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Optical bursts from X-ray irradiated accretion disk
149152. . . Adv. Space Res. Vol.1, ~i~ © COSPAR, 1981. Printed in Great Britain.
02731177/81/04010149$05.O0/O
OPTICAL BURSTS FROM X-RAY IRRADIATED ACCRETION DISK S. Hayakawa Department ofAstrophysics, Nagoya University, Nagoya, Japan P~BSTRACT Optical radiation is emitted from an accretion disk which is irradiated by X—rays. In the outer part the disk is heated mainly by X—rays, and its scale height is greater than that without X-ray heating. Hence the outer region in which X-ray heating is dominant gives a main contribution to optical emission. Since the temperature in this region is several times lO~K, optical emission is roughly explained by the Rayleigh-Jeans law. When the X-ray source emits an X-ray burst, the disk also emits an optical burst with some time delay. This explains the time profile of an optical burst with respect to that of an X—ray burst, as observed for MXB 1636 — 536. INTRODUCTION Since the discovery of the simultaneous occurrence of X—ray and optical bursts from MXB 1935 — 44 [1,2], a number of simultaneous bursts have been observed from several sources. It has been suggested that optical radiation is emitted from the photosphere of a companion star or from the surface of an accretion disk irradiated by X-rays, and the latter model is preferred on the basis of the absence of modulation associated with binary motion (1,21. It is worth remarking that simultaneous events observed from MXB 1735 — 44, 1837 + 05 [3], and 1636 — 53 [41are similar to each other in the following respects: the optical to X-ray flux ratio ~for steady emission is around ~ the ratio for burst peaks is smaller by an order of magnitude, the optical burst is delayed by about 2s, and the time spread after subtraction of the average delay is 1 - 2 s. These features common to these sources would favour the disk origin, since it would be unlikely that these three binary systems have similar geometries. If a disk origin of optical bursts is taken for granted, the simultaneous X—ray and optical observations provide a powerful means of obtaining properties of the accretion disk. As a step towards this purpose, we discuss optical emission from an X—ray irradiated disk, referring to the standard disk model [5]. X-RAY IRRP~DIATED DISK An accretion disk formed about a compact star of mass and radius R is heated both by the viscosity of accretion flow and by X-rays from the compact star. The heating rates at radial distance r per unit area by these respective processes
149
ISO
S. Hayakawa
are (6] ~ Qg
=
GM.~ 3R ~ = ~ —i- L,~
—
(1)
where G is the gravitational constant, M is the accretion is the X-ray luminosity, and ~1 —
d h 2lrr dr (Aj L)
rate,
and L~
GM,~M/R
aAh —
~—
—~-
r
L,
(2)
where A is the fraction of X—rays absorbed by the disk, h is the scale height of the disk and h/r ~ ra. The temperatures at the midplane of the disk and at the surface are given respectively by +
(1 + ~-t)Qg~
where t is the optical depth of the disk, and
where Y is the Stefan—Boltzmann constant. Since P and Tc are not much different in the outer disk region of interest, where Qx >> Q~,the vertical structure may be determined by the hydrostatic equilibrium of an isothermal column. For Q~< (3/8)TQg the disk structure is essentially the same as that of the non— irradiated disk so[5],thatthat 1/8. T For 2g.> (3/B)tQg the disk expands by X—ray heating, a =is, 2/7.a = Since = 4~l71~/5, Q~= (3/8)TQg is attained at a radial =
distance 1.1 x
io1°(2A)8’~’9 Mx1”3
819 cm,
M 17
(5)
R6
where N,A is measured in units of the solar mass. The region of r > r is mainly responsible for optical emission, since h/r increases more rapidly wish r and the area of an annular ring is proportional to r. In this region we obtain the scale height h/r
(2~ )l/7 M M ~ x37 x x and the surface temperature T 2.7 x l0~ (2AL )2”7M —1/7 r3’17 K, =
2.6 x 102
x37
r2”7
=
(7)
x
where r is measured in units of light seconds. The o~tical luminosity annular ring of r = 1 is, M = 1 and L l0~~erg s is dL /dr opt
(6)
per
1.4 x 10 34 erg s —l is —l .
(8)
In the region r > 1. is the optical emission is suppressed, since the effective optical depth for thermal radiation becomes so small that X-ray photons are not well thermalized. We estimate the maximum radius effective for optical emission to be somewhat smaller 4than 2 is. Hence we have L~~ot/L~ “-. l0~, which is greater than 2 x l05, 1 x 10 and 6 x l04 for the X-ray sources mentiond. This Implies that we are observing the disks at glancing angles. OPTICAL BURSTS
If the disk is irradiated by an X—ray burst, the disk structure cannot adjust
Optical Bursts from Accretion Disks
151
itself within the duration of a burst. Hence h/r in equation (6) is dictated by the steady luminosity ~1~b-while temperature in equation (4) is given the Thus the we obtain the surface temperature duringby a burst X—ray burst luminosity Tb
=
2.7 x ~
(2A)2”7 (L
37)l~~28(L b 1/73/7
37)M
K.
(9)
The optical luminosity thus calculated is given by a solid line in figure 1, where the maximum burst luminosity is assumed to be 1038 erg s~-, close to the Eddington limit for the unit solar mass. The dot-dashed line indicates the optical luminosity for the Rayleigh—Jeans law; a deviation therefrom is due to the fact that the temperature is not high enough for the Rayleigh—Jeans law to hold in the optical band. 1o_11~....I
I
I
MXB 1636—536 Burst 1979. 6. 28d O~55m DeLay 2.3s
E U
5
j
io~ ~
—
10
~
~-l3
.
~ 9 i0
X-ray
~
RISE
,
DECAYS
108
io7
X-ray Intensity Ix (erg.cm~s’)
Fig.l. Correlation between the X-ray and optical intensities for a burst of MXB 1636 — 536 on 28 June 1979. The intensities in 3 second bins are compared after shifting the optical data by 2.3 s with respect to the X—ray data. The numbers attached with observed points indicate the bin numbers. The solid line represents the calculated result with the present model. The dot-dashed line represents that expected from the Rayleigh—Jeans law. The observed data are taken for a clean burst of MXB 1636 - 53, X-ray data with Hakucho in the energy range 0.8 - 24.5 key and optical data by Pederson with the ESO telescope, both data being analyzed by T. Ohashi. For comparison the optical data are shifted by 2.3 s to make the burst profiles in these two bands coincide. The following comments may be worth mentioning. From five simultaneous bursts one sees that the time profiles of X-ray and optical bursts are similar. The optical emission cannot be smeared out for a time longer than one second. This re~uires that the travel time of both X-rays and optical radiation does not spread over a period longer than 1 s, and that the time for converting X-rays to optical radiation in the disk is shorter than 1 5. The former is attainable, since optical emission is concentrated in an annular ring of radius ‘\‘ 1 is, and we are
152
S. Hayakawa
probably observing the disk at a glancing angle, so that only the far side of the ring is accessible over the ring edge, as expected from large positive and negative Doppler shifts of the Bowen lines [7]. A short reprocessing time results since both the geometrical and optical thicknesses of the disk at r ‘~‘ 1 is are small enough for photons to cross the disk within a fraction of second. The time profile of an optical burst is better correlated with that of X-rays with energies lower than 10 key, as noted by S. Miyamoto. This also gives evidence that optical emission arises from an X—ray heated surface, since compton scattering is dominant over photoelectric absorption at energies greater than 6 key. In conclusion, fair agreement between the model and the observed data encourages us that quantitative information on the accretion disk will be obtainable by more refined observations of X—ray and optical bursts. The him the the
author expresses his thanks to the Hakucho-ESO—MIT collaboration for showing the observed data promptly. The present paper is prepared as a part of publications of the Hakucho group, but is published by the responsibility of present author. REFERENCES
1.
J.E. Grindlay, J.E. McClintock, C.R. Canizares, J. van Paradijs, L. Cominsky, F.K. Li, and W.H.G. Lewin, Nature 274, 567 (1978).
2.
J.E. McClintock, J.E. Grindlay, C.R. Canizares, J. van Paradijs, F.K. Li, and W.H.G. Lwein, Nature 279, 47 (1979).
3.
J.A. Hackwell, G.L. Grasdalen, R.D. Gehrz, J. van Paradijs, L. Cominsky, and W.H.G. Lewin, Astrophys J. Letters 233, Lll5 (1979).
4.
Hakucho-ESO-MIT Collaboration
5.
N.I. Shàkura and R.A. Syuyaev, Astron. Astrophys. 24, 337 (1973).
6.
V.M. Lyutyi and R.A. Syunyaev, Soy. Astron.-A.J. 20, 290 (1976).
7.
C.R. Canizares, J.E. McClintock, and J.E. Grindlay, Astrophys. J. 234, 556 (1979)
L. Cominsky,
(1979).
02731177/81/04010149$05.O0/O
OPTICAL BURSTS FROM X-RAY IRRADIATED ACCRETION DISK S. Hayakawa Department ofAstrophysics, Nagoya University, Nagoya, Japan P~BSTRACT Optical radiation is emitted from an accretion disk which is irradiated by X—rays. In the outer part the disk is heated mainly by X—rays, and its scale height is greater than that without X-ray heating. Hence the outer region in which X-ray heating is dominant gives a main contribution to optical emission. Since the temperature in this region is several times lO~K, optical emission is roughly explained by the Rayleigh-Jeans law. When the X-ray source emits an X-ray burst, the disk also emits an optical burst with some time delay. This explains the time profile of an optical burst with respect to that of an X—ray burst, as observed for MXB 1636 — 536. INTRODUCTION Since the discovery of the simultaneous occurrence of X—ray and optical bursts from MXB 1935 — 44 [1,2], a number of simultaneous bursts have been observed from several sources. It has been suggested that optical radiation is emitted from the photosphere of a companion star or from the surface of an accretion disk irradiated by X-rays, and the latter model is preferred on the basis of the absence of modulation associated with binary motion (1,21. It is worth remarking that simultaneous events observed from MXB 1735 — 44, 1837 + 05 [3], and 1636 — 53 [41are similar to each other in the following respects: the optical to X-ray flux ratio ~for steady emission is around ~ the ratio for burst peaks is smaller by an order of magnitude, the optical burst is delayed by about 2s, and the time spread after subtraction of the average delay is 1 - 2 s. These features common to these sources would favour the disk origin, since it would be unlikely that these three binary systems have similar geometries. If a disk origin of optical bursts is taken for granted, the simultaneous X—ray and optical observations provide a powerful means of obtaining properties of the accretion disk. As a step towards this purpose, we discuss optical emission from an X—ray irradiated disk, referring to the standard disk model [5]. X-RAY IRRP~DIATED DISK An accretion disk formed about a compact star of mass and radius R is heated both by the viscosity of accretion flow and by X-rays from the compact star. The heating rates at radial distance r per unit area by these respective processes
149
ISO
S. Hayakawa
are (6] ~ Qg
=
GM.~ 3R ~ = ~ —i- L,~
—
(1)
where G is the gravitational constant, M is the accretion is the X-ray luminosity, and ~1 —
d h 2lrr dr (Aj L)
rate,
and L~
GM,~M/R
aAh —
~—
—~-
r
L,
(2)
where A is the fraction of X—rays absorbed by the disk, h is the scale height of the disk and h/r ~ ra. The temperatures at the midplane of the disk and at the surface are given respectively by +
(1 + ~-t)Qg~
where t is the optical depth of the disk, and
where Y is the Stefan—Boltzmann constant. Since P and Tc are not much different in the outer disk region of interest, where Qx >> Q~,the vertical structure may be determined by the hydrostatic equilibrium of an isothermal column. For Q~< (3/8)TQg the disk structure is essentially the same as that of the non— irradiated disk so[5],thatthat 1/8. T For 2g.> (3/B)tQg the disk expands by X—ray heating, a =is, 2/7.a = Since = 4~l71~/5, Q~= (3/8)TQg is attained at a radial =
distance 1.1 x
io1°(2A)8’~’9 Mx1”3
819 cm,
M 17
(5)
R6
where N,A is measured in units of the solar mass. The region of r > r is mainly responsible for optical emission, since h/r increases more rapidly wish r and the area of an annular ring is proportional to r. In this region we obtain the scale height h/r
(2~ )l/7 M M ~ x37 x x and the surface temperature T 2.7 x l0~ (2AL )2”7M —1/7 r3’17 K, =
2.6 x 102
x37
r2”7
=
(7)
x
where r is measured in units of light seconds. The o~tical luminosity annular ring of r = 1 is, M = 1 and L l0~~erg s is dL /dr opt
(6)
per
1.4 x 10 34 erg s —l is —l .
(8)
In the region r > 1. is the optical emission is suppressed, since the effective optical depth for thermal radiation becomes so small that X-ray photons are not well thermalized. We estimate the maximum radius effective for optical emission to be somewhat smaller 4than 2 is. Hence we have L~~ot/L~ “-. l0~, which is greater than 2 x l05, 1 x 10 and 6 x l04 for the X-ray sources mentiond. This Implies that we are observing the disks at glancing angles. OPTICAL BURSTS
If the disk is irradiated by an X—ray burst, the disk structure cannot adjust
Optical Bursts from Accretion Disks
151
itself within the duration of a burst. Hence h/r in equation (6) is dictated by the steady luminosity ~1~b-while temperature in equation (4) is given the Thus the we obtain the surface temperature duringby a burst X—ray burst luminosity Tb
=
2.7 x ~
(2A)2”7 (L
37)l~~28(L b 1/73/7
37)M
K.
(9)
The optical luminosity thus calculated is given by a solid line in figure 1, where the maximum burst luminosity is assumed to be 1038 erg s~-, close to the Eddington limit for the unit solar mass. The dot-dashed line indicates the optical luminosity for the Rayleigh—Jeans law; a deviation therefrom is due to the fact that the temperature is not high enough for the Rayleigh—Jeans law to hold in the optical band. 1o_11~....I
I
I
MXB 1636—536 Burst 1979. 6. 28d O~55m DeLay 2.3s
E U
5
j
io~ ~
—
10
~
~-l3
.
~ 9 i0
X-ray
~
RISE
,
DECAYS
108
io7
X-ray Intensity Ix (erg.cm~s’)
Fig.l. Correlation between the X-ray and optical intensities for a burst of MXB 1636 — 536 on 28 June 1979. The intensities in 3 second bins are compared after shifting the optical data by 2.3 s with respect to the X—ray data. The numbers attached with observed points indicate the bin numbers. The solid line represents the calculated result with the present model. The dot-dashed line represents that expected from the Rayleigh—Jeans law. The observed data are taken for a clean burst of MXB 1636 - 53, X-ray data with Hakucho in the energy range 0.8 - 24.5 key and optical data by Pederson with the ESO telescope, both data being analyzed by T. Ohashi. For comparison the optical data are shifted by 2.3 s to make the burst profiles in these two bands coincide. The following comments may be worth mentioning. From five simultaneous bursts one sees that the time profiles of X-ray and optical bursts are similar. The optical emission cannot be smeared out for a time longer than one second. This re~uires that the travel time of both X-rays and optical radiation does not spread over a period longer than 1 s, and that the time for converting X-rays to optical radiation in the disk is shorter than 1 5. The former is attainable, since optical emission is concentrated in an annular ring of radius ‘\‘ 1 is, and we are
152
S. Hayakawa
probably observing the disk at a glancing angle, so that only the far side of the ring is accessible over the ring edge, as expected from large positive and negative Doppler shifts of the Bowen lines [7]. A short reprocessing time results since both the geometrical and optical thicknesses of the disk at r ‘~‘ 1 is are small enough for photons to cross the disk within a fraction of second. The time profile of an optical burst is better correlated with that of X-rays with energies lower than 10 key, as noted by S. Miyamoto. This also gives evidence that optical emission arises from an X—ray heated surface, since compton scattering is dominant over photoelectric absorption at energies greater than 6 key. In conclusion, fair agreement between the model and the observed data encourages us that quantitative information on the accretion disk will be obtainable by more refined observations of X—ray and optical bursts. The him the the
author expresses his thanks to the Hakucho-ESO—MIT collaboration for showing the observed data promptly. The present paper is prepared as a part of publications of the Hakucho group, but is published by the responsibility of present author. REFERENCES
1.
J.E. Grindlay, J.E. McClintock, C.R. Canizares, J. van Paradijs, L. Cominsky, F.K. Li, and W.H.G. Lewin, Nature 274, 567 (1978).
2.
J.E. McClintock, J.E. Grindlay, C.R. Canizares, J. van Paradijs, F.K. Li, and W.H.G. Lwein, Nature 279, 47 (1979).
3.
J.A. Hackwell, G.L. Grasdalen, R.D. Gehrz, J. van Paradijs, L. Cominsky, and W.H.G. Lewin, Astrophys J. Letters 233, Lll5 (1979).
4.
Hakucho-ESO-MIT Collaboration
5.
N.I. Shàkura and R.A. Syuyaev, Astron. Astrophys. 24, 337 (1973).
6.
V.M. Lyutyi and R.A. Syunyaev, Soy. Astron.-A.J. 20, 290 (1976).
7.
C.R. Canizares, J.E. McClintock, and J.E. Grindlay, Astrophys. J. 234, 556 (1979)
L. Cominsky,
(1979).