XMM-Newton observation of the nearby pulsar B1133+16

1.1 MB·

by  Andrzej Szary

Draft version January 11, 2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
XMM-NEWTON OBSERVATION OF THE NEARBY PULSAR B1133+16.
Andrzej Szary1,2, Janusz Gil1, Bing Zhang3, Frank Haberl4, George I. Melikidze1,5, Ulrich Geppert1,6, Dipanjan
Mitra7,1,8, Ren-Xin Xu9
Draft version January 11, 2017
ABSTRACT
WeconstraintheX-raypropertiesofthenearby(360pc),old(5Myr)pulsarB1133+16with∼100ks
effective exposure time by XMM-Newton. The observed pulsar flux in the 0.2−3keV energy range
is ∼10−14ergcm−2s−1, which results in the recording of ∼600 source counts with the EPIC pn and
7
MOS detectors. The X-ray radiation is dominated by nonthermal radiation and is well described by
1
0 both a single power-law model (PL) and a sum of blackbody and power-law emission (BB+PL). The
2 BB+PLmodelresultsinaspectralphotonindexΓ=2.4+0.4 andanonthermalfluxinthe0.2−3keV
−0.3
energy range of (7±2)×10−15ergcm−2s−1. The thermal emission is consistent with the blackbody
n
a emission from a small hot spot with a radius of Rpc ≈14+−75m and a temperature of Ts =2.9+−00..64MK.
J Assuming that the hot spot corresponds to the polar cap of the pulsar, we can use the magnetic flux
0 conservation law to estimate the magnetic field at the surface Bs ≈ 3.9×1014G. The observations
1 are in good agreement with the predictions of the partially screened gap model, which assumes the
existence of small-scale surface magnetic field structures in the polar cap region.

] Subject headings: stars: neutron — pulsars: general — pulsars: individual (B1133+16)
E
H
. 1. INTRODUCTION Over the years, both models have been modified signif-
h
icantly, however, no consensus has been reached on the
p The vast majority of detected neutron stars are ob-
mechanism of plasma generation.
- servedasradiopulsars(Manchesteretal.2005). Almost
o half a century of pulsar observations have not given the The SCLF model assumes that surface charges can
r definite answer to one of the most intriguing questions, freely flow into the magnetosphere. The density of the
t plasma extracted from the surface equals the Goldreich-
s namely, how the plasma that is responsible for gener-
a Julian charge density at the surface, but is insufficient
ating the radio emission is produced. Although many
[ to screen the charge at higher altitudes (Hibschman &
modelswereproposed,noclearconsensusexistsoverthis
Arons 2001). In the SCLF model, pairs are created near
1 fundamental problem until now. There are two quali-
the so-called ”pair-creation front” at altitudes ranging
v tatively quite different models that in principle can ex-
fromonemeterupto10km(Harding&Muslimov2001,
4 plain how a magnetosphere of a rotating highly magne-
2002). Although a connection between acceleration of
5 tized neutron (NS) can be filled by an electron-positron
plasma in the SCLF model and radio emission was not
5 plasma. These two models are the vacuum gap (VG)
2 model of Ruderman & Sutherland (1975) and the space found, free particle outflow from the stellar surface is a
0 charge limited flow (SCLF) model of Arons & Scharle- common assumption in most of the current pulsar mod-
1. mann (1979). The aim of both models is to provide a els.
Inordertounderstandthephenomenonofthedrifting
0 mechanism that yields a sufficiently large number of ul-
subpulses, Gil et al. (2003, 2006b,a) developed a modifi-
7 trarelativistic charges (electrons and positrons), which
cation of the VG model, the so-called partially screened
1 eventuallycreatetheobservedradiowaves. Inbothmod-
gap (PSG) model. The PSG model is based on a ther-
: els, the plasma responsible for the generation of radio
v mostat regulation of the thermionic release of iron ions
emission is produced and accelerated in a region of the
i into the inner acceleration region (IAR). According to
X openmagneticfieldlinesabovethepolarcapofapulsar.
Medin & Lai (2007) the cohesive energy that holds the
r [email protected] ions within the crystal lattice is strongly dependent on
a 1Janusz Gil Institute of Astronomy, University of Zielona the magnetic field strength at the stellar surface. The
G´ora,Szafrana2,65-516ZielonaG´ora,Poland
2ASTRON, the Netherlands Institute for Radio Astronomy, PSG model requires the surface temperature in the po-
Postbus2,7990AA,Dwingeloo,TheNetherlands larcapregiontobeclosetotheso-calledcriticaltemper-
3DepartmentofPhysicsandAstronomy,UniversityofNevada ature that is defined by the surface magnetic field (see
LasVegas,NV89154,USA,[email protected] Medin&Lai2007). X-rayobservationssuggesttheexis-
4Max-Planck-Institut fu¨r extraterrestrische Physik, Giessen-
tence of small hot spots with temperatures of a few mil-
bachstraße,85748Garching,Germany
5Abastumani Astrophysical Observatory, Ilia State Univer- lion Kelvin (see Becker 2009; Szary 2013, and references
sity,3-5CholokashviliAve.,Tbilisi,0160,Georgia therein). Assuming that the hot spots are actual polar
6German Aerospace Center, Institute for Space Systems, caps heated by backstreaming of ultrarelativistic parti-
Robert-Hooke-Str. 7,28359Bremen,Germany
7NationalCentreforRadioAstrophysics,Ganeshkhind,Pune cles accelerated in the IAR, we can conclude that an ac-
411007,India tualareaofapolarcap,Apc,isconsiderablysmallerthan
8PhysicsDepartment,UniversityofVermont,Burlington,VT the conventional polar cap area A ≈ 6.2×104P−1m2
05405 dp
9SchoolofPhysicsandKavliInstituteforAstronomyandAs- (calculatedassumingadipolarconfigurationofthemag-
trophysics,PekingUniversity,Beijing100871,China neticfield),hereP isthepulsarperiodinseconds. Thus,
2 Szary et al.
thesurfacemagneticfieldhastobeconsiderablystronger
Table 1
than the dipolar component (see Szary et al. 2015, for a
ObservedandderivedparametersofPSRB1133+16
detailed description).
The possibility to create such field structures at the
polarcapsurfacesandtomaintainthemoverthetypical
lifetime of pulsars has been demonstrated recently by Parameter Value
Geppertetal.(2013);Geppert&Vigan`o(2014). Viathe
Hall drift, the magnetic energy, which is stored in large-
R.A.(J2000) .......................... 11h36m03s.1829(10)
scale toroidal field configurations in deep crustal/outer
Decl.(J2000) .......................... +15◦51(cid:48)09(cid:48).(cid:48)726(15)
core layers, is transformed into small-scale poloidal field
Epochofposition(MJD) .............. 51544
components at the polar cap surface.
Rotationfrequency,ν(Hz) ............ 0.84181003670065(48)
Since the predicted surface temperature of the polar Frequencyderivative,ν˙(Hzs−1) ....... −2.645070(29)×10−15
cap is expected to exceed 106K, X-ray observations are Frequencysecondderivative,ν¨(Hzs−2) 1.2×10−15
essential to test the model prediction, eventually leading Epochoffrequency(MJD) ............ 56935.339344
to understanding the radio emission. Such high temper- Dipolarsurfacemagneticfield,B (G) . 2.13×1012
d
atures at the polar cap are close to the critical temper- Spin-downpower,E˙(ergs−1) ......... 8.8×1031
ature above which iron ions can enter the IAR. There- Characteristicage,τc(yr).............. 5.04×106
fore,theobservationofA –sufficientlysmallandsuffi- Inclinationangle,α(◦) ................ 52.5
pc
cientlyhot–wouldprovideastrongsupportforthePSG Openingangle,ρ(◦)................... 7.4
model. The same is true for the ratio A /A . Given Impactparameter,β (◦)............... 4.5
dp pc DispersionMeasure,DM(cm−3 pc) ... 4.86
a typical dipolar surface field strength of radio pulsars
Distancefromparallax,D (pc) ........ 357(19)
B ∼ 1011...13 G, magnetic flux conservation arguments
d
require that A /A ∼10...1000.
dp pc
The first observations that indicated both the differ-
Notes. ThepositionanddistancearefromBriskenetal.(2002),
ence in Apc and Adp as well as the surface tempera- whilethefrequencyanditsderivativeswereobtainedbytheJodrell
tures of these areas have been performed over the past Bank Pulsar Group (valid since 56190 MJD to 57681 MJD). The
10 years, e.g. for pulsars B0943+10 (Zhang et al. 2005), zerophasewasdefinedbetweenthetwopeaksintheradioprofile.
B1133+16(Kargaltsevetal.2006),andJ0108-14(Pavlov
et al. 2009). Although the X-ray photon statistics was
not excellent, these results triggered more and longer
observations with XMM-Newton of pulsars B0834+06
and B0826-34 that strengthened the idea of the PSG
model (Gil et al. 2008). The discovery of synchronous
mode switching in the radio and X-ray emission of PSR
B0943+10 (Hermsen et al. 2013) further contributed to
the increase in number of high statistics X-ray observa-
tions of pulsars.
The main aim of this paper is to foster the backing
for the PSG model by the evaluation of another XMM-
Newton observation of PSR B1133+16 (see Table 1 for
pulsarparameters),carriedoutin2014May/June. With
thisobservation,thephotonstatisticsissignificantlybet-
ter than that of Kargaltsev et al. (2006). Therefore,
much more reliable values of the hot spot area and its
respective temperature could be derived. The fact that
theyfulfilltherequirementsofthePSGmodelisdemon-
strated in the following sections.
In order to see the correlation between the thermal
states of the polar cap region and the radio emission,
simultaneous observations of PSR B1133+16 in the X-
ray and radio wavelength range have been performed.
The results of these combined efforts will be presented Figure 1. X-ray images of the field around PSR B1133+16 in
and discussed in a forthcoming paper. the0.2−12keVband. Thetoppanelcorrespondstothepnimage
(6(cid:48)×4(cid:48)),whilethebottom-leftandbottom-rightpanelscorrespond
2. OBSERVATIONSANDDATAANALYSIS to the MOS1 and MOS2 images (3(cid:48)×3(cid:48) each), respectively. The
sourceextractionregionsaremarkedwithredandthebackground
The data were collected during five XMM-Newton ob- regionswithbluecircles.
serving sessions performed from 25th of May to 28th of
mode (timing resolution of 0.3s).
June 2014. In the analysis, we have used the data ob-
To reduce and analyze the data collected by XMM-
tained with the pn and MOS1/2 CCD cameras, which
Newton we used the Science Analysis System (SAS ver.
are part of the EPIC instrument (Stru¨der et al. 2001;
14.0.0) with the latest calibration files (CCF ref. 330)
Turner et al. 2001). In all of the observing sessions the
and for the spectral fits we used XSPEC (ver. 12.9.0g).
thin optical blocking filters were used. The pn camera
operated in the full frame mode (with timing resolution
2.1. Data selection
of73ms),whilebothMOSoperatedinthesmallwindow
XMM-Newton observation of PSR B1133+16 3
Table 2
ObservationtimesofXMM-Newton
Obs.ID Start/End time (UT) Observation Times (ks)
(YYYY-MM-DD hh-mm-ss) pn ()∗ MOS1 MOS2
0741140201 2014-05-25 12:18:42 2014-05-25 19:20:22 22.34 (11.05) 24.00 (17.12) 23.96 (16.89)
0741140301 2014-05-31 11:34:51 2014-05-31 17:58:11 20.04 (7.31) 21.70 (18.40) 21.66 (18.23)
0741140401 2014-06-14 07:47:26 2014-06-14 18:20:46 35.04 (21.63) 36.70 (31.49) 36.66 (32.04)
0741140501 2014-06-22 07:22:13 2014-06-22 17:02:13 31.84 (27.41) 33.50 (30.36) 33.46 (31.73)
0741140601 2014-06-28 10:58:52 2014-06-28 17:55:32 22.04 (18.81) 23.70 (22.43) 23.66 (22.00)
∗ Values in parentheses correspond to the effective exposure times used in our analysis.
are initially binned using a constant bin size of 5eV and
1− 10-2 sboaucrkcgeround 15eV for pn and MOS1/2 detectors, respectively, to be
V
ke compatible with the response files, which are based on
1s− 10-3 the instrument channel width. The response files are
nts generatedusingthermfgenandarfgentasks. Duetothe
ou moderate number of counts, we use both the chi-square
C 10-4 and the Cash statistics (Cash 1979) in the fitting pro-
10-2 0.5 1 2 3 source 10 cedures. For the Chi-square statistics the spectral files
1− background aregroupedusing thespecgroup taskwith aminimumof
keV 10-3 Channel energy [keV] 20 counts in each energy bin, while for the Cash statis-
1s− 10-4 tics with a minimum of one count in each energy bin.
nts Note that, to avoid adding any unnecessary error, we do
ou 10-5 not combine spectra from different observing sessions;
C
instead, we use a joint fit to the data sets.
0.5 1 2 3 10 In order to better constrain model parame-
Channel energy [keV] ters for some fits, we fixed the hydrogen column
density, N . The pulsar’s dispersion measure,
H
DM=4.86cm−3pc, corresponds to an electron col-
Figure 2. EPIC-pnspectrafromsourceandbackgroundregions
inthe0.2−12keVenergyrange. Thetoppanelcorrespondstothe umn density Ne =1.49×1019cm−2. Assuming the
binneddata,whilethebottompanelcorrespondstotheunbinned typical 10% ionization of the interstellar medium, we
data. obtain N =1.49×1020cm−2.
The total observing time was 130ks for pn and 140ks H
In Tables 3 and 4, we show the results from fitting
for each of the MOS detectors. In the analysis, we con-
binned and unbinned spectra, respectively. The fit of
sider only photons with single and double pixel patterns
theabsorbedblackbodymodel(BB)withbothfixedand
for the pn detector (≤4) and up to quadrupole patterns
free N results in poor goodness of fit with χ2 > 1.3
for MOS1/2 (≤ 12). We use the espfilt task to remove H ν
for binned data, and Pearson-χ2 > 3 for the unbinned
soft proton contamination and any X-ray background ν
data. Ontheotherhand, theabsorbedpower-lawmodel
flares. After removing all contaminated time intervals,
(PL) with both fixed and free N describes the spec-
the net exposure times are 86ks, 120ks and 121ks for H
the pn and MOS1/2 detectors, respectively (see Table tra reasonably well with χ2ν = 1.07 for binned data
2). The source counts for the spectral and timing anal- and Pearson-χ2 = 1.3 for unbinned data (see Figure
ν
ysis are extracted from a circular region with a radius 3). The BB+PL model fits the data equally well with
of 15(cid:48)(cid:48) centered on the pulsar position. The background χ2 <1.04 for binned data and Pearson-χ2 =1.3 for un-
ν ν
counts are extracted from nearby source-free regions in binneddata(seeFigures4and5). Thespectralfitsresult
the same CCD as the target (see Figure 1). In Figure 2, in consistent parameters for both binned and unbinned
weshowsourceandbackgroundspectraforthepndetec- data. For the binned data, the observed temperature is
tor. Due to the small number of high-energetic photons, kT∞ =0.19+0.06keVwiththecorrespondingradiusofan
−0.05
we restrict the analysis to the 0.2–3 keV energy range. emitting equivalent sphere R∞ =17+18m, while for the
⊥ −8
unbinned data kT∞ =0.19+0.04keV, and R∞ =17+7m
2.2. Spectral analysis −0.03 ⊥ −5
(seeTables3and4forallspectralfitparameters). Ifnot
In previous studies, spectral properties of PSR
statedotherwise, hereafter, weusethefitparametersfor
B1133+16 were derived based on 33 counts (Kargaltsev
theunbinneddatabecausetheyareestimatedwithlower
et al. 2006). The new XMM-Newton observation results
statistical errors.
in 378±52, 97±29, and 102±33 counts registered by
thepn,MOS1andMOS2detectors,respectively. Forev-
ery observing session, we create source and background
spectra separately for all three detectors. The spectra
4 Szary et al.
Table 3
Parametersfromspectralfits(BinnedData).
Parameter PL PL∗ BB BB∗ BB+PL BB+PL∗
NH (1020 cm−2) 4+−43 1.5(fixed) <5 1.5(fixed) <3 1.5(fixed)
Photonindex 2.6+0.4 2.3+0.1 ... ... 2.0+1.3 2.4+1.5
−0.3 −0.1 −1.2 −0.7
F0.2−3keV (10−15 ergcm−2 s−1) 8+1 9+1 ... ... 5+5 7+2
PL −1 −1 −3 −3
kT∞ (keV) ... ... 0.19+0.01 0.18+0.01 0.18+0.06 0.19+0.06
−0.01 −0.01 −0.04 −0.05
T∞ (MK) ... ... 2.2+0.1 2.1+0.1 2.1+0.7 2.2+0.7
−0.1 −0.1 −0.4 −0.6
F∞ (10−15 ergcm−2 s−1) ... ... 7+5 8+5 4+3 3+3
bb −3 −3 −3 −3
R∞ (m) ... ... 25+3 29+4 19+15 17+18
⊥ −3 −4 −9 −8
χ2/dof 1.07/18 1.07/19 1.31/18 1.38/19 1.04/16 1.00/17
ν
Nullhypothesisprobability 0.38 0.38 0.17 0.12 0.41 0.46
Notes. Errors correspond to 1σ. F0.2−3keV is the unabsorbed nonthermal flux in the 0.2−3keV energy range, F∞ is the thermal
PL bb
bolometric flux, T∞ is the observed temperature, and R∞ is the observed radius of an emitting equivalent sphere, ∗ indicates fits with
⊥
fixedNH.
Table 4
Parametersfromspectralfits(unbinneddata).
Parameter PL PL∗ BB BB∗ BB+PL BB+PL∗
NH (1020 cm−2) 5+−32 1.5(fixed) <5 1.5(fixed) <2.2 1.5(fixed)
Photonindex 2.7+0.3 2.3+0.1 ... ... 2.0+0.4 2.0+0.4
−0.2 −0.1 −0.4 −0.4
F0.2−3keV (10−15 ergcm−2 s−1) 8.4+0.5 9.3+0.4 ... ... 5+3 7+2
PL −0.8 −0.5 −1 −2
kT∞ (keV) ... ... 0.21+0.01 0.21+0.01 0.19+0.03 0.19+0.04
−0.01 −0.01 −0.02 −0.03
T∞ (MK) ... ... 2.5+0.1 2.4+0.1 2.2+0.3 2.2+0.3
−0.1 −0.1 −0.3 −0.3
F∞ (10−15 ergcm−2 s−1) ... ... 7+3 8+4 4+3 3+3
bb −2 −3 −3 −2
R∞ (m) ... ... 15+2 17+2 18+7 17+9
⊥ −2 −2 −6 −6
C-stat/dof 267/336 271/337 289/336 295/337 262/333 262/334
P-χ2 1.30 1.31 3.24 3.85 1.31 1.31
ν
Notes. Errorscorrespondto1σ. SeenotesinTable3.
XMM-Newton observation of PSR B1133+16 5
pn
-2
10 MOS1
MOS2
1V− 10-3
e
k
1−
s
nts 10-4
u
o
C
-5
10
0.5 1 2
Channel energy [keV]
Figure 3. AbsorbedPLfitwithfixedNH=1.5×1020cm−2 for Figure 5. AbsorbedBB+PLfitwithfixedNH=1.5×1020cm−2
the binned pn (red), MOS1 (green), MOS2 (blue) data. In the for the unbinned pn (red), MOS1 (green), and MOS2(blue) data.
bottom panel we show the residuals in units of sigma deviations. The black dashed and dotted lines correspond to individual BB
The black solid line corresponds to a single PL component fitted and PL components fitted to the pn data. The black solid line
tothepndata. ThemodelsforMOS1andMOS2areomittedfor represents the total spectrum. The models for MOS1 and MOS2
clarity. areomittedforclarity.
Figure 4. AbsorbedBB+PLfitwithfixedNH=1.5×1020cm−2
forthebinnedpn(red),MOS1(green),andMOS2(blue)data. In
the bottom panel, we show the residuals in units of sigma devia-
tions. Theblackdashedanddottedlinescorrespondtoindividual
BBandPLcomponentsfittedtothepndata. Theblacksolidline
represents the total spectrum. The models for MOS1 and MOS2
areomittedforclarity.
6 Szary et al.
0.5 1.0 1.5 0.5 1.0 1.5 0.5 1.0 1.5
50 (a) 0.2-0.5 keV (b) 0.5-1.2 keV (c) 1.2-3.0 keV 50
PF = 0.61 PF = 0.32 PF = 0.48
40 40
30 30
20 20
10 10
0 0
0.5 1.0 1.5 0.5 1.0 1.5 0.5 1.0 1.5
100 (d) 0.2-3.0 keV
PF = 0.38
80
s
nt 60
u
o
C
40
20
0
0.5 1.0 1.5
Phase
Figure 6. Folded pn + MOS1/2 source light curves in four different energy ranges. The blue dashed lines show fits with sinusoidal
functions, while the red solid line shows the Effelsberg radio profile at 4.858GHz in arbitrary units. The green line corresponds to the
backgroundlevel. Notethatthelightcurvesarecorrectedforbackground. Twophasecyclesareshownforclarity.
XMM-Newton observation of PSR B1133+16 7
2.3. Timing analysis
Table 5
The source light curves are extracted from a circular PropertiesofX-RayLightCurvesofPSRB1133+16.
region with a radius of 15(cid:48)(cid:48) centered on the pulsar po-
sition, while the background light curves are extracted
fromnearbysource-freeregions. Weusethebarycentask
EnergyRange Counts X-Ray/RadioDelay PulsedFraction
and ephemeris of PSR B1133+16 given in Table 1 to
(keV) (◦) (%)
convert photon arrival times to the Barycentric Dynam-
ical Time. Both absolute corrections (vignetting, bad
pixels, chip gaps, quantum efficiency, etc.) and relative 0.2−0.5 398±71 70±8 61±5
corrections (background counts, dead times, etc.) are
performed with the epiclccorr task. The pulse phases of 0.5−1.2 442±73 44±9 32±4
the counts are computed using the phasecalc task with
ephemeris of the pulsar (see Table 1). The uncertainties 1.2−3 299±64 92±7 48±3
in pulsar ephemeris result in a negligible delay of 0.01◦.
In Figure 6, we show the folded pulse profiles in four 0.2−3 581±95 64±7 38±3
energy ranges: 0.2−0.5keV, 0.5−1.2keV, 1.2−3keV,
and 0.2−3keV. The light curves are broadly sinusoidal
Notes. The individual columns are as follows: (1) considered
andarecharacterizedwithadelayofabout70◦ fromthe
energy range, (2) source counts in the considered energy range,
radio main pulse (see the red solid line in panel (d) in (3)delaybetweenX-rayandradioprofiles,and(4)pulsedfraction
Figure6). AssumingthatX-raypulsationsareconnected defined as the amplitude of the sinusoid divided by the average
with the polar cap radiation, we can estimate the polar value. Theuncertaintiescorrespondtoonesigma.
cap dislocation from the magnetic axis: d = δRsinα, where ∆V is the potential drop in a VG and η is the
max
where δ is the delay in radians, R is the neutron star screeningfactor. Thescreeningfactorischaracterizedby
radius, and α is the inclination angle. Using the incli- the ratio of the density of iron ions ρ to the Goldreich-
i
nation angle of the pulsar, α = 52.5◦, and R = 10km Julian co-rotational density ρ as follows.
GJ
we get the polar cap dislocation d ≈ 9.7km. Such a
η =1−ρ/ρ . (2)
largedislocationisnotpossibleassumingcrustanchored i GJ
small-scalemagneticanomaliesandwouldrequireanon- Medin & Lai (2007) showed that, for the observed sur-
dipolar global magnetic field. Thus, the phase-shift be- face temperatures (a few million Kelvin), electrons can
tween X-ray maximum and radio peak suggests a non- easilyescapefromthestellarsurface,therebycompletely
thermal origin of the X-ray pulsed emission. In Table 5 screening the acceleration potential above the polar cap.
we show the properties inferred from the light curves in Thus,forneutronstarswithΩ·B>0,wedonotexpect
differentenergyranges. TheuncertaintiesinX-ray/radio the formation of any acceleration region above the polar
delays and pulsed fractions were estimated based on 100 cap, hereΩistheneutronstarrotationaxis. Inthecase
light curves constructed using different good time inter- of neutron stars with Ω·B < 0, positive charges (iron
vals. The difference in the good time intervals is due to ions) are responsible for the screening of the potential
the randomization of photons’ energy and arrival times drop. Since the density of the iron ions in the neutron
according to the energy/time resolution. Interestingly, starcrustismanyordersofmagnitudelargerthantheco-
in the energy range of 0.5−1.2keV, where the influence rotationalchargedensity,onlyasmallfractionisenough
of the BB component on the spectrum is strongest (see to completely screen the accelerating potential. In order
Figures4and5),boththedelayfromtheradiopeakand toformPSG,thesurfacetemperatureT needstobebe-
s
thepulsedfractionarelower. Thissuggeststhepresence lowtheso-calledcriticalvalueT , i.e. thetemperature
crit
oftheBBcomponentwithaconsiderablysmallerpulsed atwhichthedensityoftheoutflowingthermalionsequals
fraction and smaller delay from the radio peak than the the Goldreich-Julian co-rotational density. The cohesive
PL component. energy of iron ions is mainly defined by the strength of
the magnetic field. By fitting to the numerical calcula-
3. PHYSICALIMPLICATIONSFORIAR tionsofMedin&Lai(2007),wecanfindthedependence
Under the assumption that the thermal component of of the critical temperature, T , on the pulsar parame-
crit
the pulsar X-ray emission comes from the actual hot po- ters
lar cap, the XMM-Newton data allows us to constrain T ≈2×106B0.75K, (3)
crit 14
the pulsar polar cap physics and to test the predictions where B = B /(cid:0)1014G(cid:1), B = bB is a surface mag-
of the PSG model. 14 s s d
neticfield,andb=A /A (applicableonlyifthepolar
dp pc
cap radiation is revealed with A <A ).
3.1. Partially Screened Gap pc dp
The PSG model was introduced by Gil et al. (2003, 3.2. Observations of the polar cap
2006b,a) in order to explain the observational rates of
Theblackbodyfittotheobservedspectrumofapulsar
drifting subpulses. In PSG, the full vacuum potential
allows us to obtain the redshifted (measured by a dis-
drop is largely reduced by thermal iron ions Fe56 ther-
tant observer) effective temperature T∞ and redshifted
mallyejectedfromthehotsurfaceofthepolarcap,there-
total bolometric flux F∞. The unredshifted (actual) pa-
fore reducing drift rates that result from the VG model.
rameters can be estimated by taking into account the
The potential drop of PSG can be described as
(cid:112)
gravitationalredshift,g = 1−2GM/Rc2,determined
r
∆V =η∆V , (1) by the neutron star mass M and radius R, here G is
max
8 Szary et al.
Table 6
PolarCapPropertiesofPSRB1133+16.
RadiationSource (cid:104)cosi(cid:105) (cid:104)f(cid:105) Rpc Ts logLbb PulsedFraction
(m) (MK) (ergs−1) (%)
Primaryspot 0.40 0.61 16+9 2.9+0.6 28.5+0.4 64
−6 −0.4 −0.4
Antipodalspot 0.07 0.25 26+14 2.9+0.6 28.9+0.4 100
−10 −0.4 −0.4
Twospots 0.48 0.86 14+7 2.9+0.6 28.4+0.4 9
−5 −0.4 −0.4
Notes. Theindividualcolumnsareasfollows: (1)assumedsourceofradiation,(2)time-averagedcosineoftheanglebetweenthemagnetic
axisandthelineofsight,(3)fluxcorrectionfactor(includinggravitationalbendingoflight),(4)radiusofthepolarcap,(5)temperature
ofthepolarcap,and(6)Bolometricluminosity. ThegravitationalbendingeffectwascalculatedusingM =1.4M(cid:12) andR=10km.
the gravitational constant. The actual effective temper-
total f=0.86
ature and actual total bolometric flux can be estimated 1.0 primary spot f1 =0.61
as Ts = gr−1T∞, Fbb = gr−2F∞ (see, e.g., Zavlin 2007). antipodal spo›t ffi2 =0.25
If the distance to the neutron star, D, is known, we 0.8 › fi
can use T and F to calculate the size of the radiating
region. Assuming that the radiation is isotropic (e.g. F0 0.6
/
radiation from the entire stellar surface), we can esti- F
mate the radius as R = g R∞ = D(cid:112)g2F∞/(σT∞4), 0.4
⊥ r ⊥ r
whereσ ≈5.6704×10−5ergcm−2s−1K−4 istheStefan–
0.2
Boltzmann constant.
If we assume that the radiation comes from the hot
spot (or spots) on the stellar surface, the modeling of 0.2 0.4 0.6 0.8
thermal radiation is more complicated. The follow- Phase
ing factors must be taken into consideration: the time-
averaged cosine of the angle between the magnetic axis Figure 7. Observed flux fraction f as a function of the rotation
and the line of sight (cid:104)cosi(cid:105), the gravitational bending phase for PSR B1133+16. The following parameters were used:
of light, as well as the number of the radiating spots, α=52.5◦,β=4.5◦,M =1.4M(cid:12),R=10km.
i.e. whether the radiation comes from two spots (e.g.,
As shown in the previous section, knowing the pul-
from opposite poles of the star) or from one hot spot
sar geometry (Lyne & Manchester 1988; Kijak & Gil
only. The observed radius of the radiating spot is in-
1997), we can estimate the observed flux depending on
fluenced by the geometrical factor f, which depends on
the source of thermal radiation. In Figure 7 we present
the following angles: α between the spin and magnetic
the observed flux fraction as a function of the rotational
axesandζ betweenthelineofsightandthespinaxis,as
phase for PSR B1133+16. If the two polar caps have
well as on g and whether the radiation comes from the
r the same properties (temperature and size), the gravita-
star’s two opposite poles or from a single hot spot only:
tional bending increases contribution of radiation from
Rpc =grf−1/2R⊥∞. the antipodal spot from about 15% to 30%. In Table
Since the radius of a neutron star is only a few times 6, we present flux fractions and corresponding polar cap
larger than the Schwarzschild radius, a strong gravita- properties calculated assuming different sources of ra-
tionalfieldjustabovethestellarsurfacecausesthebend- diation, i.e. the primary polar cap only, the antipodal
ingoflight. ForaSchwarzschildmetric,wecancalculate polarcaponly,orthetwopolarcaps. InthePSGmodel,
the observed flux fraction from the primary and antipo- an actual temperature at the polar cap depends on the
dalspotswithrespecttothemaximumpossiblefluxthat magnetic field strength in that region, and thus on the
isobservedwhentheprimaryspotisviewedface-on(Be- non-dipolar configuration. In general, there is no reason
loborodov 2002): that the configuration of the magnetic field at two op-
f = cosi(cid:0)1− rg(cid:1)+ rg, if cosi>− rg posite polar caps should be similar. Therefore, for the
f12 = −cosi(cid:0)1−RrRg(cid:1)+RrRg if cosi< (R(R−rg−rgr)g,) (4) gtoeoumseetarythorfeePScoRmBp1o1n3e3n+t fi16t:tthweobbelsatcksobloudtyionanwdopuoldwebre-
law components. Unfortunately, the count statistics is
here rg = 2GM/c2 is the Schwarzschild radius and cosi notenoughtoperformsuchafit. Ontheotherhand, we
is the cosine of the angle between the magnetic axis and can use the pulsed fraction information from the timing
the line of sight (see, e.g., Szary 2013). Note that when analysis to answer the question of the origin of the ther-
−rg/(R−rg)<cosi<rg/(R−rg) both spots are seen mal emission. The pulsed fraction in the 0.5−1.2keV
andtheobservedfluxfractionisfmin =f1+f2 =2rg/R. energy range decreases by about 10% with respect to
the neighboring energy ranges (see Table 5). This sug-
3.3. PSR B1133+16
gests that the pulsed fraction of thermal emission is be-
XMM-Newton observation of PSR B1133+16 9
Itindicatesthepossibilitytoformanacceleratingpoten-
tial gap above the polar cap. It can generally be stated
this recent XMM-Newton observation of PSR B1133+16
supports the ideas on which the PSG model of the inner
accelerating gap physics are based.
Ontheotherhand, however, wehavetonotethelarge
systematic uncertainty in the analysis of X-ray data of
pulsars. The X-ray spectrum of pulsars can be inter-
preted in the framework of a completely different fam-
ily of models, i.e. the neutron star atmosphere models.
In such models the thermal component is emitted from
a very thin, ∼ 0.1−10cm, neutron star surface layer.
Light-element atmosphere models result in a tempera-
ture T that is significantly lower than the blackbody
atm
temperatureT ,withatypicalratioofT /T ∼2−3
bb bb atm
and considerably larger emitting area, by a factor of
∼50−200(see,e.g.,Pavlovetal.1996,2001;Ponsetal.
2002; van Adelsberg & Lai 2006). The atmosphere mod-
els are used to study the thermal evolution of neutron
Figure 8. Diagramofthesurfacetemperature,Ts,vs. thesurface
magnetic field, Bs. The dashed line represents the dependence of stars,toconstraintheequationofstateandcomposition
Tcrit onBs accordingtoMedin&Lai(2007),andthegrayregion ofthesuperdensematterintheneutronstarinteriorand
corresponds to uncertainties in the theoretical predictions. Error other issues beyond the scope of this paper. Note that
bars correspond to 1σ. Pulsars: (1) J0108-1431, (2) B0355+54,
if the outer layers of a neutron star consist of light ele-
(3) B0628-28, (4) J0633+1746, (5) B0834+06, (6) B0943+10,
(7) B1133+16, (8) B1451-68, (9) B1719-37, (10) B1929+10, (11) ments, the formation of PSG is not possible due to the
J2021+4026,(12)J2043+2740,(13)B2224+65 low cohesive energy of the ions (Medin & Lai 2007). In
(seeBecker2009;Szary2013,andreferencestherein). such a case, SCLF can be responsible for plasma gener-
low 30%. The predicted pulsed fractions of the thermal ation and acceleration.
component (see Table 6) suggest that thermal radiation The X-ray data of PSR B1133+16, whose analysis is
originates from both primary and antipodal polar caps. presented here, were obtained in an XMM-observation
We found that regardless of the assumed source of radi- carriedoutsimultaneouslywithradioobservationsofthis
ation (primary, antipodal, or two hot spots), the prop- pulsar that employed the GMRT, Effelsberg, Kunming,
erties of blackbody radiation, Ts ≈2.9MK, Rpc ≈14m, andtheLOFARradiotelescopes. Inaforthcomingpaper
and the derived surface magnetic strength at the pole, wewillpresentadetailedtiminganalysisofradioandX-
Bs ≈3.9×1014G, are in full agreement with the predic- ray data and discuss further conclusions.
tions of the PSG model (see Figure 8).
4. CONCLUSIONS Thispaperisdedicatedtothememoryofourcolleague,
the late Professor Janusz Gil, who pioneered the PSG
ThespectrumofB1133+16canbewelldescribedbya
single PL component (see Table 4). The ∼70◦ misalign- model and many other seminal works in Pulsar Astro-
physics. ThisworkissupportedbyNationalScienceCen-
mentbetweenX-rayandradiopeaksconfirmsanonther-
tre Poland under grants DEC-2012/05/B/ST9/03924
mal origin of the X-ray pulsed emission. In the energy
and DEC-2013/09/B/ST9/02177 and by the Nether-
rangeof0.5−1.2keV,boththedelayfromtheradiopeak
lands Organisation for Scientific Research (NWO) under
and the pulsed fraction are significantly lower than in
project ”CleanMachine” (614.001.301). RXX acknowl-
the neighboring energy ranges. This suggests the pres-
edges supports from NSFC (grant No. 11673002 and
ence of an additional component, namely the thermal
U1531243). We thank the Jodrell Bank Pulsar Group
emission with considerably smaller pulsed fraction than
fortheupdatedephemerisobtainedwiththeLovellTele-
the nonthermal component. To produce thermal emis-
scope funded by the STFC. We thank the anonymous
sion with a relatively low pulsed fraction, radiation has
referee for constructive comments that helped us to im-
to originate from two polar caps (see Figure 7). The
prove the paper significantly. Special thanks to Jason
blackbody spectral fit indicates a surface temperature of
HesselsandBenjaminStappersforprovidinguswiththe
T = 2.9MK and a radius of the heated polar caps of
s necessarydatatoperformadjustmentofradioandX-ray
R ≈ 14m. Relating this radius to the radius given by
pc observations.
thelastopenfieldlineofthedipolarmagneticfieldcom-
ponentR ≈130m,thelocalpolarcapsurfacemagnetic
dp
field strength B ≈3.9×1014G. REFERENCES
s
The main conclusion from the XMM-Newton observa-
Arons,J.,&Scharlemann,E.T.1979,ApJ,231,854
tions of PSR B1133+16 can be drawn from Figure 8.
Becker,W.2009,AstrophysicsandSpaceScienceLibrary,357,91
One can see from the figure that most rotation powered
Beloborodov,A.M.2002,ApJ,566,L85
normal radio pulsars line within 1σ from the Medin-Lai Brisken,W.F.,Benson,J.M.,Goss,W.M.,&Thorsett,S.E.
critical value. The only exceptions are pulsars either 2002,ApJ,571,906
with a number of photons that is too low to reliable fit Cash,W.1979,ApJ,228,939
Geppert,U.,Gil,J.,&Melikidze,G.2013,MNRAS,435,3262
theirspectra(e.g.,B0834+06(No. 5),B1451-68(No. 8),
Geppert,U.,&Vigan`o,D.2014,MNRAS,444,3198
B1719-37(No. 9),andJ2043+2740(No. 12))orwithout
Gil,J.,Haberl,F.,Melikidze,G.,etal.2008,ApJ,686,497
anydetectedradioemission(e.g.,J2021+4026(No. 11)). Gil,J.,Melikidze,G.,&Zhang,B.2006a,ApJ,650,1048
10 Szary et al.
—.2006b,A&A,457,L5 Pavlov,G.G.,Kargaltsev,O.,Wong,J.A.,&Garmire,G.P.
Gil,J.,Melikidze,G.I.,&Geppert,U.2003,A&A,407,315 2009,ApJ,691,458
Harding,A.K.,&Muslimov,A.G.2001,ApJ,556,987 Pons,J.A.,Walter,F.M.,Lattimer,J.M.,etal.2002,ApJ,564,
Harding,A.K.,&Muslimov,A.G.2002,ApJ,568,862 981
Hermsen,W.,Hessels,J.W.T.,Kuiper,L.,etal.2013,Science, Ruderman,M.A.,&Sutherland,P.G.1975,ApJ,196,51
339,436 Stru¨der,L.,Briel,U.,Dennerl,K.,etal.2001,A&A,365,L18
Hibschman,J.A.,&Arons,J.2001,ApJ,554,624 SzaryA.,2013,PhDthesis,Univ.ZielonaG´ora
Kargaltsev,O.,Pavlov,G.G.,&Garmire,G.P.2006,ApJ,636, Szary,A.,Melikidze,G.I.,&Gil,J.2015,MNRAS,447,2295
406 Turner,M.J.L.,Abbey,A.,Arnaud,M.,etal.2001,A&A,365,
Kijak,J.,&Gil,J.1997,MNRAS,288,631 L27
Lyne,A.G.,&Manchester,R.N.1988,MNRAS,234,477 vanAdelsberg,M.,&Lai,D.2006,MNRAS,373,1495
Manchester,R.N.,Hobbs,G.B.,Teoh,A.,&Hobbs,M.2005, Zavlin,V.E.2007,ApJ,665,L143
AJ,129,1993 Zhang,B.,Sanwal,D.,&Pavlov,G.G.2005,ApJ,624,L109
Medin,Z.,&Lai,D.2007,MNRAS,382,1833
Pavlov,G.G.,Zavlin,V.E.,Truemper,J.,&Neuhaeuser,R.
1996,ApJ,472,L33
Pavlov,G.G.,Zavlin,V.E.,Sanwal,D.,Burwitz,V.,&Garmire,
G.P.2001,ApJ,552,L129