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Astron. Astrophys. 364, 587-596 (2000)

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5. Application example: Scorpius X-1

Sco X-1 is the brightest LMXB with B [FORMULA], making it a good candidate for optical/UV polarization measurements. On the basis of its X-ray timing properties it is classified as a Z source, indicating neutron star primary and near-Eddington accretion rate (Hasinger & van der Klis 1989). X-ray timing analysis shows also that magnetic field of the neutron star is extremely low (van der Klis et al. 1997), so the inner disk radius is [FORMULA]. The mass accretion rate ([FORMULA]), outer disk radius ([FORMULA]) and fraction of X-rays absorbed to the accretion disk ([FORMULA]), have been estimated from IUE observations (Kallman et al. 1991), giving [FORMULA], [FORMULA] and [FORMULA]. The inclination of the system is quite low, most probably below [FORMULA] (Crampton et al. 1976). The temperature of the disk is affected by both viscous energy release and X-ray irradiation, so the real temperature profile is

[EQUATION]

where [FORMULA] is an efficiency factor and other symbols have their usual meanings. Setting [FORMULA], [FORMULA] and [FORMULA] in Eq. (16) we get

[EQUATION]

X-ray irradiation is important for the temperature profile in the outer disk. At the outer edge of the disk, the temperature is [FORMULA], so the entire disk should be ionized. The optical luminosities derived from this model are a few times larger than those observed (Kallman et al. 1991). The values of [FORMULA], [FORMULA], [FORMULA] and [FORMULA] were adopted. The simulations predict small but observable polarization values for Sco X-1. (Fig. 6). No significant wavelength dependence is seen from the results. More detailed modelling of the disk rim and opacity in the cooler disk regions could result to lower polarization levels in the longest wavelengths, as some of the scattered radiation in the outer disk would be absorbed. Similar polarization values could be obtained from Fig. 4. To estimate the polarization variations caused by radial temperature profile, simulations with other temperature profiles were made. Of the two models used, one has constant disk temperature, which should be a rough estimate of a disk heated by scattering fron the corona (ADC-model). The other model had a steep temperature profile, [FORMULA]. The inner disk temperature is same as in the model for Sco X-1. The results are represented in Fig. 7 and Fig. 8. No significant change in value or wavelength dependence of polarization is seen with steeper temperature profile. As the temperature profile effects on polarization are minimal, the radial structure of the disk does not influence polarization, and no detailed information on the radial disk structure is needed for the interpretation of observations.

[FIGURE] Fig. 6. Linear polarization vs. wavelength. Simulation for Scorpius X-1, assuming axisymmetric pure electron scattering disk. Crosses, diamonds and triangles correspond to inclination values of 30o, 20o and 10o

[FIGURE] Fig. 7. Linear polarization vs. wavelength. Simulation for the density distribution of Fig. 6, with constant disk temperature [FORMULA]. Crosses, diamonds and triangles correspond to inclination values of 30o, 20o and 10o

[FIGURE] Fig. 8. Linear polarization vs. wavelength. Simulation for the density distribution of Fig. 6, with steep temperature profile [FORMULA]. Crosses, diamonds and triangles correspond to inclination values of 30o, 20o and 10o

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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