text:
\section{INTRODUCTION}

Observations of H$_3^+$ in diffuse molecular clouds \citep[diffuse clouds in which a significant fraction of the hydrogen is in molecular form;][]{snow2006} have led to various unexpected discoveries.  The very first detection of H$_3^+$ along a diffuse molecular cloud sight line (toward Cyg OB2 12) showed an abundance about 10 times greater than expected for the environment \citep{mccall1998a}.  This surprising overabundance---also found toward several more diffuse cloud sight lines---led to the eventual conclusion that the ionization rate of H$_2$ due to cosmic rays, $\zeta_2$, must be about 1 order of magnitude larger than previously thought \citep{mccall2003,indriolo2007}.  Another puzzling outcome from H$_3^+$ observations is that the average excitation temperature derived from the two lowest energy states \citep[$\langle T({\rm H}_3^+)\rangle\approx30$~K;][]{indriolo2007} differs significantly from the average excitation temperature derived from the two lowest rotational states of H$_2$ \citep[$\langle T_{01}\rangle\approx70$~K;][]{savage1977,rachford2002,rachford2009}.  Given that both species are expected to be thermalized to the cloud kinetic temperature by collisions, such a discrepancy is unexpected.

Despite the fact that the $J=0$ and $J=1$ levels of H$_2$ are essentially different ``species''---conversion between the even--$J$ {\it para} and odd--$J$ {\it ortho} nuclear spin states is only possible through reactive collisions---it has long been assumed that $T_{01}$ is a good approximation for the kinetic temperature, $T_{kin}$, in diffuse molecular clouds.  This is because H$_2$ molecules are expected to experience many reactive collisions with protons during their lifetimes.  As a result, the {\it ortho} and {\it para} populations of H$_2$ should be brought into thermal equilibrium with the proton kinetic temperature \citep{dalgarno1973}.

Similarly, H$_3^+$ also has {\it ortho} and {\it para} nuclear spin states ($(J,K)=(1,1)$ is the lowest lying {\it para} state, and $(J,K)=(1,0)$ the lowest lying {\it ortho} state).  For H$_3^+$ though, the relative population between the two states has been expected to be thermalized by reactive collisions with H$_2$ \citep{mccall1998b,mccall2003,gibb2010}.  As the average values of $T_{01}$ and $T({\rm H}_3^+)$ do not agree, this does not seem to be the case.

However, out of the 66 and 18 sight lines used to compute $\langle T_{01}\rangle$ and $\langle T({\rm H}_3^+)\rangle$, respectively, only 2 are shared between both samples.  While previously reported values of $T_{01}$ and $T({\rm H}_3^+)$ do differ for these sight lines toward $\zeta$~Per and X~Per by about 30~K \citep{savage1977,rachford2002,indriolo2007}, such a small sample does not provide particularly meaningful results.  In order to increase the number of sight lines with {\it ortho} and {\it para} column densities determined for both H$_2$ and H$_3^+$, we have made observations searching for H$_3^+$ absorption features along sight lines with measured H$_2$ column densities.  These observations and our data reduction procedures are described in Section 2.  Section 3 discusses and justifies many of the assumptions made concerning molecular hydrogen and $T_{01}$ in diffuse molecular clouds. In Section 4, we examine the H$_3^+$\ + H$_2$\ reaction and present steady state models to explore the temperature discrepancy between $T_{01}$ and $T$(H$_3^+$). Section 5 reviews the observations and modeling, and presents our conclusions from the work.

\section{OBSERVATIONS \& DATA REDUCTION}

Target sight lines were selected based on H$_2$ column densities \citep{savage1977,rachford2002,rachford2009} and $L$-band magnitudes.  We required that the $J=0$ and $J=1$ column densities of H$_2$ ($N(0)$ and $N(1)$, respectively) both be known, and that the total H$_2$ column density ($N({\rm H}_2)$) be greater than $10^{20}$~cm$^{-2}$.  The $L$-band magnitude was required to be brighter than 6~mag so that the necessary integration times would be relatively short.  Observations focused on the $R(1,1)^u$, $R(1,0)$, and $R(1,1)^l$ transitions (at 3.668083~$\mu$m, 3.668516~$\mu$m, and 3.715479~$\mu$m, respectively) which arise from the $(J,K)=(1,1)$ and $(1,0)$ levels of the ground vibrational state of H$_3^+$, the only levels expected to be significantly populated at average diffuse cloud temperatures ($T\sim70$~K).

Spectra in support of this project were obtained using the Phoenix spectrometer \citep{hinkle2003} at the Gemini South Telescope and the Cryogenic High-resolution Infrared Echelle Spectrograph (CRIRES)~\citep{kaufl2004} at the Very Large Telescope (VLT).  Observations at Gemini South were made in queue mode, and the Phoenix spectrometer was used with its echelle grating and 0.17'' slit to produce a resolving power of about 70,000, and with the L2734 filter to select the order containing the $R(1,1)^u$ and $R(1,0)$ transitions.  Observations at the VLT were made in service mode, and CRIRES was used with its 0.2'' slit to provide a resolving power of about 100,000, and a reference wavelength of 3715.0~nm to cover the $R(1,1)^u$ and $R(1,0)$ transitions on detector 1 and the $R(1,1)^l$ transition on detector 3.  The adaptive optics system was used with CRIRES to maximize starlight passing through the narrow slit.  In addition to the science targets, bright, early-type stars were observed for use as telluric standards.  For all observations, the star was nodded along the slit in an ABBA pattern in order to facilitate the removal of atmospheric emission lines and dark current via the subtraction of neighboring images.  A log containing the observed sight lines and respective integration times is given in Table \ref{tblobs}.

\begin{deluxetable*}{llccc}
\tablecaption{Observations \label{tblobs}}
\tablehead{
 & & & \colhead{Integration Time} & \\
\colhead{Object} & \colhead{Date(s) of Observation} & \colhead{Telescope} & \colhead{(min)} & \colhead{Standard}
}
\startdata
HD 149404  & 2009 Aug 05 & Gemini South & 32 & $\lambda$ Sco \\
$\chi$ Oph & 2009 Aug 30 & Gemini South & 12 & $\lambda$ Sco \\
HD 152236  & 2009 Aug 30 & Gemini South & 16 & $\lambda$ Sco \\
HD 154368  & 2009 Aug 30 & Gemini South & 32 & $\lambda$ Sco \\
HD 53367   & 2009 Dec 03 & VLT          & 30 & $\kappa$ Ori \\
HD 73882   & 2009 Dec 03 & VLT          & 30 & $\zeta$ Pup \\
           & 2010 Jan 17 & VLT          & 30 & $\zeta$ Pup  \\
HD 110432  & 2010 Jan 27 & VLT          & 10 & $\eta$ Cen \\
           & 2010 Feb 28 & VLT          & 20 & $\eta$ Cen \\
           & 2010 Mar 02 & VLT          & 40 & $\eta$ Cen \\
$\mu$ Nor  & 2010 Apr 05 & Gemini South & 72 & $\lambda$ Sco
\enddata
\end{deluxetable*}

Various standard IRAF\footnote{http://iraf.noao.edu/} procedures were used in the data reduction process.  Given the different state of data available from Phoenix versus CRIRES, different amounts of processing were required for data from the 2 telescopes.  For each night of Phoenix observations, a bad pixel map was created from the average of several dark frames, and these pixels were interpolated over in the object and flat frames.  Flats were then combined to create a normalized flat field which was divided out of the object frames.  Neighboring AB image pairs were subtracted from each other to remove atmospheric emission and dark current.  Finally, one-dimensional spectra were extracted using {\it apall}.  In the case of CRIRES observations, data were processed through the CRIRES specific pipeline, resulting in fully reduced two-dimensional spectral images for each target (given the product codes SCOM and PCOM by the pipeline).  One-dimensional spectra were extracted from these images.  All such spectra from both telescopes were then imported to IGOR Pro\footnote{http://www.wavemetrics.com/} where the remainder of reduction was performed.

Individual Phoenix spectra within an exposure sequence for a given target were then added together.  Science target spectra from both telescopes were divided by telluric standard spectra to remove atmospheric absorption features and to normalize each spectrum.  These normalized spectra were wavelength calibrated with a typical accuracy of $\sim2$~km~s$^{-1}$ using the vacuum wavelengths of the atmospheric absorption lines.  Calibrated spectra were then shifted into the local standard of rest (LSR) frame, and spectra of the same target from different nights were combined using a variance-weighted mean.  For each sight line the continuum surrounding the absorption features was then fit with an $n^{\rm th}$ order polynomial ($n=7-9$) and the spectrum was divided by the fit to re-normalize the continuum level.  The resulting spectra for sight lines with H$_3^+$ absorption features---HD 154368, HD 73882, and HD 110432---are shown in Figure \ref{figspectra}.  Although H$_3^+$ spectra for $\zeta$~Per and X~Per (the other 2 sight lines with both H$_2$ and H$_3^+$ data) are reported in \citet{indriolo2007}, the reduction process utilized in that study did not combine spectra using a variance-weighted mean, nor did it fit fluctuations in the continuum level with a polynomial function.  For the purpose of consistency, we have reprocessed the data from both sight lines.  No new data have been added, but differences in the method of processing have resulted in output spectra with slightly better signal-to-noise ratios (S/N).  These spectra are also shown in Figure \ref{figspectra}.

\begin{figure}
\epsscale{1.0}
\plotone{spectra_v3.eps}
\caption{Spectra showing absorption lines from the $(J,K)=(1,1)$ and $(1,0)$ states of H$_3^+$.  Spectra for $\zeta$~Per and X~Per were taken at UKIRT and are reprocessed versions of the data previously reported in \citet{indriolo2007}.  The spectrum for HD 154368 was taken at Gemini South, while those for HD 73882 and HD 110432 were taken at the VLT.  Large deviations from flat continuum levels in the spectra for HD 154368, HD 73882, and HD 110432 are the combination of 2 effects: (1) artifacts due to continuum fitting at wavelengths far away from the H$_3^+$ absorption lines; (2) inability to remove the strong atmospheric methane line immediately shortward of the $R(1,1)^u$ line.  Vertical lines mark the expected positions of the H$_3^+$ absorption lines given previously determined interstellar gas velocities along each sight line.}
\label{figspectra}
\end{figure}

Absorption features due to H$_3^+$ were fit with Gaussian functions in order to determine equivalent widths, velocity full-width at half-maxima (FWHM), and interstellar gas velocities.  Our fitting procedure uses the functional form of a Gaussian where area (as opposed to amplitude) is a free parameter, and includes a fit to the continuum level, $y_0$.  In the case of the $R(1,1)^u$ and $R(1,0)$ lines, both absorption features are fit simultaneously and a single best-fit continuum level is found.  Uncertainties on the equivalent widths ($\delta W_{\lambda}$) and continuum level ($\delta y$)---both at the 1$\sigma$ level---were output by the fitting process.  To estimate the systematic uncertainties due to continuum placement, we forced the continuum level to $y_0+\delta y$ and $y_0-\delta y$ and re-fit the absorption lines.  Variations in the equivalent widths due to this shift are small compared to those reported by the fitting procedure and so are not included in our analysis (i.e., $\sigma(W_{\lambda})$=$\delta W_{\lambda}$).
Assuming optically thin absorption lines and taking transition dipole moments and wavelengths from \citet{goto2002} and references therein, column densities were derived from equivalent widths using the standard relation.  All of these results are shown in Table \ref{tbllineparam}.

\begin{deluxetable*}{llcccccc}
\tablecaption{Absorption Line Parameters \label{tbllineparam}}
\tablehead{
 & & \colhead{$v_{\rm LSR}$} & \colhead{FWHM} & \colhead{$W_{\lambda}$} & \colhead{$\sigma(W_{\lambda})$} &
\colhead{$N(J,K)$} & \colhead{$\sigma(N)$} \\
\colhead{Object} & \colhead{Transition} & \colhead{(km s$^{-1}$)} & \colhead{(km s$^{-1}$)} &
\colhead{($10^{-6}~\mu$m)} & \colhead{($10^{-6}~\mu$m)} & \colhead{($10^{13}$ cm$^{-2}$)} & \colhead{($10^{13}$ cm$^{-2}$)}
}
\startdata
$\zeta$ Per& $R(1,1)^u$ &  7.7 &11.0 & 0.99 & 0.13 & 4.09 & 0.53 \\
           & $R(1,0)$   &  6.1 & 9.0 & 1.00 & 0.11 & 2.53 & 0.29 \\
X Per      & $R(1,1)^u$ &  8.2 & 9.1 & 0.80 & 0.17 & 3.34 & 0.69 \\
           & $R(1,0)$   &  6.3 &10.2 & 1.30 & 0.18 & 3.29 & 0.45 \\
HD 154368  & $R(1,1)^u$ &  5.4 & 6.0 & 1.79 & 0.30 & 7.43 & 1.24 \\
           & $R(1,0)$   &  5.2 & 5.6 & 1.12 & 0.29 & 2.83 & 0.74 \\
HD 73882   & $R(1,1)^u$ &  5.9 & 3.9 & 1.44 & 0.21 & 5.97 & 0.86 \\
           & $R(1,0)$   &  5.7 & 3.2 & 1.16 & 0.19 & 2.94 & 0.48 \\
           & $R(1,1)^l$ &  5.4 & 3.5 & 1.34 & 0.15 & 6.15 & 0.69 \\
HD 110432  & $R(1,1)^u$ & -3.8 & 6.9 & 0.74 & 0.06 & 3.08 & 0.24 \\
           & $R(1,0)$   & -3.3 & 7.5 & 0.83 & 0.07 & 2.11 & 0.17 \\
           & $R(1,1)^l$ & -3.1 & 8.1 & 0.69 & 0.06 & 3.15 & 0.28 \\

\enddata
\tablecomments{Column 3 ($v_{\rm LSR}$) gives the interstellar gas velocity in the local standard of rest frame.  Column 4 (FWHM) gives the full width at half-maximum of the absorption features.  Columns 5 and 6 show the equivalent width, $W_{\lambda}$, and its $1\sigma$ uncertainty, $\sigma(W_{\lambda})$, respectively.  Columns 7 and 8 give the column density of H$_3^+$ in the state each transition probes, $N(J,K)$, and its uncertainty, $\sigma(N)$, respectively. Values for these parameters in the $\zeta$~Per and X~Per sight lines were previously reported in \citet{indriolo2007}.  The new values for both absorption lines toward $\zeta$~Per and the $R(1,0)$ line toward X~Per are consistent with the previously published results within uncertainties.  However, the new and old results for the $R(1,1)^u$ line toward X~Per are inconsistent.  Upon inspection, we found this to be due to a bad fit to that line during the 2007 analysis.  In all cases, the values published herein should be taken to supersede those from \citet{indriolo2007}.}

\end{deluxetable*}

These observations increase the total number of sight lines with both H$_3^+$ and H$_2$ detections from 2 to 5.  Column densities, $para$-fractions, and excitation temperatures for both species along all 5 sight lines are collected in Table \ref{tblresults}.
H$_2$ data come from \citet{savage1977} and \citet{rachford2002}.  Uncertainties on all values are $1\sigma$. The excitation temperatures inferred from the $R(1,0)$, $R(1,1)^u$, and $R(1,1)^l$ absorption lines of H$_3^+$ range from $20\leq T$(H$_3^+$)$\leq 46$ K, while those reported for H$_2$ vary from $51\leq T({\rm H}_2)\leq 68$ K.  In 4 sight lines $T_{01}$ is greater than $T({\rm H}_3^+)$ by about 30 K, while for X~Per $T_{01}$ and $T({\rm H}_3^+)$ are consistent within uncertainties.  Still, these observations clearly show that for the same interstellar material along 4 different diffuse molecular cloud sight lines the excitation temperatures derived from H$_3^+$ and H$_2$ do not agree.

\begin{deluxetable*}{lcccccc}
\tablecaption{Target Sight Line Properties \label{tblresults}}
\tablehead{
& & \colhead{$\zeta$ Per\tablenotemark{ab}} & \colhead{X Per\tablenotemark{ac}} & \colhead{HD 154368\tablenotemark{c}} & \colhead{HD 73882\tablenotemark{c}} &\colhead{HD 110432\tablenotemark{cd}}
}
\startdata
& & & H$_3^+$ Results & & & \\
\hline \\
$N(1,1)$  & ($10^{13}$~cm$^{-2}$) & $4.09\pm0.53$  & $3.34\pm0.69$    & $7.43\pm1.24$  & $6.08\pm0.12$  & $3.11\pm0.05$   \\
$N(1,0)$  & ($10^{13}$~cm$^{-2}$) & $2.53\pm0.29$  & $3.29\pm0.45$    & $2.83\pm0.74$  & $2.94\pm0.48$  & $2.11\pm0.17$   \\
$p_3$\tablenotemark{e} &          & $0.62\pm0.04$  & $0.50\pm0.06$    & $0.72\pm0.06$  & $0.67\pm0.04$  & $0.60\pm0.02$   \\
$T({\rm H}_3^+)$  & (K)           & $28\pm4$       & $46^{+21}_{-13}$ & $20\pm4$       & $23\pm3$       & $30\pm2$        \\
\hline \\
& & & H$_2$ Results & & & \\
\hline \\
log$[N(0)]$ & (cm$^{-2}$)         & $20.51\pm0.09$ & $20.76\pm0.03$   & $21.04\pm0.05$ & $20.99\pm0.08$ & $20.40\pm0.03$  \\
log$[N(1)]$ & (cm$^{-2}$)         & $20.18\pm0.09$ & $20.42\pm0.06$   & $20.54\pm0.15$ & $20.50\pm0.07$ & $20.27\pm0.04$  \\
$p_2$\tablenotemark{f} &          & $0.68\pm0.06$  & $0.69\pm0.04$    & $0.76\pm0.07$  & $0.76\pm0.05$  & $0.57\pm0.03$   \\
$T_{01}$  & (K)                   & $58\pm6$       & $57\pm4$         & $51\pm8$       & $51\pm6$       & $68\pm5$        \\
\enddata
\tablecomments{Measured column densities for the lowest lying \textit{ortho}\ and \textit{para}\ states of H$_2$ and H$_3^+$ are shown for the 5 sight lines with all such data available.  Also shown are the \textit{para}-fractions for each species and the rotational temperatures derived from a simple 2-state system analysis.}
\tablenotetext{a}{Updated analysis of H$_3^+$ data originally presented in \citet{indriolo2007}}
\tablenotetext{b}{H$_2$ data from \citet{savage1977}}
\tablenotetext{c}{H$_2$ data from \citet{rachford2002}}
\tablenotetext{d}{May be affected by multiple velocity components \citep{crawford1995}}
\tablenotetext{e}{\textit{p}-\hhh\ fraction: $N(1,1)/(N(1,0) + N(1,1))$}
\tablenotetext{f}{\textit{p}-\hh\ fraction: $N(1)/(N(0) + N(1))$}
\end{deluxetable*}

\section{H$_2$\ THERMALIZATION}

Given the large discrepancies between $T_{01}$ inferred from H$_2$ and the excitation temperature of H$_3^+$, it is important to re-examine the assumption that the inferred $T_{01}$ accurately reflects the kinetic temperature of the diffuse molecular clouds.   If this assumption were incorrect, it would be conceivable that H$_3^+$ provides the true (lower) temperature of diffuse molecular clouds.  There are at least 4 reasons this assumption could be invalid: (1) observational errors in the determination of the $J=0$ and $J=1$ column densities of H$_2$; (2) an insufficient frequency of H$^+$ + H$_2$ collisions to achieve steady state; (3) the steady state of this reaction being different from the thermodynamic equilibrium; and (4) errors caused by a varying $J=0:1$ ratio along the line of sight.  In the following subsections, we investigate each of these possibilities in turn.

\subsection{Observational Determination of H$_2$\ Columns}

The measurement of the column densities of $J=0$ and $J=1$ of H$_2$ is performed by profile fitting to spectra of the Lyman ($A$-$X$) band in the ultraviolet, recorded with Copernicus or FUSE.  The H$_2$ transitions are optically thick, and are completely opaque in the line cores.  Given the difficulties in accurately retrieving column densities from optically thick transitions, one might worry that the inferred $T_{01}$ is contaminated by uncertainties caused by radiative transfer.

According to B.~L.~Rachford (private communication, 2010), the detailed shape of the combined profile of the $J=0$ line and the two $J=1$ lines is quite sensitive to the ratio of the column densities of these two rotational levels, and thus provides a very useful probe of $T_{01}$.  Because multiple vibronic bands of H$_2$, which are known to be relatively free of contamination by stellar lines, are used in the determination of $T_{01}$, it is difficult to envision any systematic errors that could affect the measurements.  The statistical errors in the column density measurements are typically $\sim$0.1 dex, and we can therefore conclude that the ultraviolet measurements provide an accurate and fairly precise measure of the ratio of $N(0)$ to $N(1)$ for H$_2$.

\subsection{Frequency of H$^+$ + H$_2$\ Reactions}

The $J=0$ and $J=1$ rotational levels of H$_2$ belong to different spin modifications ({\it para} and {\it ortho}, respectively) and are therefore not thermalized by non-reactive collisions or radiative transitions.  Only chemical reactions, in which the protons are exchanged, can affect the nuclear spin modification of H$_2$.\footnote{Strictly speaking, large inhomogeneous magnetic fields, such as found on the surface of paramagnetic catalysts, can also affect the nuclear spin modification of H$_2$, but we assume that such effects are negligible in interstellar conditions.}

Since H$_2$ is formed in a highly exothermic reaction on grain surfaces, its nascent rotational (and spin) distribution is presumed to represent a high temperature \citep{takahashi2001}.  In the high temperature limit, H$_2$ should be formed with an \textit{ortho}:\textit{para}\ ratio of 3:1.  If an insufficient number of reactive collisions occur between the formation of an H$_2$ molecule and its subsequent destruction (by photodissociation or cosmic-ray ionization), then the average \textit{ortho}:\textit{para}\ ratio of H$_2$ may lie somewhere between the nascent value (3:1) and the thermalized value (1:2 at 60 K, for example).  This could lead to $T_{01}$ overestimating the true cloud kinetic temperature.

The number of reactive collisions suffered by an average H$_2$ molecule in its lifetime can be expressed as ${\cal N}_{rxn}\equiv\tau_{life}/\tau_{rxn}$, where $\tau_{life}$ is the average lifetime of an H$_2$ molecule and $\tau_{rxn}$ is the average time between reactive collisions.  If ${\cal N}_{rxn}\gg1$, then the \textit{ortho}:\textit{para}\ ratio of H$_2$ should reflect the steady-state of the reaction in question.

In diffuse molecular clouds, H$_2$ is formed on grains at a rate of $R n_{\rm H} n({\rm H})$, where $R$ is the grain formation rate \citep[typically taken to be about $3\times10^{-17}$~cm$^3$~s$^{-1}$; e.g.][]{spitzer1978,gry2002}, $n_{\rm H} \equiv n({\rm H}) + 2n({\rm H}_2)$ is the total number density of hydrogen nuclei, and $n({\rm H})$ is the number density of atomic hydrogen.  The destruction of H$_2$ is dominated by cosmic-ray ionization and photodissociation (following absorption in the Lyman bands), and has a rate of $(\zeta_2+\Gamma) n({\rm H}_2)$, where $\Gamma$ is the photodissociation rate.  In steady state, these two rates are equal, and we can solve for
$\tau_{life} = (\zeta_2+\Gamma)^{-1} = n({\rm H}_2)/[R n_{\rm H} n({\rm H})]$.  By using the
definition of the local molecular fraction $f^n_{{\rm H}_2} \equiv 2n({\rm H}_2)/n_{\rm H}$ (which we will simply call $f$), we can rewrite this expression
as $\tau_{life} = f/[2R n_{\rm H}(1-f)]$.

Assuming that the reaction of H$^+$ + H$_2$ dominates the interconversion of \textit{o}-\hh\ and \textit{p}-\hh (\textit{ortho}- and \textit{para}-H$_2$, respectively), we can write $\tau_{rxn} = [k_{ic}n({\rm H}^+)]^{-1}$, where $k_{ic}$ is the rate coefficient for the interconversion reaction.  Substituting into the equation for ${\cal N}_{rxn}$, we find
\begin{displaymath}
{\cal N}_{rxn} = \frac{k_{ic}}{R} \frac{n({\rm H}^+)}{n_{\rm H}} \frac{f}{2(1-f)}.
\end{displaymath}

To estimate the number density of H$^+$, we consider the steady state of its formation and destruction.  H$^+$ is formed by cosmic-ray ionization of H atoms, at a rate of $\zeta_{\rm H}n({\rm H})$, where $\zeta_{\rm H}$ is the cosmic-ray ionization rate of H \citep[$2.3\zeta_{\rm H}\approx1.5\zeta_2$;][]{glassgold1974}.  Given the abundances of various species in diffuse clouds and the rate coefficients for reactions between H$^+$ and such species, chemical models \citep[e.g.][]{woodall2007} predict that H$^+$ is destroyed predominantly by charge transfer to atomic oxygen, with a rate of $k_{ct} n({\rm H}^+) n({\rm O})$.  Equating these rates of formation and destruction and solving for $n({\rm H}^+)$, we find
$n({\rm H}^+)=\zeta_{\rm H}(1-f)/[k_{ct}x({\rm O})]$, where $x({\rm O})\equiv n({\rm O})/n_{\rm H}$.  Finally, substituting this into the expression for ${\cal N}_{rxn}$ gives
\begin{displaymath}
{\cal N}_{rxn} = \frac{k_{ic}}{R} \frac{\zeta_{\rm H}}{k_{ct}} \frac{f}{2n_{\rm H}} \frac{1}{x({\rm O})}.
\end{displaymath}
Adopting values of $k_{ic}=2.2\times10^{-10}$ cm$^3$ s$^{-1}$ \citep{gerlich1990}, $R=3\times10^{-17}$~cm$^3$~s$^{-1}$, $\zeta_2=4\times10^{-16}$~s$^{-1}$ \citep{indriolo2007}, $k_{ct}=7.31\times10^{-10}(T/300)^{0.23}e^{-225.9/T}$~cm$^3$~s$^{-1}$ \citep{woodall2007}, $x(\textrm{O})\approx 3 \times 10^{-4}$ \citep{cartledge2004,jensen2005}, and typical diffuse cloud values of $f = 0.9$\footnote{While the line-of-sight molecular fraction is lower, that quantity integrates over atomic gas not associated with the diffuse molecular cloud. We are therefore using the local molecular fraction typical of diffuse molecular clouds.}  and $n_{\rm H} = 100$ cm$^{-3}$ \citep{snow2006}, we find that at $T\sim70$ K, ${\cal N}_{rxn} \sim 1400$. Thus, the typical H$_2$ molecule will experience over 1000 reactive collisions during its lifetime, and we can safely assume that the initial \textit{ortho}:\textit{para}\ ratio of H$_2$ is irrelevant; instead, the observed \textit{ortho}:\textit{para}\ ratio should reflect the steady state of the reactive collisions.

\subsection{Steady State of H$^+$ + H$_2$\ Reactions}

From a thermodynamic perspective, one would expect that the steady state of the H$^+$ + H$_2$ reaction would represent a thermal distribution of \textit{o}-\hh\ and \textit{p}-\hh, if no other processes influence the spin modifications.  This expectation has been confirmed by a phase space theoretical calculation by \citet{gerlich1990}, who found that the \textit{ortho}:\textit{para}\ ratio could be expressed at low temperatures (30--80 K) by the expression $9.35\exp(-169.4/T)$, quite close to the thermodynamic expectation of $9\exp(-170.4/T)$.  Evidently the nuclear spin selection rules for this chemical reaction, which suppress the \textit{ortho}-to-\textit{para}\ conversion by a factor of 6, do not significantly impact the final distribution.

\subsection{Line of Sight Integration Effects}

One remaining concern regards the estimation of $T_{01}$ in a diffuse molecular cloud from the column densities of $J=0$ and $J=1$, which are integrated quantities along the line of sight.  If some of the H$_2$ resides in hotter, mostly atomic gas where H$_3^+$ is not abundant, that hot H$_2$ would cause the observed line-of-sight $T_{01}$ to exceed $T_{01}$ in the molecular cloud.  We expect that such contamination would not be a major effect, as H$_2$ is known to self-shield very effectively from the interstellar radiation field; thus, the amount of H$_2$ in primarily atomic (and presumably warmer) gas is likely to be quite small compared to the amount of H$_2$ in the molecular cloud itself.

To estimate the magnitude of this effect more quantitatively, we take a simple cloud model with a hotter outer region and cooler inner region.  Assuming that $T_{01}=100$~K in the outer region \citep[based on Copernicus observations of diffuse atomic clouds;][]{jenkins1983}, we varied $T_{01}$ in the inner region between 10~K and 100~K for a set of models where the outer region contained 1/2, 1/4, 1/8, and 1/16 of the material in the cloud.  We then computed the line-of-sight $T_{01}$ that would be derived considering both regions of gas.  The result of this analysis is shown in Figure \ref{figT01LOS}.

\begin{figure}
\epsscale{1.0}
\plotone{los_temp_v2.eps}
\caption{The line-of-sight rotational temperature, $T_{01}$, is determined for a cloud containing both a warm and cold component.  The cold, inner component is varied between 10~K and 100~K, while the warm, outer component is set at 100~K.  Different curves show the results for cases where the warm component contains 1/2, 1/4, 1/8, and 1/16 of the total material in the cloud, and are labeled accordingly. Cross hairs mark the inferred inner cloud values of $T_{01}$ given the observed line-of-sight values of $T_{01}$ and estimated fractions of H$_2$ in a 100~K cloud component for the 5 sight lines considered herein.  From left to right the cross hairs mark HD 73882, HD 154368, $\zeta$ Per, X Per, and HD 110432.}
\label{figT01LOS}
\end{figure}

Taking the diffuse cloud model of \citet{neufeld2005} with a constant density ($n_{\rm H}=100$~cm$^{-3}$) and standard UV radiation field ($\chi_{\rm UV}=1$) illuminating the cloud from one side, we then determined the amount of H$_2$ expected to be in the outer region for comparison with observed H$_2$ column densities in diffuse clouds.  We define the transition from the outer to inner regions to be at $E(B-V)=0.04$ ($N_{\rm H}\approx2.3\times10^{20}$~cm$^{-2}$), about half of the total color excess (hydrogen column density) found to supply self-shielding effects in H$_2$ \citep{savage1977,gillmon2006}.  Integrating $n({\rm H}_2)$ in the outer region gives $N_{outer}({\rm H}_2)=6\times10^{19}$~cm$^{-2}$.  Because this model effectively only treats one side of a cloud, we compare this value to half of the total H$_2$ column densities reported in Table \ref{tblresults}.  The two extreme cases are HD 110432 and HD 154368, where the outer region accounts for about 1/4 and 1/12 of the total cloud, respectively.  Taking the observed values of $T_{01}$ and using the appropriate curves on Figure 2, we estimate the temperature of the inner cloud region for each of the 5 sight lines considered herein.  The results are marked in Figure 2 as cross hairs, and show that the line-of-sight values of $T_{01}$ overestimate the inferred inner cloud values of $T_{01}$ by only about 5--10 K.  As such, the observed values of $T_{01}$ should be relatively close to the true values of $T_{01}$ in molecular clouds. We therefore assume for the remainder of this paper that the line of sight $T_{01}$ does represent the diffuse molecular cloud kinetic temperature.

\subsection{Summary on H$_2$ Temperature}

From the preceding discussions, we conclude that UV measurements accurately measure the column densities of
$J=0$ and $J=1$ of H$_2$ in diffuse clouds, that the chemical reaction between H$^+$ and H$_2$ occurs $\sim10^3$ times during the life of an average H$_2$, and that the steady state of this chemical reaction leads to an \textit{ortho}:\textit{para}\
ratio that closely reflects the kinetic temperature of the gas.  Furthermore, we conclude that it is unlikely that the integration along the line of sight introduces significant contamination of the inferred $T_{01}$.  In summary, then, measured values of $T_{01}$ in diffuse molecular clouds should accurately reflect the cloud kinetic temperature.  Consequently, the excitation temperature of H$_3^+$, which is significantly lower than $T_{01}$, must not always reflect the kinetic temperature.

\section{\textit{ORTHO} AND \textit{PARA} H$_3^+$}

Having shown that the temperature discrepancy between $T_{01}$ and $T$(H$_3^+$) in diffuse molecular clouds is real and that $T_{01}$ accurately reflects the cloud kinetic temperature, we now consider the processes related to H$_3^+$\ thermalization in diffuse molecular clouds to examine why $T$(H$_3^+$) might not match the kinetic temperature.

\subsection{Nascent and Thermalized \textit{Para}-H$_3^+$ Fractions} \label{nasctherm}

H$_3^+$ is produced by the reaction
\begin{equation}
\label{formrxn}
\rm{H}_2 + \rm{H}_2^+ \rightarrow \rm{H}_3^+ + H,
\end{equation}
which follows the cosmic-ray ionization of H$_2$ to form H$_2^+$.  The nuclear spin modification of the product H$_3^+$ depends on the nuclear spin modifications of the reactant H$_2$ and H$_2^+$ according to the selection rules given by \cite{oka2004}.  It is most convenient to express the nuclear spin modifications in terms of the \textit{para}-fractions, rather than the \textit{ortho}:\textit{para}\ ratios, so we define
\begin{displaymath}
 p_2 \equiv \frac{n(\textrm{\textit{p}-\hh})}{n(\textrm{\textit{p}-\hh})+n(\textrm{\textit{o}-\hh})} \label{p2def}
\end{displaymath}
and
\begin{displaymath}
 p_3 \equiv \frac{n(\textrm{\textit{p}-\hhh})}{n(\textrm{\textit{p}-\hhh})+n(\textrm{\textit{o}-\hhh})} . \label{p3def}
\end{displaymath}

As the cosmic-ray ionization of H$_2$ is not expected to affect the nuclear spin modification, we can further assume that the \textit{para}-fraction of H$_2^+$ is also given by $p_2$.  Table \ref{tblh3pform} demonstrates, using these reactant fractions and the nuclear spin branching fractions, that the \textit{para}-fraction of newly formed H$_3^+$ is $p_3 = (1/3) + (2/3)p_2$, assuming that the rate for the H$_2^+$ + H$_2$\ reaction is independent of nuclear spin configuration.

In diffuse molecular clouds, the vast majority of the H$_2$\ population lies in the lowest \textit{ortho}\ and \textit{para}\ states, as the temperature of 70 K is well below the energy of the next states (the $J=2$ state lies 510 K above $J=0$, and $J=3$ lies 844 K above $J=1$). Therefore, to derive $p_2$ from astronomical observations we use the formula $p_2 = N(0)/[N(0)+N(1)]$. H$_3^+$\ on the other hand does have energetically accessible \textit{para}\ states, as the (2,2) and (2,1) states lie only 151.3 and 249.2 K above the (1,1) ground state. However, the (2,2) and (2,1) states are expected to quickly undergo radiative decay to the (1,1) state at the temperatures and densities of the diffuse molecular clouds \citep{oka2004b}. Furthermore, population in the next \textit{ortho}\ state, (3,3) has not been observed in these environments \citep{oka2005}, so the vast majority of \textit{o}-\hhh\ is in the (1,0) state. Consequently, to calculate $p_3$ from the astronomical observations, we use $p_3 = N(1,1)/[N(1,1)+N(1,0)]$.

\begin{deluxetable*}{cccc}
\tablecaption{Nascent Para H$_3^+$ Fraction \label{tblh3pform}}
\tablehead{
\colhead{Reaction} & \colhead{Collision Fraction}  & \colhead{Branching Fraction} & \colhead{\textit{p}-\hhh\ Fraction}
}
\startdata
p-H$_2^+$  +  \textit{p}-\hh\ & $(p_2)^2$ & 1 & $ p_2^2$ \\
p-H$_2^+$ + \textit{o}-\hh\ & $p_2(1-p_2)$ &  2/3 & $(2/3)(1-p_2)p_2$ \\
o-H$_2^+$ + \textit{p}-\hh\ & $(1-p_2)p_2$ &  2/3 & $(2/3)(1-p_2)p_2$ \\
o-H$_2^+$ + \textit{o}-\hh\ & $(1-p_2)^2$ &  1/3 & $(1/3)(1-p_2)^2$ \\
\hline \\
Total & -- & -- & $(1/3) + (2/3)p_2$
\enddata
\tablecomments{This table presents the calculation of the nascent \textit{p}-\hhh\ fraction formed in diffuse molecular clouds from the H$_2^+$ + H$_2$\ reaction, assuming that cosmic ray ionization of H$_2$\ to form H$_2^+$ does not affect its nuclear spin configuration. The collision fraction represents the fraction of total H$_2^+$ + H$_2$\ collisions with the specified nuclear spin configurations. The branching fractions are for \textit{p}-\hhh\ formation, and are derived from nuclear spin selection rules \citep{quack1977,oka2004}. The final column presents the calculation of the nascent \textit{p}-\hhh\ fraction.}
\end{deluxetable*}

Figure \ref{p3p2_1} shows the nascent $p_3$ distribution as a function of $p_2$. This figure also shows the total \textit{para}-fraction of a thermalized sample of H$_3^+$\ at various temperatures, calculated using the energy levels $E(J,K)$ from \citet{lindsay2001}.  Also plotted in the figure are the results of the astronomical observations presented in Table \ref{tblresults}. In diffuse molecular clouds, $p_3$ generally appears to lie between the nascent $p_3$ and the thermal $p_3$ values, suggesting an incomplete thermalization of the nuclear spin modifications of H$_3^+$.

As discussed by \citet{oka2004b}, the aforementioned spontaneous emission from the (2,2) and (2,1) states decreases $T$(H$_3^+$) relative to $T_{01}$. They show that for a cloud density of 100 cm$^{-3}$ and $60 \leq T_{01} \leq 120$ K, $T$(H$_3^+$) should fall in the range of 40-50 K, and this accounts for a $\sim40-80$ K difference between $T_{01}$ and $T$(H$_3^+$). However, in the temperature ranges discussed here, the \textit{para}-fractions of H$_3^+$\ and H$_2$\ are nonlinear with respect to these excitation temperatures. In terms of $p_3$, all $T$(H$_3^+$) above about 40 K should have about the same $p_3$, while $p_3$ changes substantially when $T$(H$_3^+$) falls below 40 K, as can be seen in Figure \ref{p3p2_1}. Spontaneous emission will raise the apparent $p_3$ [as derived from the N(1,1):N(1,0) ratio] relative to the thermalized $p_3$ and consequently lower $T$(H$_3^+$) with respect to $T_{01}$. However, Figure \ref{p3p2_1} illustrates that the magnitude of this effect cannot account for the discrepancy observed in the astronomical observations in these environments in terms of the \textit{para}-fractions, with the possible exception of X Per.

\begin{figure}
\epsscale{1.0}
\plotone{nascent_v3.eps}
\caption{The nascent (dashed line) and thermalized (numbers, in K) \textit{p}-\hhh\ fraction as a function of the \textit{p}-\hh\
fraction.  The circles represent the observations of diffuse molecular clouds summarized in Table \ref{tblresults} with 1$\sigma$ uncertainties.}
\label{p3p2_1}
\end{figure}

\subsection{The Reaction of H$_3^+$\ with H$_2$}

As in the case of H$_2$, the nuclear spin modifications of H$_3^+$ cannot effectively be changed by radiative transitions or by non-reactive collisions; only chemical reactions can do so.  In this case, the reaction H$_3^+$\ + H$_2$\ $\rightarrow$ (H$_5^+$)* $\rightarrow$ H$_2$\ + H$_3^+$\ is the most efficient mechanism for interconverting \textit{o}-\hhh\ and \textit{p}-\hhh.  When H$_3^+$\ and H$_2$\ collide, there are three possible reaction outcomes:

\begin{mathletters}
\begin{eqnarray}
{\rm \tilde{H}}_3^+ + {\rm H}_2 \rightarrow & {\rm \tilde{H}}_3^+ + {\rm H}_2 & {\rm (identity),} \label{id} \\
{\rm \tilde{H}}_3^+ + {\rm H}_2 \rightarrow & {\rm H}_2{\rm \tilde{H}}^+ + {\rm \tilde{H}}_2 & {\rm (hop), and} \label{hop} \\
{\rm \tilde{H}}_3^+ + {\rm H}_2 \rightarrow & {\rm H}{\rm \tilde{H}}_2^+ + {\rm H}{\rm \tilde{H}} & {\rm (exchange).} \label{exch}
\end{eqnarray}
\end{mathletters}

In the case of reaction \ref{id}, the nuclear spin configurations of the H$_3^+$\ and H$_2$\ remain unchanged, while in reactions \ref{hop} and \ref{exch} the configuration may change. However, like reaction \ref{formrxn}, the hop and exchange pathways must obey nuclear spin selection rules \citep{quack1977,oka2004}. For instance, in order for a reaction between \textit{p}-\hhh\ and \textit{p}-\hh\ to form \textit{o}-\hhh\, the reaction must be an exchange, and \textit{o}-\hh\ must also be formed to conserve the total nuclear spin angular momentum.

A potential energy surface based on high-level \textit{ab initio} calculations is available for the H$_5^+$ system~\citep{xie2005}. Based on the surface stationary points, a barrier of 52.2 cm$^{-1}$ must be overcome for a hop reaction (\ref{hop}) to occur, and a barrier of 1565.9 cm$^{-1}$ for an exchange reaction (\ref{exch}) to occur. The dissociation energy $D_e$ is calculated to be 2903 cm$^{-1}$; therefore (H$_5^+$)$^*$ formed from association of H$_3^+$\ with H$_2$\ has sufficient energy to overcome these barriers. As such, the complex may undergo many hop and exchange processes over its lifetime, and given sufficient time, the product distribution may approach a statistical limit. As the statistical weights for the hop and exchange reactions are 3 and 6, respectively, the branching ratio $\alpha \equiv k_{\ref{hop}}/k_{\ref{exch}}$ is 0.5 in the statistical limit. Quantum reactive scattering calculations are presently unavailable on this potential energy surface, so experimental data are necessary for determining the value of $\alpha$, as well as its temperature dependence.

The only experimental determination of $\alpha$ for the H$_3^+$\ + H$_2$\ system was performed by \cite{cordonnier2000}. This study was done by spectroscopically measuring the \textit{ortho}-to-\textit{para}\ ratio of H$_3^+$\ formed in a discharge of pure \textit{p}-\hh\ at 400 K, and under these conditions, the value $\alpha = 2.4$ was derived. No measurements at lower temperatures have been reported for this system, but the isotopically-substituted reaction D$_3^+$ + H$_2$\ has been studied at a variety of collision energies using an ion trap/guided beam technique~\citep{gerlich1993}. It was observed that $\alpha$ varies substantially with the D$_3^+$-H$_2$\ collision energy. As this energy decreases, $\alpha$ approaches the statistical value of 0.5, and the value 2.4 is reached at an energy corresponding to the average collision energy at $\sim$440 K, in general agreement with the study by \cite{cordonnier2000}. However, a direct comparison of these results to H$_3^+$\ in the interstellar medium is problematic owing to the endothermicity of the reaction channel and the nonthermal reactant internal state distribution in the experimental measurement.

The final consideration for this reaction is the fraction of reactions that lead to no change in the nuclear spin modification, $S^{id}$. A large value for $S^{id}$ would indicate that nuclear-spin-changing collisions are a small fraction of the total number of H$_3^+$\ + H$_2$\ collisions, and the thermalization process would be slower than the collision rate. In fact, there is experimental evidence for this, as studies of the H$_3^+$\ + HD $\rightarrow$ H$_2$D$^+$ + H$_2$\ reaction give a rate coefficient of $3.5 \times 10^{-10}$ cm$^3$ s$^{-1}$ \citep{gerlich2002}, much slower than the Langevin rate coefficient $1.7 \times 10^{-9}$ cm$^3$ s$^{-1}$. These results lead to $S^{id} \sim 0.8$, but it is possible that $S^{id}$ could be different for the purely hydrogenic system, which is thermoneutral rather than exothermic.

\subsection{Steady State \textit{Para}-H$_3^+$ Fraction from H$_3^+$ + H$_2$: ``Bimolecular Reactive Equilibrium''}

After taking into account its chemical physics, does the steady state of the H$_3^+$\ + H$_2$\ chemical reaction lead to a completely thermalized $p_3$ in the interstellar medium?  To consider this question, we have constructed a simple steady-state model for \textit{ortho}\ and \textit{para}-H$_3^+$, in terms of nuclear-spin-dependent rate coefficients $k_{xxxx}$ for each potential sub-reaction (e.g., $k_{oppo}$: \textit{o}-\hhh\ + \textit{p}-\hh\ $\rightarrow$ \textit{p}-\hhh\ + \textit{o}-\hh).  The derivation of this model, which we shall call the ``bimolecular reactive equilibrium'' (BRE) model, is presented in the Appendix, and the resulting expression for $p_3$ is given in the Appendix as equation (\ref{eqp3}).

The rate coefficients themselves were computed using the prescription of \cite{park2007}, which takes into account both the nuclear spin branching fractions as well as energetic considerations at the state-to-state level, using a microcanonical approach.  This work has since been extended by \cite{hugo2009} to deuterated versions of this chemical reaction, and the latter authors report quantitative agreement between the two sets of calculations.  We therefore judge these rate coefficients to be reliable within the context of this theoretical approach.

The Park \& Light code (provided by K. Park, private communication 2009) requires five input parameters: the kinetic temperature, the rotational temperature of H$_3^+$\ and H$_2$, and the three branching fractions $S^{id}$, $S^{hop}$, and $S^{exch}$. For these calculations, the rotational temperature was held at 10 K in each nuclear spin manifold in order to have the vast majority of \textit{o}-\hhh\ in (1,0) and \textit{p}-\hhh\ in (1,1). Therefore, we express the inputs to the model in terms of only three parameters: $T \equiv T_{kin}$, $S^{id}$, and $\alpha$, as $S^{id} + S^{hop} + S^{exch} = 1$ and $\alpha = S^{hop}/S^{exch}$. The code then outputs all of the rate coefficients required in equation (\ref{eqp3}). For a single set of branching fraction values, the rate coefficients were calculated for $10\leq T \leq 160$ K in steps of 10 K, and $p_2$ was set to its thermal value for each calculation.

Figure \ref{p3p2_2} shows the results of the BRE model for a fixed value of $\alpha=0.5$ for various values
of $S^{id}$ ranging from 0.1-0.9; similarly, Figure \ref{p3p2_3} shows results for fixed $S^{id}=0.5$ and various $\alpha$ ranging from 0-$\infty$.  The results of the calculation are not particularly sensitive to the fraction of collisions that are reactive (as traced by $S^{id}$) or the ratio of the hop to exchange outcomes ($\alpha$). Since in all cases $p_3$ falls near its thermal value, these results suggest that regardless of the values of $\alpha$ or $S^{id}$, the H$_3^+$\ + H$_2$\ reaction should essentially thermalize the H$_3^+$\ nuclear spin species. This stands in clear contradiction to the reported astronomical observations in diffuse molecular clouds, with the exception of X Per. The discrepancy between $T_{01}$ and $T$(H$_3^+$) cannot be explained by the BRE model, and must then be explained by a lack of equilibration via this chemical reaction.

\begin{figure}
\epsscale{1.0}
\plotone{h3h2_astro_alpha_color.eps}
\caption{BRE calculations of the \textit{para}-H$_3^+$ fraction as a function of the \textit{para}-H$_2$
fraction, under the influence of the H$_3^+$ + H$_2$ reaction.  The thin solid line represents the thermal limit
(as in Figure \ref{p3p2_1}), and the circled crosses represent the results of our calculations (based on
Park \& Light's model) for $\alpha=0.5$ and various values of $S^{id}$ ranging from 0.1 (small purple) to 0.9 (large brown). Each cluster of crosses represents a calculation at a single temperature, ranging from 10 K (upper right) to 160 K (lower left) in steps of 10 K. Also plotted are the nascent H$_3^+$\ distribution and the astronomical observations.}
\label{p3p2_2}
\end{figure}

\begin{figure}
\epsscale{1.0}
\plotone{h3h2_astro_sid_color.eps}
\caption{Same as Figure \ref{p3p2_2}, except that $S^{id}$ is held at 0.5 and $\alpha$ varies between 0 (small purple) and $\infty$ (large brown).}
\label{p3p2_3}
\end{figure}

An interesting aspect of these results is that the steady state $p_3$ at some temperatures is actually {\em below} the value of 0.5 expected based on statistical weights alone (often called the ``high-temperature limit'').  This appears to be a robust result for $\alpha > 0.5$, at least in the range of $S^{id}$ explored here.  This effect may have been observed experimentally in our group's recent measurements of supersonically expanding hydrogen plasmas.  \cite{tom2010} reported $p_3 = 0.491 \pm 0.024$ for a normal hydrogen ($p_2=0.25$) plasma at $\sim80$ K, and \cite{kreckel2010} reported $p_3 = 0.479 \pm 0.02$ in a warmer ($\sim200$ K) normal hydrogen and argon plasma.\footnote{Recent measurements in our laboratory have confirmed, with higher statistical significance, $p_3 < 0.5$ in hollow cathode plasmas containing normal hydrogen.  These results will be reported elsewhere, but it should be noted that $p_3$ in these plasmas may be influenced by three-body collisions due to the higher number densities.} Finally, in work outside our laboratory, \cite{kreckel2007} have reported $p_3 = 0.4$ in a low-temperature ion trap. All of these measurements suggest that it is in fact possible to achieve $p_3 < 0.5$, and lend some evidence to support the calculated results.

\subsection{Steady State \textit{Para}-H$_3^+$ Fraction from H$_3^+$ + H$_2$ and H$_3^+$ + e$^-$}

We now consider whether there are enough reactive collisions within the lifetime of an average H$_3^+$ in
diffuse molecular clouds to bring the spin modifications into BRE.  The destruction of H$_3^+$ in
such clouds is dominated by dissociative recombination (DR) with electrons, and the lifetime is simply $\tau_{life} = (k_{DR} n(e^-))^{-1}$ (the reciprocal of the destruction rate), where $k_{DR}$ is the dissociative
recombination rate coefficient.  The average time between reactive
collisions can be expressed as $\tau_{rxn} = (k_{rc} n(\rm{H}_2))^{-1}$, where $k_{rc}$ is the reactive
collision rate for H$_3^+$ + H$_2$.  The average number of collisions an H$_3^+$ will experience is then ${\cal N}_{rxn} = \tau_{life}/\tau_{rxn} = [k_{rc}/k_{DR}] [n(\textrm{H$_2$})/n(e^-)]$.

Assuming for the moment that $k_{DR}$ is independent of the nuclear spin modification, we adopt a typical value (for $T\sim70$ K) of $k_{DR}=2 \times 10^{-7}$ cm$^3$ s$^{-1}$ \citep{mccall2004}.  The ratio $n(\textrm{H$_2$})/n(e^-)$ can be rewritten as $f/2x_e$, where $x_e$ is the electron fraction, typically $1.5 \times 10^{-4}$ assuming charge neutrality and that C$^+$ is the dominant ionic species \citep{cardelli1996,sofia2004}.  If we adopt $f=0.9$, and take $k_{rc}$ to be the full collision rate of H$_3^+$ + H$_2$ \citep[$1.5 \times 10^{-9}$ cm$^3$ s$^{-1}$;][]{adams1987}, we find that ${\cal N}_{rxn} \sim 20$.  However, if we instead adopt the smaller reactive rate coefficient $\sim 3 \times 10^{-10}$ cm$^3$ s$^{-1}$ of \cite{gerlich2002}, we find that ${\cal N}_{rxn} \sim 5$.  With such a small number of collisions in the lifetime of H$_3^+$, $p_3$ may not reach the value predicted by equation \ref{eqp3}.  In the appendix we derive a more complete steady state expression (equation \ref{ssp3}) including the effects of both the H$_3^+$ + H$_2$ reaction and nuclear-spin-dependent DR rates ($k_{e,p}$ and $k_{e,o}$ for \textit{p}-\hhh\ and \textit{o}-\hhh).

We call this model simply the ``steady state'' model, and we adopt the values $f=0.9$ and $x_e = 1.5 \times 10^{-4}$ as before. Figure \ref{p3p2_4} shows the results of this steady state model if we assume that the DR rate coefficient is the same for both nuclear spin modifications \citep[we have adopted the temperature-dependent value of][]{mccall2004}. In this case, the values of $p_3$ depend quite sensitively on $S^{id}$, as this represents the fraction of H$_3^+$\ + H$_2$\ collisions that are nonreactive during the relatively short lifetime of H$_3^+$.  Consequently with higher values of $S^{id}$ (larger circles in Figure \ref{p3p2_4}), the \textit{p}-\hhh\ fraction in steady state is closer to the nascent fraction.  For $S^{id}=0.9$, which corresponds to a reactive rate coefficient of $k_{rc}=1.9\times10^{-10}$ cm$^{3}$ s$^{-1}$, the calculated $p_3$ are in reasonable agreement with most of the observations. The upper range of the X Per uncertainty is consistent with $S^{id}=0.7$.

\begin{figure}
\epsscale{1.0}
\plotone{dreq_astro_alpha_color.eps}
\caption{Steady state calculations of the \textit{para}-H$_3^+$ fraction as a function of the \textit{para}-H$_2$
fraction, under the influence of both the H$_3^+$ + H$_2$ reaction and dissociative recombination.
The plotted quantities are analogous to those in Figure \ref{p3p2_2}. In this case, the \textit{o}-\hhh\ and \textit{p}-\hhh\ DR rate coefficients $k_{e,o}$ and $k_{e,p}$ are assumed to be equal and taken from \cite{mccall2004}. Each vertical cluster of points represents a calculation at a single temperature, beginning at 160 K in the lower left and decreasing by 10 K each point moving to the right.}
\label{p3p2_4}
\end{figure}

In Figure \ref{p3p2_5}, we instead consider the calculated DR rate coefficients for \textit{ortho}\ and \textit{para}-H$_3^+$ presented in \cite{santos2007}.  Their prediction is that \textit{p}-\hhh\ is destroyed considerably faster by electrons at low temperatures than \textit{o}-\hhh; consequently, even for large values of $S^{id}$, the steady state $p_3$ does not approach either the nascent or astronomically-observed values. In the absence of the H$_3^+$ + H$_2$ reaction ($S^{id}=1$), $p_3$ would be governed by a steady state determined by the competition between the formation and the spin-dependent DR processes, and this is shown in Figure \ref{p3_noh3h2}.

\begin{figure}
\epsscale{1.0}
\plotone{drds_astro_alpha_color.eps}
\caption{Same as Figure \ref{p3p2_4}, except using the spin-dependent dissociative recombination rate coefficients from \cite{santos2007}.}
\label{p3p2_5}
\end{figure}

\begin{figure}
\epsscale{1.0}
\plotone{p3_dronly_v2.eps}
\caption{Steady state calculations of the \textit{para}-H$_3^+$ fraction as a function of the \textit{para}-H$_2$
fraction, under the influence of formation and dissociative recombination only.  The solid line shows the thermal limit, and the dotted line represents the results of our calculations, where we have used the spin-dependent dissociative recombination rate coefficients from \cite{santos2007}. Also plotted are the nascent H$_3^+$\ distribution (dashed line) and the astronomical observations.}
\label{p3_noh3h2}
\end{figure}

If the calculated rate coefficients of \cite{santos2007} are correct, it is difficult to explain the observed $p_3$. This is because, with the exception of X Per, the observed $p_3$ are higher than the curve resulting from the steady state of H$_3^+$\ formation and destruction using these DR rate coefficients, and inclusion of the H$_3^+$\ + H$_2$\ reaction further drives $p_3$ toward the value expected for thermal equilibrium.  Recent storage ring experiments by \cite{tom2009} and \cite{kreckel2005} both saw an increased DR cross-section when H$_3^+$\ is produced from \textit{p}-\hh; however, recent imaging results presented in \cite{kreckel2010} suggest that the ions in these experiments have been heated during extraction from the ion sources, and the difference between the \textit{o}-\hhh\ and \textit{p}-\hhh\ may therefore have been overestimated.  Further experimental work is clearly needed to pin down the enhancement (if any) in \textit{p}-\hhh\ DR, and confirmation of the theoretical predictions would also be quite helpful.

To summarize, according to our models the reaction of H$_3^+$\ with H$_2$\ is expected to effectively thermalize the nuclear spin configurations of H$_3^+$\ at steady-state, provided that sufficient collisions occur within the lifetime of an H$_3^+$. In diffuse molecular clouds, however, the average number of reactive collisions with H$_2$\ suffered by an H$_3^+$\ is small, indicating that the formation and destruction rates of the two nuclear spin species should be important. A more complete model which takes these factors into account reaches reasonable agreement with observations in 4 of 5 sight lines provided $S^{id}$ is on the order of 0.9 and \textit{o}-\hhh\ and \textit{p}-\hhh\ are destroyed at equal rates owing to DR. Reconciling the observations with the spin-dependent theoretical rates of \cite{santos2007} is difficult, and accurate experimental measurements of the spin-dependent DR rates of H$_3^+$\ at low temperature are needed.

\section{CONCLUSIONS}

While all evidence seems to suggest that $T_{01}$ inferred from ultraviolet spectroscopy of H$_2$ accurately reflects the kinetic temperature of diffuse molecular clouds, the observed excitation temperature of H$_3^+$ is clearly non-thermal in 4 of the 5 measured sight lines.  Based on the microcanonical model of \cite{park2007}, we have constructed a steady state model to predict the \textit{para}-H$_3^+$ fraction ($p_3$) if reactive collisions between H$_3^+$ and H$_2$ control the spin modifications of H$_3^+$.  Those results show $p_3$ slightly below the limit expected for full thermalization, and far from the observations.  However, a steady state model that incorporates both the H$_3^+$ + H$_2$ reaction as well as the H$_3^+$ formation (following cosmic-ray ionization) and destruction (by electron recombination) can reproduce the observed $p_3$ if the reactive collision rate is somewhat slow and the dissociative recombination rates for \textit{ortho}\ and \textit{para}\ H$_3^+$ are comparable.  Our interpretation, given the currently available data, is that H$_3^+$ suffers relatively few spin-changing collisions with H$_2$ in its lifetime, and is thus incompletely equilibrated by this reaction.  The observed \textit{para}-H$_3^+$ fraction therefore lies between the nascent fraction and the nearly-thermal fraction that would be reached with sufficient reactive collisions. If our model is correct (and the spin-dependent DR rates of H$_3^+$\ are nearly equal at low temperature), this marks the first determination of the reactive rate coefficient of the H$_3^+$\ + H$_2$\ reaction, and suggests a value on the order of $10^{-10}$ cm$^{-3}$ s$^{-1}$.

Fully quantum reactive scattering calculations of the H$_3^+$ + H$_2$ reaction would be highly desirable, as they would pin down the state-to-state rate coefficients needed to predict the interstellar \textit{para}-H$_3^+$ fraction.  Further experiments and theoretical calculations to elucidate the dependence (if any) of the dissociative recombination on the nuclear spin modification of H$_3^+$ are also urgently needed.  Once the effects of the reactive collisions and dissociative recombination are fully understood, the \textit{para}-H$_3^+$ fraction in diffuse molecular clouds can be calculated as a function of the kinetic temperature and the ratio of the molecular fraction to the electron fraction.  This, in turn, suggests that H$_3^+$ may become a useful ``thermometer'' for diffuse molecular clouds with high extinction, where ultraviolet measurements of H$_2$ are not feasible.  However, the calibration of this thermometer will require further experimental and theoretical efforts.

\mbox{}

The authors thank Brian L. Rachford for helpful discussions about the $T_{01}$ determinations, Takeshi Oka for helpful conversations about \textit{ortho}\ and \textit{para}-H$_3^+$, Kisam Park for providing the code to determine the nuclear-spin-dependent rate coefficients for the H$_3^+$\ + H$_2$\ reaction, and the anonymous referee for helpful comments.  This work has been supported by NSF grant PHY08-55633.  This work is based in part on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia),
Minist\'{e}rio da Ci\^{e}ncia e Tecnologia (Brazil) and Ministerio de Ciencia, Tecnolog\'{i}a e Innovaci\'{o}n Productiva (Argentina).  Gemini/Phoenix spectra were obtained through programs GS-2009B-Q-71 and GS-2010A-Q-60.  This paper is also based in part on observations obtained with the Phoenix infrared spectrograph, developed and operated by the National Optical Astronomy Observatory.

redpajama_set_name: RedPajamaArXiv


Druids call this time of year 'The light of the water', which, apart from being superbly poetic, is perfect for our British autumn. There is certainly plenty of water; storm Aileen (come on, Aileen! Sorry… sorry…) has hit hard across the country, with 75mph winds and flash floods. I saw evidence of the intense destruction outside a friend's house a few days ago: a horse chestnut tree had been almost rent in two. A neighbour told us how the noise came as an almighty crack when the tree came down in the middle of the night, narrowly avoiding a parked car. A display of enormous power and perhaps enormous luck, certainly for the owner of the car. Although, he is a fellow Pagan, so maybe he had honoured the right gods that week?
Naming storms is a very Pagan thing we do, isn't it? It's not just Thor, or Zeus anymore; not just the wrath or hubris of a single storm god, but the personification of every storm, every weather front; every hurricane. Donald Trump recently commented about Hurricane Harvey, saying Harvey was such an 'innocent' name, which he was roundly mocked for (at the time it was a bizarrely irrelevant comment). But it is strange, how we choose these odd, often unassuming names for these great forces of nature. Are we trying to downplay them, in the hope that they will pass us by? Is it a kind of sympathetic magic, like making a tiny poppet of a giant, to bring them down to size?
Even if this could work, I think more notice needs to be taken of the names we are choosing. Harvey means 'battle worthy'; not really as innocent as one may think, then. Irma, recently battering Barbuda, Florida and the surrounding areas, means entire, or universal. The universal hurricane. Aren't we just asking for trouble, giving storms names like this?
Closer to home, our very own Aileen means light, or light bearer, bringing us back around to the concept of Alban Elfed: light of the water. Although the equinox (physically the moment where light and dark are as equal as they can be) is a moment of balance, it is also a time of great potential. To pause in the moment of decision; to reflect before stepping forward; these are great, liminal moments in our lives, which contain massive amounts of potential energy. At its most primal, it is the moment we realise that dark is about to start winning. Winter is truly just a breath away, just the briefest turn of the earth. We can shiver and turn from that realisation, or we can embrace it; embrace the dark, and the cold, and the shadowy parts of ourselves, and keep stepping onward regardless.
The sun will turn from the golden, shining face of Lugh to a cold, silver reflection dulled by autumn clouds, seeming more like the moon than a star. The trees will shudder and disrobe, leaving a playful carpet that will eventually rot to become the beginnings of spring. And the light on the water is silver in the storm, blue on the frosty car window, then every colour in the rainbows that inevitably appear after the autumn storms have huffed and puffed themselves out.
Pause, reflect, and keep moving forward. Weather your storms, and keep an eye out for those who may struggle to weather their own.


I've taken many journeys throughout my life always trying to find my passion. It took a health crisis for me to make a move.
March 2017 I was walking in New Orleans, I stepped on Burbon Street and almost passed out. My body became numb, my breathing short and my left jaw began to tingle. This started a 15 month process of trying to figure out what was wrong with me. On top of having every typical stroke symptom, I also began to suffer with debilitating migranes and anxiety. I visited neurologists, physical therapists, acupunturists, chiropractors (note the plural on each specialist)...over 18 physicians (Western and Eastern medicine), multi MRI's and too many emergency room visits to name. I fed my soul with the Word of God, my ultimate source for healing, and I also took my natural health care into my own hands. A complete holistic diet, yoga, and meditation supported my return to health.
My goal is to support you as you return to a healthier you.
The name Leigh & Ollie is derived from my grandmother's name - Mrs. Neathel Leeollie Thornton Warner. Each of my passions directly connects with her in some way. I spent hours in the kitchen rolling dough for homemade dumplings, measuring chocolate for homemade chocolate cake and shelling peas – just so I could drink the pot likker (or pot liquor for those who think pot likker is just a little too country). And before I was allowed to get my hands on the real food she would let me make mud pies from the Alabama red dirt. Her house was filled with treasures – trunks, suitcases, washtubs, a Singer sewing machine from the late 1800's – on which my great grandmother Amanda Thornton made her living.


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Cinepolis kukatpally has huge auditoriums and it feels as though one is watching a movie in a good single screen cinema hall.Highly recommended.
fullhyd.com has 700,000+ monthly visits. Tell Hyderabad what you feel about Cinepolis (Kukatpally)!


This is a great phone, takes good pictures and work very well with the network providers, the call quality is clear and crisp. Fingerprint sensor works as it should. Fingerprint sensor works as it should. If you're looking for a new phone in this price range, you won't be disappointed. So smooth and works great.
The latest powerful smartphone from Xiaomi. Redmi 6 Pro follows the latest trend that is the notch on the front. The device does looks attractive. So far, I am loving the overall improved experience. The call quality is also crisp.
The latest budget smartphone from the company. I bought it but immediately regret the decision. I should have went with Realme 2 Pro. Redmi 6 packs very old processor with poor build quality.
A powerful budget device which looks stunning. The device has compact form factor, killer battery life, decent performance and solid display.
Redimi 6 pro is the latest offering by xiaomi and i wanted to give it a try. So far this has been a great phone with great performance, sufficient battery life which last for the whole day, then the camera's performance in proper lighting is exceptional so over all it is an all rounder and is totally worth it.
It's a powerful device with lots of good features and Mi brand tag.The display is exceptionally good but i wish they got rid of notch it takes a lot of space.Cameras are great.Performance is decent and can handle heavy gaming easily.It has a dedicated SD slot which is really helpful.
8 Pricebaba users have written their experience with Xiaomi Redmi 6 Pro 64GB.
If you own Xiaomi Redmi 6 Pro 64GB, please do leave your feedback too.
Lowest price of Xiaomi Redmi 6 Pro 64GB price in India starts at Rs. 10,990 Xiaomi Redmi 6 Pro 64GB is available on Flipkart at Rs. 10,999 and on Amazon at Rs. 10,990. Prices updated on 24th April 2019.


I don't know what came over me, but I decided to forgo my everyday make-up for a holiday navy eye. A bit dramatic for my trip to the grocery store, but perfect for any upcoming holiday parties or winter nights out.
I wanted to start with a full-coverage flawless base since theoretically I would be at previously mentioned holiday party. I used the Nars Radiant Cream Compact Foundation in the shade Siberia with a BeautyBlender. My perfect match is Mont Blanc, but I ran out of that shade so I mixed a teeny bit of Tarte's Amazonian Clay Foundation in Light, since that one is a bit dark and is also full-coverage.
To start the eye look, I applied Urban Decay's Primer Potion. For the eyes, I mainly used the Sleek i-Divine Eyeshadow Palette in Storm. First, I took the frosted champagne shade and applied that to a little over half of my lid, in the inner corner, and on the first half or so of my lower lash line. Next, I took a bit of the first gold shade on the same brush and placed that on the center of the lid, just for some added dimension. I made sure to blend these two shades very well. Flipping my brush over, I took the gorgeous navy blue shade from the same palette and applied that to the remaining part of my lid, roughly creating the shape I wanted. I then used a smaller brush to more precisely add the navy to form the outer-V shape and apply below my lash line. At this point it looked a bit crazy, so I used the lighter matte brown shade from the Sleek palette as a transition colour, applying that with a fluffy brush. I added a bit of the matte black to the outer-v to deepen it up, just a little more. For under my brow, I used Foxy from the Urban Decay Naked 2 palette. Next, I lined my eyes with liquid liner. I use Jordana Fabuliner for the line, Wet 'n Wild H20 Proof for the flick, and set it all with Blackout from UD Naked 2. I lined both my waterline and tightline with the Sumita eyeliner in Black. Finally for the eyes, I curled my lashes and applied a generous amount of tarte Gifted mascara.
For my eyebrows, I wanted them to be on the bold side to work with the dark shadows. I used tarte's the Brow Architect to fill in a strong shape. I then concealed under my eyes using the Nars Radiant Creamy Concealer in Vanilla. I contoured using the Sleek Contour Kit in Light. For blush, I used NYX Dusty Rose. As a highlight, I went all out with theBalm's Mary Lou-Manizer. It's crazy shiny. For lips, I went with Urban Decay Super Saturated Lip Pencil in Lovechild, for an easy pink. And that's it! If I had really been going to a holiday party or out-on-the-town, I would dose up on an Urban Decay setting spray.
So I am really feeling the holiday spirit! I think this is a perfect winter glam look. I'm getting a Snow Queen, Ice Princess vibe. It's fun to go a bit intense with the make-up, even without an occasion. I will definitely be posting more holiday-inspired looks in the upcoming weeks!
What are some holiday looks you would like to see next?


text:
Der Erdigriechende Schleimkopf (Phlegmacium variecolor, Syn.: Cortinarius variecolor, Cortinarius variicolor, Cortinarius nemorensis) ist ein Blätterpilz aus der Familie der Schleierlingsverwandten (Cortinariaceae). Es ist ein sehr variabel gefärbter Pilz mit einem anfangs schmierig bis klebrigen Hut, der jung mehr oder weniger violett gefärbt ist, sich aber schon bald vom Scheitel her braun verfärbt. Seine Lamellen sind in der Jugend graublau bis blass grauviolett und der knollenlose Stiel ist weder klebrig noch schleimig. Das erdig-muffig riechende Fleisch schmeckt mild und verfärbt sich mit KOH gelb. Der Schleimkopf hat warzige mehr oder weniger mandelförmige Sporen. Die Fruchtkörper des Mykorrhizapilzes erscheinen gesellig von Juli bis Oktober überwiegend in Bergnadelwäldern. Der Pilz gilt als ungenießbar oder sehr minderwertig.

Merkmale

Makroskopische Merkmale
Der fleischige Hut ist 5–15 cm breit. Anfangs ist er halbkugelig, später gewölbt bis ausgebreitet und erst im hohen Alter verflacht er. Der Hutrand bleibt lange Zeit eingerollt und kann später bisweilen hochgeschlagen sein. Die Oberfläche ist zumindest anfangs am Rand schmierig-klebrig und später trocken und schwach eingewachsen radialfaserig. Bei Feuchtigkeit kann die Huthaut aber auch deutlich schleimig sein. Der Hut ist jung violett bis lila gefärbt, wird aber schon bald vom Scheitel her fuchsig-braun. Die Violetttöne können im Alter ganz verschwinden, sodass er dann mehr oder weniger Graubraun gefärbt ist.

Die ausgebuchtet angewachsenen Lamellen stehen relativ dicht. Sie sind anfangs graublau bis graubeige gefärbt und haben oft auch eine Lilatönung. Im Alter sind sie durch das Sporenpulver mehr oder weniger zimtbraun gefärbt. Die Lamellenschneiden sind weißlich.

Der feste, volle und mehr oder weniger keulige Stiel ist 5–15 cm lang und l,5–3 cm breit. Er ist jung weißlich-grau, eventuell auch blassbläulich gefärbt und wird im Alter rotbräunlich. Er ist vom braunen Velum überfasert. Im unteren Teil ist er oft mit flüchtigen bläulich braunen Zonen geschmückt.

Das Fleisch ist anfangs weißlich und hat einen leichten Lilaton. Es verfärbt sich im Alter mehr oder weniger bräunlich. Das Fleisch hat einen deutlichen, unangenehm erdig-muffigen Geruch, der ein wenig an Rote Rüben erinnert. Mit Ammoniak oder Kalilauge verfärbt sich das mild schmeckende Fleisch lebhaft gelb.

Mikroskopische Merkmale
Die warzigen, mandelförmigen Sporen messen 10–12 × 5,5–7 µm.

Artabgrenzung
Der Pilz ist wie viele Schleierlinge und Schleimköpfe nicht leicht zu bestimmen, da der Schleimkopf sehr unterschiedlich gefärbt sein kann. Typisch für ihn ist sein unangenehmer, erdartiger Geruch, der dem Pilz den Namen gab, außerdem ist er ein typischer Nadelwaldpilz. Sein Doppelgänger Cortinarius nemorensis kommt in Buchenwäldern vor. Dieses Taxon zählt allerdings nicht mehr als eigene Art, sondern wird teils Phlegmacium largum, dem Blassen Schleimkopf, teils dem Erdigriechenden Schleimkopf zugerechnet. Die Abgrenzung ist schwierig, da der Erdigriechende Schleimkopf auch im Buchenwald vorkommen und es auch eine geruchlose Variante geben soll.

Ökologie und Verbreitung

Der Pilz kommt in Nordamerika (Kanada, USA), Asien (Japan) und Europa vor. Er ist nahezu ganz in Europa verbreitet. Im Süden reicht sein Verbreitungsgebiet von Spanien bis nach Griechenland und Bulgarien im Südosten. Er kommt ebenso im ganzen südlichen Fennoskandinavien vor. In Großbritannien findet man ihn sehr zerstreut in Schottland und England. Auch in Nordirland wurde er nachgewiesen. In den Niederlanden ist der Schleimkopf sehr selten,  während er in den Alpenländern Schweiz, Österreich und Liechtenstein recht häufig ist. Im Norden überschreitet er kaum den 58. Breitengrad. Der höchstgelegene Fundort liegt in der Schweiz auf 2060 m NN und in Österreich über 1700 m. In Deutschland ist der Schleimkopf gebietsweise häufig, kann dafür aber in anderen Gebieten sehr selten sein oder ganz fehlen.

Man findet ihn meist in Bergfichtenwäldern, wo er gerne an Waldrändern, an grasigen Stellen und in der Nadelstreu wächst. Die Fruchtkörper erscheinen meist gesellig von Juli bis Oktober (November). Oft wachsen sie in Reihen oder Ringen. Der Mykorrhizapilz ist meist mit Fichten vergesellschaftet, kommt aber auch bei Kiefern vor. Der Erdigriechende Schleimkopf bevorzugt Kalkböden, auf Silikatböden trifft man ihn wesentlich seltener an. Das Verhältnis von Ca zu Si ist 2,6. Die Höchsttemperatur liegt etwa 9 °C und die Optimaltemperatur bei 8 °C.

Systematik
Der Erdigriechende Schleimkopf wurde erstmals 1801 durch Christiaan Hendrik Persoon als Agaricus variecolor beschrieben. Dieser Name wurde 1821 durch Elias Magnus Fries sanktioniert. 1838 stellte Fries den Pilz in die Gattung Cortinarius. Dabei änderte Fries (unklar ist ob absichtlich oder unabsichtlich) die Schreibweise des Artepithetons auf variicolor, auch wenn in vielen wissenschaftlichen Werken und Datenbanken der Name Cortinarius variecolor verwendet wird. Der Name Cortinarius variecolor wurde in älteren Werken auch für Phlegmacium praestans, die Schleiereule, verwendet. Neben dem gültigen Binomen gibt es mindestens zwei weitere homotypische Synonyme: So stellte Paul Kummer den Schleierling als Pholiota variicolor 1871 in die Gattung Pholiota und Friedrich Otto Wünsche 1877 als Phlegmacium variecolor in die Gattung Phlegmacium. Daneben gibt es zahlreiche heterotypische Synonyme. Das wichtigste davon ist Cortinarius nemorensis  im Sinne von Moser und anderen Autoren, während Cortinarius nemorensis im Sinne von J.E. Lange heute mit Cortinarius largus synonymisiert wird. Der 1892 von Max Britzelmayr beschriebene Cortinarius largiusculus ist ein weiteres Synonym. Auch der 1959 beschriebene Cortinarius pseudovariecolor  wird von einigen Autoren nur als Synonym angesehen.

Weitere Synonyme sind laut Checklist of Basidiomycota of Great Britain and Ireland: Cortinarius crassus im Sinne der britischen Autoren und Cortinarius cyanopus, sowie Cortinarius varius im Sinne von Cooke.

2022 wurde die ehemalige Untergattung Phlegmacium, die den Erdigriechenden Schleimkopf beinhaltet, als eigene Gattung ausgegliedert. Deshalb heißt die Art jetzt wieder Phlegmacium variecolor.

Bedeutung
Obwohl der Erdigriechende Schleimkopf in älteren Pilzbüchern teilweise als essbar, wenn auch als sehr minderwertig bezeichnet wird, gilt er heute weitgehend als ungenießbar. Speisepilzsammler, die auf der Suche nach den ähnlichen Schleiereulen (Phlegmacium praestans) sind, sollten auf den Geruch achten. Der Erdigriechende Schleimkopf unterscheidet sich durch seinen erdigen, an Rote Bete erinnernden Geruch.

Quellen

Einzelnachweise

Weblinks

Schleierlingsverwandte
Ungenießbarer Pilz

redpajama_set_name: RedPajamaWikipedia


text:
userID password
Top run
TOP RUN WORKING FLAT OUT ON SUBARU WRX STI CARS
22nd June, 2015
The Top Run team is working flat out to build the TCR-spec Subaru WRX STi in time to make its maiden appearance in the TCR International Series event at Singapore on September 20th.
The first two cars were delivered to the workshop of the Italian team last week.
"We are working on the first car to prepare the shell and fit the roll-cage, while the second one is being used to fix the aerodynamics," explained Team Principal Antonio Agnello, who added: "We haven't waited for the cars to start working. We have made headway by building the gearbox, the braking system and most of the aerodynamic kit. We have already received the dampers and the wheels. Now we must check which pieces of the original parts of the suspension may be retained and which ones need to be re-designed. The most difficult task is to convert the car to front-wheel drive, which also implies a complete re-distribution of weight."
The agreement between Top Run and Subaru provides for delivery of two further cars per month. The next step will be to start track testing.
Agnello revealed: "We aim to start testing by the first week of August and, if everything goes according to plan, we will apply for the homologation immediately afterwards. To race in Singapore is a priority goal. We are aware that we have a great deal of work to do, but in our rally years we have built a lot of experience in this respect. And this makes us confident!"
Fabio Ravaioli
TCR Media
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We are hosting our next #KotaDay in February and we would love to see you there, especially if you are a woman entrepreneur or work in a nonprofit with a mission to empower women. The theme for this year's #KotaDay is Storytelling for Women's Empowerment. You are also welcome to join us if you are a student interested in women's empowerment and storytelling.
The first half of the day is dedicated to our guest speakers. Our keynote speaker is the Education Director of Democracy Now: Simin Farkondeh, an award-winning filmmaker, artist, educator and activist. In addition, there will be expert insights on public speaking, theater as medium, website design, photography, virtual and augmented reality followed by afternoon workshops on actual storytelling challenges faced by nonprofits.
Read more about our speakers and workshop leaders here and take a look at the program below!


text:
Esi Awuah is a Ghanaian academic and former vice chancellor of the University of Energy and Natural Resources in Sunyani, Ghana.

Early life and education
Esi Awuah is the eldest child of Emmanuel Broni Asare and Margaret Annan. Her father is from Akim Oda, Ghana and served as the Deputy Chief Conservator of Forestry in the Ashanti and Brong Ahafo regions. Her mother, Margaret Annan, is a retired nurse's aid is from the village of Gomoa Dago in Ghana. Awuah completed her ordinary level education at Akim Oda in 1973 and finished her advanced level education at Aburi Girls' Secondary School in 1975. She earned a Bachelor of Science at the University of Science and Technology (renamed Kwame Nkrumah University of Science and Technology, KNUST) in Kumasi.

After completing her national service at the Forest Products Research Institute in Kumasi (now the Forestry Research Institute of Ghana), she took a job as a research assistant at the Department of Civil Engineering. In 1981, Awuah obtained a World Health Organization scholarship to study environmental sciences in the United States at the State University of New York College of Environmental Science and Forestry in Syracuse. In 1998, she was awarded a fellowship from the Dutch government to pursue a PhD in waste-water treatment at the Institute of Infrastructural, Hydraulic, and Environmental Engineering (now UNESCO-IHE) at Delft in the Netherlands.

Career
Awuah began her academic career at KNUST in 1986 in the Department of Civil Engineering. She became a senior lecturer in 1996, an associate professor in 2002, and applied for full professorship in 2008.

Awuah has taught courses at KNUST, the University of Cape Coast, and the University of Education, Winneba, at both the undergraduate and graduate levels. She has also developed curricula in several disciplines used to establish academic programs in Ghana and Liberia.

As a researcher with special interests in water supply, sanitation, waste water treatment, hygiene, and environmental risk assessment, Awuah supervised several water quality analysis projects to raise awareness about pollution in urban streams and ground water contamination from onsite sanitation systems. Her research developments include weighting systems for impact assessment of water developments in Ghana and arsenic removal from ground water using local materials. Other focus areas include major pathogen removal mechanisms in waste stabilization ponds, the role of arsenic in Buruli ulcers as well as environmental practices and risk factors associated with the disease, risk factors associated with waste-water use in agriculture, the role of arsenic and health impacts associated with charcoal production, and food vendor hygiene.

Awuah has over 100 publications to her credit in refereed journals, conference papers, environmental reports, and book chapters. She has supervised more than 200 undergraduate students and over 50 postgraduate students and directed several international research collaborations in water supply, environmental health, and sanitation. Notable among them are the EU-funded SWITCH project on urban water management and the CapWa project on capturing of water vapor to conserve water and energy in industries, the African SNOWS project on research capacity building for water supply, environmental health, and sanitation, and the SMART sanitation project to develop smart toilet technologies for the urban poor. These projects have generated millions of dollars for the institutions involved and established Awuah as a worldwide expert.

In addition to her 32-year teaching career, Awuah has held several leadership positions at KNUST. She was head of the Department of Environmental and Technology at its Institute of Science and Technology for Africa from 2004 to 2006, head of the Civil Engineering department from 2006 to 2008, and dean of the Faculty of Civil and Geomagnetic Engineering from 2008 to 2010. In addition, she served on the College of Engineering Appointments and Promotions Committee, the College Infrastructural Committee, and the College of Engineering Library Committee. She was also a member of the Disciplinary Committee, and as a member of the Faculty of Social Science Board, is the lecturer in charge of Environmental Quality Engineering.

She is an executive board member, representing the African region, of the Organization of Women in Science from the Developing World, and serves on several other local and international boards, including the World Water Supply and Sanitation Collaborative Council, the International Foundation for Science, SPLASH, the EU Body for Water Supply and Sanitation, Water Aid Ghana, and Zoom-lion Ghana Limited.

In the late eighties and early nineties, Awuah devoted attention to addressing the issue of HIV/AIDS. She also led a team of Cornell University students to organize a workshop on hygiene education in Bimbilla. The group also purchased and installed water pumps in the community.

Among her professional honors, Awuah received a UNESCO Mondialogo Award in 2007 for innovative research in engineering. She was also recognized in 2008 by the Ministry of Local Government and Rural Development in Ghana during the international year of sanitation. In 2011, she received the silver award for best research in the area of environment, water, and sanitation, during the first National Science Congress in Ghana.

Personal life
Awuah attends the Mount Zion Methodist Church in Kotei, Kumasi, where she is an organist and choir member. She is married to R. T. Awuah, a plant pathologist and former principal of the College of Agriculture at the University of Education, Winneba (Ashanti Mampong Campus), and former dean of the Faculty of Agriculture at KNUST. The couple have two sons, Ato and Kobbina.

References

External sources
 Esi Awuah

Fellows of the African Academy of Sciences
Living people
Year of birth missing (living people)
Vice-Chancellors of universities in Ghana
Alumni of Aburi Girls' Senior High School


Find a new Kia Soul at your local Peoria, IL Kia dealership.
Overview Totally transformed from what you've seen before, the 2018 Kia Soul at Mike Miller Kia in Peoria, Illinois is a feast for the eyes that promises to be kind to your wallet. The 2018 Kia Soul is a compact four-door ideal for getting you in and out of the city in the most efficient way possible, all while making it easy to grab a parking spot. Its compact design is still roomy, giving you and friends plenty of space during your next weekend getaway. What's more, the 2018 Kia Soul boasts the latest in safety innovations to give you peace of mind on the road ahead. See this compact crossover for yourself by visiting Mike Miller Kia today.
Why Us? At Mike Miller Kia in Peoria, IL we're committed to giving you a car-buying experience you won't soon forget. That starts with our team touring the lot with you and helping you find vehicle that suits your lifestyle best. Afterwards you can speak with our seasoned financing team, one ready to work with you and your credit history to find the best possible auto loan rate. Contact us today to experience our stellar customer service first hand.
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text:
Holiday online auction aids student scholarships
Wendy Patton
Executive Director of the Foundation
wpatton@cgcc.edu, (541) 506-6104
Columbia Gorge Communty College Foundation launches its first-ever Holiday Online Auction Wednesday, Dec. 1, offering people an early start to holiday shopping while supporting student scholarships.
"More students are returning to Columbia Gorge Community College, working hard to complete their education in spite of the pandemic," said Wendy Patton, CGCC Foundation executive director. "This is welcome news, but it comes as our capacity to fundraise has been constrained by COVID-19."
The holiday auction is modeled after the Foundation's successful online auction this past spring. Bidding starts Dec. 1 and concludes Dec. 4. The Foundation invites sponsors and donations of auction items or experiences.
Bidding will happen on-line. Winners will be notified by email, and may pick up their items at either The Dalles or Hood River campuses.
"It's a great way to support students' success and get a jump on your holiday shopping," Patton added. To donate or sponsor, email foundation@cgcc.edu, or visit www.cgccfoundation.org . For information, call Wendy Patton, (541) 506-6104.
"At the CGCC Foundation, we believe our entire community benefits when every student has access to the tools and resources needed to support success in school and in life," Patton said. "Your financial support allows the foundation to further its mission of building dreams and transforming lives by creating opportunities for lifelong learning. A commitment to education truly affects and improves the lives of people in our community."


I am still new (in my mind at least) as I only started blogging in June of this year.
It's getting to know new bloggers, I have discovered so many new book-blogs these past few months, and I love reading other people's point of view on books I have already read. It has also made my already convoluted TBR list bigger. There are so many passionate bloggers out there who make me want to read even more books that I usually read.
My favorite books that I've read this year are Chasing Magic, Stormdancer, The Iron Prince and Anna Dressed in Blood.
One is finding so many new friends. Another is that I actually sometimes get ARC's now. I love being able to read books before every other reader gets their hands on them.
Hmmm...I don't know about BIGGEST, but I'm currently reading The Diviners by Libba Bray and it is full of 1920s slang. I can almost always get the context, but some of the phrases are really weird.
For example: "Ida was a real tomato who was not hitting on all sixes."
Another character translates for the adult in the room: "She was pretty gullible."
Sounds like a lot of fun! There's nothing like having to decipher slang.
Wow that is not what I would think upon reading that. Shows you how much I know about 1920s slang. lol I think I would be really lost in that book. Yikes!
My word is really out there. Okay, at least it was for me, but maybe I am either too old or was too sheltered. lol Have a great weekend.
it must be fun to have a book like that.
I really couldn't think of a word today! I know I did check one this week, but do you think I can remember it??
Hi Allison--old follower. Unless I can determine a word from context, I will revert to the good ole dictionary.....see my post at bethartfromtheheart.blogpot.com...it's a big word!
Yeah that would be difficult if the book is based in another time! I would be looking words up too!
Wow, I never would have guessed from the first slang what it meant. The 1920s seems to be a really interesting era, and I love those flapper dresses! Hehe.
That's a great quote. One of the reasons I love historical novels is the lingo.
Thanks for stopping by last week.
I really want to read The Diviners. I love lingo like that actually!!
Just stopping by to share the FF love :) I am so excited to be featured by you today!!
My God! so many words and my mind just went blank!
Thanks again for hosting this great blog hop! I have to say, I don't know if I could tolerate a whole book like that :-) Thanks for sharing.
Slang is always interesting to read. Like you I can usually figure out the meaning through context, but it does take time. Old follower.
I love learning new words, and slang is always fun too :) Thanks so much for stopping by! Hope you have a wonderful weekend!
one of the things I love about my Kindle Fire, is how handy it is to look up words , or to see how to pronounce them as well, I always highlight them, to look back later on as well.
Thanks for stopping by my FF Post! Slang from a different time period can be difficult! I usually have to try and infer the meaning from the surrounding sentences. Have a great weekend!
That's definitely new slang to me. I wouldn't have thought that's what that meant! Here's my F&F post!
Ooh slang is difficult- and not as easy to look up! I am only about 100 pages into Casual Vacancy - I think you are further along with the audiobook! :) Thanks for stopping by my FF post!
I love books written in the olden days so thats an interesting answer to me.
thnx for stopping by my FF!
Hi, there. I'm a brand new book blogger and am following your blog.
Hey Alison! Sorry I missed this week #FF. I went to the Austin Teen Book Festival this weekend :) I hope you have a great week.
I'm new to the whole blogging world, but I'm excited none the less! I would have never guessed there were so many blogs I would love out there, the link list is awesome.


Easy 2-3 mile, 300 ft gain hike on nature trail loop in scenic Ed Davis Woodlands Park. Outstanding Ash, Black Walnut, and Oak woodlands. Meet 9 AM at Santa Clarita Rideshare outside gate to Park. Bring water and snack.


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