Physical Characteristics of the Spectral States of Galactic Black Holes

Using simple analytical estimates we show how the physical parameters characterizing different spectral states of the galactic black hole candidates can be determined using spectral data presently available. SPECTRAL STATES OF GBHC Galactic black hole candidates (GBHC) radiate in one of several spectral states, and some of them switch suddenly from one state to another. These states can be typified by their extremes: a “hard” state (HS, also called “low”, because of relatively low flux in standard X-ray 2 – 10 keV band), and a “soft” state (SS, a “high” state with relatively strong 2 – 10 keV flux). The broad band spectra in both states can be described as the sum of a blackbody and a power-law with an exponential cut-off. The black body component (probably from the optically thick accretion disk) is more prominent in the SS, when it has a temperature of 0.3 – 1 keV. The lower temperature of the black body in the HS makes it difficult to detect, due to the interstellar absorption. The power-law energy index, α, is 1.0 – 1.5 in the SS, and roughly 0.3 – 0.7 in the HS [1,2]. Recent OSSE observations reveal that the cut-off energy, Ec, of the power-law is correlated with the spectral state; the power-law turns over at ∼ 100 keV in the HS, and Ec > ∼ 200 keV in the SS [3,4]. There are also indications of that the amplitude of the Compton reflection “bump” increases when spectrum steepens [2]. The physical nature of the existence of the different spectral states and spectral transitions is not yet completely understood, although a number of models has been proposed (e.g. [5–8]). Recent progress on the theoretical side (we now understand much better how thermal Comptonization works, when the seed photons are produced mainly by reprocessing a part of the hard Xray output, [11–13]) and the existence of broad band simultaneous spectral c © 1995 American Institute of Physics 1 2 SPECTRAL STATES OF GALACTIC BLACK HOLES data for some of the sources (e.g., [4,9,10]) give us an opportunity to use the observed spectral characteristics in these states to determine the geometry and energy dissipation distribution in an accreting black hole system. The goal of the present investigation is to infer physical parameters of GBHC purely on the basis of radiation physics, this later can be used to guide efforts to obtain dynamical explanations for the changes in spectral state. A more detailed discussion can be found in [14]. ANALYTICAL ARGUMENTS It is natural to attribute the two components with which the spectra are fitted to two physically related regions: an optically thick (quasi-thermal) accretion disk, which is responsible for the blackbody component, and an optically thin hot region (corona), which radiates the hard X-rays. The intrinsic dissipation rates in the “disk” and “corona” are L s and Lh, respectively. The size of the region over which the “disk” radiates most of its energy is Rs, and the size of the corona is Rh. The hard X-rays are assumed to be produced by thermal Comptonization (e.g. [15]) of the seed photons that are partly created locally (by thermal bremsstrahlung or cyclo-synchrotron radiation [16]) and partly in the quasithermal region. The “soft” luminosity, Ls is partly due to local energy dissipation and partly due to reradiation of hard X-rays, created in the “corona”. The shape of the Comptonized spectrum produced by the “corona” may be described by two parameters: the power-law slope α, and the exponential cut-off energy Ec. Also two parameters (the effective temperature Ts and L obs s ) define the soft part of the radiation. The relative ratio of the observed hard luminosity to the observed soft luminosity, L h /L obs s , and the magnitude of the reflection bump (described by the parameter, C, the fraction of solid angle that the optically thick region occupies around the “corona”) complete the set of observables. These phenomenological parameters are determined by two dimensional quantities, the total dissipation rate and Rs, and four dimensionless physical parameters: the ratio L s /Lh; the Compton optical depth of the “corona” τT ; the fraction D of the light emitted by the thermal region which passes through the “corona”; and the ratio S of intrinsic seed photon production in the “corona” to the seed photon luminosity injected from outside. Another dimensionless parameter, the compactness lh ≡ LhσT/(mecRh), may be used to determine the relative importance of e pairs in the corona. In this context it is also useful to distinguish the net lepton Compton optical depth τp from the total Compton optical depth (including pairs), τT . We will show how all these parameters, as well as several others of physical interest, may be inferred from observable quantities. Some of the physical parameters of the system may be derived (or at least J. POUTANEN ET AL. 3 constrained) almost directly from observables. For example, the electron temperature in the corona (measured in electron rest mass units) is very closely related to the cut-off energy of the hard component: Θ ' fxEc/(mec ) , (1) where fx ∼ 0.7. Similarly, Lh ' L obs h /{1− C[1− a]}, (2) where a is the albedo for Compton reflection. The intrinsic disk luminosity is L s ' L obs s − CLh[1− a]. (3) Taking the local disk emission to be approximately black body, disk’s inner radius is Rs ' { L s /4πσT 4 s }1/2 , (4) where Ts is the effective temperature at the inner edge. A number of correction factors (accounting for difference between color and local effective temperature [17] and incorporating the general relativistic corrections [18] etc.) were omitted in these formulae. We next employ the two following analytic scaling approximations for thermal Comptonization spectra found by [12]: D(1 + S) = 0.15αLh/[L intr s + CLh(1− a)] (5)