An RXTE Archival Search for Coherent X-ray Pulsations in LMXB 4U 1820-30

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by  Rim Dib

An RXTE Archival Search for Coherent X-ray Pulsations in
LMXB 4U 1820−30
Rim Dib∗, Scott Ransom∗, Paul Ray† and Victoria Kaspi∗
∗McGillUniversity
4 †NavalResearchLaboratory
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2 Abstract. Aspartofalarge-scalesearchforcoherentpulsationsfromLMXBsintheRXTEarchive,wehavecompleteda
n detailedseriesofsearchesforcoherentpulsationsof4U1820−30—anultracompactLMXBwithabinaryperiodof11.4
a minuteslocatedintheglobularclusterNGC6624.Thesmallbinaryperiodleadstoaveryhighacceleration,soweusedphase
J modulationsearchesaswellasaccelerationsearchestogivesignificantsensitivitytomillisecondpulsations.Wesearcheda
totalof34archivalRXTEobservations,32ofwhichhadanon-sourceintegrationtimelongerthan10ks,andsomeofwhich
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were made consecutively which allowed us to combine them. While we found no pulsations, we have been able to place
1 thefirststringent(95%confidence)pulsedfractionlimitsof∼<0.8%forallrealisticspinfrequencies(i.e.∼<1kHz)andlikely
v companionmasses(0.02M⊙≤Mc≤0.3M⊙).BycontrastallfiveLMXBsknowntoemitcoherentpulsationshaveintrinsic
pulsedfractionsintherange3%to7%whenpulsationsareobserved.
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1 INTRODUCTION CHARACTERISTICSOF 4U1820−30
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4 One of the great scientific expectationswhen the Rossi The source 4U 1820−30 is an atoll LMXB in globu-
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X-ray Timing Explorer (RXTE) was launched in 1995 lar cluster NGC6624.Ithasan orbitalbinaryperiodof
/
h wasthediscoveryofcoherentpulsationsfromlow-mass 685 s (11.4 min) [1], the shortest known binary orbital
p X-raybinaries(LMXBs).Atpresent,onlyfiveaccreting period in an LMXB. 4U 1820−30 undergoes a regular
-
o millisecond pulsars are known. All five are faint tran- ∼176 day accretion cycle [2] switching between high
r sient sources where the pulsations at the spin period of andlowluminositystates.Inthelowstate,regularTypeI
t
s the pulsar were discovered during an outburst (see the burstsareseen±23daysaroundtheminimumluminos-
a contributionsofD.ChakrabartyandC.Markwardttothe ity[3].Inthelowstate,4U1820−30hasalsoshownan
:
v proceedingsofthisconference). extremely energetic superburst, likely due to deep igni-
i Therearemanythingsthatwecanlearnfromsearch- tion of a carbonlayer [4]. Severallow frequencyQPOs
X
ingformoreexamplesofdirectpulsationsfromLMXBs. [5] as well as two peaks of kHz QPOs [6] have been
r
a For example, coherent pulsations give the precise rota- observed from this source. Faint UV and optical coun-
tion rate of the neutron star and test the connectionbe- terpartsof4U1820−30havealsobeenobserved[7,8].
tweenrecycledMSPsandLMXBs.Theyhelpconstrain If the secondarystar in the system is a white dwarf, its
the modelsof kHzQPOs andburstoscillations.Timing mass is estimated to be 0.058 to 0.078 M⊙ [9]. If the
of the coherent pulses would also allow measurements secondaryisamainsequencestar,theupperlimitonits
of the accretion torques,the orbitalparameters,and the massis0.3M⊙ [10].
companionmasses.Inaddition,alongwithX-rayandop- OfallknownLMXBs,wesearched4U1820−30first
ticalspectra,pulsetimingcangiveinformationaboutthe because a lot of high time resolution long data sets of
compactnessandtheequationofstateoftheneutronstar. thissourceareavailableinthearchives,becausethepres-
Finally, setting stringent upper limits to coherent pul- enceofkHzQPOsinthissourcemayindicatefavorable
sations in several sources in a variety of spectral states conditions for detecting pulsations, and because of its
will impose constraints on the possible mechanism for small orbital period: the phase modulation search tech-
supressing coherent pulsations in these sources. For all nique that we are using is most sensitive (and provides
these reasons, we have started a large-scale search for thebiggestincreaseinsensitivityoverpreviousmethods)
coherentpulsationsfromLMXBs. whentheobservationsarelongerthantwocompletebi-
naryorbits[17].
THERXTE OBSERVATIONS cludedinthestandardsearchpipelinethatwearegoing
tousetosearchtheothersources.
We searched 34 archival RXTE observations collected
between1996and2002.Theobservationswereavailable
in event modes, and had a time resolution of 125 m s PhaseModulationSearches
or better. 32 of the observations had a total time on
sourcebiggerthan10ks.Thelongestofthesewas25ks Inordertoanalyzelongerobservationsweusedanew
long with a total time on source of 16 ks. Some of ‘phase-modulation’or‘sideband’searchtechnique[17].
the observations were segments of longer observations This technique relies on the fact that if the observation
whichallowedustoconcatenatethemandanalysethem time is longer than the orbital period, the orbit phase-
together. The longest of the concatenated observations modulatesthepulsar’sspinfrequency:phasemodulation
was77.5kslongwithatotaltimeonsourceof46.5ks. results in a family of evenly spaced sidebands in the
frequencydomain,aroundtheintrinsicpulsarsignal.The
constantspacingbetweenthesidebandsisrelatedtothe
THEDATAANALYSIS binaryorbitalperiod.
A phase modulation search is conducted by taking
Each observation was downloaded, filtered, barycen- shortFFTs ofthepowerspectrumof a fullobservation.
tered, and then split into four energy bands: Soft (2-5 The short FFTs cover overlapping portions of various
keV),Medium(5-10keV),Hard(10-20keV),andWide lengths(toaccountforthe unknownsemi-majoraxisof
(2-20keV), in order to attempt to maximizethe signal- the LMXB) over all the Fourier frequencyrange of the
to-noise ratio of the unknown pulsations. This process- original power spectrum (to account for the unknown
ing used custom Python scripts that call the standard pulsation period). They are then searched for peaks in-
FTOOLs. The processed events were then binned into dicatingregularlyspaced sideband(to detectthe orbital
hightimeresolution(either0.122msor0.244ms)time period of the LMXB). A detection providesinitial esti-
series. Fast Fourier Transforms of the four time series matesofthepulsarperiod,theorbitalperiod,andthepro-
were then computed. Acceleration searches of FFTs of jectedradiusoftheorbit,whicharerefinedbygenerating
various durations were performed. ‘Phase-Modulation’ a seriesof complex-valuedtemplateresponsesto corre-
searches were conducted on each of the full duration late with the original Fourier amplitudes (i.e. matched
FFTs. Finally, candidates above our threshold were ex- filteringintheFourierdomain)[17].
amined using brute-force folding techniques to deter-
mineiftheyweretruepulsations.
RESULTS ANDUPPER LIMITS
THESEARCH TECHNIQUES Oursearchesdidnotdetectpulsations.
To set an upper limit on the pulsed fraction of de-
Afterwepreparedandbinnedthedatasets,wesearched tectable pulsations from 4U 1820−30 we used the fol-
them for pulsations in the Fourier domain using two lowing procedure: we ran our searches on several data
typesofsearcheswhichwesummarizebelow. sets containing simulated pulsations of various pulsed
fractions for a range of companion masses (see Figure
1) and for several spin frequencies. For the purpose of
Acceleration Searches the simulations, we assumed an orbital period of 685
seconds,thetypicallengthofa longRXTE observation
This is the method traditionally used to compensate (20.5ks),aninclinationangleof60degrees,andacircu-
for the effects of orbital motion [11, 12, 13, 14, 15]: larorbit.Ofthe searchesthatwe ran,phasemodulation
A time series is stretched or compressed appropriately searchesrunonthefulldurationdatasetswerethemost
to account for a trial constant frequencyderivative (i.e. sensitive. Figure 1 shows the results of the simulations
constant acceleration), Fourier transformed, and then for this type of search run on data sets containing fake
searchedforpulsations.WeusedaFourier-domainvari- 3mspulsations.Everypointinthefigurecorrespondsto
ant of this technique [16]. Unfortunately acceleration 100 searcheddata sets. The shadingof everypointcor-
searches can detect only the strongest pulsations from responds to a sigma detection level. The line of sigma
systems like 4U 1820−30 where the orbital period is = 5 indicatesthe valueof our upperlimit on the pulsed
short. So while we did notexpectaccelerationsearches fractionforasignalperiodof3ms.Thisvaluevariedbe-
tofindpulsations,westillusedthembecausetheyarein- tween0.55%and1.0%(backgroundsubtracted)overthe
rangeofcompanionmassesthatweused.Thevaluede-
> 15 sigma
10 sigma
5 sigma
No Detection
FIGURE 1. Monte-Carlo derived sensitivity calculations for the pulsation searches of archival RXTE observations of
4U 1820−30. The plotted sensitivities are 95% confidence limitsusing phase modulation search technique for a typical RXTE
observation assuming a pulsar spin period of 3ms. We would easily have detected any coherent pulsations with a pulsed frac-
tion>0.8%forallrealisticcompanionmassesandspinperiods.
creasedslightlywhentheperiodofthesignalwaslarger POTENTIAL REASONS FORTHELACK
by a few milliseconds. This means that if there were a OFOBSERVED PULSATIONS
3mscoherentpulsationcomingfrom4U1820−30with
a pulsed fraction equal or higher than the upper limit Several theories exist to explain why pulsations with a
statedabove,oursearcheswouldhaveeasily(witha95% higherpulsedfractionthanourupperlimitarenotseen.
confidence)detectedit. Tobeginwith,anunfavorablerotationalgeometry,anun-
Our upper limit on the pulsed fraction of possible favorableviewinggeometry,orbothcanmakepulsations
signalsfrom4U1820−30wasabout0.8%(background undetectable.Thepulsedfractionmaybereduceddueto
subtracted) for spin periods under 10 ms. The pulsed scatteringinthesurroundingmedium[22].Gravitational
fractionsofthesignalsdetectedfromthe5LMXBswith lenseffectsontheemissionfromthehotpolarcapscan
known signal period ranged between 3% and 7%, for also greatlyreducethe pulsedfraction[23, 24].Finally,
signal frequenciesbetween 2 ms and 6 ms [18, 19, 20, screening of the stellar magnetic field by the accreting
21]. This means that our searches would have detected matter can lead to a less preferentialheatingof the sur-
the pulsationsfrom4U 1820−30if theywere asstrong face (i.e. no polar caps) and thereforeto the absence of
asthepulsationsdetectedfromtheother5sourcesandin observablepulsations[25].
thesameperiodrange.
ACKNOWLEDGMENTS
This work was supported by the Natural Sciences and
Engineering Research Council (NSERC) Julie Payette
researchscholarship.Itwouldalsohavebeenimpossible 24. Meszaros,P.,Riffert,H.,andBerthiaume,G.,ApJ,325,
todothisworkwithoutthecomputingpoweroftheBe- 204–206(1988).
owulf computercluster operatedby the McGill Univer- 25. Cumming,A.,Zweibel,E.,andBildsten,L.,ApJ,557,
958–966(2001).
sityPulsarGroupandfundedbytheCanadaFoundation
forInnovation.
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