aa r X i v : . [ a s t r o - ph ] O c t Glitches in Anomalous X-ray Pulsars
Rim Dib , Victoria M. Kaspi , and Fotis P. Gavriil ABSTRACT
We report on 8.7 and 7.6 yr of
Rossi X-ray Timing Explorer (RXTE) obser-vations of the Anomalous X-ray Pulsars (AXPs) RXS J170849.0 − − RXTE
AXPmonitoring program, have allowed us to study the long-term timing, pulsed flux,and pulse profile evolution of these objects. We report on four new glitches, onefrom RXS J170849.0 − − −
045 is among the largest ever seen in a neutron star in terms offractional frequency increase. With nearly all known persistent AXPs now seento glitch, such behavior is clearly generic to this source class. We show that interms of fractional frequency change, AXPs are among the most actively glitch-ing neutron stars, with glitch amplitudes in general larger than in radio pulsars.However, in terms of absolute glitch amplitude, AXP glitches are unremarkable.We show that the largest AXP glitches observed thus far have recoveries that areunusual among those of radio pulsar glitches, with the combination of recoverytime scale and fraction yielding changes in spin-down rates following the glitchsimilar to, or larger than, the long-term average. We also observed a large long-term fractional increase in the magnitude of the spin-down rate of 1E 1841 − ν/ ˙ ν = 0 .
1. These observations are challeng-ing to interpret in standard glitch models, as is the frequent occurence of largeglitches given AXPs’ high measured temperatures. We speculate that the stellarcore may be involved in the largest AXP glitches. Furthermore, we show thatAXP glitches appear to fall in two classes: radiatively loud and radiatively quiet.The latter, of which the glitches of RXS J170849.0 − − Department of Physics, McGill University, Montreal, QC H3A 2T8 NASA Goddard Space Flight Center, Greenbelt, MD.
Subject headings: pulsars: individual(RXS J170849.0 − −
1. Introduction
The past decade has seen significant progress in our knowledge of the observationalproperties of Anomalous X-ray Pulsars (AXPs; see Woods & Thompson 2006; Kaspi 2007,for recent reviews). From a timing point of view, the presence of binary companions has beenpractically ruled out (Mereghetti et al. 1998; Wilson et al. 1999), and subsequently their po-tential for great rotational stability was demonstrated (Kaspi et al. 1999), thereby allowingthe discovery that AXPs can exhibit spin-up glitches (Kaspi et al. 2000; Kaspi & Gavriil2003; Dall’Osso et al. 2003), and large (factor of ∼
10) torque variations (Gavriil & Kaspi2004). From a radiative point of view, AXPs are now known to show a variety of differ-ent variability phenomena, including long-lived flares (Gavriil & Kaspi 2004), short SGR-like bursts (Gavriil et al. 2002, 2004; Woods et al. 2005), large outbursts (Kaspi et al. 2003;Ibrahim et al. 2004; Israel et al. 2007a; Dib et al. 2007b; Tam et al. 2006; Tam et al., submit-ted), and slow, low-level flux and pulse profile variability (Dib et al. 2007a; Gonzalez et al.,submitted). Spectrally, though previously studied only in the soft X-ray band, AXPs are nowseen in the radio band (Camilo et al. 2006), through the mid- (Wang et al. 2006) and near-IR(e.g., Israel et al. 2002; Wang & Chakrabarty 2002; Hulleman et al. 2004; Tam et al. 2004;Rea et al. 2004; Durant & van Kerkwijk 2005), in the optical range (e.g., Kern & Martin2002; Dhillon et al. 2005), up to hard X-ray energies (Kuiper et al. 2006). The evidencethus far argues strongly that AXPs, like their close cousins, the Soft Gamma Repeaters, aremagnetars – young, isolated neutron stars powered by a large magnetic energy reservoir,with surface fields of > − G (Thompson & Duncan 1996; Thompson et al. 2002).In spite of this progress, however, many aspects of AXPs remain mysterious. Particularlyso are their variability properties. What is the origin of the variety of different types ofvariability? Although bursts can be explained as sudden crustal yields, slower evolution (e.g.,Gavriil & Kaspi 2004; Dib et al. 2007a) has been suggested to be due to slow magnetospherictwists (Thompson et al. 2002). Some support for this picture has been argued to come fromobserved correlations between flux and spectral hardness (Woods et al. 2004; Rea et al. 2005;Campana et al. 2007), although ¨Ozel & Guver (2007) argue that such a correlation need notoriginate uniquely from the magnetosphere and could be purely thermal. At least someradiative variability has been seen to be correlated with timing behavior. The best exampleof this occured in the 2002 outburst of AXP 1E 2259+586 in which the pulsar suffered a 3 –large spin-up glitch apparently simultaneously with a major X-ray outburst (Kaspi et al.2003; Woods et al. 2004). Israel et al. (2007a) describe a similar radiative outburst in AXPCXOU J164710.2 − − − − − Rossi X-ray TimingExplorer ( RXTE ). We report the discovery of one new glitch and three new glitch candi-dates in RXS J170849.0 − − − −
045 which reveal little or no evidence for correlated changes with glitches, al-though RXS J170849.0 − − −
045 are frequent glitchers. They also demonstrate that although AXP timingglitches can occur simultaneously with significant long-lived radiative enhancements, theyneed not always do so.
2. Observations
The results presented here were obtained using the PCA on board
RXTE . The PCAconsists of an array of five collimated xenon/methane multi-anode proportional counterunits (PCUs) operating in the 2 −
60 keV range, with a total effective area of approximately6500 cm and a field of view of ∼ ◦ FWHM (Jahoda et al. 1996). Our 294 observations ofRXS J170849.0 − −
045 are of various lengths (seeTables 1 and 2). Most were obtained over a period of several years as part of a long-termmonitoring program, but some are isolated observations (see Figures 1 and 2).For the monitoring, we used the
GoodXenonwithPropane data mode except during Cy-cles 10 and 11 when we used the
GoodXenon mode. Both data modes record photon arrival 4 –times with 1- µ s resolution and bin photon energies into one of 256 channels. To maximizethe signal-to-noise ratio, we analysed only those events from the top xenon layer of eachPCU.
3. Phase-Coherent Timing
Photon arrival times at each epoch were adjusted to the solar system barycenter. Result-ing arrival times were binned with 31.25-ms time resolution. In the RXS J170849.0 − − −
045 we included events in theenergy range 2 −
11 keV.Each barycentric binned time series was folded using an ephemeris determined iterativelyby maintaining phase coherence as we describe below. Resulting pulse profiles, with 64 phasebins, were cross-correlated in the Fourier domain with a high signal-to-noise template createdby adding phase-aligned profiles from all observations. The cross-correlation returned anaverage pulse time of arrival (TOA) for each observation corresponding to a fixed pulsephase. The pulse phase φ at any time t can usually be expressed as a Taylor expansion, φ ( t ) = φ ( t ) + ν ( t − t ) + 12 ˙ ν ( t − t ) + 16 ¨ ν ( t − t ) + . . ., (1)where ν ≡ P is the pulse frequency, ˙ ν ≡ dν / dt , etc . , and subscript “0” denotes a parameterevaluated at the reference epoch t = t . The TOAs were fitted to the above polynomial usingthe pulsar timing software package TEMPO .Note that we also searched for X-ray bursts in each 2–20 keV barycentered, binned timeseries using the methods described in Gavriil et al. (2004), however no bursts were found inany of our RXS J170849.0 − −
045 data sets. − Figure 3 and Table 3 summarize our results for RXS J170849.0 − § ν/ν = 2 . × − , and no obviousrecovery. This glitch amplitude is intermediate between those of the previous two observedglitches, and the lack of recovery is similar to what was seen in the first glitch, but in markedcontrast with the second glitch, as is clear from Figure 4. A sudden change in post-glitchspin-down rate for the third glitch is difficult to constrain, because of a possible additionalglitch that occured not long after, as we describe below. Indeed glitch-induced long-termchanges in ˙ ν aside from that following the first glitch, as described by Kaspi et al. (2000),are difficult to identify given the apparent timing noise processes. Table 4 summarizes theparameters of the three certain glitches of RXS J170849.0 − ν and ˙ ν and a frequency change ν d that decayed on atime scale of τ d , i.e., ν = ν ( t ) + ∆ ν + ∆ ν d e − ( t − t g ) /τ d + ∆ ˙ ν ( t − t g ) , (2)where ν ( t ) is the frequency evolution pre-glitch, ∆ ν is a instantaneous frequency jump, ∆ ν d is the post-glitch frequency increase that decays exponentially on a time scale τ d , t g is theglitch epoch, and ∆ ˙ ν is the post-glitch change in the long-term frequency derivative.For the second glitch, residuals after subtraction of a simple glitch with fractional ex-ponential recovery have clear remaining trends, as is clear in Figures 3 (second panel) and 4(bottom panel). Systematic trends after simple glitch model subtraction were also reportedby Woods et al. (2004) for the 2002 glitch in 1E 2259+586. We also find this in the largestglitch in 1E 1841 −
045 (see § − σ away from the value 0.090885327(8) Hz thatwe measure at the same epoch using our post-glitch ephemeris. The numbers in parenthesesare 1 σ uncertainties. We do not understand this difference. − Figure 6 and Table 7 summarize the long-term timing behavior of 1E 1841 − − −
045 is well characterized by regular 7 –spin-down punctuated by occasional sudden spin-up events, plus timing noise. Ephemeridesin Table 7 are given for the glitch-free intervals indicated in the top panel of Figure 6. As forRXS J170849.0 − ∼ − ∼
50% larger. The glitch fractional amplitudewas ∆ ν/ν = 1 . × − (see Table 8), among the largest yet seen from any neutron star. Afraction Q ≡ ∆ ν d / (∆ ν d + ∆ ν ) = 0 .
64 of the glitch recovered on a time scale of 43 days. Thisglitch is thus similar to the second certain glitch seen in RXS J170849.0 − − −
045 isnot well modelled by Equation 2, as is clear in the residuals plot in Figure 7. Accompanyingthis frequency glitch was a substantial long-term increase in the the magnitude of ˙ ν , withfractional increase ∆ ˙ ν/ ˙ ν = 0 . ± . § ν = 0 . ν = − . × − Hz s − , ¨ ν = − . × − Hz s − ,and d ν/dt = 8 . × − Hz s − at the reported glitch epoch MJD 52464.00448, withRMS phase residual of 0.019. This ephemeris disagrees with ephemeris B in the shape ofthe recovery (see dotted curve in Panel 3 of Fig. 6) but agrees with it after the end of therecovery. Using the parameters of this alternate ephemeris, the change in ν at the glitchepoch would be 2 . × − Hz much smaller than the one reported in Table 8. However,we hesitate to interpret the glitch using this ephemeris because of the very unusual andunique shape of the recovery it predicts. Note that this alternate ephemeris also shows along-term increase in the magnitude of ˙ ν after the glitch.We also report the detection of two additional, smaller glitches, as summarized in Table 8and displayed in Figures 6 and 7. Neither glitch displays significant recovery, and both arewell modelled by a simple permanent frequency jump. 8 –
4. Pulse Profile Changes
Another interesting AXP property we can study thanks to
RXTE monitoring is theevolution of the pulse profile. We performed a pulse profile analysis on each AXP usingFTOOLS version 5.3.1 . We used the following steps: for each observation, we ran theFTOOL make_se to combine the GoodXenon files. We then used the FTOOL fasebin to make a phase-resolved spectrum of the entire observation with 64 phase bins across theprofile. When we ran fasebin , we selected layer 1 of the detector, disregarded the propanephotons, and included the photons from PCUS 1, 2, 3, and 4. We omitted PCU 0, forwhich an independent analysis of AXP 4U 0142+61 revealed spectral modeling irregularities(Dib et al. 2007a). fasebin also took care of barycentering the data. For each observation,we then used seextrct to make a phase-averaged spectrum for the same set of detectorlayers and PCUs. The phase-averaged spectrum was then used by the perl script pcarsp tomake a response matrix.We loaded the phase-resolved spectra and the response matrices into the X-ray SpectralFitting Package (XSPEC ) and selected photons belonging to three energy bands: 2 − −
4, and 4 −
10 keV. Using XSPEC, we extracted a count-rate pulse profile for each of theenergy bands. The profiles included XSPEC-obtained 1 σ error bars on each of the phasebins. To obtain a pulse profile in units of count rate per PCU, we divided the overall profileby a PCU coverage factor that took into account the amount of time each PCU was on.We then aligned the 64-bin profiles with a high signal-to-noise template using a similarcross-correlation procedure to the one used in the timing analysis. Then, for each glitch-freeinterval, we summed the aligned profiles, subtracted the DC component, and scaled theresulting profile so that the value of the highest bin is unity and the lowest point is zero. − Average profiles for RXS J170849.0 − http://heasarc.gsfc.nasa.gov/ftools http://xspec.gsfc.nasa.gov Version: 11.3.1 χ statistic from a fit to a constant value); thedecline of the second and third harmonics in the hard band have probabilities of 0.0007%and 0.0012%, respectively, of being due to chance. Thus in the hard band the profile iscertainly becoming more sinusoidal, in agreement with what is inferred by eye.The above analysis shows that the profile is changing, but not whether these changesare truly correlated with the glitch epochs, since changes could be occuring throughout. Tosearch for pulse profile changes correlated with glitch epochs, as were claimed by Dall’Osso et al.(2003), we divided glitch-free intervals into several sub-intervals (typically of duration ∼ χ of the best fit, found that the probabilitiesof the fluctuations being due to random noise are 68, 96 and 69% for n = 1 , ,
3, respectively.This analysis thus shows no evidence for profile changes associated with the glitch epochs,including the second glitch. However the reduced signal-to-noise ratios in the sub-intervalaverage profiles, required for interesting time resolution, makes us insensitive to subtle profilechanges. To search for glitch-correlated pulse profile changes in a different way, for each sub-interval we calculated the reduced χ of the difference between that sub-interval’s averageprofile and the previous one. The time series of these χ values is shown in the bottom panelof Figure 10. There is clearly no evidence for any profile change at the second glitch, or at thethird certain glitch. There is some hint of profile changes at the first and second candidateglitches, however a K-S test shows that our χ values as a group have a probability of 39% oforiginating from χ distribution. Interestingly though, the probability of the single high χ value we measure at the second candidate glitch occuring randomly is only 1 . × − ; thatat the first glitch is 1.7% and at the first glitch candidate is 0.4%. Thus we do find possibleevidence in this analysis for glitch-correlated pulse profile changes, though the best evidencefor significant changes occurs only at two candidate glitches, i.e., the lowest amplitude events. 10 – − Summed profiles for 1E 1841 −
045 in three energy bands for the five glitch-free intervalsdefined in the top panel of Figure 6 are shown in Figure 11. As for RXS J170849.0 − − −
045 viaFourier analysis. Figure 12 shows the evolution of the first three profile harmonics with timein each energy band. Interestingly, in contrast to RXS J170849.0 − χ test shows the probability of this behavior being due torandom noise is 18%, too large to exclude.To look for pulse profile changes correlated with glitches, again, sub-intervals withinglitch-free intervals were chosen and summed profiles computed and Fourier analysed. Theevolution of the first three harmonics is shown in the top panel of Figure 13. Fluctuationsare apparent although none is particularly remarkable at any of the glitch epochs, includingthe first and largest, and the time series for n = 1 , , − χ valuesof these difference profiles are shown in the bottom of Figure 13; no significant features arepresent.
5. Pulsed Flux Time Series
RXTE monitoring also allows the study of the evolution of the pulsed flux of thesesources. To obtain a pulsed flux time series for RXS J170849.0 − − § σ error bars on the flux value in each of the phase bins. 11 –The pulsed flux for each of the profiles was calculated using the following RMS formula: F = vuut n X k =1 (( a k + b k ) − ( σ a k + σ b k )) , (3)where a k is the k th even Fourier component defined as a k = N P Ni =1 p i cos (2 πki/N ), σ a k is theuncertainty of a k , b k is the odd k th Fourier component defined as b k = N P Ni =1 p i sin (2 πki/N ), σ b k is the uncertainty of b k , i refers to the phase bin, N is the total number of phase bins, p i is the count rate in the i th phase bin of the pulse profile, and n is the maximum number ofFourier harmonics to be taken into account. We used n = 6 for both RXS J170849.0 − − F is equivalent to the simple RMS formula F = √ N qP Ni =1 ( p i − p ) (where p i is the count rate in the i th phase bin of the pulse profileand p is the average count rate), except that we have subtracted the variances (to eliminatethe upward statistical bias) and only included the statistically significant Fourier components.For a detailed discussion on pulsed flux estimates, see Archibald, Dib & Kaspi (in prep.). − Our pulsed flux time series for RXS J170849.0 − ∼ −
045 is in the same time interval (see § § − § ∼ − § − § − Our pulsed flux time series for 1E 1841 −
045 is shown in the bottom panel of Figure 6.Each data point represents the average of pulsed fluxes measured over ∼ −
045 appear to be “quiet,” at least in pulsed flux, on time scales comparable toor longer than our sampling time.
6. Discussion6.1. AXP Glitches
We have now observed a sufficiently large sample of AXP glitches that we can makemeaningful phenomenological comparisons with glitches in radio pulsars, a much betterstudied phenomenon. Detection of systematic differences in AXP and radio pulsar glitchproperties would be interesting as it could signal structural differences between magnetarsand conventional radio pulsars.Figure 15 shows the fractional and non-fractional amplitude distributions of radio pulsarand AXP glitches. As is clear from the figure, although the fractional glitch amplitudes of 13 –AXPs are generally large by radio pulsar standards, the AXP absolute glitch amplitudes,more directly related to the angular momentum transfer during the glitch, are neither es-pecially large nor especially small. Thus, glitching in neutron stars is clearly not correlatedwith frequency as some studies of radio pulsars have suggested (Lyne et al. 2000).Given the spectacular radiative outburst contemporaneous with the large 2002 1E 2259+586glitch, we can speculate that larger angular momentum transfers that occur in radio pulsarscould result in even more dramatic outbursts in affected AXPs, possibly like those seen inXTE 1810 −
197 (Ibrahim et al. 2004) and in the AXP candidate AX J1845 − − ν/ν ≃ × − , ∆ ν ≃ × − )glitch (Israel et al. 2007a), and AXP 1E 1048.1 − −
045 around the time of its first observed glitch, which was over afactor of two larger than that in 1E 2259+586 in terms of absolute frequency jump, arguesagainst this idea. Clearly, the data are indicating that AXP glitches, even large ones, canbe either radiatively loud or quiet.Glitch activity has been defined as a g = 1∆ t X ∆ νν , (4)where ∆ t is the total observing span and the sum is over all glitches, and includes decayingcomponents (McKenna & Lyne 1990). We refer to a g as fractional activity, since it involvesthe sum of fractional frequency changes. One can also define an absolute glitch activity, A g = 1∆ t X ∆ ν, (5)where the sum is over the absolute frequency changes (e.g., Wang et al. 2000). The quantities a g and A g , introduced for the study of radio pulsars, are approximately interchangeable forthose objects, given that the range of frequencies encompassed by glitching radio pulsarsis relatively small. By contrast, when considering AXPs and their much smaller rotationfrequencies, a comparison with radio pulsars for a g and A g are very different (see, e.g.,Heyl & Hernquist 1999). Also, for establishing the average amount of spin-up imparted tothe crust over time, the total frequency increase at each epoch is relevant. However, in someinstances, the quantity of interest is the unrelaxed portion of the glitch, i.e., the permanentfrequency jump only. In general, for radio pulsars, Q is small so this distinction is notimportant. However for AXPs, given the paucity of glitches we have observed thus far aswell as the fact that several, particularly the largest, of these have had large values of Q (e.g., Q ≃ − a g and A g , although this choice should be kept in mind.With 8.7 yr of monitoring of RXS J170849.0 − a g = 2 . × − s − and A g = 2 . × − s − . Including candidateglitches only increases these numbers by ∼ −
045 isevidently a very active glitcher as well. Its glitch activity parameters are a g = 7 . × − s − and A g = 6 . × − s − . Indeed A g for 1E 1841 −
045 is the highest glitch activity seenthus far in any neutron star, radio pulsar or AXP, to our knowledge. We also calculated atentative glitch activity for AXP 1E 2259+586, for which we have observed two glitches, thewell documented one in 2002 (Kaspi et al. 2003; Woods et al. 2004) and a second, smallerglitch that occured very recently and had fractional amplitude 8 . × − and no recovery(Dib et al., in prep.). Using these events and given that we have observed this source with RXTE for 9.4 yr, we find a g = 1 . × − s − and A g = 2 . × − s − .We can plot these activities as a function of pulsar age (as estimated via spin-downage ν/ ν ) and ˙ ν ; see Figure 16. Previous authors have noted interesting correlations onthese plots for radio pulsars (e.g., Lyne et al. 2000; Wang et al. 2000); these are seen in ourplots as well. Note that upper limits for some radio pulsars of relevant ages fall well belowthe apparent correlations (e.g., Wang et al. 2000); we choose not to plot those because, asdiscussed in that reference, a single glitch of average size would bring them roughly in linewith the correlation. Note that the radio pulsar outlier at small age and high ˙ ν in all plotsis the Crab pulsar, long-known to exhibit few and small glitches. We also looked for a trendin a plot of a g or A g versus surface dipolar field (as estimated via 3 . × p P ˙ P G) butfound none.As a group, the AXPs do not especially distinguish themselves when either activity, a g or A g is plotted versus spin-down age, though they do increase the scatter. This suggests auniversal correlation with spin-down age. The same is true of A g plotted versus ˙ ν . However,interestingly, the AXPs as a group all stand out on the diagram of a g versus ˙ ν (Fig. 16),such that for similar spin-down rates, their fractional glitch activities are much larger thanin radio pulsars.Link et al. (1999) argued that a g provides a strict lower limit on the fraction of the mo-ment of inertia of the neutron star that resides in the angular momentum reservoir (generallyassumed to be the crustal superfluid) tapped during spin-up glitches, I res . They showed that I res /I c ≥ νa g / | ˙ ν | ≡ G , where I c is the moment of inertia of the crust and all componentsstrongly coupled to it, and G is a “coupling parameter.” For radio pulsars, they argued 15 –for a universal G that implies I res /I c ≥ . G plotted versus age forradio pulsars and AXPs. As is clear, the Link et al. (1999) relation seems to hold for theradio pulsars, even with increased glitch statistics. Also, AXPs RXS J170849.0 − −
045 lie among the radio pulsars, suggesting similar reservoir fractions. Howeverthe outlier point, 1E 2259+586, has G = 0 .
25, much larger than the others. Admittedly,for this AXP, a g is estimated from two glitches only, with the 2002 event greatly dominat-ing, so the values are tentative. Still, the large G , if real, suggests that at least ∼
25% ofthe stellar moment of inertia is in the angular momentum reservoir (see also Woods et al.2004). We note that the analysis of Link et al. (1999) ignores recovery, important for the2002 1E 2259+586 glitch, which dominates its a g . However in the 2002 glitch, the recoveryfraction was only ∼ G for 1E 2259+586 is surprisinglyhigh.As described by Kaspi et al. (2003) and Woods et al. (2004), the 2002 1E 2259+586glitch was unusual when compared with those of radio pulsars. Specifically the combinationof the recovery time scale and the large recovery fraction Q conspired to make the pulsarspin down, for over two weeks post-glitch, at over twice its long-term average spin-downrate. Although spin-down rate enhancements post-glitch are often seen in radio pulsars (e.g.,Flanagan 1990), they usually amount to only a few percent. A remarkably large post-glitchspin-down rate enhancement was seen also in the second glitch of RXS J170849.0 − − − −
045 could have been missed due to our sparse sampling.One way to quantify the enhanced spin-down more precisely is using Equation 2 at t = 0, and noticing that the instantaneous spin-down rate at the glitch epoch due to theexponential recovery is given by ∆ ν d /τ . Comparing this quantity for the AXP glitchesthat show recovery with the pre-glitch time-averaged spin-down rate ˙ ν , we find that for1E 2259+586 ∆ ν d /τ = (8 . ± .
6) ˙ ν , ∆ ν d /τ = (0 . ± .
6) ˙ ν for RXS J170849.0 − ν d /τ = (0 . ± .
08) ˙ ν for 1E 1841 − − rad of a circular patch of crust offset in azimuth from the rotation axiscould result in sufficient spin-down of the crustal superfluid to account for the properties ofthe 2002 glitch in 1E 2259+586. They noted further that such a twist also produces X-raysof the luminosity observed in that outburst (Thompson et al. 2002). The absence of anysignificant radiative changes at the time of largest glitches in RXS J170849.0 − −
045 is thus problematic for the crustal twist, and hence lag reversal, model. Wenote that it has been argued independently that a similar suggested lag reversal betweencrust and crustal superfluid in the Vela pulsar is unphysical (Jahan-Miri 2005).We also note that the large and long-term increase in the magnitude of ˙ ν following thelarge glitch in 1E 1841 −
045 (see § I res /I c ≥ ∆ ˙ ν/ ˙ ν . For the large 1E 1841 −
045 glitch, this implies I res /I c ≥ .
1, much larger than has been seen in any radio pulsar.One possibility that can explain the large G for 1E 2259+586, the large transient in-creases in the magnitude of ˙ ν in all three large glitches, as well as the large extended ˙ ν change in the first 1E 1841 −
045 glitch, is that core superfluid is somehow involved, as itis expected to carry the bulk of the moment of inertia. We note that core glitches havebeen discussed in the radio pulsar context for some time, albeit for very different reasons.Although Alpar et al. (1984b) argued that the crust and core should be strongly coupled onvery short time scales, Jones (1998) found that crustal pinning of superfluid vortices cannotbe occuring in neutron stars, because the maximum pinning force is orders of magnitudesmaller than the estimated vortex Magnus force. Donati & Pizzochero (2003) argue thatcrustal vortex pinning cannot occur for independent reasons. If these authors are correct,pulsar glitches would generally not originate in the crust.Why would the clearest evidence for core glitches come from AXPs? The interactionbetween vortices and quantized magnetic flux tubes in a core superfluid could provide resis-tance to outward motion of vortices (Jones 1998; Ruderman et al. 1998; Jones 2002). The 17 –interior magnetic field playing a role in vortex pinning as studied by Ruderman et al. (1998)could help explain why such unusual glitch recoveries are seen preferentially in AXPs, whichappear to have much larger magnetic fields than conventional radio pulsars. Perhaps thelarger field, which implies a higher density of flux tubes, can effectively pin more superfluidvortex lines in a magnetar core; with greater magnetic activity, sudden magnetic reconfigu-rations would result in large core vortex reconfigurations. We note that Kaspi et al. (2000)and Dall’Osso et al. (2003) argued that the Ruderman et al. (1998) model must be inappli-cable to AXPs as that model predicts no glitches for periods greater than ∼ . − ∼
10 yr, that observed spectral and flux variations were correlated with glitchepoch. They predict, given apparent flux increases seen in mid-2004 and mid-2005, that aglitch should occur soon thereafter (see Fig. 14). Indeed as we have shown (see Table 4),an unambiguous glitch occured just following their mid-2005 observation. On the otherhand, the first candidate glitch (Table 5) occured when the total flux was very low andapparently declining. Thus, if there is a causal connection between long-term flux variationsin RXS J170849.0 − − − The approximate stabilities of the pulsed fluxes of RXS J170849.0 − − §
5) are in contrast to those seen for AXPs 1E 2259+586 and 1E 1048.1 − − ∼
60% in 2004-2005, while the pulsed flux is not, with maximumcontemporaneous change of < RXTE observations. This suggests an anti-correlation between pulsed fraction andtotal flux that acts to ensure that the pulsed flux is roughly constant. If so, pulsed fluxis not a good indicator of total energy output for RXS J170849.0 − − − RXTE . However this would not jibewith the reported correlation of the phase-averaged fluxes with power-law index (Rea et al.2005; Campana et al. 2007). We also note that in the phase-averaged flux analysis, theequivalent hydrogen column N H was allowed to vary from observation to observation, ratherthan being held fixed at a constant. This inconsistency could bias the comparison, thoughlikely not by a large amount. It is tempting to question the relative calibrations of the differ-ent instruments used to measure the phase-averaged flux of RXS J170849.0 − XMM-Newton and
Swift observations, and eventhe two
Chandra X-ray Observatory observations were obtained with different instruments.Still, admittedly, relative systematic calibration uncertainties are not expected to yield a >
50% dynamic range, as is reported. Regular monitoring with a single imaging instrumentcould settle this issue.Changes in pulse profile seem to be generic in AXPs and, as discussed above, are notalways correlated with glitches, although in some cases, e.g., 1E 2259+586, 4U 0142+61, 19 –and possibly RXS J170849.0 − − −
7. Summary
We have reported on long-term
RXTE monitoring of AXPs RXS J170849.0 − − − − − − ν increases, as well as the large G value for 1E 2259+586.Radiatively, we have found that the pulsed fluxes of RXS J170849.0 − − − − − −
045 bothevolve; such evolution appears also to be a generic property of AXPs. However, no clearpatterns in AXP pulse profile changes have yet emerged beyond occasional correlation withglitches. Hopefully further monitoring will shed physical light on this phenomenon.We are grateful to Andrew Lyne for providing his unpublished glitch catalog. We thankAndrew Cumming, Chris Thompson and Pete Woods for useful comments. This work wassupported by the Natural Sciences and Engineering Research Council (NSERC) PGSD schol-arship to RD. FPG is supported by the NASA Postdoctoral Program administered by OakRidge Associated Universities at NASA Goddard Space Flight Center. Additional supportwas provided by NSERC Discovery Grant Rgpin 228738-03, NSERC Steacie SupplementSmfsu 268264-03, FQRNT, cifar, and CFI. VMK holds the Lorne Trottier in Astrophysicsand Cosmology and a Canada Research Chair in Observational Astrophysics.
REFERENCES
Alpar, M. A., Anderson, P. W., Pines, D., & Shaham, J. 1984a, ApJ, 278, 791Alpar, M. A., Chau, H. F., Cheng, K. S., & Pines, D. 1993, ApJ, 409, 345Alpar, M. A., Cheng, K. S., & Pines, D. 1989, ApJ, 346, 823Alpar, M. A., Langer, S. A., & Sauls, J. A. 1984b, ApJ, 282, 533Alpar, M. A., Pines, D., & Cheng, K. S. 2000, Nature, 348, 707Anderson, P. W. & Itoh, N. 1975, Nature, 256, 25Arzoumanian, Z., Nice, D. J., Taylor, J. H., & Thorsett, S. E. 1994, ApJ, 422, 671Camilo, F., Ransom, S., Halpern, J., Reynolds, J., Helfand, D., Zimmerman, N., &Sarkissian, J. 2006, Nature, 442, 892Campana, S., Rea, N., Israel, G. L., Turolla, R., & Zane, S. 2007, A&A, 463, 1047Dall’Osso, S., Israel, G. L., Stella, L., Possenti, A., & Perozzi, E. 2003, ApJ, 599, 485Dhillon, V. S., Marsh, T. R., Hulleman, F., van Kerkwijk, M. H., Shearer, A., Littlefair,S. P., Gavriil, F. P., & Kaspi, V. M. 2005, MNRAS, 363, 609 21 –Dib, R., Kaspi, V. M., & Gavriil, F. P. 2007a, ApJ, 666, 1152Dib, R., Kaspi, V. M., Gavriil, F. P., & Woods, P. M. 2007b, ATEL 1041Donati, P. & Pizzochero, P. M. 2003, Phys. Rev. Lett., 90, 211101+Durant, M. & van Kerkwijk, M. H. 2005, ApJ, 627, 376Flanagan, C. S. 1990, Nature, 345, 416Gavriil, F. P. & Kaspi, V. M. 2004, ApJ, 609, L67Gavriil, F. P., Kaspi, V. M., & Woods, P. M. 2002, Nature, 419, 142—. 2004, ApJ, 607, 959Gavriil, F. P., Kaspi, V. M., & Woods, P. M. 2006, ApJ, 641, 418Gavriil, F. P., Kaspi, V. M., Woods, P. M., & Dib, R. 2007, ATEL 1076Gonzalez, M. E., Dib, R., Kaspi, V. M., Woods, P. M., Tam, C. R., & Gavriil, F. P. 2007,submitted; (astro-ph/0708.2756)Gotthelf, E. V., Gavriil, F. P., Kaspi, V. M., Vasisht, G., & Chakrabarty, D. 2002, ApJ, 564,L31Heyl, J. S. & Hernquist, L. 1999, MNRAS, 304, L37Hobbs, G., Lyne, A. G., Kramer, M., Martin, C. E., & Jordan, C. 2004, MNRAS, 353, 1311Hulleman, F., van Kerkwijk, M. H., & Kulkarni, S. R. 2004, A&A, 416, 1037Ibrahim, A. I., Markwardt, C. B., Swank, J. H., Ransom, S., Roberts, M., Kaspi, V., Woods,P. M., Safi-Harb, S., Balman, S., Parke, W. C., Kouveliotou, C., Hurley, K., & Cline,T. 2004, ApJ, 609, L21Israel, G. L., Campana, S., Dall’Osso, S., Muno, M. P., Cummings, J., Perna, R., & Stella,L. 2007a, ApJ, 664, 448Israel, G. L., Gotz, D., Zane, S., Dall’Osso, S., Rea, N., & Stella, L. 2007b, (astro-ph/0707.0485v2)Israel, G. L., Covino, S., Stella, L., Campana, S., Marconi, G., Mereghetti, S., Mignani,R., Negueruela, I., Oosterbroek, T., Parmar, A. N., Burderi, L., & Angelini, L. 2002,ApJ, 580, L143 22 –Jahan-Miri, M. 2005, New Astronomy, 11, 157Jahoda, K., Swank, J. H., Giles, A. B., Stark, M. J., Strohmayer, T., Zhang, W., & Morgan,E. H. 1996, Proc. SPIE, 2808, 59Jones, P. B. 1998, MNRAS, 296, 217—. 2002, MNRAS, 335, 733Kaspi, V. M. 2007, Ap&SS, in press (astro-ph/0610304)Kaspi, V. M., Chakrabarty, D., & Steinberger, J. 1999, ApJ, 525, L33Kaspi, V. M. & Gavriil, F. P. 2003, ApJ, 596, L71Kaspi, V. M., Gavriil, F. P., Woods, P. M., Jensen, J. B., Roberts, M. S. E., & Chakrabarty,D. 2003, ApJ, 588, L93Kaspi, V. M., Lackey, J. R., & Chakrabarty, D. 2000, ApJ, 537, L31Kern, B. & Martin, C. 2002, Nature, 415, 527Kuiper, L., Hermsen, W., den Hartog, P., & Collmar, W. 2006, ApJ, 645, 556Link, B., Epstein, R. I., & Lattimer, J. M. 1999, Phys. Rev. Lett., 83, 3362Livingstone, M. A., Kaspi, V. M., Gavriil, F. P., & Manchester, R. N. 2005, ApJ, 619, 1046Lyne, A. G., Shemar, S. L., & Graham-Smith, F. 2000, MNRAS, 315, 534McKenna, J. & Lyne, A. G. 1990, Nature, 343, 349Mereghetti, S., Israel, G. L., & Stella, L. 1998, MNRAS, 296, 689Muno, M. P., Gaensler, B. M., Clark, J. S., de Grijs, R., Pooley, D., Stevens, I. R., &Portegies Zwart, S. F. 2007, MNRAS, 378, L44¨Ozel, F. & Guver, T. 2007, ApJ, 659, L141Pines, D. & Alpar, M. A. 1985, Nature, 316, 27Rea, N., Israel, G. L., Testa, V., Stella, L., Mereghetti, S., Tiengo, A., Oosterbroek, T.,Mangano, V., Campana, S., Covino, S., Curto, G. L., & Perna, R. 2004, The As-tronomer’s Telegram, 284 23 –Rea, N., Oosterbroek, T., Zane, S., Turolla, R., M´endez, M., Israel, G. L., Stella, L., &Haberl, F. 2005, MNRAS, 361, 710Ruderman, M., Zhu, T., & Chen, K. 1998, ApJ, 492, 267Tam, C. R., Gavriil, F. P., Dib, R., Kaspi, V. M., Woods, P. M., & Bassa, C., submitted;(astro-ph/0707.2093)Tam, C. R., Kaspi, V. M., Gaensler, B. M., & Gotthelf, E. V. 2006, ApJ, 652, 548Tam, C. R., Kaspi, V. M., van Kerkwijk, M. H., & Durant, M. 2004, ApJ, 617, L53Thompson, C. & Duncan, R. C. 1996, ApJ, 473, 322Thompson, C., Lyutikov, M., & Kulkarni, S. R. 2002, ApJ, 574, 332Tiengo, A., Mereghetti, S., Turolla, R., Zane, S., Rea, N., Stella, L., & Israel, G. L. 2005,A&A, 437, 997Wang, N., Manchester, R. N., Pace, R., Bailes, M., Kaspi, V. M., Stappers, B. W., & Lyne,A. G. 2000, MNRAS, 317, 843Wang, Z. & Chakrabarty, D. 2002, ApJ, 579, L33Wang, Z., Chakrabarty, D., & Kaplan, D. L. 2006, Nature, 440, 772Wilson, C. A., Dieters, S., Finger, M. H., Scott, D. M., & van Paradijs, J. 1999, ApJ, 513,464Woods, P. M., Kaspi, V. M., Thompson, C., Gavriil, F. P., Marshall, H. L., Chakrabarty,D., Flanagan, K., Heyl, J., & Hernquist, L. 2004, ApJ, 605, 378Woods, P. M., Kouveliotou, C., Gavriil, F. P., Kaspi, M., V., Roberts, M. S. E., Ibrahim,A., Markwardt, C. B., Swank, J. H., & Finger, M. H. 2005, ApJ, 629, 985Woods, P. M. & Thompson, C. 2006, in Compact Stellar X-ray Sources, ed. W. H. G. Lewin& M. van der Klis (UK: Cambridge University Press)
This preprint was prepared with the AAS L A TEX macros v5.2.
24 –Fig. 1.— Epochs of observations of RXS J170849.0 − RXTE . Gaps near theend/start of each year are due to Sun avoidance. See Table 1 for details. 25 –Fig. 2.— Epochs of observations of 1E 1841 −
045 with
RXTE . Gaps near the end/start ofeach year are due to Sun avoidance. See Table 2 for details. 26 –Fig. 3.— Spin and pulsed flux evolution in RXS J170849.0 − ν and ˙ ν . Bottom: Pulsed flux in the 2–10 keV range. All panels: Unambiguous glitch epochsare indicated with solid vertical lines. Candidate glitch epochs are indicated with dashedvertical lines. 27 –Fig. 4.— The three unambiguous glitches observed in RXS J170849.0 − − − ν and ˙ ν .Bottom: Pulsed flux in the 2–10 keV range. All panels: Glitch epochs are indicated withsolid vertical lines. The dashed vertical line indicates the start of ephemeris B2, which doesnot include the two immediate post-glitch observations (indicated with unfilled squares). 30 –Fig. 7.— The three glitches in 1E 1841 − − n th harmonic to thetotal power in the 2–10 keV pulse profile of RXS J170849.0 − n = 1,squares n = 2, and triangles n = 3. Solid vertical lines indicate epochs of glitches; dashedvertical lines are epochs of candidate glitches. Middle panel: Same as left panel but for2–4 keV. Right panel: Same as middle but for 4–10 keV. 33 –Fig. 10.— Top panel: Time evolution of the ratio of the power in the n th harmonic to thetotal power in the 2–10 keV pulse profile of RXS J170849.0 − n = 1, squares n = 2, and triangles n = 3. Solid and dashed vertical lines indicate epochs ofglitches and candidate glitches, respectively. The probability that the observed fluctuationsare due to random noise are 68%, 97% and 69% for n = 1 , ,
3, respectively. Bottom panel:reduced χ per degree of freedom for successive profile differences (see text § −
045 for the fiveglitch-free intervals defined in the top panel of Figure 6. Different data qualities in eachenergy range are due to different net exposure times. Two cycles are shown for each profilefor clarity. 35 –Fig. 12.— Left panel: Time evolution of the ratio of the power in the n th harmonic to thetotal power in the 2–10 keV pulse profile of 1E 1841 − n = 1, squares n = 2, and triangles n = 3. Solid vertical lines indicate epochs of glitches. Middle panel:Same as left panel but for 2–4 keV. Right panel: Same as middle but for 4–10 keV. 36 –Fig. 13.— Top panel: Time evolution of the ratio of the power in the n th harmonic tothe total power in the 2–10 keV pulse profile of 1E 1841 − n = 1,squares n = 2, and triangles n = 3. Solid vertical lines indicate epochs of glitches. Theprobabilities that the observed fluctuations arise from random noise are 99%, 97% and 96%for n = 1 , ,
3, respectively. Bottom panel: reduced χ per degree of freedom for successiveprofile differences (see text § − ν/ ν ) and versus ˙ ν for radiopulsars and AXPs. Fractional activity a g is defined using the sum of the fractional frequencychanges, while activity A g is defined using the absolute frequency jumps. The only radiopulsars included (filled circles) are those having exhibited three glitches or more duringcontinual (e.g., bi-monthly) monitoring, as recorded in the unpublished glitch catalog kindlysupplied by A. Lyne. The AXPs included here (open circles) are RXS J170849.0 − − − G (as defined by (Link et al. 1999); see § ν/ ν ). Solid points are radio pulsars with three or more observed glitches,as recorded in the unpublished catalog of A. Lyne. Open circles are AXPs 1E 2259+586,RXS J170849.0 − − RXTE
Observations of RXS J170849.0 − Obs. Typical Typical No. of Total First – LastCycle Exp. a Separation a Obs. b Exp. c MJD d First Date − Last Date(ks) (days) (ks)3 2.5 15 29 75 50825.7 − − − − − − − − − − − − − − − − e − − a The exposure and separation are approximate. Note that the PCA effective area changed with timeprimarily due the reduction of the average number of PCUs operational during an integration. This effectis not incorporated in the tabulated integration times. b When the last digits of the observation ID of two successive data sets are different, the two data sets areconsidered separate observations. c The total exposure does not include Earth occultation periods. d First MJD and Last MJD are the epochs, in Modified Julian Days, of the first and the last observationsin a Cycle. e Cycle 11 not yet completed.
42 –Table 2. Summary of
RXTE
Observations of 1E 1841 − Obs. Typical Typical No. of Total First – LastCycle Exp. a Separation a Obs. b Exp. c MJD d First Date − Last Date(ks) (days) (ks)4 4.5 27 26 120 51224.4 − − − − − − − − − − − − − − e − − a The exposure and separation are approximate. Note that the PCA effective area changed with time primarilydue the reduction of the average number of PCUs operational during an integration. This effect is not incorporatedin the tabulated integration times. b When the last digits of the observation ID of two successive data sets are different, the two data sets areconsidered separate observations. c The total exposure does not include Earth occultation periods. d First MJD and Last MJD are the epochs, in Modified Julian Days, of the first and the last observations in aCycle. e Cycle 11 not yet completed.
43 –Table 3. Long-Term Spin Parameters for RXS J170849.0 − a Ephemeris A Ephemeris B Ephemeris C Ephemeris D Ephemeris E Ephemeris F Ephemeris GParameter Spanning MJD Spanning MJD Spanning MJD Spanning MJD Spanning MJD Spanning MJD Spanning MJD50826 − − − − − − − ν (Hz) 0.090913818(2) 0.090906071(3) 0.090906089(3) 0.090892731(13) 0.090887608(18) 0.090885281(8) 0.090884082(9)˙ ν (10 − Hz s − ) − − − − − − − ν (10 − Hz s − ) − − − − − − d ν/dt (10 − Hz s − ) − − − d ν/dt (10 − Hz s − ) − − − − − − − d ν/dt (10 − Hz s − ) − − − − − − d ν/dt (10 − Hz s − ) − − − − − − − ∆ ν d b (Hz) − − × − − − − − t d b (days) − − − − − − Epoch (MJD) 51445.3846 52016.48413 52016.48413 52989.8475 53366.3150 53549.15095 53635.6772RMS residual (phase) 0.0079 0.0150 0.0154 0.0132 0.0142 0.0112 0.0154 a Numbers in parentheses are TEMPO-reported 1 σ uncertainties. b Parameters held fixed at values determined from local glitch fits as shown in Table 4.
44 –Table 4. Local Ephemerides of RXS J170849.0 − a Ephemeris Ephemeris EphemerisParameter Near Glitch 1 Near Glitch 2 Near Glitch 3MJD range 51186.503 − − − ν (Hz) 0.090913822(2) 0.090906068(2) 0.090885035(9)˙ ν (10 − Hz s − ) − − − ν (Hz) 5.1(3) × − × − × − ∆ ˙ ν (Hz s − ) − × − − × − − × − ∆ ν d (Hz) − × − − t d (days) − − RMS residual (phase) 0.0102 0.0193 0.0140 a Numbers in parentheses are TEMPO-reported 1 σσ
44 –Table 4. Local Ephemerides of RXS J170849.0 − a Ephemeris Ephemeris EphemerisParameter Near Glitch 1 Near Glitch 2 Near Glitch 3MJD range 51186.503 − − − ν (Hz) 0.090913822(2) 0.090906068(2) 0.090885035(9)˙ ν (10 − Hz s − ) − − − ν (Hz) 5.1(3) × − × − × − ∆ ˙ ν (Hz s − ) − × − − × − − × − ∆ ν d (Hz) − × − − t d (days) − − RMS residual (phase) 0.0102 0.0193 0.0140 a Numbers in parentheses are TEMPO-reported 1 σσ uncertainties.
45 –Table 5. Local Ephemerides of RXS J170849.0 − a Ephemeris Ephemeris EphemerisParameter Near Candidate 1 Near Candidate 2 Near Candidate 3MJD range 52745.790 − − − ν (Hz) 0.0908927493(18) 0.090887617(5) 0.090884020(8)˙ ν (10 − Hz s − ) − − − ν (Hz) 2.8(4) × − × − × − ∆ ˙ ν (Hz s − ) 0 b − × − × − ∆ ν d (Hz) − − − t d (days) − − − RMS residual (phase) 0.0153 0.0099 0.0110 a Numbers in parentheses are TEMPO-reported 1 σ uncertainties. b Entries with the value ‘0’ are consistent with being zero.
46 –Table 6. Alternate Ephemerides of RXS J170849.0 − a Ephemeris Ephemeris EphemerisParameter Near Candidate 1 Near Candidate 2 Near Candidate 3MJD range 52745.790 − − − ν (Hz) 0.0908928173(6) 0.0908876402(13) 0.090884059(2)˙ ν (10 − Hz s − ) − − − ν (10 − Hz s − ) 1.2(4) 4(2) 0 b d ν/dt (10 − Hz s − ) − − − d ν/dt (10 − Hz s − ) − − a Numbers in parentheses are TEMPO-reported 1 σ uncertainties. b Entries with the value ‘0’ are consistent with being zero.
47 –Table 7. Long-Term Spin Parameters for 1E 1841 − a Ephemeris A Ephemeris B Ephemeris B2 Ephemeris C Ephemeris DParameter Spanning MJD Spanning MJD Spanning MJD Spanning MJD Spanning MJD51225 − − − − − ν (Hz) 0.0849253002(9) 0.084904428(7) 0.084889922(3) 0.084890135(6) 0.084868767(7)˙ ν (10 − Hz s − ) − − − − − ν (10 − Hz s − ) 3.30(14) − − − d ν/dt (10 − Hz s − ) 0.9(2) − − − − d ν/dt (10 − Hz s − ) − − − − − d ν/dt (10 − Hz s − ) 1.5(3) − − − − d ν/dt (10 − Hz s − ) − − − − − ∆ ν d b (Hz) − × − − − − t d b (days) − − − − Epoch (MJD) 51618.000 52464.00448 52997.0492 52997.0492 53823.9694RMS residual (phase) 0.029 0.025 0.028 0.033 0.022 a Numbers in parentheses are TEMPO-reported 1 σ uncertainties. b Parameters held fixed at values determined from local glitch fits as shown in Table 8.
48 –Table 8. Local Ephemerides of 1E 1841 −
045 Near Glitch Epochs a Ephemeris Ephemeris EphemerisParameter Near Glitch 1 Near Glitch 2 Near Glitch 3MJD range 52001.684 − − − ν (Hz) 0.084903950(2) 0.084889815(3) 0.084868657(4)˙ ν (10 − Hz s − ) − − − ν (Hz) 4.78(7) × − × − × − ∆ ˙ ν (Hz s − ) − × − × − × − ∆ ν d (Hz) 8.1(6) × − − − t d (days) 43(3) − − RMS residual (phase) 0.022 0.015 0.022 a Numbers in parentheses are TEMPO-reported 1 σσ