Figure 1: An artist’s conception of an X-ray binary. Courtesy NASA’s HEASARC web page.

Abstract

We present first modeling results of the rapid spectral variability of flares in the X-ray binary Cygnus X-1 in the high/soft state. The coupled radiation transfer and electron heating/cooling problem was solved with a fully time dependent 2-D Monte-Carlo/Fokker-Planck code. Starting with an initial soft state model consisting of an optically thick accretion disk sandwiched by a hot corona, we modeled a high energy flare through an impulsive energy release in that corona. This flare could be representative of a reconnection event of magnetic field lines anchored in the disk. We found that such a scenario provides a good fit to the rapid (millisecond timescales) spectral evolution recently observed in Cyg X-1.

Two Dimensional Monte Carlo/Fokker-Planck Code

Figure 5: Light curve during high/soft flare. Black crosses are RXTE observations with error bars, red line is simulated with the following parameters: m dot =0.05, a =0.1, t flare =0.02 s, ( D T/T)²=7.

What are X-ray binaries?

Often times, a “normal” star will orbit near a compact object with intense gravity (a black hole or a neutron star). Matter of the outer layers of the normal stars may be transferred to the compact object. This material will not fall onto the it right away; it will slowly circle the object first, like water going down a drain, forming an

accretion disk

. Viscosity causes the plasma in this disk to heat up to T~ 10 7 K, which then emits blackbody radiation in the X-rays. X-ray spectra for these objects consist of a disk blackbody and a hard power law tail, with variability on the order of milliseconds to months.

Cygnus X-1

• Cygnus X-1 is the first-discovered, most-observed X-ray binary. Consists of a “normal” O9 supergiant star and a 10 solar mass black hole.

• Has been observed in two major states; the

low/hard state

, and the

high/soft state

(see Figure 2).

• In the low/hard state, Cyg X-1 has a

lower

luminosity, and emits mostly

harder

(i.e., more energetic) X-rays. In the high/soft state, Cyg X-1 has a

higher

luminosity, and emits mostly

softer

(i.e., less energetic) X-rays.

• Cyg X-1 spends most of its time in the low/hard state.

Figure 2: Energy Spectra and illustration of (a) the low/hard state and (b) the high/soft state. Courtesy Zdziarski & Gierlinski (2004).

Spectra of X-ray Binaries

•Soft blackbody photons are thought to come from the disk, while the hard power law tail is thought to be from photons Compton up-scattered in optically thick

corona

.

• In the low/hard state, Cyg X-1 is thought to have a large corona, and a less extended accretion disk.

• In the high/soft state, it is thought to have a smaller corona and a more extended accretion disk.

Figure 3: Simulation geometry illustration from Böttcher, Jackson & Liang (2003).

• A cylindrical series of vertical and radial zones was used to represent the corona. Each zone has its own set of variables (temperature, density, magnetic field, etc.); see Figure 3. Blackbody photons are injected from below, representing the accretion disk.

• A Monte Carlo technique is used to simulate photon transport; the electron evolution was calculated with the locally isotropic Fokker-Planck equation.

• In each time step, photon scattering and the plasma’s evolution are calculated; photons that stay in the simulation volume are stored for the next step, while the ones that leave the volume are stored in an “event file” and used to calculate light curves and spectra.

Simulations of Cyg X-1 Millisecond Flares

• Powerful millisecond flares were discovered in Cyg X-1 in the low/hard and high/soft states by Gierlinski & Zdziarski (2003).

• A possible cause of the flare: a magnetic field reconnection event in the corona, which increases the temperature in an active region for a few milliseconds.

• A flare in the high/soft state has been successfully simulated with the 2-D MC/FP code.

• Our flare simulation involved a sudden increase in proton temperature in part of the corona. The electron temperature responds to this, as shown in Figure 4.

• Observed in the high/soft flare were an increase in luminosity as well as a hardening of the spectrum, both of which were reproduced in our simulation. • Figure 5 shows the observed and simulated light curves. Figure 6 shows the spectrum before, during, and after the flare; clearly there is a hardening. This is also seen in Figure 7 which shows the spectral index, a measure of hardness.

Figure 4: coronal electron temperature profiles (a) before (b) during and (c) after the flare. Contours are labeled in keV.

Figure 6: Simulated Cyg X-1 spectra before (black) during (red) and after (green) the flare.

Figure 6: observed (black) and simulated (red) spectral indices ( G ) during the flare. F(E) ~ E G ; the lower G , the harder the spectra.

The Future?

• Simulations of other observed flares in Cyg X-1, especially those in the low/hard state.

• Develop a more efficient, versatile, parallelized Monte Carlo/Fokker-Planck code.

References

Böttcher, M., Jackson, D. R., Liang, E.P., 2003, ApJ, 586, 389 Gierlinski, M., Zdziarski, A. A., 2003, MNRAS, 343, L84 Zdziarski, A. A., Gierlinski, M., 2004, PThPh, in press (astro-ph/0403683)