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Asaf Pe'er

## Theory of photospheric emission from relativistically expansing plasmas

Motivated by the need to explain the observed prompt spectra of gamma-ray bursts (GRBs), I study photospheric emission from relativistically expansing plasmas. While naively one may expect a "Planck" function to emerge, due to relativistic abberation of light, the observed spectrum is in fact very different. This is in fact the relativistic version of the "limb darkening" effect known from observing the sun.

By definition, the photosphere is the inner most region from which an electromagnetic signal can reach the observer. In the inner parts of the outflow - of many astronomical objects, not necessarily GRBs (e.g., AGNs or XRBs), the density is so high that the optical depth exceeds unity; photons are trapped. As the outflow expands, the density decreases, and photons can eventually escape. In 3-dimensional (e.g., spherical) expansion, the optical depth is a strong function of the angle to the line of sight. I showed in my 2008 paper that in fact, for angles θ > 1/Γ, the photospheric radius is r_{ph} ∝ θ^2.

However, this is only part of the story; the photospheric radius is, by definition, the surface in space which fullfills the following condition: the optical depth for a photon that is emitted (or last scattered) from a point on this surface to reach the observer, equals exactly 1. However, photons have finite probability of being emitted (or scattered) in every point in space which is not empty. Thus, the definition of the photosphere as the place where photons last scatter, leads to the concept of "vague photosphere" (in the figure to the left, every point in r-θ plane represent the last scattering location of a photon emerging from spherical, relativistically expanding plasma jet).

This concept of vague photosphere implies that the observed spectra is very different than the naively expected "Planck" spectrum, due to 2 effects: (1) Different photons arrive from differnt angles, hence are observed with different Doppler boosts; and (2) Photons decouple the plasma at a range of radii, hene they suffer diferent adiabatic losses before escaping. Over all, these two effects leads to a significant modification of the "Planck" spectra (see figure to the right), which is the relativistic version of the "limb darkening" effect.

##### Selected Publications

Pe'er, A. (2008), "Temporal Evolution of Thermal Emission from Relativistically Expanding Plasma" Ap.J., 682, 463
Pe'er, A., & Ryde, F. (2011), "A Theory of Multicolor Blackbody Emission from Relativistically Expanding Plasmas" Ap.J., 732, 49