and have relatively long wavelengths when compared to the other modes described by the local dispersion relation, being the most likely to exist in a turbulent disc. More specifically, a $(m,n)=(1,1)$ mode can be identified with a warp as its vertical displacement is independent of the vertical coordinate $z$ and varies with $\phi$ at each radius, giving rise to a tilting (movement with respect to the disc plane). A $(m,n)=(1,0)$ mode corresponds to eccentric disc since its radial displacement is independent of $z$ and varies with azimuthal angle, originating an elliptic orbit (movement within the disc plane). The $m=1$ modes are global in the sense that only they can have a wavelength much larger than the semi-thickness of the disc over a wide range of radius. This can be confirmed in Fig. \ref{lambdah} where we show the variation with $r$ of the local wavelength in units of $H$, for several values of $a$, for both the warp and eccentricity.

In \cite{ferreiraogilvie2008} we worked with a simplified set of hydrodynamic equations in order to deal with the nonlinear couplings of different wave modes. Within this framework we obtained an equation for the warp tilt $W$ at each radius \citep[similar to the one given by][]{papaloizoulin1995} assuming the warp to be a zero-frequency mode propagating in a strictly isothermal, relativistic disc. In addition to being valid only where $c_\textrm{s}$ is constant and where viscous effects are negligible, the equation derived does not hold for large radius, where the wavelength of the warp becomes comparable to $r$, since some terms were omitted in our local approximation. A similar method was used to derive an equation for the eccentricity at each radius $E$ valid only for an inviscid and strictly isothermal disc.

Here we consider the more general description of a stationary, wave-like warp and eccentricity given by \cite{lubowetal2002} and \cite{goodchildogilvie2006}, respectively. These theories are less general than the ones formulated by \cite{ogilvie2000,ogilvie2001} since they consider deformations to have small amplitude, and not all viscous or turbulent effects are included. Also, the \cite{goodchildogilvie2006} calculation uses a highly simplified, 2D disc model. However, the secular theories of \cite{lubowetal2002} and \cite{goodchildogilvie2006} are appropriate for thin discs of any given structure, and allow for viscous (turbulent) damping of deformations.

\subsection{Black hole states and high-frequency QPOs}

Observations indicate that black hole systems can be found in different spectral states, going from the quiescent state to low, intermediate, high and very high states as the mass accretion rate increases \citep{bhbbook}. The very high state is the one where high-frequency QPOs, i.e., modulations seen in the spectra of black hole systems that are not strictly periodic and have frequencies $\ga 100$ Hz, are almost exclusively detected \footnote{In the X-ray binary XTEJ1550-564, a HFQPO was detected at a photon count rate below the VHS \citep[see][and references therein]{klisbook}.}. This is the dominating state close to the Eddington limit.

The accretion flow has different characteristics in different black hole states. If the disc properties are such that the warp and eccentricity can propagate to the inner region, the interaction between relativistic effects and global deformations can give rise to interesting phenomena. In particular, the warp and eccentricity can have a fundamental role in exciting trapped inertial modes, which may explain high-frequency QPOs \citep{nowaketal1997}, as previously suggested by \cite{katowarp2004,kato2008} and \cite{ferreiraogilvie2008}.

In this paper we show that the inward propagation of warp and eccentricity is facilitated for high accretion rate. For fixed viscosity, global deformations reach the inner region of the disc with a modest amplitude when the accretion rate is high, and can take part in the excitation mechanism for inertial modes trapped in this region. If high-frequency QPOs can be identified with these trapped inertial waves, we can argue that they are predominantly detected in the very high state, where the accretion rate is close to Eddington, because only in this case global deformations can reach the inner region with non-negligible amplitude and excite the trapped modes.

\subsection{Plan of the paper}

In section 2, we introduce the disc model in which we study the propagation of global deformations. We consider a disc with a polytropic structure in the vertical direction, constant opacity, and with gas and radiation contributing to the total pressure. In section 3 we describe the propagation of global disturbances, by solving equations for the warp tilt and eccentricity at each radius. To mimic several possible conditions in a disc with a fixed viscosity $\alpha$ around a black hole of a given mass and spin, we vary the accretion rate and the damping of the warp and eccentricity. The results obtained are discussed in section 4. Conclusions are presented in section 5.

\section{Disc model}

\subsection{Viscosity prescription}

In the famous \cite{ss73} model, the disc is assumed to be geometrically thin and optically thick. The gas in the disc is heated by viscous dissipation and cooled by radiative diffusion through the vertical boundaries. Angular momentum is transferred outwards at a rate which is taken to be proportional to the height-integrated total pressure, with the efficiency of the process being parametrised by a dimensionless quantity $\alpha$, independently of the nature of the stress. The disc is taken to be composed of three parts: in the innermost regions (a) and (b), electron scattering is the main contribution to the opacity (which is then given by the constant, Thomson value, $\kappa_{\textrm{T}}$), while free-free absorption is dominant in the outer region (c). In (a) the pressure is determined by the radiation pressure ($p\propto T^4$), while gas pressure ($p\propto \rho T$) dominates in (b) and (c). The radiation-dominated region exists only if the accretion rate is larger than a few percent of the Eddington rate, being important in accretion discs around black holes.

Despite neglecting to treat the vertical structure of the disc, not considering other contributions to the cooling and heating rates of the gas, and despite the simple parametrization for the angular momentum transfer, the Shakura \& Sunyaev $\alpha$-model is still the standard reference for the radial structure of accretion discs, if gas pressure is dominant. Region (a) has always been more problematic. In fact, the assumption that stress scales with the total pressure in the radiation pressure dominated regime leads to viscous \citep{le74} and thermal \citep{ss76} instabilities. These can be avoided by simply assuming that the stresses scale with the gas pressure \citep{sc81}, or with a combination of both gas and radiation pressure \citep[e.g.][]{tl1984,mf2002}, recent simulations by Hirose et al. (ApJ, submitted) suggest that turbulent stresses may indeed be correlated with the total pressure. However, fluctuations in stress \citep[now known to be magnetic in nature,][]{mri} are the ones driving pressure fluctuations, contrary to the usual assumption that changes in pressure give rise to changes in stress; this seems to avoid thermal instability (which has a faster growth rate than viscous instability). With these results in mind, we consider the $\alpha$ viscosity prescription in the form,

\begin{equation}
\mu=\alpha\frac{p}{\Omega},
\label{avp}
\end{equation}
so that the viscosity $\mu$ and total pressure $p$ correlate, as in the original Shakura \& Sunyaev model. Here we consider $\alpha$ to be a function of radius only; in this section $\Omega=\Omega_K=\sqrt{GM/R^3}$ is the Keplerian angular velocity, and $R=rGM/c^2$ is the dimensional radius.

\subsection{Vertical structure}

Independently of the viscosity prescription, the radiation-pressure dominated region might suffer from another type of instability. In the Shakura \& Sunyaev model, the dissipation rate per unit volume is independent of $z$. If the dissipation rate per unit mass is also vertically constant, then the density is independent of $z$, vanishing abruptly at the vertical boundaries of the disc, $z=z_0(R)$ \citep{ss73}.
A disc with these properties is subject to convective instability \citep{bb77}.

Simulations of radiation-dominated discs by \cite{turner2004} indicate that neither is the dissipation per unit mass constant nor is the density independent of $z$. In fact, the computed density profile resembles more that of a polytropic model with index $s=3$ \citep[see also][]{agoletal2001}. Using the polytropic law, $p\propto \rho^{4/3}$, in the hydrostratic equilibrium equation

\begin{equation}
\frac{\partial p}{\partial z}=-\Omega_z^2\rho z \quad (\textrm{Keplerian disc: $\Omega_z=\Omega=\sqrt{GM/R^3}$}),
\label{he}
\end{equation}
it is straightforward to get

\begin{equation}
\rho=\rho_0(R) \left[1-\left(\frac{z}{z_0}\right)^2\right]^3 \quad (-z_0<z<z_0).
\label{rho}
\end{equation}
This result was used by \cite{bb77}, who argued that convection in the radiation-pressure dominated region would establish a vertically isentropic structure ($T^3/\rho=$ constant in $z$).

The $s=3$ polytropic structure has the convenient property of allowing for a ratio of radiation to gas pressure,

\begin{equation}
\beta=\frac{p_\textrm{r}}{p_\textrm{g}}=\frac{4\sigma\mu_\textrm{m} m_{\textrm{p}}}{3ck_B}\frac{T^3}{\rho},
\end{equation}
independent of $z$. Using (\ref{rho}) in the hydrostratic balance equation we get $p=p_0(R)\left[1-\left(z/z_0\right)^2\right]^4$, where

\begin{equation}
p_0=\frac{\Omega_z^2z_0^2}{8}\rho_0=\frac{\Omega^2z_0^2}{8}\rho_0.
\label{he2}
\end{equation}
This is consistent with the equation of state

\begin{equation}
p=p_{\textrm{g}}+p_{\textrm{r}}=\frac{k_B}{\mu_\textrm{m} m_{\textrm{p}}}\rho T+\frac{4\sigma}{3c}T^4,
\end{equation}
provided $T=T_0(R)\left[1-\left(z/z_0\right)^2\right]$, and independently of the variation of $\beta$ with radius, i.e., the polytropic vertical structure with $s=3$ can be used to model not only the radiation pressure dominated regime but also the gas pressure dominated region. In fact, a full treatment of the vertical structure of a gas pressure dominated disc in hydrostatic (\ref{he}) and radiative equilibrium \citep[e.g.][]{accretionpower}:

\begin{equation}
\frac{\partial F}{\partial z}=\mu\left(R\Omega'\right)^2 \quad \textrm{(energy balance)},
\label{eb}
\end{equation}
\begin{equation}
F=F_{\mathrm{rad}}=-\frac{16\sigma T^3}{3\kappa_\textrm{T}\rho}\frac{\partial T}{\partial z} \quad \textrm{(radiative diffusion law)},
\label{rdl}
\end{equation}
indicates that the resulting profiles are very similar (except perhaps $F(z)$ for large $z$) to those obtained for a polytropic model with $s\approx 2.7$ (Ogilvie 2001, unpublished lecture notes). This result, and the simulations in radiation-pressure dominated regions, indicate that assuming a polytropic vertical structure with $s=3$ throughout the radial extent of the disc is a good approximation, provided the opacity remains constant. This is true of the innermost regions ((a) and (b) in the Shakura \& Sunyaev model) of the disc. Since we are most interested in the propagation of global deformations in these regions, we take the opacity to be constant throughout the disc, i.e., region (c) is neglected in our model. In fact, the physics of region (c) is more complicated than assumed by \cite{ss73}, because of the presence of different sources of opacity and the importance of irradiation and partial ionisation.

\subsection{Radial structure}

The assumptions of hydrostatic equilibrium and vertical isentropy (or equivalently, $s=3$ polytropic structure in $z$), together with the equation of state, are enough to determine the vertical structure of the disc, i.e., determine the variation of $\rho$, $p$ and $T$ with $z$, without the requirement of radiative balance \citep[see discussion in section 3.1 of][]{agoletal2001}. However, to fully determine the radial structure: $\rho_0(R)$, $p_0(R)$, $T_0(R)$ and $z_0(R)$, two more equations are needed since the polytropic relation is not valid in the radial direction.

Since matter is being accreted in the disc, there are radial drift motions which transport mass and angular momentum. In steady thin discs the conservation of both mass and angular momentum can be express in the form \citep[e.g.][]{pringle1981},
\begin{equation}
\bar{\nu}\Sigma=\frac{\dot{M}}{3\pi}f, \quad \textrm{with}\quad f=1-\sqrt{\frac{R_\textrm{in}}{R}},
\label{cam}
\end{equation}
where $\dot{M}$ is the mass accretion rate, $R_\textrm{in}$ is the radius of the inner edge of the disc taken to be the marginally stable orbit, and the (density-weighted) mean kinematic viscosity $\bar{\nu}(R)$ is defined by

\begin{equation}
\bar{\nu}\Sigma(R)=\int^{z_0}_{-z_0}\mu(R,z) \textrm{d}z=\alpha\frac{P}{\Omega},
\end{equation}
where

\begin{equation}
\Sigma(R)=\int^{z_0}_{-z_0}\rho(R,z)\textrm{d}z=\frac{32}{35}\rho_0z_0,
\end{equation}
\begin{equation}
P(R)=\int^{z_0}_{-z_0}p(R,z) \textrm{d}z=\frac{256}{315}p_0z_0
\end{equation}
are the surface density and vertically integrated pressure, respectively.

The final equation comes from energy considerations. It is traditional to assume that the disc is in radiative equilibrium. However, convection, turbulence or other motions can also contribute to the transport of energy to the disc surface. In fact, if the disc has a polytropic vertical structure with $s=3$, the radiative diffusion law gives us $F_{\textrm{rad}}$ proportional to $z$. If $F=F_{\textrm{rad}}$, i.e., if radiative diffusion carries the entire energy flux, then (\ref{eb}) gives us a dissipation rate per unit volume independent of $z$, which is neither consistent with the $\alpha$ viscosity prescription assumed here (\ref{avp}) since $p=p_0(R)\left[1-\left(z/z_0\right)^2\right]^4$, nor is in agreement with simulations of radiation-pressure dominated discs \citep{turner2004}. Therefore, here we use the energy balance equation in the form

\begin{equation}
\int_{0}^{z_0}\frac{\partial}{\partial z}\left(F_{\textrm{rad}}+F_{\textrm{extra}}\right)\textrm{d}z=\int_{0}^{z_0}\mu\left(R\Omega'\right)^2\textrm{d}z,
\end{equation}
where the energy transport by other motions rather than by radiative diffusion is encompassed in $F_{\textrm{extra}}$. Since radiation is supposed to carry the entire heat flux at the photosphere $z=z_0$, we assume that the extra term integrates to zero so that the energy balance can be written as,

\begin{equation}
F_{\textrm{rad}}(R,z_0)=\frac{1}{2}(R\Omega')^2\left(\alpha\frac{P}{\Omega}\right),
\end{equation}
since $F_{\textrm{rad}}(R,z=0)=0$ by symmetry.

Here we take $\mu_\textrm{m}=0.615$, $\kappa_T=0.33\textrm{ cm}^2\textrm{g}^{-1}$, and use non-dimensional parameters to represent the dependence in mass, accretion rate and radius. The radial structure of the disc can be represented in terms of $\Sigma(R)$, $P(R)$, $\beta(R)$ and $H(R)$, the (density-weighted) scale-height of the disc defined by:

\begin{equation}
H^2=\frac{\int_{-z_0}^{z_0}\rho z^2\textrm{d}z}{\int_{-z_0}^{z_0}\rho\textrm{d}z}=\frac{z_0^2}{9}.
\label{dt}
\end{equation}
The equations read:
\begin{equation}
\Sigma=2.5\times10^5\, \dot{m}^{3/5}\alpha^{-4/5}m^{1/5}f^{3/5}r^{-3/5} (1+\beta)^{-4/5},
\label{rsc}
\end{equation}
\begin{equation}
P=3.0\times10^{22}\,\dot{m}\,\alpha^{-1}fr^{-3/2},
\label{rsd}
\end{equation}
\begin{equation}
\beta (1+\beta)^{-3/5}=3.6\times10^2\, \dot{m}^{4/5}\alpha^{1/10}m^{1/10}f^{4/5}r^{-21/20},
\label{rsa}
\end{equation}
\begin{equation}
H=1.7\times10^3\,  \dot{m}^{1/5}\alpha^{-1/10}m^{9/10}f^{1/5}r^{21/20} (1+\beta)^{2/5},
\label{rsb}
\end{equation}
where $m$ is the mass in units of $M_\odot$, $\dot{m}$ is the accretion rate in units of the Eddington accretion rate assuming an efficiency of $0.1$, $r$ is in units of the gravitational radius and $f=1-\sqrt{r_\textrm{in}/r}$, where $r_\textrm{in}$ is the dimensionless, spin dependent, radius of the marginally stable orbit; $H$, $\Sigma$ and $P$ are in cgs units. It should be noted that in the limits $\beta\gg1$ ($P_{\textrm{r}}$ dominates) and $\beta\ll1$ ($P_{\textrm{g}}$ dominates) we recover the same dependencies in $m$, $\dot{m}$, $\alpha$, $r$ and $f$ as in regions (a) and (b), respectively, of the Shakura \& Sunyaev model:\newline
\newline
\textbf{(a) $\mathbf{\beta\gg1}$:}
\begin{equation}
\Sigma=1.9\,\alpha^{-1}\dot{m}^{-1}r^{3/2}f^{-1},
\end{equation}
\begin{equation}
\beta =2.4\times10^6\, \dot{m}^{2}\alpha^{1/4}m^{1/4}f^{2}r^{-21/8},
\end{equation}
\begin{equation}
H=6.1\times10^5\dot{m}\,m\,f.
\label{ha}
\end{equation}
\vspace{5pt}
\textbf{(b) $\mathbf{\beta\ll1}$:}
\begin{equation}
\Sigma=2.5\times10^5\,\alpha^{-4/5}\dot{m}^{3/5}m^{1/5}r^{-3/5}f^{3/5},
\label{sdb}
\end{equation}
\begin{equation}
\beta=3.6\times10^2\, \dot{m}^{4/5}\alpha^{1/10}m^{1/10}f^{4/5}r^{-21/20},
\end{equation}
\begin{equation}
H=1.7\times10^3\,\alpha^{-1/10}\dot{m}^{1/5}m^{9/10}r^{21/20}f^{1/5}.
\label{hb}
\end{equation}
The expression for the total pressure in both regions is the same and is given by (\ref{rsd}). The differences in the numerical factors are due to the treatment of the vertical structure, to the small difference in the values used for $\kappa_T$ and $\mu_\textrm{m}$, to the different normalization of radius, and also because here we consider the $r\phi$ component of the stress tensor, $T_{r\phi}=\mu r\Omega'$, to be $-(3/2)\alpha p$, instead of the usual Shakura \& Sunyaev value $-\alpha p$.

\begin{figure*}
\begin{center}
\includegraphics[width=0.48\linewidth]{model1.eps}
\includegraphics[width=0.48\linewidth]{model2.eps} \\
\vspace{-5mm}
\includegraphics[width=0.48\linewidth]{model3.eps}
\includegraphics[width=0.48\linewidth]{model4.eps}
\end{center}
\caption{Log-log plot of the variation of (a) $\beta=P_\textrm{r}/P_\textrm{g}$, (b) surface density, (c) vertically integrated pressure and (d) sound speed in units of $c$ with radius for $\dot{m}=0.1,\,0.5$, $\alpha=0.1$, $a=0.5$ and $m=10$. The full lines represent the disc model with a combination of gas and radiation pressure when the stress scales with total pressure, while the dashed lines correspond to solutions in regions (a) and (b) when the stress scales with the gas pressure only.}
\label{model}
\end{figure*}

In order to get a smooth transition between the two regions, and to allow for a combination of gas and radiation pressure throughout the disc, we solve equation (\ref{rsa}) numerically.
The resultant function, $\beta(r)$, is then used in (\ref{rsb}) and (\ref{rsc}), in order to get expressions for $H(r)$ and $\Sigma(r)$. The radial disc structure obtained here is used in the study of the warp and eccentricity propagation, which is described in the following section.

One reason that we take some care over the basic disc model is that it is important to obtain a smooth density profile for the disc in order to calculate the propagation of the warp and eccentricity. Also, since $H^2$ appears in the equations for those quantities, the factor of $1/9$ in equation (\ref{dt}) makes a significant difference.

For comparison, we also include in this section the expressions obtained for region (a), if the stress scales with the gas pressure instead of total pressure ($\mu=\alpha p_g/\Omega$). The semi-thickness of the disc is independent of the viscosity prescription, so that (\ref{ha}) is still valid. The surface density is given by (\ref{sdb}) while $\beta$ and $P$ are given by:

\begin{equation}
P=3.9\times10^{27}\, \dot{m}^{13/5}\alpha^{-4/5}m^{1/5}f^{13/5}r^{-18/5},
\end{equation}
\begin{equation}
\beta =1.3\times10^5\, \dot{m}^{8/5}\alpha^{1/5}m^{1/5}f^{8/5}r^{-21/10}.
\end{equation}

In Fig. \ref{model} we show how $\beta$, the surface density, the vertically integrated pressure and the isothermal sound speed (squared), $c^2_{\mathrm{s}}=p_0/\rho_0=\frac{9}{8}\Omega^2H^2$, vary with radius for a disc with $\alpha=0.1$, $a=0.5$ and $m=10$, for two different values of the accretion rate. The differences in the disc structure when the stress scales with the total pressure or with the gas pressure are more evident in the innermost region of the disc, and for higher accretion rate, i.e., where radiation pressure is more important. The exception is the sound speed, proportional to the thickness of the disc, since $H$ in the radiation-pressure dominated region is independent of the viscosity prescription.

Finally, it should be noted that the model presented in this section is Newtonian. The effect of the black hole appears only in the choice of the inner radius, which is taken to be the marginally stable orbit and is, therefore, dependent on the rotation of the compact object. The relativistic correction factors of \cite{nt73} are not of great importance here since the most important relativistic effects in the study of warp and eccentricity propagation are the apsidal and nodal precession.

\section{Stationary propagation of warp and eccentricity}

In the general case, the warp tilt and the eccentricity are not only functions of space but also of time, and their evolution has been studied by (e.g.) \cite{lubowetal2002} and \cite{ogilvie2001}, respectively. However, the characteristic time-scale for the precession of a global warp or eccentricity is small when compared to the orbital frequency in the binary system, which implies that the frequency of these global deformations is negligible compared to the characteristic frequencies in the inner part of the disc. Therefore, we choose to study the steady shape of a warped or eccentric disc around a black hole.

\subsection{Equations}

In this section we present the equations that are used to describe the stationary wave-like propagation of warp and eccentricity in the disc model presented in the previous section.

The variation of the tilt of the disc, $W$, with radius can be obtained from \citep{lubowetal2002}

\begin{equation}
\frac{\textrm{d}}{\textrm{d}R}\left[\left(\frac{PR^3\Omega^2}{\Omega^2-\kappa^2+2i\alpha_\textrm{W}\Omega^2}\right)\frac{\textrm{d}W}{\textrm{d}R}\right]=\Sigma R^3(\Omega_z^2-\Omega^2)W.
\label{luboweq}
\end{equation}
This equation describes how propagating bending waves communicate the warp through the disc and is valid for small-amplitude warps; $W$ describes the amplitude and phase of the inclination of the disc. The local wavelength of these bending waves is approximately the one given by the dispersion relation (\ref{disprelation}) for $(\omega,m,n)=(0,1,1)$, if $\alpha_\textrm{W}=0$. The warp propagation is subject to viscous decay, which is described here by a dimensionless viscosity parameter designated $\alpha_\textrm{W}$. In the general case of non-isotropic viscosity, $\alpha_\textrm{W}\neq\alpha$ as the former is related to the $T_{rz}$ and $T_{\phi z}$ components of the stress tensor \textbf{\textsf{T}} while the latter is related to $T_{r\phi}$ \citep[see][and references therein]{lubowetal2002}.

The stationary propagation of a small eccentricity through the disc can be described, in the simplest case, by \citep[e.g.][]{goodchildogilvie2006}

\begin{equation}
\frac{\textrm{d}}{\textrm{d}R}\left[\left(\gamma-\textrm{i}\alpha_\textrm{E}\right)PR^3\frac{\textrm{d}E}{\textrm{d}R}\right]+R^2\frac{\textrm{d}P}{\textrm{d}R}E=\Sigma R^3(\kappa^2-\Omega^2)E,
\label{ecceq}
\end{equation}
where $E$ is a (possibly) complex function representing the amplitude and phase of the eccentricity at a given radius; $\gamma$ is the ratio of specific heats. In a strictly isothermal disc $\gamma=1$ and the global modes described by this equation have a local wavelength which is approximately the one given by the dispersion relation (\ref{disprelation}) for $(\omega,m,n)=(0,1,0)$, if $\alpha_\textrm{E}=0$. The equation describing the eccentricity propagation is based on, and agrees with the local dispersion relation of, a 2D disc; 3D effects are discussed by \cite{ogilvie2001,ogilvie2008}. The parameter $\alpha_\textrm{E}$ in equation (\ref{ecceq}) is essentially a bulk viscosity. Effects of shear viscosity are not included as its direct implementation may lead to growing eccentric waves \citep[viscous overstability,][]{kato1978} \citep[see also][and references therein]{ogilvie2001}. The process of turbulent eccentricity damping is poorly known and the simplest way of describing it is by using a dimensionless bulk viscosity parameter.

In order to include relativistic effects in the problem, we take $\Omega^{-1}=(GM/c^3) (r^{3/2}+a)$ and use expressions (\ref{relkappa}) and (\ref{relomegaz}) for the radial and vertical epicyclic frequencies, respectively. For the surface density $\Sigma$ and vertically integrated pressure $P$, expressions (\ref{rsc}) and (\ref{rsd}) are used.

\subsection{Numerical method}

We solve equations (\ref{luboweq}) and (\ref{ecceq}) numerically, using a
4th order Runge--Kutta method. In the case of the warp we use the boundary condition that corresponds to zero torque at the inner edge: $\mathrm{d}W/\mathrm{d}R(R_\mathrm{in})=0$. In order for the amplitude of the solution to be fixed, we specify the value $W_0=W(R_\mathrm{in})$ at the inner edge, which corresponds to the (small) inclination of the inner edge of the disc with respect to the equator of the black hole. For the eccentricity we use similar boundary conditions: $\mathrm{d}E/\mathrm{d}R(R_\mathrm{in})=0$ and $E_0=E(R_\mathrm{in})$. To avoid the formal singularity of the equations at the marginally stable orbit, here we take $R_\textrm{in}=R_\textrm{ms}+\delta$, where $\delta\ll R_\textrm{in}$ is an arbitrary value; the solutions for $W(R)$ and $E(R)$ are practically independent of the choice of $\delta$. The solutions are linear and can be renormalized to obtain any desired $W_\textrm{out}$ and $E_\textrm{out}$, the values of disc tilt and eccentricity at the outer radius. This normalisation is particularly meaningful in the case of $W(R)$ since $W_\textrm{out}$ is the (constant) disc tilt at large radius, which can be related to observations.

To solve the warp and eccentricity equations we consider a black hole with 10 solar masses, i.e. $m=10$, and spin $a=0.5$. The ratio of specific heats is given by \citep[e.g.][]{stellar}\footnote{Note that in many references $\beta$ is used to represent the ratio of gas pressure to total pressure while here $\beta=p_\textrm{r}/p_\textrm{g}$.},

\begin{equation}
\gamma=\frac{5+40\beta+32\beta^2}{3+27\beta+24\beta^2}.
\end{equation}
In regions (a) and (b) this expression gives $\gamma\approx4/3$ and $\gamma\approx5/3$, respectively. We regard the dimensionless viscosity parameter $\alpha$ as constant throughout the disc as in \cite{ss73}. Although simulations suggest values of $\alpha$ of the order $10^{-2}$, according to \cite{kingetal2007} observations indicate a typical range of $\alpha\sim0.1-0.4$. Here we choose to fix the viscosity parameter to $0.1$. Parameters $\alpha_\textrm{W}$, $\alpha_\textrm{E}$ and $\dot{m}$ can be varied. To mimic the transition between different black hole states we fix the viscous damping and vary the mass accretion rate. The results and corresponding discussion are presented in the next section.

\section{Results and Discussion}

\subsection{Undamped propagation}

\begin{figure*}
\begin{center}
\includegraphics[width=0.48\linewidth]{W02.eps}
\includegraphics[width=0.48\linewidth]{E02.eps} \\
\vspace{-5mm}
\includegraphics[width=0.48\linewidth]{W04.eps}
\includegraphics[width=0.48\linewidth]{E04.eps} \\
\vspace{-5mm}
\includegraphics[width=0.48\linewidth]{W08.eps}
\includegraphics[width=0.48\linewidth]{E08.eps}
\end{center}
\caption{Radial variation of (a) the warp tilt and (b) eccentricity normalised to their values at the outer radius for $\alpha_\textrm{W}=0= \alpha_\textrm{E}$ (i.e., no viscous damping) for (1) $\dot{m}=0.2$, (2) $\dot{m}=0.4$, (3) $\dot{m}=0.8$. The full line represents the real part of the disturbance while the imaginary part is represented by the dashed line. A logarithmic scale is used for the x-axis.}
\label{free}
\end{figure*}

\begin{figure*}
\begin{center}
\includegraphics[width=0.48\linewidth]{Wwkbtp.eps}
\includegraphics[width=0.48\linewidth]{Ewkbtp.eps} \\
\vspace{-5mm}
\includegraphics[width=0.48\linewidth]{Wwkbgp.eps}
\includegraphics[width=0.48\linewidth]{Ewkbgp.eps}
\end{center}
\caption{Solutions for (a) warp and (b) eccentricity propagation in region (a) ($\beta\gg1$) for $\alpha_\textrm{W}=0= \alpha_\textrm{E}$, $m=10$, $a=0.5$, $\dot{m}=0.1$, when the stress scales with the (1) total pressure and the (2) gas pressure. The full line represents the real part of the disturbance while the imaginary part is represented by the dashed line. The dot-dashed curves show the radial variation of the amplitude of the deformations, as predicted by the WKB analysis.}
\label{wkb}
\end{figure*}

In Fig. \ref{free} we show the variation with radius of the warp tilt and eccentricity for increasing accretion rate when $\alpha_\textrm{W}=0= \alpha_\textrm{E}$. In this case no dissipation is present in the equations for global deformations, so they propagate everywhere with non-negligible amplitude. Since the imaginary part of the solutions is zero, the warp comprises a pure tilt, i.e., the disc is not twisted \citep{lubowetal2002}. For small accretion rate the warp has an oscillatory shape as previously predicted by \cite{ivanovillarionov1997}. The wavelength increases with radius and, at large $R$, $W$ tends to a constant value, the inclination of the outer disc with respect to the equator of the black hole. Note, however, that contrary to the results of \cite{bardeenpetterson1975} the inner disc is not necessarily aligned with the mid-plane of the compact object, as previously shown by \cite{lubowetal2002}. The simulations of \cite{globalsimulations} also found hints of an oscillatory structure characterised by a long-wavelength with no indication of the Bardeen-Petterson effect. Eccentricity also has an oscillatory structure but its wavelength is shorter (yet much longer than the semi-thickness of the disc) and has a slower increase with radius. The shortening of the wavelengths at small radius of both the warp and eccentricity implies a sharp increase of the gradients $\textrm{d}W/\textrm{d}R$ and $\textrm{d}E/\textrm{d}R$ in the inner region of the disc. This is an important feature in terms of wave coupling in this region since the growth rate for inertial modes that are trapped below the maximum of the epicyclic frequency, and interact with global deformations, is proportional to $|\textrm{d}W/\textrm{d}R|^2$ or $|\textrm{d}E/\textrm{d}R|^2$, as found by \cite{ferreiraogilvie2008}.

The basic behaviour of the numerical solutions presented in this section can be explained using WKB theory. In particular, it is possible to predict how the wavelength and amplitude of the several solutions scale with radius. A WKB analysis of the secular theories can be performed by assuming the deformations $W$ and $E$ to be proportional to $\exp(\int\textrm{i}\,b\,\textrm{d}R)$, where $b$ is a function of $R$ to be determined. The $\textrm{d}P/\textrm{d}R$ term in equation (\ref{ecceq}) can be ignored in the WKB analysis since relativistic precession dominates the propagation of eccentricity. Letting $D_\textrm{W}=W(R)$ and $D_\textrm{E}=E(R)$, we can write equations (\ref{luboweq}) and (\ref{ecceq}) in the form

\begin{equation}
\frac{\textrm{d}}{\textrm{d}R}\left(g_i\frac{\textrm{d}D_i}{\textrm{d}R}\right)+h_iD_i=0, \quad i=\textrm{W},\textrm{E}.
\end{equation}
The WKB solution is valid where the radial variation of $g_i$ and $h_i$ is slow and is given by,
\begin{equation}
D_i\approx(g_ih_i)^{-1/4}\exp\left[\pm \int \textrm{i}\sqrt{h_i/g_i}\textrm{d}R\right].
\end{equation}
In the inviscid case ($\alpha_\textrm{W}=0=\alpha_\textrm{E}$), $g_\textrm{W}\approx PR^3 / 6 r^{-1}$, $h_\textrm{W}\approx\Sigma R^3\Omega^24ar^{-3/2}$, $g_\textrm{E}=\gamma PR^3$, and $h_\textrm{E}\approx\Sigma R^3\Omega^26r^{-1}$, keeping only the lowest-order terms in the expressions for $\Omega^2-\kappa^2$ and $\Omega^2-\Omega_z^2$. Remembering that $P=\Omega^2H^2\Sigma$ (from \ref{he2}), we can write

\begin{equation}
W\propto r^{1/8}(\Sigma H)^{-1/2}\exp\left[\pm \int \textrm{i}\sqrt{\frac{24a}{r^{5/2}H^2}}\textrm{d}R\right],
\label{wwkb}
\end{equation}
\begin{equation}
E\propto r^{1/4}(\Sigma H)^{-1/2}\exp\left[\pm \int \textrm{i}\sqrt{\frac{6}{\gamma r H^2}}\textrm{d}R\right],
\label{ewkb}
\end{equation}
where we have ignored the variation of $\gamma$ with radius. If the stress scales with the total pressure, these expressions indicate that the amplitude of the warp should be proportional to $r^{-5/8}$ in region (a) and to $r^{-1/10}f^{-2/5}$ in region (b); the amplitude of the eccentricity is proportional to $r^{-1/2}$ in the radiation-pressure dominated regime and to $r^{1/40}f^{-2/5}$ when gas pressure dominates. If the stress scales with the gas pressure only, the amplitudes in region (a) are proportional to $r^{17/40}f^{-4/5}$ and $r^{11/20}f^{-4/5}$ in the case of the warp and eccentricity, respectively. The results for region (a) can be confirmed in Fig. \ref{wkb}. In region (b) $r\gg r_{\textrm{in}}$, $f\approx 1$, so that the radial variation of both warp and eccentricity amplitudes is slow, as seen in Fig. \ref{free}. The eccentricity does not tend to a constant at large radius because its amplitude is slowly increasing when $r$ increases. The warp amplitude decreases with $r$ but does not tend to zero as indicated by the WKB scaling. The reason for this apparent contradiction is in the failure of the WKB approximation at large radii where the wavelength tends to infinity.

The radial variation of the wavelength of the deformations can also be understood in light of the WKB theory. From equations (\ref{wwkb},\ref{ewkb}), we see that the wavelengths are given by $\lambda_\textrm{W}\approx H \pi r^{5/4}/\sqrt{6 a}$, and $\lambda_\textrm{E}\approx 2H\pi r^{1/2}\sqrt{\gamma/6}$, for the warp and eccentricity respectively. These dependencies are in agreement with the results shown in Fig. \ref{free}, where it is clear that the wavelengths of the deformations increase with radius and with the disc thickness (or equivalently with the accretion rate, cf. (\ref{ha},\ref{hb})). The increase in $\lambda$ when $\dot{m}$ increases is evident: in particular, for $\dot{m}=0.8$ the wavelength of the warp becomes so large that it practically loses its oscillatory character, but still maintains the sharp increase in $\textrm{d}W/\textrm{d}R$. Even in this case, the inner disc is not aligned with the equator of the black-hole as in the \cite{bardeenpetterson1975} picture. Unfortunately the behaviour of the solutions very close to the marginally stable orbit cannot be trusted in detail because the singularity of the disc model there ought to be resolved by the transition to a supersonic inflow.

\subsection{Damped propagation}

\begin{figure*}
\begin{center}
\includegraphics[width=0.48\linewidth]{W02d.eps}
\includegraphics[width=0.48\linewidth]{E02d.eps} \\
\vspace{-5mm}
\includegraphics[width=0.48\linewidth]{W04d.eps}
\includegraphics[width=0.48\linewidth]{E04d.eps} \\
\vspace{-5mm}
\includegraphics[width=0.48\linewidth]{W08d.eps}
\includegraphics[width=0.48\linewidth]{E08d.eps}
\end{center}
\caption{Radial variation of (a) the warp tilt and (b) eccentricity normalised to their values at the outer radius for $\alpha_\textrm{W}=0.15$ and $\alpha_\textrm{E}=0.25$ for (1) $\dot{m}=0.2$, (2) $\dot{m}=0.4$, (3) $\dot{m}=0.8$. The full line represents the real part of the disturbance while the imaginary part is represented by the dashed line. A logarithmic scale is used for the x-axis.}
\label{damp}
\end{figure*}

In Fig. \ref{damp} we show the variation with radius of the warp tilt and eccentricity in the case where a significant attenuation is present. The values of $\alpha_\textrm{W}=0.15$ and $\alpha_\textrm{E}=0.25$ are both larger than the viscosity value $\alpha$ used to model the disc, and are chosen so that the warp and eccentricity have negligible amplitude at the inner region of the disc, for small accretion rate ($\dot{m}=0.2$). For dissipation values smaller than these ones, the global deformations propagate everywhere with non-negligible amplitude even for small accretion rate, although with larger amplitude in the inner region for larger $\dot{m}$.

An important difference between the results presented here and the ones in Fig. \ref{free} is the existence of a non-zero imaginary part in the solutions. This shows that the reflection of the global deformations from the stress-free boundary is no longer perfect since they are affected by viscous attenuation and, in consequence, their amplitude is reduced as they propagate to smaller radii; a wave with inward group velocity, as opposed to a standing wave, is set up.

It is evident from Fig. \ref{damp} that when the accretion rate increases the global deformations propagate to the inner region of the disc more easily, i.e., the amplitude of warp and eccentricity in the inner region increases with $\dot{m}$. This result can be explained in light of the WKB analysis introduced in 4.1. If a small viscosity is present ($\alpha_\textrm{W}, \, \alpha_\textrm{E}\neq 0$), the WKB solution for the warp and eccentricity includes an attenuation factor due to the presence of a imaginary wavenumber $k_\textrm{i}$,

\begin{equation}
k_\textrm{i}^\textrm{Warp}\approx \pm\frac{\alpha_\textrm{W}}{3H}\sqrt{\frac{6a}{r^{1/2}}}, \qquad k_\textrm{i}^\textrm{Ecc}\approx \pm\frac{\alpha_\textrm{E}}{2\gamma H}\sqrt{\frac{6}{\gamma r}}.
\end{equation}
If $H/r$ varies slowly with radius, the logarithm of the attenuation factor is

\begin{equation}
\int^{\infty}_{R_\textrm{in}} |k_\textrm{i}| \textrm{d}R\sim\frac{\alpha_i}{H/r} \quad (\alpha_i=\alpha_\textrm{W},\,\alpha_\textrm{E}),
\end{equation}
indicating that, for fixed viscosity, the attenuation is smaller if the thickness of the disc (or equivalently $\dot{m}$) is larger.

The results presented in this section indicate that global deformations can reach the inner region of accretion discs under a wide variety of conditions. In particular, even when subject to large viscous attenuation, both warp and eccentricity can reach the inner disc provided the black hole is accreting mass at a large enough rate.

Some caveats accompany the solutions obtained for $W(R)$ and $E(R)$. The equations used assume that these quantities are small enough so that non-linear effects can be neglected. They also assume that the quantities $|1-\Omega_z^2/\Omega^2|$ and $|1-\Omega_z^2/\Omega^2|$ are smaller than, or of the order of, $H/r$ which is not true of the inner region of relativistic discs. Another important caveat relates to the effects of viscosity in the propagation of global deformations. Here they are parametrised using viscous coefficients $\alpha_\textrm{W}$ and $\alpha_\textrm{E}$; this is the simplest way of describing the poorly understood process of turbulent damping in accretion discs. In the particular case of the eccentricity equations only a bulk viscosity is present so that the complications of viscous overstability can be avoided. However, the latter may be present resulting in growth (as opposed to decay) of eccentricity at small radii.

\subsection{Relation to global modes}

The above results are for strictly stationary deformations such as may be induced by a misalignment between the rotational axis of the binary orbit and the spin axis of the black hole. We have also computed slowly precessing global eccentric modes in binary stars by a method similar to \cite{goodchildogilvie2006} but including the relativistic expressions for the characteristic frequencies. When relativistic precession is included, the global modes have almost the same precession and decay rates as in a Newtonian model, while the solution in the inner part of the disc resembles the stationary solutions described above.

\section{Conclusion}

In this paper we studied the propagation of warp and eccentricity in discs around black holes to determine the conditions under which these disturbances can propagate to the inner regions of accretion discs. High-frequency QPOs have previously been identified with inertial oscillations trapped in the inner region of discs, and are detected mainly when black holes are in the very high state where accretion rate is maximum. We find the accretion rate to have a vital role in the damped propagation of global deformations. Our results suggest that the activation of the inner region, and consequent excitation of trapped oscillations by these disturbances, may be possible only when the accretion rate is close to its Eddington value, i.e., when the black hole is in the very high state.

When the propagation of global disturbances (found to have an oscillatory structure in the radial direction) is not affect by viscous damping, the increase in mass accretion rate gives rise to a lengthening in their wavelength, in agreement with the WKB analysis of the warp and eccentricity equations. The most interesting results of our calculations are obtained when the more realistic situation of damped propagation of global disturbances is considered. In this case, the increase of accretion rate facilitates the propagation of warp and eccentricity, i.e., their amplitudes in the inner region increase with $\dot{m}$. In particular, when the accretion rate is only a small fraction of Eddington and the viscous damping is strong enough to completely suppress the propagation of global deformations, an increase in $\dot{m}$ to the values expected in the very high state results in their amplitude in the inner region being increased to a non-negligible value.

A limitation of the disc model used in our calculations and introduced in section 2 is the fact that it does not include relativistic effects. For example, the law for angular momentum conservation in relativistic discs \citep{nt73} is slightly different from the one used here (cf \ref{cam}). However, relativistic corrections are small and their inclusion is not expected to significantly affect the final results. Also, since the terms on the right-hand side of equations (\ref{luboweq},\ref{ecceq}) dominate the warp and eccentricity propagation, it is more important to introduce relativistic effects in these equations by using expressions (\ref{relomega})--(\ref{relomegaz}) for the characteristic frequencies, as they correctly describe apsidal and nodal relativistic precession rates, related to $\Omega_z^2-\Omega^2$ and $\kappa^2-\Omega^2$.

\section*{Acknowledgments}

We thank Omer Blaes and Chris Fragile for helpful discussions. The work of BTF was supported by FCT (Portugal) through grant no. SFRH/BD/22251/2005.

redpajama_set_name: RedPajamaArXiv


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Category Archives: History
The Appeal and Influence of Parsi Theater
Posted on 14 January, 2022 by yazdi	One comment
Nichola Pais explores the Parsi theater, a highly influential movement in the realm of modern Indian theatre, and its impact on cinema.
What is Parsi theatre?
Parsi theatre's aesthetics and strategies greatly influenced the concept, organisation and production of modern Gujarati, Hindi and Urdu theatres in India. It had absorbed several features of eastern traditional or folk performing arts, such as music, mime, and comic interludes.
While theatre in India may be traced back to Sanskrit dramatist Kalidasa's plays, it was with Parsi natak mandalis that drama developed in colonial times. Focusing on entertainment with a social message, Parsi theatre was a highly influential movement in the realm of modem Indian theatre. A professional theatre movement, it was sponsored by the Parsis and the Zoroastrian traders who migrated in the 17th century from Pars in Iran to India, to settle in Gujarat's coastal areas, before many chose to move to nearby Bombay for trade and commerce. A rich and prominent business community in the city, the Parsis had predominantly adopted English ways of living. They went on to develop theatre both for their personal amusement and commercial purposes. Flourishing between the 1850s up until the 1930s, Parsi theatre was the result of the blending of European techniques and local folk forms of Indian theatre. It marked the beginning of a new tradition in Indian theatrical culture; before this, the only kind of Indian theatrical practice in existence was folk theatre performances. Popularising proscenium-style theatre in regional languages, Parsi theatre was melodramatic and entertaining in nature, with the plays incorporating humour, melodious songs and music, sensationalism and stagecraft.. success led to the development of bhasha theatre in regional languages. Parsi theatre's aesthetics and strategies greatly influenced the concept, organisation and production of modem Gujarati, Hindi and Urdu theatre in India. It had absorbed several features of eastern traditional or folk performing arts, such as music, mime, and comic interludes. Thus, Parsi theatre plays were not a mere imitation of western theatre but a blend of Eastern and Western dramatic techniques. Neither purely based on Western theatre nor on eastern theatre, it was a hybrid which was successful in garnering the attention of audiences, as its influence quickly spread across India.
Commercial Parsi theatrical productions had a number of unique and interesting elements. Three actors would chant a prayer before the drama began, after which one actor would deliver the prologue. In marked similarity to the Bengali indigenous dramatic production, Jatra, music played a significant part in Parsi theatre. The end of a play would see an actor come forward to offer a vote of thanks, ending with a farewell song. Parsi theatre was also rooted in community identity, with community members sharing a sense of oneness with the theatrical productions, and fostering identity and community culture. Communicating in the local languages like Gujarati, Hindi and Urdu, it used European-style proscenium with richly painted backdrop curtains and trick stage effects. It also depended on spectacle and melodrama to appeal to its audiences. It ushered in the conventions and techniques of realism, as it marked the transition from stylised open-air presentations to a new urban drama.
Novel dramatic devices
Plays mixed elements of realism with fantasy, music, dance, narrative and spectacle, dialogue and ingenuity of stage presentation, within a dramatic discourse of melodrama.
A predominant feature of Parsi theatre was the alternation of deep and shallow scenes. While the deep scenes contained serious subject matter, the shallow scenes were largely comic in nature, to amuse the audience. The shallow scenes would be mostly presented on the front stage and the deep scenes in the deeper part of the stage. While the shallow scenes ran at the foreground of the stage with a painted curtain generally depicting a street as backdrop, the deep scenes would be prepared during this time. The shallow scenes, enacted by the 'lower class' characters, served as links in the development of the plot Their main purpose however w. to keep the audience engaged while the deep scenes, which showed interior of palaces, royals parks, and other such visually opulent sets, were being changed or decorated. While important characters rarely appeared in the street scenes, the comic characters kept their place in the deep scenes. The characteristics of shallow scene of Parsi theatre have evidently come from Shakespeare, where the technique was used for 'comic relief' in his tragedies. However, while Shakespeare used comic relief as mental comfort for the audience just after the blood-shed on stage, Parsi theatre used shallow scenes for the passing of time when the scene preparation was in progress for the deep scene. Shallow scene incorporated comic dialogues, romantic scenes, highly dramatic actions, and some risque scenes. Parsi theatre always used back and middle curtains to change the location or scene. The painted curtain dropped from pulleys was used for the changing of scenes rather than using props on the stage. Parsi theatre also directly presented melodrama on the stage like death and blood-shed, thus producing aesthetic pleasure in the audience's mind. Plays mixed elements of realism with fantasy, music, dance, narrative and spectacle, dialogue and ingenuity of stage presentation, within a dramatic discourse of melodrama. Additionally, special kind of language was used for special kinds of characters, in another similarity with Shakespeare's use of language in his plays. Thus, characters in the play spoke according to their social status, with the higher class speaking in figurative and beautiful language while the lower class used prose or communicative language. With the audience for Parsi theatre largely hailing from the middle and lower working class, there were wide usage of songs, metrical and rhythmic lines. Background music was also used in order to produce aesthetic pleasure or Rasa in the play, even as it helped the director create the illusion, reality on stage. Interestingly, the usage of music was borrowed from Indian folk theatre. Parsi theatre was thus a new and experimental movement on various levels, opening a hitherto unseen way of presenting a play on the Indian stage. In a nutshell, it promoted the use of both deep and shallow scenes, introduced secularism in content, and enabled the performance of plays in proscenium theatres.
Read the full interesting article at https://www.cinemaazi.com/feature/chalo-natak-the-appeal-and-influence-of-parsi-theatre
ZANZIBAR REVOLUTION DAY & FREDDIE MERCURY
January 12, was Zanzibar Revolution day – a day to remember for a story of a country's freedom and also the story of a forgotten genocide. A thread on Zanzibar Revolution, Parsees of Gujarat and a flamboyant rockstar we've all heard about.
For centuries, Zanzibar – a Tanzanian archipelago – was ruled by Muslim Sultanate and a hot destination for Indian traders. Indians, both Hindus and Muslims, had their families established within a flourishing community until one dark day arrived.
On this day back in 1964 a violent coup by African allied parties, fueled by ethnic pride & anger over slavery in the past, not only ended 200 years of Muslim rule but also murdered and expelled thousands of Arabs and Indian civilians in broad daylight.
The Indians, who were settled there, were mostly wealthy merchants and traders from Northwestern India. One of them was Bomi Bulsara, a Persian cashier from Western India.
Bomi was originally a Parsi from the Gujarat region of the Bombay Presidency in Colonial India. His family name was derived from the Bulsar or Valsad – a town in Gujarat from where they were originated.
There is a very interesting legend about how the Zoroastrians fled from their Persian homeland to Gujarat to escape religious prosecution. As per the epic poem Qissa-i Sanjan when they arrived in Gujarat, they met Jadi Rana, the local King.
The King sent a vessel of milk filled to the very brim to the newly arrived Persis signifying his kingdom is already full and couldn't accept refugees.
In response, they returned the vessel adding a pinch of sugar indicating Persis would only make their life sweeter.
When Bomi moved to Zanzibar as a cashier at a British Colonial Court he was fairly young. He was said to work at 'House of Wonders' – a landmark building in famous Stone Town. It was so named as it was the 1st building in Zanzibar with electricity.
A few years later Bomi married another Persian girl Jer from India and a few years later their son Farrokh Bulsara was born on 5th September 1946 in Zanzibar Government Hospital.
Farrokh was sent for schooling in India and when he came back in 1963, the bloody Zanzibar Revolution was impending. On the fated day, over 20,000 Arabs had been murdered, along with thousands of Indians. Rest fled the country.
This is possibly the only genocide that was entirely filmed live and made as a documentary. ( refer 'Africa Addio') There is apparently no memorial for the victims even today.
Among the Indians who were fortunate enough to escape Zanzibar before the revolution started were Bomi and Jer Bulsara, and their children, Farrokh and Kashmira.
Bomi was able to escape the situation in time and flee to England before the genocide began. Today we know Farrokh as Freddie Mercury – the iconic lead vocalist of the rock band Queen.
If the Bulsara family had failed to flee to England escaping the genocide, the world would have probably never known Freddie Mercury and you would possibly never heard of Bohemian Rhapsody!
Courtesy : Jehangir Bisney
Rast Goftar – the first Parsi newspaper
Dadabhai Naoroji was its editor…
This is the front page of the Parsi newspaper 'Rast Goftar' of February 1861. Did you know about it? I didn't. And I have been a newspaperman and an editor all my working life. 'Rast Goftar' meant 'The Truth Teller'. This was an Anglo-Gujarati daily first published in Bombay in 1854 by Dadabhai Naoroji and Kharshedji Cama to champion social reform among Parsis in India.
The story, according to Wikipedia, is that a riot between Parsis and Muslims over the printing of a picture of Prophet Mohammed in 1851 was the immediate cause of the founding of 'Rast Goftar'. As riots in Bombay flared up alarmingly, Parsis reportedly became disillusioned with their leaders, and Dadabhai Naoroji started the paper with the purpose of voicing the grievances of his people.
Back in the day postal rates tended to limit the circulation of newspapers to local or nearby areas. But sometimes enthusiasm for a cause led the managers of a paper to distribute several copies of each issue free. Thus, the founders of the 'Rast Goftar' lost some 10,000 rupees by distributing the first issues of the paper free, impatient at the state of Parsi society, obviously in a hurry to reform it.
In 1857 the proprietors in Bombay converted their property into a joint-stock concern so that Nasarvanji Cama, who had financed the paper from the beginning, would not be the sole loss-bearer. K. R. Cama, Sorabji Shapoorji Bengalee and Navrozji Fardunji all became proprietors. The local governments subsidized it by subscribing to a certain fixed number of copies of the journal.
In 1858, circulation rose from 432 to 852, a number then unheard of for native journalism. The content widened from exclusively Parsi topics to larger questions of Indian politics. During the Rebellion of 1857, the paper remained loyal to the British, and even began the first English columns, mostly written by Navrozji Fardunji, a 19th century reformer, academic, activist and freedom fighter.
By the 1870s 'Rast Goftar' was one of the four daily newspapers operating in Bombay, and it was not only vigorous in itself, but was also the cause of vigor in other journals either by way of antagonism or support. That's about all I can tell you about the 'Rast Goftar'. I don't know when it ceased publication and why. If any Parsi can come up with this delectable slice of history, I would be grateful.
MARK MANUEL
"Cyrus The Great" Monument In Sydney, Australia.
"Cyrus the Great" is believed to have lived from 600 BC to 530 BC.
The third photo shows the Cyrus Cylinder, which is presently located in the British Museum in London, England.
The Cyrus Cylinder or Cyrus Charter (Persian: استوانه کوروش) is an ancient clay cylinder, now broken into several pieces, on which is written a declaration in Akkadian cuneiform script in the name of Persia's Achaemenid King Cyrus the Great. It dates from the 6th century BC and was discovered in the ruins of Babylon in Mesopotamia (modern Iraq) in 1879. It is currently in the possession of the British Museum, which sponsored the expedition that discovered the cylinder. It was created and used as a foundation deposit following the Persian conquest of Babylon in 539 BC, when the Neo-Babylonian Empire was invaded by Cyrus and incorporated into his Persian Empire. The text on the Cylinder praises Cyrus, sets out his genealogy and portrays him as a King from a line of Kings.
It is believed to be the first-ever documented evidence of the "Charter of Human Rights".
Zoroastrians in Patna
Posted on 8 December, 2021 by yazdi	2 comments
The city of Patna is a place of reverence not only for the Sikhs but closely associated with the Parsi community in India, as well. The great Zoroastrian saint Dastur Azar Kaiwan of the 16th century, lived and spent the major part of his life in Patna.
From a well researched treatise of Ervad Dr. Jivanji Modi, it is gathered that Dastur Azar Kaiwan was born around 1533 in Iran in an illustrious family of priests who traced their genealogy right upto the Mai Abad dynasty. Azar Kaiwan was drawn to things spiritual right from early childhood and it is said that he reduced his food and sleep from the age of five and started practicing severe spiritual experiments and penances. One of the strict rigours he undertook at a very early age was to live within a "khumb" or large earthen vase or pot for a period of 28 years.
Dastur Ajar Kaiwan, voluntarily left his abode in Mount Demavand in Iran and came to Patna, India along with a group of close disciples. A saintly soul, he chose Patna as his spiritual centre. Dastur Azar Kaiwan, was well known in his time. Both Dastur Azar Kaiwan and his disciples were believed to possess enormous spiritual powers and various miracles and near-impossible feats were attributed to them. News of his spiritual prowess reached the court of the Mughal emperor Akbar (1556-1605), who invited Dastur Azar Kaiwan to his court. The Dastur however refused to appear in front of him and finally it was Akbar who travelled to Punjab to meet hime.
His teachings were universal in nature and open for all to follow. People of all religion respected him. He instructed his followers to remain faithful to their religion. He advised his followers to follow the threefold path of Asha (Good Thoughts, Good Words and Good Deeds) . He urged his followers that:
* The best way of keeping one's soul aligned with God is by helping others and by spreading happiness;
* The spiritual equality and duty of men and women are alike;
* Being good for the sake of goodness and without the hope of reward.
He had a large following, and was renowned throughout Asia. Dastur Azar Kaiwan died around 1618 at the age of 85, and was buried in Patna itself. His relics are preserved in a Dargah near Patthar ki Masjid and worshipped by the people of all religion. This is the brief, but remarkable outline of the life of this extraordinary Master.
Till recently the Parsi community in India, though knowing that Ajar Kaiwan is buried somewhere in Patna did not know it's exact location. On the request of some Parsi friends from Mumbai, SKILL Foundation did extensive research and reconnaissance and finally located the holy shrine of this renowned Parsi saint. So now Skill Foundation regularly organises and host the visit of Parsi outstation guests. The students enjoy and learn while taking the guests out on a historical walk to the holy shrine.
A few days back a group of Parsi guests from Mumbai came to pay their homage at this holy shrine of this great Zoroastrian saint. Sharing some snapshots of the recent visit of these Parsi guests from Mumbai.
JAMSHEDJI JEEJEEBHOYS LETTER TO THE PARSEE COMMUNITY ON HIS BEING PRESENTED KNIGHTHOOD
Posted on 25 November, 2021 by yazdi	One comment
VOLUME 2 BY DOSABHAI FRAMJI KARAKA.
[CHAP. II. PG 93-95
BY THE BRITISH GOVERNMENT AND THE DEED OF SETTLEMENT MADE BY HIM FOR THE BENEFIT OF THE "PARSEES" ( "a person or persons following the religion of Zoroaster")
"MY DEAR FRIENDS-I feel deeply gratified to you for the address which you have just presented to me. So distinguished a mark of the esteem of my fellow-countrymen is an honour of which I, and those who are most dear to me, may justly be proud.
"To have been selected by my Sovereign as the native through whom she was graciously pleased to extend the order of knighthood to her Indian subjects was, and ever must be, a source of deep personal gratification to myself. But to receive the congratulations of my fellow-countrymen in a manner at once so kind and flattering, -to have this auspicious event commemorated by the creation of a charity, to be connected with my name, and in the objects of which I so cordially concur, is a source of inward pride and satisfaction, which, rising higher than the gratification of mere worldly titles, will live with me to my dying day.
"Your too kind and favourable mention of my acts of charity has much affected me. The only merit I have a right to claim for them is that they proceeded from a pure and heartfelt desire, out of the abundance with which Providence has blessed me, to ameliorate the condition of my fellow-creatures. With this no unworthy motive was mixed; I sought neither public honours nor private applause, and, conscious of a singleness of purpose, I have long since had my reward. When, therefore, Her Majesty's most gracious intentions were communicated to me, I felt deeply gratified that I had unconsciously been the means of eliciting so signal a mark of the good feelings of England towards the people of India, and it is in this light that I prefer to consider the distinguished honour Her Majesty has conferred upon me, and that also which I have received at your hands this day.
"Nothing could please me more than the purposes to which you propose to devote the funds that have been submitted. I shall ever wish my name to be connected with every endeavour to diffuse knowledge amongst our people; and the surest way to incite them to elevate and improve themselves, to fit them to appreciate the blessings of the Government under which they live, and to deserve those honours which have now for the first time been extended to India, is to spread far and wide amongst them, gratuitously or in a cheap form, translations into our own language of the most approved authors.
Connected with this subject is a scheme that I have long contemplated for relieving the distresses of the Parsi poor of Bombay, Surat, and its neighbourhood. You know full well the state of misery in which many of our people are living, and the hopeless ignorance in which their children are permitted to grow up. My object is to create a fund, the interest of which shall be applied towards relieving the indigent of our people and the education of their children, and I now propose to invest the sum of Rs. 300,000 in the public securities, and place it at the disposal of trustees, who with the interest shall carry out the object I have mentioned; and this trust I hope you will take under your care. "And now, my dear friends, let me once again thank you for your kindness. There is nothing I value so highly as the good opinion of my countrymen, nor anything I more anxiously desire than their welfare and happiness."
The patent of knighthood was publicly presented to Sir Jamshedji Jijibhai by Sir George Anderson, Governor of Bombay at the time, in the following appropriate terms. He said : "SIR JAMSHEDJI JIJIBHAI-Her most Gracious Majesty the Queen having been graciously pleased to confer upon you the dignity of knighthood of the United Kingdom, the patent has been transmitted to me to present to you; and both Lord Fitzgerald, the President of the Board of Control, and the Honourable the Court of Directors, in transmitting this instrument to me for this purpose, have expressed their high gratification at your having received this distinguished honour.
"The dignity of knighthood has ever, amongst the natives of Europe, been considered as most honourable. To attain this distinction has continually been the ambition of the highest minds and noblest spirits, either by deeds of most daring valour or by the exercise of the most eminent talent."
THE DEED OF SETTLEMENT OF SIR JAMSHETJI JEEJEEBHOYS PARSI BENEVOLENT FUND.
FOR RELIEVING THE POOR AND NEEDY OF OUR PEOPLE AND THE EDUCATION OF THEIR CHILDREN.
"IN ORDER TO OBVIATE ALL DOUBTS RESPECTING THE MEANING OF THE WORD PARSEE IN THIS INDENTURE, IT IS HEREBY DECLARED THAT THE WORD PARSEE MEANS IN THIS INDENTURE THROUGHOUT A PERSON OR PERSONS PROFESSING THE RELIGION OF ZOROASTER." (Fourth line from the bottom of the page.)
A Tribute To Mrs. Meherbano Marker
Dr. Shahida Jaffrey reminisces her relationship with the esteemed Mrs. Meherbano Marker who formed the Quetta Girl Guide and All Pakistan Women Association (APWA) Quetta Wing and worked till her last breath at the age of 103 for the betterment of the underprivileged women.
Quetta, 2001
Mrs Meherbano Marker
Mrs. Arnaz Marker, the wife of Mr. Jamsheed Marker, called me from Karachi saying:
"Will you plant 100 Chinar trees somewhere in Quetta to commemorate Mama's 100th birthday? We will pay for all costs".
Mama was Mrs. Meherbano Kekobad Marker, wife of Mr. Kekobad Marker, and mother of Mr. Jamsheed Marker, Mr. Khursheed Marker and Mr. Minocher (Minoo) Marker.
Mrs. Marker turned 100 years in the month of August 2001.
Mrs. Marker had dedicated her entire life working for the poor and underprivileged people of Quetta, "The trees will provide shade to the people and also keep the land, and environment of the city
clean and healthy", said Arnaz.
Sikandar Jamali, my husband, was appointed Chief Secretary Balochistan and later was Federal Secretary Environment. It was the month of August 2001, and Quetta was very hot and dry.
On Arnaz's request, Sikandar arranged for one Chinar tree through Balochistan Forest and Environment department and a simple ceremony was arranged in the Askari Park, Airport Road Quetta. Mrs. Marker arrived in her chauffeur-driven Mercedes Benz accompanied by her granddaughter, Mrs. Meher Marker Noshirwani, and her nurse. She was in her wheelchair.
All of us – Sikandar Jamali, Director Environment, his staff and I were present.
The tree was planted, photographs taken and prayers said. Unfortunately, the tree soon died: it did not survive Quetta's August dry heat. Mrs. Marker left for Karachi beginning of winter that year, as was her routine, but was unable to return to Quetta due to illness.
She passed away in her Karachi home in 2004 at the age of 103, with her loving family beside her.
Brief on Kekobad and Meherbano
"Kekobad was the son of Ardeshir, born on February 25, 1896, in the house of his maternal grandfather Mr. Jamshedji Eduljee Chinoy in Secunderabad, Deccan, India.
"He married Meherbano, daughter of Aimai and Dadabhoy Ferozshah Pestonji, on March 28, 1921, at Secunderabad, and Meherbano accompanied her husband to Quetta. The newly married couple settled in an annex specially built for them in the compound of the Marker Cottage on Lytton Road and they have been in Quetta since.
"They lived in a very beautiful house on what was Lytton Road, which was also known as the 'Thandi Sarak', (the cool road) as it was lined with huge Chinar trees. A Boot House was built in the compound by Kekobad Marker for his granddaughter Aban in 1958. The unique structure is visible from the main road and is affectionately referred to as the 'Joote Walla Ghar'."
The Marker home was and has always been very socially active; with classy lunches, garden parties, and dinners attended by the renowned Quetta families.
It was also a home where Mrs. Marker hosted and held discussions and consultations with her workers and project beneficiaries, women and men who worked on numerous projects, that she personally funded and supervised, under the umbrella of All Pakistan Women's Association, APWA Balochistan.
APWA Balochistan and Girls Guide Balochistan were established by her at Pakistan Independence, 1947, and she was Life Time President of both.
Initially, some funding was received from small donors, later, all projects were funded by her personal and family monies. Wives of well to do and affluent Quetta families were very actively involved with these organisations, and gave their all. Numerous institutions were established and run; large and small free schools; free health and family planning centers; and many income generation activities.
I remember, once accompanying her to a small mud building, a girls school in Killi Ismail – a small village, on the outskirts of Quetta, with a sparkle in her eyes she said:
"One day some of these girls will become teachers, nurses, and LHVs. I will be very happy."
Thousands of poor girls have gone through those small schools improving and changing their lives.
Another area she felt strongly about was population planning and always worried about the population growth in the country. Her great contribution was the establishment of the Idara -e- Niswaan, the APWA hand embroidery center, that was the first of its kind, that introduced Balochistan embroideries as a cottage industry.
Prior to that, local exquisite embroideries were created by women for personal and family use only, and there was no concept of selling their embroidery work.
Idara-e-Niswan created table linen of top quality that adorned the homes of upper-class customers and provided income to needy skilled women artisans, trained by APWA. Currently, Quetta markets are loaded with hand-embroidered different products providing income to poor skilled rural women.
Chinar Trees
I would often remember Arnaz Marker's request of planting 100 Chinar trees and felt guilty, as I failed to fulfill her request.
The opportunity came when in 2004, I was appointed by Governor Balochistan/Chancellor, Engineer Owais Ahmed Ghani, the Vice-Chancellor of the newly established university for women, the Sardar Bahadur Khan Women's University, SBKWU, at Quetta. The old TB hospital, Sardar Bahadur Khan Sanatorium with beautiful English style buildings spread over 45 acres of the mountain on Brewery Road, the property of Pakistan Railways, was given to me to establish a university.
Students at SKBWU Campus
As the Vice-Chancellor I was able to execute Arnaz Marker's tree plantation request.
She had asked me to arrange to plant the Chinar trees and the family will pay all costs of tree procurement, maintenance and care.
The sanatorium and its land were once rich with vegetation: pine groves, fruit orchards, and beautiful flower gardens. Hazara pine trees were brought by the then Medical Superintendent, Dr. Saeed Hai from Abbottabad. Gardens and orchards were watered with fresh water from there on the premises tube wells. After Dr. Saeed Hai left the hospital and Quetta, and the tube wells dried, the area became a sad desert.
The university was able to recharge and sink new tube wells, very good water from the aquifers watered the land, and the soil was very rich. During Spring 2005, I took my personal old Toyota Prado, from Islamabad to a Haripur plant nursery, and purchased 110 young Chinar plants. I was amazed to see, the nursery owner had set aside 1000 Chinar plants to be taken to Afghanistan.
I took my trees to Quetta by road, about 1000 km, and planted them on the campus grounds.
The trees did remarkably well and all survived and flourished in rich healthy soil, abundant clean groundwater, and particularly, attention and care of the team of a university dedicated staff and gardeners.
In a span of three years, the trees grew fast, their tops touching the roofs of the buildings, and today 16 years later, the old hospital buildings are camouflaged by the thick Chinar jungle – trees having wide trunks and their thick foliage provides oxygen, cool shade to the over eleven thousand students, faculty and staff and it is a pollution-free mountain island!
Chinar trees have grown over the years
Chinar on campus, autumn colours
The SBKWU gifted and dedicated the trees, their maintenance, and upkeep to the memory of Mrs. Marker who gave so much to the women and children of Balochistan.
As was my commitment to the Markers, I organized another tree plantation ceremony on campus grounds. The Markers, graciously attended, Mr. Jamsheed Marker, Mr. Khursheed Marker, and Mrs. Arnaz Marker, who specially came to Quetta on my invitation, and planted one ceremonial Chinar tree. Sikandar Jamali too was present.
Planting a Chinar tree: Jamsheed Marker, Khursheed Marker and Arnaz Marker
Prayers after the tree plantation
When the Markers arrived for the tree plantation ceremony
As the Vice-Chancellor, I lived in a very beautiful house occupied by the Medical Superintendent, Dr.Saeed Hai, which was once a fruit orchard that too had dried.
Author at Chinar Cottage
I planted more than a dozen Chinars and gave the cottage the name "Chinar Cottage".
Marble Plaque and Inscription
A marble plaque was created by the granddaughter, Mrs. Aban Marker Kabraji and family, and sent from Karachi to Quetta, which was erected at a strategic location in the grounds of Sardar Bahadur Khan Women's University campus where 110 Chinaar trees were planted in 2005 – with this inscription:
These trees were planted in memory of
Mrs. Meher Bano Kekobad Marker
August 1901-January 2004 who did her utmost to improve the lives of the poor and unfortunate.
Her spirit remains in the mountains and in the Quetta valley which she loved and with its people.
Marble Plaque erected on SBKWU campus
As Arnaz had wished, "Young women will enjoy the shade of the trees, and Mama will be very happy."
Arnaz's wish was fulfilled.
Allah blessed mama with a few more years, and she passed away in January 2004 at the age of 103 – constantly saying, "I miss my work and I miss my Quetta".
The mantlepiece of her Karachi home often displayed vases full of fresh-cut flowers brought from her Quetta home.
Mrs. Marker taught me a lesson, that I often quote: "When does one stop working?" She worked and devoted her full time to it, till she passed away at 103, even when she was unable to be in Quetta.
Mr Khursheed Marker
She directed Baji Razia, her Quetta based supervisor/employee on the phone, and knew all that was happening, she was fully in control.
She is a role model not only to her family but to all of us.
Mr. Jamsheed Marker passed away, June 21, 2018, And Mr. Khursheed Marker passed away, 11 December 2010.
When Arnaz made the request to plant 100 trees, Sikandar Jamali, commented:
"This noble family thinks and works for humanity. By their request for planting 100 trees to celebrate Mrs. Marker's birthday, they are thinking of humanity, environment, and the trees will benefit and provide shade and comfort to thousands of people and for several generations; not many people think like this".
Author planting a tree
And since I executed this project, I wished to document and share with the world, the humanitarian and noble face of the Marker family.
Mr Jamsheed Marker
Ms Arnaz Marker
Shahida Jaffrey
Dr. Shahida Jaffrey was the first woman Vice Chancellor and founder of the Sardar Bahadur Khan Women's University in Balochistan. She holds a Master's Degree in English Literature from the University of Punjab Lahore and PhD in Education from the University of Philippines. She is the Chairperson of Behbud, Balochistan, which provides preventive healthcare to underprivileged women in the rural area of District Mastung. She has also served as the Chief Executive of the largest Rural Support Programme in Balochistan, the Balochistan Rural Support Programme.
https://nayadaur.tv/2020/06/remembering-mrs-meherbano-marker-a-friend-to-women-and-chinaar-trees/
$4.7 million allocated to UNESCO-designated Pasargadae
A budget of 200 billion rials has been allocated to Pasargadae after President Ebrahim Raisi visited the Achaemenid site earlier in October, a senior tourism official, Javad Vahedi, said on Friday.
"The Pasargadae complex, as a magnificent World Heritage site, has a high tourism potential in the field of cultural and historical tourism, and we must plan to attract more tourists," the official explained.
Situated about 50 km north of Persepolis, Pasargadae was the first dynastic capital of the Achaemenid Empire, founded by Cyrus II the Great, in Pars, the homeland of the Persians, in the 6th century BC.
Its palaces, gardens, and the mausoleum of Cyrus are outstanding examples of the first phase of royal Achaemenid art and architecture and exceptional testimonies of Persian civilization.
The UNESCO World Heritage site is also home to a complex water supply system for the time that comprises cisterns, tunnels, underground canals, and ducts, which are locally known as qanats.
It is believed that the development of qanats began about 2,500 or 3,000 years ago in Persia (Iran), and the technology spread eastward to Afghanistan and westward to Egypt. Although new qanats are seldom built today, many old qanats are still used in Iran and Afghanistan, chiefly for irrigation.
The 160-ha archaeological site of Pasargadae presents some of the earliest manifestations of Persian art and architecture. It includes, among other monuments, the compact limestone tomb on the Morgab plain that once held Cyrus the Great's gilded sarcophagus; Tall-e Takht ("Solomon's Throne"), a great fortified platform built on a hill and later incorporated into a sprawling citadel with substantial mud-brick defenses; and the royal ensemble, which consists of several palaces originally located within a garden layout (the so-called "Four Gardens"). Pasargadae became a prototype for the Persian Garden concept of four quadrants formally divided by waterways or pathways, its architecture characterized by refined details and slender verticality.
Pasargadae stands as an exceptional witness to the Achaemenid civilization. The vast Achaemenid Empire, which extended from the eastern Mediterranean and Egypt to the Hindus River in India, is considered the first empire to be characterized by a respect for the cultural diversity of its peoples. This respect was reflected in the royal Achaemenid architecture, which became a synthesized representation of the empire's different cultures. Pasargadae represents the first phase of this development into a specifically Persian architecture which later found its full expression in the city of Persepolis.
https://www.tehrantimes.com/news/466456/4-7-million-allocated-to-UNESCO-designated-Pasargadae
Lesser known facts about the Father of India's Nuclear Programme – Homi Bhabha
Homi Jehangir Bhabha Birth Anniversary: Lesser known facts about the Father of India's Nuclear Programme
Homi Jehangir Bhabha is considered to be the 'Father of the Indian nuclear programme'
Homi Jehangir Bhabha was born on October 30, 1909, in Mumbai. He was an Indian nuclear physicist, founding director, and professor of physics at the Tata Institute of Fundamental Research (TIFR).
His contribution towards India's growth has been impeccable. He had a great visionary ability which resulted in impactful development for the country. TIFR and AEET were the cornerstone of Indian development of nuclear weapons under the direction of Homi Bhabha.
Homi Jehangir Bhabha is considered to be the ''Father of the Indian nuclear programme'.
Here are some interesting facts about the legend:
Homi Jehangir Bhabha was born into a prominent wealthy Parsi family. He completed his education at Bombay's Cathedral and John Connon School and entered Elphinstone College, before joining Caius College of Cambridge University.
Homi Bhabha birth anniversary: 10 interesting facts about The Father of India's Nuclear Programme
His immense love and interest for mathematics never stopped and in 1932, he obtained first-class on his Mathematical Tripos. He was awarded the Rouse Ball travelling studentship in mathematics.
His first scientific paper, "The Absorption of Cosmic radiation" received a lot of appreciation.
Homi Bhabha served as the Reader in the Physics Department of the Indian Institute of Science in 1939.
Homi Bhabha understood the need of better research schools. He made up his mind and in March 1944, he sent a proposal to the Sir Dorabji Tata Trust for establishing 'a vigorous school of research in fundamental physics'.
The Tata Institute of Fundamental Research, was inaugurated in 1945.
Homi Bhabha represented India in the International Atomic Energy Forums as President of the United Nations Conference on the Peaceful Uses of Atomic Energy, in Geneva, Switzerland in 1955. He was also elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1958.
Bhabha believed in vast thorium reserves rather than its meagre uranium reserves. His strategic objective became India's three stage nuclear power programme.
Homi Bhabha was awarded the Adams Prize in 1942, and Padma Bhushan 1954. He was also nominated for the Nobel Prize for Physics in 1951 and 1953–1956.
Bhabha died in a plane crash near Mont Blanc on 24 January 1966. Many believed that it was an assassination.
https://www.freepressjournal.in/india/homi-jehangir-bhabha-birth-anniversary-lesser-known-facts-about-the-father-of-indias-nuclear-programme
FPJ Web Desk
Notable Zoroastrians

redpajama_set_name: RedPajamaCommonCrawl


✓ Many reports indicate that going to Settings > Messages and toggling iMessage off and on again a few times will fix the problem.
✓ Some users report having to sign out and sign back into iMessage on their iPhones. You can do that by going to Settings > Messages > Send & Receive. Tap on the Apple ID at the top and then Sign Out. Then, sign back in.
✓ Other users report that completely un-pairing and re-pairing their Apple Watch from their connected iPhone will also alleviate the problem.


text:
Добрун је мјесна заједница у општини Вишеград, Република Српска, Босна и Херцеговина. Дијелом своје богате историје Добрун је био и утврђени град, а касније и општина.

Географија
Стари Добрун је подељен на: Доњи Добрун, Горњи Добрун и Добрунску Ријеку, док Мјесну заједницу Добрун поред поменутих чине и насеља: Бијела, Тасићи, Столац, Велетово, Ченгићи, Босанска Јагодина, Смријечје, Жагре, Златник, Турјак, Заножје, Богилице, Јабланица, Грање, Веље Поље, Небоговине, Бјељајци и Пољанице.

Мјесна заједница Добрун се простире на 85,64 -{km²}- и граничи се на истоку са Општином Ужице, а на сјевероистоку са Општином Бајина Башта, односно Републиком Србијом. Са јужне стране граничи се са Општином Рудо, а са осталих дијелова граничи се са селима која припадају мјесним заједницама Прелово, Вардиште, Дринско и Вишеград-центар.

Историја
Град Добрун је најпознатији средњовековни град у овој области, а био је познат још у 15. веку. Град се налази на путу Вишеград-Ужице, на око 12 километара од Вишеграда. Он се састојао од тврђаве са жупским двором и три куле-стражарнице. Према народном предању град је саграђен око 1440. године, а подигла га је "проклета Јерина", жена Ђурђа Бранковића. Ипак за ове тврдње на постоје поуздани историјски докази. У току средњег вијека око града је постојало насеље у коме су боравили дубровачки трговци.

Постоји још једно народно предање о постанку града које је забележио свештеник Алекса Ђуровић 1887. године. У њему се помиње како је град подигао Ђурађ Смедеревац после Битке на Косовом пољу. Турски султан Селим одлучио је да освоји град и довео је бројну војску из Санџака. Војска је опколила град, али није успела да га освоји, јер је он био подигнут у стенама. Град је по предању освојен тако што је манастирски кмет Јован Калауз издао град. Он је рекао да ће из града изаћи сватови и отићи по девојку у околину Пријепоља. Султан је напао сватове и после тога се турска војска упутила према граду прерушена у сватове. Сви из града су изашли да дочекају "сватове " тако да су их Турци лако побили и заузели град. Када су га заузели опачкали су га и разорили до темеља, а варош спалили. У том нападу је страдао и Манастир Успења Пресвете Богородице у Добруну. Од некадашњег града Добруна данас постоје само рушевине и гробови око његових утврђења.

Стара црква је рестаурирана 1939.

Становништво

Галерија

Види још
 Манастир Добрун
 Општина Вишеград
 Стари град (Добрун)

Референце

Општина Вишеград
Насељена мјеста у Републици Српској
Википројект географија/Насеља у Босни и Херцеговини
Тврђаве у Републици Српској

redpajama_set_name: RedPajamaWikipedia


Home › Cartier Wishknot VS1 F Diamond Necklace In 18k White Gold in good condition.
Cartier Wishknot VS1 F Diamond Necklace In 18k White Gold in good condition.
Chain length ........................ 16 inches long.
Diamond weight .................. Approx 1 carat.
Comes in a used Cartier necklace box along with a cleaning receipt from Cartier.
This necklace was serviced at Cartier in Japan & the cleaning receipt is written in Japanese.


text:
Dirc Potter (ca. 1370 - 30 april 1428) was een Nederlands dichter, prozaschrijver, hoge ambtenaar en diplomaat.

In 1385 werd Potter benoemd tot 'clerc'. Hij werd later secretaris van de opeenvolgende graven van Holland. Eerst diende hij in die hoedanigheid graaf Albrecht van Beieren, vervolgens diens zoon Willem VI en daarna Jacoba van Beieren. In 1415 werd hij voor zijn diensten beloond door graaf Willem en ontving hij de hofstede Ter Loo bij Voorburg. Een tijdlang was hij baljuw van 's-Gravenhage.

Potter ondernam tal van diplomatieke missies in binnen- en buitenland. In 1411-1412 was hij in Rome voor de grafelijke huwelijkspolitiek. Door het lange antichambreren vond hij tijd voor zijn eerste werk, Der minnen loep (de loop der minne), een berijmd didactisch werk over diverse aspecten van de liefde.

Op latere leeftijd schreef hij twee prozawerken. Bloeme der doechden vertoont overeenkomst met het 13e-eeuwse Italiaanse werk 'Fiore di Vertù' van Tommaso Gozzadini. Mellibeus gaat via een Franse vertaling terug op het 'Liber consolationis' van Albertanus da Brescia uit 1246.

Dirc Potter was de vader van Gerrit Potter van der Loo. Nadat deze het landgoed De Loo in Voorburg in leen gekregen had voegde hij Van der Loo toe aan zijn naam. Een andere zoon was de kanunnik Jacob Potter van der Loo.

Werk
 Der minnen loep (ca. 1411)
 Blomme der doechden (na 1415)
 Van Mellibeo ende van sinre vrouwen Prudencia (na 1415) (meestal kort aangeduid als Mellibeus)

Literatuur

 A.M.J. van Buuren, Der Minnen loep van Dirc Potter. Studie over een Middelnederlandse Ars amandi. Utrecht 1979.
 F.P. van Oostrom, 'Dirc Potter', in: Het woord van eer. Literatuur aan het Hollandse hof omstreeks 1400. Amsterdam 1987, hoofdstuk VI, p. 225-268.
 Sabrina Corbellini, Italiaanse deugden en ondeugden. Dirc Potters Bloeme der doechden en de Italiaanse Fiore di Virtù. Amsterdam 2000.

Externe links

 Leven en werk van Dirc Potter, uit Geschiedenis der Nederlandsche Letterkunde, deel 1, G. Kalff
 Literatuur en levensloop, de succesmoraal van Dirc Potter door F.P. van Oostrom, oproepbaar in pdf
 Der minnen loep, de tekst met inleiding en verklarende woordenlijst in Google books
 Scans uit Der minnen loep
 Dirc Potter over het onderwijs op literatuurgeschiedenis.org

Voetnoten

Middelnederlands schrijver
Nederlands dichter
14e-eeuws schrijver
15e-eeuws schrijver
Baljuw van Den Haag


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Hello friends! Today's sweet pig craft is a perfect Chinese New Years Craft AND Valentine's Day Craft too.
Looking for an easy Chinese New Year Craft that you can make with kids of all ages? Try making these paper chain dragons. Can't draw? Don't worry! Download the free printable below and you'll be making tons of dancing paper dragons in no time!
Looking for a fun, winter-themed kid activity? Try painting an ice snowman. This is a perfect activity for kids who are stuck inside and looking for something creative to do!
Here's how to draw these sleepy three-dimensional heart drawings with your kids.
A great Sharpie and Colored Pencil art project for kids!
Looking for a quick New Years craft for 2019? Here's a super easy printable crown that the kids can color and wear!
Today I'm sharing the final snowflake craft of the year! I'm taking a short break over Christmas and thought I'd leave you with one final snowflake design. These nativity snowflakes are really simple and pretty. They're a great way to celebrate the season.
We're still on the snowflake craft kick! Today I'm sharing these super sweet Rudolph inspired reindeer snowflakes!
Have you heard of Pusheen the Cat? I recently found out about this super cute feline sensation and fell in love with her squishy, huggable body. So, today we're adding to our ever-expanding list of snowflake crafts with this uber adorable Pusheen snowflake craft!
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Are you ready to make the cutest llama winter craft ever?
Ahhhh! I introduce to you this llama snowflake design! Ok, ok. I've gone kinda bonkers with paper snowflake crafts. But I can't help it... I just looooove them so much. And we don't get snow here in southern California.... so I have to make do with these paper flakes.
Winter time means snowflake cutting time. Today I'm sharing a design for magical and cute unicorn snowflakes!
Every winter our family enjoys cutting paper snowflakes together. And every year I try to come up with new cute character themed snowflakes (like these Lego Men Snowflakes and these Snowman Snowflakes.) This year I designed these fun Pokemon Snowflakes since the rest of my family has gone Pokemon crazy. Tada!
Who loves turtles? Here's an easy way to turn an old glove into a cute turtle puppet! My youngest son loves puppets of all sorts, so I whipped this turtle puppet up during naptime. Here's how I made it!
Brr, it's cold outside! Lately I've been enamored with quilt designs and origami crafts. Their bold colors and gorgeous geometric patterns really make me swoon! Today's post combines my love for both crafts. These origami paper quilts are really quite beautiful to look at. Folding them can be a bit of challenge, because there are so many units to fold. But, make them with some friends and you're sure to have some indoor fun during these cold winter nights.
Note: This post contains affiliate links. This means I make a small bit of change when you purchase items through the links. Thank you for your support and the grocery money. For my full disclosure policy, click here.
This past weekend we celebrated Lunar New Year with several friends. There were tons of yummy snacks and (of course) several Chinese New Year crafts and activities! One of my favorites was this giant, collaborative Dragon painting, so I thought I'd share it here today.
Here's a fun Valentine's Day Activity that also includes a bit of math too- Heart Tangrams!
Today I'm sharing a simple and beautiful Valentine's Day Craft.
Chinese New Year is coming up! Today we're adding to the blog's growing list of Chinese New Year Crafts with this super easy, modern, and colorful folded paper lantern craft!
Should snowflake crafts only be done during December? No way! Snowflake crafts are year round over here. It's almost February and I am loving nights where I can just sit and cut out beautiful designs from paper. Today I'm giving Valentine's Day Crafts a snowflake twist. Tada! How about cutting some paper heart snowflakes?