Proton Cyclotron Lines inThermal Magnetar SpectraS. Zane, R. Turolla, L. Stella and A. TrevesMullard Space Science Laboratory UCL , University of Padova, Roma Observatory, University of Milano

In the last few years increasing observational evidence gathered in favour of the existence of ultra-magnetized neutron stars (NSs), with surface field >1014 G. Magnetars were first hypothesized by Thompson and Duncan (1993), who realized that strong convective motions during the core collapse can strongly amplify the seed magnetic field.

In magnetars magneto-dipolar radiation will cause rapid spin-down at a rate ~ 10-11(B/1014 G)2/P ss-1, and it has been the detection of a secular spin down of the same order in two Soft -repeaters (SGRs) that for the first time suggested the association of these sources with ultra-magnetized NSs.

Besides their bursting activity, SGRs show also persistent X-ray emission with L~1034-1036 erg/s and the possible presence of a thermal component at KT~0.5 keV. In the magnetar model, this is believed to originate from the star surface which is kept hot by the dissipation of the B-field.

Magnetars have been also invoked to explain another enigmatic class of galactic high energy sources, the Anomalous X-ray pulsars (AXPs). AXPs have periods in a very narrow range (P~6-12 s) luminosities similar to SGRs and show no evidence of a massive binary companion. They show a stable spin period evolution with a long term spin down trend.The emission of AXPs has a thermal component at ~0.5 keV and, like SGRs, some of them are associated with a supernova remnant.

The many similarities between AXPs and SGRs strengthen the idea that the two classes of sources are powered by the same mechanism, dissipation of a super-strong B-fieldin a magnetar.

Artist impression of a magnetar

Chandra and XMM-Newton can already provide the required energy resolution to allow for a detailed comparison with theoretical models and to probe the existence of such huge fields. Detailed radiative transfer calculations are therefore needed.

Following Zane, Turolla and Treves (2000), we modelled thermal emission from the NS surface, exploring the ranges 1013G<B<1015G and 1034 erg/s<L<1036 erg/s, believed to be typical of magnetars in quiescent SGRs and AXPs. The NS atmosphere has been treated assuming plane-parallel symmetry and a constant field parallel to the vertical axis. Emerging spectra are shown below. They are nearly planckian in shape and show a small hardening with respect to the blackbody at star effective temperature..

Table 1. Model Parameters

Note that the value of the line energy is not corrected for the gravitational redshift. The value observed at Earth is a factor yg ~0.8 lower.

The position of two SGRs. Data from Cosmic Background Explorer.

The most prominent spectral signature is the absorption feature at the proton cyclotron resonance, Ecp ~ yG0.63(B/1014 G), which falls in the soft-medium X-rays for such high fields (yG ~ 0.8

accounts for gravitational redshift). The line equivalent width, EW, and the inverse of the required resolving power for detection, E/E, are reported in table 1.

0.060.116.31.8100A6

0.100.103.151.750A5

0.63310A4

0.310.050.3295A3

0.470.010.06701A2

0.670.010.0621A1

E/EEW

keV

E c,p

keV

L

10 34 erg/s

B

1013 G

Model

Two main effects contribute to this feature: the intrinsic resonance in the magnetic absorption coefficients that essentially gives Fraunhofer absorption lines and the mode crossing at the mode collapse point, the latter being amplified when collapse points introduced by vacuum effects fall near the line energy and in the photosferic region (as in model A4).

The assumption of constant B is reasonable for polar cap emission, but breaks down if radiation comes from the entire NS surface. For a dipolar field, the change of B in both magnitude and direction produces a broadening of the cyclotron lines. Moreover, in magnetized NSs a meridional temperature variation is expected.

We have estimated the broadening due to both these effect within a simple, approximated model in diffusion approximation. Results are reported in the table and in the figure below.

B p

10 13 G

L

10 34 erg/s

EWD

keV

EWD /EW|| Ec,D

keV

E cD /Ec, ||

1 0.1 0.035 1.17 0.046 0.73

1 1 0.035 1.20 0.046 0.73

1 10 0.035 1.22 0.047 0.75

10 0.1 0.35 1.14 0.49 0.78

10 1 0.35 1.12 0.47 0.75

10 10 0.34 1.08 0.46 0.73

Note: D = dipolar field; ||= constant B field. E c is the line centroid; energies have not been corrected for gravitational redshift.

Table 2. Line Broadening

As expected, the proton cyclotron line turns out to be broader when emission comes from the entire star surface, typically by 10-20%. Also, the change of the field strength produces a shift of the line centroid toward lower energies of 20-30%.Both these effects are quite independent on the values of B and L.

Our calculations confirm the existence of a strong absorption feature at the proton cyclotron energy in the thermal spectrum of magnetars, as first suggested by Thompson (2000).

The line equivalent width is 0.1 keV and, for B~1014-1015 G, the line centre is located at ~ 0.5-5 keV. The detection of the main cyclotron line is well within the range of both Chandra and XMM-Newton grating spectrometers. Its actual observation in the soft X-ray spectra of AXPs and SGRs may therefore not only give a definite confirmation of their magnetar nature, but also an independent measure of the magnetic field.

HETGS+ACIS-S observations of SGR 1900+14 and AXP 1E1048-59 have already been scheduled.

Spectral Models

Broadening Effects