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A Resonant cyclotron scattering model for the
X-ray emission of magnetars: spectra and
polarization properties.
S. Zane (MSSL, UCL, UK) , L. Nobili, R. Turolla (Univ of Padua, It)
on behalf of a larger collaboration
1) Introduction
Highly magnetized neutron stars (aka “magnetars”) recently
underwent a phase of renewed interest in high-energy astrophysics.
These extreme objects comprise the Anomalous X-ray Pulsars (AXPs)
and the Soft Gamma-ray Repeaters (SGRs), two classes of sources
observationally very similar in many respects (see Mereghetti et al.
2008 for a review).They are all slow X-ray pulsars with spin periods
clustered in a narrow range (P ~ 2-12 s), relatively large period
derivatives (dP/dt ~ 10-13 -10-10 s/s), spin-down ages of 103 -104 yr,
and magnetic fields, as inferred from the classical magnetic dipole
spin-down formula, of 1014 -1015 G, larger than the electron quantum
critical field (Bqed ~ 4.4x1013 G). AXPs and SGRs are strong persistent
X-ray emitters, with X-ray luminosities of about 1034 -1036 erg/s.
In the 0.1-10 keV energy band, magnetars spectra are relatively soft
and usually modelled by an absorbed blackbody (kT~ 0.2-0.6 keV) plus
a power-law (~ 2-4).Thanks to INTEGRAL and RXTE-HEXTE, hard
X-ray emission up to ~200 keV has been recently detected for some
sources. This discovery opened a new window in magnetars study,
making crucial to revise their classification as soft X-ray sources.
Through our knowledge of magnetars greatly increased in the last
few years, thanks to the large theoretical effort of several groups
around the world, a number of important issues still remain to be
clarified. In particular, the basic mechanism responsible for the
observed spectral shape in X-ray and gamma-ray is still only glimpsed.
Different spectral components have been identified through pulse
phase spectroscopy, but this was only possible for the brightest
sources.
Among the most interesting recent results is the discovery of
transient, "outbursting" behaviour from a few AXPs, 1E2259+586,
1E1048.1-5937, and XTE1810-19, that underwent an outburst with a
flux increase of a factor of 10-100. XTEJ1810-19, for instance, was
a former soft and dim (L~ 1033 erg/s) thermal emitting Einstein and
ROSAT source, which quiescent properties were not dissimilar from
those of hundreds uncatalogued ROSAT X-ray sources. This means
that AXPs can undergo several outbursts separated by only a few
years. Similarly, just a few weeks ago a former quiescent ROSAT
source suddenly emitted a series of short bursts (detected by
SWIFT) and has been recognized to be a new SGR, SGR0501+4516.
These findings imply that a relatively large number of members of
this class has not been discovered yet, and some sources which are
now quiescents may manifest themselves in future though a similar
phenomenology.
The AXPs outbursts has proven to be a unique laboratory to monitor
the timing and spectral properties of a cooling/decaying AXPs as a
function of flux (varied over two orders of magnitude; Gotthelf &
Halpern 2005, Israel et al. 2007). However, so far this has only been
possible at relatively bright flux levels. And, again, the proper
identification of the varying components in the spectrum requires a
detailed modelling of the atmosphere and magnetosphere of the star.
Only very recently detailed 3D numerical models of magnetospheric
emission have been developed by us and other groups (Fernandez &
Thompson 2007; Nobili, Turolla & Zane 2008a,b). In particular, our
magnetic Monte Carlo 3D radiative code is the only one available that
has been used for quantitative data fitting (being implemented in
XSPEC) and properly deals with relativistic quantum effects in the
scattering cross section. Our code accounts for resonant cyclotron
upscattering of soft thermal photons (emitted by the star surface),
by a population of relativistic electrons threated in the
magnetosphere. Polarization and QED effects are consistently
accounted for, as well different configurations for the
magnetosphere. Here we present a summary of its capabilities, in
connection with future IXO observations.
3) Spectra: a few examples
Ordinary seed photons


In order to model the surface emission, the star surface is divided
into patches by an angular grid. Each patch has its own temperature
and beaming prescription to reproduce different thermal maps
(tests shown here refer to blackbody, isotropic emission). We
assume that magnetospheric charges move along the field lines and
are characterized by a bulk velocity, bulk, and by a velocity
spread. The electron velocity distribution is then a 1D relativistic
Maxwellian at a temperature Te and centered at bulk (along the
field direction ) plus and a set of Landau levels in transverse
direction. In the XSPEC implementation, in order to minimize the
number of free parameters, Te has been related to bulk via equipartition. In all models e-/e+pairs are neglected.
We implemented in XSPEC two model tables. The first one is angleaveraged, and spectra depend on 4 parameters:
- kT: the BB temperature of the seed surface photons;
- bulk: the bulk velocity of the magnetospheric currents
- : the twist angle of the magnetosphere (zero for untwisted dipole)
- K: a normalization constant.
In the second model we introduced two additional parameters, i.e.
two viewing angles, , , which account for a disalignement
between magnetic field/spin axis with respect to the line of sight.
This second model is particularly useful when we need to
disentangle details in the light curve or in phase resolved spectra.
Just as an example, here we present a few spectral results.
Since we properly deal with polarized radiative transfer in the
magnetosphere, our code will provide not only models for
spectra and light curves, but also quantitative predictions for
the amount of X-ray polarization. Fig. 5 show the amount of
polarization expected as a function of some of the model
parameters. We found that, would the seed photons be
unpolarised, then the amount of polarization gained by
radiation as due to magnetospheric effects is of order of a
few tens of percents. If future X-ray polarimeters will
measure an excess over this value, this has to be attributed to
the radiation emerging from the crust/atmosphere (see Fig. 6)
Fig.1. Computed spectra for B= 1014 G and different values
of the colatitude : 27˚
(long dashed), 64˚ (dashed-dotted-dotted-dotted), 90˚ (dashed-dotted), 116˚
(short dashed) and 153˚ (dotted). The solid line is the seed blackbody, units are
arbitrary.
Note the lack symmetry between the two hemispheres: as  increases, spectra
become more and more comptonized. This reflects the preferential direction of the
currents flow, in this example assumed to be from north to south.
= 116˚
 bulk
Fig.5. Degree of polarization expected for
B= 1014 G and KT = 0.5 keV,
as a function of bulk and of the twist angle. The polarization fraction is
energy-integrated, and is integrated over all viewing angles at infinity.
Solid line: ordinary seed photons; dotted line: extraordinary seed
photons; dashed line: unpolarized seed photons.
Fig.2. Left: Computed spectra for B= 1014 G and bulk: 0.3,
0.5, 0.7, 0.9. The solid
line is the seed blackbody
Note the shift in the peak: if electrons are more relativistic Comptonization
starts to saturate, and photons fill the Wien peak of the Bose-Einstein
distribution  the spectrum is not peaked at ~kT, but at ~kTe.
Right: This means that for some parameters values we expect double hamped
spectra. The first peak is related to the neutron star surface temperature, while
the second peak, at higher energy, gives a direct information on the energy of the
magnetospheric electrons. This has never been measured so far, possibly due to the
scarcity of data taken simultaneously at soft/hard energies. Here B = 1014G,  =
0.2. Solid line: KT = 0.1 keV, bulk = 0.7; dashed line: KT = 0.6 keV, bulk = 0.6
Fig.6. Amount of polarization expected
Testing QED. Two spectra computed for the same set of parameters, but with
(right) and without (left) QED effects and electron recoils accounted for in the
scattering cross section (the seed BB is shown for comparison).
When QED and relativistic effects are accounted for, the spectrum exhibits a typical
break. The break energy moves down (eventually entering the soft X-ray range) as
electrons become more and more relativistic.
We follow the idea, proposed by Thompson, Lyutikov and Kulkarni
(2002), that most of the magnetars phenomenology can be
explained by the onset of a long-lasting magnetospheric twist.
Basically, in magnetars the strong toroidal component of the
internal magnetic field stresses the star crust inducing a
deformation of the surface layers and twisting up the external
field. Twisted magnetospheres are permeated by selfinduced electric fields that in turn can lift particles from the
stellar surface, maintain currents and eventually initiate avalanches
of pair cascades. The charge carriers can provide a large optical
depth to resonant (cyclotron) scattering and hence reprocess the
thermal photons originating from the star surface, giving rise to
the typical observed blackbody plus power law spectral shape. In
order to test quantitatively this model against X-ray data, we
developed a self-consistent physical model of resonant cyclotron
scattering, by performing detailed Monte Carlo simulations. We
refer for all details to Nobili, Turolla & Zane 2008a,b.
with Polaroid glasses
Extraordinary seed photons
Fig.3.
2) Monte Carlo Code
5) Looking at magnetars
4) Application to XMM data
1E 1547-5408
from a thin atmospheric layer in
radiative equilibrium, computed using the atmospheric models in Zane at
al, 2000. Different curves are for different values of magnetic field and
effective temperature.
The fraction of polarization strongly depends on the energy band and
shows a variety of different behaviors. Its sign is determined by the
competition between plasma and vacuum properties in the photospheric
layers. However, independently of the model parameters, the degree
of polarization crosses zero at the very vicinity of the proton
cyclotron energy, where the mode absorption coefficients of the two
modes (O-X) cross each other. This means that measures of
polarization can correctly identify a proton cyclotron line (against an
electron cyclotron one), ultimately providing a powerful tool for
determining the magnetic field of the source, even in the absence of
pulsations.
6) Summary
Significant progresses have been obtained in Neutron Star
physics by current observatories (such as XMM, Chandra,
Rossi-XTE, Swift, Integral) and even much stronger
constraints are expected to come from next generation
detectors with larger collective area, as IXO.
The unprecedented capabilities of IXO will allow for the first
time to test detailed and self consistent models of atmospheric
and magnetospheric emission against data even at low flux
levels, ultimately disentangling the spectral components which
are at present beyond reach with XMM-Newton or Chandra.
The large collective area of IXO will allow for the first time:
CXOU J1647-4552
- to follow the evolution of transient outbursts up to the
faintest levels, and to perform complete observation of the
post burst cooling history. This is fundamental for probing the
neutron star interior through the way in which the heat is
deposited and released in the star crust and envelope.
- to perform phase-resolved spectroscopy of the faintest
sources, mapping with unprecedented detail the different
regions of the surface and magnetosphere of the neutron star.
Figs 4: Fits of the XMMNewton EPIC-pn spectra of
three different AXPs, taken
ad different epochs
(courtesy of G.L. Israel and
N. Rea).
The model has been already
preliminary applied to XMMNewton data, allowing to
probe the properties of the
magnetospheric currents.
The typical charge densities
is found to be ~103 times
larger than the stanrdard
Goldreich-Julian value. This is
a strong probe for the
presence of magnetic field
configurations much more
complex than simple dipolar
ones.
We believe the development of detailed theoretical models, as
the one presented here, is therefore timely and fundamental.
Polarization studies have already started at low energies (IR),
and future X-ray polarimeters as those on board IXO will
extend them over a broader spectral band. Polarimetry will add
a new and unique dimension to the problem, through the
knowledge of polarization degree and swing angle. This,
together with phase-resolved spectroscopy, will enable us:
- to obtain a direct mapping of the emission regions in the
magnetosphere and investigate QED effects in spectral
formation and polarization pattern;
1E 1048-5937
- to disentangle the amount of polarization emerging from
different regions (crust, atmosphere, magnetosphere)
of/around the neutron star;
- to determine the magnetic field of the source, even in
absence of pulsations.