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.Comment: 5 pages, 3 figures, to appear in the Proceedings of 4th Compton
  Symposium, April 27-30, 1997, Williamsburg, Virginia, US

Krolik, Julian H.

Poutanen, Juri

Ryde, Felix

English

arXiv

Juri Poutanen

Julian H. Krolik

Felix Ryde

Crossref

Physical characteristics of the spectral states of galactic black holes

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Physical Characteristics of the Spectral
States of Galactic Black Holes
Juri Poutanen∗, Julian H. Krolik† and Felix Ryde‡
∗Uppsala Observatory, Box 515, SE-75120 Uppsala, Sweden
†Johns Hopkins University, Baltimore, MD 21218
‡Stockholm Observatory, SE-13336 Saltsöbaden, Sweden
Abstract. 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 un-
derstand much better how thermal Comptonization works, when the seed photons
are produced mainly by reprocessing a part of the hard X-ray output, [11–13]) and
the existence of broad band simultaneous spectral 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
SPECTRAL STATES OF GALACTIC BLACK HOLES
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 Lintrs 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 quasi-thermal 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, Lobsh /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 quanti-
ties, the total dissipation rate and Rs, and four dimensionless physical parameters:
the ratio Lintrs /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 compact-
ness lh ≡ LhσT/(mec
3Rh), 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 con-
strained) 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
2) , (1)
J. POUTANEN ET AL.
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
Lintrs ≃ L
obs
s − CLh[1− a]. (3)
Taking the local disk emission to be approximately black body, disk’s inner radius
is
Rs ≃
{
Lobss /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) = 0.15α4Lh/[L
intr
s + CLh(1− a)] (5)
and
τT = 0.16/(αΘ). (6)
The first expresses how the power-law hardens as the heating rate in the corona
increases relative to the seed photon luminosity; the second expresses the trade-off
in cooling power between increasing optical depth and increasing temperature.
Finally, both C and D may be written in terms of Rh and Rs. If the corona is
a sphere centered on the black hole, and the disk is an annulus of inner radius Rs
and infinitesimal vertical thickness,
C ≃ Rh/(6Rs) and D ≃ (1/16)(Rh/Rs)
3. (7)
The coefficient in the definition of C is most accurate when the emissivity is uni-
form within the sphere and it has order unity optical depth; the coefficient in the
definition of D assumes the disk surface brightness is ∝ r−3 and its intensity dis-
tribution is isotropic. The relationship between Rh/Rs and C or D is somewhat
different in other geometries, but the scaling tends to be similar. Equations (7)
may be regarded as giving independent estimates of Rh/Rs. If C is used, this ratio
is constrained by the observed magnitude of the Compton reflection bump; if D is
used, it is determined by the observed hard and soft luminosities, and the slope of
the hard X-ray power-law. The corona is assumed roughly spherical.
SPECTRAL STATES OF GALACTIC BLACK HOLES
RESULTS AND CONCLUSIONS
The method described above can be applied to find physical parameters of the
system Θ, τT , Rs, D(1 + S), Rh/Rs, L
intr
s /L
obs
h and lh from the set of observables
α,Ec, Ts, L
obs
s , C and L
obs
h /L
obs
s . Unfortunately, existing data are good enough only
for a small number of objects. This method applied to Cyg X-1 (see [14]) shows
that the inner edge of the cold disk shrinks by roughly a factor of 5 between the
hard and soft states (from ∼ 40rg to ∼ 8rg, assuming 10 M⊙ black hole), while
the corona shrinks in radial scale by only factor of two. In the SS, corona covers a
sizable portion of the inner disk (see Fig. 1 and [8,9]).
Despite the change in coronal size and luminosity, the compactness of the corona
almost does not change during the hard-soft transition. However, its optical depth
drops by an order of magnitude from ∼ 1 − 2 to ∼ 0.1. Electron temperature of
the corona is ∼ 100 keV in the HS and probably is higher in the SS. In the HS the
disk receives only a minority of the dissipation, Lintrs /Lh ∼ 0.1, but is the site of
most of the heat release in the SS, Lintrs /Lh ∼ 3.
Detailed calculations based on the method by [19], that allow us to solve for the
energy and electron-positron pair balance together with the self-consistent treat-
ment of the Comptonization in the corona, confirm the conclusions made from
simple analytical arguments. We also are able to show that in the case of thermal
electrons there are very few e± pairs in the HS, but they can be comparable in
number to the net electrons in the SS. In contrast the amount of pairs in the SS
can be significant. This means that the fall in τp from the HS to the SS is greater
than the fall in τT .
We close by noting that simultaneous broad band observations from soft X-rays
up to gamma-rays are necessary in order to make strong conclusions regarding the
FIGURE 1. Geometry of the accretion flows around black holes in the hard (top) and soft
(bottom) states.
J. POUTANEN ET AL.
geometry and physical conditions in the accretion flows around black hole.
REFERENCES
1. Tanaka, Y., and Levin, W. H. G., “Black-hole binaries” in X-ray Binaries, Cam-
bridge: Cambridge University Press, 1995, pp. 126-174.
2. Ebisawa, K., Ueda, Y., Inoue, H., Tanaka, Y., and White, N. E., ApJ 467, 419
(1996)
3. Phlips, B. F., Jung, G. V., Leising, M. D. et al., ApJ 465, 907 (1996)
4. Grove J. E. et al., “Two gamma-ray spectral classes of black hole transients” in The
Transparent Universe, Proc. 2nd INTEGRAL Workshop, ESA SP-382, 1997, pp.
197-200
5. Ichimaru, S., ApJ 214, 840 (1977)
6. Chen, X., and Tamm, R. E., ApJ 466, 404 (1996)
7. Ebisawa, K., Titarchuk, L., and Chakrabarti, S. K., PASJ 48, 59 (1996)
8. Esin, A. A., McClintock, J. E., and Narayan, R., ApJ submitted (astro-ph/9705237)
9. Gierliński, M., Zdziarski, A. A., Done, C., Johnson, W. N., Ebisawa, K., Ueda, Y.,
Haardt, F., Phlips, B. F., MNRAS, in press
10. Zdziarski, A. A., Johnson, W. N., Poutanen, J., Magdziarz, P., and Gierliński, M.,
“X-rays and gamma-rays from accretion flows onto black holes in Seyferts and X-
ray binaries,” in The Transparent Universe, Proc. 2nd INTEGRAL Workshop, ESA
SP-382, 1997, pp. 373-380.
11. Ghisellini, G., and Haardt, F., ApJ 432, L95 (1994)
12. Pietrini, P., and Krolik, J. H., ApJ 447, 526 (1995)
13. Stern, B. E., Poutanen, J., Svensson, R., Sikora, M., Begelman, M. C., ApJ 449,
L13 (1995)
14. Poutanen, J., Krolik, J. H., and Ryde, F., MNRAS, submitted
15. Shapiro, S. L., Lightman, A. P., Eardley, D. N., ApJ 204, 187 (1976)
16. Narayan, R., and Yi, I., ApJ 452, 710 (1995)
17. Shimura, T., and Takahara F., ApJ 445, 780 (1995)
18. Zhang, S. N., Cui, W., and Chen, W., ApJ 482, L155 (1997)
19. Poutanen, J., and Svensson, R., ApJ 470, 249 (1996)


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