A ccepted for publication in A pJ Letters: M ay 22,2002
X M M -N ew ton observations of the neutron star X -ray transient
K S 1731{260 in quiescence
arXiv:astro-ph/0202398v2 22 May 2002
R udy W ijnands1;2,M atteo G uainazzi3,M ichielvan der K lis4,M ariano M endez5
A B ST R A C T
W e report on X M M -N ewton observations perform ed on 2001 Septem ber 13{
14 ofthe neutron star X -ray transient K S 1731{260 in quiescence. T he source
was detected at an unabsorbed 0.5{10 keV ux ofonly 4 8 10 14 erg cm 2
s 1,depending on the m odelused to t the data,w hich for a distance of7 kpc
im plies a 0.5{10 keV X -ray lum inosity of approxim ately 2 5 1032 erg s 1.
T he Septem ber 2001 quiescent ux ofK S 1731{260 is lower than that observed
during theC handra observation in M arch 2001.In thecooling neutron starm odel
for the quiescent X -ray em ission ofneutron star X -ray transients,this decrease
in the quiescent ux im plies that the crust ofthe neutron star in K S 1731{260
cooled dow n rapidly between the two epochs, indicating that the crust has a
high conductivity. Furtherm ore, enhanced cooling in the neutron star core is
also favored by our results.
Subjectheadings: accretion,accretion disks| stars:individual(K S 1731{260)|
X -rays: stars
1. Introduction
X -ray transients are characterized by long episodes (years to decades) ofvery low X ray lum inosities (1030 34 erg s 1) w ith occasionalshort (weeks to m onths) outbursts during
1
C enterforSpaceR esearch,M assachusettsInstituteofTechnology,77 M assachusettsA venue,C am bridge,
M A 02139-4307,U SA ;rudy@ space.m it.edu
2
C handra Fellow
3
X M M -N ew ton Science O peration C enter,V ILSPA -ESA ,A partado 50727,E-28080 M adrid,Spain
4
A stronom icalInstitute \A nton Pannekoek",U niversity ofA m sterdam ,K ruislaan 403,N L-1098 SJ A m sterdam ,T he N etherlands
5
SR O N ,N ationalInstitute for Space R esearch,Sorbonnelaan 2,3584 C A ,U trecht,T he N etherlands
{2{
w hich they can be detected at lum inosities of1036 39 erg s 1 (e.g.,C hen,Shrader,& Livio
1997). T he huge increase in lum inosity is thought to be due to a correspondingly large
increase in the m ass accretion rate onto the com pact object in those system s,although the
exact m echanism s behind the outbursts are not fully understood (Lasota 2001). Sim ilarly,
theexactorigin ofthequiescentX -ray em ission rem ainselusive. Forthosesystem sharboring
a neutron star,ithasbeen argued (e.g.,C am pana etal.1998b;Brow n,Bildsten,& R utledge
1998) that the observed em ission below a few keV originates from the neutron star surface:
the neutron starcore isheated by the nuclearreactionsoccurring deep in the crustw hen the
starisaccreting and thisheatisreleased astherm alem ission during quiescence. T heem ission
above a few keV (as observed in severalsystem s;e.g.,A saiet al. 1996,1998;C am pana et
al. 1998a,2000) cannot be explained by this m odel. M odels proposed for this com ponent
include residualaccretion eitheronto the neutron starsurface ordow n to itsm agnetospheric
radius,ortheradio pulsarm echanism (e.g.,C am pana etal.1998b;C am pana & Stella 2000).
A sub-class oftransients are characterized by very long accretion episodes ofyears to
decadesinstead ofweeksto m onths. R ecently,one ofthose system s(K S 1731{260)suddenly
turned o after having actively accreted for over 12.5 years. A C handra observation taken
a few m onths after this transition showed the source at a 0.5{10 keV lum inosity of 1033
erg s 1 (W ijnands et al. 2001),assum ing a distance of7 kpc (M uno et al. 2000). If the
cooling neutron star m odel is responsible for the quiescent em ission in this system , then
it should be in quiescence between outbursts for > 1000 years, assum ing alloutbursts are
sim ilar to the one observed and standard cooling processes (e.g.,m odi ed U rca;C olpietal.
2001;U shom irsky & R utledge 2001) occur in the neutron star core. H owever,R utledge et
al. (2002) argued that for system s like K S 1731{260,the long accreting episodes w illheat
the crust to high tem peratures and it m ight take years to decades for the crust to com e
into therm alequilibrium w ith the core. U ntilthis happens,the quiescent em ission w illbe
dom inated by the therm alstate ofthe crustand notthatofthe core. R utledge etal.(2002)
calculated crustcooling tracksforthissourceassum ing di erentscenariosofthem icrophysics
involved (the heat conductivity ofthe crust;standard vs. \enhanced" core cooling).
Burderiet al. (2002) reported on a BeppoSA X observation ofK S 1731{260 perform ed
a few weeks before the C handra observation. T hey detected K S 1731{260 ata lum inosity of
atm ost 1033 erg s 1.In addition to the cooling neutron starm odel,they discussed several
alternative explanations for the observed quiescent em ission (such as residualaccretion or
the onset of the radio pulsar m echanism ). By considering those alternative m odels, they
were able to set an upper lim it of1 4 109 G auss on the m agnetic eld strength ofthe
neutron starin K S 1731{260.H ere we reporton X M M -N ewton observationsofK S 1731{260
taken approxim ately halfa yearafterthe C handra and BeppoSA X observations. W ith these
X M M -N ewton observationswe areableto study thetim eevolution ofthequiescentem ission.
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2. O bservation, analysis, and results
W e have analyzed X M M -N ewton observationsofK S 1731{260 perform ed on 13 Septem ber 2001 01:54{09:01 U T C and 13{14 Septem ber 2001 22:43{05:58 U T C .A llinstrum ents
were active; here we only discuss the data as obtained w ith the three European Photon
Im aging C am era (EPIC ) instrum ents (due to the very low ux of the source, it was not
detected in the RG S instrum ent). T he two EPIC M O S cam eras and the EPIC pn cam era
operated in fullw indow m ode w ith the thin opticalblocking lter. To analyze the data,
we used the Science A nalysis System (SA S6;version 5.2). W e used the calibrated pipeline
product data to extract im ages,light curves,and spectra using the tools available in SA S.
Severalbackground ares occurred during our observations,w hich were ltered out before
analyzing the data to m inim ize the e ectsofthose strong background areson the quality of
the X -ray spectra;we did notuse those data during w hich the countrate exceeded 7 counts
s 1 forthe M O S cam eras(using tim e binsof10 seconds)and 20 countss 1 forthepn cam era
(also using 10 seconds tim e bins). T hese criteria resulted in a totalgood tim e of 23 ksec
for the pn cam era and 33 ksec for both M O S cam eras. N o di erence in the count rates
between the two X M M -N ewton observations was observed,and,therefore,we com bined the
data ofboth observations to increase our sensitivity.
W e com bined the data ofthe three EPIC cam erasto create one im age ofthe eld ofK S
1731{260,representing the m ost sensitive im age ofthis region so far obtained. In Figure 1,
we show both the C handra/A C IS-S (left)and the X M M -N ew ton/EPIC (right)im agesofK S
1731{260.T heC handra im agewasrebinned by a linearfactorof8 to obtain roughly thesam e
pixelsize as thatofthe X M M -N ewton im age (3.9500 forthe C handra im age vs. 4.3500 forthe
X M M -N ewton im age)and both im ages have been sm oothed using a G aussian function w ith
a w idth equalto the pixelsize ofthe im age. W e clearly detected K S 1731{260 togetherw ith
the nearby star 2M A SSIJ173412.7{260548 (Fig.1 right),both ofw hich were also detected
during the C handra observation (Fig.1 left;W ijnands et al. 2001). To allow for a visual
com parison,we used a scaling such thatthe appearance ofthis2M A SS starisvery sim ilarin
both im ages (below we w illshow that the ux ofthis star is consistent w ith being constant
between the two observations). A com parison ofthe im agesindicatesthatK S 1731{260 has
decreased in lum inosity between the C handra and X M M -N ewton observations. In principle,
system atic e ects due to the di erence in the energy response ofthe instrum ents and the
di erent X -ray spectra ofthe two detected sources m ight be responsible for this dim m ing
ofK S 1731{260 relative to the 2M A SS star. H owever,below we show that the decrease in
lum inosity as observed for K S 1731{260 is real.
6
See http://xm m .vilspa.esa.es/user/sastop.htm l
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2.1. T he source spectra
T he spectrum of K S 1731{260 in each EPIC cam era was extracted using a circle of
15 in radius on the source position. T he background spectra were extracted from a circle
w ith a radius of 5000 close to K S 1731{260 (di erent background regions resulted in very
sim ilar results) w hich did not contain any other point source (the standard practice ofusing an annulus around the source position as background could not be used because ofthe
presence ofthe 2M A SS source 3000 away from K S 1731{260).T he extracted spectra were
rebinned using the FT O O LS routine G R PPH A into bins w ith a m inim um of10 counts per
bin. W e used the ready-m ade response m atrices provided by the calibration team (available
at http://xm m .vilspa.esa.es/ccf/epic/). W e tted the three spectra sim ultaneously using
X SPEC version 11.1 (A rnaud 1996).W e used severalm odelsto tthe data,and the neutral
hydrogen colum n density N H waseither xed to 1:1 1022 cm 2 (see,e.g.,Barretetal.1998
or N arita et al. 2001) or left as a free param eter. A llsingle-com ponent m odels resulted in
acceptable ts. C urrently, the two m odels m ost often used to t the quiescent spectra of
neutron starsystem sare the blackbody and the neutron staratm osphere m odels. T herefore,
we concentrated on those m odels,w ith the neutron star atm osphere m odelbeing that described by Zavlin,Pavlov,& Shibanov 1996 (the non-m agnetic case). In certain system s,a
power-law tailabove a few keV wasfound,and although such power-law com ponentwasnot
required by the data,we tted the spectra w ith the above two m odelsincluding a power-law
com ponent w ith a photon index of1 or 2 to obtain an upper lim it on this com ponent.
00
T he spectralresults are listed in Tab.1 and the pn spectrum is show n in Fig.2. W e
have also plotted the spectrum obtained w ith C handra (W ijnands et al. 2001),w hich again
suggests that the source was fainter during our X M M -N ewton observation than during the
C handra observation. W hen left free,N H was consistent w ith the value previously obtained
w ith other instrum ents, although for the atm osphere m odel a slightly higher value was
preferred, resulting in a slightly higher unabsorbed ux com pared to the xed N H case.
W hen N H was xed,the atm osphere m odelm easured a sim ilar ux asthe blackbody m odel,
5 10 14 erg cm 2 s 1 (unabsorbed and for 0.5{10 keV ). To obtain the errors on the
uxes, we have calculated the 1 error contours for the tem perature and norm alization,
xing N H at the value in Table 1 in each case,and obtained the uxes associated w ith the
circum ference ofthe error ellipse. T he tem perature kT and N H are strongly correlated in
the ts,and w hen both are free no usefulconstraints could be obtained on the unabsorbed
ux. T he best- t tem perature was in allcases 0.3 keV for the blackbody ts and 0.1
keV for the atm osphere m odel. In the latter m odel,the neutron star radius could not be
constrained and was xed to the best t radius of15 km (at in nity;the other param eters
are not very sensitive to its actualvalue). W hen including a power-law com ponent in the
t,it could not be detected signi cantly and its 0.5{10 keV ux could be constrained to be
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less than 25% ofthat obtained from the blackbody or atm osphere com ponent.
T he im ages and spectra ofK S 1731{260 both indicate that the ux decreased between
the two observation epochs.To investigate w hethertheapparent ux decrease isstatistically
signi cant, we have tted the C handra and X M M -N ewton data sim ultaneously. W hen all
spectral param eters were tied between the two data sets, a blackbody t is statistically
unacceptable,w ith 2 = 83 for38 degreesoffreedom ,corresponding to a probability ofonly
3 10 5 that the source did not change. W e obtained a sim ilar result w hen we used other
m odels (e.g.,atm osphere m odels) instead ofa blackbody. W hen we did not tie the spectral
param eters(exceptN H w hich wasassum ed to be constant),we obtained acceptable ts.T he
t results using a blackbody or an atm osphere m odelare listed in Table 1. In allcases,the
ux di erence between the C handra and X M M -N ewton data issigni cantata 3 to 4 level.
A lthough this show s that the ux ofK S 1731{260 decreased,this could conceivably be
due to a calibration error in one or both ofthe instrum ents. A lthough this is unlikely (e.g.,
Ferrando et al. 2002;W eisskopf et al. 2002),we can perform a check on this in the sam e
data set by analyzing the data ofboth instrum ents ofthe 2M A SS star assum ing that the
star has a constant spectrum . To this end, we have extracted the spectra of this source
from the C handra and X M M -N ewton data.W e tted allobtained spectra ofthe 2M A SS star
sim ultaneously keeping allspectralparam eterstied between both instrum ents(notethatdue
to low statistics the C handra data alone did not allow to constrain the source spectrum ).
Either a blackbody or a power-law spectrum tthe data well,yielding a probability ofonly
0.12 (blackbody m odel)or0.09 (power-law m odel)thatthe ux ofthe 2M A SS starchanged
by the sam e factor (a factor of3.5) as we observed for K S 1731{260.Furtherm ore,a recent
cross calibration study between X M M -N ewton and C handra (Snow den 2002)indicates that,
forsourcesw ith di erent intrinsic spectra,the m easured uxes ofboth instrum ents agree to
w ithin 10% . Both these results reinforce the idea that,the ux decrease we observed in K S
1731{260 is real,and not due to calibration problem s in any ofthe two instrum ents.
In thecooling neutron starm odel,this ux decreaseisdueto a tem peraturedecrease.To
investigate this,we tted the two data sets sim ultaneously w ith a blackbody m odel,letting
kT oat between the two observations,but keeping the sam e N H and em itting radius. T his
0:06
resulted in a kT of0:33+ 0:
05 and 0.27 0.04 keV forC handra and X M M -N ewton,respectively.
T he error ellipse ofthe two tem perature param eters (Fig.3) exclude the line kTC handra =
kTX M M N ew ton ,w hich show s that in the constant-radius blackbody m odela system atically
lower kT is preferred to t the X M M -N ewton spectrum than the C handra one,suggesting
that the tem perature decreased between the two epochs. T he resulting uxes are 11 2
(C handra)and 4.8 0.8 10 14 erg cm 2 s 1(X M M -N ewton). T hisresults in a ux decrease
between the two data sets of6 2 10 14 erg cm 2 s 1,w hich is signi cant at the 3 level.
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3. D iscussion
W e have reported on X M M -N ewton observations perform ed on 2001 Septem ber 13{14
ofthe neutron star X -ray transient K S 1731{260 w hen it was in quiescence. W e detected
the source at an unabsorbed 0.5{10 keV ux of 4 8 10 14 erg cm 2 s 1,w hich for a
distance of7 kpc im plies a 0.5{10 keV lum inosity of 2 5 1032 erg s 1,depending on
the m odelused to tthe data.T hislum inosity islowerthan w hathasbeen reported forthe
source during the C handra observation perform ed about halfa year earlier (W ijnands et al.
2001;R utledge etal. 2002).K S 1731{260 isnotthe only system forw hich X -ray variability
in quiescence hasbeen observed. Severalotherneutron starsystem shave also been found to
be variable in quiescence by factorsof3 to 5 on tim e scalesofdaysto years(see U shom irsky
& R utledge 2001 for a sum m ary ofthe observed variability).
Itisexpected thatatsom eleveltheneutron starin K S 1731{260 should em itX -raysdue
to the therm alcooling ofthe neutron star core. O ur low X -ray ux provides an upper lim it
to the therm al ux from the core. Ifthe crust ofthe neutron star has a higher tem perature
than the core (R utledge et al. 2002 argued that the crust should be considerably hotter
than the core due to the prolonged accretion episode ofK S 1731{260) and/or ifadditional
X -ray production m echanism s are at work in the system (e.g., residual accretion, radio
pulsar m echanism ), then the therm al ux related to the core w ill be even lower. Based
on the Brow n et al. (1998) m odel and assum ing standard core cooling, W ijnands et al.
(2001) already calculated that K S 1731{260 had to be in quiescence for over a 1000 years
between outbursts in order to em it at the low ux levelm easured w ith C handra (see also
R utledge et al. 2002 or Burderi et al. 2002). H owever, for the factor of 2 to 4 lower
quiescent lum inosity we observed w ith X M M -N ewton, this inferred cooling tim e increases
by approxim ately the sam e factor. T his would m ake the quiescent intervals ofK S 1731{260
extrem ely long. H owever, if we assum e that enhanced cooling takes place in the neutron
star core (e.g.,due to enhanced neutrino production),this inferred quiescent intervalwould
decrease considerably,m aking it m ore sim ilar to that ofthe ordinary transients.
In the cooling neutron starm odel,the variability we observe would have to be explained
by assum ing thattheneutron starsurfacehascooled between theC handra and X M M -N ewton
observations. In the previous section we have presented evidence that the m easured tem perature decreased,supporting thisinterpretation. ForK S 1731{260,R utledge etal.(2002)
calculated four crust cooling curves assum ing di erent values of the crustal conductivity
and the di erent cooling processes in the core ofthe neutron star (standard vs. enhanced
cooling).A com parison ofthe observed decrease in lum inosity w ith those cooling curves(see
Figure 3 in R utledge et al. 2002),suggests that our data are only consistent w ith a highly
conductive crust,and likely also enhanced core cooling occurs. For a low heat conductivity
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in the crust, the X -ray lum inosity of the system should rem ain constant or even increase
slightly,in contrast to w hat we observed. For a highly conductive crust but only standard
core cooling a decrease in lum inosity isalso predicted,butby an am ountthatislessthan we
have observed. H owever ouruncertainties in the actuallum inosity decrease are considerable
and our data m ight still be consistent w ith this possibility. A s explained above, the low
m easured ux ofthe system by itselfalready suggests that enhanced core cooling occurs.
In order to calculate the cooling curves, R utledge et al. (2002) assum ed quiescent
episodesforK S 1731{260 of1500 years,w hich wascalculated assum ing standard corecooling.
H owever,ifenhanced core cooling occurs,the neutron star core can coolm ore rapidly than
assum ed and the system could have quiescent episodes ofonly yearsto decades. T hishasto
be taken into accountin the m odeling ofthe cooling curves. A lthough the exactim plications
are unclear,our conclusion that the crust has to be highly conductive to explain the rapid
cooling ofthe crust isunlikely to change. T herefore,w ithin the cooling neutron starm odel,
ournew resultsindicate thatthe neutron starin K S 1731{260 hasa highly conductive crust
and enhanced cooling is likely to occur in its core. C olpiet al. (2001) suggested that w hen
the m ass ofthe neutron star exceeds 1:6 M ,such enhanced core cooling m ight occur.
A m assive neutron star in K S 1731{260 is not unexpected because a signi cant am ount of
m atter m ust have been accreted in order for the neutron star to be spinning rapidly. A fast
spinning neutron star(w ith a spin frequency of 524 H z)in K S 1731{260 hasbeen inferred
from the burst oscillations detected in this system (Sm ith,M organ,& Bradt 1997).
A lternative m odels explaining the quiescent em ission in neutron star X -ray transients
have to be considered aswell. In m odelsassum ing thatthe em ission isdue to residualaccretion onto the neutron starsurface,eitherdirectly orvia leakage through the m agnetospheric
barrier,or dow n to the m agnetospheric radius,the detected lum inosity decrease can be explained by assum ing that the accretion rate has decreased considerably. T hese alternative
m odelswere discussed in detailby Burderietal.(2002)and because the lowerlum inosity of
K S 1731{260 doesnotstrongly a ecttheirconclusions(an upperlim iton the m agnetic eld
strength ofthe neutron star can be obtained that is a factor 2 lower),we w illnot discuss
those m odels here in detail. N ote,thatifthe lum inosity is indeed due to residualaccretion,
the decrease in accretion rate inferred from ourlum inosity decrease m ightcause a change in
the X -ray production m echanism due to the factthatthe m agnetospheric radiusm ightm ove
outside the co-rotation radius or outside the light cylinder (see also Burderiet al. 2002).
W ith furtherm onitoring observationsofK S 1731{260 in quiescence,the quiescentpropertiesofthissource and theirtim e evolution w illbe betterconstrained. M ore detailed observationsofotherquiescent neutron starsystem s w illhelp to understand how sim ilarthey are
to K S 1731{260. So far,at least two other system s have been identi ed w ith sim ilar prop-
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erties: X 1732{304 (W ijnands,H einke,& G rindlay 2002)and 4U 2129+ 47 (W ijnands 2002;
N owak,H einz,& Begelm an 2002). T hose system s also have very long outburst durations,
and from their quiescent properties it has been inferred that they should be in quiescence
for hundreds ofyears ifonly standard neutron star core cooling occurs. T his spurred W ijnands et al. (2002) to suggest that in the standard cooling scenario a correlation between
the duration ofthe outburst episodes and that ofthe quiescent intervals m ight be required.
H owever, such a correlation is di cult to understand in accretion disk instability m odels
(Lasota 2001). T his could indicate that enhanced cooling takes place in the neutron star
cores ofthose system s (W ijnands etal. 2002).O urresults indicating thatenhanced cooling
m ay occur in the neutron star core ofK S 1731{260 lends further support to this idea.
W e thank X M M -N ewton project scientist Fred Jansen for scheduling the observations
used in this Letter. RW was supported by N A SA through C handra PostdoctoralFellow ship
grant num ber PF9-10010 awarded by C X C , w hich is operated by SA O for N A SA under
contractN A S8-39073.T hisresearch hasm adeuseofthedata and resourcesobtained through
the H EA SA RC online service,provided by N A SA -G SFC .
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T his preprint was prepared w ith the A A S LATEX m acros v5.0.
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Fig.1.| T heC handra/A C IS-S (left;rebinned by a factorofeight)and X M M -N ewton (right;
theM O S1,M O S2,and pn arecom bined to producethisim age)im agesofK S 1731{260.Both
im ageshave been convolved w ith a G aussian function w ith a w idth equalto the im age pixel
sizes. T he source in the center is K S 1731{260 and the other source to the right bottom is
2M A SSIJ173412.7{260548.T he im ages were scaled in such a way that the constant source
2M A SSI J173412.7{260548 has roughly the sam e appearance in both im ages,to show the
decrease in lum inosity ofK S 1731{260.
{ 11 {
Chandra/ACIS-S
XMM-Newton/EPIC-PN
Fig. 2.| T he C handra/A C IS-S (top spectrum ;see also W ijnands et al. 2001) and X M M N ewton/EPIC -pn (bottom ) quiescent spectra ofK S 1731{260.T he solid lines represent the
best blackbody ts to the data.
{ 12 {
Fig. 3.| T he error ellipse ofthe C handra tem perature kTC handra versus the X M M -N ewton
tem perature kTX M M N ew ton . T he m odel used in X SPEC was the bbodyrad m odel. T he
plus represent the best t value. T he ellipses are for 1,2,and 3 con dence level(for two
param eters). T he solid line is the line kTC handra = kTX M M N ew ton .
{ 13 {
Table 1. Spectralresults
Param eter
X M M -N ewton data
Blackbody
H ydrogen atm osphere
0:6
0:3
N H (1022 cm 2)
1:1+ 0:
1.1 ( xed) 1:3+ 0:
1.1 ( xed)
4
4
+ 0:06
+ 0:04
+ 0:03
04
kT (keV )
0:30 0:05
0:30 0:03 0:11 0:04
0:12+ 0:
0:02
1:0
2:3
3
F
4.8+ 0:
4.8 1.0
7:4+ 1:
5:6+ 1:
9
6
1:1
2
/dof
15.7/23
15.8/24
15.9/23
16.0/24
C om bined C handra and X M M -N ewton data
Param eter
Blackbody
H ydrogen atm osphere
+ 0:4
22
2
N H (10 cm )
0:9 0:3
1.1 ( xed) 1.0 0.2 1.1 ( xed)
0:04
0:04
03
kTX M M N (keV ) 0.31 0.05 0:30+ 0:
0:14+ 0:
0:12+ 0:
03
05
0:02
0:06
0:03
kTC handra (keV ) 0:29+ 0:
0.27 0.03 0:11+ 0:
0.11 0.02
05
04
+ 0:7
+ 1:2
FX M M N
3:8 0:5
5 1
5:0 0:8
6 1
+3
+4
+4
F C handra
13 2
17 3
18 3
20+ 54
F
9 + 23
12+ 34
13+ 34
14+ 54
2
/dof
23.8/36
24.6/37
23.2/36
23.1/37
N ote: T he error bars represent 90% con dence levels,except for
the uxes forw hich the errors represent 68% con dence levels. T he
uxesareunabsorbed,in the0.5{10 keV range,and in unitsof10 14
erg cm 2 s 1. For the blackbody we used the bbodyrad m odelin
X SPEC .For the hydrogen atm osphere m odelwe used the m odelof
Zavlin et al. 1996 (the non-m agnetic case) and for this m odelthe
neutron star m ass was xed to 1.4 M ,its radius at in nity to 15
km ,the distance was assum ed to be 7 kpc,and the tem perature is
for an observer at in nity