------------------------------------------------------------------------ gcnews.tex MNRAS, submitted Message-Id: <20070508163033.43BF1140659@cervantes.colorado.edu> Date: Tue, 8 May 2007 10:30:33 -0600 (MDT) From: jcuadra@cervantes.colorado.edu (Jorge Cuadra) X-MailScanner-Information: Please contact the postmaster@aoc.nrao.edu for more information X-MailScanner: Found to be clean X-MailScanner-SpamCheck: not spam, SpamAssassin (not cached, score=0, required 5, autolearn=disabled) X-MailScanner-From: jcuadra@cervantes.colorado.edu X-Spam-Status: No %arXiv:0705.0769 %http://www.arxiv.org/ps/0705.0769 \documentstyle[natbib2, epsfig,natbibmnfix,epstopdf]{mn2e} %%%%% AUTHORS - PLACE YOUR OWN MACROS HERE %%%%% \def\aap{A\&A} \def\apj{ApJ} \def\apjl{ApJL} \def\mnras{MNRAS} \def\aj{AJ} \def\nat{Nature} \def\aaps{A\&A Supp.} \def\araa{ARA\&A} \def\msun{{\,{\rm M}_\odot}} \def\kms{km$\,$s$^{-1}$} \def\ergs{erg$\,$s$^{-1}$} \def\simlt{\lower.5ex\hbox{$\; \buildrel < \over \sim \;$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title{Variable accretion and emission from the stellar winds in the Galactic centre} \author{Jorge Cuadra, Sergei Nayakshin, Fabrice Martins} \begin{document} \date{Accepted XXX. Received XXX; in original form XXX} \pagerange{\pageref{firstpage}--\pageref{lastpage}} \pubyear{2007} \maketitle \label{firstpage} \begin{abstract} We present numerical simulations of stellar wind dynamics in the central parsec of the Galactic centre. We are particularly interested in accretion of gas on to Sgr~A*, the super-massive black hole. Unlike our previous efforts, here we use the state of the art observational data on orbits and wind properties of individual wind-producing stars.{ Since wind velocities were revised upwards and non-zero eccentricities were considered}, our new simulations show fewer clumps of cold gas and no conspicuous disc-like structure. The accretion flow circularisation radius is roughly unchaged, $\sim 5000$ Schwarzschild radii. The accretion rate is dominated by a few close `slow wind stars' ($v_{\rm w} \le 750\,$\kms), and is consistent with the Bondi estimate, but variable on time-scales of tens to hundreds of years. { This variability is due to the stochastic in-fall of cold clumps, as in earlier simulations, and to the eccentric orbits of stars}. The present models fail to explain the higher luminosity of Sgr~A* a few hundred years ago implied by {\it Integral} observations, but we argue that the accretion of a cold clump with a small impact parameter could have caused it. Finally, we show the possibility of constraining { the total mass-loss rate of the `slow wind stars' } using near infra-red observations of gas in the central few arcseconds. \end{abstract} \begin{keywords} {Galaxy: centre -- accretion: accretion discs -- galaxies: active -- stars: winds, outflows} \end{keywords} \section{Introduction} Sgr~A* is identified with the $M_{\rm BH} \sim 3.5 \times 10^6 \msun$ super-massive black hole (SMBH) at the centre of our Galaxy \citep[e.g.,][]{Schoedel02, Ghez05}. By virtue of its proximity, Sgr~A* may play a key role in the understanding of Active Galactic Nuclei (AGN). Unlike any other SMBH, observations detail the origin of the gas in the vicinity of Sgr~A*. This information is absolutely necessary for the accretion problem to be modelled self-consistently. One of Sgr~A* puzzles is its very low luminosity with respect to estimates of the accretion rate. Young massive stars in the inner parsec of the Galaxy emit in total $\sim 10^{-3} \msun\,$yr$^{-1}$, filling this region with hot gas. From {\em Chandra} observations, one can measure the gas density and temperature around the inner arcsecond\footnote{One arcsecond ($1''$) corresponds to $\sim 0.04\,$pc, $\sim 10^{17}$cm, or $\sim 10^5 R_{\rm S}$ for Sgr~A*.} and then estimate the Bondi accretion rate \citep{Baganoff03}. The expected luminosity is orders of magnitude higher than the measured $\sim 10^{36}\,$erg$\,$s$^{-1}$. The hot gas, however, is continuously created in shocked winds expelled by tens of young massive stars near Sgr~A*, and the stars themselves appear to be distributed in two discs \citep{Genzel03a, Paumard06}. The situation then is far more complex than in the idealised -- spherically symmetric and steady state -- Bondi model. An alternative approach is to model the gas dynamics of stellar winds, assuming that the properties of the wind sources are known \citep{Coker97, Rockefeller04, Quataert04, Moscibrodzka06}. Unfortunately, in the calculations just cited the motion of the stars was not taken into account. \cite{CNSD05, CNSD06} modelled the wind accretion onto Sgr~A*, for the first time allowing the wind-producing stars to move, and showed the influence of the orbits on the accretion. In addition, they found that the winds create a complex two-phase medium and that the accretion rate has a strong variablity on time-scales of tens to hundreds of years. The stars, however, were modelled as a group of sources whose features broadly reproduced the observed distribution of orbits and mass loss properties. In this paper we present our new simulations that treat the stellar population more realistically. We now use the stellar positions and velocities as determined by \cite{Paumard06}, and the wind properties derived by \cite{Martins07} from the analysis of individual stellar spectra. This paper starts with a description of our input parameters and a brief account of the simulation method in \S~\ref{simul}. In \S~\ref{acc} we characterise the simulated accretion flow in terms of origin, angular momentum, time-variability, and expected X-ray emission. The morphology of the gas on a larger scale and its expected atomic line emission are then explored in \S\S~\ref{morph} and \ref{line}. We finally discuss our results in \S~\ref{discuss}. \section{Simulations} \label{simul} The simulations were ran using the method described and tested in detail by \cite{CNSD06}. We use the SPH/$N$-body code {\sc Gadget-2} \citep{Springel05b} to simulate the dynamics of stars and gas in the gravitational field of the SMBH. { To model the stellar orbits more accurately, we also include the gravitational potential of the (old) stellar cusp, as determined by \cite{Genzel03a}. } The gas hydrodynamics are solved with the SPH \citep[smoothed particle hydrodynamics; e.g.,][]{Monaghan92} formulation, in which the gas is represented by a finite number of particles that interact with their neighbours. { We include optically thin radiative cooling}. The SMBH is modelled as a `sink' particle \citep{Bate95,Springel05a}, with all the gas passing within a given distance from it ($0.05''$ in the present simulations) disappearing from the computational domain. To model the stellar winds, new gas particles are continously created around the stars. As wind sources, we include 30 of the stars that \cite{Paumard06} identify as Wolf--Rayet's (see Table~\ref{table:winds}). The remaining two stars, 3E and 7SE2, were not included in the models because of the poor constraints on their orbits. None of these stars is very close to the black hole, nor should they have large mass loss rates\footnote{7SE2 is a WC9 star very similar to 7W which has $\dot{M} = 10^{-5} \msun\,$yr$^{-1}$. 3E is a WC5/6 star and \cite{Hillier99} derived $\dot{M} = 1.5 \times\ 10^{-5}\msun\,$yr$^{-1}$ for a WC5 star.}. Consequently, we do not expect these two stars to have a strong influence on the accretion rate. \subsection{Stellar wind data} We used the wind properties derived for 18 of the mass-losing stars by \cite{Martins07}. In that study, $H$ and $K$ band spectra of the Wolf--Rayet stars in the central parsec of the Galaxy were analysed by means of state-of-the-art atmosphere models. Mass loss rates ($\dot M_{\rm w}$) and terminal wind velocities ($v_{\rm w}$) were derived from the strength and width of emission lines. The models assumed inhomogeneous (clumpy) winds, which lead to lower mass loss rates for the 8 stars previously analysed by \cite{Najarro97} by means of homogeneous models. In addition, wind velocities of stars displaying P-Cygni profiles were found to be larger than in \cite{Paumard01} because the latter authors used only the emission part of the P-Cygni profile to estimate the terminal velocity of the winds. For the 12 remaining stars, those not analysed in detail by \cite{Martins07}, we set their wind parameters by simply using those of similar stars that were properly studied. Table~\ref{table:winds} shows the list of stars we use with their wind properties. \begin{table} \caption{Mass-losing stars and wind properties used in this paper.} \begin{tabular} {r||l|r|r|r|} \hline ID&Name \ddag&$v_{\rm w}$&$\dot M_{\rm w}$&Note\\ &&\kms&$\msun\,$yr$^{-1}$&\\ \hline 19&16NW& 600& 1.12$\times 10^{-5}$&1\\ 20&16C& 650& 2.24$\times 10^{-5}$&1\\ 23&16SW& 600& 1.12$\times 10^{-5}$&2\\ 31&29N& 1000& 1.13$\times 10^{-5}$&3\\ 32&16SE1& 1000& 1.13$\times 10^{-5}$&3\\ 35&29NE1& 1000& 1.13$\times 10^{-5}$&3\\ 39&16NE& 650& 2.24$\times 10^{-5}$&4\\ 40&16SE2& 2500& 7.08$\times 10^{-5}$&1\\ 41&33E& 450& 1.58$\times 10^{-5}$&1\\ 48&13E4& 2200& 5.01$\times 10^{-5}$&1\\ 51&13E2& 750& 4.47$\times 10^{-5}$&1\\ 56&34W& 650& 1.32$\times 10^{-5}$&1\\ 59&7SE& 1000& 1.26$\times 10^{-5}$&1\\ 60&--& 750& 5.01$\times 10^{-6}$&5\\ 61&34NW& 750& 5.01$\times 10^{-6}$&1\\ 65&9W& 1100& 4.47$\times 10^{-5}$&1\\ 66&7SW& 900& 2.00$\times 10^{-5}$&1\\ 68&7W& 1000& 1.00$\times 10^{-5}$&1\\ 70&7E2& 900& 1.58$\times 10^{-5}$&1\\ 71&--& 1000& 1.13$\times 10^{-5}$&3\\ 72&--& 1000& 1.13$\times 10^{-5}$&3\\ 74&AFNW& 800& 3.16$\times 10^{-5}$&1\\ 76&9SW& 1000& 1.13$\times 10^{-5}$&3\\ 78&B1& 1000& 1.13$\times 10^{-5}$&3\\ 79&AF& 700& 1.78$\times 10^{-5}$&1\\ 80&9SE& 1000& 1.13$\times 10^{-5}$&3\\ 81&AFNWNW& 1800& 1.12$\times 10^{-4}$&1\\ 82&Blum& 1000& 1.13$\times 10^{-5}$&3\\ 83&15SW& 900& 1.58$\times 10^{-5}$&1\\ 88&15NE& 800& 2.00$\times 10^{-5}$&1\\ \hline \label{table:winds} \end{tabular} \\Notes:\\ (\ddag) IDs and names from \cite{Paumard06}.\\ (1) From \cite{Martins07}.\\ (2) Use 16NW.\\ (3) Use the average of 7W and 7SE.\\ (4) Use 16C.\\ (5) Use 34NW.\\ \end{table} \subsection{Orbital data} For each star we take the current 3D velocity and the position in the sky determined by \cite{Paumard06}. The $z$-coordinate, i.e., its distance from Sgr~A* projected along the line of sight, can be chosen using different assumptions for the orbital distribution. We tried a range of reasonable assumptions, described in \S\S~\ref{sec:circ}--\ref{sec:2discs} below. \subsubsection{Almost circular orbits} \label{sec:circ} The simplest assumption one can make for the stellar orbits is to say they are circular. However, for a given set of values $\vec v, x, y, M_{\rm BH}$ (3D velocity, 2D position, and central mass), it is not possible in general to find a solution $z$ that satisfies at the same time the two requirements for a circular Keplerian orbit: $v^2 = GM_{\rm BH}/r$ and $\vec v \cdot \vec r = 0$, where $\vec r = (x,y,z)$. Instead, we look for the value of $z$ that minimises the eccentricity, $e = \sqrt{1 + (2 \ell^2\epsilon)/(G^2M_{\rm BH}^2)}$, where $\vec \ell = \vec r \times \vec v$ and $\epsilon = v^2/2 - GM_{\rm BH}/r$ are the angular momentum and energy per unit mass of the orbiting star, respectively. For the first run, {\sc min-ecc}, we set the current $z$-coordinate to that value. \subsubsection{One stellar disc} \label{sec:1disc} \cite{Levin03} found that many of the young stars in the Galactic centre, those rotating clockwise in the sky, have velocity vectors that lie in a common plane. They interpreted this as a signature that these stars are orbiting Sgr~A* in a disc. From updated observations, \cite{Beloborodov06} estimated the thickness of this disc to be only about $10^\circ$ and then calculated the most likely $z$-coordinate for its stars. In our second orbital configuration, {\sc 1disc}, we used the $z$-coordinate calculated in this way by \cite{Beloborodov06} for the stars they identified as disc members, while for the rest of the stars we use our previous assumption of low eccentricity orbits (\S~\ref{sec:circ}). \subsubsection{Two stellar discs} \label{sec:2discs} \cite{Genzel03a} realised that the majority of the young stars in the Galactic centre are actually confined to two almost perpendicular discs. The second disc, with stars rotating counter-clockwise in the sky, however, is not that well defined, being two times thicker than the clockwise system \cite[see also \citealt{Lu06}]{Paumard06}. It is not possible to obtain a robust estimate of the $z$-coordinate in this case. For definitiveness we simply set $z = - (x n_x + y n_y) / n_z$ for this third orbital configuration, {\sc 2discs}, where $(n_x, n_y, n_z)$ is the vector perpendicular to the best fitting counter-clockwise disc\footnote{With this setting, two of the stars (16NW, 29N) would have acquired orbits with pericentres $< 0.1''$, comparable to the size of our inner boundary. To avoid numerical problems, we changed their velocities within the error bars, putting them in orbits that do not take them so close to the black hole.}. For the clockwise rotating stars, we used the \cite{Beloborodov06} $z$-coordinates, as described in \S~\ref{sec:1disc}. \subsubsection{The `mini star cluster' IRS 13E} Two of the wind emitting stars belong to IRS 13E, a group of stars located 0.13 pc away from Sgr~A* in projection. The velocities of its components are remarkably similar, so it appears to be bound. Since the SMBH tidal force would quickly disrupt such a group, it is believed that it harbours more mass than what is observed as massive stars, perhaps in the form of an intermediate-mass black hole \citep{Maillard04, Schoedel05, Paumard06}. To take this into account when calculating the $z$-coordinate of its components, we replaced their individually measured velocities with the average group motion reported by \cite{Paumard06}. Moreover, we include in the simulations a $350\,\msun$ `dark matter' particle to keep the group bound. \subsubsection{Setting the initial conditions} Once the $z$-coordinates are set using any of the assumptions described above (\S\S~\ref{sec:circ}--\ref{sec:2discs}), we ran $N$-body calculations to evolve the orbits back in time for 1100 yr. The final stellar positions and velocities from those runs were used as initial conditions for the winds simulations.\footnote{We made an additional run starting 3000 yr ago. No significant differences were found, so we concentrate on simulations starting 1100 yr ago in this paper.} \section{Accretion on to Sgr~A*} \label{acc} \begin{figure} \centerline{\epsfig{file=acc_minecc13-18.eps,width=.49\textwidth}} \caption{Top panel: Accretion rate as a function of time for run {\sc min-ecc}. The accretion curve is created by sampling the accreted mass every $\sim 30\,$yr and a time value of zero corresponds to the present time. The black solid line shows the total accretion rate while the coloured broken lines show the contribution of the three stars that dominated accretion on to Sgr~A* during the simulation. Bottom panel: Distance from the innermost stars to the black hole as a function of time for the same simulation. The curves are labelled with the star names and the three most important stars are shown with the same line properties as in the top panel.} \label{fig:acc_circ} \end{figure} \begin{figure} \centerline{\epsfig{file=acc_belo13-18.eps,width=.49\textwidth}} \caption{Same as Fig.~\ref{fig:acc_circ} for run {\sc 1disc}.} \label{fig:acc_1disc} \end{figure} \begin{figure} \centerline{\epsfig{file=acc_2discs13-18.eps,width=.49\textwidth}} \caption{Same as Fig.~\ref{fig:acc_circ} for run {\sc 2discs}.} \label{fig:acc_2discs} \end{figure} \subsection{Variability and origin of the accretion} We define the accretion rate on to Sgr~A* as the rate at which mass enters the inner boundary ($0.05''$) of our computational domain. The upper panel of Fig.~\ref{fig:acc_circ} shows the so-defined accretion rate for run {\sc min-ecc}, where the orbits were made as circular as possible. The lower panel shows the distance from the innermost stars to the black hole as a function of time for the same simulation. In this case most of the accreted material comes from the innermost stars 16SW and 16C, whose orbits oscillate in the range $\sim1.5$--$2"$. These stars have relatively slow wind velocities, $v_{\rm w} \approx 600\,$\kms. Additionally, star 33E, that was further away but has even slower winds with $v_{\rm w}=450\,$\kms, makes an important contribution to the accretion rate. The slow winds from these three stars are captured by Sgr~A$^*$ more easily than winds from stars like 29N and 16SE1. The latter two were at comparable distances from the black hole, but have faster winds that were not accreted at all. Figures~\ref{fig:acc_1disc} and \ref{fig:acc_2discs} show the accretion rate corresponding to runs {\sc 1disc} and {\sc 2discs}, respectively. The accretion is again dominated by stars with wind velocities of at most $750\,$\kms. The accretion rate history is however different among the simulations. When the orbits are almost circular (Fig.~\ref{fig:acc_circ}), the accretion rate is more stable, with only a few narrow peaks produced by { the dense clumps resulting from the cooling of slow winds (see \S~\ref{morph})}. When the stars are set in one or two discs, the orbits typically have higher eccentricities (notice the variation in the $R_*$ vs time plots), changing the quantity of gas that can be captured by the black hole as a function of time. { This is especially true for run {\sc 2discs}, where the innermost star 16NW has quite an eccentric orbit.} \cite{CNSD06} used only circular orbits and found that, while the total amount of accretion was dominated by hot gas (temperature $T > 10^7\,$K), the variable accretion rate was mainly caused by the infall of cold clumps. In these new simulations, the accretion is again dominated by hot gas, but there is almost no accretion of cold gas at all. The reason for this is most likely the eccentricity of the orbits -- closer to the black hole the stars acquire high orbital velocities that increase the total velocity of the wind, giving it a large kinetic energy which is then thermalized. Only in the run with orbits closer to circular we see a few sharp peaks in the accretion rate, originated by cold clumps that survived the hot inner region and reached the black hole. On the other hand, the accretion of hot gas shows larger variability than in our previous calculations. The value of the accretion rate is of the order of a few $\times10^{-6}\msun\,$yr$^{-1}$, consistent with the expectations from the Bondi model \citep{Baganoff03}. This means that the reason for Sgr~A* low luminosity lies in the physics of the inner accretion flow that we cannot resolve here, and not in how much material is captured by the black hole at distances $\sim 10^4 R_{\rm S}$. \subsection{Accretion luminosity}\label{sec:xray} We shall try to estimate the X-ray luminosity produced by the accretion flow based on the accretion rate measured at the inner boundary $R= 0.05''$ of the computational domain. Physically, gas that reached this point will still spend of order the flow viscous time, $t_{\rm visc}$, to reach Sgr A*. This is effectively smoothing out any variability in the accretion rate that proceeds on timescales $\Delta t < t_{\rm visc}$. Therefore, to calculate the luminosity of the flow we first average the instantaneous accretion rate over time intervals $t_{\rm visc}$. From the standard accretion theory \citep{Shakura73}, the viscous time-scale can be estimated as \begin{equation} t_{\rm visc} = \frac{1}{ \alpha \Omega_{\rm K}} (\frac{R}{H})^2 = 6.8\,\hbox{yr} \, R_{0.05''}^{3/2} \alpha_{0.1}^{-1} (\frac{R}{H})^2 , \end{equation} { where $\alpha = 0.1\alpha_{0.1}$ is the standard viscosity parameter, $\Omega_{\rm K}$ is the Keplerian orbital frequency, $R = 0.05" R_{0.05''}$ is the distance from the black hole, and $H$ is the disc thickness.} If we take $\alpha=0.1$, and a geometrically thick disc, $H/R \approx 1$, appropriate for radiatively inefficient accretion, the viscous timescale can be as short as $t_{\rm visc} \approx 5\,$yr. While for a thin disc this timescale can be of course much longer, we concentrate in the $t_{\rm visc} \sim 5\,$yr regime. The radiative efficiency of the flow is highly uncertain. We therefore use two prescriptions for the X-ray luminosity of the accretion flow $L_{\rm X}$ as a function of the accretion rate $\dot M$, \begin{equation} L_{\rm X} = 0.01 (\frac{\dot M}{\dot M + \dot M_{\rm crit}})^\beta \dot M c^2, \end{equation} { where the parameter $\beta$ is set to either 1 or 2 and $c$ is the speed of light}. The critical value of the accretion rate, where it would switch to an efficient state, is set at $\dot M_{\rm crit} = 0.01 \dot M_{\rm Edd} \approx 7.7\times10^{-2}\msun\,$yr$^{-1}$, as suggested by studies looking for different modes of accretion in AGNs \citep[e.g.,][]{Maccarone03}. \begin{figure} \centerline{\epsfig{file=acclum_belo13-18.eps, width=.48\textwidth}} \caption{Luminosity from the accretion flow in run {\sc 1disc}. The solid and crossed lines correspond to the estimates with $\beta=1,2$, respectively.} \label{fig:acclum_belo} \end{figure} As an example, we show in Fig.~\ref{fig:acclum_belo} the resulting X-ray luminosity of run {\sc 1disc}. As can be seen from the figure, the choice $\beta = 1$ gives a typical luminosity for Sgr~A* that is too large compared with the $\sim 2\times10^{33}\,$\ergs currently observed. The case $\beta = 2$ gives more reasonable results, with typical values $L_{\rm X} \sim 10^{33}$--$10^{34}\,$\ergs, { and is actually closer to the relation ($ L_{\rm X} \propto \dot m^{3.4}$) calculated for very inefficient accretion by \cite{Merloni03}.} Interestingly, our simulations show that in the recent past Sgr~A* X-ray luminosity could have reached more than $10^{37}\,$\ergs. On the observational side, \cite{Revnivtsev04} detected hard X-rays from molecular clouds in the vicinity of Sgr~A* with {\it Integral}, and interpreted them as reflection from a bright source, implying a past luminosity of $\sim 10^{39}$\ergs\ for Sgr~A* that lasted at least a dozen years. It seems difficult to reproduce such high values with our models, especially because tweaking the viscous time-scale to make the peaks higher would at the same time make them narrower than the required duration. However, the in-fall of a low angular momentum clump may have produced it (see \S~\ref{discuss}). \subsection{Angular momentum and circularisation radius} \begin{figure} \centerline{\epsfig{file=minecc13-18_angmom.eps, width=.48\textwidth}} \caption{Spherically averaged angular momentum profile of the inner region of the accretion flow of the simulation {\sc min-ecc}. The profile is built using several snapshots in the range $t \approx 0 \pm 37\,$yr.} \label{fig:angmom_circ} \end{figure} \begin{figure} \centerline{\epsfig{file=belo13-18_angmom.eps, width=.48\textwidth}} \caption{As Fig.~\ref{fig:angmom_circ}, but for run {\sc 1disc}.} \label{fig:angmom_belo} \end{figure} \begin{figure} \centerline{\epsfig{file=2discs13-18_angmom.eps, width=.48\textwidth}} \caption{As Fig.~\ref{fig:angmom_circ}, but for run {\sc 2discs}.} \label{fig:angmom_2discs} \end{figure} One important piece of information to characterise the accretion on to Sgr~A* is the angular momentum of the gas that it accretes. Figures~\ref{fig:angmom_circ}--\ref{fig:angmom_2discs} show the angular momentum profile of the different simulation at $t \approx 0$, corresponding to the present time. { The gas close to our inner boundary has an average angular momentum $\ell \approx 0.25$, in units where a circular Keplerian orbit at $R=1''$ would have $\ell = 1$. The angular momentum will prevent the gas from in-falling directly on to the black holes. Instead, we expect it to circularise at radius $R_{\rm circ} = \ell^2 \sim 0.05'' \sim 5000 R_{\rm S}$.} In all three cases, the angular momentum profile is roughly flat with radius within region $R \simlt 0.7''$ or so. We interpret this as evidence that the flow in this region is well mixed and mostly decoupled from variations in the larger region caused by the stellar motion. The angular momentum of gas is constant because it is simply advected radially: the local viscous time is longer than the inflow time. We also plotted the different components of the gas angular momentum. While the magnitude of the specific angular momentum of gas in all the three simulations is similar near the inner boundary, its direction varies significantly. These simulations thus predict different orientations for the midplane of the accretion flow, which is not surprising given a rather significant difference in stellar orbits between the simulations. { The angular momentum also varies as a function of time, as the geometry of the stellar system changes. Fig.~\ref{fig:angmomtime} shows the average angular momentum of the gas in the inner $0.3"$ as a function of time for the simulation {\sc 1disc}. Both the magnitude and the orientation of the angular momentum change by up to a factor 2 on time-scales of tens of years. A sudden change in the angular momentum vector, as that seen in this simulation at $t \approx -100\,$yr, can strongly perturb the inner accretion flow and produce an episode of enhanced accretion. \begin{figure} \centerline{\epsfig{file=belo13-18_angmomtime.eps, width=.48\textwidth}} \caption{Average angular momentum of the inner $0.3"$ as a function of time from simulation {\sc 1disc}.} \label{fig:angmomtime} \end{figure} } \section{Gas morphology} \label{morph} Figure \ref{fig:largeview_belo} shows the resulting morphology of the gas at present time from run {\sc 1disc}. { The other two simulations show no important differences, so we concentrate on this intermediate case.} The cool and dense clumps originate from the slow winds. When shocked, these slow winds attain a temperature of only around $3\times10^6$ K, and, given the high pressure environment of the inner parsec of the GC, cool radiatively over a time-scale comparable to the dynamical time \citep{CNSD05}. On the other hand, the fast winds do not produce much structure by themselves. They reach temperatures $> 10^7\,$K after shocking, and do not cool fast enough to form clumps. This temperature is comparable to that producing X-ray emission detected by {\em Chandra}. Gas cooler than that would be invisible in X-rays due to the finite energy window of {\em Chandra} and the huge obscuration across the Galactic plane. \begin{figure*} \begin{minipage}[b]{.49\textwidth} \centerline{\includegraphics[height=10cm]{dens_belo_60.eps}} \end{minipage} \begin{minipage}[b]{.49\textwidth} \centerline{\includegraphics[height=10cm]{temp_belo_60.eps}} \end{minipage} \caption{Gas morphology at the present time ($t=0$) from the simulation {\sc 1disc}. Left panel: Column density of gas in the inner $6''$ of the computational domain, as it would be observed from Earth. Stars are shown with green symbols, with labels indicating their names. Right panel: Averaged temperature of the same region. Notice the dense cold clumps forming around the slow-wind-emitting star 33E. Clumps also form in the region around the 13E group, where the slow winds from 13E2 collide with the faster ones comming from its neighbour 13E4. On the other hand, winds from the powerful WR star 9W have not collided yet with any other winds and remain cold but diffuse.} \label{fig:largeview_belo} \end{figure*} The new simulations confirm our previous results that the winds create a two-phase medium in the Galactic centre \citep{CNSD06}. The quantity of cold gas, however, is very much reduced in the new simulations. We also notice that there is no disc-like structure like the one previously found \citep[Fig.~9 in][]{CNSD06}. There are several reasons for the differences. The wind velocity of the slow wind stars -- from whose winds the cold clumps are mostly formed -- were revised upward from $300\,$\kms to typically $650\,$\kms. As the radiative cooling strength for this gas is a strong function of its initial velocity \citep{CNSD05}, a much smaller fraction of gas can cool and form clumps. Additionally, the mass loss rates we use for the slow wind stars went down by a factor of a few compared to our previous calculations, so there is even less material that could potentially form clumps. \cite{An05} found that Sgr~A* flux at $\sim 1\,$GHz increased by a factor $\sim 2$ from 1975 to 2003.{ These authors attribute the change to a decrease in the free--free opacity produced by a factor 9 change in the column-integrated density squared, $\int n^2 dl$. As it is clear from Fig.~\ref{fig:largeview_belo}, the motion of clumps of gas can easily account for such a change in the obscuration.} Further observations should be able to estimate the time-scales on which the change of obscuration happens and therefore confirm the identification of cold clumps with the obscuring material. \section{Line emission} \label{line} To compare better the outcome of our simulations with actual observations, we create emission maps of { strong near-infrared} atomic lines that are expected from gas at $T \sim 10^4\,$K. In the simulations the minimum temperature is set to $T = 10^4\,$K. This is justified since the powerful UV radiation from the stars in the region ensures that most of the gas remains ionised\footnote{For one single star with ionising radiation rate $Q = 10^{48} Q_{48}\,$s$^{-1}$, the Str\"omgren radius is $ 1.38\,$pc$\,Q_{48}^{1/3} n_2^{-2/3}$.}. Only a limited comparison with the data is possible at this stage. Our simulations do not include the Mini-spiral, a rather massive ($\sim 50 \msun$) and large scale ionised gas feature{ composed of several dynamically independent structures \citep[e.g.,][]{Paumard04}. While the origin of that gas is not quite clear, they seem to follow eccentric orbits originating outside the inner parsec.} Fortunately for us here, there does not seem to be much of the Mini-spiral material within few arc-seconds of Sgr~A*, so we choose to concentrate on the inner region of the computational domain. Our aim is to find out whether the gas that is produced by the stellar winds would produce a level of emission that is too high compared to the observed value. If that is the case, either the physics of our model is wrong, or the input parameters we are using (stellar properties and orbits) should be revised. In particular, we create maps of Pa$\alpha$ emission and compare them with the observations of \cite{Scoville03}. We calculate the luminosity per unit volume as \begin{equation} 4 \pi j_{\rm Pa\alpha} = 6.41 \times 10^{-18}\, {\rm erg\,cm}^{-3}\,{\rm s}^{-1} (\frac{T}{6000\,{\rm K}})^{-0.87} (\frac{n}{10^4\,{\rm cm}^{-3}})^2 \end{equation} \citep{Osterbrock89} and then integrate it along the line of sight. An example from simulation {\sc 1disc} is shown in Fig.~\ref{fig:paa_belo}. Only a few pixels have a surface brightness comparable to that measured in the Galactic centre inner few arc-seconds \citep[their Fig.~7]{Scoville03}, making the present simulations compatible with the observations. This is in contrast to our earlier simulations \citep{CN06}, the analysis of which shows too much atomic line emission in the near infrared. This is not unexpected as these simulations produced much more cold gas in the inner region (see \S \ref{morph}). \begin{figure} \centerline{\epsfig{file=paa_belo_60.eps,width=.49\textwidth}} \caption{Pa$\alpha$ surface brightness from the stellar winds in run {\sc 1disc}, as it would be observed in the sky at present time. Stars are shown as black asterisks. The level of emission is too low to be detected on top of the other gas complexes in the GC region.} \label{fig:paa_belo} \end{figure} { While a more detailed analysis is left to future work, it is clear that in general the gas luminosity depends on the wind properties. Once more robust orbital data is obtained, it may be possible to constrain the properties of the stellar population, in particular the total mass loss rate from `slow wind stars' using this method that is complementary to the stellar spectra analysis \citep[e.g.,][]{Martins07}.} \section{Discussion} \label{discuss} We presented our new simulations of stellar wind dynamics in the Galactic centre. We use the state of the art data on the stellar orbits \citep{Paumard06} and stellar winds properties \citep{Martins07}. Unfortunately, this does not eliminate the uncertainty in the models completely. The $z$-coordinate of the stellar wind sources, i.e., the distance along the line of sight to the GC, cannot be obtained observationally. We therefore made several simulations each with a different assumption about the dynamics of these stars, from almost circular orbits to orbits confined in two planes. The main result of our simulations, compared with results of \cite{CNSD05, CNSD06}, is the much smaller quantity of cool gas at $T \simlt 10^4$ K. We find no cool and geometrically thin disc formed from radiatively cooled stellar winds. This is due to two factors. Firstly, the updated stellar wind velocities are significantly higher, implying that radiative cooling time becomes too long for the shocked winds to form cool clumps. Secondly, the orbits of the important mass loosing stars are less disc-like, { i.e, circular and coplanar, } compared with some of our previous tests. On the other hand, similar to the results of \cite{CNSD05, CNSD06}, we find a substantial time variability in the accretion rate histories for Sgr~A* in all the three different models explored here. In the simulation with small eccentricities ({\sc min-ecc}) the accretion is relatively constant, except for the episodic in-fall of cold clumps that produce sharp peaks in the accretion rate. When the orbits are preferentially in one or two planes (simulations {\sc 1disc} and {\sc 2discs}), stars acquire higher eccentricities. The accretion rate history is then strongly variable on time scale of tens to hundreds of years mainly due to stars on eccentric orbits. The accretion rate peaks are nearly coincident with times when these stars are at pericentres of their orbits. Even though the accretion history looks quite different among the simulations, the average accretion rate and the circularisation radii we obtain are the same within a factor of 2--3. In particular, time-averaged accretion rates of all of the simulations are consistent with the values obtained from observations of hot gas at the Bondi radius. The accretion flow properties in the sub arc-seconds region are also similar, with the circularisation radius of the order of $\sim 5\times 10^3$ Schwarschild radii. However, the orientation of the accretion flow midplane is different in all the three simulations. Better measured velocities and constraints on the accelerations \citep[e.g.,][]{Lu06} should be obtained during the next years of observations, allowing us to improve the determination of the 3-dimensional orbits and get more definitive answers. Having that, one could embark on a more ambitious higher resolution study of the inner accretion flow in an attempt to connect that to the non-radiative models developed in the literature { \citep[e.g.,][]{Yuan03}, and the observational constraints on the inner accretion flow orientation \citep[e.g.,][]{Meyer06,Trippe07}.} We already attempted some of this in terms of a very simplified approach in which we estimated the X-ray luminosity {\em within} our inner boundary (\S \ref{sec:xray}). We found that in the past it could have been much higher than its present value, and could have varied by several orders of magnitude. Nethertheless, none of the peaks reached the $\sim 10^{39}$ \ergs needed to explain the putative flare in Sgr A* X-ray luminosity few hundred years ago \citep[see also \cite{Muno07}]{Revnivtsev04}. It might still be possible that a cold clump falling into the inner region, such as those seen as peaks in Fig.~\ref{fig:acc_circ}, has a low enough angular momentum to circularise at a very small radius, say $\sim 0.001"$. In that location, the clump mass would be more massive than the non-radiative flow mass by a few orders of magnitude. Regardless of whether the cold clump gets evaporated by the hot flow, or sheared away and mixed with it, in the end there would be much more mass in the inner flow region. The accretion flow could then cool much quicker than it did before, becoming more of a standard accretion disc. The viscous time of that flow can be quite long, of the order of 100 yr at that location for a disc thickness $H/R \sim 0.01$, making Sgr~A* stay in this state until this excess mass is accreted. Assuming a maximum radiative efficiency for this kind of flow, the bolometric luminosity would be $\sim 10^{40}\,$\ergs, enough to give the observed luminosity in the X-rays for the required time. We note that there were no such low angular momentum clumps in the present simulations, but it is not clear how robust this conclusion is with respect to changes in the model parameters. The wind properties we used are based on the spectroscopic study by \cite{Martins07}. The uncertainty of their results is typically only of the order of a few $\times$10\%, so we did not explore different realisations of the wind data. There is more uncertainty in the wind properties from the 13E group, whose nature is not clearly established yet, and 16SW, which is part of a binary \citep{Martins06, Peeples07}. The analysis of these sources is not yet robust enough and they are important contributors to the accretion. However, we still do not expect changes in the results to be larger than those resulting from the different orbital configurations. We can still use our previous work \citep{CNSD05, CNSD06, CN06} to understand the effect of changing the wind properties. Clearly, larger mass-loss rates and slower wind velocities produce more gas that is able to cool and form clumps. Too much of that gas can be problematic in the sense that it would overproduce the atomic line emission expected from gas at $T \sim 10^4\,$K. The same clumps increase the variability of the accretion rate on time-scales of 10--100 yr. Our results on the origin of the accreted material differ from those obtained by \cite{Moscibrodzka06}. These authors argued that the accretion on to Sgr~A* is dominated by the material expelled by 13E. One reason for the discrepancy is that they used the older values for mass loss rates compiled by \cite{Rockefeller04}, that give a rather extreme value for $\dot M_{\rm 13E}$. \cite{Moscibrodzka06} also neglected the orbital velocity of the innermost stars, that are usually comparable to their wind velocity. Other models in the literature have focused on the accretion of winds form the OB main sequence stars in the inner arc-second -- the `S-stars' \citep{Loeb04, Coker05}. While the inclusion of these stars would certainly make the models more realistic, their mass loss rates are probably at most $\sim 10^{-7}\msun\,$yr$^{-1}$. The star $\tau$~Sco has a spectral type (B0.2V) similar to S2 and the estimates of its mass loss rate range from $6 \times\ 10^{-8}\msun\,$yr$^{-1}$ \citep{Mokiem05} down to $< 6 \times\ 10^{-9} \msun\,$yr$^{-1}$ \citep{Zaal99}. Since mass loss rates are known to scale with luminosity \citep{Kudritzki00} and S2 is the brightest of the S stars, all of them should have very low $\dot{M}_{\rm w}$. Hence, we believe that the effect of the S stars would not affect our conclusions. \section*{Acknowledgments} { We thank T.\ Paumard for useful discussions on the stellar orbits and the observability of the gas emission. JC acknowledges support from NASA Beyond Einstein Foundation Science grant NNG05GI92G. FM acknowledges support from the Alexander von Humboldt foundation. The simulations were performed on the JILA Keck-cluster, sponsored by the W.\ M.\ Keck Foundation. Earier calculation were ran at the Rechenzentrum Garching and at the University of Leicester. JC acknowledges the hospitality of the Theoretical Astrophysics group in Leicester, where part of this work was done. } \bibliography{biblio.bib} \bibliographystyle{mnras} \label{lastpage} \end{document}