Table Of ContentProceedingsofthe363.WE-HeraeusSeminaron:“NeutronStars and Pulsars”(Postersand contributedtalks)
Physikzentrum BadHonnef, Germany,May.14−19,2006, eds.W.Becker,H.H.Huang, MPEReport291,pp.116-119
A multicomponent model for the optical to γ-ray emission
from the Crab Pulsar
R. Campana1, E. Massaro1, G. Cusumano2, and T. Mineo2
1
Department of Physics, Universityof Rome“La Sapienza”, Rome, Italy
2
INAF– IASF-Pa,Palermo, Italy
7
0
0
2
n Abstract. We present a multicomponent model to ex- theemissionofthesecondpeak(P2)becomeshigherthan
a plain the features of the pulsed emission and spectrum the first one (P1), and where it is present a significant
J of the Crab Pulsar, on the basis of X and γ-ray ob- emission from the region between the two peaks (bridge
9 servations performed with BeppoSAX, INTEGRAL and orinterpeak,IP).Thisbehaviourcontinuesuptoabout10
CGRO. This model explains the evolution of the pulse MeV, where the pulse almost sharply returns to a shape
1
shapeandofthe phase-resolvedspectra,rangingfromthe similar to the optical light curve. A satisfactory explana-
v
3 optical/UV to the GeV energy band, on the assumption tion for these changes has not been found so far.
5 that the observed emission is due to several components. Onthe basisofhighqualityBeppoSAXdata,covering
2 The first component, CO, is assumed to have the pulsed a wide energy range (from 0.1 to 300 keV), we already
1 double-peaked profile observed at the optical frequencies, proposed a two component model (Massaro et al., 2000)
0
7 while the second component, CX, is dominant in the in- toexplainthebehaviourofthelightcurve.Hereweextend
0 terpeak and second peak phase regions. The spectra of this model, reanalysing the whole set of BeppoSAX Crab
/ these components are modelled with log-parabolic laws. observations with new ISGRI-INTEGRAL data at higher
h
p Moreover,toexplainthepropertiesofthepulsedemission energies (Mineo et al., 2006). We found that the energy
- in the MeV-GeV band, we introduce two more compo- spectraofthesecomponentsarenotdescribedbyasimple
o nents, COγ and CXγ, with phase distributions similar to power law, but show a spectral steepening towards high
r
t those of CO and CX and log-parabolic spectra with the energies. We model these components with log-parabolic
s
a same curvature but different peak energies. This multi- spectraldistributions.Moreover,toexplainthebehaviour
: componentmodelisabletoreproduceboththebroadband in the MeV/GeV band as observed by COMPTEL and
v
i phase-resolved spectral behaviour and the changes of the EGRETonboardCompton-CGRO,twomorecomponents
X pulse shape with energy. We also propose some possible are introduced, both with a similar shape and spectrum
r physical interpretations in which CO and CX are emitted of the X-ray counterparts. A complete description of the
a
by secondary pairs via a synchrotron mechanism while data analysis and of the model can be found in Massaro
COγ and CXγ can originate either from Compton scat- et al. (2006).
tered or primary curvature photons.
2. The two-component model: optical to hard
X-rays
1. Introduction
The study of the phase distributions of pulsars’ signals As presented in Massaro et al. (2000), Crab X-ray light
in the various bands of the electromagnetic spectrum is curve is well reproduced by two phase-components. The
important to obtain information on the geometry and lo- first component, called CO, is assumed to have the same
cation of the emission regions in the magnetosphere. At pulsed profile observed at optical frequencies, while the
γ-ray energies, in particular, the three brightest sources second component, CX, is described by an analytical
(Vela, Crab and Geminga) show remarkably similar pat- model whoseshape is determinedby comparingCO+CX
terns with two main peaks at a phase separation ranging with the observed pulse profiles, and that dominates at
from 0.40 to 0.48. the interpeak (IP) and second peak (P2) phase regions
The CrabPulsar(PSRB0531+21)is characterizedby (Fig. 1).
a rather stable phase distribution throughout the whole Usingthehigh-statisticsobservationsofBeppoSAXwe
electromagnetic spectrum with a double peak structure. performed a phase-resolved spectral analysis and found
It is wellknownthat the pulse shape of the Crabchanges that the photon indices of P1, P2 and IP are changing
with energy in the X and soft gamma-ray ranges where with energy, and linearly increasing with Log E (Fig. 2).
R.Campana et al.: A multicomponent model for theoptical to γ-ray emission from theCrab Pulsar 117
100
-1s]
2 m
c
V
e
k
F [
2 E
10-1
Fig.1. The two components CO and CX of the model at 100 101 102 103 104 105 106 107
theenergiesof8.85keV(left)and75.2keV(right).Inthe Energy [keV]
upper panels: the model comparedwith BeppoSAX data.
Fig.3. Broadband spectra of the total averaged pulse
In the lower panels: C and C (adapted from Massaro
O X with the four components of the model. Upward point-
et al. 2000).
ing triangles: LECS; brown circles: MECS; diamonds:
HPGSPC; downward pointing triangles: PDS; leftward
2.6 pointing triangles: FIGARO II; squares: COMPTEL;
P1 (First peak) crosses: EGRET. Dashed line: C ; dash-dotted line: C ;
O X
Ip (Interpeak)
2.4 dot-dot-dashed line: C ; dash-dash-dotted line: C .
P2 (Second peak) Oγ Xγ
Offpulse (Nebula)
2.2
x
e 2
d
n 3. Extension of the model to the MeV/GeV
I
n band: the need for two more components
o1.8
ot
h
P CGRO COMPTEL and EGRET observations (Kuiper et
1.6
al.,2001;Thompson,2004)providedabove∼10MeVlight
curves of a good statistical quality which show that the
1.4
pulse shapeissimilartothatofC ,althoughsomeminor
O
1.2 differencesarepresent.Atenergieshigherthan∼500MeV
the emission from IP and P2 increases, and this seems to
0.1 1 10 100
Energy [keV] reproduce the behaviour of the X-ray emission. In order
to explain such a finding, we assume that there are two
Fig.2. Photon indices of P1, IP and P2 as measured by more, high-energy spectral components, C and C ,
Oγ Xγ
the four NFI of BeppoSAX and by INTEGRAL-ISGRI. both with a log-parabolic spectral distribution and with
the same pulse shape of the lower-energycomponents C
O
andC .TobeconsistentwiththeupperlimitstotheTeV
X
WefoundthatthespectraofCO andCX arewellfitted pulsed emission (e.g. Lessard et al., 2000) we added also
by a log-parabolic spectral law, anexponentialcutofftobothC andC ,attheenergy
Oγ Xγ
E = 15 GeV. This model therefore has 6 adjustable pa-
c
F(E)=KE−(a+bLogE) (1) rameters,i.e.thepeakenergies,curvaturesandnormaliza-
tionsoftheC andC components.Assumingthatthe
Oγ Xγ
where K is the flux at 1 keV and E is the energy in curvatures are equal to the C and C ones (b = 0.16),
O X
keV.Theparameterbdescribesthe“curvature”ofthelog- wearethenabletoreproducethebroadbandenergyspec-
parabola.Theenergy-dependentspectralindexcanbeob- trum of the total (averaged) pulse and of the P1, IP and
tained from the previous equation: α(E)=a+2b Log E. P2 phase regions (see Figs. 3, 4 and 5) and the ratios of
According to this spectral law, the spectral energy dis- P2/P1 and IP/P1 fluxes (in the same phase intervals of
tribution (SED) has a maximum at the energy E = Kuiper et al., 2001;Figs.6 and7). We stress thatthere is
p
10(2−a)/2b. The curvature parameter b is equal to 0.16 for no constraintonE :infig.6we plotalsothe P2/P1ratio
c
bothC andC ,whilethe peakenergiesarerespectively for various values of C cutoff energy ranging from 9 to
O X Oγ
12 keV and 178 keV. 15 GeV.
118 R.Campana et al.: A multicomponent model for theoptical to γ-ray emission from the Crab Pulsar
2.5
2
-1s]
2 cm atio1.5
V 10-1 1 r
F [ke P2/P
2 E 1
0.5
100 102 104 106 100 101 102 103 104 105 106 107 108
Energy [keV] Energy [keV]
Fig.4. Broadband spectra of P1 with the four compo- Fig.6. P2/P1 ratio as derived from the model. Data
nents of the model. Upward pointing triangles: LECS; pointscomefromvariousexperiments(Kuiperetal2001).
brown circles: MECS; diamonds: HPGSPC; downward Thevariousextrapolationsabove1GeVcorrespondtodif-
pointing triangles: PDS; leftward pointing triangles: IS- ferent values of the cut-off energy of the C spectrum;
Oγ
GRI;squares:COMPTEL;crosses:EGRET.Dashedline: from top to bottom: 9, 11, 13 and 15 GeV.
C ;dash-dottedline:C ;dot-dot-dashedline:C ;dash-
O X Oγ
dash-dotted line: C .
Xγ
0.8
100
0.6
o
ati
2 -1ms] P/P1 r0.4
c I
v 10-1
ke 0.2
F [
2 E
0
100 101 102 103 104 105 106 107
10-2 Energy [keV]
100 101 102 103 104 105 106 Fig.7.IP/P1ratioasderivedfromthemodel.Datapoints
Energy [keV]
come from various experiments (Kuiper et al 2001).
Fig.5. Broadband spectra of P2 with the four compo-
nents of the model. Upward pointing triangles: LECS;
brown circles: MECS; diamonds: HPGSPC; downward
high-energy pulsar emission models, either in the polar
pointing triangles: PDS; leftward pointing triangles: IS-
cap or outer gap models (e.g. Cheng et al., 2000; Zhang
GRI;squares:COMPTEL;crosses:EGRET.Dashedline:
& Cheng, 2002).
C ;dash-dottedline:C ;dot-dot-dashedline:C ;dash-
O X Oγ
Assuming that the lower-energy components C and
dash-dotted line: C . O
Xγ
C are produced by synchrotron emission of secondary
X
electron-positron pairs created in the pulsar magneto-
sphere,thehigher-energycomponentsC andC could
4. Physical interpretation Oγ Xγ
be due to:
An open question is the physical origin of these compo-
nents, that phenomenologically explain the observations 1. Emissionofcurvatureradiationfromprimaryparticles
with a very good approximation,in the framework of the accelerated in the magnetospheric gaps.
R.Campana et al.: A multicomponent model for theoptical to γ-ray emission from theCrab Pulsar 119
2. Emission from inverse Compton scattering of the syn- Lessard R. W., Bond I. H., Bradbury S. M., et al., ApJ, 531,
chrotron photons by the secondary pairs themselves 942-948, (2000).
(Synchrotron-Self-Compton mechanism). Massaro E., Cusumano G., Litterio M., and Mineo T., A&A,
375, 397-404, (2000).
The different shape of the “O” and the “X” components MassaroE.,CampanaR.,CusumanoG.,andMineoT.,A&A,
is presumably due to the different location in the magne- 459, 859-870, (2006). [astro-ph/0607410]
tosphere of the emission regions. Mineo T., Ferrigno C., Foschini L. et al., A&A, 450, 617-623,
(2006).
Thompson D. J., in Cosmic Gamma Ray Sources, Kluwer
5. Conclusions ASSL series, 304, edited by K. Cheng and G. Romero,
(2004). [astro-ph/0312272]
Several models have appeared in the literature based on Zhang L. and Cheng K. S., ApJ,569, 872-877, (2002).
either polar cap or outer gap geometries. Usually, these
models are focused on reproducing either the total spec-
trumorthe phaseprofile,andgenerallythey arenotfully
satisfactory in explaining the complex observational pic-
ture. Moreover, the possibility that the observed features
ofthepulsedsignalcanarisefromthesuperpositionoftwo
or more distinct components is not taken into account.
We followedanother approachand searchedfor a pos-
sible interpretation of the Crab signal based on the su-
perposition of two or more components that provides a
consistent description of the spectral and phase distri-
butions. Clearly, it is only a phenomenological model,
but it could furnish some constraints to more detailed,
physically-based emission models. In particular it is im-
portanttoverifywhetheratenergieshigherthan∼1GeV
the pulse shape tends to be dominated by C . The
Xγ
GLAST/LAT experiment (Gehrels et al., 1999), with its
large collecting area, will give us very useful data in this
range that will permit to better estimate the model pa-
rameters.
Another interesting perspective is whether this model
can be adapted to the other γ-ray pulsars. For Vela and
Geminga the main problem is that their pulse profiles
changeverymuchindifferentspectralbandsandno clear
trend, like the P2/P1 ratio in Crab, has been found to
now.Inthe γ-rayband, however,Kanbach(1999)showed
thatthepeakratiosofallthesethreepulsarshavearather
similarbehaviour.Thiscanbe anindicationthatgeomet-
rical effects may be more relevant at energies lower than
γ-rays and that components like C or C , if existing
O X
in Vela and Geminga, are not detected because they are
more beamed than the high energy photons.
Acknowledgements. This work was financially supported by
Universit`a di Roma La Sapienza. R.C. also acknowledges the
support by theWE-Heraeus foundation duringthe seminar.
References
ChengK.S.,RudermanM.,andZhangL.,ApJ,537,964-976,
(2000).
Gehrels N., Michelson P., et al., Aph,11, 277-282, (1999).
Kanbach G., Proc. 3rd INTEGRAL Workshop, Astrophys.
Lett. Comm., 38, 17, (1999).
KuiperL.,HermsenW.,CusumanoG.,etal.,A&A,378,918-
935, (2001).
