text:
\section{Introduction}
The discovery of gravitational waves from black hole mergers detected with the LIGO/VIRGO interferometers provided us with a new channel to study astrophysical black holes. Interestingly, the generally high mass/low spin values inferred by these experiments \citep{Abbott16} are consistent with primordial black holes (PBHs) properties predicted by theoretical models (e.g. \citealt{sasaki16, Bird16, Clesse17}).

Primordial black holes (PBHs) are expected to be formed by gravitational collapse of overdense regions in the early Universe \citep{hawking74}, during the radiation dominated era. Given their early origin, PBHs can affect several properties of the Universe, such as the amplitude of primordial inhomogeneities \citep{Bellido17}, and the matter distribution in the early Universe (e.g., \citealt{Afshordi, Inman19}). In addition, extra energy injection due to PBHs accretion or evaporation affects the thermal history of the Universe \citep{Mena19, Junsong21}.

PBHs are non-baryonic Dark Matter candidates \citep{carr16}, and their abundance is described with the parameter $f_{\rm PBH}=\Omega_{\rm PBH}/\Omega_{\rm DM}$, i.e., the fraction of dark matter composed by PBHs. Under the standard assumption of a monochromatic PBH mass distribution, several constraints already exist on $f_{\rm PBH}$ from different astrophysical processes. The low-mass end of the PBH mass spectrum ($M<10^{-16}M_{\odot}$) is constrained through PBHs evaporation using the out-coming radiation as an observable. For instance, an upper limit of $10^{-8}<f_{\rm PBH}<1$ was found in the mass range $10^{-19}{\rm M}_{\odot}< M_{\rm PBH}<10^{-16} {\rm M}_{\odot}$ by comparing the gamma-ray radiation expected from PBH evaporation with the observed gamma-ray background \citep{Chen22}. Different constraints on $f_{\rm PBH}$ were set by the comparison between the BH merger rates detected by LIGO and the ones predicted by PBH models \citep{Kamionkowski17, Ballesteros18}. In the subsolar mass range ($10^{-8}{\rm M}_{\odot} \leq M_{\rm PBH}\leq 1~{\rm M}_{\odot}$), gravitational lensing has been the dominant process used to search for PBHs signature (e.g., \citealt{Tisserand07, Niikura19, Smyth20}) allowing for only a small fraction ($f_{\rm PBH} \simlt 10^{-2}$) of DM in the form of PBHs.
The comparison between the CMB anisotropies value predicted when the contribution of accreting PBHs is accounted for and the observed one was used by \citet{Poulin17} and \citet{Ali-haimoud17} to set constraints ($f_{\rm PBH} < 10^{-3}$) in the mass range $10^2\leq M_{\rm PBH}\ \leq 10^5$. For higher masses, the dynamical effects induced by PBHs (e.g. tidal disruption of dwarf galaxies) dominate the constraints (e.g., \citealt{Monroy14, CarrSilk18, Zoutendijk20} allowing only a small fraction of DM ($f_{\rm PBH}\leq 10^{-5}$) to be comprised of PBHs.

The entire mass spectrum is thus widely constrained, leaving only one window (i.e., $10^{-16}-10^{-11} M_{\odot}$, \citealt{carr20}, corresponding to the asteroid mass range) in which PBHs could constitute the entirety of dark matter. Although adopting a broader mass distribution allows the entirety of DM to be comprised of PBHs without exceeding existing constraints \citep{Hasinger2020}, such an approach requires a physically unjustified fine-tuning of the mass distribution.

The presence of a (still unrecovered) population of accreting black holes at high redshift can be used to explain several observational results. For instance, a signal in excess of that produced by known sources was measured by several works \citep[e.g.][]{Hickox06, Hickox07, Cappelluti17} in the Cosmic X-ray Background (CXB) using the Chandra space telescope. The origin of such excess has been ascribed to the presence of still undiscovered, high-$z$ BHs \citep[$z>6$,][]{Salvaterra12, Kashlinsky16, Ananna20}.

The Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission (ARCADE2) experiment measured measured an absolute sky brightness of $T_b= 54 \pm 6\ \rm mK$ at $3.3\rm~ GHz$. This implies an excess in the Cosmic Radio Background (CRB) of $5\times$ with respect to prediction from theoretical models \citep{ARCADE2}. In particular, the ARCADE2 results suggested the possibility that the CMB may not be the dominant source of the extragalactic radio background \citep{Ewall20}. The measurement was used, together with previous ones, to fit the radio-excess with a power-law spectrum, finding a spectral dependence $\nu^{-0.6}$ typical of the synchrotron radiation. The power-law results in 480 mK at 1.4 GHz or 21 cm.

PBHs can also explain the anomalous 21-cm absorption signal reported by the Experiment to Detect the Global EoR Signature \citep[EDGES, ][]{Bowman18}.
EDGES aims at measuring single dipole signal in the sky-averaged global signal of the $21\rm cm$ radiation, in order to trace the volume-averaged ionization and thermal IGM evolution with redshift. This experiment has reported the detection of a strong absorption signal with a depth that is almost twice as strong as the expectation from the contribution of the Cosmic Microwave Background (CMB) alone \citep{Bowman18}. Given the expression for the differential brightness temperature $\delta T_b$ \citep{ewall}:
\begin{align}
\delta T_b \propto \left(1-\frac{T_{\rm CMB}+T_\gamma}{T_s}\right),
\end{align}
where $T_{\rm CMB}$ is the CMB brightness temperature, $T_s$ is the spin temperature, and $T_{\gamma}$ is a the brightness temperature of an extra component in the radio background. Two theoretical explanation have been proposed for the \citet{Bowman18} result: the first one is that the $T_s$ value is lower than expected at $z \sim 17$. This hypothesis has been explored by different works \citep{barkana18, loeb18, fialkov18}; the second one is the presence of an additional contribution to the CRB as suggested by \citet{EDGES} and other works e.g. \citet{ewall, radioloud21}.

In this work, we explore the possiblity that PBHs are the sources of the excess signals in the CXB and CBR, and can explain the EDGES absorption signal. A widely used approach to model PBH accretion in the eary Universe (e.g., \citealt{ricotti08, ricotti09, Mena19, Hasinger2020}) is to assume that PBHs are surrounded by a uniform gas distribution, thus neglecting accretion from denser gas, located in virialized structures. In this work we add this important ingredient, i.e. PBH accretion inside DM halos. A similar approach was undertaken by \citet{gaggero17} in a Milky Way context. We build up on that work, further modeling the PBH-gas interaction in a cosmological framework.

The paper is organized as follows. In Sec. \ref{model} we describe the model\footnote{We adopt a $\Lambda$CDM cosmology in agreement with Planck18 \citep{Planck18} results: $\Omega_{\rm m}=0.315$,
$\Omega_{\rm \Lambda}=0.685$, $\Omega_{\rm b}=0.049$, $\sigma_8 = 0.811$, $n_s=0.965$,
and $H_{\rm 0}=100 \,h$~km~s$^{-1}$~Mpc$^{-1}=67.4$~km~s$^{-1}$~Mpc$^{-1}$.} adopted in this work, in Sec. \ref{heation} we review the model implications for the IGM thermal history; Sec. \ref{results} contains the main findings of this work. In Sec. \ref{PBHconst} we compare our results with previous ones, and Sec. \ref{conclusion} presents a brief summary.

\section{Model}\label{model}
In this section, we describe the theoretical model adopted to distribute PBHs in the Universe (Sec. 2.1), to compute their accretion (Sec. 2.2), the resulting X-ray and radio emission (Sec. 2.3), and the corresponding cosmic backgrounds (Sec. 2.4).

\subsection{PBHs cosmological distribution}
In this work, we assume that PBHs constitute a fraction of dark matter $f_{\rm PBH}=\Omega_{\rm PBH}/\Omega_{\rm DM}$. The PBH density distribution is assumed to track dark matter, which is in turn organised into virialized objects (halos) and a diffuse component at the mean cosmic density, i.e. the intergalactic medium (IGM). The PBH number density, $n_{\rm PBH}$, at redshift $z$ is then given by:
\begin{equation}
n_{\rm PBH}(z)=\frac{\Omega_{\rm DM}\rho_c f_{\rm PBH}(1+z)^3}{M_{\rm PBH}}=n_{\rm PBH}^{\rm IGM}(z)+n_{\rm PBH}^{h}(z),
\end{equation}
where $\rho_c = 3 H^2/8 \pi G$ is the critical density of the Universe, $M_{\rm PBH}$ is the PBH mass, and $n_{\rm PBH}^{\rm IGM}$ ($n_{\rm PBH}^{h}$) represents the number density of PBHs in the IGM (DM halos). We assume a monochromatic PBH mass distribution, in the range $1 \leq M_{\rm PBH}\leq 1000 ~{\rm M}_{\odot}$.

The relative abundance of PBHs in halos and IGM depends on the fraction of dark matter that collapses into virialized structures per comoving volume, that can be computed through the Press-Schechter formalism \citep{PS74}:
\begin{equation}
  f_{\rm coll}(\> M_{\rm min}, z)=\mathrm{erfc}\left[\frac{\delta_c(z)}{\sqrt{2}\sigma_M} \right],
\end{equation}
where $\delta_c=1.686/D(z)$ is the critical density for collapse, $D(z)\propto (1+z)^{-1}$ is the growth factor, $\sigma_M$ is the standard deviation of the linearly extrapolated matter power spectrum, and $M_{\rm min}$ is the minimum halo mass such that efficient cooling processes are triggered (see Sec. \ref{backint}).
\subsubsection{PBHs in the IGM}
The number density of PBHs in the IGM is given by:
\begin{equation}\label{n_h}
  n_{\rm PBH}^{\rm IGM}(z)=\frac{\Omega_{\rm DM}\rho_c(1+z)^3(1-f_{\rm coll}(z))f_{\rm PBH}}{M_{\rm PBH}}.
\end{equation}
This expression shows that $n_{\rm PBH}^{\rm IGM}$ decreases with decreasing redshift. Besides cosmic expansion, this redshift evolution is due to the on-going structure formation, as more dark matter falls onto virialized halos, more PBHs are locked into DM halos than in the IGM.

\subsubsection{PBHs in dark matter halos}
The total amount of PBHs inside dark matter halos can be expressed, as a function of redshift, as:
\begin{equation}\label{n_igm}
  n_{\rm PBH}^{h}(z)=\frac{\Omega_{\rm DM}\rho_c(1+z)^3f_{\rm coll}(z)f_{\rm PBH}}{M_{\rm PBH}}.
\end{equation}
To distribute PBHs into a DM halo of mass $M_{\rm vir}$, we assume that they follow a Navarro, Frenk \& White \citep[NFW,][]{NFW97} density profile:
\begin{equation}
\rho_{\rm DM}(r)=\frac{\rho_c\delta_c}{cx(1+cx)^2},
\end{equation}
where $x=r/r_{\rm vir}$ denotes the radial distance in units of the virial radius $r_{\rm vir}$ \citep{barkana2001beginning}:
\begin{equation}
\begin{split}
  r_{\rm vir}=\ &0.784\ \left(\frac{M_{\rm vir}}{10^8\ h^{-1}\ M_{\rm \odot}}\right)^{1/3}\left[\frac{\Omega_m}{\Omega^z_m}\frac{\Delta_c}{18\pi^2}\right]^{-1/3}\ \\
  &\left(\frac{1+z}{10}\right)^{-1}h^{-1}\ \mathrm{kpc},
\end{split}
\end{equation}
 where the overdensity relative to $\rho_c$ at the collapse redshift can be expressed as $\Delta_c=18\pi^2+82d-39d^2$, with $d=\Omega_m^z-1$ and $\Omega_m^z=\Omega_m(1+z)^3/(\Omega_m(1+z)^3+\Omega_{\Lambda})$; $\Delta_c$ is related to $\delta_c$ through the following relation:

\begin{equation}\label{overD}
\delta_c=\frac{\Delta_c}{3}\frac{c^3}{ln(1+c)-c/(1+c)}=\frac{\Delta_c}{3}\frac{c^3}{F(c)},
\end{equation}
where $c$ is the concentration parameter that depends on $M_{\rm vir}$:
\begin{equation}
\log c=1.071-0.098(\log M_{\rm vir}-12).
\label{maccio}
\end{equation}
The last relation is the result of N-body simulations developed by \citet{maccio07}; in Appendix \ref{concentration}, we discuss its applicability to low-mass ($M<10^8 {\rm M}_{\odot}$)and high-redshift ($z>6$) objects.

The total number of PBHs inside the halo can be computed by imposing that the halo mass is constituted of a fraction $f_{\rm PBH}$ of PBHs:
\begin{equation}\label{ntot}
N_{\rm tot}=f_{\rm PBH}\left(\frac{M_h}{M_{\rm PBH}}\right).
\end{equation}
The number of PBHs within any given radial distance is then given by:
\begin{equation}
N_{\rm PBH}(r)=f_{\rm PBH}\frac{4\pi}{M_{\rm PBH}}\int^{r}_{\rm 0}\rho_{\rm DM}(r')r'^2dr'.
\end{equation}
Fig. \ref{NUMDENS} shows the baryonic and DM density distributions (left axis), and the number of PBHs normalized to their total number (right axis), as a function of the radial distance from the center of the halo. According to our formalism, at a given redshift, less massive halos ($M_{\rm vir}=10^3 M_{\odot}$) are more concentrated than more massive ones ($M_{\rm vir}=10^9 M_{\odot}$); thus, 50\% of $N_{\rm PBH}$ reside at smaller radial distances in the less massive halos ($0.3~r_{\rm vir}$ vs. $0.5~r_{\rm vir}$). Similarly, at a given fixed virial mass (e.g. $M_{\rm vir}=10^6 M_{\odot}$), low redshift ($z=6$) DM halos are more concentrated than high redshift ($z=20$) ones. As a result, 50\% of $N_{\rm PBH}$ reside at smaller radial distances in the less massive halos ($0.4~r_{\rm vir}$ vs. $0.6~r_{\rm vir}$).
\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{images/Tripledens.png}
\caption{Baryon density, dark matter density, and PBHs integrated number as a function of the virial radius. Lines correspond to different halo masses. The solid, dashed, dotted line stays for a halo of mass $M_h=10^3 {\rm M}_{\odot}$, $M_h=10^{6} {\rm M}_{\odot}$, $M_h=10^{9} {\rm M}_{\odot}$, respectively. Different colors represent different quantities: orange PBHs cumulative number, violet baryon density, purple dark matter density. The 3 panels present 3 redshifts: $z=6, 20, 30$. PBHs mass is set at $30 M_{\odot}$.}\label{NUMDENS}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{images/accrhalo.png}
\caption{Accretion rate (for a single $30\ M_{\odot}$ black hole) as a function of the virial radius. The solid (dashed/dotted) line represents the redshift $z=6$ ($z=20/z=30$). Different colors denote different halo masses: black $M_h=10^3 {\rm M}_{\odot}$, violet $M_h=10^{6} {\rm M}_{\odot}$, and orange $M_h=10^{9} {\rm M}_{\odot}$. The horizontal purple line is the Eddington rate for a $30 M_{\odot}$ black hole.}\label{accretiionZ}
\end{figure}

\subsection{PBH accretion}
We assume that, both in the IGM and in halos, PBHs accrete according to the Bondi-Hoyle-Lyttelton model:
\begin{equation}\label{accrex}
\dot{M}_{\rm PBH}=\lambda \frac{4\pi G^2M_{\rm PBH}^2\rho_{\rm gas}}{(c^2_{\rm s}+v^2_{\rm BH})^{3/2}},
\end{equation}
where $G$ is the universal gravity constant, $\rho_{\rm gas}$ is the gas density, $c_s$ is the sound speed, $v_{\rm BH}$ is the relative velocity between the black hole and the gas, and $\lambda = 0.01$ is the accretion eigenvalue, that accounts for non-gravitational effects in the process \citep{Xie12}. We prevent the gas accretion to exceed the Eddington rate $\dot{M}_{E}=L_E/(\varepsilon~c^2)$, where $L_E$ is the Eddington luminosity:
\begin{equation}
L_{E}=\frac{4\pi GM m_p c}{\sigma_T}=1.3\times10^{38}\biggl(\frac{M_{\rm PBH}}{M_{\rm \odot}}\biggl)\ {\rm erg\ s^{-1}} ,
\end{equation}
and $\varepsilon=0.1$ is the assumed radiative efficiency\footnote{The value of the radiative efficiency is strongly dependent on the geometry of accretion, and can vary from $\varepsilon\ <\ 10^{-4}$, in the case of spherically symmetric accretion to $\varepsilon\ <\ 0.43$ for disk accretion processes \citep{Shakura73, shapiro73}}.

PBH accretion in the IGM and inside halos proceeds in a considerably different manner \citep{ricotti08,deluca20}. In what follows we characterize $\rho_{\rm gas}$, $c_s$, and $v_{\rm BH}$ in these two cases, separately. \\

\subsubsection{PBH accretion in the IGM}
Given the number density in eq. \ref{n_igm}, the accretion from all the PBHs distributed in the IGM per comoving volume can be written as:
\begin{equation}
  \dot{M}(z)=4\pi \lambda G^2M_{\rm PBH}^2\frac{\rho_{\rm IGM}(z)}{[c_s(z)^2+v_{\rm rel}(z)^2]^{3/2}}n_{\rm PBH}^{\rm IGM}(z),
\end{equation}
where $\rho_{\rm IGM}$ is the gas density, $c_s$ is the sound speed in the IGM, and $v_{\rm rel}$ is the relative velocity between dark matter and baryons.
Following \citet{ricotti09}, we assume that PBHs in the IGM are surrounded by a uniform distribution of gas with density:
\begin{equation}
  \rho_{\rm IGM}=250\, \mu m_p \biggl(\frac{1+z}{1000} \biggl)^3\ \mathrm{g\ cm^{-3}},
\end{equation}
where $m_p$ is the proton mass and $\mu = 1.22$ is the mean molecular weight of a neutral gas of primordial composition.
The IGM sound speed is
\begin{equation}
c_s=( k_BT_{\rm IGM}/\mu m_p)^{1/2},
\end{equation}
where $k_B$ is the Boltzmann constant, and ${T_{\rm IGM}}$ is the gas temperature that depends on large scale effects, as discussed in Sec. \ref{heation}.

\begin{figure*}
\begin{center}
\includegraphics[width=1\textwidth]{images/Tripleaccr.png}
\caption{{\it Left panel}: baryon density (normalized to the critical density, $\rho_c$) as a function of halo mass, $M_h$, and redshift, $z$.
{\it Middle}: same as left panel for sound speed, $c_s$. {\it Right}: same as left panel for the accretion rate of a $30\ M_{\odot}$ PBH (normalized to the Eddington rate). Note that accretion is more efficient in small halos at low redshift due to their higher density and lower sound speed. All values have been computed at $r=0.01\ r_{\rm vir}$, where the baryon density and accretion rate reach their maximum. In each panel, the hatched grey regions represents the excluded region of the parameter space. The continuous white lines are an extension of the excluded region for the different $M_{\rm min}$ considered. We discuss how to select $M_{\rm min}$ in Sec. \ref{heation}.
}\label{AccretionVariables}
\end{center}
\end{figure*}

For what concerns the relative velocity between dark matter and baryons, we adopt the relation proposed by \citet{Ali-haimoud17}:
\begin{equation}\label{rel_vel}
  v_{\rm rel}(z)\simeq 30 \min\biggl[1, \left(\frac{1+z}{1000}\right)\biggl]\, \mathrm{km\ s^{-1}}.
\end{equation}
\subsubsection{PBH accretion in halos}
Inside halos, the accretion rate strongly depends on the radial distance $r$:
\begin{equation}\label{accrex_halo}
\dot{M}_{\rm BHL}(r)=\lambda \frac{4\pi G^2M_{\rm PBH}^2\rho_{\rm gas}(r)}{(c^2_{\rm s}+v^2_{\rm BH})^{3/2}}.
\end{equation}
We adopt the gas density distribution from \cite{makino98}:
\begin{equation}\label{ro_bar}
\rho_{\rm gas}=\rho_0\ \exp\left\{-\frac{\mu m_p}{2k_BT_{\rm vir}}[v^2_e(0)-v^2_e(r)]\right\},
\end{equation}
where $\rho_0(M)$ is the central gas density\footnote{The constant $\rho_0$ is set such that $M_b=({\Omega_b}/{\Omega_m})M_h$.}, $T_{\rm vir}$ is the virial temperature of the halo:
\begin{equation}\label{Tvir}
\begin{split}
T_{\rm vir}=\ & 1.98\times 10^4\ \left(\frac{\mu}{0.6}\right)\ \left(\frac{M_{\rm vir}}{10^8\ h^{-1}\ M_{\rm \odot}}\right)^{2/3}\ \\ & \left[\frac{\Omega_m}{\Omega^z_m}\frac{\Delta_c}{18\pi^2}\right]^{1/3}\left(\frac{1+z}{10}\right)\ \rm K,
\end{split}
\end{equation}
and $v_e$ is the escape velocity that can be obtained through the following relations:
\begin{align*}
M(r)&=\int^{r}_{0}4\pi \rho(r')dr'=M_{\rm vir}\frac{F(cx)}{F(c)},\\
v^2_c(r)&=\frac{GM(r)}{r}=v^2_{\rm c,vir}\frac{F(cx)}{F(c)},\\
v^2_e(r)&=2\int^{r_{vir}}_{r}\frac{GM(r')}{r'^2}dr'\approx 2v^2_c\frac{F(cx)+\frac{cx}{1+cx}}{xF(cx)},\\
\end{align*}
where $F(c)$ is defined in Eq. \ref{overD}, and $v^2_{\rm c,vir}=GM_{\rm vir}/r_{\rm vir}$ is the circular velocity. We further assume that inside the halo the sound speed is constant and equal to:
\begin{equation}\label{cs}
c_s=( k_BT_{\rm vir}/\mu m_p)^{1/2} {\rm km\ s^{-1}}=8.3\ T^{1/2}_{\rm vir,4}\ \rm km\ \rm {s}^{-1},
\end{equation}
where $T_{\rm vir,4}$ is the virial temperature in units of $10^4\ \rm K$. We finally set to zero the relative velocity between PBHs and baryons, assuming that dark matter and baryons are in hydrodynamical equilibrium.

In Fig. \ref{accretiionZ}, we show how the accretion rate varies within the virial radius, for different halo masses and redshifts. For a fixed halo mass, the accretion rate is higher at low redshift; for a fixed redshift, the accretion rate is higher for less massive halos. To understand these trends, in the left and middle panels of Fig. \ref{AccretionVariables} we plot the redshift and $M_h$ dependence of the gas density and sound speed, which govern the PBH accretion rate (eq. \ref{accrex_halo}). For illustration, both quantities are computed at $r=0.01 r_{\rm vir}$. The baryon overdensity $\rho_b/\rho_c$ inside halos remains almost constant around a value $\simeq 100$ along cosmic history, but slightly increases for low $z$ and/or small DM halos. Instead, the sound speed decreases both with halo mass and redshift.

These two combined effects, explain the results shown in the right panel of Fig. \ref{accretiionZ}, where the accretion rate at $r=0.01\ r_{\rm vir}$ is shown as a function of $M_h$ and $z$. Accretion is more efficient in the central region of low mass halos ($M \leq 10^6 M_{\odot}$), at any given $z$. In these objects, accretion is so efficient that it compensates the reduced total number of PBHs that scales linearly with $M_h$ (Eq. \ref{ntot}). Given that small halos are also more numerous relative to more massive ones, we expect their PBH emission to be dominant.

\subsection{X-ray and radio luminosity}\label{luminosity}
Given the bolometric luminosity $L_{\rm B}=\varepsilon \dot{M} c^2$ of an accreting PBH, the X-ray luminosity ($L_X$) can be computed by means of a bolometric correction $f_X$, i.e.
\begin{equation}
L_X=f_XL_{\rm B}.
\end{equation}
Following \citet{ewall}, we assume $f_X=0.1$ in the $2-10\ \mathrm{keV}$ band \citep[see also][]{Poulin17, Mena19, 21cmForestPBH}. We model the X-ray spectra of accreting PBHs with a power-law with an exponential cut-off at high energies \citep{Poulin17, Mena19, 21cmForestPBH}, and compute the specific luminosity in the X-ray band ($L_{X,\nu}$) as:
\begin{equation}
  L_{X,\nu} \propto {\nu}^{-\alpha}e^{(-\nu/\nu_{\rm cut})},
\end{equation}
where\footnote{Typical values of spectral indices in the X-ray band are in the range $\alpha = [0.7, 1.3]$ \citep{Yuan14}) and $\nu_{\rm cut}$ is the cut-off frequency, such that $h\nu_{\rm cut}=200\ \mathrm{keV}$.} $\alpha=0.7$ is the spectral index in the X-ray band, and $\nu_{cut}$ is the cut-off frequency.

For what concerns the radio luminosity $L_R$, we assume the fundamental plane relation \citep{Gallo03, merloni03, wang06}. In particular, following \citet{Hasinger2020}, we adopt the relation found by \cite{wang06}, based on the radio luminosity measured at 1.4 GHz and the X-ray luminosity in the 0.1-2.4 keV band:
\begin{equation}
\begin{split}
  & \log\left(\frac{L_R}{10^{40}\mathrm{erg\ s^{-1}}}\right) = \\ & = 0.85\log\left(\frac{L_X}{10^{44}\mathrm{erg\ s^{-1}}}\right)+0.12\log\left(\frac{M_{\rm PBH}}{10^{8}\mathrm{M_{\rm \odot}}}\right).
\end{split}
\end{equation}

We finally assume for the radio luminosity a typical spectral index of syncrothron emission, $L_{R,\nu}\propto \nu^{-0.6}$.

\subsection{Background intensity}\label{backint}
The comoving specific emissivity due to PBHs accreting in the IGM can be written as:

\begin{equation}
  \dot{\rho}_{\rm IGM}(\nu, z)= L_{\nu}(z) n_{\rm IGM}(z)\ \mathrm{erg\ s^{-1}\ Mpc^{-3} Hz^{-1}}.
\end{equation}
where $\nu$ is the (rest-frame) frequency, and $L_{\nu}$ represents the X-ray or radio specific luminosity computed with the formalism described in the previous section.
For what concerns the emissivity from halos, $\dot{\rho}_h$, we first compute the integrated luminosity from a single object of mass $M_{\rm vir}$:
\begin{equation}\label{halum}
L_{\nu}(M_{\rm vir})= \int^{r_{\rm vir}}_{\rm 0}L_{\nu}(r')n_{\rm PBH}(r')dr',
\end{equation}
and then we integrate over the halo mass function \citep{HMFcalculator}:
\begin{equation}\label{bhint}
\dot{\rho}_{h}(\nu, z)=\int^{M_{\rm max}}_{\rm M_{\rm min}}L_{\nu}(M', z)\ n_h(M', z)dM',
\end{equation}
where $n_h(M, z)$ gives the number of halos of mass $M$ at redshift $z$, $M_{\rm max} = M_h(T_{\rm vir}=10^4 \mathrm{K})$ is the minimum DM halo mass for star formation to happen, and $M_{\rm min}$ is the minimum mass of DM halos that can virialise and form a baryon overdensity:
\begin{equation}
  M_{\rm min}(T_{\rm IGM}, z)=1.3\times 10^3 M_{\rm \odot} \left(\frac{10}{1+z}\right)^{3/2} \left(\frac{T_{\rm IGM}(z)}{1\ \mathrm{K}}\right)^{3/2}.
\end{equation}
The latter depends on the IGM temperature evolution and will be computed in Sec. \ref{neutral_regions}.

Finally, we proceed to compute the background intensity, $I_{\rm PBH}$, as follows:
\begin{equation}\label{intensity}
I_{\rm PBH}(\nu, z)=\frac{c(1+z)^3}{4\pi \nu}\int_z^{\infty}\frac{\dot{\rho}(\nu, z')}{(1+z')H(z')}dz',
\end{equation}
where $H(z)$ is the Hubble parameter. Usually, in the radio frequency range the background intensity, $I$, is more conveniently expressed in terms of the brightness temperature, $T_b$:
\begin{equation}
T_b(\nu, z)=\frac{I(\nu, z) c^2}{2 k_B\nu^2}.
\end{equation}

\begin{figure*}
\begin{center}
\includegraphics[width=1\textwidth]{images/IONTEMPMIN.png}
\caption{IGM ionized fraction (left panel), Temperature (middle panel), Minimum mass (right panel) evolution with redshift inside neutral regions. Different colors represent different $f_{\rm PBH}$ values: black continuos line $f_{\rm PBH}=1$, violet dashed line $f_{\rm PBH}=10^{-1}$, purple dotted line $f_{\rm PBH}=10^{-2}$, red dashed-dotted line $f_{\rm PBH}=10^{-3}$, and orange continuous line $f_{\rm PBH}=10^{-4}$. We maintain this line style and color code thorough the rest of this paper. In all three panels a PBHs mass of $30\ M_{\odot}$ is assumed.
}\label{IONTEMPEVO}
\end{center}
\end{figure*}
\section{IGM Heating and Ionization by PBHs}\label{heation}
Radiation emitted by accreting PBHs is injected into the IGM, thus heating and ionizing the gas. The background intensity described in the previous section can be used to self-consistently account for these large scale effects.

To compute the amount of energy injected into the IGM by the X-ray emission we follow the formalism described in \cite{Mesinger13}. The heating rate per baryon, $\epsilon_{\rm PBH}$, is a function of the X-ray background produced by PBHs, and can be expressed as:
\begin{equation}
  \epsilon_{\rm PBH}(z)=\int_{\rm \nu_{\rm min}}^{\infty}d\nu \frac{4\pi I_{\rm \nu}}{h\nu}(h\nu-E^{th})f_{\rm heat}\sigma_H(\nu),
\end{equation}
where $h\nu_{\rm min}=0.5\ \mathrm{keV}$, $I_{\rm \nu}$ is the angle-averaged specific-intensity X-ray background, $E^{th}$ is the ionization threshold, $f_{\rm heat}=0.3$ is the fraction of primary electron energy going into heat \citep{Furlanetto2010}, and $\sigma_H$ is the hydrogen ionization cross section.

We then compute the impact of X-ray photons from accreting PBHs on the heating\footnote{We neglect the impact of UV ionizing radiation emitted by PBHs (see Appendix \ref{noION})} and ionization of the IGM, following \citep{Puchwein19}. The evolution of the IGM ionized fraction $x_e$ and temperature $T_{\rm IGM}$ are computed by solving the following coupled differential equations:
\begin{subequations}
\begin{equation}
  \frac{dx_e}{dz}=\frac{dt}{dz}[\Gamma - \alpha_R(T) C x_e^2 n_b],
\end{equation}
\begin{equation}
\begin{split}
  \frac{dT_{\rm IGM}(z)}{dz}=&\frac{2}{3k_B(1+x_e)}\frac{dt}{dz}\sum_i \epsilon_i\\
  &+\frac{2T_{\rm IGM}}{3n_b}-\frac{T_{\rm IGM}}{1+x_e}\frac{dx_e}{dz},
\end{split}
\end{equation}
\end{subequations}

where $\Gamma$ is the photoionization rate, $\alpha_R$ is the case A recombination coefficient , $C=2$ is the clumping factor \citep{Mesinger13}, $n_b$ is the mean baryon density, and $\epsilon_i$ is the heating rate per baryon per process $i$.

To properly evaluate PBHs accretion in the pre-overlap phase of the cosmic reionization process, we solve the above coupled differential equations separately for the ionized and neutral regions. The assumption of volume-averaged values for the IGM temperature and ionized fraction would lead to a miss evaluation of the gas accretion onto PBHs, and subsequently of their emission.
\subsection{Ionized regions}
We fix the IGM temperature in the ionized regions to $T_{\rm IGM, ion}\ =\ 10^4\ \mathrm{K}$; the coupled differential equations then become:
\begin{subequations}
\begin{equation}
  \frac{dx_{\rm e, ion}}{dz}=\frac{dt}{dz}[\Gamma - \alpha_R C x_{\rm e, ion}^2 n_b],
\end{equation}
\begin{equation}
  \frac{dT_{\rm IGM, ion}(z)}{dz}= 0.
\end{equation}
\end{subequations}
In the case of ionized regions, PBHs accretion is strongly suppressed because of the increased sound speed. The redshift evolution of the ionized fraction $x_{\rm e, ion}$ traces the evolution of the volume filling factor of ionised regions, namely the fraction of volume occupied by ionized regions. We rewrite the IGM number density of PBHs dividing the ionized and neutral components as follows:
\begin{equation}
  n_{\rm IGM}(z)=n_{\rm IGM}(z)x_{\rm e, ion}(z)+n_{\rm IGM}(z)(1-x_{\rm e, ion}(z)).
\end{equation}
\subsection{Neutral regions}
\label{neutral_regions}
In the case of neutral regions, the coupled equations can be written as follows:
\begin{subequations}
\begin{equation}
  \frac{dx_{\rm e, n}}{dz}=\frac{dt}{dz}[\Gamma_{\rm PBH} - \alpha_R(T_{\rm IGM, n}) C x_{\rm e, n}^2 n_b],
\end{equation}
\begin{equation}
\begin{split}
  \frac{dT_{\rm IGM, n}(z)}{dz}=&\frac{2}{3k_B(1+x_e)}\frac{dt}{dz} \epsilon_{\rm PBH}\\
  &+\frac{2T_{\rm IGM, n}}{3n_b}-\frac{T_{\rm IGM}}{1+x_e}\frac{dx_{\rm e, n}}{dz},
\end{split}
\end{equation}
\end{subequations}
where $x_{\rm e, n}$ represents the fraction of free electrons in neutral regions, and $\Gamma_{\rm PBH}$ is the ionization rate due to PBH X-ray emission. PBHs accreting in neutral regions represent the main contributors to the cosmic backgrounds, because of their lower gas temperature that both lowers the sound speed (thus increasing the accretion rate) and allows mini-halos to virialise more easily. In neutral regions, the sole heating and ionizing contribution comes from X-ray photons, since UV photons are easily absorbed by neutral hydrogen, while X-rays can penetrate larger gas column densities before getting absorbed.

The resulting IGM ionized fraction and temperature evolution in the neutral regions is shown\footnote{We limit our analysis at redshift $z = 6$ since, according to our model \citep{Puchwein19}, this epoch sets the end of the reionization process; thus at lower redshifts the IGM is completely ionized.} in the left and middle panel of Fig. \ref{IONTEMPEVO}, respectively. This figure clearly shows that the impact of accreting PBHs on the global thermal and ionization history of the early Universe would be particularly relevant if dark matter were completely composed of PBHs ($f_{\rm PBH}=1$): in this case, the IGM ionized fraction and temperature would increase by a factor of about 50 at $z\sim 6$; for lower values ($f_{\rm PBH}=10^{-2}$) the increment of $x_e$ and $T_{\rm IGM}$ would be limited to a factor of few.

Finally, in the right panel of Fig. \ref{IONTEMPEVO}, we show the $\rm M_{min}$ evolution with redshift taking into account the IGM temperature evolution before reionization\footnote{The minimum halo mass after reionization is fixed to $M_{\rm min}= M_h(T_{\rm vir}=10^4\ \rm K)$.}. As a consequence of X-ray heating by PBHs, also $M_{\rm min}$ increases. In particular, $M_{\rm min}$ appears to be more strongly affected by the presence of accreting PBHs: in the case of $f_{\rm PBH}=1$ ($f_{\rm PBH}=10^{-2}$), $M_{\rm min}$ increases by factor of 1000 (10). This trend is shaped by the following combined effects: on the one hand, the relation between $M_{\rm min}$ and $T_{\rm IGM}$ is nonlinear ($M_{\rm IGM} \propto T_{\rm IGM}^{3/2}$); on the other hand, an higher value of $M_{\rm min}$ shorten the integration interval in eq. \ref{bhint}, thus reducing the resulting PBH X-ray emission from eq. \ref{intensity}.

\section{Results}\label{results}
In this Section, we constrain the fraction of dark matter in the form of PBHs by computing the contribution of PBHs to the CXB, the CRB, and the 21-cm signal.
The PBH contribution to CXB and CRB can be evaluated at different epochs. Here, we compare our cumulative model predictions at $z=0$ with the observed CXB and CRB to test to which extent the extra radiation from accreting PBHs can explain the observed excesses in the CXB and CRB. Furthermore, we constrain the possible contribution of PBHs to the CRB at $z=17$, namely the epoch at which the \hbox{H~$\scriptstyle\rm I $~} 21 cm signal detected by the EDGES experiment shows a deep absorption feature.

\subsection{X-ray background}\label{xback}
About $\sim 70 \%$ of the CXB arises from resolved sources (mostly AGN) both in the soft and hard bands \citep{Cappelluti17}. The remaining contribution from unresolved sources can be attributed to a still unknown BH population (e.g., accreting BHs in heavily obscured conditions, \citealt{Gilli2007, Treister09}) and additional unresolved sources (e.g., extended X-ray emission from galaxy clusters \citealt{Gilli99}). To test the hypothesis that PBHs provide the origin of such unresolved background, we quantify their contribution to the X-ray background in the soft ($0.5-2\ \mathrm{keV}$) and hard ($2-10\ \mathrm{keV}$) X-ray bands by using Eq. \ref{intensity}.

In Fig. \ref{Xbackevo}, we compare our predictions as a function of $f_{\rm PBH}$ with observational limits reported in \citet{Cappelluti17}. The authors analyzed Chandra data \citep[COSMOS-Legacy survey,][]{Elvis09, Civano16} finding a XRB intensity at $1~ \rm keV$ to be $10.91\pm 0.16\, \rm keV\ cm^{-2} s^{-1} deg^{-2}$ and spectral index $\Gamma = 1.45 \pm 0.02$. After subtracting the X-ray detected sources they found that the unresolved CXB intensity in the soft band\footnote{In \citet{Cappelluti17} two different values are reported for the CXB, one from {\it unresolved} sources and one called {\it non-source}. The latter one refers to the observed intensity obtained when both X-ray and HST-ACS observed sources are masked. We compare our predicted value with the {\it non-source} CXB intensity.} ($I_{0.5-2 \rm keV}=2.90\times 10^{-12}\rm \ erg\ s^{-1}cm^{-2}deg^{-2}$) is smaller than in the hard band ($I_{2-10 \rm keV}=6.47\times 10^{-12}\rm \ erg\ s^{-1}cm^{-2}deg^{-2}$). We thus consider the soft band data to obtain the most stringent constraints on $f_{\rm PBH}$.

For high values of $f_{\rm PBH}$($\gtrsim 0.1$), the contribution of accreting PBHs to the soft CXB rises steeply at early epochs: for example, assuming $f_{\rm PBH}=1$, the X-ray emission from $z>40$ PBHs already overshoots the observed CXB. The integrated contribution of PBHs flattens below a critical redshift which depends on $f_{\rm PBH}$. For example, for $f_{\rm PBH}=10^{-1}$ ($f_{\rm PBH}=10^{-3}$) the PBHs cumulative emission reaches the value of 1 (10) $\rm erg~s^{-1}~cm^{-2}~deg^{-2}$ at $z\sim 20$ ($z\sim 10$) and remains almost constant afterwards. This trend is related to the redshift evolution of $M_{\rm min}$ (right panel of Fig. \ref{IONTEMPEVO}), that rises more rapidly with $f_{\rm PBH}$, as a consequence of a more efficient X-ray heating from PBHs. We find that our predictions are consistent with Chandra data only if $f_{\rm PBH} \leq 3\times 10^{-4}$. Independently from $f_{\rm PBH}$, the PBHs contribution to the XRB drops after the reionization epoch ($z<6$), since both the high gas temperature ($>10^4$~K), and the small filling factor of neutral regions make PBHs accretion extremely inefficient.

In Fig. \ref{relfluxes} we present the redshift evolution of the ratio between the soft X-ray intensity arising from halos ($I_{X, h}$, black line) or from the IGM ($ I_{X,\rm IGM}$, orange line) and the total intensity($ I_{X,\rm tot}$). At very early epochs ($z>40$), the total signal is always dominated by IGM contribution. At $z\sim40$, the two curves cross each other, as density perturbations start to collapse into virialized structure. At later epochs,
the total X-ray intensity is dominated by emission from PBHs in DM halos, whereas PBHs in the IGM provides only a minor contribution ($\lesssim$ 5\%). We stress that 99\% of the signal arises from mini-halos ($M_h \leq 10^6\ M_{\odot}$), whose X-ray emissivity peaks at $z\sim 6$. Independently from the value of $f_{\rm PBH}$ the total signal is dominated by the emission produced into halos, up to a maximal ratio of $I_{h}/I_{\rm IGM}\sim 50$ for $f_{\rm PBH}=10^{-4}$. The contribution from PBH accreting in the IGM increases with $f_{\rm PBH}=1$, although remaining subdominant, as a consequence of the X-ray heating feedback: as the minimum mass increases, $f_{\rm coll}$ decreases, thus raising the PBHs number density into the IGM.

In Table \ref{tabX}, we report our prediction for the background intensity in the soft and hard X-ray bands for different values of $f_{\rm PBH}$\footnote{As discussed in Sec. \ref{luminosity} the spectral index adopted for this work in the X-ray band is $\alpha = 0.7$, which is slightly steeper than the one corresponding to the background excess $\alpha = 0.57$.}. The predicted intensity appear to be stronger in the soft band for $f_{\rm PBH} \leq 10^{-3}$, and vice versa. We attribute this effect to the exponential cut-off (at $200\ \rm keV$) in the X-ray spectrum that suppresses contribution from high redshift to the hard band. In the case of a shallower intensity evolution (high values of $f_{\rm PBH}$, see Fig. \ref{Xbackevo}) a non-negligible fraction of the total radiation in the hard band is produced in the redshift interval $20\simlt z \simlt 30$ . For $f_{\rm PBH} \leq 10^{-3}$ the radiation feedback is not strong enough to suppress the signal at early epochs ($20\simlt z \simlt 30$) resulting in a steeper evolution of the CXB intensity, and consequently a lower contribution to the hard band from high redshift ($z>20$).

\begin{figure}

\includegraphics[width=0.47\textwidth]{images/XBACK.png}
\caption{Integrated soft X-ray background intensity $I_{0.5-2\mathrm{keV}}$ cumulative evolution, for different values of $f_{\rm PBH}$ as reported in the legend. The blue shaded regions represent the observed excess background \citep{Cappelluti21}. The background intensities are computed for $M_{\rm PBH}=30 M_{\odot}$.}\label{Xbackevo}

\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.47\textwidth]{images/Xbackrel.png}\caption{Redshift evolution of the relative contribution to the soft ($0.5-2$ keV) X-ray background from halos and IGM, $I_{h}/I_{\rm tot}$ and $I_{\rm IGM}/I_{\rm tot}$, respectively. Different line styles correspond to different $f_{\rm PBH}$, as shown in the label. Black (orange) lines correspond to the halos (IGM) contribution. The relative background intensities are computed for $M_{\rm PBH}=30 M_{\odot}$. }\label{relfluxes}
\end{center}
\end{figure}

\begin{table}
\centering
\caption{X-ray background intensity in units of $10^{-12}\mathrm{erg\ s^{-1}\ cm^{-2}\ deg^{-2}}$. We report our predictions for soft ($0.5-2$ keV) and hard ($2-10$ keV) X-ray bands for the values of $f_{\rm PBH}$ considered in this work.}
\label{tabX}
\begin{tabular}{|l|c|r|}
\hline
$f_{\rm PBH}$ & $I_{0.5-2\mathrm{keV}}$ & $I_{2-10\mathrm{keV}}$ \\
\hline
\hline

$1$  & $68.2$ & $81.2$ \\

$0.1$ & $20.0$ & $22.2 $\\

$0.01$ & $6.01$ & $6.21$\\

$10^{-3}$ & $1.80$ & $1.74$ \\

$10^{-4}$ & $0.52$ & $0.47$ \\
\hline
\end{tabular}
\end{table}

\subsection{Radio background}
The observed background radio-excess is well fitted with a power-law spectrum between 22 MHz and 10 GHz \citep{ARCADE2}:
\begin{equation}
T_b=(24\pm 2.1\rm K) \times \left(\frac{\nu}{310\ \rm MHz}\right)^{-2.599\pm0.036}.
\end{equation}
In our model, the X-ray emission in the accretion process is associated to jet production and thus to radio emission (see Sec. \ref{luminosity}). We thus compute the contribution of PBHs to the radio background at 1.4 GHz, at redshift $z = 0$, and compare our results with ARCADE2 data ($480~\rm mK$). In Fig. \ref{myarcade}, we show the brightness temperature of the radio background, as predicted by our calculations, at varying $f_{\rm PBH}$. The amplitude of the radio background increases sub-linearly with $f_{\rm PBH}$ (see also Tab. \ref{tabR}), while the shape assumed for synchrotron emission fairly reproduces observations, and does not depend on $f_{\rm PBH}$.

In the case $f_{\rm PBH} = 1$, the PBHs contribution to the CRB would represent $92 \%$ of the observed excess, thus explaining most of the unexplained signal. However, if we take into account CXB constraints, PBHs cannot explain the radio excess, since they would contribute only 1\% to the CRB.

\subsection{21 cm signal}
The radio background due to accreting PBHs may affect the amplitude of the 21-cm global signal. The absorption depth of the signal can be computed as follows \citep{Mesinger13}:
\begin{equation}
\begin{split}
  \delta T_b = & 27 x_{\rm HI} (1+\delta) \biggl(\frac{\Omega_b h^2}{0.023} \biggl)\biggl(\frac{0.15}{\Omega_m h^2}\frac{1+z}{10}\biggl)^{1/2} \\
  & \frac{\partial_{r}v_r}{H(z)1+z}\biggl(1-\frac{T_r}{T_s}\biggl),
\end{split}
\end{equation}
where $x_{\rm HI}=1-x_e$ is the neutral hydrogen fraction, $\partial_{r}v_r$ is the comoving gradient of the line of sight component of the comoving velocity, $T_r$ is the radio background temperature, $T_s$ is the spin temperature. \citet{fialkov19} pointed out that, given a radio background of amplitude $\rm A_r$ in addition to the CMB, the radio background temperature can be written as follows:
\begin{equation}
  T_r=T_{\rm CMB}(1+z)\biggl[1+A_r\biggl( \frac{\nu_{\rm obs}}{78\ \rm MHz}\biggl)^{-2.6} \biggl],
\end{equation}
where $\nu_{\rm obs}$ is the observed frequency by the EDGES instrument at $78\ \rm MHz$, which corresponds to $z = 17$. Thus, the presence of a radio background in addition to the CMB, may push the absorption signal to larger depths, possibly explaining the results obtained with the EDGES experiment \citep{EDGES}. In particular, to recover an absorption signal consistent with EDGES, an extra radio background with an amplitude $A_r > 1.9$ is required.

In Tab. \ref{tabR}, we report our predictions on the brightness temperature of the 21 cm at $z = 17$, as predicted by our calculations, varying $f_{\rm PBH}$: for $f_{\rm PBH}=1$ ($f_{\rm PBH}=10^{-4}$), we obtain $A_r=10$ ($0.01$); in order to reproduce the entire EDGES absorption feature, $f_{\rm PBH} \gtrsim 4\times 10^{-2}$ is required. However this value would exceed the constraints derived from the CXB. The maximum value allowed by the CXB provides $T_R=0.59\ \rm K$: this radio background temperature can explain only $1\%$ of the entire EDGES signal.

We point out that our result can be modified by further modeling the physics of the 21-cm signal (e.g. the impact of PBHs radiation on $T_s$ via Lyman-$\alpha$ coupling). Even if our results only provide a first order of magnitude estimate, we do not expect the PBHs contribution to the 21-cm signal to be relevant even with further improvement of the model.

\begin{figure}
\begin{center}
\includegraphics[width=0.45\textwidth]{images/arcade.png}
\caption{Radio background brightness temperature at $z=0$ as a function of frequency for the values of $f_{\rm PBH}$ considered in the work. The blue triangles represent the data points \citep{ARCADE2}; the continuous blue line is the best fit for the same data. The horizontal red dotted dashed line shows the CMB temperature. The brightness temperature is computed at $1.4\ \rm GHz$ for PBHs of $30\ M_{\odot}$.}\label{myarcade}
\end{center}
\end{figure}

\begin{table}
\centering
\caption{Predictions for the radio background brightness temperature (in units of [K]), both at $z = 0$, and $z = 17$ for the values of $f_{\rm PBH}$ considered in this work.}
\label{tabR}
\begin{tabular}{|l|c|c|r|}
\hline
$f_{\rm PBH}$ & $T_b(z=0)$/K & $T_b(z=17)$/K & $A_r$ \\
\hline
\hline
$1$  & $0.402$ & $579.67$ & $11.80$\\
$0.1$ & $0.123$ & $174.42$ & $3.55$ \\
$0.01$ & $0.035$ & $42.81$ & $0.87$ \\
$10^{-3}$ & $0.009$ & $7.59$ & $0.15$\\
$10^{-4}$ & $0.002$ & $1.10$ & $0.02$ \\
\hline
\end{tabular}
\end{table}
\section{PBHs as dark matter: constraints}\label{PBHconst}
Fig. \ref{constraint} summarises the main results of this work and compares them with previous ones in the literature.
Dashed lines in the plot show existing constraints from the accretion process. The line labelled "dwarf galaxy heating" refers to the results obtained in \citet{Lu20} through the analysis of gas heating due to PBHs accretion. \citet{Manshanden19} modeled the X-ray and radio emission from accreting PBHs in the Milky Way. Source counting in those bands only allows for a small fraction ($f_{\rm PBH} \leq 10^{-3}$) in the $10 \leq M_{\odot}\leq 100$ mass range.

The EDGES-21cm marks the constraints by \citet{Hektor18}, who evaluated the impact of heating and ionization from PBHs accreting in the IGM only\footnote{We underline that in our work we instead take into account PBH accretion in halos as well.}, by imposing that $T_{\rm IGM}(z=17)\leq 8\ \rm K$.

The most stringent constraint in the considered mass range ($1 M_{\odot} \leq M_{\rm PBH} \leq 10^3 M_{\odot}$) has been set by \citet{Serpico20}, who evaluated the impact of PBHs energy production on CMB anisotropies. In their work they considered two different models for PBHs accretion, assuming either spherical or disk accretion, finding two different upper limits on $f_{\rm PBH}$. In the case in which PBHs are not the sole constituent of DM, $f_{\rm PBH} < 1$, the authors modeled PBH-DM interaction, and assumed a dark matter halo to form around each PBH. This effect was already discussed in \citet{ricotti08}, and it results in a time-increasing halo mass surrounding the PBH, $M_{h}(z)=(3000/1+z) M_{\rm PBH}$. The result is a boost factor of PBH accretion rate of $\sim 10^2$ at ($z=10$). We do not account for PBH-DM interaction in the case $f_{\rm PBH} < 1$, and note that accounting for it would strengthen our results, boosting PBHs accretion and consequently the CXB and CRB contributions. Even in the absence of PBH-DM interaction we can set the strongest constraint at $M_{\rm PBH}=30 M_{\odot}.$

We show in Fig. \ref{constraint} the upper bound on $f_{\rm PBH}$ as a function of PBHs mass, and the new, strong constraint $f_{\rm PBH}\leq 3\times 10^{-4}(30 M_{\odot}/M_{\rm PBH})$ from the X-ray background. The dependence $M_{\rm PBH}^{-1}$ follows from the halo X-ray luminosity relation, $L_X \propto M_{\rm PBH}^2/M_{\rm PBH}\propto M_{\rm PBH}$, where the factor $M_{\rm PBH}^2$ ($1/M_{\rm PBH}$) arises from black hole accretion (number density of PBHs in the halo). In Fig. \ref{constraint} we also show the lower limit required to recover the EDGES depth as a blue dashed line. We note that the entire region is excluded by the X-ray background constraint.
We stress that we set the strongest constraint on $f_{\rm PBH}$ by comparing the predicted value of the soft CXB with the observed one. PBHs are thus unable to contribute significantly to the CRB at any epochs, and consequently their emission is unable to affect the global 21-cm signal.

We briefly comment on the implication of the new constraint on extended PBHs mass distributions (e.g. \citealt{Bellido19, Jedamzik21}). Several multi-peaked mass functions present their main peak at $\sim 1\ M_{\odot}$. Constraining the low-end of the solar mass window implies that we limit the height of the main peak at $f_{\rm PBH} \sim 10^{-2}$, value which is typically overshoot. This would imply a reconsideration of some properties (e.g height and location of the main peak) for those mass distributions. We stress that to properly evaluate the impact of our analysis on extended mass distributions the approximation of a monochromatic PBHs spectrum has to be relaxed.

\begin{figure*}
\begin{center}
\includegraphics[width=1\textwidth]{images/Constraints.png}
\caption{Constraints on $f_{\rm PBH}$ derived taking into account PBHs accretion. The red solid line represents the constraint obtained in this work from the cosmic X-ray background. The blue dashed line defines the minimum $f_{\rm PBH}$ value to recover the EDGES signal depth. Dashed gray lines correspond to existing constraints: (a) dwarf galaxy heating: derived by evaluating the impact of gas heating due to PBHs accretion in dwarf galaxies \citep{Lu20}; (b) X-ray and radio: obtained through the comparison of the number of X-ray and radio emitters in the Milky way center and the predicted number by a PBHs accreting model from \citet{Manshanden19}; (c) CMB: derived by evaluating the impact of radiation emitted by PBHs on CMB anisotropies assuming spherical or disk accretion \citep{Serpico20}; (d) EDGES 21cm: computed by considering the impact of heating feedback from PBHs accretion on the IGM, and comparing the results with the predicted value \citep{Hektor18}. Figure created by modifying the publicly available Python code PBHbounds \citep{Kavanagh19}.}\label{constraint}
\end{center}
\end{figure*}

\section{Summary}\label{conclusion}
In this work, we presented a new semi-analytical model to compute the accretion rate and the relative luminosity of PBHs in dark matter halos and in the IGM, and explored the possibility that radiation emitted by accreting PBHs could contribute to the X-ray (CXB) and radio (CRB) backgrounds. Our main results are the following:
\begin{enumerate}
\item By comparing the cumulative X-ray emission from PBHs predicted by our model with the observed CXB, we set the strongest existing constraint on $ f_{\rm PBH} \leq 3\times 10^{-4}\ (30/M_{\rm PBH})$ in the mass range $1-1000\, M_\odot$.
\item We compare the PBH radio emission predicted by our model with the measured 21cm line feature and CRB. In the first case the extra radio background is able to recover only a fraction $f = 1 \%$ of the absorption depth claimed by \citet{Bowman18}.
Similarly, the allowed brightness temperature $T_b(\rm 1.4~GHz)\sim 0.004~K$ represents only a fraction $f \sim 1\% $ of the radio excess observed by ARCADE2.
\item Depending on the minimum halo mass considered, we show that the contribution from PBHs accreting into DM halos dominates over those accreting from the IGM ($60\%<I_{h}/I_{\rm tot}<99\%$).
\item Most of the CXB/CRB emission is produced by PBHs in DM mini-halos ($M_h \leq 10^6\ M_{\odot}$) at early epochs ($z>6$).
\item We also evaluated the impact of PBHs radiation on the thermal state of the IGM. We find that the X-ray heating impacts the IGM temperature in neutral regions and consequently the minimum halo mass. This effect introduces a nonlinear dependence of the background intensity on $f_{\rm PBH}$.
\end{enumerate}

As a final caveat, we stress that we have assumed a monochromatic PBH mass function; in future work this assumption can be relaxed. An additional assumption concerns the use of a standard $\Lambda \rm CDM$ halo mass function. For consistency, one should include the modifications induced by the presence of a fraction $f_{\rm PBH}$ of dark matter in the form of PBHs. We do expect this inclusion to boost the number of mini-halos. As these are the major contributors to the CXB and CRB, we predict that the upper limits on $f_{\rm PBH}$ could be pushed to even smaller values.

\section*{Data Availability}
Data generated in this research will be shared on reasonable request to the corresponding author.

\section*{ACKNOWLEDGEMENTS}
We thank A. Mesinger, A. Pallottini, Y. Qin for useful discussions.

redpajama_set_name: RedPajamaArXiv


text:
Q: The meaning of "within view of" I have always understood "with view of someone" to mean can be seen by someone. But I have seen several sentences where the phrase seemingly means can see something from a vantage point, e.g.:

The safari-style glamping situation offers in-tent bathrooms, showers, king-size beds, and solar power all within view of Lincoln's stony face.

This line (from here) talks about a camping site near Mount Rushmore. Merriam Webster also seems to suggest this phrase has two distinct and almost opposite meanings, but there's some ambiguity in its examples. So is this usage common/accepted?

A: I don't think MW is confused. If A is within view of B, then, under normal circumstances, B is also within view of A. It is normally a reciprocal relation. MW does seem to draw a distinction between when people are being discussed and when places are being discussed, a distinction that makes sense because places do not see.
So MW says that when used with respect to two people, "within view" means that they can presumably see each other, and thus the phrase may mean capable of being seen or capable of seeing.
MW also says that when used with respect to a place, it means only capable of being seen. That is logical and probably reflects common practice, but your quotation shows that it is not universal practice.
Personally, I would have said "with a view of Lincoln's face" because the statue of Lincoln's face is not viewing anything. But then people who write ad copy are not noted for their sensitivity to English usage.

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text:
Q: Modified Bessel function of first kind While reading a research article, I come accros this expression:
$$
{\sum\limits_{m = 0}^\infty  {\left( {\frac{{p - \sqrt {{p^2} - {\alpha ^2}} }}{{\alpha \beta }}} \right)} ^m} = \frac{\lambda }{{{\beta ^{m + 1}}}}\left[ {{I_{m - 1}}\left( {\alpha \left( t \right)} \right) - {I_{m + 1}}\left( {\alpha \left( t \right)} \right)} \right]{e^{ - \left( {\lambda  + \mu } \right)t}},$$
where

*

*$p = s + \lambda  + \mu$ ,

*$\alpha  = 2\sqrt {\lambda \mu } $  ,and

*$\beta  = \sqrt {\frac{\lambda }{\mu }} $.

Please help me how they arrived this expression


text:
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The following is an excerpt from Practice Perspectives: Vault's Guide to Legal Practice Areas.
John Gardiner, Partner—Litigation
John L. Gardiner is global co-head of Skadden's international litigation and arbitration group. He concentrates his practice in the resolution of complex, high-exposure, multijurisdictional disputes before leading arbitral institutions as well as before federal and state courts in the United States.
John repeatedly has been listed in Chambers Global: The World's Leading Lawyers for Business, The Best Lawyers in America, International Who's Who of Commercial Arbitration and Chambers USA: America's Leading Lawyers for Business. His extensive litigation, arbitration, and mediation experience covers a wide range of disputes in the energy, insurance/reinsurance, telecommunications, construction, auditing and accounting, and finance sectors. John also has acted as arbitrator in complex international corporate disputes and as mediator in intricate corporate and partnership separation situations. He has participated as counsel in many successful mediations and expert proceedings both internationally and domestically.
John is a graduate of University College Dublin.
Please provide an overview of what, substantively, your practice area entails.
The international litigation and arbitration group represents clients in disputes before international arbitral institutions around the world, as well as before state and federal courts in the United States. We participate in all forms of alternative dispute resolution, including mediation and arbitration. In short, we are retained to resolve international disputes worldwide.
What types of clients do you represent?
Our clients come from all industries, including telecommunications, pharmaceutical, financial services, insurance and reinsurance, construction and energy sectors, among many others. We also are called upon to resolve disputes with sovereign states through investment treaty arbitration.
What types of cases/deals do you work on?
Because of the nature of our practice, many of the disputes we handle are confidential and are often resolved on a confidential basis. However, we recently advised clients in a few public disputes, such as Devas Multimedia Private Limited in an ICC arbitration against Antrix Corporation Limited, which resulted in an award of damages in excess of $500 million in favor of our client. The ICC tribunal held that Antrix had unlawfully repudiated a contract with Devas regarding a hybrid satellite and telecommunications network planned for India. We also have been representing Starr International in connection with a $40 billion claim against the United States arising out of the nationalization of AIG in 2008.
How did you decide to practice in your area?
In the mid-1990s, the firm decided to expand its international arbitration practice. At the time, I had recently become partner in the general Litigation Group, but having qualified to practice law in Ireland, England, and Wales, I began to redirect my practice towards international arbitration. Since then, the practice has grown enormously.
What is a typical day or week like in your practice area?
We work across many different time zones and are frequently dealing with counsel and arbitral institutions at all hours of the day and night. We make filings and report to clients around the clock. International travel is a routine (but great) part of the job. Most of our matters involve multiple jurisdictions and filings are often made simultaneously in those jurisdictions.
What is the best thing about your practice area?
The broad scope of the practice brings us into contact with different cultures every day. And the people in our practice group, who are from diverse backgrounds (e.g., Ireland, Australia, France, United States, United Kingdom, Canada, Pakistan, India, Hong Kong, Ukraine, and Russia) bring their own unique perspectives to our decision-making process on every case. For example, common law trained lawyers learn the perspective of civil law lawyers and vice versa.
What is the most challenging aspect of your practice area?
As I mentioned earlier, the constant interactions with clients that are often on the other side of the world can pose challenges, particularly when filings have to be made in multiple jurisdictions simultaneously. International travel can also be demanding at the best of times.
What training, classes, experience, or skills development would you recommend to someone who wishes to enter your practice area?
Persons interested in this area of practice would benefit from being business fluent in English (requisite) and at least one other language that is used in every day international commerce (e.g., Spanish, French, German, Italian, Japanese, Mandarin, and Cantonese). Taking a number of international law and international arbitration courses are also a plus. Clerkships at any of the leading arbitral institutions such as the ICC or LCIA can also be useful.
What misconceptions exist about your practice area? What do you wish you had known before joining your practice area?
In this day and age there is so much information about practice areas readily available that it is hard to say that misconceptions exist about what our group does. But certainly anyone interested in this type of career should be knowledgeable about, and interested in, international business affairs and international institutions that resolve disputes between parties from different backgrounds and cultures.
What is unique about your practice area at your firm?
This practice group has grown from two partners and three associates in 1996 to 11 partners, four counsel, and more than 40 associates today, primarily located in New York and London, with additional partners and counsel in other foreign offices on multiple continents. We typically advise on every aspect of multibillion dollar cross-border disputes and handle the advocacy in those matters ourselves.
What activities do you enjoy when you are not in the office, and how do you make time for them?
Hanging out with my family and car racing, horse racing, and other sports. In our business, it's important to find time for outside activities.

redpajama_set_name: RedPajamaCommonCrawl


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Amir Teilhaber
Contact: amir.heinitz@mail.huji.ac.il
M.A. in Islamic and Middle Eastern Studies, Hebrew University Jerusalem; B.A. in International Affairs, Vesalius College – Vrije Universiteit Brussel; undergraduate studies in Social Sciences and Applied History, Universität Siegen.
Orientalist scholarship and International politics in the Age of German Empire. Life, Career and Oeuvre of Friedrich Rosen, 1856-1935
Amir Heinitz's dissertation looks at the relationship of Oriental studies and Orient politics during the German Kaiserreich. The German diplomat, orientalist and later foreign minister Friedrich Rosen (1856-1935) serves as key actor and focal point of a history traversing twelve cities on three continents. How power and knowledge relate is investigated in chapters on the translation of Persian poetry as a means of cultural understanding, Urdu at the court of the British viceroy in India, Orientalist congresses in northern climes, jihad in German foreign policy, and cultural sensitivity in high-level political negotiations. Amir pursues his Ph.D. at the Technical University Berlin.
With Marian Reda. "On the Egyptian Revolution: E-Mail Discussions by Two Former Cairo Flatmates." The Critical Stage. Young Voices on Crucial Topics, No. 6, 2016.
"Migration and Security in the Eastern Mediterranean." Geneva Centre for the Democratic Control of Armed Forces, 2013
Journalistic publications with openDemocracy, +972mag, zenith and MAGDA


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Ralf Schönborn (* 17. August 1966 in Walhausen) ist ein deutscher Politiker (AfD). Er wurde bei der Landtagswahl 2021 in den rheinland-pfälzischen Landtag gewählt.

Schönborn ist Vorsitzender des Kreisvorstands der AfD Rhein-Hunsrück und AfD-Fraktionsvorsitzender im dortigen Kreistag. Bei den Wahlen 2021 wurde er über die Landesliste seiner Partei (Platz 9) in den Landtag gewählt, trat aber auch ohne Erfolg als Direktkandidat im Wahlkreis Rhein-Hunsrück an. Als Schwerpunkte seiner politischen Arbeit gibt er Umweltschutz, Verkehr und Gesellschaft an.

Schönborn lebt in Dickenschied. Er ist als Angestellter in der Automobilindustrie tätig.

Weblinks

Einzelnachweise

Landtagsabgeordneter (Rheinland-Pfalz)
Politiker (21. Jahrhundert)
AfD-Mitglied
Deutscher
Geboren 1966
Mann

redpajama_set_name: RedPajamaWikipedia


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News / Music Friday: Silver Earrings, Gold Bracelet Play Key Roles in 1999's 'All I Left Behind'
Music Friday: Silver Earrings, Gold Bracelet Play Key Roles in 1999's 'All I Left Behind'
Welcome to Music Friday when we bring you wonderful tunes with jewelry, gemstones or precious metals in the title or lyrics. Today, jewelry items play key roles in "All I Left Behind," a hauntingly beautiful song featuring the harmonies of Emmylou Harris and Linda Ronstadt.
Recounting the story about a woman who unselfishly puts her life on hold to go on the road with her lover, "All I Left Behind" details the items she lost along the way, which include her silver earrings and her dad's gold bracelet. In the end, she loses her lover, as well.
Harris and Ronstadt sing, "Silver earrings in Wichita / Beaded moccasins in Tonopah / But I had you so, I just let them go."
In a later verse, they tell the story of a cherished keepsake: "And the gold bracelet with my father's name inscribed / On the back by the one who loved him all her life / The way I too could have loved you."
Written by Harris, along with sisters Kate and Anna McGarrigle, "All I Left Behind" appeared as the 12th track on Western Wall: The Tucson Sessions, a Ronstadt/Harris duet album featuring songs written by some of the most successful names in the business, including Jackson Brown, Rosanne Cash, Sinéad O'Connor and Bruce Springsteen. Singing background vocals and playing the harmonica on the album was none other than Neil Young.
"It took more than 25 years, two divergent careers and plenty of false starts, near-misses and might-have-beens, but Linda Ronstadt and Emmylou Harris have finally made an album together," wrote Bill DeYoung for Goldmine magazine back in 1999.
"I believe that there's a poetic thread that holds [the songs] together," Harris told Goldmine. "I think they all deal with very deep issues about life and love and longing and loss. For me, an album has to be a string of pearls, but they're all slightly different. They're not perfectly matched pearls."
The album — featuring the songbird soprano of Harris and the velvety alto of Ronstadt — earned critical acclaim, hitting #6 on the Billboard Country albums chart while earning several Grammy nominations.
(The photo, above, shows Ronstadt and Harris receiving honorary doctorate degrees from Boston's Berklee College of Music in 2009.)
The 75-year-old Emmylou Harris boasts a stellar career spanning seven decades. Since recording her first album in 1969, she has accumulated 14 Grammy awards and 48 Grammy nominations. She became a member of the Country Music Hall of Fame in 2008 and was presented with the Grammy Lifetime Achievement Award in 2018.
Ronstadt, 76, is a 2014 inductee into the Rock and Roll Hall of Fame. She has released 24 studio albums and charted 38 Billboard Hot 100 singles. She has earned 11 Grammy Awards, three American Music Awards, two Academy of Country Music awards, an Emmy Award, a Tony nomination and a Golden Globe nomination.
We hope you enjoy the audio track of Harris and Ronstadt performing "All I Left Behind." The lyrics are below if you'd like to sing along…
"All I Left Behind"
Written by Emmylou Harris, Kate McGarrigle and Anna McGarrigle. Performed by Linda Ronstadt and Emmylou Harris.
All I left behind should come as no surprise
To me since I fell through the black hole of your eyes
Only little things inconsequential I could say
Of all I left behind with you along the lost highway
Silver earrings in Wichita
Beaded moccasins in Tonopah
But I had you so, I just let them go
The flannel shirt I wore to keep me from the cold
When we drove from Boston all the way to Buffalo
The leather boots I bought, so many miles ago
I took them off to follow you into the Ohio
Never did my armor feel so thin
Silk was all I had between me and your skin
Like Waterloo, I lost that too
And the gold bracelet with my father's name inscribed
On the back by the one who loved him all her life
The way I, too, could have loved you
The Spanish shawl, I put across the broken shade
Of the lamp that lit the room that last night near Coeur d'Alene
Credit: Photo by Eric Frommer, CC BY-SA 2.0, via Wikimedia Commons.
— Howard Cohen


Steve couldn't wait to get inside!
I drank a Race Rocks Ale from local legends Lighthouse Brewing Company.
Michael and Yvonne were waiting for us at the bar. Greg joined us there, too. It was officially a crawl!
Hey, on a totally unrelated note, I couldn't help but notice that our BC Hydro smart meter was installed while we have been away living in Edinburgh. And guess what else I couldn't help but notice...? Nothing horrible happened!


Battling Big Box Competitors - how do you compete?
Protection for the Business Owner - if you couldn't work, how would you pay the bills?
Now What? - important steps to take after your automatically enrolled in your employer's retirement savings plan.
Profile - beginning to prepare for the sale of a business.
Line Items - News you can use.


ANAIS is bursting with Spring confidence. These large blooming hydrangeas have been painstakingly tooled by hand in black and pink satin and pale blush organza. Arranged in large balls with enamelled glossy black leaves. A beautiful face veil in black diamond veiling completes the headpiece.


We offer complementary valet, don't worry about finding a place to park.
Urban Grub is a casual fine dining bar and eatery located in a renovated carwash in Nashville's iconic 12 South district.
The design of the restaurant features a rustic elegance, filled with custom woodwork, stone fireplaces and rounded booths tucked in intimate corners. Urban Grub offers both indoor and outdoor seating with a combination of the two in the beer garden, accompanied a view of the restaurant's meat curing room, as well as a covered gazebo for larger parties.
From the inviting indoor-outdoor atmosphere to the elevated Southern cuisine of fresh seafood, house-made charcuterie, and prime dry-aged steaks, the experience is unforgettable.
Jonathan our waitir was amazing. Such a good job !!
Great food and very good atmosphere! I enjoyed it folks!!
The atmosphere was nice, but it was extremely warm inside. My table was pestered with gnats buzzing around us during our meal. The food was delicious. I highly recommend the wood fire oysters and shrimp and grits. The service was shockingly terrible. Our server greeted us with menus and water only to disappear for 30 minutes after that. We asked another server to please tell ours that we were ready to order. Another "team" server came to take our order to which we explained to please bring everything at once since we had tickets for a show. The wine suggestions did not match our tastes, but no one followed up afterwards to know anyways. The food was spaced out oysters/salad, then entrees followed a good 15 minutes later despite our initial request. When our entrees were delivered we asked to please bring the check since we were on a time crunch. No one ever came to check on us after our food was delivered, bothered to pre-bus the table after oysters/salads, and then we had to request our check again after we sat there with our finished plates stacked to the side of the table. We were seated at 5:00pm and were finally able to leave at 6:45pm.
I truly enjoyed my time here! My family and I came for Easter dinner. The food and drinks were fantastic (special mention: crab cakes, macaroni and cheese, The Primm and andouille sausage).
Our service was amazing! Everyone we interacted with was kind, fun and professional - ensuring our experience was the very best it could be. Ask for Otis!
Otis and James father son wait team were amazing!
Food was fresh and plentiful.
Went for brunch on Easter Sunday and it was magnificent. Got the seafood and charcuterie bar, great amount of food and selection for the price. Will definitely be coming back!
Oyster bar is a great place to sit for a late night snack or just to relax and enjoy a good meal. Guys at the oyster bar are always great and always welcome us each time.
WONDERFUL service and the food was great We will definitely will be back again soon.
The service was fantastic! The waiter did an excellent job describing all of the brunch options and providing guidance.
The food was incredible! We had the buffet and the shrimp and grits were absolutely amazing! The buffet is 100% worth the money and then some. Then there was the creamed brussel sprouts with barbecue spiced naan - heaven. Absolute heaven in my mouth.
Overall it was a great experience the only complaint I have is that I ordered a rare steak and when it came out it was luke warm. The flavor was amazing I didn't want to send it back because I didn't want it over cooked. Other than that it was an amazing time.
Mom's birthday. It was fantastic!!
Consistently delicious. Just as many Nashville restaurants, the cost of their entrees is high especially when they do not come with sides.
Fabulous service, ambiance and FOOD!!! Portions were large making it possible to share with the rest of the table. Still enough left to take home. This is a MUST dining spot when you are in Nashville.
Excellent service. We had an early dinner reservation 5:00 had the place nearly to ourselves for a half hour or so. Service was outstanding. Food excellent. Try the pork chop even if you're not a big pork chop person.
We came in for cocktails + lots of apps.
Trey, our server, was professional yet FUN! He had excellent recommendations for Oysters on the half shell, Baked Oysters, Pork Fries (YUM!) & cocktails.
We look forward to having him take care of us for a Full Dining experience soon!
Fantastic!! Excellent , fresh seafood and amazing aged steaks. Ambiance was also superb!
Birthday dinner...Nashville girls weekend! Pork chop was epic! Lobster Mac and cheese...insanely good! Scallops amazing!
Ask for James Webb. You won't be disappointed. He's an amazing waiter. Food selection is wonderful as always. Try the double cut pork chop, the bacon wrapped trout, or whatever James may recommend. Enjoy!
We had the cream brussel sprout app and Filet for dinner and both were wonderful.
Best Rib Eye steak I've ever had. I'd pay 100 dollars more for that steak. Incredible.
Been there a couple times, I love the place. The server was terrible and I told him I wanted the toppings on my pork chops on the side, so he took it back and scrapped them off after I told him I wanted fresh ones.
I believe it was the first time I have ever "NOT" left a tip. I do not like to penalize the server for other people's issues but the level of service and the attitude of the hosts and a manager was simply terrible. Waited too long for a table with reservations and the hosts did not seem to care at all. Waited so long for dinner one of our party had to leave. When a manager was called he was exceptionally short and rude. Urban Grub is not the type of place you would expect that type of service. I wrote a note on the bill apologizing to the server and explained it was ll attributed to the Manager.
Enjoyed a full dinner at the oyster bar where we received friendly and attentive service. The oysters were very good, the filet was tender with a nice smokiness and the ribs were good. For the sides, the cuban corn was my favorite with the Mac & Cheese being too mild for my taste and the mash potatoes ho-hum.
Love Urban Grub. Food is great, lots of choices. Their garlic Parmesan grilled oysters are very fresh & flavorful. The Double bone in pork chop is all you need, it's at least 16oz, well and their Mac & Cheese. Wife had Club Carbonara Rigatoni w/ smoked chicken. Go there, you'll be a fan.
The food was great as usual! This is a pricier restaurant...$15 for a Sangria. The quality and service are great though.
Excellent food in a quaint setting.
Pork chop was completely raw on the interior. The other people in our party were not impressed with their food. Service and ambiance are great but food is consistently poor as I have eaten here 4 times but will not be headed back. They need to seriously consider a new chef.
Great service. (James) The food was delicious.
We hadn't planned to eat out, at least at a restaurant, after visiting a farmers market; but we found ourselves on 12 South. Although Urban Grub ended up being full by the time we had finished, we were able to sneak in early. The table was nicely situated in a bay window, allowing us views both in and out. Additionally conversation was possible without shouting. As to the food and beverage: the wine by the glass were good, but perhaps priced $3-4 per glass more than most restaurants (a Sancerre and a white Bordeaux). We were in a meat mood, so we elected the lamb shank and the double cut pork chop. Both were ginormous and perfectly prepared. The only gripe? Not enough puréed celery root under the shank.
Can't decide whether the food or the service was the best part of our visit. Had enjoyed Urban Grub for a couple of work dinners, and wanted to share this place with my wife so booked a table for two for our anniversary and they did not disappoint. From the moment we walked in and were wished a happy anniversary from the hostess (due to clicking the special occasion button on open table) the entire staff made our evening very special. Well done Urban Grubb!
Came to Nashville for my husband's birthday and couldn't wait to try Urban Grub. We were immediately disappointed when we were seated at a table that was literally placed in the middle of the walkway. Every time someone passed by, my chair got bumped, purse got knocked off my chair or waitstaff had to shimmie by. Our waiter was friendly and offered some great food and wine suggestions. However, halfway through the evening, he disappeared and we barely saw him again the whole evening. Another waiter brought our food out which was cold. I had to send it back to be re-heated. (I have never sent food back at a restaurant). The manager offered no apology much less any kind of compensation. There are so many great restaurants in Nashville, but this one was a disappointment.
Everything was excellent at Urban Grub and I will make another visit. We were a party of two and it was on the expensive side but that can be controlled by the consumer.


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Closing the tuition gap
Should out-of-state students pay more than in-state students?
Parents packing car for a move to college
In-state tuition is a powerful incentive for high schoolers to attend their state's schools, but it creates a substantial loss for many students across the US, according to a paper in the February issue of the American Economic Journal: Economic Policy.
"It always struck me as a peculiar system," author Brian Knight said in an interview with the AEA. "Just because I was a resident of Ohio, why would I necessarily need to attend college within the state, given the great selection of universities across the whole US?"
Knight and co-author Nathan Schiff showed that reducing out-of-state tuition would have large benefits for nonresidents and comparatively little cost for students who attend in-state universities.
I think the best hope is to encourage more reciprocity agreements, where states agree to accept each other's students at lower prices.
The authors argued that states have a special interest in their own residents which has led them to charge nonresidents more to attend their universities—what the authors called the "tuition gap." States worry that offering a subsidized education to nonresidents might leave them footing another state's education bill.
But distinguishing between residents and nonresidents creates missed opportunities from a national perspective.
For example, imagine two students get accepted to the school of their choice. One student lives in Wisconsin but wants to attend Indiana University, the other lives in Indiana but wants to attend the University of Wisconsin-Madison.
But suppose that neither can afford the out-of-state tuition and choose to attend their second-choice, state school instead. If both students could pay the in-state tuition rate at the out-of-state school, then they would both be better off and the universities would make the same amount in tuition revenue as when both students chose to go in-state.
In reality, schools charge different tuition rates, extra amenities matter to students, and universities differ in the quality of education they provide. These details complicate the story, but the authors show that if out-of-state tuition is cut, then very little of the revenue loss has to be made up by residents because price cuts will attract more nonresidents.
In-state vs out-of-state tuition costs
The map below shows the average tuition rate for each state. Use the bottons below to toggle between in-state and out-of-state tuition rates.
Source: College Board, Annual Survey of Colleges
The authors addressed many of the real-world complications, but their approach to solving one in particular was novel.
Besides tuition, a critical factor for choosing a college is how far a school's campus is from home. This makes it difficult to tell which students choose a college because it is close to home and which choose a college because of the in-state tuition discount, Knight said.
The authors sidestepped this issue by comparing students who lived near each other—within roughly two miles—but on opposite sides of a state border. They found that public universities enroll six times as many students from just inside their state's border compared to students from just on the other side.
In an ideal world, state universities wouldn't distinguish between residents and nonresidents, according to Knight, but political obstacles make such an outcome unlikely.
"I think the best hope is to encourage more reciprocity agreements, where states agree to accept each other's students at lower prices," Knight said.
States like Minnesota and Wisconsin have already cooperated to completely remove out-of-state tuition markups and other barriers for each other's residents.
However, the authors caution that if low-income students are more likely to go to in-state institutions, then they might experience a jump in tuition to make up for lost out-of-state revenue.
States will have to figure out what's in their residents' best interests, but the authors show that there are gains to be had.
"The Out-of-State Tuition Distortion" appears in the February issue of the American Economic Journal: Economic Policy.
Fancy Dorms Aren't The Main Reason Tuition Is Skyrocketing
A piece in FiveThirtyEight on the rising cost of tuition at U.S. public universities highlighted a 2014 study from the American Economic Journal: Economic Policy
From tax credits to college credits
Tax refunds can boost college enrollment among low-income families.
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Can White People Speak And Act About White Privilege In A Way That's Not "Performative"?
White male millionaire podcasters should only invite non-white non-male non-millionaires onto their shows and open the conversations with, "I think I may be part of the problem. How can I be part of the solution?"
"The ultimate measure of a man is not where he stands in moments of comfort and convenience, but where he stands at times of challenge and controversy." ~ Martin Luther King
We need to eliminate systems that have been corrupted by white males to benefit white males and create nondiscriminatory and compassionate means of interacting with all people, not just the ones with our skin color, religious beliefs, and financial luck. For example, at this point in the history of Western uncivilization, after the public executions of George Floyd and countless other people of color, white male millionaire podcasters should only invite non-white non-male non-millionaires onto their shows and open the conversations with, "I think I may be part of the problem. How can I be part of the solution?" White male millionaires interviewing other white male millionaires is extraordinarily unhelpful. Irrespective of any noble intentions, white male millionaire podcasters are drowning out the voices of the disenfranchised and should make room for them. If you think that "familiarity breeds contempt," then check out the egregious nepotism rife throughout our media.
Do you think there is a course at Howard University entitled "Great White Male Mathematicians"? What would you think if you learned that Hitler and Goebbels sat around discussing "Jews we admire"? So how is it acceptable for Bret and Eric Weinstein in 2020 to sit around casually chatting about "Black intellectuals we admire" on Bret's Dark Horse podcast? Until Bret and Eric fully understand the extent of their white privilege and use it to empower the disenfranchised, they remain part of the problem. Please attach all of the photos of white male millionaire podcasters as brave as "Naked Athena" or Colin Kaepernick. Uh, that would be zero… because none of them want to risk pissing off their advertisers. Due to their liberal good intentions, people such as les frères Weinstein have deluded themselves into thinking they are part of the solution, but until we ACT — not talk, but actually DO SOMETHING — to help dismantle all of the systems corrupted by white men that favor white men and their/our offspring, we are no better than blatant elitists such as Mitch McConnell and Donald Trump and latent elitists such as Jordan Peterson.
Here are actionable points that progressives can work on together to help remedy the inequalities caused by systems corrupted by white men and establish the authentic EQUALITY OF OPPORTUNITY that we desperately need:
Our taxation system favors rich white men. Capital expands faster than labor, according to Thomas Piketty. This is correctable: institute a flat tax on all corporate earnings and all income including capital gains with no exemptions. Better yet, tax capital gains and/or higher marginal incomes at higher rates than labor earnings (cf. Robert Reich). And although rich white men like Bill Gates argue that higher taxes would stymy their incentive to innovate, this is obviously self-serving malarkey. Our taxation system has been horribly corrupted and needs to be revised completely and immediately.
Use the aforementioned taxpayer contributions to establish a free university system as well as a universal healthcare system — working models for both already exist throughout Europe. Our educational system has been horribly corrupted (cf. Scott Galloway) and our healthcare system is obviously subpar for the $3.5 trillion dollars per year that we spend on it.
Similarly, eliminate all tax deductions for charitable contributions. Decent human beings do not need a tax incentive to make the world a better place. Millions of rich people as well as religious institutions skirt their tax obligations by establishing 501c3s and/or donating to them. This system has been corrupted. Churches are businesses that should be taxed just like all corporations (oh, need I mention the pedophilia?). The 501c3 non-profit distinction has been egregiously corrupted — what sane person would agree that Harvard University's $40 billion dollar endowment should be tax exempt???
Our voting system has been corrupted by white male millionaire's gerrymandering. Either figure out a way to ensure that all votes are equal throughout all districts and/or eliminate the Electoral College.
Impose Federal judge term limits. President Trump has appointed a plethora of young, conservative white male judges to fight against women's and minorities' rights such as abortion and same-sex marriage. These people should not govern our appeal system for the next fifty years.
Remove all campaign contributions from the electoral system. There are better ways of electing representatives than the way we currently elect representatives. Abolish K-Street, abolish all political action committees, make lobbying illegal, strike the current system of systemic bribery, and let the constituents vote on the issues, not by being brainwashed by market-researched advertisements or hateful propaganda financed by 8 figure campaigns.
There are more than 328 million firearms in our fair nation of 328 million people, so the impending American revolution is not going to begin or end with a whimper. White male millionaire podcasters interviewing other white male millionaire podcasters is seriously unhelpful. We need to make room for the voices of non-white non-male non-millionaires.
RacisminAmerica
Psychotherapist & Author
Psychotherapist Ira Israel is the author of "How To Survive Your Childhood Now That You're and Adult: A Path to Authenticity and Awakening," which is endorsed by Sting, Reverend Michael Beckwith, Marianne Williamson, Jack Kornfield, Shauna Shapiro, Warren Farrell, Katherine Woodward Thomas, Jai Uttal, Joanne Cacciatore, Lorin Roche, Fred Luskin and many many others. Ira teaches workshops on authenticity and happiness at Esalen and Kripalu and has written over 300 articles on psychology, philosophy, Buddhism, yoga, film, art, music & literature for The Huffington Post, Good Men Project, Mind Body Green, Thrive Global, and Medium. Ira is also the producer, writer and actor of the best-selling DVDs and videos "Authenticity and Awakening for Lovable Idiots," "A Beginner's Guide to Happiness," "A Beginner's Guide to Mindfulness Meditation," "Mindfulness for Depression," "Mindfulness for Anxiety," and "Yoga for Depression and Anxiety." He graduated from the University of Pennsylvania and has graduate degrees in Psychology, Philosophy, and Religious Studies. For more information please visit www.IraIsrael.com


THE BORO DJs SHOW: EWF On Deck. – Radio for the People, by the People.
THE BORO DJs SHOW: EWF On Deck.
Saturday is here, and we aim to please. The Boro brings the sounds for your Saturday night ride. With new and old joints in the first hour. The second brings in The Sucker-Free Sector, hosted by Slow Flow with his observations and crazy banter. We also have in the second hour our segment called "The Digger's Block"(formally In The Cut) focusing on the super group Earth, Wind & Fire. So join the crew of the Boro this eve @6pm(pst) in studio 2B for your soundtrack of the night.


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Orry History, Family Crest & Coats of Arms
Early Origins of the Orry family
The surname Orry was first found in Ayrshire (Gaelic: Siorrachd Inbhir Àir), formerly a county in the southwestern Strathclyde region of Scotland, that today makes up the Council Areas of South, East, and North Ayrshire.
One of the first records of the name was Adam Urri who appears as burgess of Irvine in 1260 and Huwe Urry of Ayrshire who rendered homage to King Edward I of England in his brief intrusion into Scotland in 1296. Reginald Urry held land in Irvine in 1323 and William Urri resigned the lands of Fulton in 1409. [1]
Another branch of the family was found in the Fetteresso parish, Kincardineshire and for the most part, these names included "de" denoting "of." Hugh de Urre swore fealty at St. John of Perth and later with a different spelling as Hugh Uny at Forfar, 1296. [1] This latter entry is presumably another person rendering homage to King Edward I.
Further south in England where the Hurry, Hurrey and Hurrie variants tends to more popular, early records were typically found in the Latin form: Urrius de la haie c.1148 in Herefordshire; Walter, Herueus Urri in the Curia Regis Rolls for Surrey in 1208 and in the Pipe Rolls for Norfolk in 1209; Gilbert Uri in the Curia Regis Rolls for Lincolnshire in 1214; Alan Hurry in the Feet of Fines for Essex in 1219; Geoffrey Orry in the Liber Feodorum for Shropshire in 1235; and later Walter Horry for the Isle of Wight in 1290; and John Ourry in 1297. [2]
Early History of the Orry family
This web page shows only a small excerpt of our Orry research. Another 180 words (13 lines of text) covering the years 1300, 1279, 1302, 1273, 1366, 1387, 1650, 1677, 1666, 1715, 1650, 1778, 1857, 1619 and 1677 are included under the topic Early Orry History in all our PDF Extended History products and printed products wherever possible.
Orry Spelling Variations
Spelling variations of this family name include: Urie, Ure, Urey, Hurry, Hurrie, Horrey, Orrey and many more.
Early Notables of the Orry family (pre 1700)
Notable amongst the family at this time was Sir John Urry (or Hurry) (died 1650), a Scottish professional soldier; and his brother, Sir William Urry (died 1677), a Scottish Royalist officer during the Wars of the Three Kingdoms, he joined Charles II in exile during the Interregnum; and his son, John Urry (1666-1715), an Irish-born, Scottish noted literary editor and medieval scholar. Isaac Ewer, Ewers or Ewres (died c.1650), was an English soldier probably born in...
Another 75 words (5 lines of text) are included under the topic Early Orry Notables in all our PDF Extended History products and printed products wherever possible.
Migration of the Orry family
Some of the first settlers of this family name or some of its variants were: William and Andrew Ure, who arrived in New York in 1820 along with Elizabeth; James Ure, who arrived in Boston in 1768; as well as Patrick Urie, who arrived in East New Jersey in 1686..
Contemporary Notables of the name Orry (post 1700) +
Peter Orry Larsen (b. 1989), Norwegian footballer
Curia Regis Rolls
Feet of Fines
King Edward I
Pipe Rolls
The Orry Motto +
The motto was originally a war cry or slogan. Mottoes first began to be shown with arms in the 14th and 15th centuries, but were not in general use until the 17th century. Thus the oldest coats of arms generally do not include a motto. Mottoes seldom form part of the grant of arms: Under most heraldic authorities, a motto is an optional component of the coat of arms, and can be added to or changed at will; many families have chosen not to display a motto.
Motto: Sans tache
Motto Translation: Without stain.
^ Black, George F., The Surnames of Scotland Their Origin, Meaning and History. New York: New York Public Library, 1946. Print. (ISBN 0-87104-172-3)
^ Reaney, P.H and R.M. Wilson, A Dictionary of English Surnames. London: Routledge, 1991. Print. (ISBN 0-415-05737-X)
Orry (Scottish)


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Dominican cuisine can be quite complicated, but Karl-Anthony Towns likes to keep it simple.
Sancocho, the Dominican Republic's national dish, includes beef, chicken and sometimes even pork, all meats that are regular staples in most Dominican meals.
But whether it's his food preference or his love for his mother's Dominican heritage, the Minnesota Timberwolves big man is committed to what he truly enjoys.
"I love arroz con pollo," Towns told The Undefeated. "I keep it really simple and plain, to the point. My mom makes some of the best chicken and rice and I know why. She makes it how my grandmother makes it and the recipe was passed down. There is nothing better than having some of mom's homemade cooking.
Towns got some early lessons on his Dominican heritage during weekend barbecues at his grandmother's home in Perth Amboy, New Jersey. There was always lots of Dominican food. Towns and his first cousin, Michael Quezada, loved eating pollo empanizado (breaded chicken) with white rice beans and plantains. They always played basketball in the backyard, too, while listening to lively music in the background.
"What I really enjoyed was just being in the backyard barbecuing," Towns said. "We had a lot of talking. Listening to music, that's where my love for it started. Me and my family did a lot at my grandmother's house. We always had, every Saturday or Sunday, barbecues at her house in the summer.
Karl-Anthony Towns with family from his mother's side.
There was always bachata, merengue and salsa music playing as well. Despite Towns' unique height and big feet, his sister actually taught him how to dance. Towns said he has Latin music saved on his cellphone to play on special family occasions.
"My family loves to dance. They tried to grab anyone who was near to dance. The house was full of music. It's just a lot of fun. A lot of great memories," Towns said.
Towns said his mom took him on his first trip to the Dominican Republic when he was 15 years old. They visited Santo Domingo, the capital and largest city in the Dominican Republic. It was during this visit that Towns truly fell in love with his mother's homeland as they took in the history, monuments and sites.
"My whole life leading up to that point I'd only seen the USA. To see the way my mom's country is, how beautiful it is, see a different side of the world, it was eye-opening. It was amazing. I had so much fun. I enjoyed it," he said.
Towns rose to a height of 6-feet-11 by the time he was 16 years old and earned elite basketball skills to boot. ESPN.com ranked him as a top 10 prospect in the Class of 2014. It was safe to say that USA Basketball would have had strong interest in the American big man to compete in the 2012 London Games.
Towns, however, opted to play for his mother's native Dominican Republic instead. In July 2012, he was introduced to the basketball world when he played against a USA team led by Kobe Bryant and LeBron James in an exhibition game.
There was no rematch though, as the Dominican Republic didn't qualify. The country known for baseball dominance has never made an Olympic appearance in men's basketball, while USA has won 15 gold medals in 18 appearances.
Towns decision to play for the Dominican Republic made him ineligible to join Team USA. Had he been eligible, he could have qualified for the USA's team in the 2016 Rio de Janeiro Games. Even so, he doesn't regret his decision to play for his mother's home country.
Karl Towns #12 of the Dominican Republic Senior Men's National Team posts up during an exhibition game at the Thomas and Mack Center on July 12, 2012 in Las Vegas, Nevada.
Considering the pride that Towns' family and followers in the Dominican Republic and in the New York area have toward him, his loyalty is understandable.
"My grandmother comes back with tons of newspaper articles from the Dominican Republic every time she visits," Quezada said. "Everyone knows who her grandson is. I'm from Washington Heights, New York City, and he's huge over there. He's the most talked-about player in all the Dominican barbershops.
Towns starred at the University of Kentucky for a season before being drafted with the No. 1 pick in the 2015 NBA draft. He averaged 18.3 points, 10.5 rebounds and 1.7 blocks per game last season, and has improved, averaging a double-double of 21.5 points and 11.5 rebounds through 34 games this season while scoring a career-high 47 points against the New York Knicks on Nov. 30. While the Timberwolves' poor record will likely be held against him, an individually worthy Towns will learn whether he will be selected for his first NBA All-Star appearance later this month.
And once he gets some free time, Towns said, he hopes to learn Spanish fluently in 2017. He has asked his mom and sister to speak to him exclusively in Spanish to help further his growth. He hopes to eventually be comfortable conducting media interviews in Spanish and would like to return to the Dominican Republic next off-season.
"I understand Spanish, but I can't speak it very well," Towns said. "I understand what you're saying so I mostly speak like a Spanglish. My grandmother, my mom and my sister speak to me in Spanish and I speak back in English.