Proton Cyclotron Lines in
Thermal Magnetar Spectra
S. Zane, R. Turolla, L. Stella and A. Treves
Mullard Space Science Laboratory UCL , University of Padova,
Roma Observatory, University of Milano
Broadening Effects
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.
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 ultramagnetized 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.
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.
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.
Spectral Models
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..
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.
Table 1. Model Parameters
Model
B
1013 G
L
10 34 erg/s
E c,p
keV
EW
keV
E/E
A1
1
2
0.06
0.01
0.67
A2
1
70
0.06
0.01
0.47
A3
5
9
0.32
0.05
0.31
A4
10
3
0.63
A5
50
1.7
3.15
0.10
0.10
A6
100
1.8
6.3
0.11
0.06
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 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-field
in a magnetar.
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.
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).
Table 2. Line Broadening
Bp
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
10 13 G
Note: D = dipolar field; ||= constant B field. E c is the line centroid;
energies have not been corrected for gravitational redshift.
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.