------------------------------------------------------------------------ From: Eliot Quataert equataer@jupiter.harvard.edu To: Galactic Center Newsletter Subject:paper on Sgr A* Mime-Version: 1.0 %astro-ph/9810136 %\documentstyle[12pt,aasms4,flushrt]{article} \documentstyle[11pt,aaspp4,flushrt]{article} %\documentstyle[emulateapj]{article} %\documentstyle{article} \parskip=8pt \newcommand{\Ref}{\hangindent=20pt \hangafter=1 \noindent} \newcommand{\StartRef}{\hyphenpenalty=10000 \raggedright} \newcommand{\rb}[1]{\raisebox{1.5ex}[0pt]{#1}} \newcommand{\beq}{\begin{equation}} \newcommand{\eeq}{\end{equation}} \newcommand{\NarrowMargins}{ \setlength{\oddsidemargin}{+0.3in} \setlength{\evensidemargin}{-0.0in} \setlength{\textwidth}{6.2in} \setlength{\topmargin}{-0.75in} \setlength{\textheight}{9.25in} } \catcode`\@=11 % This allows us to modify PLAIN macros. \def\xmp{{x_M^{\prime}}} \def\lsim{\mathrel{\mathpalette\@versim<}} \def\gsim{\mathrel{\mathpalette\@versim>}} \def\tt{\times 10^{-3}} \def\tfo{\times 10^{-4}} \def\tfi{\times 10^{-5}} \def\tsi{\times 10^{-6}} \def\tse{\times 10^{-7}} \def\te{\times 10^{-9}} \def\mo{\dot m_{\rm out}} \def\ro{r_{\rm out}} \def\vp{v_{\parallel}} \def\Ep{E_{\parallel}} \def\om{\omega} \def\omt{\tilde \omega} \def\op{\Omega_p} \def\rp{\rho_p} \def\kp{k_{\perp}} \def\lp{\lambda_p} \def\md{\dot m} \def\mc{\dot m_{\rm crit}} \def\Md{\dot M} \def\be{{b^2 \over 8 \pi}} \def\ve{{1 \over 2} \rho u^2} \def\ep{\boldmath \epsilon \unboldmath} %\special{!userdict begin /bop-hook{gsave 150 90 translate %0 rotate /Times-Roman findfont 50 scalefont setfont %-145 -70 moveto 0.9 setgray %(- Draft - Draft - Draft - Draft -) show %grestore}def end} \def\@versim#1#2{\vcenter{\offinterlineskip \ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr\sim\crcr } }} \catcode`\@=12 % at signs are no longer letters \NarrowMargins %\input{psfig} \begin{document} \title{Spectral Models of Advection-Dominated Accretion Flows with Winds} \author{Eliot Quataert and Ramesh Narayan} \affil{Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138} \medskip \setcounter{footnote}{0} \begin{abstract} We calculate spectral models of advection-dominated accretion flows, taking into account the possibility that significant mass may be lost to a wind. We apply the models to the soft X-ray transient V404 Cyg in quiescence and the Galactic center source Sgr A*. We show that there are qualitative degeneracies between the mass loss rate in the wind and parameters characterizing the microphysics of the accretion flow; of particular importance is $\delta$, the fraction of the turbulent energy which heats the electrons. For small $\delta$, current observations of soft X-ray transients and Sgr A* suggest that at least $\sim 10 \%$ of the mass originating at large radii must reach the central object. For large $\delta \sim 0.3$, however, models with significantly more mass loss are in agreement with the observations. We also discuss constraints on advection-dominated accretion flow models imposed by recent radio observations of NGC 4649 and other nearby elliptical galaxies. We conclude by highlighting future observations which may clarify the importance of mass loss in sub-Eddington accretion flows. \noindent {\em Subject headings:} accretion, accretion disks -- black hole physics \end{abstract} \section{Introduction} A number of authors have argued that, at sub-Eddington accretion rates, the gravitational potential energy released by turbulent stresses in an accretion flow may be stored as thermal energy, rather than being radiated (Ichimaru 1977; Rees et al. 1982; Narayan \& Yi 1994, 1995; Abramowicz et al. 1995; Chen et al. 1995; see Narayan, Mahadevan, \& Quataert 1998b, and Kato, Fukue, \& Mineshige 1998 for reviews). Narayan \& Yi (1994,1995) noted that such advection-dominated accretion flows (ADAFs) have the interesting property that their Bernoulli parameter, a measure of the sum of the kinetic energy, gravitational potential energy, and enthalpy, is positive; since, in the absence of viscosity, the Bernoulli parameter is conserved on streamlines, the gas can, in principle, escape to ``infinity'' with positive energy. Narayan \& Yi speculated that this might make ADAFs a natural candidate for launching the outflows/jets seen to originate from a number of accretion systems. Blandford \& Begelman (1998; hereafter BB98) have recently suggested that mass loss via winds in ADAFs may be both dynamically crucial and quite substantial. They construct self-similar ADAF solutions in which the mass accretion rate in the flow varies with radius $R$ as $\dot M \propto R^p$. If the wind carries away roughly the specific angular momentum and energy appropriate to the radius from which it is launched, they show that the remaining (accreting) gas has a negative Bernoulli parameter only for large values of $p \sim 1$. They therefore propose that the majority of the mass originating at large radii is lost to a wind. For example, for $p=1$, only a fraction $\sim(R_{in}/R_{out})\ll1$ of the mass would accrete onto the central object, where $R_{in}$ and $R_{out}$ are the inner and outer radii of the ADAF. In a separate study, Di Matteo et al. (1998; hereafter D98) measured the flux of radio and submillimeter emission from the nuclei of nearby elliptical galaxies and found fluxes significantly below the values predicted by the ADAF model. Their observations are difficult to reconcile with Fabian \& Rees's (1995) proposal that these galactic nuclei contain ADAFs. D98 discuss a number of explanations for the ``missing'' flux; one of their suggestions is that a significant wind may carry off much of the accreting mass in the ADAF. Spectral models of ADAFs without mass loss have been applied to a number of low luminosity accreting black hole systems. They give a satisfying description of the spectral characteristics of several quiescent black hole binaries (Narayan, McClintock, \& Yi 1996, Narayan, Barret, \& McClintock 1997; Hameury et al. 1997) and low luminosity galactic nuclei, e.g., Sgr A* (Narayan, Mahadevan, \& Yi 1995; Manmoto et al. 1997; Narayan et al. 1998) and NGC 4258 (Lasota et al. 1996a, Gammie, Narayan, \& Blandford 1998). Our goal in this paper is to use broad-band spectral observations to test for the presence of mass loss in low luminosity accreting black holes, paying special attention to the implications of uncertainties in the microphysics of the accretion flow. Specifically, we attempt to answer the following question: are the no-mass loss ADAF models in the literature, which fit the observations reasonably well, unique ``ADAF'' fits to the data, or are models with substantial mass loss also viable? If the latter, since it is unlikely that purely theoretical arguments will be definitive, can we distinguish between no-wind and wind models with future observations? As a first step toward addressing these questions, we calculate spectral models of ADAFs with $\dot M \propto R^p$, and compare them with observations of the X-ray binary V404 Cyg in quiescence, the Galactic center source Sgr A*, and the nucleus of the elliptical galaxy NGC 4649. We assume throughout that all observed radiation from the systems under consideration is due to the accretion flow, i.e., the wind/outflow does not radiate significantly. In the next section (\S2), we discuss our modeling techniques. We then show models for V404 Cyg (\S3) and Sgr A* (\S4) and compare the models to observations, focusing on the available theoretical parameter space. In \S5 we discuss D98's results on the radio emission in nearby ellipticals. We then propose several future observations which may help clarify the physics of ADAFs (\S6). Finally, in \S7 we summarize and discuss our results. \section{Modeling Techniques} Over the last few years, ADAF models have seen a series of improvements such that the modeling techniques used currently are much superior to earlier methods. The first published spectral models of ADAFs used the self-similar solution of Narayan \& Yi (1994) to model the dynamics, but this was soon replaced by global models, initially for a pseudo-Newtonian potential (Narayan, Kato, \& Honma 1997, Chen, Abramowicz, \& Lasota 1997), and more recently in the full Kerr metric (Abramowicz et al. 1996, Peitz \& Appl 1997, Gammie \& Popham 1998). The spectral modeling too has seen improvements, particularly in the treatment of the electron energy equation and the Comptonization. The electron energy equation was originally taken to be local (e.g., Narayan, McClintock, \& Yi 1996), with heating due to Coulomb collisions and turbulent heating balancing cooling. As emphasized by Nakamura et al. (1997), however, the electron entropy gradient (electron advection) generally cannot be neglected, and so this is now included (see eq. [\ref{ee}]). Narayan et al. (1998a) discuss how the predicted spectra have changed as the modeling techniques have improved. The changes have generally been fairly modest, at least compared to the large changes we see in the present paper when we include mass loss from the accretion flow. In this paper, we use the latest techniques for numerically calculating spectral models of ADAFs (plus any thin disk at large radii), as described in detail by Narayan et al. (1998a; see also Esin, McClintock, \& Narayan 1998 and Narayan, Barret, \& McClintock 1997). Here we mention only the relevant differences. As in Narayan et al. (1998a) and Esin et al. (1997), we solve the full electron energy equation, including the electron entropy gradient. The equation takes the form \beq n_e v {d \over dR } \left({k T_e \over \gamma_e - 1}\right)= k T_e v {d n_e \over d R}+H_e +q_{ie}-q_e^-, \label{ee} \eeq where $T_e$ is the electron temperature, $\gamma_e$ is the adiabatic index of the electrons, $n_e$ is the electron number density, $v$ is the radial velocity, $H_e$ is the turbulent heating rate of the electrons, $q_{ie}$ is the energy transferred to the electrons from the ions by Coulomb collisions, and $q_e^-$ is the radiative cooling rate of the electrons. The first term on the right hand side of equation (\ref{ee}) describes the increase in the electron internal energy due to $PdV$ work, and is the volumetric version of $q_c$ defined in equation (\ref{comp}) below. A difference in this paper, relative to earlier work, is that we take $\gamma_e$ to be that of a monatomic ideal gas ($5/3$ in the non-relativistic limit, decreasing to $4/3$ in the relativistic limit). Esin et al. (1998) argued that $\gamma_e$ should include contributions from the magnetic energy density in the flow. As discussed in Quataert \& Narayan (1998; their Appendix A), this is incorrect if MHD adequately describes the accretion flow. This is of some significance for models of low luminosity systems. For example, in the ``standard'' ADAF model of Sgr A*, the electrons are, to good approximation, adiabatically compressed. The larger $\gamma_e$ used in this paper yields higher electron temperatures (by a factor of $\sim 3$) and significantly more synchrotron emission. As a result, to produce a radio flux comparable to that in Narayan et al. (1998a), we require a noticeably weaker magnetic field. We describe the turbulent heating of the electrons via a parameter $\delta$, defined by $H_e \equiv \delta q^+$, where $q^+$ is the usual ``viscous'' dissipation rate of accretion theory (e.g., Kato et al. 1998). Thus, $\delta$ is the fraction of the total energy generated by turbulent stresses in the fluid ($q^+$) that directly heats the electrons. As discussed in Quataert \& Narayan (1998), there is a subtlety in interpreting $q^+$ in ADAFs which is not present in thin disks; namely, only a fraction $\eta$ ($\sim 1/2$) of $q^+$ is likely to end up in the particles; the rest is used to build up the magnetic field and turbulence as the accreting gas flows in.\footnote{Essentially, the parameter $\eta$ reflects the fact that, just as one must account for advection by the particles, one must also account for advection by the turbulence.} Of the fraction $\eta$, a fraction $\delta_H$ goes into electrons and $(1-\delta_H)$ goes into ions. Thus, in terms of $\eta$ and $\delta_H$, the $\delta$ we use in this paper is $\delta \equiv \delta_H\eta$. Accounting for a variable mass accretion rate in the flow, the continuity equation becomes \beq \dot M = - 4 \pi R^2 H_\theta \rho v = \dot M_{\rm out} \left({R \over R_{\rm out}}\right)^p, \label{cont} \eeq where $H_\theta$, $\rho$, and $v$, are, respectively, the angular scale height, mass density, and radial velocity in the flow. The quantity $\dot M_{\rm out}$ is the accretion rate at the radius $R_{\rm out}$, where winds become important. We take the radial velocity, angular velocity, and sound speed of the flow from the global, relativistic, models of Gammie \& Popham (1998), and then use equation (\ref{cont}) to calculate the density, $\rho$. This is, strictly speaking, inconsistent, as Gammie \& Popham's models were derived under the assumption of constant $\dot M$. The error made in this approximation should, however, be of order unity. From a spectral modeling point of view, the primary importance of the wind is that it modifies the density in the flow; this is correctly captured by equation (\ref{cont}). Generically, ADAFs with winds will rotate more quickly than those without winds. This is seen in the self-similar solution of BB98, where the rotational support enables the enthalpy of the gas to decrease, thus permitting the Bernoulli parameter to become negative. The shear and the viscous dissipation per unit mass in the flow are therefore expected to be larger in the presence of a wind.\footnote{This is actually true only for certain ``types'' of winds (in particular, depending on BB98's parameters $\epsilon$ and $\lambda$). As discussed in, e.g., Blandford \& Payne (1982), it is possible for a wind to take away all of the angular momentum and energy flux from the disk, leaving it cold and dissipationless.} We have crudely accounted for this effect as follows. In non-wind models, the flow structure is, among other things, a function of $\gamma_g$, the adiabatic index of the fluid. In calculating models of systems with winds and high $\delta$ (Figures 2b, 4b, 7, \& 8), we have chosen $\gamma_g$ such that it yields a rotation rate in the interior of the flow which is comparable to that expected from the self-similar wind solution of BB98. In particular, a self-similar, non-relativistic, ADAF has a Bernoulli parameter equal to zero only if $\Omega/\Omega_K \approx [2p/(p + 5/2)]^{1/2}$. For our typical value of $p = 0.4$, this yields $\Omega/\Omega_K \approx 0.53$. In this case we take $\gamma_g \approx 1.5$ in our global calculations, since it reproduces this rotation rate well. Note that it is important to get the right $\Omega$ only for high $\delta$. For low $\delta$, since turbulent heating of electrons is unimportant, the exact $\gamma_g$ we use is not important. We have confirmed this by calculating models with various choices of $\gamma_g$ at low $\delta$ and making sure that the spectral models are only weakly modified. We are reasonably confident that, even though we have used an ad hoc prescription in choosing the global solutions, our parameter estimates are fairly accurate. Ultimately, of course, global, relativistic, models of ADAFs with winds will be needed to correctly assess some of the issues addressed in this paper. \subsection{Choice of parameters} We measure black hole masses in solar units and (radially varying) accretion rates in Eddington units: $M = m M_{\odot}$ and $\dot M = \dot m \dot M_{edd}$. We take $\dot M_{edd} = 10L_{edd}/c^2 = 2.2 \times 10^{-8} m M_{\odot} {\rm yr}^{-1}$, i.e., with a canonical 10 \% efficiency. We measure radii in the flow in Schwarzschild units: $R = r R_s$, where $R_s = 2GM/c^2$ is the Schwarzschild radius of the black hole. The parameters of our models are $m$, $\mo = \dot M_{\rm out}/\dot M_{\rm edd}$, $\beta$, $\alpha$, $\delta$, $\ro$, and $p$. Our primary focus is to consider the effects of winds via the parameter $p$ (defined in eq. [\ref{cont}]). As we show, however, variations in $p$ are qualitatively degenerate with variations in other parameters of the problem. The mass of the central black hole, $m$, is estimated from observations. As in all previous work, we fix $\mo$ by adjusting it so that the X-ray flux in the model fits the available data. For all of the models presented here, $\ro=10^4$. Note that $\ro$ and $p$ are, roughly speaking, degenerate; what is of primary importance is $\ro^{-p}$, the fraction of the incoming mass accreted onto the central object. Typical values of $p$ considered are $p = 0$ (no winds) and $p = 0.4$ (moderately strong wind). The quantities $\beta \equiv P_{\rm gas}/P_{\rm mag}$, $\alpha$, and $\delta$ are microphysical parameters representing the magnetic field strength in the flow, the efficiency of angular momentum transport, and the fraction of the turbulent energy which heats the electrons, respectively.\footnote{Our definition of $\beta$ is that utilized in the plasma physics literature. A number of workers in the accretion literature define a ``$\beta$'' via $\beta_{\rm adv} \equiv P_{gas}/P_{tot}$, with $P_{tot} = P_{gas} + P_{mag}$. This is related to our $\beta$ by $\beta_{\rm adv} = 3\beta/(3\beta + 1)$ or $\beta_{\rm adv} = \beta/(\beta + 1)$, depending on whether one defines the magnetic pressure to be $B^2/24 \pi$ or $B^2/8 \pi$ (as we do here).} Recent ADAF models in the literature have favored the values $\beta = 1$, $\alpha = 0.25$, and $\delta = 10^{-3}$ (cf. Narayan et al. 1998a), and have considered only factor of few variations in $\alpha$ and $\beta$ and factor of $\sim 10$ variations in $\delta$. There is, however, considerable uncertainty in the microphysics of ADAFs; each of the above parameters must be regarded as uncertain to at least an order of magnitude, likely more. As we will show in this paper, mass loss from the accretion flow has a dramatic effect on theoretically predicted spectra. If we were to restrict ourselves to the values of the microphysics parameters given above, significant mass loss would be all but ruled out by the observations. Such a restriction would, however, be an inaccurate reflection of the theoretical uncertainty in the microphysics of the flow. The philosophy adopted in this paper is therefore somewhat different from previous studies. We allow $\alpha$, $\beta$ and $\delta$ to vary over a much larger range, but one which we believe correctly encompasses the theoretical uncertainties. For purely theoretical reasons (see below) we take our ``canonical'' values to be different from those of previous studies, namely, $\beta = 10$, $\alpha = 0.1$, and $\delta = 10^{-2}$. By canonical we mean (only) that, when one of the parameters is varied (e.g., $p$), the others (e.g., $\delta$) are typically fixed at their canonical values. A major point of this paper will be that, depending on the importance of winds, these values may or may not be consistent with observations. Theoretical work on particle heating in ADAFs (Gruzinov 1998, Quataert 1998, Quataert \& Gruzinov 1998) and ``fluid'' models for the evolution of the turbulent energy in an ADAF (Quataert \& Narayan 1998) suggest that subthermal magnetic fields may be likely; we consider $\beta = 10$ to be a plausible value. We take, however, a range of $\beta$, from $\beta=1$ (strict equipartition of gas and magnetic pressure) to $\beta=100$ (weak fields). If the turbulent stresses arise solely from magnetic fields, we expect the viscosity parameter to scale roughly as $\alpha\sim1/\beta$ (Hawley, Gammie \& Balbus 1996). We do not always enforce this relation in our models, but sometimes vary $\alpha$ and $\beta$ independently. We consider values of $\alpha$ ranging from 0.03 to 0.3. We should note, however, that large values of $\alpha \approx 0.25$ are needed in applications of the ADAF model to X-ray binaries such as Nova Muscae 1991, Cyg X--1 and GRO J0422+20 in the low/hard state (Narayan 1996, Esin, McClintock \& Narayan 1997, Esin et al. 1998). If $\alpha$ is much smaller than 0.25, the maximum accretion rate, $\dot m_{crit}$, up to which the ADAF solution is possible decreases significantly, and the maximum luminosity of the models becomes much smaller than the observed luminosities. We have confirmed that this limit on $\alpha$ is not modified if winds are included in the models. The value of the parameter $\delta$ is uncertain. Traditional ADAF models have taken $\delta$ to be small ($\sim 10^{-3})$ and never considered $\delta \gsim 0.03$. A number of studies have been carried out to investigate the heating of protons and electrons in hot plasmas. Quataert (1998) and Gruzinov (1998; see also Blackman 1998, Quataert \& Gruzinov 1998) considered particle heating by MHD turbulence and concluded that $\delta$ might be small so long as $\beta$ is greater than about $\sim 10$. Bisnovatyi-Kogan \& Lovelace (1997; see also Quataert \& Gruzinov 1998), however, argue that magnetic reconnection, and its presumed electron heating, may lead to large values of $\delta \sim 1$.\footnote{Despite our disagreement with some of Bisnovatyi-Kogan \& Lovelace's arguments (see Blackman 1998), their basic point, that reconnection may be crucial for ADAF models, is nonetheless important.} In this paper, we avoid theoretical prejudice and consider values of $\delta$ ranging from 0 to 0.75. Since the maximum value of $\delta$ is $\eta$, the fraction of the turbulent energy that goes into the particles, the value $\delta = 0.75$ likely corresponds to a situation where electrons are heated much more strongly than ions. \subsection{Description of Spectra} In the following sections we compare theoretical spectra of ADAFs, both with and without winds, to observations of low-luminosity systems. In preparation for this we introduce here the main features of the calculated spectra. Three radiation processes are of importance in ADAF spectra: synchrotron emission, Compton scattering, and bremsstrahlung. Each of these produces distinct and easily recognized features in the spectrum. The relative importance of each mechanism is a function of the temperature and density of the plasma, and thus of the model parameters, $\alpha$, $\beta$, $\delta$, $p$, $m$, and $\dot m$. Thermal synchrotron emission in ADAFs is invariably self-absorbed and produces a sharply cutoff peak, with a peak frequency that depends on the mass of the black hole: $\nu_{s} \sim10^{15}m^{-1/2}$ Hz. The synchrotron peak is in the optical band for stellar-mass black holes, and in the radio for supermassive black holes. Synchrotron emission from different radii in the flow occurs at different frequencies. The peak emission, however, is always from close to the black hole and reflects the properties of the accreting gas near $r \sim 1$. In spectra of quiescent systems of the sort we discuss in this paper ($\dot m_{in}\lsim10^{-3}$), and especially in the absence of winds, the synchrotron peak is the most luminous feature in the spectrum. The maximum value of $\nu L_\nu$ is given by (Mahadevan 1997) \beq \nu_s L_{\nu,s} \propto B^3 T^7_e \propto \beta^{-3/2} \dot m_{in}^{3/2} T^7_e, \label{lsynch} \eeq where all quantities should be evaluated at $r \sim 1$ and $\dot m_{in}$ is the accretion rate near $r \sim 1$. Note the very steep dependence on the electron temperature. In writing equation (\ref{lsynch}), we have taken $\rho \propto \dot m$, but independent of $\alpha$, as is appropriate near the central object. This can be understood by noting that, near the central object, the self-similar scaling $\rho \propto \dot m/\alpha$ fails. The dynamics in the synchrotron and Compton emitting regimes is dominated by the presence of a sonic point at $r \sim 3-5$ (Narayan, Kato, \& Honma 1997, Chen et al. 1997, Gammie \& Popham 1998). Near this radius the flow velocity is $\sim$ the sound speed, independent of $\alpha$. By the continuity equation, then, the density in the interior scales as $\rho \propto \dot m$, with only a weak dependence on $\alpha$. The density on the outside, however, does scale as $\rho \propto \dot m/\alpha$ because, away from the sonic point, self-similarity is reasonably valid. Compton scattering of synchrotron photons by the hot electrons in the accreting gas produces one, or sometimes two peaks in the spectrum at frequencies higher than the synchrotron peak. The peaks correspond to successive scatterings by the electrons. As with the synchrotron peak, the Compton features are again sensitive to the properties of the gas near the black hole. The frequency of the first Compton peak $\nu_{c}$ is related to $\nu_{s}$ by the Compton boost factor $A$, which is a function only of the electron temperature \beq {\nu_{c}\over\nu_{s}}=A=1+4\theta_e+16\theta_e^2, \qquad \theta_e={kT_e\over m_ec^2}={T_e\over 5.9\times10^9~{\rm K}}. \label{A} \eeq The power in the Compton peak relative to that in the synchrotron peak depends on both $A$ and the optical depth of the flow to electron scattering ($\tau$) \beq \nu_c L_{\nu,c} \approx \nu_s L_{\nu,s} \left({\nu_c \over \nu_s}\right)^{\alpha_c}, \qquad \alpha_c = 1 + {\ln \tau \over \ln A}. \label{compt} \eeq The relative power in the synchrotron and Compton peaks therefore provides some information on the density in the inner regions of the flow, and thus on $\dot m_{in}$. Note that for the low luminosity systems considered here, $\tau \ll 1$ and $\alpha_c < 0$, so that the synchrotron luminosity dominates the Compton luminosity. Finally, bremsstrahlung emission produces a peak that typically extends from a few to a few hundred keV. In contrast to the other two processes discussed above, this emission arises from all radii in the flow. To see this, consider a self-similar ADAF with a wind, for which $\rho \propto r^{-3/2 + p}$ and $T_e \propto r^{-\epsilon}$ ($\epsilon \sim 1$ at large radii). Let the minimum flow temperature be $T_{min}$ (which occurs at $r_{out}$) and the maximum temperature be $T_{max}$ (near $r\sim1$). At photon energies $\ll kT_{min}$, the bremsstrahlung emission is given roughly by $\nu L_\nu \propto \nu$ (the spectral index is a little different from unity because of the Gaunt factor, which we ignore for simplicity), while for $kT_{min} \ll h \nu \ll kT_{max}$, it is $\nu L_\nu \propto \nu^{1/2 - 2p/\epsilon}$. In each case, the emission comes from the largest radius which satisfies $h \nu \sim k T(r)$. In our models, $T_{min}$ is $\sim (10^{12}/\ro)$ K; therefore, for $\ro=10^4$, $kT_{min}$ is $\sim 10$keV. For X-ray observations in the range $0.1-10$keV, $h \nu \lsim kT_{min}$. By above, $\nu L_{\nu}$ should be roughly proportional to $\nu$, but should flatten beyond about 10 keV; $\nu L_\nu$ will vary as $\nu^{1/2}$ beyond 10 keV if there is no wind ($p = 0$) and it will be flatter or even turn over (in $\nu L_\nu$) if there is a strong wind (large $p$). In all cases, the hardest emission, at $\gsim 100$ keV, occurs from the inner $r \lsim 100$, while the softer emission comes from $\sim \ro$ (this is particularly true for $p > 0$). Observations in the 1--10 keV X-ray band are therefore most sensitive to the outer regions of the ADAF. In these regions, the electron temperature is fairly well-determined since the gas is essentially virial and one-temperature. Therefore, observations of the bremsstrahlung emission at a few keV give direct information on the density of the outer flow, and thereby the accretion rate on the outside $\dot m_{out}$. In the sources that we consider below, the synchrotron peak is isolated and well observed (in X-ray binaries, the companion must be subtracted out); it occurs in softer bands, either in the optical or radio. The Compton and bremsstrahlung peaks, however, can sometimes be superposed in the X-ray band. In particular, an important consequence of the $m$ dependence of the frequency of the synchrotron peak ($\nu_s$) is that, without winds, the X-ray spectrum of ADAF models of low luminosity galactic black hole candidates is usually dominated by the first Compton peak. In low luminosity AGN, however, the precise behavior in the X-ray band is sensitive to the details (microphysics, accretion rate) of the model, being a competition between the second Compton peak and bremsstrahlung. This is because the peak synchrotron emission is at substantially lower frequencies and a synchrotron photon must be scattered more than once (or off of hotter electrons) in order to be scattered into the X-ray band; this tends to suppress the importance of Comptonization. Note that bremsstrahlung and Comptonization can be readily distinguished by their different spectral slopes in the X-ray band. If there is a thin disk outside the ADAF, as in our models of X-ray binaries (\S3), the emission of the disk is seen as a blackbody-like feature in the spectrum. This emission is in the red or near infrared for quiescent X-ray binaries in which the disk is restricted to $r>\ro\sim10^4$. \subsection{The Effects of Winds on Spectral Models} Bremsstrahlung emission at $\sim 1-10$ keV is rather insensitive to the presence of a wind (i.e., to $p$) since it originates in the outer regions of the flow and essentially measures $\mo$. At higher energies, $\gsim 10$ keV, however, the bremsstrahlung emission decreases with increasing $p$ ($\nu L_\nu \propto \nu^{1/2 - 2p/\epsilon}$) and thus provides a powerful probe of the flow density and the value of the parameter $p$ (see \S 6.2). By contrast, the predicted synchrotron emission decreases strongly with increasing $p$. There are two reasons for this. First, increasing $p$ decreases the density of the plasma near $r \sim 1$, where the high frequency synchrotron emission originates. This implies a lower gas pressure and hence a weaker magnetic field (for fixed $\beta$). Perhaps more importantly, the electron temperature decreases as $p$ increases. For the low luminosity systems considered in this paper, and for small $\delta$, the electrons are nearly adiabatic, i.e., $T_e \propto \rho^{\gamma_e - 1} \propto r^{(-1.5 + p)(\gamma_e -1)}$. When $p$ is large, the density profile is flatter, adiabatic compression is less efficient, and hence $T_e$ is smaller. By equation (\ref{lsynch}), the synchrotron emission is particularly sensitive to the electron temperature. Therefore, the synchrotron emission falls very rapidly with increasing $p$. This effect can, as we show explicitly below, be countered by increasing $\delta$, since a larger $\delta$ means stronger turbulent heating of the electrons and thus larger $T_e$. The Compton power decreases with increasing $p$ even more strongly than the synchrotron does. As equation (\ref{compt}) shows, $\nu_c L_{\nu,c}$ depends on both $\nu_s L_{\nu,s}$ and $\alpha_c$, both of which decrease because of the wind ($\alpha_c$ decreases because $\tau$ and $\theta_e$ both decrease). Increasing $\delta$ to restore the synchrotron power also increases the Compton power, as discussed in the following sections. \section{Soft X-ray Transients in Quiescence} Soft X-ray transients (SXTs) are mass transfer binaries which occasionally enter a high luminosity, ``outburst,'' phase, but most of the time remain in a very low luminosity, ``quiescent,'' phase. The spectra of quiescent SXTs are not consistent with a thin accretion disk model, which is unable to account for the fluxes and spectral slopes in the optical and X-ray bands consistently (e.g., McClintock et al. 1995). Narayan, McClintock, \& Yi (1996; see also Narayan et al. 1997a, Hameury et al. 1997) showed that this problem can be resolved if quiescent SXTs accrete primarily via ADAFs, with the thin disk confined to large radii, $r>r_{\rm out} \sim 10^4$. (Note that $r_{out}$ is taken here to be the same as the transition radius, $r_{tr}$, defined in previous papers. However, it need not be if winds only become important well inside the outer boundary of the ADAF.) In this section, we give a detailed description of models of the SXT V404 Cyg in quiescence. The X-ray data on V404 Cyg (Narayan et al. 1997a) are much superior to the data on other SXTs, which makes this system better suited for the parameter study we present. Table 1 lists the various parameter combinations we have tried for modeling V404 Cyg, and some of the characteristics of these models, including the microphysical parameters, the maximum electron temperature, and the radiative efficiency. Following Shahbaz et al. (1994), we have taken the mass of the black hole to be $m = 12$. Outbursts in SXTs are believed to be triggered by a thermal-viscous instability in the thin disk (enhanced mass transfer from the companion may also be important). Initial ADAF models of black hole SXTs in quiescence (Narayan, McClintock, \& Yi 1996) assumed that the observed optical emission from these systems was blackbody emission from a steady state outer thin disk. Wheeler (1996) and Lasota, Narayan, \& Yi (1996) pointed out that this was inconsistent because quiescent thin disks are not likely to be in steady state. Furthermore, in non-steady quiescent disks, the mass accretion rate decreases rapidly with radius (so as to maintain a roughly constant effective temperature $\sim$ a few thousand K; e.g., Cannizzo 1993). This implies a limit on $\ro$; if $\ro$ is too small, then the disk cannot supply sufficient mass to the inner ADAF to fit the X-ray observations. Quantitatively, the limit is $\ro \gsim 10^4$ for V404 Cyg (it is slightly smaller for A0620-00). We fix $\ro = 10^4$ in all the models presented here, and we take the thin disk to extend from $r = 10^4$ to $10^5$. \subsection{Spectral Models of V404 Cyg} Figure 1a shows spectral models of V404 Cyg for different $p$ for our standard microphysics parameters: $\alpha = 0.1$, $\beta = 10$, and $\delta = 0.01$. We see two important effects of changing $p$. First, in the X-ray band, models with weak winds (small $p$) have Compton-dominated X-ray spectra, while models with strong winds (large $p$) are bremsstrahlung dominated. The reason for this has already been explained in \S2. The Compton emission comes from near the black hole, while the bremsstrahlung comes from the outer regions of the ADAF. As the wind becomes stronger, the inner mass accretion rate $\dot m_{in}=\dot m_{out}\ro^{-p}$ becomes significantly smaller than $\dot m_{out}$, reducing the importance of Comptonization relative to bremsstrahlung. Associated with this switch is another interesting feature. For weak winds (small values of $p$), we see that $\dot m_{in}$ remains roughly constant when we change $p$ (e.g. $\dot m_{in}= 10^{-3}, 9 \times 10^{-4}$, for $p=0$, 0.2), while for large values of $p$, it is $\dot m_{out}$ that remains roughly constant (e.g. $\dot m_{out}=0.016$, 0.02, for $p=0.4$, 0.6). This is again easy to understand once we realize that the mass accretion rate is adjusted so as to reproduce the X-ray flux. When the model is Compton-dominated, the X-ray flux depends on $\dot m_{in}$, and so this quantity remains roughly the same as $p$ varies. However, when bremsstrahlung dominates, the X-ray flux depends on $\dot m_{out}$ and so it is $\dot m_{out}$ that remains constant. The second effect that is seen in Figure 1a (and even more clearly in Fig. 4a for Sgr A$^*$) is that the synchrotron emission becomes weaker as the wind becomes stronger. Once $p$ is large enough ($\gsim0.2$) for the model to become bremsstrahlung-dominated, $\dot m_{out}$ is more or less frozen at a fixed value. For yet larger $p$, $\dot m_{in}$ decreases rapidly with increasing $p$. Since the synchrotron emission depends primarily on $\dot m_{in}$, the synchrotron peak drops significantly in magnitude. The decrease in the synchrotron power at large $p$ is actually more dramatic than is apparent in Figure 1a (see Fig. 4a). Most of the optical/infrared flux in the $p=0.4$, 0.6 models in Figure 1a is blackbody emission from the outer disk, which depends only on $\dot m_{out}$, and does not change with $p$ at large $p$. This emission is cool (it is limited by the disk's effective temperature, which is about 5000 K) and the peak occurs at lower frequencies. The above analysis hinges on the change in the flow density with $p$. How is it modified if the microphysical parameters are varied from the canonical values taken above? Figure 1b shows models with a moderate wind, $p = 0.4$, for various values of the parameter $\beta$, which determines the strength of the magnetic field ($\alpha$ and $\delta$ are fixed at their canonical values of 0.1 and 0.01, respectively). Changing $\beta$ has little effect in the X-ray band since bremsstrahlung emission does not depend on the magnetic field strength. Increasing $\beta$ to $\sim 1$ naturally increases the synchrotron flux (eq. [\ref{lsynch}]). Even for $\beta = 1$, however, the synchrotron luminosity is too low by a factor of $\sim 2-3$. Note that, for $\beta = 1$, the optical emission in the models of Figure 1b is primarily synchrotron, while for $\beta \gsim 10$ it is primarily disk emission. Figure 2a shows models of V404 Cyg for $p = 0.4$ for several $\alpha$ ($\beta$ and $\delta$ are fixed at their canonical values of 10 and $10^{-2}$). These models show little variation in X-ray behavior with $\alpha$, but there is a decrease in optical emission as $\alpha$ decreases. This can be understood as follows. In the self-similar regime (reasonably valid at large radii), the flow density in an ADAF is $\rho\propto {\dot m}/\alpha$. Furthermore, the X-ray flux, which we fix to the observed value, arises from the outer regions of the ADAF via bremsstrahlung. Since the bremsstrahlung luminosity is $\propto \rho^2$, $\mo/\alpha$ remains roughly constant as $\alpha$ varies ($\mo = 5 \times 10^{-3}, 1.6 \times 10^{-2}$, $2.6 \times 10^{-2}$ for $\alpha = 0.03, 0.1$, $0.3$). All three models therefore have nearly the same density and temperature on the outside, which accounts for the lack of significant change in the X-ray band. For these models, however, the optical is dominated by disk emission, which is proportional to $\dot m_{out}$, rather than $\dot m_{out}/\alpha$. For smaller $\alpha$, $\mo$ is smaller and thus the disk emission decreases, as seen in Figure 2a. Finally, Figure 2b shows models of V404 Cyg for $p = 0.4$ for several $\delta$ ($\beta = 10$, $\alpha = 0.1$). For small $\delta\lsim10^{-2}$, the electrons are heated primarily by adiabatic compression (the first term on the right in eq. [\ref{ee}]) and so the results are nearly independent of the value of $\delta$. However, once $\delta\gsim10^{-2}$, turbulent heating ($H_e$) becomes the dominant heating mechanism. In this regime, increasing $\delta$ causes the electrons to become hotter (see Table 1), thereby increasing the synchrotron emission and Comptonization. For sufficiently large $\delta \gsim 0.1$, Comptonization dominates bremsstrahlung in the X-ray band, and the spectra begin to resemble the no-wind model shown by the solid line in Figure 1a. The above results are for ADAF models with winds, since that is the primary focus of this paper. For completeness, we have considered the sensitivity of no-wind (or weak wind) models to variations in $\alpha, ~\beta$ and $\delta$. Figure 3a shows models of V404 Cyg with $p = 0$ taking, for brevity, $\alpha \sim \beta^{-1}$, as suggested by numerical simulations of thin accretion disks (Hawley, Gammie, \& Balbus 1996). We see that larger values of $\alpha$ (and lower $\beta$) lead to more synchrotron emission. Figure 3b shows models for various $\delta$. Increasing $\delta$ leads to a noticeable increase in the electron temperature. This is seen explicitly in Table 1 and also in the larger ``displacement'' of the Compton peak relative to the synchrotron peak (see eq. [\ref{A}] for the Compton A parameter). Since the synchrotron and Compton emission increase strongly with temperature, the model with the largest $\delta$ has a significantly lower $\dot m$ (Table 1). \subsection{Comparison with Observations} Figures 1-3 show the available observational constraints on the spectrum of V404 Cyg (taken from Narayan et al. 1997a). The optical data give the luminosity of the source and constrain the effective temperature of the radiation to be $\gsim10^4$ K. There is an upper limit on the EUV flux, which is not very interesting since it is easily satisfied by all the models considered here. Thanks to an excellent ASCA observation, the luminosity in the X-ray band is known accurately, and the spectral index is also well constrained; in terms of $\nu L_{\nu} \propto \nu^{2-\Gamma}$, the 2 $\sigma$ error bars on the photon index $\Gamma$ are $2.1^{+0.5}_{-0.3}$. The observations give a few important constraints. First, the $>10^4$ K temperature of the optical argues against the outer thin disk as the source of this radiation (Lasota, Narayan, \& Yi 1996b; see below). Thus, the optical has to come from synchrotron and this emission must be stronger than the disk emission. Second, the observed photon index in X-rays in V404 Cyg is incompatible with the $\Gamma = 1$ expected for thermal bremsstrahlung (\S2). This means that the X-ray emission has to be Compton-dominated. There is preliminary evidence that the same is also true for A0620-00 (Narayan et al. 1996, 1997a), but the ROSAT data on that source (McClintock et al. 1995) are not sufficiently good to trust this conclusion; on the other hand, for GRO J1655-40, preliminary ASCA data in quiescence indicate a much harder X-ray spectrum than in V404 Cyg and A0620-00 (Hameury et al. 1997). Finally, the data show that the optical emission is about an order of magnitude larger (in $\nu L_\nu$) than the X-ray flux, another constraint that has to be satisfied by models. The baseline no-wind ($p=0$) model of V404 Cyg, with canonical values for the microphysics parameters, is shown by the solid line in Figure 1a. This model fits the observations well, as emphasized by Narayan et al. (1997a). It has roughly the right luminosity and effective temperature in the optical and is consistent with the X-ray data. The model shown here differs somewhat in the X-ray band from that shown in Narayan et al. (1997a). The difference is due to the different energy equation used here, which leads to hotter electrons and more pronounced Compton bumps. The value of $\dot m$ is also lower by a factor of a few. The observed X-ray spectral index in V404 Cyg places interesting constraints on models. For weak winds ($p \sim 0$) the models are in agreement with the observed slope for a wide range of microphysical parameters (Figure 3). For strong winds, however, most of the models are too bremsstrahlung-dominated to fit the X-ray slope. For small $\delta \sim 10^{-2}$, the observed slope rules out $p \gsim 0.3$, for any $\alpha$ and $\beta$ (Figures 1-2). For the value of $\ro = 10^4$ we have taken, this means that at least $\sim 10 \%$ of the mass supplied from the companion must reach the central object. As discussed by Lasota et al. (1996b), a thin disk cannot account for the observed optical emission in quiescent SXTs. This is because thin disk annuli with effective temperatures comparable to the observed values, $\sim 10^4$ K, are thermally and viscously unstable. In fact, within the context of the disk instability model, quiescent disks in black hole SXTs have effective temperatures $\sim 3000-5000$ K (Lasota et al. 1996b), too low to account for the observations. This is an independent argument against high $p$, low $\delta$ ADAF models, since the optical emission in these models is always dominated by the disk (the synchrotron being strongly suppressed by the large $p$). Perhaps the most interesting result to come out of these comparisons is that wind models agree with the data for larger values of the electron heating parameter $\delta$. The $p=0.4$, $\delta=0.3$ model in Figure 2b is as good as the no wind low-$\delta$ model shown in Figure 1a. The increase in $T_e$ associated with increasing $\delta$ brings the synchrotron emission into rough agreement with the observed optical flux, despite the low value of $\dot m_{in}$;\footnote{The synchrotron peak is a little too cool to fit the data; given the model uncertainties, however, the difference is not large enough to argue against these models.} at the same time, it shifts the balance in the X-ray band from bremsstrahlung to Comptonization, as required by observations. \section{The Galactic Center} Observations of the Galactic Center indicate that the mass of the black hole in Sgr A* is $m \sim (2.5 \pm 0.4) \times 10^6$ (Haller et al. 1996; Eckart \& Genzel 1997; Genzel et al. 1997). The accretion rate is estimated to lie in the range $10^{-4} \lsim \mo \lsim {\rm few}\,\times 10^{-3}$ (Genzel et al. 1994; Melia 1992), with the upper end of the range considered more likely (Coker \& Melia 1997). For a radiative efficiency of 10\%, and assuming that $\dot m$ is constant in the accretion flow, the implied luminosity is between $\sim 10^{40} $erg s$^{-1}$ and $\sim 10^{42}$erg s$^{-1}$. This is well above the bolometric luminosity of $\lsim 10^{37}$erg s$^{-1}$ inferred from observations in the radio to $\gamma$--rays (see Narayan et al. 1998a for a review of the observations). An optically thin, two temperature, ADAF model is a possible explanation for the low luminosity of Sgr A* (Rees 1982; Narayan, Yi, \& Mahadevan 1995, Manmoto et al. 1997, Narayan et al. 1998a, Mahadevan 1998). An alternative explanation is that most of the gas supplied at large radii is lost to a wind and very little reaches the central black hole (BB98). We consider both possibilities in this section. There is little observational evidence in Sgr A$^*$ for (or against) a particular value of $\ro$. In addition, there is little evidence that the accretion outside $\ro$ occurs via a thin disk. In our models, we set $\ro = 10^4$ and assume that, whatever form the plasma takes at larger radii, it is non-radiating. \subsection{Spectral Models of Sgr A$^*$} The parameters of each of our models of Sgr A* are given in Table 2. Figure 4a shows spectral models of Sgr A* for various $p$, taking $\alpha = 0.1$, $\beta = 10$, and $\delta = 0.01$. As usual, the value of $\dot m_{out}$ in each model has been adjusted to fit the X-ray flux (even though the ROSAT measurement used in the fits is really only an upper limit; cf. Narayan et al. 1998a). The results in Figure 4a are similar to those shown in Figure 1a for V404 Cyg, but the effects are somewhat more pronounced. At $\sim 1$ keV, the baseline no-wind ($p=0$) model in Figure 4a corresponds to an interesting situation: there are roughly equal contributions from the second Compton bump and bremsstrahlung. Recall that increasing $p$ always shifts the balance in favor of bremsstrahlung. Therefore, once $p$ is increased above zero, the Compton flux decreases, and the spectrum becomes bremsstrahlung-dominated in the X-ray band. This switch is evident already at $p=0.2$ and it becomes more pronounced for larger $p$. The three bremsstrahlung-dominated models with $p=0.2$, 0.4 and 0.6 all have nearly the same value of $\dot m_{out} \approx 2 \times 10^{-4}$, while there is a modest change in $\dot m_{out}$ between $p=0$ and 0.2 (see Table 2). Another effect seen very clearly in Figure 4a is the decrease in the synchrotron emission in the radio with increasing $p$. This is due to a decrease in both the magnetic field strength and $T_e$ (\S2). Note, in particular, that $T_e$ decreases by a factor of $\approx 5$ from $p = 0$ to $p = 0.6$ (Table 2). The dependence of wind models of Sgr A* on the microphysical parameters is very similar to that of V404 Cyg. The one exception is that all of the $p \gsim 0.2$ models in Figure 4-6 are bremsstrahlung-dominated in X-rays; we practically never see Comptonized power in the X-ray band. This is simply because the source of soft photons -- the synchrotron peak -- is at substantially lower frequencies in Sgr A* compared to the SXTs (recall that $\nu_s \propto m^{-1/2}$; \S2.2). Figures 4b, 5a and 5b show models of Sgr A* for $p = 0.4$ and different values of $\beta$, $\alpha$ and $\delta$. We reach two conclusions from these calculations. First, no combination of $\alpha$ and $\beta$ alone is sufficient to bring the synchrotron emission of wind models back to the level seen in the baseline no-wind model (Figures 4b \& 5a). Just as in V404 Cyg, however, increasing $\delta$ has a very strong effect on the synchrotron emission. Indeed, a $p=0.4$, $\delta=0.3$ model has roughly the same synchrotron power as the $p=0$, $\delta=0.01$ no-wind model. The reason is clear --- increasing $\delta$ causes a substantial increase in $T_e$ (Table 2), which compensates for the reduced density and field strength due to the wind. By contrast, neither $\alpha$ nor $\beta$ has a comparable effect. As Figure 5a shows, decreasing $\alpha$ decreases the radio emission in Sgr A*. This is because, near the central object, $\rho \propto \dot m$, and is only a weak function of $\alpha$. The density on the outside, however, scales as $\rho \propto \dot m/\alpha$. If we fix the X-ray flux, $\mo$ has to decrease as $\alpha$ decreases in order to keep $\rho$ the same on the outside and thereby produce the same level of bremsstrahlung radiation. This causes a decrease in the density in the interior of the flow and thus a decrease in the synchrotron emission in the radio (Figure 5a). Small values of $\alpha$ therefore add to the decrease in synchrotron emission that is associated with a strong wind. Finally, Figure 6 shows models of Sgr A* with no winds ($p = 0$) for several $\alpha \sim \beta^{-1}$ (Fig. 6a) and for several $\delta$ (Fig. 6b). \subsection{Comparison with Observations} Figures 4-6 show the observational data on Sgr A$^*$. The source has been reliably detected only in the radio and mm bands, where there is a good spectrum available (see Narayan et al. 1998a for original references to the data). It has been convincingly demonstrated that there is a break in the radio spectrum at around 50--100 GHz, so that the source apparently has two components, one which produces the emission below the break and the other above (Serabyn et al. 1997, Falcke et al. 1998). The latter component, which cuts off steeply somewhere between $10^{12}$ and $10^{13}$ Hz, has been fitted with the ADAF model (Narayan et al. 1998a). The model does not, however, fit the low frequency radio emission. This emission may be from an outflow (e.g. Falcke 1996), or, as in the model of Mahadevan (1998), may be due to non-thermal electrons (in Mahadevan's model, these, along with positrons, are created by the decay of charged pions created in proton-proton collisions). In the following we consider a model to be satisfactory if it fits the high frequency radio data. In the infrared, Menten et al. (1997) obtained a conservative 2.2 micron flux limit of 9 mJy, after accounting for extinction. The source may, however, be variable, since in later epochs Genzel et al. (1997) observed a $K\sim15$ source at the location of Sgr A$^*$; this corresponds to $F_\nu \approx 13$ mJy (Andreas Eckart, private communication). If verified, this would suggest that the infrared flux varies around a mean value of order a few mJy. This is a potentially stringent constraint on theoretical models. We, however, adopt a more conservative approach and treat the IR data as an upper limit. The implications of an IR detection are discussed in \S6. Although we fit our models to the ROSAT X-ray observations of the galactic center, they too should be treated as an upper limit because of ROSAT's poor angular resolution ($\approx 20$'') and the presence of diffuse emission at the Galactic Center. This is again the conservative approach, since a decrease in the X-ray flux would necessitate a decrease in the importance of mass loss; see \S6. Vargas et al. (1998) have recently provided new SIGMA upper limits on hard X-ray emission from the Galactic Center: between $40-75$ keV the luminosity is $\lsim 1.4 \times 10^{35}$ ergs s$^{-1}$ while between $75-150$ keV it is $\lsim 2.0 \times 10^{35}$ ergs s$^{-1}$. We have converted these to limits in $\nu L_\nu$ by assuming that the spectrum is flat in $L_\nu$, as would be appropriate for a no-wind bremsstrahlung spectrum. The solid line in Figure 4a (and the dotted line in Figure 6) shows our standard, no-wind ($p=0$), model, with $\beta = 10$, $\alpha = 0.1$, and $\delta = 0.01$. Figure 6 shows no-wind models for a number of other microphysics parameters. All of the no-wind models are in reasonable agreement with the data. In particular, they explain the mm fluxes fairly well as synchrotron emission, and produce Compton emission in the infrared roughly consistent with the Menten et al. (1997) limit. Relatively lower $\delta$, larger $\beta$, and smaller $\alpha$ are favored if the IR limit is taken to be stringent; if, however, the Genzel et al. (1997) observations are interpreted as a detection, the opposite is true --- larger $\delta$ and/or smaller $\beta$ are favored. In addition, the small $\beta$, large $\delta$ models tend to slightly overproduce the synchrotron emission at $\sim 10^{12}$ GHz. Note that these conclusions are somewhat different from those of Narayan et al. (1998a), who advocated strict equipartition ($\beta = 1$). As discussed in \S2, this is due to our use of a monatomic ideal gas adiabatic index in the electron energy equation. For small $\delta$, the electrons in Sgr A* are nearly adiabatic; since our adiabatic index is larger than that of Narayan et al. the electrons are hotter in our models. This accounts for the increased synchrotron emission and the need for weaker fields (larger $\beta$) for a fixed radio flux. To obtain a radio flux comparable to Narayan et al's $\beta = 1$ model, we require $\beta \approx 30$ for $p = 0$, or else $p \approx 0.2$. In fact, our no-wind, low $\delta$, models of Sgr A* are rather similar to those of Manmoto et al. (1997), who noted that smaller $\alpha$ were favored if the IR limit in Sgr A* is taken to be stringent. This is because our treatment of the electron energy equation is similar to Manmoto et al.'s. They took the electron adiabatic index to be $\gamma_e = 5/3$, which is correct in not including a magnetic contribution.\footnote{It is incorrect, however, in neglecting the change to $\gamma_e \approx 4/3$ for $r \lsim 10^2$ when the electrons become semi-relativistic.} What about large $p$, dynamically important winds? Such winds decrease the density and electron temperature in the interior of the flow, thereby severely suppressing the synchrotron and Compton emission (Figure 4a). Requiring wind models to produce the observed $10^{11}- 10^{12}$ Hz emission imposes the following strong constraints on the parameters. For small $\delta$, we require $p \lsim 0.2$ if we allow $\beta \sim 1$, $\alpha \sim 0.3$. If, for theoretical reasons, we were to favor larger $\beta \sim 10-100$, the constraint is even stronger. For the value of $\ro = 10^4$ used in our models, this corresponds to at least 15 \% of the mass supplied at large radii reaching the central object. As in V404 Cyg, the strongest degeneracy in the problem is with $\delta$. For $\delta \gsim 0.3$, large $p$ models of Sgr A* are in good agreement with the data (Figure 5b). All ADAF models of Sgr A* in the literature have $\mo \sim 10^{-4}$. This is at the lower end of the values considered plausible from Bondi capture of stellar winds in the Galactic center, and may be $\sim 10-100$ times smaller than favored values (Coker \& Melia 1997). It is interesting to see that winds do not alter this conclusion (see Table 2). Neither wind nor non-wind models can have $\mo$ much greater than $\sim 10^{-4}$ because, if they did, the bremsstrahlung emission would yield an X-ray luminosity well above the observed limits. Since the bremsstrahlung emission at $\sim 1$ keV is from the largest radii in the accretion flow, this conclusion is independent of the strength of winds in the system. In this context, it is important to note that, although $p = 0$, large $\delta$ models produce spectra reasonably consistent with the observations (Fig. 6b), they require small accretion rates, $\mo \sim 10^{-5}$ (Table 2). This argues against them as viable models. \section{Nuclei of Nearby Ellipticals} D98 recently measured high frequency radio fluxes from the nuclei of several nearby giant elliptical galaxies. These galactic nuclei are known to be unusually dim in X-rays compared to the accretion rates inferred from Bondi capture (Fabian \& Canizares 1988). Fabian \& Rees (1995) explained the low X-ray luminosities by invoking accretion via ADAFs. D98 found, however, that the predicted radio emission, based on the ADAF model (for $\beta=1$), exceeded their measured fluxes by $2-3$ orders of magnitude. They suggested several explanations for this large discrepancy, including the presence of strong winds or highly subthermal magnetic fields. If, as we are inclined to believe is the case, Sgr A* is simply a scaled version of the systems observed by D98, why is the predicted emission in Sgr A* roughly in accord with the observations while that in the nearby ellipticals is so discrepant? We might expect both theoretical predictions to be wrong, or both to be right, if the same physics operates in each system. We see two potential answers to this question. One possibility lies in the X-ray constraints in Sgr A* versus those in D98's sample. In Eddington units, i.e, scaled with respect to the mass of the black hole, the X-ray detection/upper limit in Sgr A* is $\sim 2.5$ orders of magnitude below the upper limits in D98's sample. This means that we have a significantly stronger constraint on the accretion rate in Sgr A$^*$. If the X-ray luminosities (in Eddington units) of the ellipticals were as low as in Sgr A$^*$, then models similar to those that work for Sgr A$^*$ would work for the ellipticals as well. It would mean, however, that D98's estimate of $\mo$ is too large, by a factor $\sim 30$ (see below). The other possibility is that the high frequency ($>10^{11}$ Hz) radio observations of Sgr A*, which the ADAF model fits reasonably well, do not probe the accretion flow at all. If the high resolution VLBI observations at 86 GHz represent the true synchrotron emission from the ADAF in Sgr A*, and the higher frequency radio emission is from a completely different source, then typical no-wind (e.g. $p = 0$, $\beta \sim 1$) models would overpredict the synchrotron luminosity by $\sim 3$ orders of magnitude, just as D98 found for the ellipticals. To investigate these issues further, Figure 7 shows a series of models of NGC 4649, which D98 consider to be the most convincing member of their sample. The data are taken from their Table 5. We take $m = 8 \times 10^9$ (slightly higher than D98's $4 \times 10^9$ because we find this mass fits the location of the radio peak better), $\ro = 10^4$, and assume a distance of $15.8$ Mpc. All calculations were done with $\alpha = 0.1$ and $\beta = 10$. Table 3 shows the parameters for the models. The solid line in Figure 7a corresponds to our ``standard'' ADAF model: $p = 0$, $\delta = 0.01$, and $\mo = 10^{-3}$. The latter value corresponds to the Bondi mass accretion rate estimated by D98. In agreement with D98, we find that, at this accretion rate, the model overpredicts the radio emission by $\sim$ 3 orders of magnitude. To make matters worse, our model is also in violation of the X-ray upper limit, in contrast to D98, whose ``standard'' ADAF model just satisfies the upper limits. The difference is primarily because our electrons are hotter --- D98 used Esin et al's (1998) electron adiabatic index. We have varied $p$ and $\mo$ in our models to judge their sensitivity to these parameters.\footnote{Initially, we found important quantitative differences between our models with varying $p$ and $\mo$ and the models in the original version of D98's paper on astro-ph. We have determined, however, that this was due to the fact that they did not use the electron temperature profile appropriate for the given $\mo$ and $p$ (Di Matteo, private communication). In particular, they originally required $p = 1$ and $\ro = 300$ to fit the radio flux at $\mo = 10^{-3}$, while their new calculations give $p \approx 0.8$ and $\ro \approx 80$ (since they take the inner radius of the flow to be $r = 3$, this corresponds to $\approx 7 \%$ of the incoming mass accreted, comparable to our value of $\approx 10 \%$). In addition, at $p = 0$, they originally required $\mo = 10^{-6}$ to fit the radio flux, while they now require $\mo \approx 10^{-5}$, again in reasonable agreement with our value of $\mo \approx 10^{-4.5}$.} The dotted line in Figure 7a is a model with $p = 0.25$ and $\delta = 10^{-2}$. This is roughly the $p$ we need to account for the observed radio flux at low $\delta$ (note that this model is also in agreement with the X-ray upper limit). In Figure 7b we show several models of NGC 4649 for $\mo = 10^{-4.5}$. This accretion rate is $\sim 30$ times smaller than the value D98 infer from Bondi capture. The solid line shows a standard no-wind model: $p = 0$ and $\delta = 0.01$. This model is in reasonable agreement with the radio flux. If $T_e$ and $\beta$ are fixed, equation (\ref{lsynch}) shows that the peak synchrotron luminosity scales like $\nu L_\nu \propto \dot m^{3/2}$. Thus, to decrease $\nu L_\nu$ by a factor of $10^3$, as required by the observations, $\mo$ must decrease by $\sim 100$. In fact, due to other factors, the required decrease is even less, $\sim 30$. The above argument requires that $T_e(r)$ should be roughly the same for $\mo = 10^{-3}$ and for $\mo = 10^{-4.5}$. This is confirmed by the numerical results shown in Table 3, but it can also be understood simply by noting that in both models the electrons adiabatically compress as the gas flows in. To see this, it is sufficient to estimate the PdV energy gained per unit time by the electrons in a spherical shell of radius $R$ and thickness $dR \sim R$ as they accrete onto the central object (cf eq. [\ref{ee}]), \beq q_c \approx k T_e v {d n_e \over dR} 4 \pi R^3 \approx {m_e \over m_p} \theta_e(r) \dot M(r) c^2 \approx 10^{43} \left({\theta_e \over 1}\right) \left({\dot m \over 10^{-3}}\right)\left({m \over 8 \times 10^9}\right) {\rm ergs \ s^{-1}}. \label{comp} \eeq Our most luminous model (solid line, $\mo = 10^{-3}$; Figure 7a) has $\nu L_\nu \approx 10^{41.5} {\rm ergs \ s^{-1}}$ at the synchrotron peak (and a bolometric luminosity of $\approx 10^{42} {\rm ergs \ s^{-1}}$), which is $\ll q_c$. For lower $\mo$, the ratio of $\nu_s L_{\nu,s}$ to $q_c$ is even smaller. Therefore, the electrons in all of our low $\delta$ models are nearly adiabatic, and thus $T_e(r)$ is essentially unchanged as $\mo$ decreases from $10^{-3}$ to $10^{-4.5}$. The short dashed lines in Figure 7 show $p = 0.25$, $\delta = 0.3$ models for $\mo = 10^{-3}$ (Figure 7a) and $\mo = 10^{-4.5}$ (Figure 7b). As suggested by the previous results on V404 Cyg and Sgr A$^*$, these models are comparable to the $p = 0$, $\delta = 0.01$ models. In particular, for $\mo = 10^{-4.5}$, the wind model gives reasonably good agreement with D98's radio data, while for $\mo = 10^{-3}$ it is in disagreement. The results of Figure 7 thus lead to two scenarios for understanding NGC 4649, depending on which value of $\mo$ we take, $10^{-4.5}$ or $10^{-3}$. (There is, of course, a range of intermediate scenarios if we take intermediate values of $\mo$.) If $\mo \approx 10^{-4.5}$, then we require $0 \lsim p \lsim 0.25$ for $0 \lsim \delta \lsim 0.3$. As we saw for V404 Cyg and Sgr A$^*$, increasing $p$ requires a corresponding increase in $\delta$, though the precise mapping between the two parameters in the case of NGC 4649 is slightly different. As in V404 Cyg and Sgr A$^*$, strong wind, low $\delta$ models are ruled out as they cannot explain the radio data (dotted line; Figure 7b). If, on the other hand, $\mo \approx 10^{-3}$, as proposed by D98, then we require $0.25 \lsim p \lsim 0.55$ for $0 \lsim \delta \lsim 0.3$. Low $\delta$, low $p$, is ruled out by the observed radio flux (Figure 7a), which is a different result from that obtained in V404 Cyg and Sgr A$^*$. In addition, the region of $p-\delta$ space available for NGC 4649 at $\mo = 10^{-3}$, if applied to our models of V404 Cyg and Sgr A$^*$, is somewhat uncomfortable. For example, at $p \approx 0.25$ and low $\delta$ (which gives an acceptable fit in NGC 4649 if $\mo \approx 10^{-3}$), the predicted X-ray spectral index in V404 Cyg is only marginally compatible with the 2 $\sigma$ ASCA measurements (Figure 1a). Similarly, the radio luminosity of Sgr A* for $p = 0.25$ and $\delta = 0.01$ is $1-2$ orders of magnitudes below the peak observed luminosity. One might therefore have to abandon the claim that the $10^{11}- 10^{12}$ Hz emission in Sgr A$^*$ is synchrotron emission from the ADAF. If we believe that Sgr A*, V404 Cyg, and NGC 4649 are simply scaled versions of each other (in $m$ and $\mo$, and perhaps somewhat in $p$, $\delta$, $\beta$, $\alpha$, and $\ro$), the above considerations are suggestive, if only weakly, of an $\mo \sim 10^{-4.5}$ rather than $10^{-3}$ in NGC 4649. This conclusion is independent of the importance of winds. \section{Key Future Observations} There are two main conclusions from the previous sections: (i) If the electron heating parameter $\delta$ is small, current observations rule out ADAF models with moderate winds (say $p\gsim0.25$ as an average for V404 Cyg and Sgr A*). (ii) If $\delta$ is allowed to have large values --- given the uncertain role of magnetic reconnection there is no strong theoretical argument against this --- current observations provide no information on the importance of winds in ADAFs; large $\delta$, strong wind models are in as good agreement with the data as low $\delta$, weak wind models. Figure 8 shows the $p/\delta$ degeneracy explicitly for V404 Cyg (Fig. 8a) and Sgr A* (Fig. 8b). We see that the two $p = 0.4, ~\delta \approx 0.3$ models are very similar to the $p = 0, ~\delta = 0.01$ models. Indeed, there is a family of intermediate solutions with values of $p$ and $\delta$ in between these two extremes. Note, however, that the very large $p = 0.8, ~\delta = 0.75$ models shown in Figure 8 differ more noticeably. For such large $p$, the electron temperatures needed to make the X-ray spectrum of V404 Cyg Compton dominated, rather than bremsstrahlung dominated, are so large that the Compton peak moves well into the X-ray band. This is discussed further in the next subsection. In the case of Sgr A*, for $p \sim 1$, $\ro \sim 10^4$ and $\mo \sim 10^{-4}$, the inner mass accretion rate is $\dot m_{in} \sim 10^{-8}$. The density in the interior is then so low that the synchrotron emission is no longer highly self-absorbed; this accounts for the substantially broader synchrotron peak. Leaving aside the $p=0.8$ models, we conclude that there is a degeneracy between $p$ and $\delta$ such that any model in the range $0 p$ will rotate more quickly, and thus have a larger viscous dissipation per unit mass. In particular, then, our conclusion that low $\delta$ models of Sgr A* and V404 Cyg are compatible with the observations only for $p \lsim 0.25$ need not conflict with theoretical estimates that $p \sim 1$ is needed for the Bernoulli parameter of the accreting gas to be negative. It may simply mean that winds are important only over $\sim 1-1.5$ decades of radius ($r_w \approx 10-30$), instead of 4 decades as we have assumed here. 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Markovic (Cambridge: Cambridge University press) \\ } \newpage \begin{deluxetable}{lcccccccc} %\doublespace %\footnotesize \tablecaption{Model Parameters for V404 Cyg: $\ro = 10^4$, $m = 12$, $\dot M_{\rm in} \equiv \dot M_{\rm out} 10^{-4 p}$} \tablewidth{0pt} \tablehead{ \colhead{Fig.} & \colhead{$\alpha$} & \colhead{$\beta$} & \colhead{$\delta$} & \colhead{$p$} & \colhead{$\mo \times 10^2$} & \colhead{$T_{\rm e, max} \times 10^{-10}$} & \colhead{$L/{\dot M_{\rm out}} c^2$} & \colhead{$L/{\dot M_{\rm in}} c^2$}} \startdata 1a & 0.1 & 10 & 0.01 & 0 & 0.1 & 1.0 & $1.1 \times 10^{-3}$ & $1.1 \times 10^{-3}$ \nl 1a & 0.1 & 10 & 0.01 & 0.2 & 0.54 & 0.92 & $1.6 \times 10^{-4}$ & $1.0 \times 10^{-3}$ \nl 1a & 0.1 & 10 & 0.01 & 0.4 & 1.6 & 0.87 & $2.2 \times 10^{-5}$ & $8.8 \times 10^{-4}$ \nl 1a & 0.1 & 10 & 0.01 & 0.6 & 2.0 & 0.6 & $7.5 \times 10^{-6}$ & $2.0 \times 10^{-3}$ \nl \nl 1b & 0.1 & 1 & 0.01 & 0.4 & 1.2 & 0.57 & $6.0 \times 10^{-5}$ & $2.4 \times 10^{-3}$ \nl 1b & 0.1 & 10 & 0.01 & 0.4 & 1.6 & 0.87 & $2.2 \times 10^{-5}$ & $8.8 \tfo $ \nl 1b & 0.1 & 100 & 0.01 & 0.4 & 1.7 & 1.0 & $1.2 \times 10^{-5}$ & $4.8 \tfo $\nl \nl 2a & 0.3 & 10 & 0.01 & 0.4 & 2.6 & 0.89 & $1.9 \times 10^{-5}$ & $7.6 \tfo$ \nl 2a & 0.1 & 10 & 0.01 & 0.4 & 1.6 & 0.87 & $2.2 \times 10^{-5}$ & $8.8 \tfo$ \nl 2a & 0.03 & 10 & 0.01 & 0.4 & 0.59 & 0.77 & $5.5 \times 10^{-5}$ & $2.2 \tt$ \nl \nl 2b & 0.1 & 10 & $10^{-3}$ & 0.4 & 1.6 & 0.87 & $2.2 \times 10^{-5}$ & $8.8 \tfo$ \nl 2b & 0.1 & 10 & 0.01 & 0.4 & 1.6 & 0.87 & $2.2 \times 10^{-5}$ & $ 8.8 \tfo$ \nl 2b & 0.1 & 10 & 0.03 & 0.4 & 1.2 & 0.94 & $3.6 \times 10^{-5}$ & $ 1.4 \tt$ \nl 2b & 0.1 & 10 & 0.1 & 0.4 & 1.0 & 1.15 & $6.2 \times 10^{-5}$ & $ 2.5 \tt$ \nl 2b & 0.1 & 10 & 0.3 & 0.4 & 0.58 & 1.8 & $1.7 \times 10^{-4}$ & $6.8 \tt$ \nl \nl 3a & 0.3 & 1 & 0.01 & 0 & 0.1 & 0.74 & $1.8 \times 10^{-3}$ & $1.8 \tt$ \nl 3a & 0.1 & 10 & 0.01 & 0 & 0.1 & 1.0 & $1.1 \times 10^{-3}$ & $1.1 \tt$\nl 3a & 0.03 & 30 & 0.01 & 0 & 0.068 & 1.1 & $1.1 \times 10^{-3}$ & $1.1 \tt$ \nl \nl 3b & 0.1 & 10 & 0.01 & 0 & 0.1 & 1.0 & $1.1 \times 10^{-3}$ & $1.1 \tt$ \nl 3b & 0.1 & 10 & 0.1 & 0 & 0.05 & 1.3 & $2.5 \times 10^{-3}$ & $2.5 \tt$ \nl 3b & 0.1 & 10 & 0.3 & 0 & 0.01 & 2.4 & $6.4 \times 10^{-3}$ & $6.4 \tt$ \nl \nl 8a & 0.1 & 10 & 0.01 & 0 & 0.1 & 1.0 & $1.1 \times 10^{-3}$ & $1.1 \tt$ \nl 8a & 0.1 & 10 & 0.3 & 0.4 & 0.58 & 1.8 & $1.7 \times 10^{-4}$ & $6.8 \tt$ \nl 8a & 0.1 & 10 & 0.75 & 0.8 & 0.64 & 4.8 & $6.3 \times 10^{-5}$ & $0.1$ \nl \enddata \label{tab-v} \end{deluxetable} \newpage \begin{deluxetable}{lcccccccc} %\doublespace %\footnotesize \tablecaption{Model Parameters for Sgr A*: $\ro = 10^4$, $m = 2.5 \times 10^6$, $\dot M_{\rm in} \equiv \dot M_{\rm out} 10^{-4 p}$} \tablewidth{0pt} \tablehead{ \colhead{Fig.} & \colhead{$\alpha$} & \colhead{$\beta$} & \colhead{$\delta$} & \colhead{$p$} & \colhead{$\mo \times 10^4$} & \colhead{$T_{\rm e, max} \times 10^{-10}$} & \colhead{$L/{\dot M_{\rm out}} c^2$} & \colhead{$L/{\dot M_{\rm in}} c^2$}} \startdata 4a & 0.1 & 10 & 0.01 & 0 & 0.68 & 2.0 & $2.6 \times 10^{-5}$ & $2.6 \tfi$\nl 4a & 0.1 & 10 & 0.01 & 0.2 & 1.8 & 1.1 & $5.5 \times 10^{-7}$ & $3.5 \tsi$\nl 4a & 0.1 & 10 & 0.01 & 0.4 & 2.4 & 0.63 & $1.2 \times 10^{-7}$ &$4.8 \tsi$\nl 4a & 0.1 & 10 & 0.01 & 0.6 & 2.8 & 0.37 & $8.1 \times 10^{-8}$ & $2.0 \tfi$ \nl \nl 4b & 0.1 & 1 & 0.01 & 0.4 & 1.9 & 0.47 & $1.2 \times 10^{-7}$ & $4.8 \tsi$ \nl 4b & 0.1 & 10 & 0.01 & 0.4 & 2.4 & 0.63 & $1.2 \times 10^{-7}$ & $4.8 \tsi$ \nl 4b & 0.1 & 100 & 0.01 & 0.4 & 2.4 & 0.65 & $1.2 \times 10^{-7}$ & $4.8 \tsi$ \nl \nl 5a & 0.3 & 10 & 0.01 & 0.4 & 4.0 & 0.72 & $ 7.6 \times 10^{-8}$ & $3.1\tsi$\nl 5a & 0.1 & 10 & 0.01 & 0.4 & 2.4 & 0.63 & $1.2 \times 10^{-7}$ &$4.8\tsi$\nl 5a & 0.03 & 10 & 0.01 & 0.4 & 1.0 & 0.54 & $2.8 \times 10^{-7}$ &$1.1 \tfi$\nl \nl 5b & 0.1 & 10 & 0.01 & 0.4 & 2.4 & 0.63 & $1.2 \times 10^{-7}$ &$4.8\tsi$\nl 5b & 0.1 & 10 & 0.1 & 0.4 & 1.7 & 1.6 & $ 3.1 \times 10^{-7}$ &$1.2\tfi$\nl 5b & 0.1 & 10 & 0.3 & 0.4 & 1.7 & 3.5 & $3.1 \times 10^{-6}$ &$1.2\tfo$\nl \nl 6a & 0.3 & 1 & 0.01 & 0 & 0.69 & 1.6 & $7.6 \times 10^{-5}$ &$7.6\tfi$\nl 6a & 0.1 & 10 & 0.01 & 0 & 0.68 & 2.0 & $2.6 \times 10^{-5}$ &$2.6\tfi$\nl 6a & 0.03 & 30 & 0.01 & 0 & 0.48 & 1.6 & $7.7 \times 10^{-6}$ &$7.7\tsi$\nl \nl 6b & 0.1 & 10 & 0.01 & 0 & 0.68 & 2.0 & $2.6 \times 10^{-5}$ &$2.6\tfi$\nl 6b & 0.1 & 10 & 0.1 & 0 & 0.54 & 2.3 & $2.6 \times 10^{-5}$ &$2.6\tfi$\nl 6b & 0.1 & 10 & 0.3 & 0 & 0.11 & 5 & $1.0 \times 10^{-4}$ &$1.0\tfo$\nl \nl 8b & 0.1 & 10 & 0.01 & 0 & 0.68 & 2.0 & $2.6 \times 10^{-5}$ &$2.6\tfi$\nl 8b & 0.1 & 10 & 0.4 & 0.4 & 1.6 & 4.4 & $6.9 \times 10^{-6}$ &$2.7\tfo$\nl 8b & 0.1 & 10 & 0.75 & 0.8 & 1.2 & 13.0 & $3.7 \times 10^{-6}$ &$5.9\tt$\nl \enddata \label{tab-s} \end{deluxetable} \newpage \begin{deluxetable}{lcccccccc} %\doublespace %\footnotesize \tablecaption{Model Parameters for NGC 4649: $\ro = 10^4$, $m = 8 \times 10^9$, $\dot M_{\rm in} \equiv \dot M_{\rm out} 10^{-4 p}$} \tablewidth{0pt} \tablehead{ \colhead{Fig.} & \colhead{$\alpha$} & \colhead{$\beta$} & \colhead{$\delta$} & \colhead{$p$} & \colhead{$\mo$} & \colhead{$T_{\rm e, max} \times 10^{-10}$} & \colhead{$L/{\dot M_{\rm out}} c^2$} & \colhead{$L/{\dot M_{\rm in}} c^2$}} \startdata 7a & 0.1 & 10 & 0.01 & 0 & $10^{-3}$ & 1.9 & $3.1 \times 10^{-4}$&$3.1\tfo$ \nl 7a & 0.1 & 10 & 0.3 & 0.25 & $10^{-3}$ & 3.4 & $3.6 \times 10^{-5}$&$3.6\tfo$ \nl 7a & 0.1 & 10 & 0.01 & 0.25 & $10^{-3}$ & 1.0 & $2.1 \times 10^{-6}$&$2.1\tfi$ \nl 7a & 0.1 & 10 & 0.3 & 0.54 & $10^{-3}$ & 2.4 & $6.6 \times 10^{-7}$&$9.5\tfi$ \nl \nl 7b & 0.1 & 10 & 0.01 & 0 & $10^{-4.5}$ & 1.9 & $2.6 \times 10^{-6}$&$2.6\tsi$ \nl 7b & 0.1 & 10 & 0.3 & 0.25 &$10^{-4.5}$ & 3.5 & $9.1 \times 10^{-7}$&$9.1\tsi$ \nl 7b & 0.1 & 10 & 0.01 & 0.25 & $10^{-4.5}$ & 1.0 & $5.7 \times 10^{-8}$&$5.7\tse$ \nl \enddata \label{tab-ngc} \end{deluxetable} \newpage \vskip 5in \newpage \begin{figure} \plottwo{fig1a.ps}{fig1b.ps} \caption{(a) Spectral models of V404 Cyg for several values of $p$, taking $\alpha = 0.1$, $\beta = 10$, and $\delta = 0.01$. (b) Models for several $\beta$, taking $\alpha = 0.1$, $p = 0.4$, and $\delta = 0.01$.} \end{figure} \begin{figure} \plottwo{fig2a.ps}{fig2b.ps} \caption{(a) Spectral models of V404 Cyg for several values of $\alpha$, taking $p = 0.4$, $\beta = 10$, and $\delta = 0.01$. (b) Models for several $\delta$, taking $\alpha = 0.1$, $p = 0.4$, $\beta = 10$.} \end{figure} \newpage \begin{figure} \plottwo{fig3a.ps}{fig3b.ps} \caption{(a) No wind ($p = 0$) spectral models of V404 Cyg for several values of $\alpha$ and $\beta$, taking $\delta = 0.01$. (b) Models for several values of $\delta$, taking $p = 0$, $\alpha = 0.1$, and $\beta = 10$.} \end{figure} \begin{figure} \plottwo{fig4a.ps}{fig4b.ps} \caption{(a) Spectral models of Sgr A* for several values of $p$, taking $\alpha = 0.1$, $\beta = 10$, and $\delta = 0.01$. (b) Models for several $\beta$, taking $\alpha = 0.1$, $p = 0.4$, and $\delta = 0.01$.} \end{figure} \newpage \begin{figure} \plottwo{fig5a.ps}{fig5b.ps} \caption{(a) Spectral models of Sgr A* for several values of $\alpha$, taking $p = 0.4$, $\beta = 10$, and $\delta = 0.01$. (b) Models for several $\delta$, taking $\alpha = 0.1$, $p = 0.4$, $\beta = 10$.} \end{figure} \begin{figure} \plottwo{fig6a.ps}{fig6b.ps} \caption{(a) Spectral models of Sgr A* for several values of $\alpha$ and $\beta$, taking $p = 0$, $\delta = 0.01$. (b) Models for several $\delta$, taking $\alpha = 0.1$, $\beta = 10$, and $p = 0$.} \end{figure} \newpage \begin{figure} \plottwo{fig7a.ps}{fig7b.ps} \caption{Spectral models of NGC 4649 for several values of $p$ and $\delta$, taking $\alpha = 0.1$, $\beta = 10$, $\ro = 10^4$, and $m = 8 \times 10^9$. Panel (a) assumes that the accretion rate at the outer edge of the flow is $\mo = 10^{-3}$, while panel (b) takes $\mo = 10^{-4.5}$.} \end{figure} \begin{figure} \plottwo{fig8a.ps}{fig8b.ps} \caption{Spectral models of V404 Cyg (Fig. 8a) and Sgr A* (Fig. 8b) for several values of $p$ and $\delta$, taking $\alpha = 0.1$, $\beta = 10$, and $\ro = 10^4$.} \end{figure} \end{document} We feel that it is important to work with global flow dynamics rather than self-similar dynamics. Both give similar results at large radii (Narayan, Kato \& Honma 1997, Chen, Abramowicz \& Lasota 1997), but they differ significantly near the black hole; the global solutions make a sonic transition near the black hole and fall in supersonically, whereas the self-similar solutions remain subsonic throughout. Because of this, the two solutions differ in their predicted densities near the black hole. Since most of the radiation originates from close to the black hole, it is important to treat this region of the flow accurately. The difference between the global and self-similar models is especially important for small values of the viscosity parameter $\alpha$. It is also important when considering the effect of changing the value of $\alpha$. Two models with different $\alpha$ but the same value of $\dot M/\alpha$ have similar densities, temperatures and emission characteristics in the outer self-similar region of the flow. They would, however, differ markedly in the inner regions. It is worth explicitly reiterating the effects of winds on spectral models, and the resulting degeneracy with microphysics parameters. Bremsstrahlung emission at $\sim 1-10$ keV is dominated by large radii in the flow and is sensitive primarily to the mass accretion rate on the outside $\mo$; it is rather insensitive to the wind parameter $p$ (defined in eq. [\ref{cont}]) which describes how $\dot m$ varies with $r$. By contrast, synchrotron and Compton emission originate from the interior of the flow, and, for a given $\mo$, decrease significantly with increasing $p$ (increasing strength of the wind). The magnetic field strength and the optical depth in the interior of the flow decrease because of the decreased gas density and pressure at large $p$. In addition, electrons in low luminosity ADAF models are often nearly adiabatic. Since winds decrease the density contrast between the interior and exterior of the flow, the electron temperature $T_e$ is lower in wind models than in non-wind models (other parameters being equal). Self-absorbed synchrotron emission being highly temperature sensitive ($\propto T^7_e$; see eq. [\ref{lsynch}]), the decrease in $T_e$ with increasing $p$ causes a substantial decrease in the synchrotron emission. The extreme temperature sensitivity of self-absorbed synchrotron emission is the reason why strong wind models with strong turbulent heating of electrons (large values of $\delta$) are semi-quantitatively similar to weak wind, low $\delta$ models. The increased $T_e$ associated with the large $\delta$ readily compensates for the reduced synchrotron emission associated with the strong wind. By contrast, for low values of $\delta$, no combination of $\alpha$ and $\beta$ in strong wind models is able to ``mimic'' weak wind models. In particular, low values of $\alpha$ do not bring strong wind models into better agreement with weak wind models; they actually make the discrepancy worse (\S4, Figure 5a). D98 found that they needed $p \sim 1$ for $\ro \sim 100$, which corresponds to $p \approx 0.5$ at $\ro = 10^4$, a noticeably larger value. For our $p$, $\dot m$ in the interior is ``only'' a factor of $\sim 10$ smaller than $\mo$, whereas D98's $\dot m_{in}$ is 100 times smaller than $\mo$. The reason that a factor of 10 decrease in $\dot m_{in}$ is able to decrease the synchrotron luminosity by $\sim 3$ orders of magnitude is that the electron temperature also decreases as $p$ increases (see Table 3 and the discussion in \S2). By equation (\ref{lsynch}), the decrease in $T_e$ has a significant effect on the synchrotron luminosity. By contrast, D98 found that they needed to reduce $\mo$ to $\sim 10^{-6}$ to explain the radio flux with a $\beta \sim 1$, $p = 0$ model. This discrepancy is puzzling. ------------- End Forwarded Message -------------