The Nordic Optical Telescope (NOT) is a 2.5 meter optical Ritchey-Chr´etien telescope at Observatorio del Roque de los Muchachos, La Palma, Canary Islands, at 2382 m above sea level.
TURPOL (Turku Polarimeter) is a double-image five-channel (UBVRI) chopping photopolarimeter (see Piirola (1973), Piirola (1975) and the in-strument manual athttp://www.not.iac.es/). Linear and circular polar-ization as well as the flux can be measured simultaneously in five passbands (UBVRI) with effective wavelengths of 360, 440, 530, 690 and 830 nm. The instrument has also pure linear and circular polarimetry modes. Instrumen-tal polarization is negligible (less than 0.01 %), and sky background polar-ization is effectively eliminated. TURPOL can achieve a polarpolar-ization sensi-tivity of the order 0.01 % if the signal is strong enough. For a 12-magnitude star, e.g. the brightest low-mass X-ray binaries 0.1 % can be reached in 15 minutes. The biggest drawbacks of TURPOL are low quantum efficiency and lack of spatial resolution.
ALFOSC(Andalucia Faint Object Spectrograph and Camera) is the other NOT instrument with polarimetric capabilities. However, CCD cameras often have instrumental polarization produced by refracting optics and in some cases also by the surface layer of the CCD chip. High quantum ef-ficiency allows shorter integration times than with photopolarimeters. As
3.3. OPTICAL OBSERVATORIES 31 CCDs produce images, polarimetry of field stars can also be done, possibly improving the estimate of science target’s interstellar polarization. When field star distances are not known, their polarization vectors can have similar directions. In this case, any object with polarization vector different from the field probably has intrinsic polarization. Similarly, anomalies in the wavelength dependence of polarization may be caused by an intrinsic com-ponent. If the distances of the field stars can be estimated (from literature or photometric and spectroscopic observations), the behavior of their polar-ization with distance and reddening also provides an estimate for interstellar polarization (see e.g. Koch-Miramond & Naylor (1995)).
3.3.1 Polarimetric observations
Polarimetric observations are done by measuring the brightness of the object through polarizing optics. A calcite prism is used to split the light into two beams with orthogonal polarization directions. The brightness difference of the beams gives the net polarization in this direction. A rotatable retarder plate can be used to modify the polarization of the radiation before it en-ters the calcite prism. A half-wave retarder changes the direction of linear polarization, and stepping through a series of positions one can measure several polarization components. A quarter-wave retarder converts circular polarization to linear, allowing circular polarimetry, and rotating the plate through a series of suitable positions both linear and circular polarization components can be measured. The measured polarization components are then combined to get the relevant Stokes parameters. Polarimetry always produces photometry as a side product, as the Stokes I parameter corre-sponds to total brightness.
In CCD photometry, an accuracy better than 1% is often considered very good. This is because the detector response is no longer linear when there are several tens of thousands of counts per pixel. Flat-field exposures used to estimate the sensitivity differences between pixels are done in the lin-ear regime, at a level of 1−2×104counts pixel−1, resulting in flat-fielding accuracy of the order 100. If the brightnesses of the two beams are mea-sured to this accuracy, the error in Stokes parameters is of the same order.
As the typical degree of polarization is often of the order 1% or even less, the statistical accuracy of CCD polarimetry is not very good. Instrumen-tal polarization caused by the coating of some CCD chips, distortions of the point-spread function and focus position by the calcite prisms and re-tarders, and in some cases spatial variations in the polarization sensitivity of the instrument are further complications of CCD polarimetry. In contrast, photomultipliers can reach an accuracy of the order 0.01 % for the degree of polarization.
Observations of zero-polarization stars are needed to estimate the
instru-mental polarization produced by e.g. refracting elements in the beam. Zero-polarization standard stars are usually selected from stars close to Sun so they have negligible interstellar polarization. Large-polarization standards provide a known constant polarized signal. The degree of polarization of at least one large-polarization star is measured to estimate the polarization sensitivity of the detector. For linear polarimetry, the large-polarization measurement also gives a reference direction on the sky for the polarization position angle. For circular polarimetry, the sense of polarization is obtained (left-handed vs. right-handed.) For a list of polarization standards, see e.g.
Turnshek et al. (1990). Polarimetric standards are often also photometric standards, which makes extracting the photometric information even easier.
Chapter 4
Results
4.1 Polarization of Accretion Disks
4.1.1 Simulations
The polarization of an accretion disk can be estimated with the Monte Carlo method. Assuming the magnetic field is insignificant it is a relatively straightforward procedure to set up a disk model and then solve the polar-ized radiative transfer. The time requirements of the simulations increase rapidly when the model complexity increases.
Here it is assumed that opacity is due to electron scattering only, and the entire disk is fully ionized, so opacity is directly proportional to density.
This simplifies setting up the disk model. Three parameters can be used to describe density or optical depth distribution of the disk: τ0 is the vertical optical depth (τz) at the inner disk,γ describes the radial dependence of the vertical optical depth (τz ∝Rγ) andH is the scaleheight of the distribution ofτz(we commonly usedH/R= constant). The vertical optical depth from a point (R, z) to the disk surface (R,∞) is defined by:
τz =τ0 R
R0
γZ ∞ z
exp
−z H
dz, (4.1)
where R0 is the inner disk radius. This is roughly correct for the surface layers of an ionized disk where gas pressure dominates (Shakura & Sunyaev, 1973).
After defining the opacity distribution of the disk, emissivity distribution has to be added. Stokes parameters derived for different emissivity dis-tributions can be linearly combined. Two parameters τ1, τ2 were used to define the photon-generating region. All photons are emitted in a layer con-strained by the vertical optical depthsτ1andτ2. This has the advantage that
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results obtained from different photon-generating depths, e.g different emis-sion mechanisms, can be combined. The radial temperature scalesT ∝Rβ whereβshould be between−3/4 (for a viscously heated disk) and−1/2 (for an irradiated disk). A combination of these is accurate for a system with long period and neutron star primary. Long period means large disk and thus viscous energy release is small in the outermost disk. Irradiation of the outer disk by neutron star helps keeping the entire disk ionized.
For bolometric luminosity the emissivity scales roughly as ∝ T4. This is a first-order approximation for the wavelengths from very soft X-rays to ex-treme ultraviolet, and works better in short-period systems where the outer disk radius is smaller. An emissivity model easier to compare with observa-tions is a blackbody (or a physical disk atmosphere model) at the interesting wavelength or convolved with the transmission profile of a photometric fil-ter. One advantage of the Monte Carlo method is that it is easily extended to arbitrary disk models, e.g. results of hydrodynamical calculations.
The simulations presented in Paper II use the simple model described above.
One of the main results is that both single- and double-scattering approx-imations are insufficient and produce too high polarization values. Monte Carlo simulations predict a linear polarization of the order 1%. The degree of polarization depends strongly on inclination. The emissivity model also affects the polarization. Total optical depth of the disk and scaleheight have only a minor effect as long as the disk stays optically thick and disk-like.
In the optical wavelengths, the polarization has only a weak wavelength de-pendence but it is markedly different from that of interstellar polarization.
4.1.2 Observations
Polarimetric observations with NOT/TurPol (see section 3.3) were made in six runs. Her X-1 was observed in linear polarimetry mode during five runs in 1990-1992. The May 2000 run concentrated on Sco X-1 but as the transient XTE J1118+480 was in outburst, it was also observed. When the altitude of Sco X-1 was less than 30◦, SS433 was observed. In May 2000, both linear and circular polarization was measured. Temporal variability analysis of the Her X-1 data showed that the variability reported by Egonsson & Hakala (1991) is not present in later data. Both the linear and circular polarization of Sco X-1 were constant. For XTE J1118+480 there is not enough data for reliable variability analysis.
The circular polarizations of the observed sources are consistent with zero, upper limits are of the order 0.08%, 0.1% and 0.3% for Sco X-1, SS433 and XTE J1118+480, respectively. An upper limit of∼0.3% for the linear polarization of XTE J1118+480 could be derived. For both Her X-1 and Sco X-1 the linear polarization could be detected. In the case of Her X-1
4.2. X-RAY OBSERVATIONS 35