The complex behaviour of the microquasar GRS 1915+105 in the rho class observed with BeppoSAX. I: Timing analysis

3.4 MB·English

by  E. Massaro

Astronomy & Astrophysics manuscript no. AA˙2009˙12908˙Massaro˙arx (cid:13)c ESO 2010
January 25, 2010
The complex behaviour of the microquasar GRS 1915+105 in
the ρ class observed with BeppoSAX. I: Timing analysis ⋆
E. Massaro1, G. Ventura2, F. Massa2,3, M. Feroci4, T. Mineo5, G. Cusumano5, P. Casella6, and T. Belloni7
0
1
0 1 Dipartimento diFisica, Universit´a La Sapienza, Piazzale A.Moro 2, I-00185 Roma, Italy
2 2 Stazione Astronomica diVallinfreda, via del Tramonto, Vallinfreda (RM), Italy
n 3 INFN-SezionediRoma1 (retired),Roma, Italy
a 4 INAF,Istitutodi Astrofisica Spaziale e Fisica cosmica diRoma, via del Fosso delCavaliere 100, I-00113 Roma, Italy
J 5 INAF,Istitutodi Astrofisica Spaziale e Fisica cosmica diPalermo, viaU. La Malfa 153, I-90146 Palermo, Italy
5 6 Astronomical Institute,University of Amsterdam, The Netherlands
2 7 INAF,Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807 Merate, Italy

] Received ....; accepted ....
E
H
ABSTRACT
.
h
p GRS 1915+105 was observed by BeppoSAX for about 10 days in October 2000. For about 80% of the time, thesource was in
- thevariabilityclass ρ,characterised byaseriesofrecurrentbursts.Wedescribetheresultsofthetiminganalysisperformed on
o
the MECS (1.6–10 keV) and PDS (15–100 keV) data. The X-ray count rate from GRS 1915+105 showed an increasing trend
r
t withdifferentcharacteristicsinthevariousenergybands:inthebands(1.6–3keV)and(15–100keV),itwasnearlystableinthe
s first partof thepointingandincreased in arathershort timebyabout 20%, while intheenergy range(3–10 keV)theincrease
a
[ had a smoother trend.
Fourier and wavelet analyses detect a variation in the recurrence time of the bursts, from 45–50 s to about 75 s, which appear

1 well correlated with the count rate. From the power distribution of peaks in Fourier periodograms and wavelet spectra, we
v
distinguishedbetweentheregularandirregularvariabilitymodesoftheρclass,whicharerelatedtovariationsinthecountrate
6
in the3–10 keV range.
0
We identified two components in the burst structure: the slow leading trail, and the pulse, superimposed on a rather stable
4
level.Pulsesaregenerally structuredinaseriesofpeaksandtheirnumberisrelatedtotheregularitymodes:themeannumber
4
. ofpeaksislower than2in theregular modeandincreases uptovalueshigherthan3intheirregular mode.Wefound thatthe
1
change in the recurrence time of the regular mode is caused by the slow leading trails, while the duration of the pulse phase
0
remainsfarmorestable.Theevolutioninthemeancountratesshowsthatthetimebehaviourofboththeleadingtrailandthe
0
baseline level are very similar to those observed in the 1.6–3 and 15–100 keV ranges, while that of the pulse follows the peak
1
number.
:
v Thesedifferencesinthetimebehaviourandcountratesatdifferentenergiesindicatethattheprocessresponsibleforthepulses
i must produce the strongest emission between 3 and 10 keV, while that associated with both the leading trail and the baseline
X
dominates at lower and higher energies.
r
a
Key words.stars: binaries: close - stars: accretion - stars: individual: GRS 1915+105 - X-rays:stars
1. Introduction The optical counterpart was identified by Castro-
Tiradoetal.(2001)withabinarysystemoforbitalperiod
The galactic microquasar GRS 1915+105 was discovered
about33days(Greiner,Cuby&McCaughrean2001)con-
in1992inthehardX-rayband(Castro-Tirado,Brandt&
tainingablackholewhoseestimatedmassis14.0±4.4M⊙
Lund1992).VLAimagesofthe radiocounterpartshowed
(Harlaftis & Greiner 2004). The X-ray behaviour of GRS
two opposite radiojets movingatan apparentsuperlumi-
1915+105is characterised by strong variability with very
nalvelocity,andfromtheirpropermotionsbothadistance
bright and quiet phases. The spectrum is generally fit-
ofabout12kpcandaninclinationangletothelineofsight
ted by atleasttwo components:amulti-temperature disk
of about 70◦ were inferred (Mirabel & Rodriguez 1994).
black body and a power law (possibly with a variable ex-
Send offprint requests to: [email protected] ponential cut-off) extending up to several hundreds keV.
⋆ TableA.2andTableA.3areavailableinelectronicformat During the bursts, the main spectral parameters of the
CDS via anonymous ftp to cdsarc.ustrasbg.fr (130.79.128)
2 E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class
thermal component exhibit significant variations, which similar time and afterwards returned to the former one.
were interpreted as representing the emptying and refill- Transitionsfrom/totheρclassto/fromotherclasseswere
ing of the inner portion of the accretion disk (Belloni et described by Naik et al. (2002), Chakrabarti et al. (2004,
al. 1997a).Quasi-periodic oscillations were observedwith 2005), and Rodriguez et al. (2008).
the PCA experiment onboard RXTE at frequencies up A complete analysis of the timing and spectral prop-
to above 100 Hz (Morgan, Remillard & Greiner 1997; ertiesoftheρclasshasyettobeperformed.Thelongand
McClintock&Remillard2006)andastrongsignalaround nearly continuous data set, not yet published, presented
67Hz,alsostudiedbyBelloni,Mn´dez&Sa´nchez-Fernadez and analysed in this paper is unique for investigating the
(2001). A detailed account of the main properties and behaviour of GRS 1915+105 in this particular variability
modelling of GRS 1915+105 can be found in the review class. Because of the richness of the data set, we applied
paper by Fender & Belloni (2004). several techniques to obtain an as complete as possible
UsingalargecollectionofRXTEobservations,Belloni picture of the burst phenomenon, practically impossible
etal.(2000)defined12differentvariabilityclassesofX-ray to describe in a single paper. In this work,we studied the
emission,eachofthemcharacterisedbyatime profileand timing properties covering a range of timescales from a
spectral variability inferred from the dynamical hardness few seconds to a few days. We first investigated the vari-
ratio plots. This classification is potentially useful for de- ations in the mean brightness in different spectral bands
scribing the behaviour of this exceptional source and for onthe timescale ofa day andwe then applied Fourierpe-
understanding the physical processes responsible for the riodogramsandwavelettransformstostudy the temporal
X-ray emission, so we will refer to it when presenting our properties of the X-ray light curves. Finally, we investi-
results. These 12 variability classes, however, do not ex- gatedtheprofileofthebursts,overatimescaleofafewsec-
haust the very rich set of temporal patterns exhibited by onds,usingastatisticalapproach.Wesearchedforcorrela-
GRS1915+105:Klein-Woltetal.(2002)andHannikainen tionsbetweenthetimingbehaviourofGRS1915+105and
et al. (2003, 2005) reported two other variability classes. the X-ray brightness of the bursts, finding highly signifi-
Furthermore, GRS 1915+105 exhibits a wide variety of cant relations. All of these results are particularly useful
complex behaviours when class transitions occur. for addressing either the spectral analysisor studying the
GRS 1915+105 was observed by the Narrow Field onset of unstable phases in terms of chaotic processes.
Instruments (NFIs) onboard the BeppoSAX satellite These subjects will be described in detail in a couple of
(Boella et al. 1997a) on several occasions (Feroci et al. forthcoming papers.
1999, 2001; Ueda et al. 2002). The amount of data col-
lected during these pointings is very large and requires a
2. The observations
long and complex analysis. In the present article, we re-
port the results of an analysis of the time behaviour of TheBeppoSAX observationofGRS1915+105considered
GRS 1915+105 observed in the course of a long pointing in the present paper started on October 20, 2000 (MJD
in October 2000.On that occasion the source was mainly 51837.894)andterminatedonOctober 29after anoverall
observedintheρclass(Bellonietal.2000),whichischar- durationof768.79ks.Theobservationconsistedofseveral
acterised by a series of bursts, with a variable recurrence runs of a typical duration of about one day. Each run is
time from 40 to more than 100 seconds. The time pro- identifiedbyanumericcodeandconsistsofdatasegments
file of the bursts has a rather smooth rising branch (also correspondingtothevisibilityintervalsofthesourcealong
named a ‘shoulder’) followed by a series of intense and the satellite orbit. The data obtained with all the NFIs
short peaks with a fast decline. can be retrived from the BeppoSAX archive at the ASI
The first observation of GRS 1915+105 in the ρ class Science Data Center.
reported in the literature was performed on 15 0ctober In this paper, we limit our analysis to the data ob-
1996 with Rossi-XTE (Taam, Chen & Swank 1997) and tainedinthefirstsixrunsandpartiallyintheseventhone
the bursts exhibit a typical structure with two and more foratotaldurationofabout610,000seconds,whichcovers
peaks. Their typical profile in the 2–13 keV band also aboutthe80%oftheentirepointing.ThenetMECSexpo-
differed from that in the 13-60 keV band. Belloni et al. sure time is 257 ks, while the PDS net exposure amounts
(1997a,b) and Taam, Chen & Swank (1997) interpreted to 123 ks. This choice is motivated by, in this period,
this bursting activity as the result of thermal/viscous GRS1915+105remainingmainlyintheρclasswithsome
instabilities in an accretion disk, in general agreement phases of instability similar to the κ class. In the data
with the expectations of previous theoretical calculations acquared during the last few orbits of the seventh run
(Taam & Lin 1984). and during the two remaining ones, the source changed
Other RXTE observations of the same class were de- to other and more complex classes and therefore, will be
scribed by Vilhu & Nevalainen (1998), Paul et al. (1998), analysed in a forthcoming paper. The log of the observa-
and Yadav et al. (1999), who presented the results of a tion runs considered in the present paper (see Table A.1)
long pointing of GRS 1915+105 performed in June 1997 aswellasthedetailsofthe datareductionarereportedin
with the IXAE onboardthe IRS-P3 satellite. On that oc- Appendix I.
casion the source was in the ρ class for about five days, It is practically impossible to describe completely this
then changed to the κ class in which it remained for a enormous amount of data and therefore we developed a
E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class 3
600 60
A8b A8b
400 40
200 20
0 0
C2 C2
400 40
200 20
s s
s/ s/
nt 0 nt 0
u u
o E5 o E5
C C
400 40
200 20
0 0
F7 F7
400 40
200 20
0 0
0 200 400 600 800 1000 0 200 400 600 800 1000
Time (seconds) Time (seconds)
Fig.1. Segments of MECS (1.6–10 keV) light curves ex- Fig.2. Segments of PDS (15–100 keV) light curves ex-
tractedfromfourdataseries(toptobottom:A8b,C2,E5 tracted from the same times series of Fig. 1. Time bin
and F7) at different times during the BeppoSAX obser- width is 2.5 s. Note that individual bursts are more ap-
vations of October 2000. Time bin width is 0.5 s and the parentintheE5series(thidpanel)thanintheotherthree.
startingtimeofeachsegmentisarbitrarilyselectedwithin
the series. Note that the first two and the fourth panels
haviour of the source; we also note that bursts in PDS
exhibit the characteristic time profile of the ρ class, while
series appear sharper than those of the MECS.
the third panel has a more complex structure.
In the various panels in Figs. 1 and 2, there is an im-
portant indication of the change in the mean flux of the
rather simple classification scheme for the timing proper- source. Both of the last data series (F7) have count rates
ties of individual segments based on Fourier and wavelet that are significantly higher than the other three. In par-
analyses.Toachieveaclearerunderstanding,however,we ticular, the series in Fig. 1 shows an increase in the mini-
selected some data series that are representative of the mum level of about 30%from ∼120counts/s in the series
different behaviour of GRS 1915+105 and used them as A8bto∼165counts/sinF7,whilethebursts’heightdoes
examples throughout this paper. These series are named not show a comparable increase.
A8b,C2,E5,andF7(seeAppendixIIandTableA.2)and
some portions of them are of equal length, 1,000 seconds,
3. Slow variations
asshowninFig.1,fortheMECSandinFig.2forthePDS,
for which a time binning greater than MECS was used to The X-ray flux from GRS 1915+105 varied during the
increasethe signalto noise ratio(S/N).It is possiblethat observation, exhibiting a generally increasing trend with
the source exhibited the behaviour characteristic of the ρ superimposed variations on timescales of a few hours.
class of Belloni et al. (2000). We note, however that the Changes occurringonthe scale of one day orlonger (slow
light curve in the third panel (E5) exhibits behaviour in- variations) are evident from the evolution in the count
termediate between this and the κ class, characterisedby rate in the MECS and PDS bands averaged over each
broad and slow bursts. The S/N of PDS data is poorer time segment. Figure 3 shows the count rate history of
than MECS and the bursts of A8b, C2, and F7 segments the MECS (1.6–10 keV) and PDS (15 – 100 keV) energy
arebarelyapparent,while those ofthe E5segmentareall bands.ThemeancountrateoftheMECS,computedonly
clearly distinguishable. As discussed later, this finding is from time series longer than 500 seconds, increased from
a consequence of a spectral evolution related to the be- ∼200counts/satthebeginningoftheobservationtoreach
4 E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class
280
55 1.6 - 3 keV
MECS (1.6 - 10 keV)
260
50
s /s 240 45
nt
u
co 220 40
)
s
s/
200 nt 3 - 6 keV
u 160
o
c
180 e (
at 140
r
nt
60 u
PDS (15 - 100 keV) o
55 an c 120
e
m
nts/s 50 40 6 -10 keV
ou 45
c
35
40
30
35
30
0 100 200 300 400 500 600 0 100 200 300 400 500 600
Time (ks) Time (ks)
Fig.3. Long-term evolution of the X-ray count rates of Fig.4. ThetimeevolutionoftheMECSmeancountrate
GRS 1915+105 during the long observation of October in three energy bands: 1.6–3 keV, 3–6 keV and 6–10 keV
2000 in the MECS (upper panel) and PDS (lower panel) (top to bottom). The two lines (red in the electronic ver-
energybands.Thedashedlineindicatesthelinearbest-fit sion) in the upper panel are the linear best fits in the
toMECSdata.InthePDSdata,twobrightnessstatesare correspondingintervals.The thick horizontallines (black,
evident with a short transition between them, occurring redandblueinthee-version)inthebottompanelindicate
between 375 and about 400 ks. the three time segments used in our analysis of the data:
the secondintervalincludes the localexcessofcountrate.
∼250 counts/s at the end. It can be described by a linear
interpolation(thelinearcorrelationcoefficientisr=0.884) ences appear between them. The low energy plot is re-
with a positive rate of ∼7 (counts/s)/day. markablysimilartothatofthe PDS:the meancountrate
The evolutionin the mean PDS count rate appears to was almost constant around 43 counts/s up to ∼375 ks,
be different fromthat ofthe MECSand showstwo rather thenincreasedoverabout30ksto∼51counts/sandfluc-
longstatesofdifferentintensity:inthefirstone,themean tuatedaroundthishighleveluntiltheend.Intheinterme-
count rate varied between 35 and 44 counts/s,whereasin diate and high energy ranges, the count rate evolution is
thesecondstateitwasbetween48and57counts/s.These muchclosertothegeneralMECStrend.Atenergieshigher
twostatesareseparatedbyarelativelyfasttransitionthat than 6 keV, however,the countrate in the centralpartof
started at about 375 ks after the beginning of the point- the observation had a mean level of around 38 counts/s,
ing and lasted about 30 ks, thus including the time series higher than in the previous portion (∼32 counts/s). This
from E7 to E12.The mean PDS count rate changed from high level finished just before the fast increase in the low
the averagevalue 39.4 and a standarddeviation of 1.9,to energyand PDScurves.A similar changecanalsobe rec-
51.7and2.7,respectively,withacorrespondingluminosity ognized in the intermediate band, but is absent both at
increase above 15 keV by about 30%. lower energies and in the PDS. To take this feature into
To obtain a clearer description of these different be- account, we divided the entire observation into three in-
haviours, it is useful to consider the count rate evolution tervals: the first interval extends from the beginning to
in three narrow bands of the MECS, of nominal energies about 170 ks and includes the series up to B15a, the sec-
of 1.6–3,3–6,and 6–10keV (the correspondencewith the ondfrom∼170ksto∼380ks,includestheentirebumpin
true photon energy being good because the instrumental the 6-10 keV band (series B15b to E7), the third interval
response matrix is essentially diagonal) and selected to coverstheremainingtimefromtheseriesE8untiltheend.
haveasufficientlyhighS/N.Theresultingplotsareshown These intervalsare indicated by the three horizontallines
in the three panels of Fig. 4 and some interesting differ- in the bottom panel of Fig. 4.
E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class 5
4. Fourier and wavelet classification
60
s
ct/ The first approach to investigating the timescales of the
V) burst sequence in each data series is to derive the Fourier
e
k50 power spectra or periodograms. The different appearance
3
6- oftheseperiodogramsleadustointroduceapracticalclas-
1.
( sification of seriesthat is useful to a synthetic description
S
C40 ofthevariabilityinGRS1915+105inthecourseoftheob-
E
M servation. This classification is also useful to the study of
the chaotic states that appear in the complex limit-cycle
s
ct/160 phenomenology.WearguethattheGRS1915+105system
)
V in the ρ state can also exhibit states with chaotic prop-
e
k erties (see, the analysis of Misra et al. 2006), as we will
6 140
3- discuss in future work.
(
S In several data series, however, there are large varia-
C
E120 tions from one burst to the subsequent one that are not
M
described well by the corresponding periodogram. To ob-
ct/s40 tainmoreinformationaboutvariationsoccurringonscales
) ofbetweenafewtensandhundredsofseconds,weapplied
V
e the wavelet transform and devised a more complete two
k
0 35 parameter classification.
1
-
6
(
S 30
C
E 4.1. Fourier periodograms and classification
M
25
35 40 45 50 55 60 A large fraction of the Fourier periodograms (hereafter
PDS (15-100 keV) counts/s FP)exhibitasingledominantpeak,indicatingthatbursts
occurredwitharatherstablerecurrencetime,T .Incon-
rec
trast other spectra have two or more dominant features
Fig.5. The mean MECS count rates in the three bands thatdonotcorrespondtotheharmonicsofthemainpeak.
1.6-3 keV (top panel), 3-6 keV (middle panel), and 6- We prefer to use the term recurrence time instead of ‘pe-
10 keV (bottom panel) plotted against that of PDS. The riod’ because the burst sequence has never been observed
three symbols and colours corresponds to the data of the toremainverystablefortimeintervalsofaboutonehour,
threetimeintervalsoftheMECS:firstinterval(blackfilled as shown by the wavelet analysis presented in Sect. 4.2.
squares), second interval (red open circles), third interval In Table A.3, we reported the values of T and the cor-
rec
(blue filled triangles). responding FP time resolution ∆t that is an estimate of
theuncertainty.Asillustratedbytheclassificationscheme
presented in Appendix III, we introduced three types of
periodograms accordingto the power distribution: S type
The differences between the various energy bands be- when only one dominant peak is apparent in the FP, T
come clearer in plots that compare the mean count rates type whentwopeaksarepresent,andMtypeforahigher
in three MECS bands with in the PDS band (Fig. 5). As peak number. Figure 6 shows the FPs of the four MECS
expected from the similar time evolution, the 1.6–3 keV data series plotted in Fig. 1: the first FP is of S type, the
MECS and PDS count rates have a strong positive cor- third of M type, and the remainder are both of T type
relation: the linear correlation coefficient is r = 0.974, with different peak heights and separation.
confirming the very tight relationship. Similar trends are WecomputedtheFPsforthePDStimeserieswithdu-
also exhibited by the count rates in the two other MECS rations comparable to those of the corresponding MECS
bands with the exceptionof the data points in the second series. Their classification, however, is not as good as for
interval, which do not follow the correlationand show an the MECS because of the low S/N ratio. Figure 7 shows
increase in scatter with energy. There are, however,some the FPs of the already considered four series: significant
points in the second interval with a rather low count rate peaks are present at the same periods as those of the
that are mixed with those of the first interval. These se- MECS series, although the power distributions between
ries occurred in the first part of the interval and their the peaks differ. We note that the power at the first har-
behaviourwasremarkablysimilar to thatwhichis typical monic in the PDS periodograms is generally higher than
ofseriesinthefirstinterval.Theseresultscanbeassumed in the MECS.
to be indicative of a close relation between the processes AninterestingresultisthechangeofT inthecourse
rec
responsible for the emission below ∼3 keV and above 15 of the pointing. In Fig. 8, the values of T are plotted
rec
keV, while in the range (3–15 keV) an additional contri- asafunctionoftimeforthe threeintervalsusingdifferent
bution of a different origin can occasionally be observed. symbol in order to distinguish the type of each series. In
6 E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class
10 A8b (S2) 10 A8b
5 5
0 0
10 C5 (T1) 10 C5
er 5 er 5
w w
o o
p p
d 0 d 0
e e
s s
li 10 E5 (M0) li 10 E5
a a
m m
r r
o o
N 5 N 5
0 0
10 F7 (T2) 10 F7
5 5
0 0
0 25 50 75 100 125 0 25 50 75 100 125
Period (seconds) Period (seconds)
Fig.6. PeriodogramsoffourMECStimesegmentsshown Fig.7. Periodograms of four PDS time segments (from
in Fig. 1. The spectral classification based on Fourier pe- top to bottom) A8b, C2, E5, F7. Note the similarity of
riodograms and wavelet scalograms in reported in paren- power distributions with those of Fig. 3 despite the lower
thesis. S/N.
thefirstinterval,T isratherstable,whileinthesecond tionbytakingaccountofhowthepowerisdistributedover
rec
thedispersionofT andthewidthofthepeakrangesof the various timescales in the course of the series, whereas
rec
M series are much higher than in the other two. We note the standard Fourier analysis considers the entire series.
that, as in Fig. 5,some series in the initial portionof this Thisanalysiscanbeperformedbymeansofwavelettrans-
latter interval, have T values close to those found in forms and the results are described in the following.
rec
thefirstinterval.Inthethirdinterval,therecurrencetime
exhibits a generally increasing trend.
4.2. Wavelet spectra and their classification
As shown in Sect. 3, the mean count rate increases
during the pointing and one can therefore expect that it The wavelet transform permits us to decompose a signal
should be correlated with T . In Fig. 9, T is plotted using a localized function. Standard wavelet analysis is
rec rec
againsttheMECS(forthetwobands1.6–3and3–10keV) based on the computation of wavelet power spectra (also
andPDScountrates.Inthesecondinterval,nocorrelation named wavelet scalograms, hereafter WS) defined as the
is apparent,while it is clearlyapparentin the third inter- normalised square of the modulus of the wavelet trans-
val. The linear correlation coefficient is around r = 0.89 form.Ashortdescriptionofthe algorithmanddefinitions
for all three energy bands. We note also the similarity of the spectral quantities are given in Appendix IV. An
betweenthe firstandthe thirdpanelofFig.9,whichcon- advantageofthis localanalysisis thatscalogramsareless
firms the strong relation between the lowest MECS and sensitive to telemetry gaps than FP and it is possible to
PDS energy ranges. consider longer time series.
The FP classification does not provide a univocal de- The WSs for three of the MECS time series in Fig. 1
scriptionofthesourcebehaviour:inafewcases,wefound (A8b,E5,F7)arepresentedintheleft-handsidepanelsof
serieswithanapparentlyirregularsequenceofbursts(e.g., Fig. 10:eachspectrum consists of a two dimensionalmap
D3aorD8b)butthepowermostlyconcentratedinasingle where the curves of equal power define regions coded in
peak. It was therefore necessaryto improve the classifica- color/greyscale.Because of the smoothing andinterpola-
E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class 7
90 90
80
80
70
60
ds) 70
on 50 1.6 - 3 keV
c
e
T(srec 60 4040 45 50 55
90
)
s 80
50 d
n
o 70
c
e
s 60
40 (
0 100 200 300 400 500 600 c
Time (ks) Tre 50 3 - 10 keV
40
160 180 200
Fig.8. TheevolutionintherecurrencetimeoftheMECS
90
seriesinthe courseoftheobservation.Alongtheabscissa,
we plot is the time elapsed since the beginning of the ob- 80
servation. Symbols indicate series of three time intervals:
70
first interval (filled black squares) including series from
A1b to C6, second interval (open red circles) including 60
series from C7 to E7, and a third interval (filled blue tri- 50 15 - 100 keV
angles) including series to G12c. For the T series, the re-
40
currencetimesofbothpeaksareplotted(usingsymbolsof 35 40 45 50 55 60
different size), whereas the points of M series correspond counts/second
tothecentroidvalueasgiveninTableA.3andthevertical
bar to the amplitude of the range.
Fig.9. The relations between the recurrence time and
the mean count rates in the energy bands. Top to bot-
tion necessaryto draw these curves,these plots provide a tom:MECS1.6–3keV,MECS3–10keV,PDS15–100keV.
qualitative description of the evolution of the power dur- Data symbols correspond to the three time intervals de-
ing the time series. fined in text (see also Fig. 4).
The differences between both the S and T series and
theMseriesareclearlyapparent:thetwoformertypesare
characterised by an uninterrupted and nearly horizontal andshorttimescales,andnostripcorrespondstothe first
strip,centredona timescale lengthcloseto the T esti- harmonics.
rec
mated from periodograms.The coarserresolution of WSs To evaluate the stability of the time series from WSs,
comparedto FPs does not allow us to identify clearly the weadoptedacriteriumbasedontherelativevarianceratio
peak separation in the T series, which is only 2 s (panel R (seeAppendixIV).Thereisacorrespondencebetween
w
3). However, a decrease in the highest power timescale is the values of R and the periodogram classification: this
w
discernible around 1700 seconds. Another strip of lower parameter tends to increase between the series S and T,
intensityiscentredaroundthe halfvalue ofT andcor- and between the series T and M. The presence of a sin-
rec
responds to the first harmonic.Small changesin T are gle dominant peak is not necessarily indicative of a sta-
rec
alsopresentintheWSoftheSseries,althoughtheirdura- ble signal:aseriescanexhibitlargeinstabilitiesoccurring
tion is limited to only a few bursts, too short to produce within a rather small time interval or frequent changes in
a separate peak in the FP. It is unclear whether there T but with a rather stable mean value. On the other
rec
is a sort of slow modulation of the recurrence time of hand, more peaks in the FP occurring with a rather nar-
subsequent bursts. In some cases, these changes occur on row range can correspond to small variations in the re-
timescaleslongerthanthedurationoftwoorthreebursts. currence time without a large modification of the bursts’
The M series have typically a far more irregular pat- structure. To take this variety of behaviour into account
tern also over short time intervals. As for the E5 series in we defined three classes, indicated by 0, 1, and 2 in order
Fig.10,poweris concentratedwithin a ratherbroadstrip ofincreasingstability(see Appendix IV).Themajorityof
thatexhibitsmeanderings,bifurcations,andinterruptions S spectra, 30 among 45, are of S2 type, 12 are S1, and 3
corresponding to short and long recurrence intervals be- S0;wealsonotethat10oftheS1spectrahaveR smaller
w
tween subsequent bursts. A fraction of the power that is than4.0,indicatingthattheirT isonlymoderatelyun-
rec
greaterthaninthetwoothercasesispresentonbothlong stable.In contrast,M seriesare ofclass 0 and1,andonly
8 E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class
10
A8ab
16
30
32
60
64
90
0 500 1000 1500 2000 2500 3000
10
s)
Time scale (s)3600 T (secondmax 361246 E5
90
0 500 1000 1500 2000 2500 3000
10
16 F7
30 32
60 64
90
0 500 1000 1500 2000 2500 3000
0 500 1000 1500 2000 2500 3000
Time (s) Time (seconds)
Fig.10. Left panel: iso-power representation of the scalograms of three MECS time series A8ab (the two series are
joined together), E5 and F7 (top to bottom), plotted in Fig.1. In each spectrum, the time scale increases towards the
bottom.The dark stripindicates the regionwherethe highestpoweris found andcorrespondsto T ;the stripofthe
rec
firstharmonicsis alsoclearlyvisible inthe topandbottompanels,whereasitis not presentin the highly irregularE5
series.
Right panel: time evolution of the timescales of the power maxima in the scalograms of the three series in the left
panel: T increases with a log scale towards the bottom to permit a clearer comparison with the spectra in the
j,max
left panel. Dashed lines represent the values of the T peaks or the peak centroid from Fourier periodograms.
rec
fourareofclass2butwithR valueslargerthan2.5.Nine some typical bursts of two of the selected time series to
w
spectraofTseriesareofclass1,confirmingtheirinterme- take account of the energy dependence.
diate type between S and M. The complete classification
of the spectra in Fig. 10 is indicated by the labels of Fig.
5.1. The statistical analysis
6.
The results presented in this and previous Sections
Toavoidthecomplicationscausedbytherichandvariable
suggest that one can consider two modes of the ρ class,
substructures,a statistical analysiswas performedafter a
which we call regular and irregular modes. The former is
running-averagesmoothingofalldataseriesfortheentire
associatedwiththe occurrenceofSorT spectraofstabil-
MECSenergybandwithawindowof5.5seconds(11time
ity class 1 or 2, the latter with M series or stability class
bins). Despite the complex structure, the burst shape af-
0.
ter smoothing appears rather stable. We introduced peak
number or “multiplicity” classes based on the number of
distinguishablefeaturesinthesmoothedprofile.Examples
5. Analysis of the burst structure
of bursts of different multiplicity from 1 (hereafter indi-
It is also important to study how the burst structure cated as p1) to 4 (p4) are shown in the various panels of
changesinthevariousmodes.AspointedoutbyBelloniet Fig.11.This classificationwasapplied to allthe 172time
al. (2000), the individual bursts, when analysed with suf- series,for a total number of 4083bursts, also because the
ficient time resolution,exhibit severalsubstructures,such series that are too short for the Fourier analysis still con-
as sharp spikes and dips, of durations as short as to a tain a large number of useful bursts.
few hundreds of milliseconds, and probably even shorter. We measured the duration T of individual bursts
b
These substructures are highly variable and therefore it starting from the initial minimum level, which is reached
is practically impossible to study the structure of thou- just after the decay tail of the preceding one. This mini-
sands of bursts with a high time resolution. We adopted mum levelwas verifiedto be nicely constantin the course
the two following approaches:we first performed a statis- of each series. It defines a baseline level (BL) over which
tical study of a large sample of bursts to describe their theburstsaresuperimposed.Wealsodividedtheirtypical
mean properties, and afterwards studied the structure of structureinto twoparts:the shoulderorslow leading trail
E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class 9
400 p1 p2
p1
FW 75
350 HM
300
250 SLT 50
200
)
s
s/
ct 150
( 25
e BL
at 100 Tb
nt r ds)
Cou 400 p3 p4 on 0
c
e
350 s
( p2
2 75
300 T
250 , 1
T
200 50
150
100
0 20 40 60 80 0 20 40 60 80 100 25
Time (seconds)
Fig.11. Four examples of burst shapes after smoothing
with peak number classification from p1 to p4. Best fits 0
20 40 60 80 100
using 2 Gaussian components for the peak and a fourth T (seconds)
b
degree polynomialfor the slowleading trailareshownfor
the two upper bursts (dashed/red line).
Fig.12. PlotofT1 (blacksolidcircles)andT2 (openblue
circles)versusT showingthe stronglinearcorrelationsof
b
(SLT), which is followed by a Pulse (see examples of this thecentraltimesofthetwoGaussiancurveswiththetotal
partition in Fig. 11). For a small number of bursts, the duration of the bursts. Times for p1 pulses are plotted in
identificationoftheendwastrickybecausethereisafinal the upper panel and those for the p2 pulses in the lower
and clearly separated pulse that occurs before the count panel.Linearbestfits(inred)arealsoshownforeachdata
rate has reached its lowest level. We called these bursts set. The noticeable similarity of these data distributions
anomalous andexcludedthem fromthe shape analysis.A indicates that there are no significant differences between
coupleofanomalousburstsareclearlyevidentinthelight these multiplicity classes.
curve of the E5 series shown in Fig. 1. Anomalous bursts
areobservedintheirregularmodeandveryrareorabsent
in the regular one. ualbursts,measuredtobethetimeseparationT between
b
Pulses, examined athigh time resolution,havetypical the minima of two subsequent bursts. The average T in
b
structures consisting of a sequence of peaks of variable regular time series is very close to T . Figure 12 shows
rec
heightandduration,butwhenstudiedoveratimescaleof a scatter plot of T1 and T2 against Tb for the two consid-
afewsecondstheyhavemorestableprofiles,suchasthose ered multiplicities: the points are very well aligned along
in Fig. 11. Pulses of p1 and p2 bursts were modelled by a straight lines and no significant difference is evident be-
combination of two Gaussian curves and a fourth degree tweenthetwomultiplicityclasses.Linearcorrelationcoef-
polynomialwasusedto reproduceSLT,whichterminated ficients areveryhighrangingfrom0.944to0.973.Best-fit
at the half maximum height of the pulse. Best-fit curves linearrelationshaveverysimilarslopes(within∼3%)and
are shown in the upper panels of Fig. 11: the need of the this means that the difference T2−T1, which can be con-
two Gaussian components for both p1 and p2 bursts is sideredtobeanestimateofthepulsewidth,ispractically
evident. We did not calculate best fits for bursts of type independent of T .
b
p3 or higher because they required additional Gaussian This result implies that series of type S2, but with
components and in some cases we did not obtain stable mainlydifferentrecurrencetimes,musthavepulsesofsim-
solutions. ilar width. To illustrate this statement, we plot in Fig.
A first relevant result of this analysis is that the cen- 13 two short segments of the two S2 series A8b and G9:
tral times T1 and T2 (T2 >T1) of the two Gaussian com- Trec is 49 s for the former and 73 s for the latter. Data
ponents, measured starting from the initial time of the were translated such that two bursts were superimposed
burst,arestronglycorrelatedwiththedurationofindivid- two bursts: we note that they are of comparable height
10 E. Massaro et al.: Thecomplex behaviour of GRS 1915+105 in theρ class
550
140
500 120 Burst
100
450
80
e400 60
at
nt r350 40 SLT
u
o 30
ECS c300 nts/s) 20
M250 ou 10
200 es (c 1000
at Pulse
150 nt r 80
u 60
o
C
100 40
0 50 100 150 200 250 300 350
Time (seconds) 20
180
BL
160
140
Fig.13. Comparisonbetweentwoshortsegmentsofequal
120
duration of the S2 series A8b (blue) and G9 (black) time
100
seriescharacterisedbyverydifferentT andmeancount
rec 0 100 200 300 400 500 600
rates. The A8b light curve has been shifted upward by
Time (ks)
90 ct/s to match the peaks’ height. Note the very good
agreement between the pulse shapes of the two series, in Fig.15. Time history of the mean MECS (1.6–10 keV)
contrasttotheleadingedgebeingmuchlongerinG9than count rates of the various components after the subtrac-
in A8b. The bin width is 0.5 s. tion of the BL (top to bottom): total burst, SLT, and the
peak integral. The behaviour of the BL is shown in the
lastpanel.Thecountratescalesinthethreeupperpanels
100
are equal, while that of the last one has been doubled in
T
80 b length. Symbol codes indicate the three time intervals as
60 in the other figures.
40
n (s) 60 SLT ainndthweidGt9hsaetriveasrtiahnacneiwniAth8tbh.eSLT,whichismuchlonger
o 40
ati The evolution of the durations and count rates of the
Dur 20 variousburstcomponents,averagedovereachdataseries,
0 is presented in Figs. 14 and 15, respectively. We assumed
that only data series with more than five bursts provide
60 FWHM
representative mean values. For bursts of multiplicity p3
40
or higher, for which no best-fit modelling was obtained,
20 the durationsof the FWHM wereestimateddirectly from
0 thesmoothedprofiles.ThefirstpanelinFig.14showsthe
ult. 4 multiplicity evolution of the mean Tb, which for the S and T series is
m 3 similar to that of T (see Fig. 8), while the latter has
rec
an 2 a largerscatter for the M series.The duration of the SLT
e
M 1 (secondpanelinFig.14)wasfarmoreregular:itincreased
0 veryslowlyfromthebeginningoftheobservationandthis
0 100 200 300 400 500 600
trend did not show appreciable changes in the second in-
Time (ks)
terval, while a moderate increase in the rate occurred in
Fig.14. Timehistoryofthedurationsofthevariouscom- the third interval, which became higher one only in the
ponents of bursts (top to bottom): hT i, meanSLT, mean last40ks.ThemeanFWMHofpulses(thirdpanel),which
b
pulses’ FWHM. The scales on the ordinates are identi- wasnearlyconstantinthefirstinterval,showedlargevari-
cal to ease the comparison of data. In the fourth panel, ationsinthesecondinterval:itincreasedforthefirsttime
we plot the evolution in the mean multiplicity of bursts. after 170 ks from the beginning of the observation and
Symbolsthatidentifytheseriesinthethreetimeintervals returned to the previous values after a few series; it then
are the same as those of Fig. 5. increased again at about 250 ks and remained high for
about 40 ks; a third high state was finally in the last and