% 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} \newcommand{\figwidth}{0.55\textwidth} \begin{document} \title{A jet model for the broadband spectrum of XTE J1118+480} \subtitle{Synchrotron emission from radio to X-rays in the Low/Hard spectral state} \author{Sera Markoff\inst{ 1}\fnmsep\thanks{Humboldt research fellow} \and Heino Falcke\inst{1} \and Rob Fender\inst{2}} \institute{Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel 69, D-53121 Bonn, Germany \and Astronomical Institute `Anton Pannekoek' and Center for High Energy Astrophysics, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands} \titlerunning{Jet model for XTE J1118+480} \authorrunning{Markoff et al.} \offprints{smarkoff@mpifr-bonn.mpg.de} \date{\centerline{\it Accepted for publication in Astronomy \& Astrophysics Letters\hphantom{xxxxxxxxxx}}} \abstract{Observations have revealed strong evidence for powerful jets in the Low/Hard states of black hole candidate X-ray binaries. Correlations, both temporal and spectral, between the radio -- infrared and X-ray bands suggest that jet synchrotron as well as inverse Compton emission could also be significantly contributing at higher frequencies. We show here that, for reasonable assumptions about the jet physical parameters, the broadband spectrum from radio through X-rays can be almost entirely fit by synchrotron emission. We explore a relatively simple model for a relativistic, adiabatically expanding jet combined with a truncated thermal disk conjoined by an ADAF, in the context of the recently discovered black hole binary XTE J1118+480. In particular, the X-ray power-law emission can be explained as optically thin synchrotron emission from a shock acceleration region in the innermost part of the jet, with a cutoff determined by cooling losses. For synchrotron cooling-limited particle acceleration, the spectral cutoff is a function only of dimensionless plasma parameters and thus should be around a ``canonical'' value for sources with similar plasma properties. It is therefore possible that non-thermal jet emission is important for XTE J1118+480 and possibly other X-ray binaries in the Low/Hard state.\keywords{X-rays: binaries -- X-rays: individual: XTE J1118+480 -- radiation mechanisms: non-thermal -- stars: winds, outflows --black hole physics -- accretion, accretion disks} } \maketitle \section{Introduction} Observations are providing increasing evidence that black hole candidate (BHC) X-ray binaries (XRBs) produce powerful collimated outflows when in the Low/Hard X-ray state (LHS). This state is characterized by a nonthermal power-law in the X-ray band and little, if any, thermal disk contribution (e.g., \citeNP{Nowak1995,Poutanen1998}). At least three systems in the LHS (Cyg X-1, 1E 1740.7-2942 and GRS 1758-258) have directly resolved radio jets on scales from AU to parsecs. However, XRB jets also reveal themselves in the broadband LHS spectra with a flat-to-inverted radio synchrotron spectrum, analogous to the signature emission of jets in compact radio cores of AGN \cite{BlandfordKoenigl1979,HjellmingJohnston1988,FalckeBiermann1999}. Furthermore, new data suggest a continuation of this radio synchrotron emission to much higher frequencies. The spatial, spectral and temporal evidence for powerful jets from XRB BHCs in the LHS are compiled and discussed in \citeN{Fender2001}. We know that jets play a significant role in the emission of Active Galactic Nuclei (AGN), even dominating the spectrum from radio through TeV $\gamma$-rays in the case of BL Lacs, with emission from optically thin synchrotron up to even $100$ keV and higher (e.g. \citeNP{Pianetal1998}). By analogy, if the flat, optically thick synchrotron spectrum in XRBs, commonly attributed to jets, indeed extends into the NIR and optical regimes \cite{Fender2001}, one would expect a corresponding optically thin power-law from shock acceleration at even higher frequencies. This is irrespective of whether the jet emission is boosted or not, since optically thick and optically thin emission would have similar Doppler factors. Shock acceleration is likely to be present in XRBs, given that optically thin power-law spectra are observed during their radio outbursts (e.g., \citeNP{FenderKuulkers2001}, and refs. therein). Still, the majority of current models for the broadband (X-ray) spectra of BHC XRBs focus only on the contribution of thermal disk plus coronal inverse Compton (IC) emission (for a review, see \citeNP{Poutanen1998}) and ignore any jet contribution, even though jets can be an integral part of X-ray binaries and their systems (e.g., \citeNP{EikenberryMatthewsMorgan1998,MirabelRodriguez1999,Fender2001}). As an example for the possible importance of jet emission, we use the recently discovered XRB XTE J1118+480 \cite{Remillardetal2000}, which has been observed in the radio through X-rays (see \citeNP{Hynesetal2000}, hereafter H00, \citeNP{Fenderetal2001}, hereafter F01, and references therein), and is also at high enough Galactic latitude to allow the first ever EUV detections of an X-ray transient (H00). The system is likely a BHC in the LHS (H00;\citeNP{RevnivtsevSunyaevBorozdin2000,Woodetal2000}). Although jets were not directly resolved with MERLIN to a limit of $<65(d/{\rm kpc})$ AU (at 5 GHz; F01), its radio emission shows the flat characteristic jet spectrum. \section{Basic Model and Estimates} We consider that an accretion disk is responsible for the extreme-ultraviolet (EUV) data and contributes in the optical (H00; \citeNP{Garciaetal2000}). However, the power-law seen in the X-ray spectrum indicates that an additional component must be present. So far, this has been presumed to arise from the Comptonization of some `seed' photons by a hot, thermal corona (\citeNP{Poutanen1998}). One commonly invoked physical explanation for the LHS is that a standard thin, optically thick disk \cite{ShakuraSunyaev1973} exists only down to some transition radius $r_{\rm tr}\sim10^2-10^3 r_{\rm s}$, ($r_{\rm s}=2GM_{\rm bh}/c^2$), where the flow becomes hot and non-radiative (e.g., \citeNP{Liuetal1999,Esinetal2001}). We do not, however, include an entire disk model here, since there are several models already in existence exploring this issue (see above, and review in \citeNP{Poutanen1998}). Instead, we include a representative thermal spectrum for the inner edge of the cool disk both in the direct emission, in our calculations of cooling rates in the jet and as seed photons for IC. With this approach the temperature, $T_{\rm d}$, and luminosity, $L_{\rm d}$, for this inner edge can be roughly determined by fitting a black body to the EUV data. As discussed in H00, uncertainty in the local absorption leads to large variations in the possible EUV flux for XTE J1118+480. Here, we take the highest absorption value presented, $N_{\rm H} = 1.15\cdot10^{20}$ cm$^{-2}$, because it provides a solid upper limit to any thermal disk contribution (see Fig.~1). Taking the distance and BH mass to be $1.8$ kpc and $6 M_\odot$, respectively \cite{McClintocketal2001}, the fit to the EUV data gives $T_{\rm d}\sim1.5\cdot 10^5$ K and $L_{\rm d} \sim 5 \cdot 10^{35}$ erg s$^{-1}$. For an annulus with scale width $\sim r_{\rm tr}$, we find as an order of magnitude estimate $r_{\rm tr}\approx900 r_{\rm s}$, in agreement with current models (e.g., \citeNP{Liuetal1999}). The luminosity of a standard accretion disk is dominated by the inner edge and its radiative efficiency is $q_{\rm l}=\frac{1}{4} r_{\rm s}/r_{\rm tr}$ (\citeNP{FrankKingRaine1992}, Eq.~5.20), yielding a rough estimate for the accretion rate of $\dot M_{\rm d}\sim q_{\rm l}^{-1} L_{\rm d}/c^2\simeq3\cdot 10^{-8}M_\odot$ yr$^{-1}$. Hence, in the following we use a reference value of $\dot M_{\rm d}=\dot m_{-7.5}\;3\times10^{-8} M_\odot$ yr$^{-1}$. Within $r_{\rm tr}$ we consider a hot, ADAF-like flow which does not significantly contribute to the spectrum. For accreting black holes it has been argued that the jet power is of order $Q_{\rm jet}\sim q_{\rm j}\dot M_{\rm d} c^2$ with an efficiency inferred to be of order $q_{\rm j}=10^{-1}-10^{-3}$ \cite{FalckeBiermann1999}. However, $q_{\rm j}$ is essentially a free parameter, with $q_{\rm j}\ll1$, and we define $q_{\rm j,-2}=q_{\rm j}/10^{-2}$. While the jet formation itself is very difficult to model, the physics of calculating most of the jet emission is relatively straightforward because the flat-to-inverted spectrum stems from the part of the jet where it is basically undergoing free expansion. Here we build on the jet emission model outlined in \citeN{FalckeMarkoff2000}, and references therein. At the inner edge of the hot accretion flow, plasma is ejected out from symmetric nozzles, where it becomes supersonic. The jets then accelerate along the axes through their pressure gradients up to bulk Lorentz factors $\gamma_{\rm j}\simeq2-3$, and expand sideways with their initial proper sound speed $\gamma_{\rm s}\beta_{\rm s}c\simeq0.4c$ for a hot electron/proton plasma. This implies low relativistic Mach numbers around ${\cal M}\sim5$. The velocity field, density and magnetic field gradient then come naturally from the Euler equation (see, e.g., \citeNP{Falcke1996}). The dependencies of the magnetic field $B$ and density $n$ on distance are then similar to, but slightly stronger than, the canonical $r^{-1}$ and $r^{-2}$ dependencies for conical jets, respectively \cite{BlandfordKoenigl1979,HjellmingJohnston1988,FalckeBiermann1995}. In this way, the basic physical properties governing the emission at each point in the jet are fixed after specifying the jet power, and the initial conditions at the nozzle. We make the simplification of assuming a maximal jet, which follows from the Bernoulli equation (\citeNP{FalckeBiermann1995}) when the internal energy, here dominated by the magnetic field, is equal to the bulk kinetic energy of particles. This is consistent with a magnetic launching mechanism. The plasma is assumed to originate in the hot accretion flow and therefore contains equal numbers of protons and electrons, with hot electrons at a temperature approaching $T_{\rm e}=T_{\rm e,10}\cdot 10^{10}$ K in various ADAF models (e.g., \citeNP{Manmoto2000}). The electron Lorentz factor of the peak will be at $\gamma_{\rm e}\sim4\cdot T_{\rm e,10}$. In AGN jets, the high frequency, optically-thin power-laws are taken to be the result of synchrotron emission from particles being shock-accelerated along the jet (e.g., \citeNP{MarscherGear1985}). In such a case the crucial parameter for the high energy emission is the location $z_{\rm acc}$ of the first particle acceleration region in the jet. Near the shock region in each jet, $B^2(r)/8\pi\simeq0.25q_{\rm j} \dot M_{\rm d} c^2/(c\gamma_{\rm j}\beta_{\rm j} \pi r^{2})$, yielding a reference value of $B\simeq2 \cdot 10^6\,{\rm G}\cdot \sqrt{q_{j,-2}\dot m_{-7.5}/\gamma_{\rm j}\beta_{\rm j}} (r/10r_{\rm s})^{-1}$ for the parameters discussed above. Similarly, the particle density is given by $n\simeq 10^{14}\,{\rm cm}^{-3}\cdot (q_{j,-2}\dot m_{-7.5}/\gamma_{\rm j}\beta_{\rm j}) (r/10r_{\rm s})^{-2}$. Once the plasma, assumed to be injected at the base of the jet with a Maxwellian distribution, reaches the shock region, the standard diffusive shock acceleration process redistributes the particles into a power-law, starting roughly at $\gamma_{\rm e,min}\sim4 T_{\rm e,10}$. The initially injected distribution has an index $p\simeq1.5-2$ (resulting from a relativistic shock, see, e.g., \citeNP{HeavensDrury1988}\footnote{Because the plasma is mildly relativistic at the shock region, the temperature-dependent adiabatic index will be closer to 4/3 rather than the non-relativistic value of 5/3. This yields a spectral index of $1.5\la p \le 2$, where $p=2$ is for non-relativistic shock-acceleration.}) steepening by $\sim 1$ due to increased cooling above a break energy $E_{\rm b}\approx (\tau_{\rm r} \beta_{\rm cool})^{-1}$, where $\tau_{\rm r}$ is the residence time of the plasma in the acceleration region, and $\beta_{\rm cool}$ are the constants giving the energy dependence of the cooling, which for synchrotron and Compton losses go as $\dot{E}\approx-\beta_{\rm cool} E^2$. This steepened spectrum has the index of $p\simeq2.5-3$, typically found in the optically thin synchrotron emission of both AGN and X-ray binaries. For the case of XTE J1118+480, the unbroken X-ray power-law (see Fig.~1), implies $p\simeq2.6$ for $E>E_{\rm b}$. The acceleration ceases when the particles reach the energy $E_{\rm e, max}=\gamma_{e,max}m_{\rm e}c^2$ where the cooling/loss rates equal that of acceleration. These rates are dependent both on the energy of the particle, as well as the local physical parameters. The shock acceleration rate is given as \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 diffusive scattering mean free path and the gyroradius of the particle, and has a lower limit at $\xi=1$. We account for energy losses at the shock via adiabatic losses, particle escape, IC and synchrotron. In our case the latter dominates and we have \begin{equation} 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} \end{equation} where $\sigma_{\rm T}$ is the Thomson cross-section and $U_{\rm B}$ is the energy density of the magnetic field. The maximum energy is then found by solving $t_{\rm acc}^{-1}=t_{\rm syn}^{-1}$, yielding $\gamma_{\rm e,max}\sim10^8\,\left(\xi B\right)^{-0.5}\left(\frac{u_{\rm sh}}{c}\right)$. 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 maximum corresponds approximately to the rollover of the power-law cutoff, and for $u_{\rm sh}\sim\beta_{\rm s}c$, we find a cutoff of $\sim80$ keV. This cutoff 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 we would expect XRBs to have similar shock structures, once $\xi$ is roughly fixed observationally---thus determining the scattering between magnetic irregularities in the diffusive shock process---we should get similar cutoffs for different sources and accretion rates. The location of the initial shock acceleration region is set by the frequency where the flat, highly self-absorbed synchrotron spectrum turns over into the optically thin power-law produced at the shock. From back-extrapolating the X-ray power-law, we can see that this maximum self-absorption frequency has to be somewhere in the IR/optical regime at $\sim 10^{14.5}$ Hz. For the parameters discussed here this would be at a distance of roughly $z_{\rm acc}\simeq50r_{\rm s}$, with a jet radius of $r\simeq10r_{\rm s}$, and the magnetic field and particle densities derived above. The total synchrotron luminosity, integrated up to the highest energies, is a few times $10^{36}$ erg ${\rm s}^{-1}$, which is $\sim10\%$ of the total jet power ($Q_{\rm j}\sim q_{\rm j,-2}\dot m_{-7.5}\,2\cdot10^{37}$ erg s$^{-1}$). Some fraction of X-rays created close to the nucleus by the jet will of course either directly impinge on, or be scattered by hot electrons into, the cold disk, resulting in a reflection component. However, since this is very dependent on the disk geometry, and because the feature is very weak or absent for XTE J1118+480 \cite{McClintocketal2001b}, we do not calculate this process here. \section{Results of Numerical Modeling} To obtain a more detailed broadband spectrum we have used the full numerical calculations for a jet model as described in \citeN{FalckeMarkoff2000}, with the addition of a particle acceleration region. The model takes into account the relativistic Doppler shifts, adiabatic losses, electron acceleration and loss timescales at the acceleration region as described above, and integrates the synchrotron and IC emission along the jet. The resulting fit is shown in Figure 1 with the parameters given in the caption. The relevant free parameters are the inclination angle $\theta_{\rm i}$, the shock distance $z_{\rm acc}$, the scattering ratio $\xi$, and the jet power parameterized by $q_{\rm j}$. While the electron temperature $T_{\rm e}$ (or $\gamma_{\rm e,min}$) and the fraction of thermal particles accelerated can also be adjusted, they are not independent of $q_{\rm j}$ -- decreasing these parameters will decrease the radiative efficiency and increase $q_{\rm j}$. Similarly, a more realistic disk model (e.g., \citeNP{Esinetal2001}) could yield a lower $r_{\rm tr}$ and $\dot M$, also increasing $q_{\rm j}$. Because we require charge balance between protons and electrons for the jet plasma, and a low $T_{\rm e}$ in line with ADAF models, the particles are in sub-equipartition with the magnetic field. The flat spectrum from radio to optical is due to the optically thick synchrotron emission from the jet at $z>z_{\rm acc}$, while the X-ray power-law is the optically thin synchrotron emission dominated by the shock acceleration region (at $z\sim z_{\rm acc}$). For the conditions in the jet, $E_{\rm b}$ lies very close to the peak of the thermal electron distribution, and we only see the steepened power-law. Because of the large ratio between magnetic field and photon densities, IC emission does not play a significant role for the parameters chosen here (see Fig.~1). Synchrotron and IC emission from the pre-shock region ($z