Evidence of a possible second cyclotron line in
the X-ray spectrum of 4U 1538-52
J. J. Rodes, J. M. Torrejón and G. Bernabéu
Dept. Fı́sica, Enginyeria de Sistemes i Teoria del Senyal,
Escola Politècnica Superior d’Alacant, Universitat d’Alacant,
Apartat de correus 99, E03080 Alacant, Spain
rodes@dfists.ua.es
Summary. We have studied pulse phase-averaged X-ray spectra of the high mass
X-ray binary 4U 1538-52 using the Rossi X-ray Timing Explorer (RXTE). There are
about a dozen X-ray pulsars for which cyclotron lines have been detected. In this
work we discuss some evidence of a possible cyclotron resonant scattering feature
(CRSF) observed in various spectra of 4U 1538-52/QV Nor. This feature is still a
matter of discussion since it was not detected in RXTE data before [5] or not clearly
present in the spectrum in BeppoSAX data [12]. However, we provide evidence that
an absorption spectral line is present at ∼50 keV which can be interpreted as a
cyclotron line. We found a significant CRSF in some spectra of different epochs
and orbital phases. If correct, this system would be amongst the handful of sources
displaying multiple harmonics in the cyclotron lines.
1 Introduction
The source 4U 1538-52 is an accreting binary X-ray pulsar which exhibits Xray pulsations as well as X-ray eclipses. This high mass X-ray binary (HMXB)
system is formed by a compact object (neutron star) and an optical companion
B0 I supergiant star (QV Nor). Uhuru was the first satellite X-ray observatory
that detected this system [7]. The neutron star has a spin period ∼ 529 s [6]
and [1]. The orbital period is ∼ 3.728 days [4] and, assuming a distance of 5.5
kpc, the X-ray luminosity is ∼ 4 × 1036 erg/s [1] and [11].
The magnetic field plays an important role in the X-ray binary systems.
The only direct evidence for neutron star magnetic field strengths is provided
by X-ray cyclotron absorption lines. Although these quasi-harmonic lines appear in absorption, they are not absorption lines in the true sense. Cyclotron
lines are spectral features due to inelastic scattering off electrons which are
quantized in the strong magnetic fields of neutron stars. In this sense, these
lines are known as Cyclotron Resonance Scattering Features (CRSFs).
Classically, electrons moving in a uniform magnetic field are free to move
along the field lines, while the motion transverse to the field is constrained
2
J. J. Rodes, J. M. Torrejón and G. Bernabéu
to circular motion. The net result is a helical motion, with the radius of the
circular component (the gyration radius) given by:
cp⊥
,
(1)
eB
where p⊥ is the electron momentum perpendicular to the field and B the
magnetic field strength. The radius rgy decreases with increasing B, until
eventually it is of order the de Broglie wavelength (λ = h̄/p) of the electron
and quantum mechanical effects dominate. Once this is the case, the transverse
motion of the electron is quantized into Landau levels. In the non relativistic
limit the nth Landau level is given by:
rgy =
1
+ s)Ec , n0 = 0, 1, 2, . . . ,
(2)
2
where s = ±1/2 is the electron spin and Ec the cyclotron energy. The non
relativistic cyclotron resonance energy, in terms of the magnetic field B and
for n’ = 0 and s = -1/2 is:
En = (n0 +
Ec =
h̄e
B.
me c
(3)
Or equivalently, scaled by a 1012 G field and given in units of keV, can be
written as:
B
keV .
(4)
1012G
As the (n’+1/2+s) term will always result in an integer, the harmonically
spaced Landau levels are given by:
Ec ' 11.6
En = nEc , n = 0, 1, 2, . . .
(5)
The scattering process proceeds when a resonant photon is absorbed by
an electron in the n = 0 ground state which is then excited to a n ≥ 1 Landau
level (depending on whether the photon is at a single or higher multiple of
the cyclotron energy). In plasmas that are cool compared to the cyclotron
energy, the lifetime of electrons above the n = 0 ground state is very short
(and returns to the ground state by emitting a resonant photon).
For higher harmonics (n > 1) the decay process is sligthly more complex.
While the electron still may decay directly back down the ground state, it
can also cascade down through the Landau levels, producing n photons each
with energy Ec keV (known as photon spawning). Due to the prompt decay
from all Landau levels, most of the electrons in the scattering region are in
the n = 0 ground state with aligned spin (s = -1/2).
As the radius of the neutron star is only a few Schwartzschild radii, general
relativistic effects are also important in the emission region. In particular, the
CRSF will be redshifted by the neutron star gravitational field such that the
Evidence of a possible CRSF in 4U 1538-52
3
observed energy, as indicated by a scattering feature in an X-ray spectrum, is
less than the true energy. The correction term is given by:
B
(1 + z)−1 keV ,
1012G
where, z is the gravitational redshift and
Ecobs ' 11.6
(6)
1
2GMns 2
(1 + z) = 1 −
.
(7)
Rns c2
When magnetic field is sufficiently strong, relativistic effects become important. In these cases the cyclotron energies are given by [9]:
−1
(1 + 2nB 0 sin2 θ)1/2 − 1
,
(8)
sin2 θ
where θ is the angle of the incident photon relative to the magnetic field, n is
the harmonic number and
Ec = me c2
Bh̄e
,
(9)
m2e c3
is the magnetic field scale to the quantum electrodynamic field scale. This
means that the observed features will depend strongly on the spatial distribution of electrons in the scattering region.
In this work we summarize spectral fits to forty-two observations of this
source taken by RXTE archival data. The fundamental CRSF at ∼20 keV was
first reported from observations with Ginga satellite [3] and at ∼21 keV from
BeppoSAX observations [12]. However, they do not find evidence of a second
harmonic at ∼40 keV, although an absorption feature could be present at a
higher energy. We show evidence of a new cyclotron line (second harmonic)
in this source.
B0 =
2 Observations and data analysis
Three different run observations of 4U 1538-52 were performed with the Proportional Counter Array (PCA) and the High Energy X-ray Timing Experiment (HEXTE) detectors on RXTE (for details of the instrumentation see
[2], [8] or [13]). Two of them were made over one complete orbital period,
in 1997 during January (MJD 50449.94–MJD 50453.69) and in 2001 during
January (MJD 51924.60–MJD 51928.60). The third one was carried out from
1996 November 24 to 1997 December 13 taking a monthly observation.
We accumulated and analysed the data using the standard NASA released
HEASoft package of tools released by the High Energy Astrophysics Science
Archive Research Center (HEASARC). The HEASoft consists of two packages,
the FTOOLS data accumulation software and the XANADU spectral, timing
and image analysis software. For spectral analysis we used the XSPEC fitting
package, released as a part of XANADU in the HEASoft tools.
4
J. J. Rodes, J. M. Torrejón and G. Bernabéu
Fig. 1. Spectrum of 4U 1538-52 and model with only one CRSF (upper panel) and
residuals, in units of σ, with respect to the model (lower panel)
Fig. 2. Spectrum of 4U 1538-52 and model with two CRSFs (upper panel) and
residuals, in units of σ, with respect to the model (lower panel)
Evidence of a possible CRSF in 4U 1538-52
5
2.1 Spectral model
The pulse phase averaged spectra of 4U 1538-52 can be described by power
law including an exponential cutoff, which is a feature common to most X-ray
pulsars. Furthermore, the spectra in the low energy range are usually subjected
to photoelectric absorption, which is attributed to interstellar matter and, for
some cases, to circumstellar matter.
The spectra is also modified by an iron fluorescence line at ∼ 6.4 keV and
a CRSF at ∼ 20 keV discovered by Ginga [3]. Therefore, we fitted the spectra
with the components as follows:
•
•
•
•
•
a photoelectric absorption at low energies,
a power law with a high energy exponential cutoff (the custom XSPEC
model cutoffpl ),
a broad Gaussian continuum component centered at ∼12 keV,
an iron emission line at ∼6.4 keV of Gaussian shape,
one or two absorption cyclotron lines centered at ∼20 keV and ∼50 keV,
respectively.
This composite model describes all RXTE spectra in the energy range
3–100 keV properly.
2.2 Evidence for a new cyclotron line
We have fitted this previous model to the spectra and then we compared with
the F-test the significance of the second harmonic, see Sect. 2.1. In the 1997
−7
data, we found a significant absorption feature at 52+9
−3 keV (F-test: 8.8·10
+6
and orbital phase 0.34). Other results, but with lower significance, were 50−3
−2
keV (F-test: 1.4·10−2 and orbital phase 0.07), 45+13
and
−5 keV (F-test: 1.6·10
+14
−2
orbital phase 0.23) or 47−3 keV (F-test: 1.1·10 and orbital phase 0.70). The
depths are not well constrained and errors are overestimated.
For the 2001 data, we also found a couple spectra where significance of the
absorption feature is important. In this case, the energy is 49.0+4
−1.6 keV (Ftest: 4.4·10−3 and orbital phase 0.53) and its depth is 1.3+1.0
.
Another
result
−0.4
−5
obtained is 48+10
keV
(F-test:
7.7·10
and
orbital
phase
0.66)
and
its
depth
−3
is 2+5
−1 . As we can see in Fig. 1, some residuals are visible at high energies,
but when we add the second CRSF at ∼50 keV fit is improve as it is show
in Fig. 2. However, the rest of the spectra shows a low significance (F-test:
> 8 · 10−2 ) or does not improve the fit significantly.
Finally, we found that there is also a low significant (F-test: 4.5·10−2 and
orbital phase 0.13) absorption feature at 48+9
−4 keV and its depth is not well
constrained.
We also tried to confirm the presence of this CRSF using the archival
data from INTEGRAL observations of this system. Unfortunately, the level of
counts above 50 keV in the spectra was very low and we could not confirm this
6
J. J. Rodes, J. M. Torrejón and G. Bernabéu
absorption line. Nevertheless, the fall of counts at the energy of the putative
second harmonic, is still consistent with our RXTE results.
3 Discussion and conclusions
The broadband energy spectra (3-100 keV) is well fitted by an absorbed power
law with high energy exponential cutoff and a Gaussian shape at 12 keV, an
iron emission line and one/two cyclotron lines. This model describe all the
RXTE data used in this work properly. Although the choice of the continuum
model spectrum affects the results significantly, our conclusions agree with
similar studies of this source or other X-ray binary pulsars.
As Sect. 2.2 shows, we could achieve a convincing fit to the phase averaged
spectra by including a cyclotron line at ∼50 keV into the model (see Figs. 1
and 2, respectively). According to the F-test this feature is significant for
some observations at different orbital phases. The detection of the line is only
visible in few spectra. However, we think that this absorption feature could
be interpreted as the second harmonic of the 20 keV fundamental CRSF.
Cyclotron lines are due to the resonant scattering of photons by electrons
whose energies are quantized into Landau levels by the magnetic field [10]. The
quantized energy levels of electrons are to first order harmonically spaced, so
the second harmonic line seems not be coupled by a factor 2 in centroid energy, but by a factor ∼2.5 instead. A possibility to explain this difference is
taking into account the optical depths of the fundamental and second harmonic could form at different heights, where the dipolar magnetic field of the
neutron star has different intensities. Another possibility is taking account of
a displacement of the magnetic dipole momentum that could be explain the
different of energy of the two lines produced at the two magnetic poles of the
neutron star. According to this, it is expected to find a phase dependence of
the strength of these two lines. However, the low statistics at higher energies
prevents any analysis about this question.
First of all, we found this feature at different epochs (in the 1997 an 2001
orbital data and in the annual run 1996-97 data). Secondly, every significant
spectrum belong to different orbital phases. Finally, BeppoSAX data also
found an absorption feature in this source at ∼51 keV. INTEGRAL shows a
fall of counts beyond 50 keV, therefore, our conclusion is that this feature is
present but we need new observations to confirm it, due to, so far, limited fit
statistics at higher energies.
Acknowledgements. Part of this work was supported by the Spanish INTEGRAL: Observaciones multifrecuencia de sistemas binarios de rayos X
project number ESP2001-4541-PE and International Gamma Ray Astrophysics Lab. Operaciones. C3 project number ESP2002-04124-C03-03. This
research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the
NASA/Goddard Space Flight Center.
Evidence of a possible CRSF in 4U 1538-52
7
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