16 Years of RXTE Monitoring of Five Anomalous X-ray Pulsars

1.5 MB·

by  Rim Dib

16 Years of RXTE Monitoring of Five Anomalous X-ray Pulsars
Rim Dib1 and Victoria M. Kaspi2
Department of Physics, McGill University, Montreal, QC H3A 2T8
4
1
0
2

n ABSTRACT
a
J We present a summary of the long-term evolution of various properties of the five non-

4 transientAnomalousX-rayPulsars(AXPs)1E1841−045,RXSJ170849.0−400910,1E2259+586,
1 4U0142+61,and1E1048.1−5937,regularlymonitoredwithRXTE from1996to2012. Wefocus

on three properties of these sources: the evolution of the timing, pulsed flux, and pulse profile.
]
E We report several new timing anomalies and radiative events, including a putative anti-glitch
H seen in 1E 2259+586 in 2009, and a second epoch of very large spin-down rate fluctuations in
1E1048.1−5937followingalargefluxoutburst. Wecompile thepropertiesofthe 11glitchesand
.
h
4 glitchcandidates observedfromthese 5 AXPs between1996and2012. Overall,these monitor-
p
ing observations reveal several apparent patterns in the behavior of this sample of AXPs: large
-
o radiative changes in AXPs (including long-lived flux enhancements, short bursts, and pulse pro-
r filechanges)arerare,occurringtypicallyonlyeveryfew yearsper source;largeradiativechanges
t
s are almost always accompanied by some form of timing anomaly, usually a spin-up glitch; only
a
[ 20–30% of timing anomalies are accompanied by any form of radiative change. We find that

AXP radiative behavior at the times of radiatively loud glitches is sufficiently similar to suggest
1
common physical origins. The similarity in glitch properties when comparing radiatively loud
v
5 and radiatively silent glitches in AXPs suggests a common physical origin in the stellar interior.
8 Finally,theoverallsimilarityofAXPandradiopulsarglitchessuggestsacommonphysicalorigin
0 for both phenomena.
3
. Subject headings: pulsars: individual (1E 1841−045) — pulsars: individual (RXS J170849.0−400910)
1
— pulsars: individual (1E 2259+586), — pulsars: individual (4U 0142+61) — pulsars: individual
0
(1E 1048.1−5937) — stars: neutron — X-rays: stars
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1
: 1. Introduction tonishing potential these objects have for ex-
v
plosive energy releases. The source of the en-
i
X Prior to the 1995 December launch of NASA’s ergy for the bursts and this giant flare was un-
Rossi X-ray Timing Explorer (RXTE), there ex-
r known, but was proposed to be the decay of
a isted a major puzzle surrounding two apparently an enormous > 1014 − 1015 G internal mag-
distinct class of high-energysources,Soft Gamma
netic field in a young neutron star – the so-called
Repeaters (SGRs) and Anomalous X-ray Pul-
“magnetar” model (Thompson & Duncan 1993;
sars (AXPs). At the time, three SGRs were
Thompson & Duncan1995;Thompson & Duncan
known and were classified as such due to their
1996).
distinctive repeating soft gamma-ray bursts. The
Meanwhile, roughly half-a-dozen AXPs had
famous ‘March 5’ event of 1979 (Mazets et al.
been identified by van Paradijs et al. (1995) as
1979), involving SGR 0526−66in the Large Mag-
‘anomalous’X-raypulsars,spectrallydistinctfrom
ellanic Cloud and the release of over 1044 erg
conventional accreting pulsars, and lying all in
in just a few minutes, demonstrated the as-
the Galactic Plane, with one in a supernova rem-
nant. Their spin-down luminosities failed by or-
[email protected]
ders of magnitude to account for their appar-
[email protected]
ently stable X-ray luminosities. For this rea-
1
son, they were generally believed to be some same class of object, with the SGRs the more ac-
strange form of low-mass X-ray binary, although tiveofthefamily,butwithcleartransitionobjects
no evidence for binary companions was seen between the two classes (e.g. Kaspi et al. 2001;
(e.g. Mereghetti & Stella 1995; Baykal & Swank Kulkarni et al. 2003; Israel et al. 2010). In other
1996; Baykal et al. 1998). Indeed the first RXTE words, a continuum of behaviors between AXPs
observations of AXPs were done intending to and SGRs has been observedsuch that their class
search for Doppler shifts due to binary motion definitionshavebeenheavilyblurredandthevery
(Mereghetti et al. 1998). Thompson & Duncan names ‘AXP’ and ‘SGR’ seem synonymous. Nev-
(1996) however, noted some similarities between ertheless, in this paper we continue to refer to
theAXPsandtheSGRs,andsuggestedthatboth the targets as AXPs, mainly for consistency with
are magnetically powered isolated young neutron pastpublicationsbasedonsubsetsofthedata,but
stars. clearlynotingthatsuchnomenclatureissomewhat
Thepost-RXTEpictureofSGRsandAXPshas out of date.
evolved considerably and indeed following inten- Much of today’s understanding of AXPs in
sivemonitoringcampaigns,suchasthatdescribed particular comes from the long-term systematic
in this paper, these objects appear no longer par- RXTE monitoring program of five AXPs. This
ticularly ‘anomalous’, though certainly still re- program used short snapshot observations of the
markable. In particular, the discovery of X-ray five bright,persistent AXPs takenregularlyevery
pulsationsintwoSGRsduringrelativelyquiescent fewweeksinordertomaintainfullpulsephaseco-
phases, along with the direct measument of spin- herence. Thisallowedthesource’sspinparameters
down in those objects (Kouveliotou et al. 1998; to be measured with high precision, enabling sen-
Kouveliotou et al. 1999; Hurley et al. 1999), as sitivity to glitches, and providing pulsed flux and
quantitatively predicted in the magnetar model, pulse profile monitoring, in addition to sensitivity
provided compelling evidence that SGRs are in- to bursting behavior. This paper presents a com-
deed magnetars. Subsequently, the RXTEdiscov- plete analysis of all RXTE data for the five AXP
eryofSGR-likeburstsintwoAXPs(Gavriil et al. monitoring targets, which are listed along with
2002; Kaspi et al. 2003), consistent again with their basic properties in Table 1. We present here
the expectations of the magnetar model as de- asystematicanduniformanalysisofdatafromthe
scribed by Thompson & Duncan (1996), argued commencementofregularmonitoringin1998(and
strongly for the identification of both classes even, in some cases, including data prior to that)
of objects as magnetars. The latter discovery and up to the final AXP observations made just
was a result of a systematic AXP monitoring before RXTE was shut off in early 2012. In total,
program that also demonstrated the great tim- we have analyzed 3202 individual RXTE observa-
ing stability of some AXPs (Kaspi et al. 1999), tions of the targets, a total of 10 Ms taken over a
that AXPs exhibit spin-up glitches (Kaspi et al. spanof15.7years. RXTErevealedmanyprevious
2000), and a variety of other interesting AXP unknown AXP phenomena and answered many
phenomenology that is generally understand- basic questions about AXPs and magnetars, but
able in the magnetar framework (Gavriil & Kaspi asthispapershows,italsoraisedmanynewques-
2002; Dall’Osso et al. 2003; Woods et al. 2004; tionsthathavesignificantbearingonourphysical
Gavriil et al.2004;Gavriil & Kaspi2004;Gavriil et al. understanding of magnetars.
2006; Dib et al. 2007; Dib et al. 2008a, 2009a; This paper is structured as follows. In §2, we
Gavriil et al. 2011). While there are still some present a quick overview of the five AXPs moni-
who argue that the quiescent X-ray emission of toredinthisproject. In§3wedescribethe RXTE
both classes is accretion-driven (e.g. Ertan et al. observations of our targets. In §4 we summa-
2009; Alpar et al. 2011), practically all existing rize the three kinds of analysis performed: tim-
accretion models still demand magnetar-strength ing,pulsedflux,andpulseprofile. In§5,wedetail
fields to power the observed bursts and giant our results for each source. In §6, we consider the
flares. Regardless, the concensus today, based behavior of each source – as well as the collective
largely on RXTE observations like those reported behaviorsofallthe targets– anddiscussourfind-
on here, is that SGRs and AXPs are one in the ingsandtheir implicationsforthe physicalnature
2
of these objects. similar timing residuals to those obtained from a
glitch fit.
2. Overview and Previous History of the During the same time period as the RXTE
Sources monitoring,RXSJ170849.0−400910wasobserved
sparsely with different X-ray imaging satellites
2.1. 1E 1841−045
Chandra, XMM and Swift. Rea et al. (2005),
1E 1841−045 is a 7.8-s AXP located in super- Campana et al. (2007) and Israel et al. (2007)
nova remnant Kes 73 (Vasisht & Gotthelf 1997). analysed the imaging observations and reported
It was observed by RXTE roughly twice per thesource’sphase-averagefluxtobevariable. Be-
month since 1999 February. cause the pulsed flux of the source was reported
to be stable, this suggested an anti-correlation
A study of a handful of archival X-ray obser-
vations of 1E 1841−045 spanning 15 years sug- between the phase-averaged flux and the pulsed
fraction. Rea et al.(2005),Campana et al.(2007)
gested the presence of deviations from a linear
and Israel et al. (2007) also claimed a correlation
spin-down which were initially attributed to tim-
between the flux variations and the glitches. This
ing noise (Vasisht & Gotthelf 1997).
flux variationandcorrelationwithglitcheshasre-
An analysis of the 1997−2006 RXTE moni-
centlybeenshowntohavebeenspurious,however
toring observations of this source revealed that
(Scholz et al., submitted.).
glitches had occured in 2002, 2003, and 2006
RXTE monitoringresultsforRXSJ170849.0−400910
(Dib et al.2008a). Italsorevealedastablepulsed
fluxinthe2−20keVband,andastablepulsepro- are presented in §5.2.
file. Zhu & Kaspi (2010) showed that the phase-
2.3. 1E 2259+586
averaged flux was stable during the same period
oftime. AfourthglitchwasreportedbyDib et al. 1E 2259+586 is a 7-s AXP in the supernova
(2008b) and Dib et al. (2009b). The parame- remnant CTB 109 (Fahlman & Gregory 1981)
ters for the 2nd glitch were revised by Dib et al. and has been studied extensively. In particular
(2009b) and are restated in §5.1 of this work. Baykal & Swank (1996) reported fluctuations in
In 2010, 1E 1841−045 exhibited 4 episodes of the source’s flux and spin down on a timescale of
short high-energy Swift-detected bursts. Bursts years. RXTE monitoring of 1E 2259+586started
were detected on May 6 2010, 2011 February 9, in 1996.
2011 June 23, and 2011 July 2 (Lin et al. 2011). After several years of stability, 1E 2259+586
The results of the analysis of the RXTE observa- entered an outburst phase in 2002 June in which
tionscollectedaroundthetimesofthesebursts,as almost every aspect of the emission suddenly
wellastheremainingresultsofRXTE monitoring changed: thepulsedandpersistentflux,thepulsed
of 1E 1841−045,are presented in §5.1. fraction, the timing properties, the spectral prop-
erties, and the pulse profile (Kaspi et al. 2003;
2.2. RXS J170849.0−400910
Woods et al.2004). Thereisevidencethatasimi-
RXSJ170849.0−400910isan11-sAXPdiscov- lar event happened in 1990 (Iwasawa et al. 1992).
The long-term recovery from the 2002 major out-
ered in 1996 (Sugizaki et al. 1997).
burst was studied by Zhu et al. (2008).
Like 1E 1841−045, RXS J170849.0−400910
A second glitch occured in 2007 and was re-
glitches frequently. The first glitch detected
ported in Dib et al. (2008b), Dib et al. (2009b),
from this source occured in 1999 (Kaspi et al.
Dib (2009), and I¸cdem et al. (2012). In con-
2000), the second in 2001 (Kaspi & Gavriil 2003;
trast to the previous glitch, it was radiatively
Dall’Osso et al. 2003), and the third in 2005
quiet. I¸cdem et al. (2012) also reported two tim-
(Dib et al. 2008a; Israel et al. 2007). Dib et al.
ing anomalies, the second of which is discussed
(2008a)alsoreportedonseveralglitchcandidates,
in §5.3 along with a summary of the results for
and reported no significant changes in the pulsed
this AXP. Very recently Archibald et al. (2013)
flux before 2006. These events were called ‘glitch
reported on a sudden spin-down event, an ‘anti-
candidates’becausea4thor5thorderpolynomial
glitch,’ as observed using Swift after our RXTE
fit to the same data near glitchepochs resulted in
3
monitoring ended. later dates (Gavriil et al. 2006; Dib et al. 2009a).
Following the flares, in 2003, the pulsar under-
2.4. 4U 0142+61
went large (factor > 12) changes in its rotational
frequency derivative on a timescale of weeks to
4U 0142+61 is an 8.7-s AXP. It was moni-
toredwith RXTE in 1997and from 2000to 2012. months (Gavriil & Kaspi 2004), something never
Morii et al. (2005) reported on a possible glitch before seen in an AXP. It is unclear whether this
timing-relatedepisodeandtheprecedingradiative
having occured in 1999, in a data gap. Dib et al.
(2007)showedthataglitchmayhaveoccured,but flares are related. This was discussed further by
Dib et al. (2009a).
thataslowfrequencyincreasecannotberuledout.
Dib et al.(2007)furthershowedthatfrom2000to Tiengo et al. (2005) reported on an XMM ob-
2006,thesource’spulsedfluxroseby29±8%inthe servation of 1E 1048.1−5937 in 2004, when the
2−10 keV band. There were hints that the rise in phase-averaged flux was lower than in 2003 but
the pulsed flux was towards the low-energy end still not back to its 2000 value, and when the
of the band, which was consistent with the hints pulsed fraction was higher than in 2003 but still
of spectral softening reported by Gonzalez et al. not back to its 2000 value, indicating that the
(2010) from the analysis of archival XMM data. source was still recovering from the second flare.
They reportedananti-correlationbetweenthe to-
In 2006 March, 4U 0142+61 entered an active
phase. Itexhibited sixX-raybursts,asseenusing tal flux and the pulsed fraction.
RXTE,the lastandlargestofwhichwasdetected Following the above events, from mid-2004 to
in 2007 February (Gavriil et al. 2011). During 2007March,1E1048.1−5937wentthroughaquiet
the active phase, the pulse morphology changed, phase. Therewaslittlevariationinthespin-down,
then slowly recovered,and the frequency behaved in the pulsed flux measuredby RXTE, andin the
as though it were recovering from a glitch, al- total flux measuredin a handful of X-rayimaging
though the glitch parameters were difficult to de- observations (Tam et al. 2008; Dib et al. 2009a).
termine because of the pulse profile changes. The In 2007 March, the source reactivated again
pulsed flux underwent changes as well, but only (Tam et al. 2008; Dib et al. 2009a). The pulsed
forthedurationoftheobservationscontainingthe flux rose for the third time during the mon-
bursts. The results of the RXTE monitoring of itoring program, this time by a factor ∼ 3
4U 0142+61 before, during, and after the active (2−10 keV), and the total flux rose by a factor
phase are presented in §5.4. of ∼ 7 (2−10 keV). This was simultaneous with
the largest AXP glitch observed by RXTE (see
2.5. 1E 1048.1−5937 §5). A re-analysis of the RXTE data performed
by Dib et al. (2009a) showed that the previous
1E 1048.1−5937 is a 6.5-s AXP. It has a long
two flares observed from the source were also ac-
history of timing variability and flux variabil-
companied by timing events. Tam et al. (2008)
ity at many different wavebands (see for exam-
analysed imaging observations from before and
ple, Mereghetti 1995, Mereghetti et al. 1998, and
after the glitch and derived an anti-correlation
Paul et al. 2000).
between the pulsed fraction and the total flux.
1E 1048.1−5937has been dubbed the “anoma-
After the initial onset of the outburst, the tim-
lous” Anomalous X-ray Pulsar because of its
ing and radiative parameters slowly recovered. A
unique variability behavior. In 2001 and in 2002,
few months later, the source started experiencing
theAXPexhibitedtwoslow-risepulsedfluxflares,
rapid changes in the frequency derivative for the
with a risetime on a timescale of weeks, and a de-
second time. An update on these variations is
cay on a timescale of months (Gavriil & Kaspi
presentedin§5.5alongwith the remaining results
2004). Gavriil et al. (2002) also reported two
of the 1E 1048.1−5937RXTE monitoring.
bursts from the direction of this source, which
happened near the peak of the first pulsed flux
flare. One of the two bursts was accompanied
by a short-term pulsed flux enhancement. Two
other bursts were detected from this source at
4
3. Observations and Time Series Prepara- servationcorrespondingtoafixedpulsephase. To
tion estimate the uncertainty on each TOA, we added
to each folded profile many realizations of Pois-
All observations presented here were obtained
son noise and re-cross-correlated each time. The
using the Proportional Counter Array (PCA) on-
phase uncertainty is determined from the stan-
board RXTE. The PCA consisted of an array of
dard deviation of the resulting simulated TOAs
five collimated xenon/methane multi-anode pro-
(Kaspi et al. 1999). The pulse phase φ at any
portional counter units (PCUs) operating in the
time t can usually be expressed as a Taylor ex-
2−60 keV range, with a total effective area of ap-
pansion,
proximately 6500 cm2 and a field of view of ∼1◦
FWHM (Jahoda et al. 1996).
1 1
Throughout the monitoring, we used the φ(t)=φ (t )+ν (t−t )+ ν˙ (t−t )2+ ν¨(t−t )3+...,
0 0 0 0 0 0 0 0
2 6
GoodXenonwithPropane and the GoodXenon data
(1)
modes to observe our sources. Both data modes
where ν ≡ 1/P is the pulse frequency, ν˙ ≡ dν/dt,
record photon arrival times with 1-µs resolution
etc., and subscript “0” denotes a parameter eval-
and bin photon energies into one of 256 channels.
uated at the reference epoch t=t .
To maximize the signal-to-noise ratio, we ana- 0
lyzed only those events from the top Xenon layer Once the TOAs were obtained, we performed
ofeachPCU.ThetotalnumberofRXTE observa- two kinds of phase-coherent timing analyses on
tionsanalyzedforeachsource,aswellasthedates fouroftheAXPs(1E1841−045,RXSJ170849.0−400910,
ofthe firstandthe lastanalyzedobservations,are 1E 2259+586,and 4U 0142+61).
shown in Table 2. In the first type of timing analysis, we consid-
For each observation, we reduced the data to ered all stretches of time uninterrupted by timing
the solar system barycenter, and then extracted discontinuities (see below). We fitted the TOAs
clean time series binned at a resolution of 1/32 s. in each time stretch to the above polynomial us-
For the timing and pulse profile analyses we ex- ing the pulsar timing software package TEMPO1.
tracted time series that included counts from all TEMPO returned the best-fit polynomials coef-
operationalPCUsinasource-specificenergyband ficients, the phase-coherent timing solution, and
that maximizes the signal-to-noise (see Table 2). also returned an absolute pulse number for each
Forthepulsedfluxanalysis,weextractedtime se- TOA. The resulting timing solutions are plotted
riesinfivebands(2−4keV,4−10keV,2−10keV, as red lines in Panel a of Figures 1, 2, 3, and 4,
4−20 keV, and 2−20 keV), not including PCU 0 and the corresponding timing residuals are shown
and PCU 1 because of the loss of their propane in Panel c of the same Figures. Timing parame-
layers. tersfromthesefits arepresentedinTables 3,4,5,
and 6.
4. Analysis In the second type of timing analysis, we di-
vided each inter-glitch (see below) stretch of time
4.1. Timing analysis
into many short overlapping segments. The num-
ber of TOAs contained in each segmentdepended
For the timing analysis, each barycentric
on the cadence at which the source was observed.
binned time series was epoch-folded using an
To get from one segment to the next, we shifted
ephemeris determined iteratively by maintaining
byoneTOA.Foreachsmallsegment,wefittedthe
phase coherence as we describe below. When an
TOAs to the above polynomial, allowing a single
ephemeris was not available, we folded the time
frequencyderivativeν˙. Thebest-fitν andν˙ forall
series using a frequency obtained from a peri-
small segments are presentedin Panels a and b of
odogram. Resulting pulse profiles, with 64 phase
Figures1through4. The horizontalerrorbarsin-
bins (32 bins in the case of 1E 1841−045), were
dicate the length of the individual segments, and
cross-correlatedintheFourierdomainwithahigh
the vertical error bars indicate the uncertainty in
signal-to-noise template created by adding phase-
ν and ν˙.
alignedprofiles. Thecross-correlationreturnedan
average pulse time-of-arrival (TOA) for each ob-
1Seehttp://www.atnf.csiro.au/research/pulsar/tempo.
5
Sudden changes in ν and ν˙ are called glitches. tive of order n−2 (see Dierckx, 1975 for more
Slow variations in ν˙ are usually grouped under details about splines). We fit a spline function
the name ‘timing noise.’ AXPs sometimes exhibit through each pulse number time series, weighed
eventsinwhichitisdifficulttodeterminewhether by the inverse of the square of the fractional er-
achangeinthetimingpropertiesoccuredabruptly rors. To minimize oscillations in the spline due
or progressively over a short period of time. This to noise, we set the spline smoothing parameter
often happens when the event occurs near a gap to allow the RMS phase residual obtained after
in the data. When the changes in the timing pa- subtracting the spline from the data points to
rameters at the epoch of such an event do not be twice the average 1σ uncertainty in the pulse
unambiguously identify it as a glitch, but are suf- phase. The smoothing parameter controls the
ficiently abrupt (i.e., necessitating an ephemeris tradeoff between closeness and smoothness of fit
consisting of a polynomialof degree4 or5 to flat- by varying the polynomial coefficients and the
ten the residualsnear the epochof the event), the spacing between the knots. We found the uncer-
discontinuitieswerecalled‘glitchcandidates’. The tainties onthe spline by adding Gaussiannoise to
timing parameters for the glitches and glitch can- ourdatapoints500times,withmeanequaltothe
didates are presented in Table 7. 1σ uncertainty on each data point, fitting each
Since the spin-down of 1E 1048.1−5937 was time with a spline, averaging all the splines, and
particularly unstable, and phase coherence could finding the standard deviation at each point.
only be maintained for periods of at most several The derivative of the spline function gave us
monthsatatime(Kaspi et al.2001;Gavriil & Kaspi the frequency of the pulsar as a function of time
2004; Tam et al. 2008; Dib et al. 2009a), the tim- (PanelaofFig.5),andthesecondderivativeofthe
ing analysis of 1E 1048.1−5937 was done differ- spline gaveus the frequency derivative of the pul-
ently. We broke the list of TOAs into many over- sar (Panel b of Fig. 5). The corresponding timing
lapping segmentsvaryingin lengthbetween3and residualsareshowninPanel6ofthesameFigure.
16 weeks depending on the local noise level of A comparison of the timing residuals for the five
the source. For each segment we used TEMPO AXPs is shown in Figure 6; see §5.2 for details.
to fit the TOAs using Equation 1 and extracted For 1E1841−045,we supplemented our RXTE
absolute pulse numbers. We then checked that timingdatawithtwoXMM observationstakenon
the pulse numbers of the observations present in 2002October5and2002October7,madewiththe
overlappingsegmentswerethesame. Thisgaveus EPICpncamerainlargewindowmode. Wemade
confidence that the two overlapping ephemerides use of these data to help solve a phase ambigu-
were consistent with each other and that phase ity described in §5.1 below. These observations’
coherence was not lost. OBSIDs are 0013340201and 0013340101and had
Combining all overlapping segments between integration times of 6.6 and 6.0 ks, repsectively.
two given dates yielded long time series of ab- From these data, photons were extracted in a re-
solute pulse number versus TOA. The uncer- gion of radius 32.5 arcseconds around the source,
tainties on the TOAs were converted into frac- and photon arrival times were adjusted to the so-
tional uncertainties in the pulse numbers. For lar system barycenter. Then, from each observa-
1E 1048.1−5937, because of irregularities in the tion, a time series in the 1.8−11 keV range with
spin-down, timing solutions spanning long peri- a time resolution of 47.7 ms was extracted, and a
ods of time required the use of very high-order TOA was obtained from the time series using the
polynomials, which tended to oscillate at the end method explained above.
points of fitted intervals. To eliminate the oscilla-
tionsproblem,insteadofusingthese polynomials, 4.2. Pulsed Flux Analysis
we used splines. A spline is a piecewise polyno-
To determine the pulsed flux for each observa-
mial function. It consists of polynomial pieces
tion, we removed any bursts present in the time
of degree n (here n = 5) defined between points
series,foldedthe dataandextractedalignedpulse
called‘knots.’ Thetwopolynomialpiecesadjacent
profiles in several energy bands. For each folded
to any knot share a common value and common
profile, we calculated the RMS pulsed flux,
derivative values at the knot, through the deriva-
6
time bin (of duration 31.25 ms in our analysis),
the number of counts in that bin is compared to
FRMS =vuu2Xn ((ak2+bk2)−(σak2+σbk2)), aa lsotcreatlcmheoafnf.ouTrhpeullosecaplemrieoadns iosfcdaalctual,acteednteorveedr
t k=1 aroundthetimebinbeingevaluated. Awindowof
(2)
onepulsecycleisalsoadministeredsothatcounts
where a is the kth even Fourier component de-
k directly from, and immediately around, the point
fined as a = 1 N p cos(2πki/N), σ 2 is the
k NPi=1 i ak under investigation would not contribute to the
variance of ak, bk is the odd kth Fourier compo- local mean. Bursts found by our searching proce-
nent defined as bk = N1PNi=1pisin(2πki/N), σbk2 dure are presented in Table 8.
is the variance of b , i refers to the phase bin, N
k
is the total number of phase bins, pi is the count 5. Results
rate in the ith phase bin of the pulse profile, and
n is the maximum number of Fourier harmonics 5.1. 1E 1841−045
used. For each AXP, we made pulsed flux series
A summary of the behavior of 1E 1841−045
with n=2 and n=6. For all AXPs, both series
between1996and2012asseenbyRXTE isshown
had the same behavior with slightly larger scat-
in Figure 1. The long-term timing parameters of
ter when the larger number of harmonics was in-
the source are presented in Table 3.
cluded. Some of the scatter may be due to low-
PanelsaandbofFigure1revealthat1E1841−045
level fluctuations in the pulse profile; see Panel e
is a noisy source: the rotationalfrequency deriva-
ofFigures1through5. Thepulsedfluxtimeseries
tive varies significantly on a timescale of years.
for each AXP is presented in Paneld of Figures 1
Panelc shows the residuals following the subtrac-
through 5.
tion of our best-fit timing models, reported in
Table 3.
4.3. Pulse Profile Analysis
1841−045hasexhibitedfourlargeglitchessince
For eachobservation,we folded the data in the
the start of the monitoring program, marked by
same energy band used for timing using the best-
the vertical lines in Figure 1 (Dib et al. 2008a,b).
fitfrequencyfoundinthetiminganalysis. Wethen
Dib et al.(2008a)reportedtwopossiblesetsofpa-
cross-correlated the resulting profile with a stan-
rameters for the first glitch from 1E 1841−045,
dard template in order to obtain phase-aligned
with the most likely set involving an exponen-
profiles. We used 32 phase bins for the aligned
tial recovery. However the addition of two TOAs
profiles. We then subtracted the respective aver-
extracted from XMM observations revealed the
agesfromeachofthealignedprofilesandfromthe
less likely timing solution to be the correct one
template. Foreachobservation,wethenfoundthe
(Dib et al. 2009b; Dib 2009).
scalingfactorthatminimizedthereducedχ2ofthe
Therewerenosignificantchangesinthe pulsed
difference between the scaled profile and the tem-
flux in any of the five studied bands near glitch
plate. Theresultingreducedχ2 valuesareplotted
epochs, norwere there any inglitch-free intervals.
inPaneleofFigures1through5. Thesevaluesare
The 2−20 keV pulsed flux time series is shown in
generallycloseto1exceptneartheepochsofsome
Panel d of Figure 1. Zhu & Kaspi (2010) showed
major outbursts. For each AXP, the pulse profile
thatthesource’sphase-averagedfluxisalsostable,
for a typical observation, as well as the long-term
indicatingthattheglitchesof1E1841−045appear
average pulse profile, are shown in Figure 7.
radiatively quiet.
4.4. Searching for Bursts In 2010 and 2011, Swift detected several
episodes of bursts from 1E 1841−045, indicated
Inadditiontothetiming,pulsedflux,andpulse by the four blue arrows pointing upward in the
profile analyses, we performed our burst-search lower portion of Panel d of Figure 1. Lin et al.
routineintroducedinGavriil et al.(2002)anddis- (2011) studied the bursting activity with Swift
cussed further in Gavriil et al. (2004) on all the and Fermi and found that it did not have a sig-
analysedobservations. Inshort, foreachdata set, nificant effect on the persistent flux level of the
to determine whether a burst occured in the ith
7
source. RXTE observations show that the pulsed there been no change in any of the timing param-
flux of 1E 1841−045 appeared featureless around etersinornearthegap,thispeakwouldnotexist.
that time. However, because the data gap makes it impossi-
However, there were two hints in RXTE data ble to constrain how fast and when the change in
indicatingthatthesourcewasundergoingactivity the timing parameters occured, and because the
of some kind. First, there was a small burst (un- nearby TOAs can be fitted to an ephemeris con-
resolved in a 31-ms time bin) observed from the sisting of a small number of frequency derivatives
direction of 1E 1841−045on 2010 May 7, the day (here only three derivatives), we are not classify-
followingthefirstepisodeofSwift-detectedbursts ing the event as a glitch candidate. This event is
(see Table 8). Note however that in the observa- reported in Table 7 as a notable timing disconti-
tion containing the burst, only a single PCU was nuity, along with the glitch parameters obtained
on, making the pulse signal-to-noise ratio too low from the most likely glitch epoch.
to allow verification of the presence of any fluctu- PaneleofFigure1showsnosignificantRXTE-
ations in the pulsed flux within that observation. detected pulse profile changes for this source.
Alsonotethatinthe RXTE observationcollected Note however that this Figure shows the reduced
on the previous day, there were no bursts. χ2 statistics for individual pulse profiles, and al-
The second indication that 1E 1841−045 was thoughnosignificantchangesareseeninthis Fig-
undergoing activity of some kind was a timing ure, we believe there are constantly slow low-level
discontinuity (dotted line in Figure 1). The fol- changes, only detectable by summing the pulse
lowing is the sequence of events surrounding that profiles over an extended period of time; see for
discontinuity. From2010December8to2011Jan- example Figure 11 of Dib et al. (2008a).
uary 16, there were no observations of the source
5.2. RXS J170849.0−400910
made with RXTE because of the angularproxim-
ity of the source to the Sun. The first observa-
A summary plot of the behavior of RXS
tion following the data gap was nominal, with no J170849.0−400910between1996and2012asseen
detected bursts, pulsed flux enhancement, or sig-
by RXTE is shown in Figure 2. The long-term
nificant pulse profile changes. The second Swift-
timing parameters are presented in Table 4.
detectedburstepisodethenoccuredontheFebru-
Panels a and b of Figure 2, show that RXS
ary 8 and 9. This was followed again by two
J170849.0−400910 underwent timing disconti-
seemingly normal RXTE observations on Febru-
nuities: the solid lines mark the location of 3
ary9and10. However,thebehaviorofthetiming
glitches, one of which had an exponential recov-
residual around this time was peculiar: there was
ery. Panel d shows that these glitches, like those
a change in the curvature of the timing residu-
of1E1841−045,showednodetectable pulsedflux
als when a long-term polynomial timing solution
variations; the exception to this being a single
fit included the stretch of time around the second
anomalouspulsedfluxpointinthe4−20keVband
burst episode, indicating a change in one or more
in early 2010, far from the epochs of any timing
timingparametersnearthatepoch. Thechangein
discontinuities. We have studied this anomalous
the curvature of the residuals was not sufficiently
data point in detail but see no reason to distrust
abrupttowarrantcallingtheeventaglitchcandi-
it. In addition to the glitches, there were many
date. Also, because of the presence of the gap in
smaller-magnitude timing discontinuities, marked
the data, it is difficult to determine whether the
by the remaining vertical lines, and detected as
change in the timing parameters occured during
peaks in Panel b.
the gap, between January 16 and February 10, or
Note that Israel et al.(2007) analyseda subset
between February 10 and 23.
of these same data. In particular, they reporteda
The peak in Panel b of Figure 1 that is indi-
glitch corresponding to our first glitch candidate,
cated by the dotted vertical line provides another
marked by the first dashed vertical line in Fig-
way of seeing the same phenomenon: each of the
ure 2. For that event, the reported fit parameters
data points that are part of the rise and fall of
are similar though not identical to ours (see Ta-
the peak in Panel b include TOAs from before
ble7). Theyalsoreportedaglitchcoincidentwith
and after the data gap at the same time. Had
8
the third solid vertical line of Figure 2. For that enhancement in the pulsed flux (Panel d of Fig-
glitch, the reported frequency jump at the glitch ure3). The highestdata pointinthis Panelis the
epoch was similar to ours but the jump in fre- averagepulsed flux for the observationcontaining
quency derivative was significantly different. We bursts. Note, however, that the pulsed flux dur-
findthatthisdifferenceisduetotheirinclusionof ing that observationfell monotonically with time;
more post-glitch TOAs when fitting the glitch. seeKaspi et al.(2003)andWoods et al.(2004)for
It is possible to compare the degree of abrupt- details. The glitchwas alsoaccompaniedby pulse
ess of the changes in the timing parameters of profile changes (Panel e of Figure 3).
J170849.0−400910attheepochsofthevariousdis- In contrast to the first glitch, the second glitch
continuities by examining the peaks in Panel b of from this source was not followed by a recov-
Figure 6. In this Figure, timing residuals of all ery, and was radiatively quiet (Dib et al. 2008a,b,
AXPs areshownfor selectedstretches of time, af- 2009b; I¸cdem et al. 2012).
ter the removalof a long-term trend in frequency. Smallbutsignificantchangesinthe pulsedflux
The changes in the curvature of the residuals are, were again seen in two observations in 2009 Jan-
as expected, most abrupt at the location of the uary (Paneld of Figure 3) in all bands within the
glitches. This Figure also provides a good way of 2−20 keV range. The pulsar exhibited a pulse
visually comparing the amount of timing noise in profile change during the first of these two obser-
the various sources by observing the number of vations (Panel e of Figure 3). One or more of the
“wiggles”in the timing residuals for a givennum- timing parameters changed within 50 days of the
beroffrequencyderivativesintheephemerisused. anomalous observation. (This can be most eas-
PaneleofFigure2showsnosignificantRXTE- ily seen in Panel b of Figure 3 and in Panel c of
detected pulse profile changes for this source. As Figure6). TheTOAsnearthiseventcanbefitted
for 1E 1841−045,however, we believe there could bothtoasuddenjumpinfrequencyandtoapoly-
beconstantslowlow-levelchanges,onlydetectable nomial with several frequency derivatives. Since
bysummingthepulseprofilesoveranextendedpe- the polynomial has only degree n = 3, the event
riodoftime; seeforexampleFigure8ofDib et al. is not classified as a glitch candidate, but is re-
(2008a). portedasanotabletimingdiscontinuityinTable7
becauseoftheassociatedradiativechanges. More-
5.3. 1E 2259+586 over, it is also not classified as a glitch candidate
because it is difficult to determine whether the
A summary of the behavior of 1E 2259+586
changeinthetimingparametersoccuredslowlyor
between 1997 and 2012 is presented in Figure 3.
abruptly. If abruptly, the epoch of the event can
Thelong-termtimingparametersofthesourceare
only be narroweddown to within a time periodof
presented in Table 5.
50 days.
Panels a and b of Figure 3, and more clearly
This timing discontinuity is notable as when
Panel c of Figure 6, show that 1E 2259+586 ex-
a glitch fit is attempted, independent of where
hibits very little timing noise compared to the
the glitch epoch is chosen, the jump in frequency
other AXPs. As shown by the solid vertical lines
∆ν hasanegative valuebetween−1.00×10−8and
in Figure 3, 1E 2259+586 exhibited two glitches
−1.42×10−8 Hz. This fact was remarked on in
during our monitoring program.
I¸cdem et al. (2012) as well, although they did not
The recovery of the first of the two glitches
report the contemporaneous radiative changes,
could be fit by a combination of exponentials
and their reported ∆ν is 3.3-σ away from ours.
(Kaspi et al. 2003; Woods et al.2004). If the first
Finally, note that the anomalous χ2 near
post-glitch observation, which contained a large
MJD 50357 (Panel e of Figure 3) corresponds to
numberofbursts,isexcluded,thepost-glitchdata
the pulse profile of a very long observation, sup-
can also be fit with a simple ephemeris that in-
porting the idea that there are constant low-level
cludes one frequency derivative, followed by a
pulse profile changes that go undetected because
long-termephemeristhatcontainsthreefrequency
of the low signal-to-noise ratio in most observa-
derivatives(redlinesB1andB2inPanelaofFig-
tions.
ure 3). This glitch was accompanied by a large
9
5.4. 4U 0142+61 was a radiatively silent glitch: there was at most
a statistically marginalincrease in the pulsed flux
A summary of the behavior of 4U 0142+61be-
in all bands (see Fig. 4). Note that we chose the
tween 1996 and 2012 as seen by RXTE is shown
scaleofPanelaofFigure4toshowthedatabefore
in Figure 4. The long-termtiming parametersare
and after this latest glitch, making the low-level
presented in Table 6.
changes in frequency due to timing noise hard to
As can be seen from Figure 4, four noteworthy
see. However, their presence is clear in Panel d of
timing events occured during the X-ray monitor-
Figure 6.
ing of 4U 0142+61.
First, there is an offset in the frequency be- 5.5. 1E 1048.1−5937
tween the red lines representing ephemeris A and
A summary of the behavior of 1E 1048.1−5937
ephemeris B in Panel a of Figure 4. Based on the
between 1997 and 2012 as seen by RXTE is
comparisonofRXTE andASCAdata,Morii et al.
shown in Figure 5. Long-term spin parameters
(2005)pointedoutthataglitchmayhaveoccured
are not presented in a Table like those of the
in the gap between the two ephemerides. The
otherAXPsbecauseoftheverylargetimingnoise
event is marked as a glitch candidate in Figure 4
of the source, necessitating multiple short-term
and in Table 7.
ephemerides with a large number of frequency
Thesecondinterestingseriesofchangesoccured
derivatives.
when the source entered an active phase in 2006
To visually appreciate the strength the timing
(second glitch candidate in Figure 4, timing pa-
noise of the source, refer to Panel e of Figure 6.
rameters in Table 7). The pulsar’s timing param-
The timing residuals for the period of time dur-
eters changed, the pulse profile varied, and the
ing which the pulsar was exhibiting the least tim-
pulsed flux increased locally within the three ob-
ing noise are presented, after the subtraction of
servations in which bursts were detected (arrows
anephemeriscontainingfivefrequencyderivatives.
in Panel d). The details of this 2006 active phase
Similar amplitude residuals with other AXPs can
of 4U 0142+61 were discussed by Gavriil et al.
generally be obtained with only one or two fre-
(2011). The timing event associated with this ac-
quency derivatives.
tive phase is classified as a glitch candidate be-
Fromatiming pointofview,theperiodoftime
cause the claim of a large sudden frequency jump
during which 1E 1048.1−5937 was observed by
is based on a single TOA, the first of the active
RXTE was very eventful (Panels a and b of Fig-
phase, and that TOA may have been affected by
ure 5). First, from 1996 to 2001, the large timing
pulse profile changes (Gavriil et al. 2011). If this
noise and the sparsity of the data made it pos-
TOA is omitted, the initial sudden spin-up is less
sible to only obtain phase-connected timing solu-
significant, although it is clear that a change in ν˙
tions for short (i.e. months-long) periods of time
occured. Also, even if this TOA is omitted, ex-
(Kaspi et al.2001). In2001,weadoptedthestrat-
tending the post-recovery ephemeris backward in
egy ofobservingthe source in sets of three closely
time makes it look as though an ‘anti-glitch’ oc-
spacedobservations,makingphaseconnectioneas-
curred (Gavriil et al. 2011).
ier.
Next occured a small and possibly slow tim-
The source exhibited two slow-rise pulsed flux
ing discontinuity in 2009, most easily seen from
flares (time scale weeks to months) in 2001 and
Panelb of Figure 4 and from Paneld of Figure 6.
2002(PaneldofFigure5),previouslyreportedby
This discontinuity is similar to the one exhibited
by 1E 2259+586 in early 2009 (see §5.3) in that Gavriil & Kaspi (2004) and Gavriil et al. (2006).
The flares were accompanied by variations in the
it can be fit both by a local polynomial of degree
frequency derivative (Panel b of Figure 5), al-
n = 3 in frequency and by a negative frequency
jump of 1.3(2)×10−8 Hz, very similar in size to though not as large or rapid as the dramatic
changes of two orders of magnitude in the rota-
that of the 1E 2259+586 event. However, unlike
tionalfrequencyderivativewhichoccuredapprox-
the 2009discontinuity in 1E 2259+586,this event
imately a year later, starting in 2001 November
did not have contemporaneous radiative changes.
(Panel b of Figure 5). The period of dramatic
Finally, a large glitch occured in 2011 July. It
10