Resonant cyclotron scattering model

RCS is an X-ray spectral model for resonant cyclotron scattering in neutron star magnetospheres. It reproduces a scenario in which the cooling thermal radiation emerging from the neutron star surface experiences repeated resonant cyclotron scatterings onto hot electrons in the neutron star magnetosphere. The scattering efficiency is quantified by the resonant optical depth, tau_{res}, which is related to the electron density (assumed to be constant through the scattering slab).

The RCS model is based on a simplified, 1D semi-analytical treatment of resonant cyclotron up-scattering. Particles are non-relativistic and electron recoil is neglected. Magnetospheric charges are taken to have a top-hat velocity distribution centered at zero and extending up to beta_T (the thermal velocity of the magnetospheric electrons). Such a velocity distribution mimics a scenario in which the electron motion is thermal (in 1D because charges stick to the field lines; see Thompson, Lyutikov & Kulkarni (2002) and Lyutikov & Gavriil (2006) for details). In this respect, beta_T is associated to the mean particle energy and hence to the temperature of the 1D electron plasma. Since scatterings with the magnetospheric electrons occur in a shell of width H ~beta_T r/3, the scattering region is treated as a plane-parallel slab. Radiation transport is tackled by assuming that photons can only propagate along the slab normal, i.e. either towards or away from the star.

The XSPEC RCS table model has three parameters (plus the normalization factor):

  • T (0.1-1.3 keV): the blackbody temperature of the seed photons.
  • tau_{res} (1-10): the optical depth in the scattering slab.
  • beta_T (0.1-0.5): thermal velocity of the magnetospheric electrons (in units of c).

Use this table model to fit X-ray data in XSPEC as follows:
XSPEC>model phabs(atable{RCS.mod})

Warnings: as a table model, it is sometimes hard to drive the fit to a convergence, especially for data with a large number of counts. In these cases we suggest you to fix one parameter to a reasonable value, fit the rest, then thaw it and re-fit everything. Furthermore, take special care in calculating the uncertainties in the spectral parameters using 'unc' or 'err', in fact during this process a better chi-squared minimum might be found. Note that by definition beta_T and tau_{res} play a similar role in shaping the spectum, hence in some rare unlucky cases two chi2 minima might be found.

Please send your comments, suggestions, questions or any other feedback to Nanda Rea (nrea '@' If you publish results obtained using this RCS model please reference Rea, N., Zane, S., Turolla, R., Lyutikov, M. and Goetz, D. (2008, ApJ, 686, 1245).

The RCS table model file is available here as RCS.mod.

Keith Arnaud, Lab. for High Energy Astrophysics, NASA/Goddard Space Flight Center

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