------------------------------------------------------------------------ sgrxvar A&A Letters, submitted Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Length: 20935 %http://www.aoc.nrao.edu/staff/hfalcke/publications.html#sgrxvar %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 bulk 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 ($\alpha\sim1.5$). The longest timescale (10 ks) corresponds to $\sim 390 r_{\rm s}$, which argues against thermal bremsstrahlung from the outer radii, e.g. from a standard Advection Dominated Accretion Flow (ADAF; \citeNP{NarayanMahadevanGrindlay1998}). The smallest timescale 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}. 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 \cite{Biskamp1997}. It is, however, not clear whether the additional heating through these processes necessarily retains a thermal particle distribution. In fact, 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, first order diffusive shock acceleration can lead 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 bulk heating of relativistic particles, or sudden shock acceleration of the particles. \section{Results} Since no simultaneous radio or mid-infrared 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. The effect of increasing the temperature or jet power can be modeled quite easily by changing these parameters respectively in our published model (FM00, but see \citeNP{YuanMarkoffFalcke2001} for the most recent parameters). Fig.~\ref{sgra_ssc} shows the prediction for a) a jet power ($\propto B^2$) raised by a factor of $\sim3.5$ via increasing the jet nozzle magnetic field $B_0$ to $\sim35$ G (which in turn increases the electron density $n_{\rm e}$, due to equipartition assumptions), and b) an electron temperature raised by a factor of $\sim 3$ to $T_{\rm e}\sim6\cdot10^{11}$ K with respect to the quiescent values. The parameters were chosen to match the amplitude of the X-ray flare data, shown with its error box as well. As expected, the model with an increased accretion rate or jet power 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 alternative scenario, with increased bulk heating, 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 mid-infrared (MIR) range during the X-ray flare event, due to the shift of the submm-bump to higher frequencies, thereby violating many non-simultaneous MIR/NIR limits. \citeN{GenzelEckart1999} have tentatively reported one NIR flare of Sgr A*, however, this has not been yet confirmed. \begin{figure*}[t] \centerline{\hbox{\psfig{figure=fig1a.ps,width=.49\textwidth,angle=-90}\hfill\psfig{figure=fig1b.ps,width=.49\textwidth,angle=-90}}} \caption[]{\label{sgra_ssc} Fit to the flare data of \citeN{Baganoffetal2001b} (a) by raising the jet power by a factor of 3.5, and (b) by raising the temperature of the electrons by a factor of 3, compared to the quiescent state model. The radio data and IR upper limits from the data set compiled and presented in Melia \& Falcke 2001. 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 third scenario for the flare 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. It is interesting to explore what would happen if one applies an analogous model for Sgr A*, where the weak-to-absent disk emission, in contrast to AGN and even most LLAGN, would result in similar acceleration conditions. 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. It has a strict lower limit at $\xi=1$ and is typically under a few $10^2$ (e.g., \citeNP{Jokipii1987}). For a magnetic field of $20$ Gauss 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 timescale at the black hole. Setting the standard synchrotron loss rate $t_{\rm syn}^{-1}=\frac{4}{3}\sigma_{\rm T} \gamma_{\rm e} \beta_{\rm e}^2 \frac{U_{\rm B}}{m_{\rm e} c}=t_{\rm acc}^{-1}$, the maximum energy achievable by acceleration is then \begin{equation} \gamma_{\rm e,max}\sim10^8\,\left(\xi B\right)^{-0.5}\left(\frac{u_{\rm sh}}{c}\right), \end{equation} where $U_{\rm sh}$ is the velocity of the shock relative to the plasma. If we define as a reference value $\xi=\xi_2 100$, the maximum synchrotron frequency is \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. Most importantly, it is high enough to give X-rays directly from synchrotron. The particles responsible for the emission at this frequency have $\gamma_{\rm e}\sim10^5$ for $B\sim 3$ Gauss and synchrotron cooling time scales of $t_{\rm syn}\sim230$ s which requires re-acceleration along the jet but also allows rapid cooling if 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 $z_{\rm sh} \sim 10-100 r_{\rm s}$ where $r_{\rm s}=2GM_{\rm BH}/c^2$ is the Schwarzschild radius (\citeNP{MarkoffFalckeFender2001}; Markoff et al., in prep.). For Sgr A* we can easily constrain such an acceleration region by back-extrapolating the X-ray flux. Within a jet model the self-absorption frequency scales inversely with the distance from the black hole; hence the intersection of the optically thin power law with the flat radio spectrum determines $z_{\rm sh}$ as a function of the spectral index. 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 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 $z_{\rm sh}\sim10^4 r_{\rm g}$. 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=fig2.ps,width=0.49\textwidth,angle=-90}} \caption[]{\label{sgra_syn} Jet synchrotron fit to the flare data of \citeN{Baganoffetal2001b}, other data same as Fig.~1. The quiescent state disk is also included, here contributing equally in the submm-bump. If, however, the radiation from the inner edge of the accretion disk is further reduced by the transfer of matter to the jet, the overall submm flux will be somewhat lower.} \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 or via the non-thermal process of shock acceleration. A flare due to an increase in accretion rate appears very unlikely because of the generally low level of radio variability. Of the two remaining scenarios, the synchrotron case 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 extreme 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. Also, the observed X-ray flare spectrum is only marginally consistent with the model. Alternatively, the sudden bulk 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 is explained by a 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 acceleration scenario, bulk heating fits the reported X-ray spectrum much better, but also predicts significant flaring in the NIR-IR frequencies. 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}). While the SSC case is favored over pure synchrotron by the currently available data, the scenarios can be easily distinguished by means of simultaneous submm/MIR/X-ray and VLBI observations in the near future. The SSC model is very sensitive to the electron temperature of the plasma. Assuming that protons have at least the same temperature, as believed in an ADAF, one can compare 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}}\simeq7.7\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 consistent with the jet scenario. As a final note, it is interesting that essentially the same model used to explain correlated radio and X-ray emission in the low/hard state of X-ray binaries (\citeNP{MarkoffFalckeFender2001}, Markoff et al. in prep) can work here. In fact, there exists an ``off'' state in several XRBs, such as GX339-4 (see \citeNP{Kongetal2000}), which appears to be a low/hard state with much weaker flux. It is possible that Sgr A*, like its smaller cousins in stellar binary systems, exists in two or more states over its lifetime. The quiescent or ``off'' state which exists most of the time may suddenly flare into an ``on'' state that is somewhat analogous to the low/hard state of X-ray binaries. For this first-ever observed ``on'' state, it appears that Sgr A* may have behaved---at least for a few hours---like the jets in its more luminous (in Eddington units) cousins. If particle acceleration rather than bulk heating is at work, the Sgr A* jets may have become short-term cosmic ray accelerators, possibly even producing detectable $\gamma$-rays via the SSC up-scattered X-ray emission. \bibliography{aamnemonic,refs} \bibliographystyle{aa} \end{document} ---------------------------------------------------------------------------- ___ ___ _____ ___ _____ |PD Dr. Heino Falcke /__/\ /__/| /____/\ /__/| /____/\ |Max-Planck-Institut f. Radioastronomie | \ \ /| || | o \/ | || | o \/ |Auf dem Huegel 69 | |\ \//| || | __/ | ||f| __/ |D-53121 Bonn, Germany | ||\_/ | || | || | || | |\ \ |E-mail: hfalcke@mpifr-bonn.mpg.de |__|/ |__|/ |__|/ |__|/ |__|/\_||Fax: 49/(0)228/525-229 |Tel.: 49/(0)228/525-217 ---------------------------------------------------------------------------- Web: http://www.aoc.nrao.edu/staff/hfalcke ----------------------------------------------------------------------------