In this paper we present an error analysis for polarimetric data obtained with dual-beam instruments. After recalling the basic concepts, we introduce the analytical expressions for the uncertainties of polarization degree and angle. These are then compared with the results of Monte Carlo simulations, which are also used to briefly discuss the statistical bias. We then approach the problem of background subtraction and the errors introduced by an imperfect Wollaston prism, flat-fielding, and retarder plate defects. Finally, we investigate the effects of instrumental polarization and propose a simple test to detect and characterize it. The application of this method to real VLT-FORS1 data has shown the presence of a spurious polarization that is of the order of ∼1.5% at the edges of the field of view. The cause of this problem has been identified as the presence of rather curved lenses in the collimator, combined with the incomplete removal of reflections by the coatings. This problem is probably common to all focal-reducer instruments equipped with a polarimetric mode. An additional spurious and asymmetric polarization field, whose cause is still unclear, is visible in the B band.

https://www.jstor.org/stable/10.1086/497581

Error Analysis for Dual-Beam Optical Linear Polarimetry

The linear polarization of the Crab pulsar and its close environment was derived from observations with the high-speed photopolarimeter Optical Pulsar TIMing Analyser at the 2.56-m Nordic Optical Telescope in the optical spectral range (400-750 nm). Time resolution as short as 11 μs, which corresponds to a phase interval of 1/3000 of the pulsar rotation, and high statistics allow the derivation of polarization details never achieved before. The degree of optical polarization and the position angle correlate in surprising details with the light curves at optical wavelengths and at radio frequencies of 610 and 1400 MHz. Our observations show that there exists a subtle connection between presumed non-coherent (optical) and coherent (radio) emissions. This finding supports previously detected correlations between the optical intensity of the Crab and the occurrence of giant radio pulses. Interpretation of our observations requires more elaborate theoretical models than those currently available in the literature.

Optical polarization of the Crab pulsar: precision measurements and comparison to the radio emission

We present optical and near-infrared spectropolarimetry of the nuclei of four type 2 Seyfert galaxies, Mrk 463E, Mrk 1210, NGC 1068, and NGC 4388. The data were obtained simultaneously, covering the wavelength range of 0.46-2.5 μm. We model the polarizations from two dust-scattering components: (1) scattering in dusty regions in ionization cones and (2) scattering in a torus surrounding a type 1 nucleus. The polarizations from electron scattering in the cones and dichroic absorption by aligned dust grains in the torus are also compared with the observations. We confirmed that a combination of electron and dust scattering in the ionization cones is the preferred mechanism for the optical continuum polarization. For the near-infrared, dichroic absorption by aligned grains can explain the continuum polarization of Mrk 463E and Mrk 1210 as well as NGC 1068. Visual optical depths of the order of 10-20 are estimated for dichroic absorption in these nuclei. Dust scattering in the torus, whose grain size distribution is assumed to be the same as in the Galactic diffuse interstellar medium, cannot reproduce the observed spectral slope of the near-infrared polarization and total nuclear flux simultaneously. However, this might only indicate that the grain size distribution in the torus of active galactic nuclei (AGNs) is different, and dust scattering with moderate optical depth and dominated by large grains might provide a reasonable explanation for the near-infrared radiation from AGNs.

/pdf/simultaneous-optical-and-near-infrared-spectropolarimetry-of-1raapicd8y.pdf

Simultaneous Optical and Near-Infrared Spectropolarimetry of Type 2 Seyfert Galaxies

Optical spectropolarimetry and broadband polarimetry in other wavebands has been a key to understanding many diverse aspects of AGN. In some cases polarization is due to synchrotron radiation, and in other cases it's due to scattering. Recognition of relativistically beamed optical synchrotron emission by polarization was vital for understanding blazars (BL Lacs and Optically Violently Variable quasars), both physically and geometrically. Radio polarimetry of quiescent AGN is equally important, again for both purposes. Scattering polarization was central to the Unified Model for Seyferts, Radio Galaxies and (high ionization) Ultraluminous Infrared Galaxies. It provides a periscope for viewing AGN from other directions. Finally, if we could understand its message, polarization would also provide major insights regarding the nature of the AGN "Featureless Continuum" and Broad (emission) Line Region. I point out that high ionization ULIRGs have all the exact right properties to be called Quasar 2s. Mid-IR observations generally don't penetrate to the nucleus, greatly reducing their ability to diagnose the energy source. In particular, LINER ULIRGs aren't necessarily starburst-dominated, as has been claimed.

Astrophysical Spectropolarimetry: Polarization Insights for Active Galactic Nuclei

Original article can be found at: http://www.nature.com/nature/index.html Copyright Nature Publishing Group. DOI: 10.1038/310660a0 [Full text of this article is not available in the UHRA]

Infrared spectropolarimetry of Seyfert galaxy NGC1068

NGC1068 is one of the brightest galaxies included by Seyfert1 in his list of extragalactic objects having compact, luminous nuclei within which broad, high-excitation emission lines occur. It has been the subject of intensive studies at UV2,3, optical3–6, IR7–12 and radio wavelengths13–15. Unresolved questions concern the nature and relationship of the sources of the excess flux seen in the UV and IR, their connection with the collimated jets apparent in high-resolution radio maps and their association with the extended region responsible for the broad emission lines. A further question is the location of any dust and its role in modifying the optical and UV spectrum. We report here observations with two high-resolution optical spectro-polarimeters which throw new light on these questions. From detailed structure found in the linear polarization spectrum of the nucleus we conclude that dilution by starlight modifies the polarization to an extent not previously appreciated. In fact, the polarization of the non-stellar flux in the optical and near IR is approximately independent of wavelength (as expected for synchrotron emission or electron scattering) with a direction orthogonal to that of the radio jets; such an arrangement is reminiscent of certain quasars and radio galaxies16,17.

Is the polarization of NGC1068 evidence for a non-thermal source

Optical linear polarization of the Crab Nebula supernova remnant is presumed to be a good example of the astrophysical occurrence of synchrotron emission from relativistic electrons in a magnetic field1–3. However, there have been few attempts to map the spatial distribution of the polarization at the highest possible resolution and with high signal-to-noise ratio, although such observations contain information about the geometry and the small-scale structure of the magnetic field. We describe here observations of the Crab Nebula using a new charge coupled device (CCD) imaging/spectropolarimeter. Two large regions each 150 arc s across were observed with a seeing-limited spatial resolution of 1.5 arc s: the ‘eastern bay’ and the central wisps. The pulsar was included in both fields. In general, we find no evidence for substantial small-scale (1.5 arc s) structure in the projected magnetic field, but there are changes on scales of the order of 5 arc s which would be barely discernible by photographic methods. In addition, there is remarkable organization of the field over domains ranging in size from 10 to 30 arc s. The uncertainty about, the nebular polarization component near the pulsar is resolved. The presence or absence of small-scale structure in the field is important in understanding the energy transport mechanism for the relativistic electrons, and little is known about the connection between small polarization features and the remarkable filamentary structure in the nebula. Photographic maps2 had a resolution of only 5.25 arc s and rather limited polarimetric accuracy; more recent photoelectric measurements4 yielded 1 × 3 arc s resolution but only in a small patch. Instrumental technique is crucial.

C. Aspin

Papers

Is the polarization of NGC1068 evidence for a non-thermal source

High-resolution polarization images of Crab Nebula with a charge-coupled device camera