We present a study of RXTE and INTEGRAL spectra of the transient 3.6 s X-ray pulsar 4U 0115+634 taken during a giant outburst in 2008 March/April. The spectra can be almost equally well modeled by two different semi-empirical continuum models, modified by an Fe Kα fluorescence line, interstellar absorption, and cyclotron resonance scattering features (CRSFs) located at ∼10.7, 21.8, 35.5, 46.7, and 59.7 keV. One of these two models, the so called NPEX

model, leads to an anticorrelation between the centroid energy of the fundamental CRSF E_0 and the X-ray flux F_X, in agreement with previous works. The other model, consisting of a simple exponentially cutoff power law modified by a Gaussian emission feature around 10 keV, however, leads to a constant value for E_0 for the observed fluxes and a comparatively narrow line shape. We show that the cyclotron line model component resulting from the NPEX fits rather contribute to the broadband continuum model. We conclude that the previously reported anticorrelation is probably due to an artifact of the particular modeling of the continuum

Becker, P. A.

Caballero, I.

Ferrigno, C.

Fürst, F.

Grinberg, V.

Hemphill, P.

Hertel, D.

Klochkov, D.

Kreykenbohm, I.

Kühnel, M.

Martínez-Núñez, S.

Müller, S.

Obst, M.

Pottschmidt, K.

Rothschild, R. E.

Schwarm, F. W.

Schönherr, G.

Staubert, R.

Torrejón, J. M.

Wilms, J.

Wolff, M. T.

Caltech Authors - Main

P
o
S(INTEGRAL 2012)020
A constant Cyclotron Line Energy in 4U 0115+634
S. Müller∗a, C. Ferrignob, M. Kühnela, G. Schönherrc, P. A. Beckerd , M. T. Wolffe,
D. Hertela, F.-W. Schwarma, V. Grinberga, M. Obsta, I. Caballero f , K. Pottschmidtg,
F. Fürsth, I. Kreykenbohma, R. E. Rothschildi, P. Hemphilli, S. Martínez Núñez j,
J. M. Torrejón j, D. Klochkovk, R. Staubertk and J. Wilmsa
aDr. Karl Remeis-Observatory & ECAP, Universität Erlangen-Nürnberg, Bamberg, Germany
bISDC Data Center for Astrophysics, University of Geneva, Versoix, Switzerland
cLeibniz-Institut für Astrophysik Potsdam, Potsdam, Germany
dSchool of Physics, Astronomy, and Computational Sciences, MS 5C3, George Mason University,
Fairfax, VA 22030, USA
eSpace Science Division, Naval Research Laboratory, S.W., Washington, DC 20375, USA
f CEA Saclay, DSM/IRFU/SAp-UMR AIM (7158) CNRS/CEA/Université Paris 7, Diderot, Gif sur
Yvette, France
gCRESST and NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA, and Center for
Space Science and Technology, UMBC, Baltimore, MD 21250, USA
hSpace Radiation Laboratory, 290-17 Cahill, Caltech, Pasadena, CA 91125, USA
iCenter for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, CA
92093, USA
jInstituto Universitario de Física Aplicada a las Ciencias y las Tecnologías, University of
Alicante, Alicante, Spain
k Institut für Astronomie und Astrophysik, Universität Tübingen, Tübingen, Germany
E-mail: Sebastian.Mueller@sternwarte.uni-erlangen.de
We present a study of RXTE and INTEGRAL spectra of the transient 3.6 s X-ray pulsar
4U 0115+634 taken during a giant outburst in 2008 March/April. The spectra can be almost
equally well modeled by two different semi-empirical continuum models, modified by an Fe Kα
fluorescence line, interstellar absorption, and cyclotron resonance scattering features (CRSFs) lo-
cated at ∼10.7, 21.8, 35.5, 46.7, and 59.7 keV. One of these two models, the so called NPEX
model, leads to an anticorrelation between the centroid energy of the fundamental CRSF E0 and
the X-ray flux FX, in agreement with previous works. The other model, consisting of a simple
exponentially cutoff power law modified by a Gaussian emission feature around 10 keV, however,
leads to a constant value for E0 for the observed fluxes and a comparatively narrow line shape.
We show that the cyclotron line model component resulting from the NPEX fits rather contribute
to the broadband continuum model. We conclude that the previously reported anticorrelation is
probably due to an artifact of the particular modeling of the continuum.
"An INTEGRAL view of the high-energy sky (the first 10 years)" 9th INTEGRAL Workshop and celebration
of the 10th anniversary of the launch,
October 15-19, 2012
Bibliotheque Nationale de France, Paris, France
∗Speaker.
c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/
P
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S(INTEGRAL 2012)020
A constant Cyclotron Line Energy in 4U 0115+634 S. Müller
1. Introduction
4U 0115+634 is an accreting high mass X-ray binary with a pulse period of ∼3.6 s [3]. This
system consists of a neutron star which accretes matter from the O9e-type optical companion star
V635 Cas [19], resulting in violent transient X-ray outbursts of this source. Owing to the high
magnetic field strength on the surface of neutron stars, the electrons’ motion perpendicular to the
magnetic field lines is quantized into discrete Landau levels. The respective energies of the possibly
resulting cyclotron resonance scattering features (CRSFs or cyclotron lines) in the X-ray spectra
can be approximated by the 12-B-12-rule
Ecyc =
11.6B
1+ z
, (1.1)
where Ecyc denotes the centroid energy of the fundamental CRSF in units of keV, B the magnetic
field strength in units of 1012 G, and z the gravitational red shift. The centroid energies of the
higher harmonics are given to first order by multiples of the fundamental line energy. Since the
magnetic field of a neutron star can be approximated by a dipole, and Ecyc depends on the magnetic
field strength, this energy is also a function of the height of the cyclotron line. Some X-ray binary
pulsars with cyclotron lines show variability in the centroid cyclotron line energy. However, these
changes of Ecyc are not uniform. There are sources showing a positive correlation between Ecyc and
the X-ray flux FX (e.g., Her X-1 [17]), and there are systems showing an anticorrelations between
these two parameters (e.g., V 0332+53 [14]). As a third type of cyclotron sources, there are sys-
tems with a constant CRSF energy for all observed fluxes (e.g., MXB 0656–072 [9]). Theoretical
models explain these different types of variabilities with different deceleration mechanisms for the
accreted material in the accretion column [1, 7, 17]. Below a certain critical luminosity Lcrit, the
braking is dominated by gas pressure leading to a positive correlation between Ecyc and FX. For
luminosities above Lcrit, the deceleration is mainly dominated by radiation pressure, resulting in
an anticorrelation between these parameters. At intermediate luminosities, the deceleration of the
accreted material is dominated by Coulomb interactions leading to a quite stable Ecyc.
With five cyclotron lines, 4U 0115+634 is the source with the highest number of detected
CRSFs [6]. Therefore, until today, the X-ray spectra of this source have been studied in great
detail, e.g., [5, 13, 18], and references therein. Many authors found an anticorrelation between the
fundamental cyclotron line energy E0 and the X-ray flux FX [11, 13, 18]. This result indicates that
4U 0115+634 is located in the supercritical luminosity regime.
In this work we revisit the behavior of the cyclotron lines in 4U 0115+634, focussing on a
giant outburst in 2008 March/April. As displayed in Fig. 1, this outburst lasted about 40 days and
exceeded a flux of 200 mCrab in the RXTE/ASM band (2–12 keV). During this period, the source
has been monitored regularly by RXTE and INTEGRAL.
For a description of the extraction process, an observation log, and a more detailed report of
the analysis, see [12].
2. Spectral Analysis
A problem when analyzing X-ray spectra from accreting X-ray pulsars is the description of
the broadband continuum. Mostly, semi-physical models consisting of some variant of a power law
2
P
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A constant Cyclotron Line Energy in 4U 0115+634 S. Müller
RXTE
INTEGRAL
545805456054540
25
20
15
10
5
0
April 2008March 2008
300
250
200
150
100
50
0
52 101
15
14
13
12
11
10
MJD
R
X
T
E
A
S
M
c
o
u
n
t
ra
te
[c
ts
s−
1
]
ra
te
[m
C
ra
b
]
(2
–
1
2
k
e
V
)
L3−50 keVX [10
37 erg s−1]
E
0
[k
e
V
]
Figure 1: Left: RXTE/ASM light curve of the 2008 outburst of 4U 0115+634 in the 2–12 keV energy band.
The arrows indicate the RXTE and INTEGRAL observations. Right: Fundamental cyclotron line energy
versus the 3–50 keV X-ray flux. Cyan diamonds indicate the results when using the NPEX model. The color
change from reddish to dark bluish data points indicates the temporal evolution of the results when using the
CutoffPL continuum.
with a high energy exponential cutoff are used to describe the spectra [8]. The most simple model
is the so called CutoffPL, which has the form
CutoffPL(E) ∝ E−Γ exp
(
− E
Efold
)
, (2.1)
with the photon index Γ, and the folding energy Efold [16]. Often more complex continuum models
with a higher number of free parameters are used. One of these models is the so called NPEXmodel
[10] of the form
NPEX(E) ∝
(
E−Γ1 +αE+Γ2
)
exp
(
− E
Efold
)
, (2.2)
with photon indices Γ1,2 ≥ 0. However, not all pulsars can be described perfectly even with such
complex broadband continuum models. In some cases, an absorption- or emission-like feature
remains around ∼10 keV. Although the origin of the so called “10 keV feature” is still not clear, it
is usually modelled as an additive or multiplicative Gaussian line [2].
We furthermore modify the models with up to five cyclotron absorption features, i.e., we mul-
tiply the continuum model with pseudo-Lorentzian profiles given by
CYCLABS(E) = exp
(
− τ(WE/Ecyc)
2
(E−Ecyc)2 +W 2
)
, (2.3)
where W denotes the width, and τ the optical depth of the feature. In the remainder of this work,
the cyclotron line parameters are labelled with the number of the respective harmonic, where 0
corresponds to the fundamental line. Another feature required for a good description of the data is
the Fe Kα fluorescence line at 6.4 keV. Finally, to account for the interstellar absorption, we use an
updated version of TBabs 1 [20, 21].
1see http://pulsar.sternwarte.uni-erlangen.de/wilms/research/tbabs/
3
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A constant Cyclotron Line Energy in 4U 0115+634 S. Müller
a
CutoffPL
NPEX
100
10
1
0.1
0.01
b
50205 10010
1.4
1.2
1
0.8
0.6
0.4
0.2
0
CutoffPL
4
3
2
NPEX
80706050
4
3
2
1
ra
te
[c
ts
s−
1
k
e
V
−
1
]
energy [keV]
ra
ti
o
E
n
/
E
0
time (MJD-54500)
E
n
/
E
0
Figure 2: Left: a Exemplary PCA, HEXTE, and ISGRI spectra (red) together with the best fit models for
the CutoffPL (blue) and NPEX (green) model. b Ratio between the spectra and the model. Right: Ratios
of the cyclotron line energies of the higher harmonics with respect to E0 for the CutoffPL and NPEX. The
dashed lines indicate the integer values for these ratios.
To describe the spectra of 4U 0115+634, we apply both, the NPEX and the CutoffPL model
to each observation, with the latter modified by the 10 keV feature in emission [4]. Both models
give a good description of the observed spectra with respect to χ2red, but for the CutoffPL the
quality of the fit is slightly better. In agreement with earlier work [11, 13, 18], we find cyclotron
absorption features at ∼10.7, 21.8, 35.5, 46.7, and 59.7 keV. One important difference between
these two fits is the behavior of the fundamental cyclotron line (see Fig. 1). While the NPEX model
leads to the previously found anticorrelation between E0 and FX, the CutoffPL model exhibits
a rather constant E0 for all observed X-ray fluxes. Also, for NPEX the width of the fundamental
cyclotron line W0 often exceeds 5 keV, while for the CutoffPL model it is ∼2 keV or less. A
constant E0, however, is in contrast to all previous results for 4U 0115+634, e.g., [11, 13, 18].
3. Behavior of the fundamental cyclotron line
As described in the previous section, the behavior of E0 with respect to FX completely changes
when using different continuum models. Given that the fits with NPEX and the CutoffPL give
similarly good results, what is the difference between these two approaches and where does the
difference in the cyclotron line behavior come from?
The resulting fundamental cyclotron line, when using NPEX is rather broad compared to the
CutoffPL. Such broad lines can strongly influence the continuum fit. To illustrate this impact on
the broadband continuum, panel a of Fig. 2 displays the best fit models for NPEX (green) and the
CutoffPL (blue) when turning the CRSFs off, i.e., setting the parameter τ for all cyclotron lines
to zero. Panel b of this figure displays the ratio between the spectra and the best fit models after
turning off the cyclotron lines. For the CutoffPL model plus 10 keV feature, the cyclotron lines
manifest by sharp absorption lines at the respective cyclotron energies. In contrast, for the NPEX
model the pseudo-Lorentzians obviously strongly influence the broadband continuum shape rather
than describe narrow cyclotron lines. Thus, the observed variation of the fundamental cyclotron
line with flux when using the NPEXmodel accounts for changes in the broadband continuum, rather
4
P
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S(INTEGRAL 2012)020
A constant Cyclotron Line Energy in 4U 0115+634 S. Müller
than being a real physical effect of the cyclotron lines. For the fits with CutoffPL, the change
of the spectral broadband shape reveals itself through the significant variation of the continuum
parameters Γ and Efold.
Another problem regarding the NPEX fit are the ratios of the energies of the higher harmonics
and E0. These ratios turn out to deviate strongly from integer values. Slightly non-integer values are
expected when taking relativistic quantum mechanics into account, while such strong deviations as
seen when using NPEX can only be explained by complex and more exotic assumptions [15, 16].
For the CutoffPL fits, these ratios are mostly in agreement with integers or differ only slightly.
These ratios are displayed in Fig. 2 for both continuum models used.
To exclude a possible influence of the continuum parameters on the fundamental cyclotron line
energy for the CutoffPL fits, we calculated confidence contours between E0 and the parameters
of the 10 keV feature, Γ, Efold, and W0. These fits reveal no relevant cross correlations between E0
and any other free fit parameter.
4. Summary and Discussion
In this work we have shown that the X-ray spectra of 4U 0115+634 can formally be described
by several continuum models almost equally well. However, using different continuum models, in
this case the NPEX model and the CutoffPL modified by the 10 keV feature, results in a different
behavior of the fundamental cyclotron line energy E0. While there is an anticorrelation between E0
and the X-ray flux FX when using NPEX, E0 stays constant when using CutoffPL. We have shown
that the cyclotron line model component strongly influence the broadband continuum model when
using NPEX. We conclude that the previously found anticorrelation between E0 and FX is caused by
variations of the broadband continuum and that the centroid energy of the fundamental cyclotron
line actually stays constant within uncertainties in the observed flux ranges.
5. Acknowledgements
This research has been funded by the Bundesministerium für Wirtschaft und Technologie un-
der Deutsches Zentrum für Luft- und Raumfahrt grants 50OR0808, 50OR0905, 50OR1113, and
50OR1007, and by the Deutscher Akademischer Austauschdienst. MTW is supported by the US
Office of Naval Research. IC acknowledges financial support from the French Space Agency CNES
through CNRS. SMN and JMT acknowledge support from the Spanish Ministerio de Ciencia, Tec-
nología e Innovación (MCINN) through grant AYA2010-15431 and the use of the computer facili-
ties made available through the grant AIB2010DE-00057.
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A constant Cyclotron Line Energy in 4U 0115+634

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A constant Cyclotron Line Energy in 4U 0115+634

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