% aa.dem % AA vers. 4.01, LaTeX class for Astronomy & Astrophysics % demonstration file % (c) Springer-Verlag HD %----------------------------------------------------------------------- % %\documentclass[referee]{aa} % for a referee version % \documentclass{aa} \usepackage{amsmath} \usepackage{psfig} %\usepackage{rotate} \usepackage{astrobib} \usepackage{journals} %\usepackage{graphicx} \newcommand{\figwidth}{0.5\textwidth} \begin{document} \title{The Nature of the 10 Kilosecond X-ray Flare in Sgr A*} \author{Sera Markoff\thanks{Humboldt research fellow} \and Heino Falcke\and Feng Yuan \and Peter L. Biermann} \institute{Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel 69, D-53121 Bonn, Germany} \titlerunning{X-ray Flare in Sgr A*} \authorrunning{Markoff et al.} \offprints{smarkoff@mpifr-bonn.mpg.de} \date{Received ; Accepted} \abstract{The X-ray mission {\em Chandra} has observed a dramatic X-ray flare -- a brightening by a factor of 50 for only three hours -- from Sgr A*, the Galactic Center supermassive black hole. Sgr A* has never shown variability of this amplitude in the radio and we therefore argue that a jump of this order in the accretion rate does not seem the likely cause. Based on our model for jet-dominated emission in the quiescent state of Sgr A*, we suggest that the flare is a consequence of extra electron heating near the black hole. This can either lead to direct heating of thermal electrons to $T_{\rm e}\sim6\cdot10^{11}$ K and significantly increased synchrotron-self Compton emission, or result from non-thermal particle acceleration with increased synchrotron radiation and electron Lorentz factors up to $\gamma_{\rm e}\ga10^{5}$. While the former scenario is currently favored by the data, simultaneous VLBI, submm, mid-infrared and X-ray observations should ultimately be able to distinguish between the two cases. \keywords{Galaxy: center -- galaxies: jets -- X-rays: galaxies -- radiation mechanisms: non-thermal -- accretion, accretion disks -- black hole physics } } \maketitle \section{Introduction} Sgr A*, the compact radio core at the center of our Galaxy \cite{ReidReadheadVermeulen1999,BackerSramek1999a}, has been perplexing modelers since its discovery \cite{BalickBrown1974}. In contrast to nearby LLAGN \cite{Ho1999}, Sgr A* was until recently only positively detected as a radio source. Its mass is determined at $2.6\cdot10^6 M_{\sun}$ within $\sim 0.01$ pc \cite{HallerRiekeRieke1996,EckartGenzel1996,GhezKleinMorris1998} and its integrated radio luminosity has remained steady within a factor of two \cite{ZhaoBowerGoss2001}, at $\sim 10^{-9}$ orders of magnitude less than its corresponding Eddington luminosity. All models to explain the radio emission so far have focused on radiative inefficiency as the primary explanation for this dimness, and are comprised mainly of accretion/inflow solutions \cite{MeliaLiuCoker2001,NarayanMahadevanGrindlay1998} outflow solutions (\citeNP{FalckeMannheimBiermann1993}; \citeNP{FalckeMarkoff2000}, hereafter FM00) and combinations thereof \cite{YuanMarkoffFalcke2001}. A recent review of Sgr A* can be found in \citeN{MeliaFalcke2001}. Recently, Sgr A* was finally detected in the X-rays by {\em Chandra} \cite{Baganoffetal2001} with a rather soft spectrum. During the second observational cycle, \citeN{Baganoffetal2001b} detected an X-ray flare lasting about 10 ks and with a peak luminosity $\sim 50$ times higher than the quiescent state \cite{Baganoffetal2001}. The averaged flare spectrum after taking into account dust scattering is best fit with a power-law (spectral index $\alpha\sim0.3$), which is significantly harder than that of the quiescent state ($\alpha\sim1.2$). The longest time scale (10 ks) corresponds to $\sim 390 r_{\rm s}$ where $r_{\rm s}=2GM_\bullet/c^2$ is the Schwarzschild radius, which argues against thermal bremsstrahlung from the outer radii, e.g. from a standard Advection Dominated Accretion Flow (ADAF; \citeNP{NarayanMahadevanGrindlay1998}). The smallest time scale in the flare is roughly $600$ s, suggesting activity at scales of $\sim 20 r_{\rm s}$, which means the flare originated close to the central engine. The variability and the spectral index of Sgr A* in the X-rays are consistent with synchrotron self-Compton (SSC) from the innermost regions near the black hole, e.g., the nozzle of a jet (FM00; \citeNP{YuanMarkoffFalcke2001}) or a magnetic dynamo within the circularized accreting plasma \cite{MeliaLiuCoker2001}. In this picture, the X-rays are inverse Compton up-scattered synchrotron photons from the so-called submm-bump \cite{SerabynCarlstromLay1997,FalckeGossMatsuo1998}. Since the submm-bump is thought to be produced close to the black hole, very short time scale variability (several hundred seconds) was already predicted (FM00). In the following we would like to explore the various scenarios which could lead to a dramatic X-ray flare within the jet model. \section{Models} We start with our basic jet emission model (\citeNP{FalckeBiermann1999}; FM00), consisting of a conical jet with pressure gradient and nozzle. The parameters in the nozzle for the quiescent state are determined from the underlying accretion disk as described in \citeN{YuanMarkoffFalcke2001}, and as summarized below. All quantities further out in the jet are solved for using conservation of mass and energy, and the Euler equation for the accelerating velocity field. We take the distance to the Galactic center as $d_{gc}=8.0$ kpc. Clearly, in order to produce an X-ray flare, one or several parameters had to have suddenly changed in Sgr A*. In Figs. 2 and 3 in FM00, we showed how the radio and X-ray spectra in the jet model change if one changes the magnetic field -- a similar result would be expected for an increase in particle density -- or the electron temperature by a small amount. The former would be expected for an increased jet power or accretion rate, which would result in simultaneous flaring at all frequencies with little change in spectral index. In the latter scenario, however, the X-rays flare much stronger with a hardening of the spectrum, because SSC is very sensitive to changes in electron energies. This type of fast heating could in principle occur via instantaneous transfer of energy from the magnetized plasma in the accretion flow to the radiating particles, e.g. as would be expected from the sudden discharge of energy in magnetic flares through reconnection (e.g., \citeNP{Biskamp1997}). On the other hand, we know that non-thermal particle distributions are quite common in jets in AGN and X-ray Binaries (XRBs), leading to the appearance of optically thin power laws in the spectra. Observations of jets in XRBs (e.g., \citeNP{Fender2001}) and some AGN (e.g., \citeNP{MeisenheimerYatesRoeser1997}) seem to hint at a common type of power law with typical spectral index of $\alpha\sim0.6-0.8$. While the exact mechanism is not yet firmly established, and reconnection may also contribute, first order diffusive shock acceleration leads more naturally to an electron distribution with the index $p\sim2-2.6$ depending on the shock compression ratio ($\frac{dN}{dE}\propto E^{-p}$, see e.g., \citeNP{JonesEllison1991}). Such accelerated particles would result in a significant increase of optically thin synchrotron emission, with spectral slope $\alpha=(p-1)/2$. In the following we therefore explore three scenarios for the origin of the X-ray flare: increased jet power or accretion rate, increased heating of relativistic particles, or sudden shock acceleration of the particles. We will refer to these three models as the $\dot{M}$-flare, the $T_{\rm e}$-flare and the shock-flare, respectively. \section{Results} Since no simultaneous radio or mid-infrared (MIR)observations are available we include in our figures an ``upper radio envelope'', showing the highest flux ever detected at each radio frequency in long-term monitoring of Sgr A* with the VLA \cite{ZhaoBowerGoss2001}. While it is possible that this type of X-ray flare is so rare that it was never before captured by radio observations, it seems statistically unlikely given the huge radio database compared to only two cycles of Chandra observations. This argument does not hold for the poorly sampled data at other wavelengths and we only consider single-epoch measurements which most likely only reflect the quiescent Sgr A* spectrum. The effects of the $\dot{M}$-flare and the $T_{\rm e}$-flare can be modeled simply by changing the jet power and temperature, respectively, in our published models (FM00, \citeNP{YuanMarkoffFalcke2001}). We assume that the jet carries away a fixed fraction of the accretion energy $\dot{M} c^2$, and that this energy is divided evenly between the kinetic energy carried by the cold plasma, and the internal energy carried by the magnetic field and hot electrons. Once the electron temperature $T_{\rm e}$ in the nozzle is fixed, assuming a Maxwellian distribution, the jet nozzle density $n_0$ is determined via approximate equipartition from the magnetic field $B_0$. In the quiescent state, the relevant parameters for our most recent fit are $T_{\rm e}=\sim2\cdot10^{11}$ K, $n_0\sim9\cdot10^5$ cm$^{-3}$ and $B_0\sim20$ G. Fig.~\ref{sgra_ssc} shows the prediction for a) the $\dot{M}$-flare, with jet power ($\propto B^2$) raised by $\sim 3$ via increasing the jet nozzle magnetic field $B_0$ to $\sim35$ G while holding $T_{\rm e}$ fixed (which in turn increases $n_{\rm 0}$ by $\sim 3$ to $\sim 3 \cdot 10^6$ cm$^{-3}$) and b) the $T_{\rm e}$-flare for $T_{\rm e}$ raised by a factor of $\sim 3$ to $T_{\rm e}\sim6\cdot10^{11}$ K, while holding $n_0$ and $B_0$ fixed. The parameters were chosen to match the amplitude of the X-ray flare data, shown with its error box as well. For comparison we show in the figure also the quiescent jet+disk spectrum. As expected, the $\dot{M}$-flare strongly over-predicts the radio flux by a large factor. In fact, such a huge flare in the radio has never been reported and in addition, the spectral index is far too steep. The $T_{\rm e}$-flare fares much better: the predicted radio flux is close to already observed radio flare maxima and the X-ray spectrum becomes very hard during the flare. The model also predicts significant brightening in the MIR range during the X-ray flare event, due to the shift of the submm-bump to higher frequencies, which should exceed currently available non-simultaneous MIR/NIR limits. In contrast to the radio, the MIR regime has not been sampled well enough to decide whether such flares exist. However, \citeN{GenzelEckart1999} and \citeN{SerabynCarlstromLay1997} report observations where Sgr A* could have been detected during a brief period with unusually high flux densities at 350 $\mu$m and 2.2 $\mu$m. Clearly, this needs to be confirmed and reassessed in light of the new X-ray observations. \begin{figure*}[t] \centerline{\hbox{\psfig{figure=Di061_fig1a.ps,width=.49\textwidth,angle=-90}\hfill\psfig{figure=Di061_fig1b.ps,width=.49\textwidth,angle=-90}}} \caption[]{\label{sgra_ssc} Fit of the jet model {\bf (solid line)} to the flare data of \citeN{Baganoffetal2001b} (a) with the $\dot{M}$-flare, raising the jet power by a factor of $\sim 3$ , and (b) with the $T_{\rm e}$-flare by raising the temperature of the electrons by a factor of 3, compared to the quiescent jet and disk model {\bf (dashed line)}. The radio data and IR upper limits are from the data set compiled and presented in Melia \& Falcke 2001, where IR data are from single-epoch observations only. The upper radio points show the highest flux detected at that particular frequency, as compiled by \citeN{ZhaoBowerGoss2001}. The lower X-ray data show the quiescent state spectrum of \citeN{Baganoffetal2001}.}\end{figure*} The shock-flare scenario requires more discussion, as it involves the effects of diffusive shock acceleration in the jet. This has been done already by \citeN{MarkoffFalckeFender2001}, where the scaled version of the jet model previously used to explain Sgr A* (\citeNP{YuanMarkoffFalcke2001}; FM00) has successfully been applied to X-ray binaries in the low/hard state by including shock acceleration. Because the low/hard state is characterized by a very faint, possibly ADAF-like accretion disk as in Sgr A*, the ambient photon field is not strong enough to result in significant inverse Compton (IC) cooling, allowing shock accelerated electrons to achieve rather high energies. Following \citeN{MarkoffFalckeFender2001} the particles would be accelerated up to a maximum energy $E_{\rm e, max}=\gamma_{e,max}m_{\rm e}c^2$, which is reached when the synchrotron loss rate equals that of acceleration. We use the simple parallel shock acceleration rate \begin{equation} t_{\rm acc}^{-1}=\frac{3}{4}\left(\frac{u_{\rm sh}}{c}\right)^2\frac{eB}{m_{\rm e}c \xi \gamma_{\rm e}}, \end{equation} where $u_{\rm sh}$ is the shock speed in the plasma frame. The parameter $\xi< c \beta_e/u_{\rm sh}$ \cite{Jokipii1987} is the ratio between the parallel diffusive scattering mean free path and the gyroradius of the particle, and ranges from a lower limit at $\xi=1$ up to typically a few $10^2$ (e.g., \citeNP{Jokipii1987}). For a magnetic field of $\sim 20$ G as found in our model of the quiescent state, the acceleration time scale is $\sim0.1$ sec for even $\gamma_{\rm e}=10^5$ electrons, and hence is shorter than the dynamical time scale at the black hole. Setting the standard synchrotron loss rate $t_{\rm syn}^{-1}=\frac{4}{3}\sigma_{\rm T} \gamma_{\rm e} \beta_{\rm e}^2 \frac{U_{\rm B}}{m_{\rm e} c}=t_{\rm acc}^{-1}$, we can solve for the maximum electron energy achieved by acceleration $\gamma_{\rm e,max}$. If we define as a reference value $\xi=\xi_2 100$, the maximum synchrotron frequency is then \begin{equation} \nu_{\rm max}=0.29 \nu_{\rm c} \simeq 1.2\cdot 10^{20} \xi_2^{-1} \left(\frac{u_{\rm sh}}{c}\right)^2 \;\;\; {\rm Hz} \end{equation} where $\nu_{\rm c}\simeq\frac{3}{4\pi} \gamma_{\rm e,max}^2 (eB)/(m_{\rm e} c)$ is the critical synchrotron frequency. This value is not dependent on the magnetic field, the jet power, or the shock location as long as we are in the synchrotron cooling dominated regime. Because the shock accelerated particles responsible for the X-ray synchrotron will have very high energies ( $\gamma_{\rm e}\sim10^5$) for the low magnetic fields further out in the jet, the synchrotron cooling time scale will be very short, on the order of $\sim 10^2$ s. This means that re-acceleration along the jet is required to maintain the population, and will result in rapid cooling if the acceleration is switched off. We thus approximate the shock acceleration as continuous starting at a distance $z_{\rm sh}$. For X-ray binaries we found that the shock acceleration must begin relatively close to the nozzle at $z_{\rm sh} \sim 10\sim 10^2 r_{\rm s}$ (\citeNP{MarkoffFalckeFender2001}; Markoff et al., in prep.). This location is determined from the data by extrapolating the synchrotron X-ray curve to where it meets the optically-thick, flattish spectrum in the radio-IR. This intersection is unique for a fixed spectral index, and gives $z_{\rm sh}$ because the self-absorption frequency scales inversely with $z$ in the jet model. If we then fix for simplicity the fraction of accelerated particles at 50\% and keep the other parameters as in FM00 and \citeN{YuanMarkoffFalcke2001} we can calculate the resultant shock-flare model spectrum as shown in Fig.~\ref{sgra_syn}. As the spectral index becomes harder for a fixed X-ray flux, the optically thick turnover must occur at lower frequencies, i.e. further out in the jet. For a standard spectral index of $\alpha\sim0.8$ as typically seen in AGN, the shock acceleration region must be at $\sim 16 r_{\rm s}$, which is consistent with the observed time scales. However, the assumed standard AGN spectral index is only marginally compatible with the spectrum observed for the X-ray flare, which poses a problem for such a model. Taking on the other hand the reported best-fit X-ray spectral index at face value would imply $\alpha=0.3$ and require $z_{\rm sh}\sim10^4 r_{\rm s}$. This is very far in comparison to other jet systems and furthermore ruled out by the observed short time scales. \begin{figure} \centerline{\psfig{figure=Di061_fig2.ps,width=0.49\textwidth,angle=-90}} \caption[]{\label{sgra_syn} Fit to the flare data of \citeN{Baganoffetal2001b} for the shock-flare model, other data the same as Fig.~1.} \end{figure} \section{Discussion} We are able to explain the 10 ks flare in Sgr A* detected by {\em Chandra} by heating the radiating electrons within the jet model of FM00, either so they remain quasi-thermalized ($T_{\rm e}$-flare) or via the non-thermal process of shock acceleration (shock-flare). A flare due to an increase in accretion rate ($\dot{M}$-flare) appears very unlikely because of the generally low level of radio variability. Of the two remaining scenarios, the shock-flare is more intriguing because it offers a solution where the X-ray flare occurs without a great effect on the lower-frequency emission, consistent with the observed lower radio variability of Sgr A* over the last decades. At the marginal end of the fit, it can also explain the shortest variations via the location of the shock or fast radiative cooling, and predicts a spectral index consistent with that seen in other AGN systems. Although the radio flux does not change much for this case, the presence of the optically thin tail would predict a significantly larger radio profile (more extended, optically thin jet emission; see FM00 for a discussion of this point) on the sky and a shift of the centroid of the radio emission. However, in the radio astrometric work of \citeN{ReidReadheadVermeulen1999} no such shift has been detected so far. Alternatively, the $T_{\rm e}$-flare with its sudden heating of hot ($T_{\rm e}\simeq6\cdot10^{11}$ K) electrons by, e.g., magnetic reconnection, can explain the X-ray flare via increased SSC emission, similar to models for the quiescent state spectrum. The fast variability can be explained by the small source size and outflow with $v\sim c$, leading to fast adiabatic cooling, while radiative cooling is not as important ($t_{\rm syn}\sim5\cdot10^4$ for $T_{\rm e}=6\cdot10^{11}$ K electrons in the submm-bump). In contrast to the shock-flare model, the $T_{\rm e}$-flare model fits the reported X-ray spectrum much better. However, the radio variability is larger than in the synchrotron case, but still falls along the ``envelope'' of highest radio fluxes observed so far (Fig. \ref{sgra_ssc}). In addition the model predicts simultaneous MIR flaring, in a regime where no monitoring data is currently available. So although the $T_{\rm e}$-flare case is favored over the shock-flare case in terms of the fit to the X-ray flare data, only simultaneous submm/MIR/X-ray and VLBI observations in the near future will unequivocally determine its viability. For the $T_{\rm e}$-flare, assuming the protons have at least the same temperature one can compare the energy density of the plasma and the gravitational binding energy, $G M_\bullet m_{\rm p} n/R$, yielding \begin{equation} {\Gamma n k_{\rm b}T\over G M_\bullet m_{\rm p} n R^{-1}}\simeq3.4\left({\tau\over 600 {\rm sec}}\right)\left({T\over 6\cdot10^{11} {\rm K}}\right) \end{equation} for a $M_\bullet=2.6\cdot10^6M_\odot$ black hole and a relativistic plasma with $\Gamma=4/3$ (e.g., \citeNP{Konigl1980}) at a distance $R=c\tau$ from the black hole set by the variability time scale. Under such simple assumptions the plasma would not be gravitationally bound, which is certainly consistent with the jet scenario. \bibliography{aamnemonic,Di061} \bibliographystyle{aa} \end{document}