Standard Stars for Polarimetric Measurement and Their Statistics

The most important aspect of stellar polarimetry involves the studying of polarimetric standard stars. The techniques of polarimetry have advanced progressively with the associated improvement of accuracy. This has not been accompanied with establishment of better standards of reference. Two fundamental reductions must be made to the polarization data before any inferences can be drawn from observations: (A) Instrumental polarization corrections should be performed on the data by observing "zero" polarization standards, (B) Absolute position angle calibration, so that the data may be presented in a particular coordinate frame so allowing comparison of data collected on different instruments. The latter can be obtained from knowledge of the orientation of the polarimeter relative to north-South direction. Laboratory techniques should be used, where available, for absolute calibration of position angle. It is however, far more convienient to observe highly polarized stars with a well defined position angle of polarization; the equatorial coordinate frame is normally chosen for reference. These standards also provide means of testing the stability of the instrument. The aim of this study is to present a scheme that may be used to quantify some criteria for establishment of future standard polarimetric stars. There have been only few authors that have paid any attention to establishing polarimetric standards. Discussions presented in Chapter 1 deal with the present standing of polarimetric standards and the areas where further improvements are required. Since the discovery of interstellar polarization by Hall and Hiltner, there has been a significant increase in our precision of polarization measurements. It is therefore essential to investigate the statistical behaviour of errors involved with the measurements of polarization and position angle; the former has been quantitatively well studied by previous workers, but the latter has lacked the detail it deserves. We have constructed accurate confidence intervals of position angle of polarization and have provided statistical formulation of the distribution. It is demonstrated in Chapter 2 that confidence values of position angle at low levels of signal-to-noise ratio are significantly different from the Gaussian distribution assumed in the literature. Also a data simulation method was performed in order to determine the distribution of differences in two values of position angle at low signal-to-noise, since analytical solutions would be too complex to handle for this situation. The literature shows that some of the well established standards are challenged either because of their imprecise tabulated values or because of suspected polarimetric variability. Proper statistical techniques should be used however to assess correctly and accurately these findings. It is shown in Chapter 3 that because of inadequate statistical procedures applied to the data of polarimetric standards, many stars supposedly showing variations in their polarization and position angle, may still be considered as standards. We have performed, more rigid statistical tests on some previously published broad-band data. It is therefore concluded that, prior to this work presented here, all data involving standard polarimetric stars have not been statistically interpreted correctly. We have undertaken new observations on some well known polarization standards which are thought to have a variable polarization. Double channel polarimetry of 55Cyg, &phis;Cas, rhoCas, oCas, rhoLeo and 14Cep was performed and attempt were made to establish further standards in Cassiopeia and Perseus

Application of CCDs (Charge Coupled Devices) to Polarimetry and Spectropolarimetry

Ideally, we would like to have at our disposal a "universal" instrument which could record all available information, i.e. the full Stokes vectors I, Q, U, V as function of spatial coordinates X and Y and wavelength A at given time t. The practical limitations of spectral dispersers now being used for high resolution observations, narrow band filters or spectrographs each permit only the measurement of a limited sub-set of these parameters. Filters record I(?,Y) at a fixed wavelength and the spectrograph record (I,?,Y) at a fixed X, where X is the direction perpendicular to the slit and Y along it. An important element to any instrumentation is the detector system and to achieve the above, a detector system must possess 2-dimensional characteristics. The application of CCDs to stellar polarimetry has been slow, one problem being that the polarimetric modulators favoured with photomultiplier detection are not immediately applicable. Since, instrumental, observational and data reduction techniques are very different in these two detector systems. At the start of this work (1991) high-precision polarimetric data are obtained by po-larimeters which employ photomultiplier detectors, with measurement accuracy controlled by photon counting statistics. For low levels of polarization, simple error analysis provides uncertainty estimates for q and u of sigmaq = sigmau =(2/N

Placing Confidence Limits on Polarization Measurements

The determination of the true source polarization given a set of measurements is complicated by the requirement that the polarization always be positive. This positive bias also hinders construction of upper limits, uncertainties, and confidence regions, especially at low signal-to-noise levels. We generate the likelihood function for linear polarization measurements and use it to create confidence regions and upper limits. This is accomplished by integrating the likelihood function over the true polarization (parameter space), rather than the measured polarization (data space). These regions are valid for both low and high signal-to-noise measurements.Comment: 8 pages, 3 figures, 1 table, submitted to PAS

Bayesian analysis of polarization measurements

A detailed and formal account of polarization measurements using Bayesian analysis is given based on the assumption of gaussian error for the Stokes parameters. This analysis is crucial for the measurement of the polarization degree and angle at very low (and very high) signal-to-noise. The treatment serves as a framework for customized analysis of data based on a particular prior suited to the experiment.Comment: 15 page

Polarization of Broad Absorption Line QSOs I. A Spectropolarimetric Atlas

We present a spectropolarimetric survey of 36 broad absorption line quasi-stellar objects (BAL QSOs). The continuum, absorption trough, and emission line polarization of BAL QSOs yield clues about their structure. We confirm that BAL QSOs are in general more highly polarized than non-BAL QSOs, consistent with a more equatorial viewing direction for the former than the latter. We have identified two new highly-polarized QSOs in our sample (1232+1325 and 1333+2840). The polarization rises weakly to the blue in most objects, perhaps due to scattering and absorption by dust particles. We find that a polarization increase in the BAL troughs is a general property of polarized BAL QSOs, indicating an excess of scattered light relative to direct light, and consistent with the unification of BAL QSOs and non-BAL QSOs. We have also discovered evidence of resonantly scattered photons in the red wing of the C IV broad emission lines of a few objects. In most cases, the broad emission lines have lower polarization and a different position angle than the continuum. The polarization characteristics of low-ionization BAL QSOs are similar to those of high-ionization BAL QSOs, suggesting a similar BAL wind geometry.Comment: 39 pages, 6 figures (20 .gif files), accepted for publication in The Astrophysical Journal Supplement

Absolute emission altitude of pulsars: PSRs B1839+09, B1916+14 and B2111+46

We study the mean profiles of the multi--component pulsars PSRs B1839+09, B1916+14 and B2111+46. We estimate the emission height of the core components, and hence find the absolute emission altitudes corresponding to the conal components. By fitting Gaussians to the emission components, we determine the phase location of the component peaks. Our findings indicate that the emission beams of these pulsars have the nested core--cone structures. Based on the phase location of the component peaks, we estimate the aberration--retardation (A/R) phase shifts in the profiles. Due to the A/R phase shift, the peak of the core component in the intensity profile and the inflection point of the polarization angle swing are found to be symmetrically shifted in the opposite directions with respect to the meridional plane in such a way that the core shifts towards the leading side and the polarization angle inflection point towards the trailing side. We have been able to locate the phase location of the meridional plane and to estimate the absolute emission altitude of both the core and the conal components relative to the neutron star centre, using the exact expression for the A/R phase shift given by Gangadhara (2005).Comment: 10 pages, 6 figures, Accepted for Publication in A&

Statistical Assessment of Shapes and Magnetic Field Orientations in Molecular Clouds through Polarization Observations

We present a novel statistical analysis aimed at deriving the intrinsic shapes and magnetic field orientations of molecular clouds using dust emission and polarization observations by the Hertz polarimeter. Our observables are the aspect ratio of the projected plane-of-the-sky cloud image, and the angle between the mean direction of the plane-of-the-sky component of the magnetic field and the short axis of the cloud image. To overcome projection effects due to the unknown orientation of the line-of-sight, we combine observations from 24 clouds, assuming that line-of-sight orientations are random and all are equally probable. Through a weighted least-squares analysis, we find that the best-fit intrinsic cloud shape describing our sample is an oblate disk with only small degrees of triaxiality. The best-fit intrinsic magnetic field orientation is close to the direction of the shortest cloud axis, with small (~24 deg) deviations toward the long/middle cloud axes. However, due to the small number of observed clouds, the power of our analysis to reject alternative configurations is limited.Comment: 14 pages, 8 figures, accepted for publication in MNRA

Infrared and optical polarimetry around the low-mass star-forming region NGC 1333 IRAS 4A

We performed J- and R-band linear polarimetry with the 4.2 m William Herschel Telescope at the Observatorio del Roque de los Muchachos and with the 1.6 m telescope at the Observat\'orio do Pico dos Dias, respectively, to derive the magnetic field geometry of the diffuse molecular cloud surrounding the embedded protostellar system NGC 1333 IRAS 4A. We obtained interstellar polarization data for about two dozen stars. The distribution of polarization position angles has low dispersion and suggests the existence of an ordered magnetic field component at physical scales larger than the protostar. Some of the observed stars present intrinsic polarization and evidence of being young stellar objects. The estimated mean orientation of the interstellar magnetic field as derived from these data is almost perpendicular to the main direction of the magnetic field associated with the dense molecular envelope around IRAS 4A. Since the distribution of the CO emission in NGC 1333 indicates that the diffuse molecular gas has a multi-layered structure, we suggest that the observed polarization position angles are caused by the superposed projection along the line of sight of different magnetic field components.Comment: 37 pages, 9 figures, 5 tables, accepted for publication in A

Submillimeter Polarization of Galactic Clouds: A Comparison of 350 micron and 850 micron Data

The Hertz and SCUBA polarimeters, working at 350 micron and 850 micron respectively, have measured the polarized emission in scores of Galactic clouds. Of the clouds in each dataset, 17 were mapped by both instruments with good polarization signal-to-noise ratios. We present maps of each of these 17 clouds comparing the dual-wavelength polarization amplitudes and position angles at the same spatial locations. In total number of clouds compared, this is a four-fold increase over previous work. Across the entire data-set real position angle differences are seen between wavelengths. While the distribution of \phi(850)-\phi(350) is centered near zero (near-equal angles), 64% of data points with high polarization signal-to-noise (P >= 3\sigma_p) have |\phi(850)-\phi(350)| > 10 degrees. Of those data with small changes in position angle (<= 10 degrees) the median ratio of the polarization amplitudes is P(850)/P(350) = 1.7 +/- 0.6. This value is consistent with previous work performed on smaller samples and models which require mixtures of different grain properties and polarization efficiencies. Along with the polarization data we have also compiled the intensity data at both wavelengths; we find a trend of decreasing polarization with increasing 850-to-350 micron intensity ratio. All the polarization and intensity data presented here (1699 points in total) are available in electronic format.Comment: 50 pages, 26 figures, one electronic data file. Submitted to ApJ

The RINGO2 and DIPOL optical polarization catalogue of blazars

We present ∼2000 polarimetric and ∼3000 photometric observations of 15 γ-ray bright blazars over a period of 936 days (2008-10-11 to 2012-10-26) using data from the Tuorla blazar monitoring program (KVA DIPOL) and Liverpool Telescope (LT) RINGO2 polarimeters (supplemented with data from SkyCamZ (LT) and Fermi-LAT γ-ray data). In 11 out of 15 sources we identify a total of 19 electric vector position angle (EVPA) rotations and 95 flaring episodes. We group the sources into subclasses based on their broad-band spectral characteristics and compare their observed optical and γ-ray properties. We find that (1) the optical magnitude and γ-ray flux are positively correlated, (2) EVPA rotations can occur in any blazar subclass, four sources show rotations that go in one direction and immediately rotate back, (3) we see no difference in the γ-ray flaring rates in the sample; flares can occur during and outside of rotations with no preference for this behaviour, (4) the average degree of polarization (DoP), optical magnitude and γ-ray flux are lower during an EVPA rotation compared with during non-rotation and the distribution of the DoP during EVPA rotations is not drawn from the same parent sample as the distribution outside rotations, (5) the number of observed flaring events and optical polarization rotations are correlated, however we find no strong evidence for a temporal association between individual flares and rotations and (6) the maximum observed DoP increases from ∼10 per cent to ∼30 per cent to ∼40 per cent for subclasses with synchrotron peaks at high, intermediate and low frequencies, respectively