Time Evolution of the X-Ray and γ-Ray Fluxes of the Crab Pulsar
L. L. Yan
1,2,3
,M.Y.Ge
2
,F.J.Lu
2
, S. J. Zheng
2
, Y. L. Tuo
2,3
,Z.J.Li
2,3
, L. M. Song
2
, and J. L. Qu
2
1
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, Peopleʼs Republic of China; yanlinli@ihep.ac.cn
2
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, Peopleʼs Republic of China
gemy@ihep.ac.cn, lufj@ihep.ac.cn
3
University of Chinese Academy of Sciences, Beijing 100049, Peopleʼs Republic of China
Received 2018 February 7; revised 2018 August 1; accepted 2018 August 6; published 2018 September 18
Abstract
We studied the evolution of the X-ray and γ-ray spectra of the Crab pulsar utilizing the 11-year observations from
the Rossi X-ray Timing Explorer (RXTE) and 9-year observations from the Fermi Gamma-ray Space Telescope
(FGST).Byfitting the spectrum of each observation, we obtained the corresponding flux and then analyzed the
long-term evolution of the X-ray (or γ-ray) luminosities as well as their correlations with the spin-down power of
the pulsar. The X-ray flux in 5–60 keV obtained by the Proportional Counter Array of RXTE decreases with a rate
of (−2.4 ± 0.4)×10
−14
erg cm
−2
s
−1
per day. The X-ray flux in 15–250 keV obtained by the High Energy X-ray
Timing Experiment of RXTE and the γ-ray flux in 0.1–300 GeV by the Large Area Telescope onboard FGST show
similar decreasing trends but are insignificant statistically. The 5–60 keV X-ray luminosity L
X
is correlated with the
spin-down power L
sd
by
µ
L
X
sd
1.6 0.3
, which is similar to the statistical results for young pulsars.
Key words: pulsars: individual (PSR B0531+21) – stars: neutron – X-rays: stars
1. Introduction
Much effort has been devoted to statistical studies of pulsar
high-energy emission properties, with particular emphasis on
the efficiency of the conversion of the pulsar spin-down power
L
sd
into X-ray and γ-ray luminosities, so as to test the pulsar
emission models and to predict the properties of a specific
source. Previous studies show the X-ray luminosities L
X
of
pulsars have a correlation with their spin-down power L
sd
.
Seward & Wang (1988) first found that the 0.2–4 keV X-ray
luminosity
µ
L
X
sd
1.39
. Becker & Trümper (1997) used 27
pulsars detected in 0.1–2.4 keV and found that
µ
L
Xsd
. In the
higher energy band, Saito (1998) gave the relation
µ
L
X
sd
1.
in
2–10 keV, but Possenti et al. (2002) obtained a relation of
µ
L
X
sd
1.34
in the same energy band using a larger sample of 39
pulsars. However, all the X-ray luminosities above contain the
emission from the pulsar wind nebula (PWN) , which is
nonpulsed and often dominates the nonthermal emission of
pulsars. To eliminate the influence of the PWN emission,
Cheng & Zhang (1999) presented the empirical relation
between the pulsed luminosity and the spin-down power, i.e.,
µ
L
X
sd
1.15
in 2–10 keV. Because of the improvement of the
spatial resolution of detectors, Cheng et al. (2004) divided the
total X-ray emission into pulsed and nonpulsed components,
and found that the pulsed component follows
µ
L
X
sd
1.2 0.08
in
2–10 keV, which is more gentle than the nonpulsed component
and can be explained by the outer gap radiation model (Zhang
& Jiang 2006). By using the Chandra and XMM-Newton
observations, Li et al. (2008) resolved the pulsar X-ray
emission from that of the PWNe and got
µ
L
X
sd
0.92 0.04
in
the same energy band. The relation between the pulsar γ-ray
luminosity
g
and the spin-down luminosity are different from
that in the X-ray band. Saito et al. (1997) obtained
µ
g
L
sd
0.
,
and Marelli et al. (2011) further found that the relation between
log
10
( L
γ
) and log
10
(L
sd
) could not be represented by a single
linear function. These correlations are in accord with the
expectation that the X-ray and γ-ray emission of a pulsar is at
the expense of rotational energy. This could be from
magnetosphere and near the light cylinder (Becker &
Trümper 1997; Malov 2003). Specific predictions of the
correlations for emission from outside the light cylinder have
not yet been given.
However, all the previous results are obtained from the
statistics of pulsar samples. The different properties of these
pulsars, such as ages, magnetic field strengths, masses, and
directions of the magnetic and rotation axes, bring complexity
to these relations, which may in turn make it more difficult to
understand the physical process behind them. Therefore, to
obtain the exact dependence of the high-energy luminosity on
the evolutionary spin-down power of a specific pulsar in a long
time span could provide much purer information for pulsar
physics study.
Among all the known pulsars, the Crab pulsar is the
most suitable source for such studies, because it has been
frequently and comprehensively studied in almost all
wavelength bands from radio to very high-energy γ -r ays.
Recently, for this pulsar, secular changes w ith X-ray pulse
profiles and phases are reported (Ge et al. 2012, 2016;
Yan et al. 2017). However, the evolution of X-ray and γ-ray
spectra have not yet been studied in detail, which is what we
examine in the current paper. Thanks to the long-term
observations from the Rossi X-ray Timing Explorer (RXTE)
and the Fermi Gamma-ray Space Telescope (FGST),wecan
study the evolution of the spectra in 5 –60 keV, 15–250 keV,
and 0.1–300 GeV using the Proportional Counter Array
(PCA) and the High Energy X-ray Timing Experiment
(HEXTE) of RXTE and the Large Area Telescope (LAT)
onboard FG ST, respectively. These results are then used to
test the pulsar emission models.
The organization of this paper is as follows: data processing
and reduction are presented in Section 2 and the results are
given in Section 3. Discussions on the physical implications of
our results are presented in Section 4, and a short summary is
given in Section
5. Throughout the paper, errors of the
parameters are at the 1σ level.
The Astrophysical Journal, 865:21 (6pp), 2018 September 20 https://doi.org/10.3847/1538-4357/aad911
© 2018. The American Astronomical Society. All rights reserved.
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