Physics of light propagation through pulsar magnetospheres:

Abstract:

The highest known magnetic fields found in pulsars are enough to change the vacuum index of refraction in the region surrounding the stars. Since the effect depends on the polarization of the light rays, it predicts more sophisticated effects than for example what gravitational lensing does. Not only will the apparent surface area grow, the effect will be polarization dependant and therefore have a clear fingerprint that will allow the direct measurement of a pulsar's magnetic field (and not an inferred one, as is normally the case). In less impressive magnetic field strengths, that are found in more common neutron stars, more subtle effects arise when taking into consideration the rotation of the magnetosphere. Through predicted polarization phase lags, the magnetospheres can in principle be “mapped”.
 

Summary of Achievements and Discoveries:
 

1. The vacuum birefringence effect around magnetars was found to be large enough to produce significantly different images of the magnetar in two different polarizations. Each one of the images will appear to originate from an object with a different effective surface area.
2. The measurement of the polarization light curve of these objects at X-ray frequencies will allow the direct observation of the different multipole components of their magnetic fields.
3. At lower field strengths found in more common pulsars (such as the Crab) the combined effect of a rotating magnetosphere and the vacuum birefringence will produce polarization angle phase lags between different frequency bands. The measurement of this effect will allow the reconstruction of the pulsar magnetic structure.

Plans for the Near Future:

1. Using the description devised to describe the evolution of the polarization of light rays propagating around pulsars, we plan to describe the effects that plasma birefringence has. In addition to describing of the polarization effects more accurately than before, we can predict effects that appear only after previously made simplifying assumptions are alleviated. For example, we explain the observed circular polarization seen in radio pulsars.
2. Using the polarization evolution description, we wish to understand the evolution of light-rays through turbulent magnetospheres.

Collaborators:

Jeremy Heyl and Yoram Lithwick (at Caltech) on the lensing effects around highly magnetized neutron stars. Jeremy Heyl on the polarization propagation effects through a rotating magnetosphere, and recently, in collaboration with Hari Kunduri who was a summer research stundent at CITA.
 

References:

1. Nir J. Shaviv, Jeremy S. Heyl & Yoram Lithwick, "Magnetic Lensing near UltramagnetizedNeutron Stars", Mon. Not. of the Roy. Astr. Soc., 306, 333, 1999.
2. Jeremy S. Heyl & Nir J. Shaviv, "Polarization Evolution in Strong Magnetic Fields", Mon. Not. of the Roy. Ast. Soc., 311, 555, 2000

Sample Figures:

The Ray Tracing Algorithm used to image the neutron star. Rays are followed from the screen to the star (and not vice versa) using a Hamiltonian formalism for their propagation:

The ray tracing ? forming an image of a lensed object

The next image is a sample result - this is how a neutron star with a very strong magnetic field looks like(when observed at an inclination of 45^o). For the largest dipole fields known (of about 10¹⁵G), the effect is of order 5%.

The image of a lensed magnetar in one polarization

Movies showing Lensed Magnetars can be found here.

The polarization angle phase lag between different wavebands for the Crab pulsar: Plotted in the last figure is the polarization angle phase lag as a function of the waveband frequency and the time within the rotation period, assuming a Deutsch magnetic field configuration for the magnetosphere. By simultaneously measuring the polarization angle of the observed photons at different wavebands and different rotational phases of the neutron star, the structure of the magnetosphere can be mapped. Good UV and X-ray polarization measurements are required.

The phase lag/lead between frequencies as a function of rotation phase for the Crab pulsar

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