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% astro-ph/0508480

\documentclass[12pt,preprint]{aastex}

\shorttitle{A Hot Helium Plasma in the GC Region}
\shortauthors{Belmont et al.}

\begin{document}
\title{A Hot Helium Plasma in the Galactic Center Region}

\author{R. Belmont and  M. Tagger}
\affil{CEA  Service d'Astrophysique, UMR \lq AstroParticules et 
Cosmologie\rq \\ Orme des Merisiers, 91191 Gif-sur-Yvette, France}
\email{belmont@cea.fr} \email{tagger@cea.fr}
\author{M. Muno, M. Morris, and S. Cowley}
\affil{Department of Physics and Astronomy, University of California, 
Los Angeles, CA 90095, USA}
\email{mmuno@astro.ucla.edu} \email{morris@astro.ucla.edu} 
\email{cowley@physics.ucla.edu}
\altaffiltext{1}{UMR “Astro-Particules et  Cosmologie"}

\begin{abstract}
Recent X-ray observations by the space mission Chandra confirmed the 
astonishing evidence for a diffuse, hot, thermal plasma at a 
temperature of $\sim$ 9.~$10^7$~K ($\sim $ 8~keV) found by previous 
surveys to extend over a few hundred parsecs in the Galactic Centre 
region. This plasma coexists with the usual components of the 
interstellar medium such as cold molecular clouds and a soft (~0.8 keV) 
component produced by supernova remnants, and its origin remains  
uncertain. First, simple calculations using a mean sound speed for a 
hydrogen-dominated plasma have suggested that it should not be 
gravitationally bound, and thus requires a huge energy source to heat 
it in less than the escape time. Second, an astrophysical mechanism 
must be found to generate such a high temperature. No known source has 
been identified to fulfill both requirements. Here we address the 
energetics problem and show that the hot component could actually be a 
gravitationally confined helium plasma.  We illustrate the new 
prospects this opens by discussing the origin of this gas, and by 
suggesting possible heating mechanisms.
\end{abstract}

\keywords{Galaxy: center --- X-rays: ISM --- plasmas --- Galaxy: 
abundances---  ISM: magnetic fields --- ISM: abundances}

\section{INTRODUCTION}

Because of the strong dust absorption at optical wavelengths, X-ray 
astronomy is one of the most powerful tools to probe the central part 
of our Galaxy. For about twenty years, diffuse X-ray emission 
\citep*{Worall82,Warwick85} associated with intense iron emission line 
at 6.7 keV \citep{Koyama86} has been reported at the Galactic Centre. 
Although some emission is seen as far out as 4kpc, it strongly peaks in 
the~$\sim$~150 inner parsecs of the Galactic Centre region  
\citep{Yamauchi90, Yamauchi93}. More recently, the H- and He-like 
K-lines of Si, S, Ar, Ca and the H-like Fe line at 6.9 keV have been 
resolved by ASCA \citep{Koyama96}. These lines and the associated 
continuum are produced by an optically thin, hot plasma, but the 
spectra are inconsistent with a single temperature model 
\citep{Koyama96}. The low-energy spectrum results mostly from a 0.8~keV 
plasma; but the continuum at higher energy and the 6.7 and 6.9~keV iron 
lines require a thermal, 8~keV plasma \citep{Muno04}.

The temperature, patchy spatial distribution, and total energy of the 
soft (0.8~keV) component are compatible with a supernova origin 
\citep{Muno04}. Supernova remnants are the most powerful source of 
energy for heating the interstellar medium \citep{Schlickeiser02} and 
for generating plasmas in this temperature range at their shock front. 
The origin of the 8 keV plasma, on the other hand, is more puzzling. A 
simple comparison of the escape velocity at the Galactic Centre with 
the sound speed has suggested that it is not confined by the Galactic 
gravitational potential: the escape velocity estimated from different 
studies \citep{Sanders72, Breitschwerdt91, MWZ96} is about 
1000-1200~km~s$^{-1}$ whereas,  for a plasma of solar abundances, the 
typical sound speed is more than 1500~km~s$^{-1}$. Assuming the gas 
flows out at the sound speed, the time to escape from the X-ray 
emitting region \citep[$\sim$70~pc,][]{Yamauchi90} is typically 
4.$\times10^4$ years, orders of magnitude shorter than the radiative 
cooling time \citep[$\sim 10^8$~years,][]{Muno04}. The power necessary 
to heat this plasma over such a short time and in such a homogeneous 
manner exceeds by far any known or expected source and this energetics 
problem has led to much speculation.
For instance, the hot plasma has been suggested to be confined by a 
toroidal magnetic field \citep{Tanuma99}. However, besides the 
intrinsic difficulties of such a confinement (with respect to e.g. the 
Parker instability), radio observations show many magnetic non thermal 
filaments, the strongest of which are mostly perpendicular to the 
Galactic plane \citep{Yusef04}. The non thermal filaments are often 
considered as tracers of a pervasive, mostly poloidal magnetic field 
\citep{Morris96, Chandran00}, which would not confine the hot plasma.
Furthermore, there is no adequate explanation for the high temperature 
of this plasma. First, the temperature of supernova remnants has never 
been observed to be more than~$\sim$~3~keV after, at most, a few 
hundred years \citep[see][for an example]{Hwang02}. The earlier phases 
are hotter but too short to explain the energy and smoothness of the 
diffuse emission at 8 keV. Second, although the hot spectral component 
resembles the emission from faint point sources, recent Chandra 
observations put stringent upper limits on the luminosity of these 
sources, which would thus have to be so numerous that their nature 
would also be a mystery. The most favoured candidates are Cataclysmic 
Variables (CVs), which are 10 times too rare to account for the 
observed emission \citep{Muno04}. Also, Chandra observations provide no 
evidence that the hard X-ray spectrum results from the interaction 
between a single-temperature soft plasma with kT=0.3 keV and nonthermal 
electrons \citep{Masai02}; the spectra are found to be more consistent 
with a thermal origin. Finally, it has been suggested that a recent 
strong activity of Sgr A$^*$ might have heated the plasma to a high 
temperature in two ways \citep{Koyama96}. But neither matter heated in 
the very centre 50,000 years ago and expanding across the vertical 
magnetic field nor a single shock starting 300 years age would have 
travelled out to 150~pc. Moreover, in both cases such recent heating 
would have generated a plasma far from ionisation equilibrium and with 
different ion- and electron temperatures which are not supported by the 
most recent observations with Chandra \citep{Muno04}

\section{A HOT HELIUM PLASMA}

Here, we propose an alternative explanation for the 8 keV component. 
Previous models had implicitly assumed a global behavior for a plasma 
of solar abundance and had compared a global sound speed with the 
escape speed. However, we show that this is not consistent since the 
medium is collisionless on the relevant timescale.

\subsection{Ambipolar Separation of Elements}

The inferred plasma is composed of several species (electrons, protons, 
helium ions and other heavy ions) whose respective behaviours are 
different. For instance, electrons separate from ions because of their 
very low mass, and the resulting electrostatic field couples all the 
species in the plasma. The magnetic field could in principle also 
modify the particle dynamics, but we are interested in their vertical 
motion, i.e., in the geometry we consider, the direction parallel to 
the field, along which the field has no influence. The general case for 
a multi-species plasma is complex and will be discussed below, but the 
solution for a two-species plasma (electrons + one ion species) is 
enlightening. In this case, the electric field keeps ions and electrons 
closely coupled, transmitting the electron pressure gradient to the 
ions and helping them to escape. Both ions and electrons must be 
included in the discussion whether the plasma is bound or escaping; 
this can be taken into account by using a mean \lq molecular\rq~weight  
$\mu = (n_i m_i + n_e m_e)/(n_i m_p+n_e m_p) $ when estimating the 
thermal velocity. Such a plasma is bound if the mean thermal velocity 
satisfies:
$$ \bar{v}_{th}=\sqrt{\frac{k_b T}{\mu m_p}} <  v_{esc} $$
For instance, the mean thermal velocity of a pure hydrogen plasma 
($\mu$=.5) at 8~keV is 1250~km~s$^{-1}$. This is larger than the escape 
velocity and this hydrogen plasma should escape. We thus reach the same 
conclusion as previous studies which assumed a hydrogen dominated 
plasma. On the contrary, the effective thermal velocity of a pure 
helium plasma ($\mu$=4/3) is 750~km~s$^{-1}$, lower than the escape 
speed. Such a pure helium plasma would be bound by the Galactic 
potential, as would pure plasmas of heavier species.

However the hot plasma in the Galactic Center Region is composed of 
more than one ion species.
If we consider for simplicity only hydrogen and helium (the case of a 
plasma with more species is not presented here but is straightforward 
and leads to the same conclusions), their respective behavior is 
determined by their mutual interaction. On the one hand, for a plasma 
of solar abundance, the few helium ions cannot influence the protons' 
kinetics and hydrogen ions have to escape, whatever the collisional 
regime is. On the other hand, the escape of helium depends on the 
collisions with protons: in a fully collisional regime, escaping 
protons exert a strong drag on helium ions which must then also escape; 
but in a collisionless regime, helium ions do not feel protons and 
remain bound in the Galactic plane.

At the inferred number density of n$_{\rm H}$= 0.1~cm$^{-3}$, the 
collision time of protons escaping at their thermal velocity on helium 
ions for Coulomb collisions is $\tau_{\rm He/H}$= 1.$\times10^5$~years. 
This is substantially longer than their free escape time ($\tau_{\rm 
esc} \approx 4.\times10^4$~yr).  Turbulence might  cause a diffusion of 
the protons, and thus significantly lengthen their escape time to the 
point that it would become longer than their collision time with 
helium. However we believe that neither large-scale distortions of the 
magnetic field lines, nor small-scale turbulence, can be sufficiently 
strong to achieve this. For milligauss fields \citep{Morris96} or even 
fields in equipartition with the gas pressure \citep{LaRosa05}, a large 
scale turbulence would be very difficult to reconcile with the 
straightness and the vertical direction of the observed non thermal 
filaments. Furthermore with a vertical field, any turbulent 
perturbation within the disc would travel vertically out of the disc, 
so that contrary to the ordinary ISM, it would be very difficult to 
sustain a high level of turbulence. A pervasive source of turbulence of 
unknown origin would then be necessary up to more than 70~pc above the 
disc. The motion of protons relative to the bound plasma might provide 
a local source of small scale turbulence but again, we believe that it 
cannot reach a high amplitude. Indeed, contrary to e.g. the case of 
cosmic rays near shocks, the hydrogen ions escape with a streaming 
velocity close to their thermal velocity or slower; as helium and 
hydrogen have the same temperature and protons are rare, the 
stabilizing resonance of waves with helium atoms would act strongly 
against the destabilizing resonance with protons, so that it would be 
difficult for their slow escape velocity to generate turbulence and a 
diffusion capable of significantly lengthening their escape time. This 
is the reason why we consider Coulomb collisions due to a freely 
escaping plasma rather than assuming a diffusive escape with a 
coefficient of unknown origin.

The comparison of time scales lead us to suggest that protons leave 
this region without dragging other elements with them. This kind of 
selective evaporation is common in neutral stratified planetary 
atmospheres, but is slightly more complex here, because of the  ionized 
nature of the plasma. We thus simply propose that the hard emission 
associated with a 8~keV plasma originates from a helium plasma confined 
in the Galactic plane.

In the process producing this plasma, hydrogen ions are present but 
escape on the short time scale discussed above. If the lifetime of 
helium is long enough, the density of hydrogen remains thus very low 
has no significant effect on the dynamics of the bound multi-component 
plasma.
The equilibrium of this plasma  is governed by a full set of 
hydrostatic equilibrium equations coupled by the electrostatic 
potential. Assuming helium dominates, it is found that, without any 
strong mixing process, other ion species must stratify depending on 
their mass. The diffusion and stratification of ionized elements have 
also been studied in the gaseous medium of galaxy clusters 
\citep{Fabian77, Gilfanov84}, but there the strong turbulence may 
significantly inhibit the sedimentation \citep{Chuzhoy03, Chuzhoy04}.

\subsection{Revised Properties}

Because of the high temperature, hydrogen and helium are fully ionized, 
so no line can be observed. However, the assumption of a helium plasma 
changes the usual interpretation of X-ray spectra from the Galactic 
Center Region. Reconsidering the spectral fits of Chandra data on the 
diffuse emission \citep{Muno04} with this hypothesis leads to a number 
density for helium of n$_{\rm He}$= 0.04~cm$^{-3}$, slightly lower than 
the ion density (0.1~cm$^{-3}$) found in the hydrogen model. These fits 
also give an abundance ratio of iron relative to helium of only a third 
of the solar value. This may result from the source of this gas: for 
instance, since refractory elements in molecular clouds are mostly 
trapped in grains, a process which extracts the gas from these clouds 
before it gets heated (thus without extracting the grains) might 
explain a low abundance of these elements. This could be checked by 
considering the abundance of argon, which is not refractory and should 
have a normal abundance relative to helium, using its hydrogen-like K 
line at 3.3~keV. This line is very weak, but originates only in the 8 
keV plasma, without contamination from the other phases. It is thus 
possible that existing and future deep observations with XMM-Newton and 
ASTRO-E2 could provide the statistics sufficient to constrain the 
abundance ratio of argon over iron (A. Decourchelle, private 
communication).

The lifetime of the bound helium plasma is limited, either by radiative 
losses or, given the similarity between the escape and sound 
velocities, by other processes such as evaporation from high latitudes. 
Radiative losses, for instance, only require approximately 
3.$\times10^{37}$~erg/s in the central $\pi*150^2*140$~parsec$^3$, i.e. 
less than or comparable with the expected thermal energy released by 
supernovae in this region of the Galaxy \citep{Yamauchi93, Muno04}. As 
discussed above, supernovae are unlikely to create this hot phase, but 
it is now easier to seek alternative energy sources.

\subsection{Heating mechanisms}
A possibility would be to  consider the heating associated with 
instabilities and magnetic reconnection, especially in the transition 
region between the dense molecular ring at $\sim$150 pc and the 
central, hot region dominated by the pervasive poloidal field 
\citep{Chandran01}.

We also suggest that viscous friction on molecular clouds flowing 
toward the Galactic Center might be important so that the high 
viscosity of the hot plasma could permit the gravitational energy of 
the clouds to be tapped as they slowly spiral in toward the Galactic 
Centre \citep{Bally88, Miyazaki99, Oka01}. Indeed, a hot magnetized 
plasma is highly viscous \citep{Braginskii65}. This is however bulk 
viscosity, acting on compressional motions (i.e. here on the 
compressible part of the wake created by a molecular cloud), rather 
than the shear viscosity familiar in ordinary fluids. Wakes in plasmas 
have been extensively studied in the context of artificial satellites 
and of the interaction of Io with Jupiter's magnetosphere. In ordinary 
fluids they contain sound waves and vortices and in magnetized plasmas, 
they are more complex: vortices become Alfv\'en waves, and there are 
two magnetosonic waves. The wake thus has several components referred 
to as wings. The strongest are two Alfv\'en wings associated with the 
propagation of Alfv\'en waves, and extending on both sides of the cloud 
\citep{Drell65, Neubauer80}. However, because the flow around these 
wings is incompressible even in the non-linear regime, the bulk 
viscosity cannot dissipate their energy and heat the plasma. On the 
other hand, the wake also contains two slow magnetosonic wings 
\citep{Wright90, Linker91} associated with the propagation of slow 
magnetosonic waves. Those are compressible and thus subject to viscous 
damping, so that they can possibly heat the plasma from the 
gravitational energy released by the inflow of the clouds. The 
viscosity is most efficient when the collision time is comparable with 
the characteristic time scale of the problem, i.e., here the cloud 
passing time. It is interesting to note that this is exactly the case 
here: the parameters are such that the collision time is of the order 
of the interaction time for clouds of 10~parsecs moving at 
$\sim$100~km~s$^{-1}$ through a magnetized plasma at the inferred 
density and temperature.  If this is not a coincidence it might even 
suggest a self-regulation process, since if viscous heating became too 
efficient it would heat the plasma to a point where viscosity would 
decrease. A detailed calculation will be presented elsewhere (Belmont 
et al. 2005, in preparation), but we find this  mechanism efficient 
enough to heat the hot plasma over its radiative lifetime.

\section{CONCLUSION}

Finding that hydrogen, although it does escape from the Galaxy, is too 
weakly collisional to drag other elements with it, thus opens a whole 
line of possibilities to explain the observation of an 8~keV plasma in 
the Galactic Centre region. A better determination of the argon line, 
and planned XMM-Newton and ASTRO-E2 observations over a range of 
Galactic latitudes should provide a better understanding of the 
abundances and the vertical stratification. Astro-E2 will also be able 
to determine whether the plasma is in or out of equilibrium; if it 
confirms the thermal origin of the diffuse emission, the model of a 
gravitationally bound helium plasma may help to explain what otherwise 
is a very serious energetic quandary.

There would remain the problem of determining the mechanism responsible 
for the high temperature of this plasma.  We suggest the heating might 
result from the viscous friction on molecular clouds flowing toward the 
Galactic Center. We find that the collision rate in the plasma and 
velocities are such that the hot plasma is near the optimum for 
maximising the efficiency of viscous heating, which might indicate a 
self-regulation process.

\acknowledgments
The authors thank Anne Decourchelle, Thomas Chust and Thierry Foglizzo 
for numerous and very enriching discussions.

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\end{document}