High time resolution optical/X-ray cross-correlations for X-ray binaries: anti-correlations and rapid

46 Pages·2010·2.27 MB·English

Mon.Not.R.Astron.Soc.000,1–46(2010) Printed27August2010 (MNLATEXstylefilev2.2)
High time resolution optical/X-ray cross-correlations for
X-ray binaries: anti-correlations and rapid variability
0
1 Martin Durant1,2⋆, Tariq Shahbaz1,3, Poshak Gandhi5, Remon Cornelisse1,
0
2 Teodoro Mun˜oz-Darias1,4, Jorge Casares1, Vik Dhillon7, Tom Marsh8,

g Hendrik Spruit6, Kieran O’Brien9, Danny Steeghs8 and Rob Hynes10
u
A 1 Institutode Astrof´ısica de Canarias, Calle V´ıa L´acteas/n, 38205 La Laguna, Tenerife, Spain
2 Universityof Florida, 211 Bryant Space Center, Gainesville, Florida 32611-2055, USA
6 3 Departamento de Astrof´ısica, Universidad de La Laguna (ULL), 38205 La Laguna, Tenerife,Spain
2 4 Osservatorio Astronomico di Brera, via Brera 28, 20121 Milano, Italy
5 Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, chuo-ku, Sagamihara, Kanagawa 229-8510,
E] 6 Max Planck Institute for Astrophysics, Box 1317, 85741 Garching, Germany
7 Dept. of Physics & Astronomy, Univ. of Sheffield, Sheffield S3 7RH, UK
H
8 Dept. of Physics, Univ. of Warwick, Coventry CV4 7AL, UK
h. 9 European Southern Observaotry, Casilla 19001, Santiago 19, Chile
p 10 Department of Physics and Astronomy, Louisiana State University,Baton Rouge, Louisiana 70803, USA
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s
a
August2010
[

1
v ABSTRACT
2 Using simultaneous observations in X-rays and optical, we have performed a homo-
2 geneous analysis of the cross-correlation behaviours of four X-ray binaries: SWIFT
5 J1753.5−0127,GX 339−4,Sco X-1,andCyg X-2.With high time-resolutionobserva-
4 tionsusingULTRACAMandRXTE,weconcentrateontheshorttime-scale,δt<20s,
.
8 variability in these sources. Here we present our database of observations, with three
0 simultaneous energy bands in both the optical and the X-ray, and multiple epochs of
0 observation for each source, all with ∼second or better time resolution. For the first
1 time, we include a dynamical cross-correlation analysis, i.e., an investigation of how
v: the cross-correlation function changes within an observation. We describe a number
i of trends which emerge.We include the full datasetof results, andpick a few striking
X
relationships from among them for further discussion.
r We find, that the surprising form of X-ray/optical cross-correlation functions, a
a
positive correlation signal preceded by an anti-correlation signal, is seen in all the
sources at least some of the time. Such behaviour suggests a mechanism other than
reprocessing as being the dominant driver of the short-term variability in the optical
emission.Thisbehaviourappearsmorepronouncedwhenthe X-rayspectrumishard.
Furthermore,wefindthatthecross-correlationrelationshipsthemselvesarenotstable
intime,butvarysignificantlyinstrengthandform.Thisallhintsatdynamic interac-
tions between the emitting components which could be modelled through non-linear
or differential relationships.
Key words: Stars: neutron; Stars: black holes; X-rays: binaries;
1 INTRODUCTION releasesitsbindingenergy,poweringenergeticradiationand
matterout-flows.Inthemosttypicalscenario(andtheonly
X-raybinaries(XRBs)aresystemsinwhichanordinarystar
one considered here), the donor star is an evolved star at
andacompactobjectareincloseorbit.Matterfallsontothe
the end of its main sequence life, and over-filling its Roche
compactobjectandisaccretedbyit.Thein-fallingmaterial
Lobe. The compact object can be a black hole or a neu-
tron star; white dwarf systems are not normally considered
XRBs, since the majority of the luminosity is released at
⋆ E-mail:[email protected]fl.edu
2 Durant et al.
somewhatlowerenergies,correspondingtothelargerradius in response to, the higher-energy emission in the core. See
atwhichin-fallingmaterialishalted.SeeLewin et al.(1997) forexampleEikenberry et al.(2008)forthecaseofagalac-
foradescriptionofX-raybinaryphenomenologyandtheory, ticmicro-quasar,orCasella et al.(2010)forthemostrecent
and possible models for theaccretion process. suchobservationsofoneofthesystemsunderconsideration
SinceXRBsaremostmanifestintheX-rayband,much in this paper.
observation of them has focused here. This is particularly Optical high time resolution observation is still a rela-
trueoftiminginvestigation,sinceX-rayinstrumentationhas tively young field, since CCDs capable of fast readout with
been capable of high temporal resolution since the start. A low noiseare relatively new,and thepreviousgeneration of
widerange of time-domain behaviourhavebeen catalogued detectors suffered from low quantum efficiency and/or high
for the various binary systems, such as broad-band timing dead-time.Duetothedifficultyofcoordinatingtheschedul-
noise and a variety of quasi-periodic oscillations (QPOs). ing of multiple observatories, not many simultaneous sub-
See van derKlis (2004) for a review of X-ray timing obser- secondtime-resolution,multi-bandobservationsexistinthe
vations. literature.
The X-ray emission corresponds to the bulk of the lu- Kanbach et al. (2001) observed the galactic black hole
minosity and should come from thesmallest radii (andcor- XRB XTE J1118+480 simultaneously with the Rossi X-
respondingly highest particle energies) around the compact ray Timing Explorer (RXTE) and OPTIMA, an optical
object,wherethedynamicaltime-scaleistheshortest.This single-pixel fast photometer, observing white light. They
strongly suggests, therefore, that any optical variability on found two surprising results in the correlation analysis:
a similar time-scale to the X-rays must occur by reprocess- the optical auto-correlation function (ACF) had a smaller
ing, i.e., the absorption and re-emission of X-ray radiation width than X-rays, and the CCF had a small component
bycoolermaterialatgreaterradiiintheaccretiondiscoron which was negative and with negative lag (i.e., optical ar-
thesurfaceofthedonorstar.Althoughthisideaisnotnew, riving before X-rays).Neither of these factors would be ex-
van Paradijs & McClintock (1994) modelled this in detail, pectedforthesimplisticreprocessingmodel.Infurtheranal-
andpresentedevidencethattheopticalluminositieswereof ysis, Spruit & Kanbach (2002) commented that the cross-
a similar magnitude to what might be expected, if repro- correlationfunctionwasnotstablethroughtheobservation,
cessing were dominant in theoptical. and contained two statistically separable principal compo-
Opticalemissionbyreprocessingofhigher-energyradia- nents, both of similar dip-and-peak shape, but differing in
tion,e.g.X-rays,hasundoubtedlybeenseeninX-raybursts time-scale.Asimplisticexplanationwaspresentedtoexplain
(seee.g.,Grindley et al.1978;Pedersen et al.1982).Inthese theprecognitiondip,ofalocaldensityandverticalheighten-
cases,itisbelievedthattheburstoriginates inanexplosive hancementinthediscobscuringtheinnerX-rayregion,and
event on, or immediately above, the surface of the neutron then causing increased X-ray emission some seconds later
star. The optical emission is seen to rise sharply very soon as the blob is accreted. No numerical or detailed modelling
(<1s) after the X-ray burst, and can be well-modelled as wasdone,however.Furtherdiscussiononthepossiblephys-
absorption and re-emission of the original flare, mainly in icalprocessesandtime-scalesinthesystemwasprovidedby
the accretion disc at larger radii, and also from the donor Hyneset al. (2003).
starsurface(e.g.Hyneset al.(2006)).Thecross-correlation Durant et al.(2008)andGandhi et al.(2008)increased
function(CCF)forthiscaseisasinglepositivepeakcentred the numberof fast (δt<1s) optical/X-ray cross-correlation
atpositivelags.TheX-raylight-curveinsuchascenariore- analysesintheliteraturetothree.Theyalsosuggestedthat
flectsprimarily thetemperature of theneutronstar surface thefast functions seen were not compatible with reprocess-
and its short-term behaviour is not connected with the ac- ing as thedominant source of optical variability. That data
cretiondiscorjets.Nevertheless,X-rayburstsservetoshow is included in ouranalysis below.
that the optical emission, and its rapid variability, can be In summary, the reprocessing model is able to explain
dominated by reprocessing at least for a short time, given the energetics of the optical emission for X-ray binaries in
certain specific circumstances. general, and many of the details of the spectrum and long-
Reprocessing has also been demonstrated through the term behaviour that would be expected. It has problems,
technique of Doppler Tomography for individual spectral however, with the fastest time-scale variations, and it is
lines. The known period of the binary orbit is used to find these that we wish to concentrate on in this paper. Time-
the phase and velocity amplitude of emission components scales < 2s are shorter than the light-crossing time for a
within a strong (emission) line. This can be transformed typical accreting binary system (depending, of course, on
to map the emission locations within the binary system thebinary separation).
(see Casares et al. 2003, for an example of this applied to Here we analyse multiple ULTRACAM/RXTE obser-
a low mass X-ray binary). Similarly, echo tomography has vations for four XRBs: SWIFT J1753.5−0127, GX 339−4,
been attempted in a number of cases using the fast vari- Sco X-1, and Cyg X-2. For each observation, we consider
ability near the compact object and the echoes this can in- threeenergybandsintheopticalandthreeintheX-rays,in
duce(Hynes2005), especially for larger-scale accreting sys- ahomogeneous wayacross thedataset.Also,weinvestigate
tems, the active galactic nuclei (AGNs, e.g., Raiteri et al. the dynamical behaviour of the CCF, a technique which is
2008). In contrast to the optical, infra-red emission may not commonly considered. The total numberof presentable
well be contaminated or dominated by a jet: a relativis- relationships are large; we include the full set in Appendix
tic, energetic outflow originating near the compact object A,andwedrawoutafewexamplestoillustratethetypesof
and travelling along the polar axes. The emission from a behaviour we find in the data. What we see suggest that a
jet is therefore causally connected with the central accre- large fraction of thefast variability seen in optical emission
tion engine, but fluctuationsshould happen later than,and is not produced by reprocessing. Therefore, some explana-
X-ray binaries: optical/X-ray cross correlations 3
tion is required for why reprocessed variability is not more 3 ANALYSIS
pronounced.
Our aim in this paper is to compare the cross-correlation
functions between the observed X-ray and optical flux for
each source. This is a simplistic determination of the rel-
2 OBSERVATIONS ative time-variability of the two wavebands, i.e., to what
degreedotheyvaryinsimilarways,andwhatistherelative
Table 1 lists the observations considered as part of this si-
timingofthesevariations.Itprovidesaclear,uncomplicated
multaneousobservationcompilation.Asshown,someofthis
comparisonoftwosignalswithrespecttotime,butisbyne-
data has been presented before in some form.
cessity anaveraging process. Togofrom asignificant signal
ULTRACAMisa high-speed optical camera, which in-
in a CCF to a realistic picture of what the two light-curves
corporates dichroics to split the input beam into three en-
aredoingisnotalwaysstraightforward.Weendeavourtode-
ergybands.Thedetectorsarefastread-outCCDswithread-
scribethetypicalbehaviourthatgivesrisetotheCCFsseen.
out noise of only 3.5e−. Masked data buffer areas on each
We note that alternative methods for time-series compari-
chip enable an image to be very quickly shuffled from the
sonexist,suchasthecoherenceandFouriercross-spectrum,
active region and then to be read while the next is expos-
but in our experience these are no more transparent, and
ing, reducing the dead-time to near zero. By reading only
indeedareintimately related totheCCF. Weonly consider
small windows around the target and reference star, sam-
CCFs from here on.
pling up to 500Hz is possible. A dedicated GPS receiver
Wecalculated CCFs for each simultaneous observation
provides reliable time-stamping to sub ms accuracy. See
by first re-binning the light-curves to the best time reso-
Dhillon & Marsh(2001)andDhillon et al.(2007).Weanal-
lution of the poorer of the pair. CCFs were calculated in
ysedeachdatasetusingthecustomULTRACAMpipeline1,
windows of size 50s and stepping25s, i.e., overlapping sec-
usingvariable-aperturephotometryrelativetoabrightfield
tionswhereeverysecondCCFinindependent.AmeanCCF
star.Slowvariationsduetothedifferenceincolourofthetwo
isthenderivedforeachtime-seriespairforeachobservation.
starsmakenegligibleeffectonthetime-scalesunderinvesti-
Thisactseffectivelyasahigh-passfilter,andvariationswith
gation. For these observations, ULTRACAM was mounted time-scales longer than ∼50s will not appear. For the pur-
on either the 8.2m Very Large Telescope (VLT), Paranal,
poses of this paper, we are only interested in the fastest
Chile, orthe4.2mWilliam Herschell Telescope (WHT),La
variability,sincethismustbepredominantlyduetofluctua-
Palma, Spain.
tionsarisingclosetothecompactobject,wherethedynam-
The dichroics in ULTRACAM split the light into
ical timeis theshortest.
the blue, middle and red parts of the spectrum, but fil-
All the CCFs were considered, for each object, obser-
ters are typically used before each detector. For SWIFT
vation and pairs of energy bands. In Section 4 we present
J1753.5−0127 andGX339−4,broadr’g’u’filterswereused,
a selection of average CCFs, pointing out some similarities
but for Sco X-1 and Cyg X-2, narrow filters were used
between the binary systems, and some trends in the data.
in the r-continuum (i.e., a spectral region without lines),
ThefullsetofCCFsispresentedinAppendixA.Notethat,
and in the vicinity of the Bowen/He-II blend (the broad u’
although a comparison star in the field is used in each ob-
was retained). The purpose was to try to isolate the emis-
servation to mitigate atmospheric effects, the weather still
sion in the narrow emission lines, but the majority of the
greatly affects thesignal quality achieved in a CCF, see for
flux in each filter is still dominated by the continuum (see
example(Gandhi et al.2010)andthecomparisonofsucces-
Mun˜oz-Darias et al. 2007 ).
sive nights, where we find that the CCF features are most
RXTE is an X-ray observatory optimised to tim-
pronounced on the night with best weather 2007-06-18.
ing work. The Proportional Counting Array (PCA,
Jahoda et al.1996)instrumenthasalargeeffectiveareaand
issensitivetophotonswithenergies2–60keV.Hereweonly
considerthemoresensitive2–20keVrange.Althoughanum-
berofdatacollectingsettingsarepossible,theintrinsictime
resolutionisoftheorderµswithfullenergyresolutionforall
butthebrightest sources. Thelimiting factor is theteleme-
3.1 Dynamic analysis
trybandwidth.Thedatawereprocessedusingthestandard
FTOOLSpackages2,andthreebackground-subtractedlight- In the initial analysis above, the CCFs were the average
curves produced for each dataset: 2–4, 4–8, and 8–20keV. ofmany50ssections throughoutanindividualobservation.
Note that for a non-imaging instrument such as the PCA, Thesesegments can,however,beinteresting independently.
background subtraction is in general a complicated issue; AconvenientdisplayforsuchasetofCCFs,istostackthem
estimatescanbebasedonempiricalmeasurements,andde- above each other, with one line representing a single CCF,
pend on the spacecraft attitude and recent trajectory. We andcoloursalongthatlinegivingthestrengthofthecorrela-
utilised the latest South Atlantic Anomaly passage history tionforagivenlag,atagivenpointintheobservation.Such
andbackgroundmodels,2009. Forsuchbrightsourceshow- arepresentation issimilar in styletothemore common dy-
ever,thesemakelittledifference,andthenoiseattime-scales namic Fourier-gram. Note that because the segments over-
ororder1sorlessisdominatedbysourcephotonstatistics. lap, adjacent CCFs are not independent, but every second
oneis.Thisproducesslightly smoother-lookingoutput,and
is intended to catch strongly correlated events that would
1 seehttp://deneb.astro.warwick.ac.uk/phsaap/software/ultracam/ohtthmelr/wiinsdeexfa.lhltomnl the border between two segments. No ad-
2 seehttp://heasarc.gsfc.nasa.gov/lheasoft/ ditional numerical smoothing has been applied.
4 Durant et al.
Table 1.LogofsimultaneousULTRACAM/RXTEobservations
Object Date ULTRACAM Opticaltime Simultaneous Reference1
site resolution(s) coverage (s)
SWIFT J1753.5−0127 2007-06-12 VLT 0.14 2800 Durantetal.(2008)
2008-08-20 WHT 0.2 2400
GX339−4 2007-06-14 VLT 0.14 2800
2007-06-16 VLT 0.13 2700 Gandhietal.(2008)
2007-06-18 VLT 0.05 3300 Gandhietal.(2008)
ScoX-1 2004-05-17 WHT 0.1 950,760,730
2004-05-18 WHT 0.25-0.5 260,700,950 Mun˜oz-Dariasetal.(2007)
2004-05-19 WHT 0.3 115
CygX-2 2007-10-16 WHT 2.0 880
2007-10-17 WHT 2.02
2007-10-18 WHT 2.02
2007-10-19 WHT 2.0 600,710
2007-10-20 WHT 2.0 530
2007-10-21 WHT 2.0 1050
1 wherenoreferenceisgiven,thedataarepresentedhereforthefirsttime.
2 thedataqualityintheseobservationsistoopoorforconsideration.
3.2 CCF noise howwellthefeatureswithinitcanbelocalised,Thisweap-
plytothedynamicCCFs,sincewefindthepossiblevariation
Asidefromintrinsicchangesinthesignal,twotypesofnoise in peak height and location interesting.
alsocontributetothedifferencesbetweenanytwoCCFsand In order to estimate the confidence in establishing the
tothestructureswithinasingleCCF.Thefirstissimple:un- amplitudeandpositionofaparticularCCFpeak,wefollow
correlated (white) noise inherent in any measurement. This the empirical estimation of Smith & Vaughan (2007) who
isdominatedinourcasebythePoissonianstatisticsofpho- show a simple implementation of the theoretical derivation
ton counting, but read noise can also contribute. Since the by Bartlett (1955). This method considers both the corre-
cross-correlation calculation is a simple multiply-and-sum latedand un-correlatednoiseineach light-curve,asempiri-
process, these errors are easy to propagate. Longer time- cally sampled by theauto-correlation functions. It provides
scale noise is also present in the data, however. These are the uncertainty on each point in a calculated CCF. Since
due both to slow systematics (e.g., seeing variations) and themethodis onlyapplicable toastableCCF relationship,
rednoiseprocessesintrinsictotheemissionprocessesthem- our approach here is necessarily simplistic. To estimate the
selves, and act on a range of time-scales. These make the confidenceintervalonanindividualpeak,onecanfitasim-
estimation of the noise contribution to CCFs rather more ple function (e.g., a Gaussian) with a standard chi-squared
complicated. process incorporating these uncertainties. Such a fit is only
One simplistic method to establish the significance of a good estimator for the case that one has good reason to
an average CCF signal might be to measure the standard believe the Gaussian function fit is a good description of
deviationofallvaluesforagivenlag,comparedtotheaver- the data. The CCF functions are clearly more complicated
agevalue.ThiswouldonlybevalidinthecasethattheCCF thanthis,butweneverthelessthinkthisapproachisagood
isassumedtobestationary,butinourdynamicanalysiswe approximation for characterising peaks.
findthisgenerally nottobethecase,so wedonot consider
this method further.
Thefirst-orderapproximationweapply,toseewhether
4 RESULTS
there is any significant signal in a given CCF, is to empiri-
cally measure the noise in the CCF itself, given by the me- We include the complete set of cross correlations, averaged
dian of the difference between successive points. This value and dynamic, in Figures A1 to A34, in Appendix A. They
is a combination of various noise sources, and as such, a servetoillustrate,thattherangeofbehavioursthatwefind
useful estimator for analysing a given CCF. Signals falling are not particular to a small subset of thesample, butgen-
more than five times the value are likely to be significant. eral features. The figures are shown with consistent colour
In the averaged CCFs shown in Appendix A, we give both mapping.Foreachaveraged CCF,wegivebothsignificance
arawCCFscale,andaσ scale(CCF/σ),sothatthey-axis levels,based onourempiricalestimate (seeabove),and ab-
becomesaroughestimateofsignificance.Foranysignificant solute CCF values. In thisSection, we focus on afew inter-
average signal, one can inspect the corresponding dynamic esting CCFs, in order to best illustrate some of the trends
CCFplot,toseewhereintheobservationthesignalmostly in the data.
originates from; it may be steady throughout the observa- InFigures1to4wepresentaselectionoftheCCFscal-
tion, intermittent, or changeable in height and shape. culated for oursample of objects, energies and epochs. The
HavingestablishedacandidateCCFsignal,onecanask style of observation and the analysis have been conducted
X-ray binaries: optical/X-ray cross correlations 5
inahomogeneousmanner.Weextractafewtrendsthatare X-rayemissionwashardest,althoughthisgenerallyalsoco-
apparentinthedata.FirstwepresenttypicalCCFsforeach incided with times when the overall flux was the highest.
source, then look at the trends with X-ray and optical en- Note that none of the systems was seen in the classical
ergies, and finally display some examples of the dynamical High/Soft state during these observations (e.g., D’A´ı et al.
analysis. The latter requires a little more careful consider- 2007 for a typical evolution between various states for Sco
ation, since the changes seen in the CCF through a single X-1); in the high/soft state, one expects copious thermal
observation could in principle be caused by noise processes emission to dominate theluminosity, and fast variability to
alone - see Section 4.3. Although in Section 5 we attempt bemuch less apparent (e.g., Bradshaw et al. 2007).
to draw conclusions from what we find, and speculate on
the physical scenario behind them, principally the results
belowstandasaphenomenologicalstudy,forinterpretation 4.2 Energy dependence
in futuretheoretical works.
ForthepurposesoftheseexampleCCFs,wehavepicked Figure 2 shows two examples of a systematic trend in
plots that show particular features clearly. The full set are the CCFs with X-ray energy band. For the Cyg X-2 data
included in Appendix A, and the reader is encouraged to (left panel), one sees that the positive component becomes
look throughthesetoseethefrequencywithwhich thevar- strongerand peakscloser tozerolag for successively higher
ious features and trendsoutlined below occur. energies.Thechangeinstrength,from∼0to0.2isdramatic.
Thesecurvesweregeneratedfromthesameobservation.The
right-handpanelforScoX-1showsasimilarresult:thecurve
4.1 Anti-correlations becomes stronger and peaks closer to zero lag with higher
energy, while the negative component shows little change.
Figure1showsexampleCCFsforeachofthefourbinariesof
Thechangeincorrelation strengthin thiscaseis moresub-
our sample. They show thefollowing typical form: negative
tle.
correlation at negative lags (CCF < 0, δt < 0) and some-
Figure 3 shows two examples of a systematic trend in
whatweakerpositivecorrelation atpositivelags.Thesharp
the CCFs with optical band. For GX 339−4 (left panel),
slopes seen around δt= 0 indicate that in each case, much
one sees that both r’ and g’ show the same structure, anti-
ofthesignal isduetovariations attimes-scales comparable
correlation nearzerolag, exceptforasharppeakveryclose
to the the shortest measured. Even shorter time-resolution
to zero lag, but that the relationship is stronger for r’, par-
mightofcoursebepresent,butisunobservableinthesedata.
ticularly forthepositivepart.u’showssomethingdifferent,
The most important point, is that of the four systems ob-
broadnegativecorrelationatnegativelagsandpositivecor-
served, all showed a similar CCF form at least some of the
relation at positive lags. Note that, due to the lower time-
time.
resolutionoftheu’data,thesharppeakatδt=0forr’and
Not all of the observations show the typical CCF form
g’ is not excluded in the u’ CCF. The right-hand panel for
described above. In a number of observations, the level of
SWIFT J1753.5−0127 shows a different result: the g’ CCF
noise, predominantly Poissonian (with some contribution
curvehas thesame shape, butstronger than ther’ one.
from,forinstance,seeingandtransparencyvariation),make
anyCCFsignalrelativelyweakorunobservable.CCFsshow-
ing a single, strong positive peak at positive lags, as would
be expected from reprocessing, are notable by their rarity. 4.3 Dynamic behaviour
Furthermoretheoptical ACFs (notshown) areconsistently
Figure4showsthreeexamplesoftheresultsofouranalysis.
ofsimilar width orsometimesnarrower compared totheX-
EachfigurerepresentsasetofCCFsfromtwotime-seriesin
ray ACFs. It would thusseem that the majority of thefast
one particular observation. Each horizontal line is a single
variability in theoptical is not caused by reprocessing. The
CCFasmeasuredatthetimeT intheobservation.Thistime
existence of a CCF signal indicates, however, that the two
isgivenasanoffsetsincethestartofsimultaneouscoverage.
light-curves are not independent, but connected. As noted
Thecolours alongthehorizontallinerepresentthestrength
by Gandhiet al. (2008), it may be possible to describe a
ofcorrelation fordifferentvaluesoflag,δt,alongthex-axis.
complicateddip-and-peakCCFasabroadertroughandsim-
The colour scales are given for each panel individually, and
ple peak, both centred near δt=0. This was motivated for
canbecompared with thevaluesonthey-axesofFigures 1
the case of GX 339−4 by the similarity between the width
to 3, which are average CCFs, or to the whole set of CCFs
onewould ascribetothebroad troughandthewidthofthe
in AppendixA.
optical auto-correlation function.
By eye,a numberof features are apparent:
Thesourcespresentedherehavevariousemissionstates
intheirepochtoepochevolution,typicallyclassifiedbytheir • for GX 339−4, the positive component seen in the
location on an X-ray flux versus hardness (i.e., flux ratio average CCF appears for very short bursts and relatively
of a higher and lower energy band) diagram. The obser- strongly, with a low duty cycle through the observation.
vations here all refer to times when the sources were in a The negative component appears to be present whenever
low-hard state or flaring states, with a luminosity well be- thepositive component is not.
low the maximum known, and the spectral slope in the X- • for SWIFT J1753.5−0127, the negative component is
rays harder. For example, SWIFT J1753.5−0127 has since ever-present and strong, but the centroid appears to shift,
its discovery, never been seen to leave the low-hard state andsomewhatcrosstoδt>0.Likewise,theweakerpositive
(Durant et al.2009).ForScoX-1,wherethehardnessofthe componentissometimescentredatδt<0.Thestrengthand
source changed markedly during theobservation campaign, width of both components changes markedly, but without
thestrongestCCFsignaturescorrespondtotimeswhenthe any obvious trend through theobservation.
6 Durant et al.
Figure 1.ExampleaverageCCFsforoursampleofXRBs,demonstrating theubiquityananti-correlationcomponent atnegative lags
ineachcase.Theseareeachintheopticalredbandand2-4keVforX-rays.Thereisaverticaloffsetof0.15between successivecurves,
forclarity.
• forScoX-1,theformoftheCCFseemstobeconstant, data, which is clearly not the case; it is sufficient, however,
but the strength and location of the peak changes remark- for illustrative purposes.
ably throughout theobservation. Mun˜oz-Dariasetal.’s(2007)analysiswasperformedon
a180swindowcentredataroundT =450sonthisdiagram.
Had we restricted our analysis to just this section of the
The dynamic CCF diagrams clearly show a lot of vari- data, we would also have concluded that the major feature
ationwithtime.Onemustconsiderwhethersuchvariations of the CCF is a positive peak with a centre at around δt=
couldbecausedbythenoiseprocessesinherenttothelight- 5..10s.Notehoweverthattheseauthorswereattemptingto
curves under analysis. Here we present the application of measure the differences between CCFs, as a way to probe
such an investigation to a single dynamic CCF diagram theemissionlineswhicharepresentinthespectralpassband
which shows marked variations, as an illustration. We wish of one of the filters butnot theother.
totestthesignificanceofthepeakvariationsforcaseofSco Using a similar process for the rest of the dynamical
X-1(2004-05-18), becauseofalltheobservations,thisisthe CCFs, we find that the features noted above for Figure 4
one that shows the most spectacular and unexpected CCF are significant.
variations. Using the Bartlett formalism described in Sec-
tion 3.2 to assign uncertainties to every CCF bin value, we
have performed fitting to find the peaks in each line of the
5 CONCLUSIONS/DISCUSSION
dynamic CCF. We fitted a single Gaussian function to the
positivecomponent of each CCFline andminimised theχ2 Wehavepresentedanumberofoptical/X-rayCCFsfromsi-
statistic.Theuncertaintyofthelocationofthatpeakisthen multaneousobservationsof four XRBs,anddeeperanalysis
thevalue at which χ2 increases by 1. oftheenergy-andtemporaldependenceofthese.Themost
The result of such an analysis are shown in Figure 5. obvious and important result is, that for such a heteroge-
Wefindthattheshift inthelocation ofthepositivepeakis neoussample,optical-leadinganti-correlations appeartobe
highly significant,and apeak lag ofδt<0 at sometimes is typical of the emission behaviour. Currently the accepted
marginally significant.Notethathereweareassuming that standard picture is that the optical emission arising from
asingleGaussian functionisareasonabledescriptionofthe X-raybinariesisdominatedbyreprocessingoftheX-raysin
X-ray binaries: optical/X-ray cross correlations 7
0.25 0.20
8–20keV 8–20keV
0.20 4–8keV 4–8keV
2–4keV 0.15 2–4keV
0.15
0.10
0.10
CF 0.05 CF 0.05
C C
0.00
0.00
−0.05
−0.05
−0.10
−0.15 −20 −10 0 10 20 −0.10 −20 −10 0 10 20
dt(s) dt(s)
Figure2.ExampleaverageCCFsforsingleobservations(left:CygX-2,2007-10-20,u’;right:ScoX-1,2004-05-28,green)demonstrating
trendswithX-rayenergyband.
0.06 r’ 0.05 r’
g’ g’
u’
0.04
0.00
0.02
CF CF−0.05
C C
0.00
−0.02 −0.10
−0.04
−0.15
−20 −10 0 10 20 −20 −10 0 10 20
dt(s) dt(s)
Figure3.ExampleaverageCCFsforsingleobservations(left:GX339−4,2007-06-16,2–4keV;right:SWIFTJ1753.5−0127,2008-08-20,
4–8keV)demonstratingtrendswithopticalband.
theouteraccretiondisc,oronthesurfaceofthedonorstar. it is natural to ask why the reprocessing CCF signal is not
One would then expect that the cross-correlation of opti- seen. One simple answer could be that whatever is giving
cal and X-ray flux shows that any variability in the X-rays rise to the signals we observe is swamping the reprocessing
is mirrored in the optical flux, but arriving to the observer signal; but it could also be that the range of light-travel
a little later to account for the light-travel time across the times or the reprocessing time-scale is longer than previ-
binary system and the absorption/emission time-scale. In ouslythought,andthatthereforethevariablecomponentof
other words, the CCF should show a single strong, positive reprocessingiswashedoutonthetime-scalesweareprobing.
peakatpositivelags(δt>0,opticalarrivingafterX-rays.). DecomposingtheCCFintoitsfouriercomponentsandphase
lagsmaybeawaytogetaroundthisdifficulty(Malzac et al.
OurobservationsshowthattheCCFsonetypicallysees
2003, Gandhi et al. 2010). Certainly, there are strong fluo-
aremorecomplicated,andinparticular,thatsignalsofanti-
rescence lines in some of the spectra, e.g., known since as
correlationandoptical-leadingareubiquitous,atleastinthe
early as Mook et al. (1971), but notably absent for SWIFT
relatively low states in which ourbinaries were observed.It
J1753.5−0127(Durant et al.2009).Usingfastspectroscopy,
is thus difficult to reconcile the origin of the fastest vari-
itwouldbepossibletomeasurethevariabilityinlinescom-
abilityinopticalbeingduetoX-rayreprocessing. Thissug-
paredtoX-rays,asopposedtothevariabilityinthecontin-
gests that there are additional processes involved in accre-
uum (or therelative variability of lines and continuum).
tion,that arenotpart ofthestandardmodel, theaccretion
process is more complex than previously thought.
Since the column density required to reach an optical
This does not mean, however, that reprocessing is ab- depth of 1 (i.e., attenuation by a factor e) for photon en-
sent altogether: if X-rays are illuminating cooler material, ergies >2keV is of the order > 1022cm−1, and higher for
8 Durant et al.
Figure4.ExampledynamicCCFs(upperleft:SWIFTJ1753.5−0127,2007-06-12(93119-02-02-00);upperright:GX339−4,2007-06-18
(93119-01-04); bottom: Sco X-1, 2004-05-18 (90020-01-02-02); all r/2–4keV, Obs IDs in parentheses). Each horizontal line is a single
CCFfroma50ssegment,withthecoloursrepresentingnegative (blue)orpositive(red)correlation.Successivelinesoverlap,seetext.
more energetic photons, it could be simply that the pene- emissionlines.Suchananalysisshowsthatbothsomeofthe
tration depth is so deep that the optical reprocessed light short-term and of the persistent optical flux originates in
takes time to emerge (e.g. McGowan et al. (2003)). With the accretion disc, in-fall stream, surface of the donor star
the X-ray spectra moderately hard as here, a far smaller etc.Thetotalamountoffluxcontained withintheemission
proportionoftheluminosityisreleased inthethermal,0.5– linesistypicallysmall comparedtothecontinuum,andone
2keVX-rayband thanfor soft sources. Conversely, irradia- would not expect the line flux to dominate even in a nar-
tion by higher-energy photons may be expected to produce row filter centred around a stronger line. Given that there
a stronger temperature change in the surface layers of this are typically not many such fluorescence lines in the spec-
disc (Wuet al. 2001). It would be interesting to do a sim- trum, one would certainly not expect the flux measured in
ilar study at thermal energies (<2keV), and also at much a broad-band filter to be affected by lines. Therefore, the
higher energies. Furthermore, it is not necessarily justified fastvariabilitymeasuredhereisindicativeofthecontinuum
toassumethattheX-raylight-curvereachingus,isthesame emission and not of the fluorescence lines, and there is no
asthat’seen’bythematerialwhichisproducingtheoptical contradictionbetweenthemajorityoftheCCFsignalbeing
lightreachingus.Adetailedthree-dimensionalmodelwould incompatible with reprocessing, and the lines which are in-
berequiredtodescribethisprocess;howeverwehavefound deednecessarilyproducedbyreprocessing.Furthermore,we
that the light-curves are related, but not as we might have have not considered slow variability (δt > 20s) here at all,
expected. where reprocessing is known to occur.
In Section 1 we noted that for the particular circum- van Paradijs & McClintock (1994) made some theoret-
stances of an X-ray burst, optical emission by reprocessing icalpredictionsontheamountofluminositytobeexpected
is clearly observed. We also mentioned the use of Doppler fromreprocessinginanX-raybinary.Theyproposealinear
Tomography to map the sites of emission using the varia- relationship for the visual luminosity L ∝ L1/2P2/3 (P is
V X
tionsoflineprofileswithorbitalphase,forparticular,strong the binary period and L the X-ray luminosity responsi-
X
X-ray binaries: optical/X-ray cross correlations 9
Figure5.EvolutionofthepositivecorrelationcomponentofthedynamicCCFforScoX-1,2004-05-18(Figure4,lowerpanel).Asingle,
positiveGaussianhasbeenfittedtoeachline,asawaytoestimatethecentreofthepositivecorrelationpeak.Theuncertaintiesonthis
fit have been found using realistic errors (see text) and the error-bars represent 1-σ confidence limits. On the left panel, we show the
best-fitlocationinδtoftheGaussian, andit’suncertainty, andontherightpanel weshowthefitted amplitudeanditsuncertainty for
eachCCFline.Wherethemarkerandassociatederrorbararemissing,theGaussianfitfailed.
ble for reprocessing). In a linear fit to several well-studied
LMXBs, theyfind absolute magnitude
P 2/3 L 1/2
M =1.57(24)−2.27(32)log X (1)
V (cid:20)(cid:16)1hr(cid:17) (cid:16)LEdd(cid:17) (cid:21)
whereL istheEddingtonluminosity.Applyingthesame
Edd
method, and making reasonable assumptions for the un-
known L /L and using a range of possible distances,
X Edd
we have plotted the four objects in our study, plus XTE
J1118+480 nexttotherelationshipgiveninEquation1,see
Figure 6 (first discussed by Gandhi et al. 2010 for the spe-
cific case of GX 339−4). For the purposes of this plot, the
luminosity is in the 1–100keV range (as extrapolated from
spectralfits),andassumedalltocontributetoreprocessing,
andthemagnitudesarecorrectedforreddening,whichisan
additional source of uncertainty. Only for Cyg X-2 would
one expect reprocessing to be a significant fraction of the
optical emission. Perhaps it should not be a surprise, then, Figure 6. Expected absolute magnitudes predicted by
thatreprocessingdoesnotappeartomakemuchofadiffer- vanParadijs&McClintock (1994) (solid line) compared to the
ence to the CCFs; but conversely a new source of the opti- measured magnitudes for the X-ray binaries of interest (mark-
calvariability,anditsconnectiontoX-raysisrequired.Note ers). The dotted lines indicate a range of plausible distances for
thatthesystemsshowingthemostunusualtimingproperties each object. Σ is as defined by these authors, the expression in
(and the fastest variability), XTE J1118+480, GX 339−4 squarebrackets inEquation1.
and SWIFT J1753.5−0127 are also the ones lying furthest
fromthevan Paradijs & McClintock(1994)relation.Itisin-
terestingtonotethattheseareblackholesystems,whereas Uttley et al.(2005),andimpliesthatthelight-curvescannot
theneutronstarssystemsliemuchclosertotherelationship. bedescribed byasimple shotprocess ofindependentflares,
Gandhi(2009)foundthatarelationshipexistsbetween butratherthatthesizeanddurationofeventsisrelated,and
the RMS and flux for the three binary systems GX 339−4, probably connected to their location in the accretion disc.
SWIFTJ1753.5−0127 andXTEJ1118+480.Thetwoquan- Theemission thuscannotoriginatefrom manyindependent
tities can be adequately described by a linear trend (with launching sites. Thus any theory wishing to describe the
significantscatter),thatdoesnotpassthroughzero,forvari- CCFbehaviourabovemustalsoconsiderthisimportantre-
oustime-scales.SuchbehaviourhadbeenfoundinX-raysby sult.
10 Durant et al.
In our observations, variability is seen down to the infra-red emission. Fast variability from a jet-like compo-
shortesttime-scalessampledforeverysource,andtheresult- nent has been studied in detail by Eikenberry et al. (2008)
ingCCFs havesuchsharp gradientsthatsomeofthecorre- for thecase of themicro-quasar GRS 1915+105.
lationmustoccuratthesetime-scalesorfaster.Onewonders • In any scenario, and indeed in some of the ones above,
how much more structure would be discovered with higher onerequiresasourceofinstabilitytodriveemissionenhance-
timeresolution,highsignal-to-noiseobservations.Variations ments.Suchinstabilitiesmaynaturallyarisefromtheinter-
of the CCFs with X-ray or optical band is an indication actions of magnetic fieldsandmatter, and act as aprimary
that the varying component responsible for the CCF sig- channel to emit energy from the system. The presence of
natures has a different spectrum to the average spectrum. jets and of high viscosity in the accretion discs are often
Differences between the CCFs of the various bands will be seen asevidenceforstrong large-scale fields, although more
affected by the difference signal-to-noise of the individual direct evidence(suchas Zeeman linesor cyclotron harmon-
light-curve,differences that are hard to model. ics) is missing (Lovelace et al. 2009).Notethat for thecase
Anumberofqualitativemodelshaveappearedsincethe ofSWIFTJ1753.5−0127, humpswereseen inthespectrum
initial discoveryin Kanbach et al. (2001) oftheunexpected that may suggest cyclotron emission (Durant et al. 2009).
correlations for XTE J1118+480:-
In summary, there are several plausible ideas for the inter-
action of low-energy and high-energy emission in accretion
• The first attempt was by the same authors in more
systems.Typicallytheyhavebeenformulatedtoexplainone
detailedanalysis(Spruit & Kanbach2002).Theirsimplistic
particularset ofobservations,andsolack generality orpre-
description was of blobs of dense material in the accretion
dictions.
disc,havingahigherdensityandthereforelargerverticalex-
Asmentionedinsomeofthemodelswhichprovidepos-
tent. As they travel towards the central source, they would
sible explanations for our CCFs, multiple spectral compo-
partly obscure the X-ray light-source, just before being ac-
nent may be involved, some of which span large ranges of
creted and causing an increase in X-ray luminosity. Unfor-
the available EM spectrum. Both the optical range and 2–
tunately,themodeldidnotincludedetailedpredictions.We
20keV in X-raysare relatively small windows, and it is not
wouldexpect,however,eitherX-rayenergyindependentbe-
at present possible to disentangle spectral components, at
haviour (for partial covering by a dense, opaque blob) or
least for the time-varying portion. In order to separate the
variability much stronger in softer X-ray bands(for moder-
spectral componentswithin theemission, muchwider spec-
ate optical depth).
tralcoverageisrequired.SincefastIRdevicesarenowstart-
• Malzac et al.(2004)producedanalternativetoymodel
ing to be available, coupled with wide spectral range X-ray
toexplainXTEJ1118+480’sCCF.Thisinvolvesamagnetic
satellites such as SWIFT and Suzaku, it is possible to ex-
energyreservoir,wheretheenergyinputisastochasticpro-
tend this work. Naturally, observations of more sources in
cess, and the output can be channelled either to X-ray lu-
morestateswillhelpanswertheubiquityorotherwiseofthe
minosityorthejet.Thustheemissionatamomentdepends
behaviourpresented here.
not only on thecurrent accretion rate, but on the past his-
Itisclearthatanti-correlationsinCCFsarenotsimply
tory;theemissionmodesarethereforelinkedinadifferential
a curiosity restricted to a couple of sources. Here we have
relationship. Such a model can quantitatively explain the
showntheirappearance(foratleastsomeofthetime)intwo
cross-andauto-correlation function,althoughhowtomain-
blackholebinariesandtwoNSbinaries.Giventherelatively
tain such an energetic magnetised zone is not addressed.
sparse sampling and short datasets examined so far, their
Coupling between the different emission zones, at various
presenceheremaysuggestthatthisphenomenonisfarmore
time-scales is required by the flux-RMS relationship men-
common than previously thought. Longer coverage during
tioned above. (Yuanet al. 2005) developed a quantitative
various X-raystates is required to test this hypothesis.
model along the ideas of multiple contributing components
to theoptical flux.
• Casella & Pe’er(2009)provideyetanotherexplanation,
ACKNOWLEDGMENTS
thistimequestioningtheassumedsynchrotronspectrumex-
pected from a magnetised outflow. Typically a broad-band MDwassupportedbytheSpanishMinistryofScienceunder
flat Fν spectrum is assumed, breaking and falling in the grant AYA2007-66887 during part of this work, and partly
IR-range;but thisassumes a special magnetic field/outflow supported through the US National Science Foundation
configuration, developed to match flat radio spectra. For grant No. 0908733; RC, TS and JC received some support
suitablemagneticfields,itcanbethatthesynchrotronspec- from Consolider-Ingeniero 2010 Program grant CSD2006-
trum had a bump near the optical range, but also provides 00070;RCacknowledgesaRamonyCajalfellowship(RYC-
the bulk of the X-ray flux. Thus the emission in the two 2007-01046). RXTE is operated by NASA, and ULTRA-
wavebandisintrinsically connected,andtherelativetiming CAM was used as a visitor instrument at ESO and La
dependsonthemagneticfieldstrengthandgeometryinthe Palma, Spain.
jet.
• Conversely,partoftheX-rayemissioncouldbedirectly
caused by Comptonisation of the synchrotron jet compo-
REFERENCES
nent, e.g. Markoff et al. (2005). This could explain a num-
ber of the longer-term correlation trends in various X-ray Bartlett M. S., 1955, An Introduction to Stochastic Pro-
states, e.g., for GX 339−4 (Coriat et al. 2009). What the cesses. CUP
consequence of this would be on shorter time-scales is less Bradshaw C. F., Titarchuk L., Kuznetsov S., 2007, ApJ,
clear,particularlysincethemodellingmainlyconcernedthe 663, 1225