2 The mass accumulation rate

The gas supply rate into the central few parsecs, based on stellar wind measurements, is at least $\dot M_{\rm w}\sim10^{-3}\;\dot M_{\odot}$ yr^-1. Sgr A West is an HII region in the central parsec and contains the streamers of the "mini-spiral'', while the "circumnuclear disk'' (CND) is a dense, clumpy, and asymmetric ring-like feature which extends for more than 7 pc. The CND has an inner radius of ${\simeq} 1.5$ pc and surrounds Sgr A* and Sgr A West. Both the CND and Sgr A West may be additional sources of infalling gas (Mezger et al. 1996; Vollmer & Duschl 2001). The Bar, part of the "mini-spiral'' and located ${\sim} 0.1$ pc south of Sgr A*, may be intercepting some fraction of the cluster's winds. In sum, $\dot M_0\sim10^{-3}\;\dot M_{\odot}$ yr^-1is a conservative lower limit to the total rate which gas is being supplied to the central parsecs. Most of this gas, in the absence of shocks and subsequent radiative cooling, is unbound and will carve out a central cavity within Sgr A West. A fraction of $\dot M_0$,  $\dot M_{\rm A}$, is trapped but not necessarily accreted by Sgr A*.

Assuming static spherical wind sources and calculating the fraction of each star's wind that is captured by Sgr A*, Quataert et al. (1999) estimated that  yr^-1. A capture radius can be defined by

$$% R_{\rm A} \equiv {{2 GM}\over{v_{\rm w}^2}} \simeq 0.04\;{\rm pc} \simeq 10^5 R_{\rm s} \simeq 1\hbox{$^{\prime\prime}$ },$$ (1)

and the Schwarzschild radius by

$$% R_{\rm s} \equiv 2 G M / c^2 ,$$ (2)

where c is the speed of light and $v_{\rm w} ({\sim}700$ km s^-1) is the velocity of the supersonic wind flowing past a centralized object of mass M (taken to be $2.6\times10^6~M_{\odot}$). Stellar motions, wind-wind collisions, radiative cooling, and other unidentified wind sources may substantially alter this estimate. In addition, the mass-loss rates of the cluster members may have been overestimated by a factor of a few (Morris et al. 2000). The rotation of the cluster stars around Sgr A* (Genzel et al. 2000) may result in angular momentum support of their winds (but see below) and the strong magnetic fields in the central parsec may also play a role in supporting the gas against accretion. Nonetheless, it appears that $\dot M_{\rm A} \sim 10^{-5}~M_{\odot}$ yr^-1 is a good estimate of the minimum amount of gas that is being trapped in the central arcsecond by the potential well of Sgr A*.

According to all of the accretion models for Sgr A*, the actual accretion rate, $\dot M$, onto the blackhole is much less than $\dot M_{\rm A}$. In fact, the accretion rate through a radius of $R_{\rm min} \sim 1$ mas is thought to be orders of magnitude smaller than the above estimate for $\dot M_{\rm A}$. There is no evidence of any outflow from Sgr A* on scales larger than $R_{\rm min}$, so even the presence of a mini-jet or similar small-scale outflow would not alter the fact that  yr^-1is being trapped - but, seemingly, not accreted - by the gravitational potential of the blackhole. If the wind sources are WR stars as suggested by Tamblyn et al. (1996) (but see below), with a WR wind lifetime of $t_{\rm w} \sim 10^5$ yrs (Maeder & Meynet 1987), the total mass of gas that has accumulated between $R_{\rm A}$ and $R_{\rm min}$ is $\sim \dot M_0 t_{\rm w}/30 = \dot M_{\rm A} t_{\rm w} \equiv M_{\rm g} \simeq 3~M_{\odot}$.

Recent Chandra X-ray observations (Baganoff et al. 2001) show that the average ionized gas density ${\sim} 1~R_{\rm A}$ from Sgr A* is only ${\sim}10^2$ cm^-3. If $M_{\rm g}$ has accumulated within $R_{\rm A}$, then the average number density of the captured gas is $\bar n \sim 10^4 \; {\rm cm}^{-3}$. The most likely explanation for this discrepancy is that $t_{\rm w} \ll 10^5$ yrs and the GC is presently in a state of quiesence.