Pulse phase and precession phase resolved spectroscopy of Her X-1: studying a representative Main-On with RXTE

0.62 MB·English

by  D. Vasco

Astronomy&Astrophysicsmanuscriptno.pprs˙davide˙18Dec12 (cid:13)c ESO2013
January16,2013
Pulse phase and precession phase resolved spectroscopy of
Her X-1: studying a representative Main-On with RXTE
D.Vasco1,R.Staubert1,D.Klochkov1,A.Santangelo1,N.Shakura2,andK.Postnov2
1Institutfu¨rAstronomieundAstrophysik,Universita¨tTu¨bingen,Sand1,D-72076Tu¨bingen,Germany
2SternbergAstronomicalInstitute,LomonossovUniversityMoscow,Russia
e-mail:[email protected]
November2012
3
1 ABSTRACT
0
2 Aims.WeperformedadetailedpulsephaseresolvedspectroscopyoftheaccretingbinaryX-raypulsarHerX-1intheenergyrange
3.5–75keV and have established pulse phase profiles for all spectral parameters. For three parameters, the centroid energy of the
n cyclotronline,thephotonindexandthefluxofthe6.4keVironline,wehavestudiedthevariationasafunctionof35dphase.
a Methods.WeanalyzedRXTEobservationsoftheMain-OnofNovember2002usingdatafromthePCAandtheHEXTEinstruments.
J Fourdifferenttimeintervalsofabout∼1ddurationwereselectedtoprovideagoodcoverageofacompleteMain-On.Theintervals

5 arecenteredat35dphases0.03,0.10,0.15,and0.20,respectively.
1 Results.Allspectralparametersshowastrongmodulationwithpulsephase.Whilethecentroidenergyofthecyclotronlinefollows
roughlytheshapeofthepulseprofile,showinghighervaluesclosetothepeakoftheX-raypulse,boththephotonindexandtheiron

] lineintensityexhibitdistinctminimaaroundthepeakoftheX-raypulse.Withrespecttovariationsoftheobservedprofileswith35d
E
phase,wefindthatthereisaclearevolutionoftheshapeofthepulseprofiles(fluxversuspulsephase),amoderateincreaseofthe
H maximumcyclotronlineenergy(foundaroundpulsephase0.7),butnosignificantevolutionoftheshapeofthepulsephaseprofiles
. ofthecyclotronlineenergy,thespectralpowerlawindexortheironlineintensity.
h Conclusions.Thevariationofspectralparametersasafunctionofthepulsephaseprovidesimportantinformationaboutthesystem:i.
p thedisappearanceoftheFelinefluxnearthehighestcontinuumfluxmaybeanindicationofahollowconegeometryoftheaccretion
- structure;ii.Theapparentnon-dependenceofthecyclotronlineenergyprofileson35dphaseprovidesanewpossibility totestthe
o
modeloffreeprecessionoftheneutronstar,proposedtoberesponsibleforthesystematicvariationsinthepulseprofiles.
r
t
s Keywords.binaries:general–stars:neutron–X-rays:binaries–X-rays:individuals:HerX-1–pulsars:individuals:HerX-1
a
[

1 1. Introduction cycle is responsible for the Short-On with a maximum flux of
v roughlyonethirdthatoftheMain-On.
8 The X-ray source Her X-1 was discovered in 1972 by Uhuru
HerX-1was also the firstaccretingX-raypulsarforwhich
7 (Tananbaumetal.1972),andclassifiedasanaccretingX-raybi-
a cyclotron line in the X-ray spectrum has been discovered
3 nary. Her X-1 is one of the brightest and most studied persis-
3 tentbinaryX-raypulsars.Thedistancetothesystemis ∼7kpc (Tru¨mperetal.1978).Thisabsorption-likefeature,nowreferred
. to as Cyclotron Resonance Scattering Feature (CRSF), is ob-
1 and the masses of the neutron star and its companion are ap-
served around40keV and allows to estimate the neutronstar’s
0 proximately 1.5 M and 2.2 M , respectively (Reynoldsetal.
⊙ ⊙ magneticfield.ApplyingtheformulaB =(1+z)E /11.6keV
3 1997). The X-ray flux shows periodic modulation on several 12 cyc
1 different time-scales: pulsations with 1.24s due to the spin of (whereB12 isthemagneticfieldstrengthinunitsof1012Gauss,
v: the neutron star, eclipses due to the 1.7d orbital period, and a z is the gravitationalredshiftandEcyc is the centroidenergyof
thecyclotronline),thefirstdirectmeasurementofthemagnetic
i 35d super-orbitalperiod due to obscurationof the X-ray emit-
X fieldofaneutronstarwasachieved(∼3×1012GaussforHerX-
ting region by the precessing accretion disk. This 35 d period-
r icityshowsdifferentstates:twoOn-stateswiththe∼11dMain- 1). The source shows a positive correlation between the cen-
a On (at phase 0–0.31) and the ∼5d Short-On (at phase 0.57– troidenergyofthecyclotronlineandthebolometricluminosity
0.79),separatedbytwoOff-states(seee.g.Giacconietal.1973; (Staubertetal.2007;Vascoetal.2011).
Gerend&Boynton 1976; Boyntonetal. 1980; Scott&Leahy Another observational feature of Her X-1 is the evolution
1999; Scottetal. 2000; Klochkovetal. 2006). The accretion of the pulse profile as function of energy and time, or better:
disk is thought to be tilted (with respect to the orbital plane), 35d phase. For boththe Main-On and the Short-On,a system-
warpedandcounter-precessingwithasomewhatvariableperiod atic variation in the shape of the pulse profilesis found.These
of∼35d.Theonsetoftheflux(oftenidentifiedwith35dphase changesconsistofthedisappearingofsomefeaturesinthepulse
0.0)iscalledtheTurn-On(TO)andcorrespondstothetransition profilewithanincreaseinenergyand/ortime.Thesevariations
fromtheOff-statetotheMain-On.Atthistime,theouterrimof repeat systematically on a time scale of ∼35d. These changes
thediskclearstheviewtotheX-rayemittingregionclosetothe havebeenwellknownforsometime(seee.g.Deeteretal.1998;
polar caps on the surface of the neutron star, leading to an in- Scottetal. 2000; Tru¨mperetal. 1986). Recently, Staubertetal.
creaseinflux.Viceversa,thedeclineofthefluxtowardstheend (2010a,b,2012)onthebasisofRXTEobservations,gaveaquan-
oftheMain-Onisidentifiedwiththeinneredgeoftheaccretion titative description of these changes by providing a template,
diskblockingourviewtotheX-rayemittingregions.Asimilar which can be used to predict the shape of the profile in the 9–
1
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Table 1.SummaryofthefourintervalsoftheMain-Onof35d
cycleno.323.Thecolumnsare:thenumberoftheinterval,the
timeintervalinMJD,theexposuretime,thecorresponding35d
phaseinterval,andthecenterofthe35dphaseinterval.
Interval limits exposure limits center
MJD [ks] 35dphase 35dphase
1 52595.060−52596.743 25 0.007 − 0.056 0.03
2 52597.959−52598.719 25 0.090 − 0.112 0.10
3 52599.603−52600.726 25 0.137 − 0.161 0.15
4 52601.316−52602.406 28 0.186 − 0.217 0.20
13keVenergyrangeforany35dphaseduringtheMain-On.An
extensionofthisworkforotherenergyrangesandincludingthe
Short-Onisinpreparation.
Tru¨mperetal. (1986), on the basis of observations by
Fig.1.PCA lightcurveof theMain-Onofcycle323.Thegrey
Exosat, had proposed that free precession of the neutron star
zonesrepresentthefourintervalsusedforthisanalysis.Foreach
is responsible for those pulse profile changes, due to the vari-
intervalthecentered35dphaseisgiven.Detailsofthetimeand
ation of the angle of the line of sight to the X-ray emitting re-
35dphaseintervalsarelistedinTable1
gions on the surface of the neutron star. For Her X-1, the de-
.
pendence of the spectral parameters on pulse phase have been
observedby severalmissions. Early examplesare Pravdoetal.
(1978)withOSO8,Pravdoetal.(1979)andSoongetal.(1990)
with the A-4 experimentof HEAO-1 and McCrayetal. (1982)
with HEAO 2 the Einstein Observatory, Vogesetal. (1982)
with the MPE/AIT ballon experiment, Kahabka (1987) with
Exosat,Kunzetal.(1996)withMir-HEXE.Laterexamplesare
Endoetal. (2000) with ASCA, Zane&Ramsay (2001) with
XMM-Newton, Lutovinovetal. (2000) with the ART-P tele-
scopeonboardofGRANADAandKlochkovetal.(2008)with
INTEGRAL.
Inthisworkwepresentadeepinvestigationofthevariation
ofkeyspectralparametersasafunctionofpulsephasewiththe
finest resolutionso far and, for the first time, a discussion of a
possibleevolutionwith 35d phase.Changesofthespectralpa-
rameterswithpulsephasearequitecommonamongaccretingX-
raypulsarsandaregenerallyattributedtoachangeintheview-
ing angle of the accretion region (see e.g., Kreykenbohmetal.
2004andreferencestherein).Here,wefocusonthevariationof
the centroid energy E of the CRSF around 40keV, the pho-
cyc Fig.2. Mean 9-13keV pulse profiles of the four time intervals
ton index Γ and the iron line characteristics. We also address at different35d phases(see Table 1): Interval1 in black(solid
thequestionwhetherourdatasupportthefreeprecessionmodel
line), Interval 2 in green (dashed line), Interval 3 in red (dash
whichhasbeensuggestedtoexplainthevariationinshapeofthe
dottedline)andInterval4inblue(dashdotdotdottedline).For
pulseprofile.
general35ddependenceseeStaubertetal.(2010a,b).Astiming
reference for pulse phase zero we use the “sharp-edge” at the
trailingedgeoftherightshoulderofthemainpulsewhichleads
2. Observationsanddataanalysis
intoan eclipse likeminimum(Staubertetal. 2009b).Note that
TocarryoutthisanalysisweusedobservationsofHerX-1ofthe these pulse profiles are statistically so accurate that the uncer-
Rossi X-ray Timing Explorer(RXTE) performedin November taintiesaresmallerthanthelinewidth.
2002.Theseobservationscorrespondtocyclenumber323(cycle
numberingaccordingtoStaubertetal.2009b)centeredatMJD
∼52599.32 with an observed Turn-On of MJD 52594.80. The sin i=13.1831 lt-s and Tπ=52599.486440MJD. To align the
dataof thiscycleprovidethe bestcoverageofanyMain-Onof pulseprofiles,areferenceti2met =MJD52594.869900091and
0
Her X-1 observed with RXTE. Within this cycle, we sum up aspinperiodP =1.237761809swereused.As“pulsephase
spin
observations from four selected time intervals at different 35d zero” the sharp-edge feature at the trailing edge of the right
phasesin orderto have a goodcoverageof an entireMain-On, shoulderofthemainpeakwasused(seeStaubertetal.2009).
avoidingdipsandeclipses.Allintervalshaveadurationofabout The PCA was used in the energy range 3.5–60keV and
one day (details are givenin Table 1). Figure 1 shows the four HEXTEintheenergyrange20–75keV.Thedatahavebeenana-
intervalsselectedforthisanalysis. lyzedwithXSPEC12.6.01usingthehighecut2spectralmodel,
For barycentric and binary corrections orbital param-
eters and the ephemeris of Staubertetal. (2009) were 1 http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec
used: Porb=1.700167287s, P˙orb=+(2.8±0.2)×10−12ss−1,a · 2 http://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSmodelHighecut.html
2
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Fig.3.CyclotronlinecentroidenergyprofilesasfunctionofthepulsephaseforInterval1(topleft),Interval2(topright),Interval
3(bottomleft)andInterval4(bottomright).
powerlawcontinuumwithanexponentialcut-off.Thedifferen- included in the model: a multiplicativeGaussianoptical depth
tialphotonfluxf(E)isdescribedby: for the Cyclotron Resonant Scattering Feature (CRSF) and an
additiveGaussianemissionlinefortheironfluorescencefeature
f(E)= A E−Γ , ifE ≤Ecut (1) around 6.5keV. This model is the same one as used in earlier
(E−Γ·exp(cid:16)EE−fEolcdut(cid:17), ifE >Ecut aWnealhyasevse(csoeneseis.gte.,ntClyobfuorunndettahla.t2t0h0e2haingdhSetcauutbesrpteecttraal.l2m0o0d7e)l.
where Γ is the photon index, E is the cut-off energy and describesthespectrumofHerX-1best.Thediscontinuityofthis
cut
E is the e-folding energy. In addition, two line features are modelatthecut-offenergydoesnotconstituteaproblemandwe
fold
have verified that no systematic uncertaintiesare introducedin
estimating the spectral parameters. We used the PCA data up
to60keV,whichhasbecomefeasiblebynewresponsematrices
(PCA response v11.7, 2009 May 11). These high energy data
candefinitivelyimprovethephotonstatisticsatenergiesaround
andbeyondthecyclotronlinefeature.Thesamechoicehasbeen
used in previous analyses (see e.g. Ferrignoetal. 2011) and it
wasconfirmedbyRothschildetal.(2011)withRXTEobserva-
tionsofCenA.Therecorn3spectralcomponentwasalsoadded
to the model to normalize the background. After we had ver-
ified, that the energy and width of the iron K line is constant
(6.45keVand0.5keV,respctively),wefixedthosevaluesinor-
dertominimizethenumberoffreeparameters.GoodXenon4ob-
servationalmodesofthePCAforhighresolutionanalysiswere
usedtoexctractlightcurvesandspectra.Anadditionalsystem-
aticuncertaintyof1%wasaddedinusingthePCAdata.Toan-
alyze the data, version v6.11 of the HEASOFT software5 and
3 http://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/
Fig.4. The cyclotronline centroidenergyas functionof pulse
XSmodelRecorn.html
phase for the four different 35d phase intervals (see Table 1):
4 http://heasarc.gsfc.nasa.gov/docs/xte/abc/
Interval 1 in black (asterisks), Interval 2 in green (diamonds), pca issues.html#configs modes
Interval3inred(triangles)andInterval4inblue(squares). 5 http://heasarc.gsfc.nasa.gov/ftools/
3
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Fig.5.ThecyclotronlineprofilesofFig.3forthefour35dintervals(blackcrosses):Interval1(topleft),Interval2(topright),Interval3(bottom
left)and Interval 4(bottomright), normalized toacommon amplitude. Thebigredfilleddotsrepresent theweightedmean values of allfour
intervals.Thesolidbluelinerepresentsabestfitfunction(acombinationoftwocosinecomponents).Weconcludethat,withinthegivenstatistics,
thereisnoevidenceforanychangeinshapeoftheprofileswith35dphase.
backgroundestimationfilesSky VLEdated2005November28 3. Pulsephasevariability
were used.We have investigatedwhetherthere arecorrelations
Weconcentrateonthedetailedstudyofthevariationofthefol-
betweenthefitparameters:nodependenceofanysingleparam-
lowingspectralparametersasfunctionofpulse phase:the cen-
eterontheothershasbeenfound.Allspectralresultsstatedbe-
troidenergyE of thecyclotronline,the photonindexΓ, and
lowhavebeenobtainedthroughspectralfitswiththeassumption cyc
the intensity of the iron line at 6.4keV. The phase profiles of
of negligible absorption due to neutral hydrogen, both intrin-
sic to the source and interstellar (which is at 5.1 × 1019 cm−2, thesespectralparametersarecomparedwiththeshapeoftheflux
profiles(the”pulseprofiles”)forthefourdifferent35dphasein-
DalFiumeetal.1998).Theintroductionofabsorptionasafree
parameterdoesnotleadtoareductioninχ2. tervals. In Figure 2 the 9–13keV pulse profiles of the fourin-
tervalsare shown. Note that the pulse profilesare of such high
For the pulse phase resolved analysis, we have extracted statisticalqualitythattheuncertaintiesofthefluxvalues(ineach
the spectra in 14 pulse phase bins over the 1.24s pulse, the ofthe128pulsephasebins)arecomparabletothewidthofthe
widthsofwhichwerechosentohaveroughlyidenticalphoton- lineschosentoplottheprofiles.Theprofilesarerepeatedin the
statistics in each spectrum. The centers of the 14 phase bins followingfigures(asdashedlines)toallowadirectcomparison
are at pulse phases: 0.1, 0.3, 0.45, 0.55, 0.625, 0.675, 0.7125, with the profiles of the spectral parameters. For the remaining
0.7375,0.7625,0.7875,0.8250,0.8750,0.9250,and0.9750.For spectral parameters, such as the cut-off energy E , the fold-
cut
thecyclotronlineenergyEcycthisisthefinestresolutioninpulse ing energy Efold (with reference to the used spectral model -
phase everachieved(the foursmallest bins around the peak of highecut),andthewidthanddepthofthecyclotronline(σ
cyc
thepulsehaveawidthof1/80ofaphase). andτ ), we willrestrictourselvesto profilesofthe combined
cyc
Withthespectralfunctiondescribedabove,goodfitswithre- dataofcycle323.Fortheseparametersthestatisticsissuch,that
ducedχ2 between0.9and1.2aregenerallyachieved.However, nostatementscanbemadeaboutadependenceon35dphase.In
splittingupthedataintosmallpulsephaseintervalsrevealsthat allFigures,theuncertaintiesgivenareonesigma(68%)values.
larger χ2 values appear: up to ∼12 for the pulse phase range
0.775–0.85, and 1.4–2.8 for the pulse phase range 0.5–0.775.
3.1.Cyclotronlineenergy
Themainreasonforthisistheexistenceofthesocalled”10keV
feature”(seethediscussionin3.5).Modelingthisfeaturebyan The profiles of the cyclotron line energy E as a function
cyc
extra Gaussian is generally successful and brings the χ2 down of pulse phase are shown in Figures 3 and 4. Generally, E
cyc
toacceptablevalues(inafewcasesχ2 isstillfoundaround1.3, roughlyfollowsthe shape of the pulse profile:the broadmaxi-
whichis mostlikely dueto an imperfectmodelingby a simple mumisfoundtobeclosetothepeakofthepulseprofile(around
Gaussian). pulse phase 0.7) for all 35d phases. The formal uncertainties
4
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Fig.6. Photon-index profiles as function of pulse phase for Interval 1(topleft), Interval 2 (topright), Interval 3 (bottomleft) and Interval 4
(bottomright).
of E (as determinedby XSPEC) are of the orderof a few to 35d phase. The weighted mean values of the four highest val-
cyc
severalpercentforpulsephases0.0–0.6and0.9–1.0andaround uesofE ofeachgroupare40.16±0.22keV,40.89±0.20keV,
cyc
one percent or less for pulse phases 0.6–0.9 (close to the peak 41.02±0.15keVand41.52±0.20keVformean35dphases0.03,
of the pulse). Adoptingan additionalsystematic uncertaintyof 0.10, 0.15 and 0.20 (intervals 1 through 4), respectively. This
0.15keV(∼ 0.4%)foralldatapoints,theprofilesarewellrep- corresponds to an increase by ∼ 0.7keV per 0.1 units in 35d
resented by cosine functions (see below). We find slightly dif- phase.TheminimumE valueshavelargeruncertaintieswith
cyc
ferent values for the mean E and the peak-to-peak ampli- a tendency to decrease with 35d phase, but, within uncertain-
cyc
tude: a slight, but significant increase is found as function of ties,theyareconsistentwithaconstantvalue(around33.3keV).
Thepeak-to-peakamplitudeisthenslightlyincreasingwith35d
phase(withameanof∼7.6keV).
WhilethevaluesforthemaximumE andthepeak-to-peak
cyc
amplitudearedependenton35dphase,thesinusoidalshapeof
themodulationdoesnotchange.Inordertoverifythisstatement,
thefollowinganalysiswasperformed:theoriginalE profiles
cyc
(Figure 4) were scaled such that the separation of minimum to
maximumE hadaconstantvalueof7.64keV,usingthemin-
cyc
imum values measured in phase bin 0.2–0.4 and the weighted
mean of the four highest values in each of the four profiles as
reference.Inthisway,normalizedE profilesweregenerated.
cyc
ThesenormalizedprofilesareshowninFig.5,eachincompar-
isontotheweightedmeanvaluesandasmoothbestfitfunction
of the weighted mean: a combination of two cosine functions
with common mean (37.31keV), amplitude (3.82keV), period
and phase-zero values of 0.70 and 0.772 for pulse phases 0.3–
0.875 and 1.47 and 0.3 for the remaining phases, respectively.
Visually, there is no obvious deviation of any of the four data
setsfromtheweightedmean.Asquantitativestatisticaltest we
Fig.7. The photon index Γ as function of pulse phase for the performed the following: comparing the individual normalized
four different 35d phase intervals (see Table 1): Interval 1 in profiles with that profile representing the weighted mean leads
black (asterisks), Interval 2 in green (diamonds), Interval 3 in to χ2 values (normalized to the degrees of freedom) of 0.72,
red(triangles)andInterval4inblue(squares). 1.46, 0.72 and 1.32 for the four intervals, respectively. As an
5
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Fig.8.IronlineintensityprofilesasfunctionofpulsephaseforInterval1(topleft),Interval2(topright),Interval3(bottomleft)andInterval4
(bottomright).Allintensitieslessthan1.0areconsistentwithzero,wethereforeshowtwosigmaupperlimits.
additionaltest, we havethen performeda MonteCarlo simula- 3.3.Ironlineintensity
tion, in order to answer the following question. Assuming the
Anotherspectralparameterwhich showsa clearmodulationas
profiles are indeed the same for all fourintervals, that is equal
functionofpulsephaseistheironlineintensity(seeFigure8).
tothebestfitmeanprofile:whatistheprobabilitytofindanin-
Itshowsamoderateincreaseuntiltheleftshoulderofthepulse
dividualprofilewhichdeviatesfromthe meanprofileinsucha
waythattheχ2reachesorexceedstheobservedvalue?Wehave (phase∼ 0.7),afterwhichitdropsalmostto zeroaroundpulse
phase 0.8, before reaching the start value again at pulse phase
simulated 100 profiles for each of the fourintervals, reproduc-
0.9.TheminimumiscoincidentwiththepeakoftheX-raypulse
ing the statistical conditionsof each interval(that is, the width
of the Gaussian distribution from which the random numbers
weredrawnwerechosenaccordingtotheuncertaintyofthecor-
respondingmeasureddata point). Those probabilitiesare 68%,
29%,73%and4%forthefourintervals,respectively.Even4%
forInterval4isaratherhighandacceptableprobability.Wecon-
clude,that, within ourstatistical accuracy,we find noevidence
foranychangeintheshapeoftheE profileswith35dphase.
cyc
3.2.Photon-index
Figure6showstheprofilesofthephotonindexΓasfunctionof
thepulsephase.Thisspectralparameterisrelativelyconstantfor
pulsephasesupto0.6(showingasmallpositiveslope),buthas
adistinctdiparoundthepulsepeakandasmalleronearoundthe
leftshoulder.Thephoton-indecesrangebetween0.42±0.01and
1.07± 0.01forInterval1,between0.54±0.01and1.08±0.02
forInterval2,between0.36±0.01and1.10±0.49forInterval3
and between0.33±0.01and 1.07±0.01forInterval4. In gen-
eral,thespectrumgetsharderwhenthefluxincreases.Whilethe
mainfeaturesofthepulsephasedependenceofΓareverymuch Fig.9.Theironlineintensityprofilesforthefourdifferent35d
thesameinthefour35dintervals,thedepthofthenewnarrow phase intervals (see Table 1): Interval 1 in black (asterisks),
diparoundphase0.62showsacleartrendtowardssmallervalues Interval2in green(diamonds),Interval3in red(triangles)and
fromInterval1toInterval4(seeFig.7). Interval4inblue(squares).
6
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Fig.10.PulsephaseprofilesforthecutoffenergyE (topleft),thefoldingenergyE (topright),thewidthofthecyclotronlineσ (bottom
cut fold cyc
left),andthedepthτ ofthecyclotronline(bottomright)forthetotaldatasets.
cyc
(see Figure8 and 9) in a similarway as the photonindex.The to analysis with different spectral functions involving a power
ironlineintensityrangesbetween0(forallintervals)and 12.40 law (e.g., highecut,plcut,Fermi-Dirac or NPEX). The fea-
forInterval1,14.62forInterval2,13.19forInterval3and10.75 tureisthereforeconsideredtobeinherenttoaccretingX-raybi-
forInterval4.The profilesof35dintervals2–4are quitesimi- naries.Sofar,nophysicalexplanationhasbeensuggested.
lartooneanother,whileforInterval1,theironlineintensityis In our current analysis, using data from observations of
significantlylowerforpulsephases<0.6. HerX-1byRXTE,thisfeaturedoesnotplayaroleinthephase
averagedanalysis. However,in the pulse phaseresolvedanaly-
sis,largerχ2 valuesappearduetotheexistenceofthis”10keV
3.4.Otherspectralparameters
feature”: up to ∼12 for the pulse phase range 0.775–0.85, and
For the other spectral parametersE , E the width σ and 1.4–2.8forthepulsephaserange0.5–0.775.Modelingthisfea-
cut fold cyc
the depth τ , we show their pulse phase dependenceonly for turebyanextraGaussianisgenerallysuccessfulandbrings the
cyc
thetotaldatasets(notresolvedin35dphase),becauseinthese χ2 down to acceptable values (in a few cases χ2 is still found
parameters we find a considerably larger scatter, such that no around1.3, which is most likely due to an imperfectmodeling
conclusions can be drawn about a possible variation (or not) byasimpleGaussian).Thecentroidenergyisgenerallyfoundat
with 35d phase (the 35d phase resolved profiles can be found ∼ 16keVwithaσof∼ 5keV.Fig.11showsanexampleofthe
in Vasco 2012)6. The profiles are shown in Figures 10. Also spectrumofInterval3,pulsephasebin0.80–0.85,wheretheχ2
for these parameters there is significant modulation with pulse isreducedfrom5.55to1.38for224dof.Wehaveverified,that
phase, and they generally show a broad maximum around the allthe otherspectralparametersare notalteredwhenintroduc-
phaseofthepulsepeak,withtheinterestingfeaturethatforE ing this extra Gaussian. We note that this feature occurs most
fold
thereisadipinthismaximum,rightatthepulsepeak.Itisalso strongly at a pulse phase close to the peak of the pulse, where
worthnoting,that,exceptforE ,themeasuredvaluesforpulse all other spectral parameters also tend to show their strongest
fold
phases<0.4areratherhigh,notfollowingtheshapeofthepulse variability.
profiles.
4. Summaryanddiscussion
3.5.The”10keVfeature”
We have selected the best data available in the RXTE archive
It has been noticed (e.g. Coburnetal. 2002), that in fitting ob- of an observation of a Main-On of Her X-1 to perform de-
servedspectra of accretingX-ray binarieswith a cut-offpower tailed pulse phase resolved spectroscopy in the energy range
lawa”wiggle”or”bump”around∼10keVto∼15keVisfound 3.5–75keV.TheobservationsofNovember2002(cycleno.323)
in the residuals. This applies to many different sources includ- provide the best RXTE coverage of a Main-On (Vasco 2012),
ingHerX-1(alsotonon-cyclotronlinesources),toobservations suchthatanattemptcouldbemadetostudypulsephasedepen-
withdifferentsatellites(e.g.Ginga,Beppo/SAXandRXTE),and dentspectralvariationsalsoasafunctionofthephaseofthe35d
modulations- flux and shape of the pulse profiles -, which are
6 http://tobias-lib.uni-tuebingen.de/frontdoor.php?source opus=6346 believedto be dueto precessionalmotionof the accretiondisk
7
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
and,possibly,theneutronstaritself.Asspectralmodelwehave – For35d intervals 1–3, the peak of the E profile is struc-
cyc
used a power law with an exponential cut-off (the highecut tured(seeFig.3),withlocalmaximanearthemaximumof
model in XSPEC) modified by two line features, a multiplica- themainpeakofthepulseprofileandaroundthepositionof
tive cyclotron line (in absorption) and an additive iron fluores- theleftshoulderofthemainpeak.Asimilarstructureisseen
cenceline(inemission).Wehaveconcentratedonthreespectral inτ .
cyc
parameters: the centroid energy of the cyclotron line, the pho- – ThefoldingenergyE followsthepulseprofile,exceptfor
fold
ton index Γ of the powerlaw component(valid between 3keV anarrowdipinthepeakofthepulse(Fig.10,upper-right).
and∼ 20keV),andtheintensityoftheironfluorescencelineat – Similarly,thecut-offenergyE ,thewidthanddepthofthe
cut
6.4keV.Forthesethreeparameters,theanalysiswasperformed cyclotronline(σ andτ ),roughlyfollowthepulsepro-
cyc cyc
for four one day long intervals at different mean 35d phases file,exceptforhighervaluesatphases0.0–0.5(Fig.10).
(0.03, 0.10,0.15 and 0.20, respectively).For the otherspectral – Whilethestrongdipinthephotonindexprofile(Fig.6and
parameters of the applied spectral model, no 35day phase de- 7)closetothemainpulsepeakwasknown(eventhoughless
pendencewasstudied. wellmeasured),the second,verynarrowdip (aroundphase
0.61)isanewlydetectedfeature.Wenotethatthisiscloseto
thepositionoftheleftshouldercomponentofthemainpeak.
10 – The profile of the intensity of the 6.4keV iron line show a
5 distinctminimumatmaximumflux(Figs.8,and9).
χ 0
– We find that the so called ”10 keV feature” seen in the
5
− spectraofseveralaccretingbinarypulsars,isaround16keV
10 5 10 20 50 in Her X-1, with a strong pulse phase dependence: essen-
5 tially concentrated in the narrow pulse phase interval 0.8–
χ 0.9.Spectralfitsforalltheotherphaseintervalsdonotshow
0
significantresiduals.
5
− 5 10 20 50
Energy (keV)
Fig.11. Residuals of the X-ray spectrum of pulse phase bin 4.2.Precessionphasedependence
0.80-0.85forInterval3without(top)andwith(bottom)anextra
Withrespecttoanyvariationofthespectralparameters(ortheir
Gaussiancomponentinthefit.
pulsephasevariations)with35dphase,weconsideronlythecy-
clotronlineenergyE ,thephotonindexΓandtheintensityof
cyc
theironfluorescencelineat6.4keV.Fortheotherparametersthe
photonstatisticsisnotsufficienttodistinguishbetweendifferent
4.1.Pulsephasedependence 35d phases. It is the first time that a study of the variation of
spectralparameterswith35dphasewasdone.So,thefollowing
Theresultsofthepulsephaseresolvedanalysiscanbesumma-
resultsareallnew.
rizedasfollows.We distinguishbetweenresultswhichconfirm
andimproveinstatisticalsignificancewhichwasknownbefore
andnewresults. – The maximumvalue forEcyc (reachednearthe pulse peak)
showsaslight,butsignificantincreasewith35dphase.The
meanvalueis41.0±0.1keV,andtheslopeis∼ 0.7keVper
4.1.1. Confirmedandimprovedresults 0.1unitsof35dphase.
– TheminimumvalueforE (aroundpulsephase0.3)isfor-
– Allspectralparametersshowastrongmodulationwithpulse cyc
mallyconsistentwithaconstantvalueof33.5±0.5keV(we
phase.
wouldnotruleoutasmalldecrease).Togetherwiththemax-
– The strongest variations always appear around the peak of
imumincreasing,thismeansthatalsothepeak-to-peakam-
thepulse(atmaximumflux).
plitude (mean value 7.6± 0.5keV) is increasing with 35d
– TheprofileofthecentroidenergyE ofthecyclotronline
cyc
phase.
follows roughly the modulation of the pulse profile (maxi-
– TheshapeoftheE profile(seeFigs.4and5) isindepen-
mum energy around maximum flux). The shape is close to cyc
dentof35dphase.
”sinusoidal”.
– Similarly,theshapeofthe Γprofilesisindependentof35d
– The photon indexprofile (Fig. 6 and 7) shows a strong dip
phase,exceptforthenewnarrowdiparoundpulsephase0.62
close to the pulse peak. The dip around the main peak is a
(Figs.6and7),whereatrendtoasmallerdepthfromInterval
knownfeature,nicelyconfirmedhereandverywellresolved
1toInterval4isseen.
inthisanalysis.
– Theshapeoftheironlineintensityprofilesaresimilartoone
another,exceptforInterval1whichshowsadistinctlylower
4.1.2. Newresults intensityforpulsephases<0.6(Figs.8and9).
– It is the first time that for Her X-1 a phase profile of the
centroid cyclotron line energy E is produced with such
cyc 4.3.Comparisonwithpreviousresultsandphysical
a high resolution and statistical accuracy. The four small-
conclusions
est bins around the peak of the pulse have a width of 1/80
of a phase. The mean variation (minimum to maximum) is ForHerX-1,thedependenceofthespectralparametersonpulse
∼ 23% (Figs. 3 and 4). The modulation is close to ”sinu- phase have been studied by several authorson the basis of ob-
soidal”; however, at least two sinusoidal components(with servations with different X-ray instruments (see Introduction).
greatly different periods) are needed to model the modula- In the following we highlight our new findings and significant
tion. improvementsanddiscusspossiblephysicalimplications.
8
D.Vasco,R.Staubert,D.Klochkov,A.Santangelo:RXTEpulsephasespectroscopyofHerX-1
Pulsephasedependenceofthecentroidcyclotronlineen- despitetheargumentbyWhiteetal.(1983) thatthematerial in
ergy:ThismodulationisquitecommonamongaccretingX-ray thecolumnmaybetoohot.
pulsarsandisgenerallybelievedtobeduetothechangingview- We like to stress the observed fact, that at the pulse phase
ingangleunderwhichtheX-rayemittingregionsareseen(e.g., whereweseethehighestcontinuumfluxthereisessentiallyno
Kreykenbohmetal. 2004 and references therein). If we adopt Fe line flux. This should provide some constraints in finding a
theidea,thatpeaks(highX-rayflux)inthepulseprofilecanbe feasible geometry. If the above adopted scenario is correct, by
associatedwithbeamedradiationemittedfromtheaccretingre- whichwelookdownintothepencilbeamatthepulsepeak,the
gionsaroundthemagneticpoles,thentheobservedpulseprofiles Fe line result may be consistent with a hollow cone geometry,
arearepresentationoftheemissioncharacteristics.Duringafull where the majority of the radiation escapes through the empty
neutronstarrotation we may be seeing differentemitting spots center of the cone, where there is no material which can flu-
(mostlikelyfromacomplexmagneticfieldconfigurationwhich oresce, while the walls are seen at off-center angles. It is, of
deviatesfromasimpledipole(seee.g.Suchyetal.2008),possi- course, assumed that the bottom of the cone close to the neu-
blyhavingamulti-poleconfiguration)andtheemergingbeamed tronstarsurfaceisfilledwithX-rayemittingplasma.
radiationunderchangingangles.Thesituationisfurthercompli- Thenon-dependenceofthecyclotronlineenergyprofileon
catedbygravitationalbending.Itisthereforenotstraightforward 35dphaseandthemodelofneutronstarfreeprecession: One
tointerpretobservedpulseprofilesintermsofaccretiongeom- of the results of this study is the finding that the shape of the
etryandbeamingcharacteristics(seee.g.Caballeroetal.2011). cyclotron line energy profile (E vs pulse phase) is indepen-
cyc
Ifwe,however,assumethatthemainpeakinthepulseprofileof dentof35dphase(Figs.3and4),whilethemaximumcyclotron
Her X-1 is due to a reasonablynarrow pencil beam (following line energyincreasesslightlyby ∼0.7keV per0.1unitsof35d
e.g.,Pravdoetal. 1978; Klochkovetal. 2008), emitted perpen- phase.Ifweattributethestrongvariationsinpulseprofile with
dicular to the neutron star surface at the hot spot of the main 35dphasetoprecessionoftheneutronstar,thatistothechange
accreting pole, then we may associate this pulse phase with a oftheangleunderwhichweseetheX-rayemittingregions,we
situationwheretheobserverislookingdownintotheaccretion wouldexpectalsotheshapeofthecyclotronlineenergyprofile
column, parallel to the magnetic field lines and the velocity of to change with 35d phase. However, this expectation needs a
the in-falling material. At this phase we see the maximum cy- quantitativeanalysis.Recentlyconcludeddetailedmodelcalcu-
clotronlineenergyandthehardestspectrum(asharpminimum lations(Postnovetal.2012),assumingneutronstarfreepreces-
inphotonindexΓ)-thatis,wearelookingdeepdowntosmall sion, have shown, that under a specific set of assumptions (in-
distancesfromtheneutronstarsurfacewherethemagneticfield cludingacertainmulti-polegeometryandemissionintonarrow
is strongest and the temperature is highest. Here, we also find pencil beams), the observed pulse profiles in the energy range
thelargestwidthanddepthofthecyclotronline,aswellasthe 9-13keV(thesameasusedinStaubertetal.2010a,b,2012)can
highestE andalocaldipwithinabroadpeakofE . be reproduced with high accuracy. We point out here that the
cut fold
model of Postnovetal. (2012) is an attempt to give a physi-
Along similar lines, the newly discovered structure of a
calexplanationofthevariationinpulseprofilesbyneutronstar
second (very sharp) minimum in Γ around pulse phase 0.61
freeprecession,requiringseveralspecificassumptions,whilethe
(Fig. 7), corresponding to the left shoulder of the main peak,
template approach of Staubertetal. (2012), mentioned in the
may be the signature of a second pole. At this pulse phase we
Introduction, does not need any physical assumptions, it just
alsofindindicationsforanotherrelativemaximuminE (Fig.
cyc makes use of the observed pulse profiles. We plan to investi-
3).
gate whether the here described constancy of the shape of the
cyclotron energy profile is consistent with the physical model.
Pulsephasedependenceofthe6.4keVironlineflux: Figs. Inthissenseourresultopensanewchanneltotestthemodelof
8and9showasharpanddeepminimumoftheintensityofthe freeprecessionoftheneutronstar.
6.4keVironline,againcoincidentwiththemainpulsepeak.The
profileisverysimilartothatofΓ(Fig.7)andtheFelineintensity Acknowledgements. This paper is based on observational data taken by the
NASAsatelliteRossiX-rayTimingExplorer(RXTE).Weliketoacknowledge
dropsto nearzero at pulse phase ∼0.79 (where Γ is minimal).
thededication ofall people whohavecontributed tothegreat success ofthis
It is the first time, that such a sharp minimum in the 6.4keV mission.D.V.andcoauthorsthankDLRforfinancialsupportthroughgrant50
flux is observed. While Choietal. (1994), in observations by OR0702andD.K.acknowledgessupportbytheCarlZeissStiftung.Wethank
Ginga,andZaneetal.(2004),inobservationsbyXMM-Newton, theanonymousrefereeforveryvaluablecomments.
had founda sinusoidal-like modulationwith a broadminimum
aroundthepulsepeak,Oosterbroeketal.(2000),withdatafrom
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