The Accreting Millisecond X-ray Pulsar IGR J00291+5934: Evidence for a Long Timescale Spin Evolution
aa r X i v : . [ a s t r o - ph . H E ] A ug Draft version October 29, 2018
Preprint typeset using L A TEX style emulateapj v. 03/07/07
THE ACCRETING MILLISECOND X-RAY PULSAR IGR J00291+5934: EVIDENCE FOR A LONGTIMESCALE SPIN EVOLUTION
Alessandro Patruno Draft version October 29, 2018
ABSTRACTAccreting Millisecond X-ray Pulsars like IGR J00291+5934 are important because it is possible totest theories of pulsar formation and evolution. They give also the possibility to constrain gravitationalwave emission theories and the equation of state of ultra dense matter. Particularly crucial to ourunderstanding is the measurement of the long term spin evolution of the accreting neutron star. Anopen question is whether these accreting pulsars are spinning up during an outburst and spinning downin quiescence as predicted by the recycling scenario . Until now it has been very difficult to measuretorques, due to the presence of fluctuations in the pulse phases that compromise their measurementswith standard coherent timing techniques. By applying a new method, I am now able to measurea spin up during an outburst and a spin down during quiescence. I ascribe the spin up ( ˙ ν su =5 . × − Hz s − ) to accretion torques and the spin down ( ˙ ν sd = − . × − Hz s − ) tomagneto dipole torques, as those observed in radio pulsars. Both values fit in the recycling scenarioand I infer the existence of a magnetic field for the pulsar of B ≃ × G. No evidence for anenhanced spin down due to gravitational wave emission is found. The accretion torques are smallerthan previously reported and there is strong evidence for an ordered process that is present in alloutbursts that might be connected with a motion of the hot spot on the neutron star surface.
Subject headings: stars: neutron — X-rays: stars INTRODUCTION
The recycling scenario (Alpar et al. 1982, Radhakr-ishnan & Srinivasan 1982) provides an evolutionary linkbetween the young slowly rotating pulsars and the oldfast millisecond pulsars. The evolutionary phase duringwhich the pulsar is spun up happens when a neutron starin a binary accretes gas stripped from the donor com-panion. The gas is channeled onto the magnetic polesproducing X-ray pulses modulated at the rotational fre-quency of the neutron star. When the accreting pulsarstarts to spin in the millisecond range it is called an Ac-creting Millisecond X-ray Pulsar (AMXP).To establish the presence of a spin up process it iscrucial the measurement of torques. According to ac-cretion theory, the excess angular momentum broughtby the accreting gas is responsible for the accelerationof the neutron star rotation. However, if the angularmomentum of the gas is not sufficiently high, the neu-tron star can be spun down during accretion (propellerregime, see the seminal works of Illarionov & Sunyaev1975, Ghosh & Lamb 1979 and Ustyugova et al. 2006for a recent study). The magnitude of the spin up/downis correlated with the amount of accreted matter, andhence with the X-ray flux. In the past, several attemptshave been made to measure a spin up/down in severalAMXPs, and a wealth of measurements are now availablefor at least eleven out of the thirteen known AMXPs (seeWijnands 2004, Poutanen 2006 and di Salvo et al. 2008).To accomplish this, the X-ray pulse phases are measuredand a timing model is fitted to represent the orbital mo-tion, the spin frequency and its first time derivative. Inthis model one makes the assumption that the rotational
Electronic address: [email protected] Astronomical Institute “Anton Pannekoek,” University of Am-sterdam, Science Park 904, 1098 SJ Amsterdam, Netherlands parameters of the neutron star (spin frequency and itsderivatives) are coincident with the observed pulse fre-quency and time derivatives (see for example Gallowayet al. 2005 and Burderi et al. 2007).However, large deviations from this model are usuallyseen in the timing residuals. These deviations, referred toas X-ray timing noise, represent some unmodeled compo-nent in the pulse phases which has not yet a conclusiveexplanation. Recently, it has been shown that timingnoise in at least 6 AMXPs is strongly correlated with theX-ray flux (Patruno et al. 2009a). The major conclusionwas that it is the pulse phase rather than its second timederivative (i.e., the pulse frequency derivative) to be cor-related with the X-ray flux, contrary to what predictedby accretion theory. A similar problem for accretion the-ory was seen in XTE J1807-204 (Patruno et al. 2009b),in which the pulse frequency derivative has no correla-tion with the X-ray flux whereas the pulse phases arestrongly correlated at all timescales with the X-ray flux.This is particularly convincing given the presence of largefluctuations in the X-ray flux at different timescales.The first claim for a detection of an accretion torquein an AMXP was made by Falanga et al. (2005) for theAMXP IGR J00291+5934 (henceforth referred to as IGRJ00291) during the first outburst extensively observed byRXTE/PCA and INTEGRAL in 2004. Differently frommany other AMXPs, the timing residuals of IGR J00291look quite smooth, and the presence of timing noise is notas dramatic as in other AMXPs (Patruno et al. 2009a).Therefore at a first sight, it looks quite obvious to look forthe presence of a spin up which manifests as a parabolictrend in the pulse phases and can be measured accordingto standard coherent timing techniques. However, alsothe 2004 X-ray flux of IGR J00291 shows a smooth de-cay in time, and no sudden flux variations are observed.Therefore if a correlation between the X-ray flux and thepulse phases is present, it is difficult to disentangle itfrom a parabolic variation due to a true spin up, whichis expected to be uncorrelated with the X-ray flux vari-ations.Patruno et al. (2009a) studied the 2004 outburst ofIGR J00291 and claimed that already during this out-burst there is a possible correlation between flux andpulse phases as those seen in other AMXPs. Indeed,these authors questioned the presence of a torque asstrong as that detected by Falanga et al. (2005), althoughthey did not quantify the magnitude of the expectedtorque in IGR J00291.In 2008 the AMXP IGR J00291 went in outburst again(Chakrabarty et al. 2008a). This outburst was quiteanomalous with respect to the previous one observedin 2004, since it showed first a faint outburst with apeak flux of about half the value of the 2004, and thenwent into a very low flux level phase for more than 30days. During this low level activity phase, the sourcewas not detected by RXTE and was marginally detectedby XMM-Newton (Lewis et al. 2010). After this period,a new high level activity episode was recorded: the fluxslowly rose for about 6 days, before decaying again andentering into quiescence on a timescale of approximatelyone week from the outburst peak. The 2008 outbursthas shown therefore strong flux variations that might becorrelated with the pulse phases.The behavior of the 2008 outburst is also very attrac-tive for the purpose of testing accretion theory and pul-sars evolution. Thanks to the long baseline of the obser-vations, it is possible to follow the evolution of the spinparameters in IGR J00291 on a timescale of 4 years. Onlyfor two other AMXPs it has been possible to accomplishthis: SAX J1808.4-3658 (Hartman et al. 2008, Hartmanet al. 2009, Patruno et al. 2009a) and Swift J1756-2508(Patruno et al. 2010). The spin of these sources is con-sistent with very weak or no accretion torques during theoutbursts, and with a spin down during quiescence thatcan be interpreted as a magneto dipole torque like thatoperating in radio millisecond pulsars.The plan of the paper goes as follows. In Section 2I give a detailed summary of the observations used andexplain the methodology applied to analyze the pulsephases and the X-ray flux.In Section 3 I perform a detailed standard coherentanalysis of the pulse phases of IGR J00291. The assump-tion made in this section is that accretion theory providesa good description of the behavior of pulse phases andconsequently of the neutron star spin parameters, evenif timing noise is present. This analysis is made to verifywhether the minimal assumptions made in accretion the-ory are sufficient to provide a satisfactory explanation ofthe pulse phase behavior. I discuss inconsistencies in theresults obtained with this methodology.In Section 4 I study the correlations between X-rayflux and pulse phase variations. I propose an extendedversion of the method first appeared in Patruno et al.(2009a) to measure the spin frequency and accretiontorques under the assumption that X-ray flux variations have an effect on pulse phases. I call this method Cor-relation Coherent Analysis, as opposed to the StandardCoherent Analysis (see Sections 2.2 and 2.3). With thismethod I am able to remove the effects of the X-ray fluxvariations from the pulse phases and measure “cleaned” spin parameters.In Section 5 I discuss the implication of the measure-ment of the spin period of IGR J00291. I first discuss thebehavior of the pulsar spin during quiescence (Sec. 5.1)and then I consider the detection of a spin-up during the2004 outburst (Sec. 5.2). A discussion on the origin ofX-ray flux and pulse phase correlations is discussed inSection 5.3, where I suggest a possible connection of thepulse phase variations with a hot spot moving on theneutron star surface.The spin-up timescale of IGR J00291 and the conse-quences on the lack of detected sub millisecond pulsarsand the spin distribution of accreting pulsars are dis-cussed in Sections 6.Finally, the implications of the observed spin evolu-tion are summarized in the framework of the recyclingscenario (Section 7). PULSATIONS AND X-RAY LIGHT CURVE: DATAREDUCTION
I use all
RXTE
PCA public data for the 2004 and2008 outbursts of IGR J00291 (Table 1). I refer to Ja-hoda et al. (2006) for PCA characteristics and
RXTE
PCA absolute timing. I used all available Event 125 µ s and Good-Xenon data , rebinned to 1/8192 s andin the 5–37 absolute channel that maximizes signal-to-noise-ratio (S/N). The absolute channels correspond to ≈ . −
16 keV. The time of arrivals are corrected to thesolar system barycenter (TDB timescale) by using thebest available astrometric position reported in Rupen etal. (2004). An optical position has also been reportedby Torres et al. (2008) which differs by 0.25 arcsec fromthe determination of Rupen et al. (2004). If the opti-cal position is used, then a shift in pulse frequency andfrequency derivative of 4 × − Hz and 10 − Hz/s isexpected (see for example Eq. A1 and A2 in Hartmanet al. 2008). These shifts are small enough to not affectthe results reported in the paper.The light curve is folded in data chunks of differentlength, between ∼ ∼ > σ , giving < σ error. I detect only a significantnumber of pulsations at the fundamental frequency ( ν )and then fitted the phases with a Keplerian orbit plus alinear and possibly a parabolic term representing ν and˙ ν (see Section 2.2 and 2.3 for more details).I constructed the X-ray light curve using the countsin PCA Absolute channels 5-37 ( ≈ . −
16 keV). Thebackground contribution (calculated with the FTOOL pcabackest ) is subtracted from the total counts.
X-ray light curves for the 2004 and 2008 outbursts Care has to be taken when combining Events 125 µ s and Good-Xenon data, since a rigid shift of 2 − s is present in the 2004data due to a bug in an early version of the FTOOL xenon2fits(Markwardt private communication) pin evolution of IGR J00291 3 X -r a y f l u x [ c t/ s / P CU ] Time [MJD - 53342] 1st 20082nd 2008 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 14 X -r a y f l u x [ c t/ s / P CU ] Time [MJD - 53342] 2004
Fig. 1.—
X-ray light curves of the two outbursts of IGR J00291. The left panel shows the 2004 data, whereas the right one refers to the2008 data. The y-scale is the same in the two plot, while the x-axis is not. In 2008 two faint outbursts are observed,with peak luminositiesabout half the value of 2004. The shape of 2004 and the first 2008 outburst is remarkably similar, whereas the second 2008 outburstshows a bell-shape light curve. In the plot are shown only points in which pulsations are detected, which correspond to minimum countsof approximately 8 ct/s/PCU.
TABLE 1
RXTE observations for the 2004 and 2008 outburst
RXTE
Year Start End Outburst Length Program IDs(MJD) (MJD) (days)2004 53355.85 53342.28 13.6 - - The X-ray light curves for the 2004 and 2008 outburstsare shown in Figure 1. The first outburst has an ap-proximately linear decay, with pulsations detected for 14days, and a peak luminosity of 75 ct/s/PCU in the 2.5-16keV energy band, corresponding to an unabsorbed fluxof 9 . × − erg / s / cm (Markwardt et al. 2004) for anHydrogen absorption column of N H ∼ × cm − andphoton index Γ ≃ .
7. Falanga et al. (2005) used a comp-tonization model and estimated a peak bolometric flux of ∼ . × − erg / s / cm , corresponding to a bolometricluminosity of 6 . × erg s − , assuming a distance of5 kpc (the distance is taken from Falanga et al. 2005).In this paper I fix the distance at 5 kpc in all calcu-lations. The corresponding mass accretion rate, given aneutron star mass of 1 . M ⊙ and an assumed efficiency of η = 0 .
15, is therefore ˙ M ∼ × − M ⊙ yr − , accordingto the expression L bol = ˙ M η c . The mass accretion rateaveraged over the entire 2004 outburst length is insteadapproximately ˙ M outb ≃ × − M ⊙ yr − . Of courseuncertainties are present in this estimate, especially be-cause no spectral modeling has been done. Furthermore,there are uncertainties in the conversion of X-ray to bolo-metric flux and on the assumed value of η for the conver-sion of rest mass energy into radiation, so these valueshave to be taken with care and only as orders of magni-tude estimates. There is also a large uncertainty in thedistance, which has been proposed to be in the range 2-6kpc by several authors (Torres et al. 2008, Falanga et al.2005, Galloway et al. 2005).For the 2008 outburst, the analysis is separated foreach of the two weak outbursts observed. Although the2008 outburst can be considered as a single episode of high level activity, I prefer to treat it as two separateoutbursts since the coherent analysis will be also givenseparately (the reason of this choice is explained in Sec-tion 3).The first weak outburst has a very similar shape asthe 2004 outburst, but a peak flux about half the 2004value. The outburst appeared after 3.68 yr from the2004 outburst (Galloway et al. 2008). Assuming that thespectral shape remained the same as in 2004, the averagemass accretion rate is: ˙ M outb ≃ × − M ⊙ yr − . Thisoutburst lasted for approximately 5 days, after which avery low level activity was recorded (Lewis et al. 2010).The second weak outburst appeared after 30 days andshowed a different shape than the 2004 and the first weak2008 outburst. It shows a slow rise and a rapid decaythat create interesting variations in the X-ray flux shapethat can be tested against the pulse phase variations.Assuming that the spectral shape remained the same asin 2004, the average mass accretion rate is: ˙ M outb ≃ × − M ⊙ yr − .Before the 2004 outburst, other two outbursts were de-tected in the RXTE/ASM, with recurrence times of 2.80and 3.23 yr (Remillard 2004, Galloway et al. 2008). Theaverage recurrence time seems therefore to slightly in-crease on the long timescale. By using all these informa-tion, I can calculate the long term average mass accretionrate in IGR J00291 for two outburst/quiescence cycles: D ˙ M E = 7 × − × . d d . yr ≃ × − M ⊙ yr − D ˙ M E = 5 × − × . d d + 6 × − × . d d . yr ≃ × − M ⊙ yr − (1)Both values are in excellent agreement, and point to-wards an accretion rate similar to that calculated for theAMXP SAX J1808.4-3658, which has showed six out-burst/quiescence cycles with an D ˙ M E ≃ − M ⊙ yr − (Bildsten & Chakrabarty 2001). Old Method: Standard Coherent analysis
Standard coherent methods (e.g., Taylor 1992) arebased on folding procedures and to χ minimization tech-niques with a model describing the time evolution of thepulse phase φ ( t ) at the barycentric reference frame. Thepulse phases are then fitted with a Keplerian orbit anda spin frequency and its first time derivative (see for ex-ample Patruno et al. 2009b and references therein for adiscussion of the method). I performed this fit by usingthe standard coherent timing software TEMPO2 (Hobbset al. 2006). The spin frequency derivative is then as-sociated with the accretion torque N via the simple ex-pression given by accretion theory: N = 2 π I ˙ ν su (2)If the orbital and astrometric components are correctlyremoved from the pulse phases, one expects to see inthe timing residuals a set of independent values whichare normally distributed around the zero average withan amplitude that can be predicted by propagating thePoisson uncertainties due to counting statistics.I stress that this method uses the assumption thatthe pulse phases vary in time only because of the rota-tional motion of the neutron star around its spin axis andaround the orbit, while no other effect is taken into ac-count. If some other process does affect the pulse phases,then the Standard Coherent Analysis does not returnrealistic physical parameters and their statistical uncer-tainties for the accreting neutron star. New Method: Correlation Coherent Analysis
In this second method, one takes into account also pos-sible additional effects others than the rotational motionof the neutron star on the observed pulse phases. Afirst attempt to apply this method in AMXPs was madeby Patruno et al. (2009a). In that paper the authorsconsidered the possible influence of the X-ray flux onthe pulse phase, suggesting that mass accretion rate ˙ M induced hot spot motion dominates the observed pulsephase variations.The method I present here follows the same route, andsearches for higher/lower reference pulse frequencies thanthe one selected in Standard Coherent Analysis by usingthe correlation between pulse phases and X-ray flux. Imake a non-trivial assumption on the nature of the corre-lation: there is a linear relation between the pulse phasesand the X-ray flux. The selected pulse frequency is thenthe one that minimizes the χ of the linear fit betweenphase and flux, instead of the pulse frequency that mini-mizes the pulse phase residuals in the fit with TEMPO2.The reason why I choose a linear relation among all thepossible choices is because this is the simplest law, and itis by no means necessarily a universal law that can be ap-plied in all circumstances. One has to take this assump-tion as the “minimal hypothesis”, so that it is possibleto verify whether under the simplest circumstances it ispossible to already obtain results which are statisticallybetter than Standard Coherent Analysis.Differently from Patruno et al. (2009a), that used aconstant spin frequency model, I select the best pulsefrequency and pulse frequency derivative instead of vary-ing simply the pulse frequency (see also Patruno et al.2009b). I scanned 3000 pulse frequency derivatives in the range [ − − Hz s − , +10 − Hz s − ] and 1000 pulse fre-quencies for each outburst. Only for the 2004 outburstit is possible to detect a significant spin derivative, whilein 2008 only non-constraining upper limits were calcu-lated. Since no significant pulse frequency derivative isdetected in 2008, I refit the same data with a constantspin frequency model.By applying this technique I obtain results for all theoutbursts which show clear improvement in the χ of thefit when using the Correlation Coherent Analysis ratherthan Standard Coherent Analysis. It is relevant to notethat when using the Correlation Coherent Analysis in-stead of Standard Coherent Analysis, the number of pa-rameters used in the fit (and therefore the degrees offreedom) are exactly the same for the two methods, sothere is no risk to over-fit the data when using the formermethod.In the following Sections 3 and 4 I discuss the re-sults and the implications of the two methods. If oneapplies Standard Coherent Analysis, then the physicalconsequences seem contradictory and require extraordi-nary explanations. If one considers Correlation CoherentAnalysis, then the results match with a high degree of ac-curacy the predictions of Accretion Theory. STANDARD COHERENT ANALYSIS AND ACCRETIONTHEORY
The spin parameters for the three outbursts are shownin Table 2. The orbital parameters are instead shown inTable 3, 4 and 5.According to this method of analysis the spin frequencybetween the first and the second 2008 outburst decreasesby ∼ . µ Hz. This means that during the first 2008 out-burst, or in between the two 2008 outbursts, a strong spindown must have occurred. However, a spin down duringthe outburst is not a realistic hypothesis because we de-tect positive spin frequency derivatives, firmly excludingany spin down. According to this method of analysis,the required spin down must have occurred in betweenthe two 2008 outbursts and it needs to be of the order of − × − Hz s − . This value appears to be too large tobe explained with a propeller scenario. Indeed, at MJD54703, during the 30 days of low level activity, an XMM- Newton observation was performed, with upper limits onthe 0.5-10 keV X-ray flux of ∼ − erg s − cm − (Lewiset al. 2010), which are almost 5 orders of magnitude lowerthan the peak luminosity of the first 2008 weak outburst.This means that the accretion level must have been ex-tremely low, around 10 − M ⊙ yr − or less, and this isnot compatible with the required mass that need to beejected from the system (which is of the order of a few10 − M ⊙ yr − ) to explain the ∼ . µ Hz spin frequencyshift. Of course one can argue that at the onset of thepropeller a large amount of mass is still present, but theX-ray luminosity is suppressed by the lack of accretion onthe neutron star surface. However, also the productionof X-rays in the inner accretion disk must be suppressed,since the X-ray luminosity observed is comparable withthe quiescent luminosity (Campana et al. 2008; Torres etal. 2008).Also a magnetic dipole induced spin down can be con-sidered a quite unlikely possibility since the spin downbetween the two 2008 weak outbursts requires a magneticfield of at least 2 × G and there is no reason why suchpin evolution of IGR J00291 5 -0.15-0.1-0.05 0 0.05 0.1 0.15 0 10 20 30 40 50 60 70 80 P u l s e pha s e r e s i dua l [ C yc l e ] X-ray flux [ct/s/PCU]20041st 20082nd 2008
Fig. 2.—
X-ray flux vs. pulse phase correlation for the 2004 and the two 2008 outbursts. All three outbursts follow a correlation betweenflux and phase which is consistent with being the same in all three cases, within the statistical errors. The correlation has been fit with alinear relation between flux and pulse phase. The pulse phase shifts by almost 0.2 cycles during 2004 and by ∼ . χ of the fit are reported in Table 6. large spin down is not observed between the 2004 and thefirst 2008 outbursts. Indeed, the spin frequency at theend of the 2004 outburst is 598 . − × − Hz s − constantly operatingin the ∼ ∼ . µ Hz off the mea-sured spin frequency at the beginning of the first 2008outburst, and hundreds of sigma away.A final possibility to explain these mismatching spinfrequencies is via glitches occurring during quiescence ,since no signature of glitches is seen in the timing anal-ysis of the outbursts. Glitches in AMXPs have neverbeen observed and those detected in millisecond (radio)pulsars are a rare phenomenon. In these latter systems,the magnitude on the spin frequency variation duringa glitch is orders of magnitude smaller than in normalyoung pulsars (Cognard & Backer 2004). There is onlyone detection of a glitch in a slowly rotating accretingpulsars for the source KS 1947+300 (Galloway et al.2004). However, in this accreting pulsar the glitch re-sulted in an acceleration of the spin rotation, while weneed here a deceleration. Therefore, although a glitchcannot be completely ruled out, it appears an unlikelyexplanation for the measured mismatching frequencies.I ascribe this behavior of the spin frequencies to thepresence of timing noise as already suggested in Patrunoet al. (2009a). A further consequence of this is that phaseconnection between the two 2008 outbursts is not a cor-rect procedure of analysis. Indeed, although certainlypossible, the phase connection with the standard coher-ent technique ignores the presence of timing noise andassumes that the pulse phases are well behaved. There-fore the spin frequency that one finds by phase connect-ing the two 2008 outburst in this way is just an averagevalue of the spin frequencies plus torques and contam- ination of timing noise and as such it is a meaninglessquantity. However, this average value does not necessar-ily deviate from the true value by a large amount. Thisdepends on the weighted effect of several factors, likethe outburst length, the strength of timing noise and themagnitude of torques during and in between outbursts,that might also partially compensate each other and mis-lead the judgment on the validity of the results.Another problem is related with the magnitude of thespin frequency derivative detected in 2004. If one doesnot take into account the effect of timing noise, then alsothis quantity, and hence the inferred accretion torques,will appear higher than they really are. I give here anexample of this effect on the measured spin frequencyderivatives of IGR J00291. The 2004 outburst of IGRJ00291 started on December 3, and stopped on Decem-ber 21. Galloway et al. (2005) analyzed the data betweenDecember 3 to 6 and did not detect any spin frequencyderivative, with large upper limits due to the short base-line of the observation. Falanga et al. (2005) and Bur-deri et al. (2007) analyzed the pulsations from Decem-ber 7 to 21 and they both detect a consistent spin fre-quency derivative between 8 and 12 × − Hz s − . How-ever, if one splits the data differently, for example oneanalyzes the data between December 3 and 10 and be-tween 10 and the end of the outburst, one finds ˙ ν su =3 . × − Hz s − and ˙ ν su = 24(5) × − Hz s − . Soif one believes accretion theory, the torque has increased when the flux was lower, completely contradicting theexpectation that a smaller amount of mass should bringless angular momentum and produce a smaller and not ahigher spin frequency derivative. There might be possibleexplanations for that, i.e., considering modifications tothe accretion theory, but taking into account the presenceof timing noise might be a more straightforward expla-nation. Indeed something similar was observed in XTEJ1807-294 (Patruno et al. 2009b) where the short-termspin frequency derivatives were behaving in a way notpredicted by accretion theory. The conclusion was thatthe observed spin frequency derivatives were affected byred timing noise, so they were not true spin frequencyderivatives. The same conclusion applies here. In thenext Section I propose a method that takes into accountthe effect of timing noise and calculates unbiased spinfrequencies and time derivatives. CORRELATION COHERENT ANALYSIS ANDACCRETION THEORY
A possibility to explain the pulse frequency discrep-ancy of the previous Section is via the presence of timingnoise in the pulse phases. To take into account this, Ihave applied the Correlation Coherent Analysis (see Sec-tion 2.3) to the 2004 and 2008 outburst data.I used the orbital solution as found in Section 3, sincethe orbit is only marginally affected by the pulse phasenoise, which operates on completely different timescalesthan the orbital modulation. Indeed the orbital periodof IGR J00291 is ∼ . φ andthe X-ray flux f X : φ = A + B · f X . The coefficients A andB are reported in Table 6, along with the spin frequencyand its first derivative found minimizing the χ of thelinear fit. All coefficients are consistent with being thesame within the statistical uncertainties. All the statisti-cal errors are calculated for a ∆ χ = 1. The correlationsfor the three outbursts are shown in Figure 2, where it isevident that all three outbursts behave in a way which isconsistent with being the same. Of particular relevanceis the fact that also the second 2008 outburst follows asimilar correlation as the 2004 and the first 2008 out-burst, even though the shape of this X-ray light curveis very different from the other two. The pulse phasessuggest a drift of approximately 0.2 cycles in 2004 and0.1 cycles in the two 2008 outbursts.There is still some unmodeled component in the fits,which is particularly evident in 2004, where the pulsephases slightly deviate towards the end of the outburstand affect the goodness of the fit. However, the χ ofthe fits obtained with this method are statistically muchbetter than those obtained with standard coherent anal-ysis (see last column of Table 6 and 2). The uncertain-ties found with this method are larger than those foundwith standard coherent analysis because here I take intoaccount also the effect of timing noise in the fit. The sta-tistical uncertainties found in this way can be considereda good approximation of the true uncertainties, differ-ently from those obtained with standard coherent timingtechniques.In a recent work, Ibragimov & Poutanen (2009) demon-strated that pulse phase variations have an energy de-pendence in the AMXP SAX J1808.4-3658. Somethingsimilar might also happen in IGR J00291, so it is usefulto test whether the linear correlation and the best spin frequency and frequency derivative have an energy de-pendence. I split the data in two energy bands, a softband (2-7 keV) and an hard band (8-16 keV) and re-peated the entire procedure outlined above for the fullband (2-16 keV). The best spin parameters as well asthe coefficients A and B are consistent with being thesame for the soft, hard and full bands. However, sincethe photon statistics is degraded when splitting the datain sub-bands, the statistical errors in the soft and hardbands are much larger than in the full band, so that apossible energy dependence cannot be firmly excluded.The long term spin frequency evolution is reported inFigure 3. During the 2004 outburst there is a detection ofa spin up, while in the two weak 2008 outbursts it is onlypossible to set confidence intervals for the non-detectionswhich are consistent with being the same within the sta-tistical uncertainties. The long term spin frequency evo-lution requires a constant spin down during quiescence.A detailed discussion follows in the next Section. LONG TERM SPIN EVOLUTION
Pulsar spin down in quiescence
The spin-down evolution of the neutron star in IGRJ00291 is reported in Figure 3. The pulsar spin frequencyrequires a spin down between the end of the 2004 out-burst and the beginning of the first 2008 outburst. Sinceit is not possible to find a significant torque in the firstand second 2008 outbursts, the reported spin frequenciesrefer to a constant spin frequency model. The value ofthe spin down is ˙ ν sd ≃ − (3 ± . × − Hz s − .It is not possible to verify whether a spin down is alsorequired between the two 2008 weak outbursts, since theuncertainty on the spin frequencies of the first 2008 out-burst is too large ( ≃ − Hz).While other effects might also contribute to the spindown, the rotating neutron star magnetic field is al-ways present and causes a continuous emission of lowfrequency radiation. By using the force-free MHD ap-proximation of Spitkovsky (2006), the determination of˙ ν sd provides an upper limit on the dipole moment: µ < (cid:0) α (cid:1) − / × (cid:18) I g cm (cid:19) / (cid:16) ν
600 Hz (cid:17) − / × (cid:18) − ˙ ν sd × − Hz s − (cid:19) / G cm . (3)For the extreme values of α = 90 ◦ , ◦ , and consideringall sources of uncertainty (colatitude, period and periodderivative), the maximum dipole magnetic field at thepoles is B sd = [1 .
5; 2 . ± . × G (4)If the pulsar in IGR J00291 switched on as a radiopulsar during quiescence, then its position on the P − ˙ P would fall exactly in the expected region occupied byradio millisecond pulsars (see Figure 4). The Pulsar Magnetic Field
Beside IGR J00291, there are only two other AMXPs inwhich it was possible to constrain the magnetic field fromthe long term spin frequency behavior: SAX J1808.4-3658 (Hartman et al. 2008 and Hartman et al. 2009) andpin evolution of IGR J00291 7
TABLE 2STANDARD COHERENT ANALYSIS: SPIN PARAMETERS FOR IGR J00291+5934
Outburst Spin Frequency Spin Frequency Derivative Epoch χ /dof [Hz] [10 − Hz s − ] [MJD]2004 598.89213045(1) 5.6(3) 53342.27 309.15/881st 2008 598.89213061(8) 12.3(4) 54692.00 46.39/252nd 2008 598.89213046(5) 5.7(8) 54730.50 26.55/10 ν s - ν [ µ H z ] Time [MJD - 53500] S p i n D o w n − − H z / s S p i n U p + . − H z / s Fig. 3.—
Long term spin frequency evolution of the pulsar in IGR J00291. The spin frequencies are plotted with an offset ν = 598 . − × − Hz s − . TABLE 32004 Orbital parameters for IGR J00291+5934
Orbital Period [s] 8844.080(2)Projected Semi-major Axis [lt-ms] 64.995(2)Time Of Ascending Node [MJD] 53345.1619277(5)
TABLE 4First 2008 outburst: Orbital Parameters for IGRJ00291+5934
Orbital Period [s] 8844.069(12)Projected Semi-major Axis [lt-ms] 64.987(4)Time Of Ascending Node [MJD] 54692.041113(3)
TABLE 5Second 2008 outburst: Orbital Parameters for IGRJ00291+5934
Orbital Period [s] 8844.075(6)Projected Semi-major Axis [lt-ms] 64.993(5)Time Of Ascending Node [MJD] 54730.529224(4)
Swift J1756.9-2508 (Patruno et al. 2010). For SAX J1808a spin down of − . × − Hz s − was found. For SwiftJ1756 only upper limits on the spin down were given.The strength of the spin down in quiescence and henceof the magnetic field of SAX J1808 was also revised byPatruno et al. (2009a), who applied a similar techniqueto that reported in this paper, and found a spin down of − × − Hz s − and a magnetic filed of ≃ − . × G,slightly larger than the 1 . × G reported in Hartmanet al. (2009).The magnetic fields B of the three pulsars are there-fore: • IGR J00291+5934: [1 .
5; 2 . ± . × G • SAX J1808.4-3658: [2 .
0; 2 . ± . × G • SWIFT J1756.9-2508: [0 .
4; 9] × G (95% c.l.)The ranges [1 .
5; 2 .
0] and [2 .
0; 2 .
8] reflect the indetermi-nation of the colatitude of the magnetic pole, while theerrors on each determination is calculated by propagat-ing the errors on the spin parameters in Eq. (3). The B field of IGR J00291, SAX J1808, and Swift J1756 is per-fectly compatible with the minimal hypothesis that only TABLE 6CORRELATION COHERENT ANALYSIS: SPIN PARAMETERS FOR IGR J00291+5934
Outburst A σ A B σ B Spin Frequency Spin Frequency Derivative [10 − Hz s − ] Epoch χ /dof Fig. 4.—
P- ˙ P diagram for radio pulsars. The cross representsthe position of the pulsar in IGR J00291 with period and periodderivative as determined in Section 5.1 under the assumption thatthe observed spin down is caused by magneto dipole torques. Iplot also the position of SAX J1808.4-3658 (red star, Patruno etal. 2009a) and Swift J1756.9-2508 (blue circle, Patruno et al. 2010).The latter has no detected spin down during quiescence, and there-fore the position is determined by using an upper limit on the spindown. magneto dipole torques are at work. Under this assump-tion, the derived magnetic fields are exact values and notupper limits. There is no clear evidence for an alterna-tive/additional mechanism to explain the observed spindown other than magneto dipole torques. Pulsar spin up during outbursts
According to accretion theory, a pulsar accreting froma disk will experience a positive torque (spin-up) whenthe magnetospheric radius r m is smaller than the coro-tation radius r co . The latter is defined as the position atwhich the gas in the accretion disk has the same angularvelocity of the neutron star: r co ≃
17 km × (cid:18) P spin (cid:19) / (cid:18) M1 . ⊙ (cid:19) / (5)For a pulsar spinning at ∼
600 Hz like IGR J00291, thecorotation radius is at ∼
24 km, which is within approx-imately one stellar radii from the neutron star surface.The magnetospheric radius is related to the neutronstar magnetic dipole moment µ , to the neutron star mass M and to the mass accretion rate ˙ M via the equation: r m ≃
35 km ξ (cid:16) µ G cm (cid:17) / × (cid:18) − M ⊙ yr − ˙ M (cid:19) / (cid:18) . M ⊙ M (cid:19) / (6)The accretion disk model-dependent factor ξ lies inthe range ∼ . − M = 1 . M ⊙ and using the 2004 averagemass accretion rate as calculated in Section 2.1 I obtain r m = 2 −
20 km, for 0 . < ξ < r m smallerthan 8-10 km are non-physical because of the presenceof the hard surface of the neutron star. Nonetheless,given the large uncertainties in the determination of ˙ M (distance, accretion efficiency and bolometric flux) it isover-simplistic to favor values of ξ closer to one and thecalculations have to be interpreted just as order of mag-nitude estimates of the quantities involved.The condition r m = r co to enter the propeller regime is met when ˙ M ≃ − M ⊙ yr − , which corresponds toan RXTE count rate of ∼ / s / PCU, in excellent agree-ment with the minimum count rate at which significantpulsations are detected: ∼ / s / PCU. Although thisvalue depends on several additional sources of uncer-tainty , it shows that the magnetospheric radius reallylies within r co during the whole period in which pulsa-tions are observed from 2004 to 2008.The maximum observed X-ray flux, and hence themaximum mass accretion rate as determined in Sec-tion 2.1 is ˙ M = 2 × − M ⊙ yr − . The magnetosphericradius at this flux is r m ≃ . −
15 km, for 0 . < ξ < r m = r co : µ max = 2 . × G cm − (cid:18) r co ξ (cid:19) / × ˙ M − M ⊙ yr − ! / (cid:18) . M ⊙ M (cid:19) / (7)The value of µ max , and hence of the magnetic dipolefield depends on the choice of ξ and on the averageoutburst mass accretion rate. By choosing the leastconstraining values for ξ = 0 . D ˙ M E = 6 × − M ⊙ yr − , I obtain a maximum dipole magneticfield at the magnetic poles of B max ≃ . × G. For ξ = 1 the maximum B field becomes B max ≃ . × G. More recent works (like Rappaport et al. 2004 and Spruit &Taam 1993) show that the onset of the propeller is more compli-cated than simply r m = r co . However, this does not substantiallyaffect the argument used in this paper. pin evolution of IGR J00291 9These values are within the expected range for accret-ing millisecond pulsars and they match the spin downdipole magnetic field B sd as well as the upper limits of B max < × G proposed by Torres et al. (2008).To further check the self consistency of the accretiontheory, it is useful to obtain a minimum magnetic field. Iuse the same argument as used in Psaltis & Chakrabarty(1999) and Miller et al. (1998): pulsations are seen atthe outburst peak, therefore the magnetic field must bestrong enough to channel the accretion flow and enforcecorotation of the accreted gas when the accretion rate ismaximum. By using the least constraining mass accre-tion rate ˙ M = 2 × − M ⊙ yr − (see Section 2.1) andusing Eq. (11) in Psaltis & Chakrabarty (1999) I obtaina minimum magnetic field at the poles B min = 6 × G. In this calculation I have assumed the conservativequantities R = 10km, M = 1 . M ⊙ and ξ = 1 (here ξ iswhat is called γ B in Psaltis & Chakrabarty 1999).Both maximum and minimum magnetic fields as in-ferred from accretion theory are therefore consistent withthe spin-down magnetic dipole field obtained in Sec-tion 5.1. Motion of the Hot Spot
In Section 4 I showed that in both 2004 and in the twoweak outbursts of 2008 the coefficients of the linear corre-lation are consistent with being the same, which suggestssome ordered process acting during each outbursts thatprovides an identical response of the phase to a fixedperturbation of the X-ray flux.Lamb et al. (2008a) suggested a moving hot spot onthe neutron star surface as the origin of timing noise inAMXPs. Moving hot spots were also observed in MHDsimulations of Romanova et al. (2003) and Romanovaet al. (2004) although the number of simulated neutronstar rotations is still too small to reach a firm conclusion.Applying the correlation coherent technique, I findthat the pulse phases drift by approximately 0.2 cycleswhen the X-ray flux varies by a factor ∼
10 from themaximum to the minimum in 2004, and by 0.1 cycles inthe two 2008 outbursts (see Figure 2). Such variationsmight be induced by a motion of the hot spot. A move-ment along the latitude of the neutron star will produceonly minimal changes in phase, so a drift in longitude isalso required.Under the assumption that the accretion rate tracksthe X-ray luminosity, the magnetospheric radius r m willmove away from the neutron star surface and approachthe corotation radius r co as the source luminosity dropsfrom the peak of the outburst down to quiescence. Dur-ing this process, the hot spot can move about the mag-netic pole depending on the colatitude of the magneticaxis, as it was observed in MHD simulations by Ro-manova et al. (2003).In a recent work, Bachetti et al. (2010) performed de-tailed MHD simulations of accreting neutron stars, andfound that the hot spot does indeed move about themagnetic pole, with small colatitudes favoring a morepronounced motion. Although these authors could simu-late only a few rotational cycles of the neutron star, dueto computational power limitations, their results clearlyshow that the accretion flow in the pulsar magnetosphereis a highly dynamical process and questions the tradi-tional picture of a static hot spot. A detailed discussion on the modeling of the hot spotmovement is beyond the scope of this paper. A modeltaking into account variations of the X-ray flux and thehot spot motion will be presented in an accompanyingpaper. SPIN EQUILIBRIUM AND SPIN UP TIMESCALE
A self-consistent measurement of the spin frequencyand its long term evolution has been given, andby knowing the approximate duty cycle for the out-bursts/quiescence cycle of IGR J00291, it is possible todetermine a timescale for the spin up of the pulsar.I call ∆ − the inverse of the duty cycle for the out-bursts/quiescence episodes, whose value is approximately1% (2004 outburst length ∼
13 d, 2004-2008 quiescencelength ∼ ν s ≃
600 Hzand ˙ ν su ≃ × − Hz s − , with a duty cycle ∆ ≃ . t spin − up ≡ ν s ˙ ν su ∆ − ≡ Gyr (8)which means that the pulsar will not change its spinfrequency significantly for a long timescale, or in otherwords that it is close to the spin equilibrium (see forexample Campana et al. 1998).Furthermore, there is a further slow down on thistimescale deriving from the spin down observed in qui-escence. The timescale for the spin-down ( ˙ ν sd ≃ − × − Hz s − ) is: t spin − down ≡ ν s | ˙ ν sd | (1 − ∆) − ≃ t spin ≡ (cid:18) ν s ˙ ν sd × (1 − ∆) + ˙ ν su × ∆ (cid:19) ≃ The lack of Sub-Millisecond Pulsars
A very important problem in neutron star physics ishow to justify the absence of pulsars with spin period inthe sub-millisecond rage. Although only a rather limitednumber of sources were known at the time, Chakrabartyet al. (2003) and Chakrabarty (2005) studied the spindistribution of AMXPs and nuclear powered pulsars anddiscovered that this was consistent with a flat distri-bution truncated at approximately 730 Hz with a 95%confidence level. Although strong observational biasesexist for the detection of a radio pulsar above this fre-quency, X-ray observations taken with observatories likeRXTE/PCA should not be affected by a significant lossof sensitivity at least up to 2 kHz (see Chakrabarty 2008and references therein). Hence it remains unexplained0
TABLE 7Accretion and Nuclear Powered Millisecond Pulsars
Source Name Spin Frequency [Hz]Swift J1756-2508 182XTE J0929-314 185XTE J1807-294 190NGC 6440 205IGR J17511 245IGR J17191-2821 294MXB 1730-335 306XTE J1814-338 3144U 1728-34 363HETE J1900.1-2455 377SAX J1808.4-3658 4014U 0614+09 415XTE J1751-305 435SAX J1748.9-2021 442SAX J1749.4-2807 518KS 1731-260 526Aql X-1 550EXO 0748-676 552MXB 1659-298 5564U 1636-536 581IGR J00291-5934 599SAX J1750.8-2900 6014U 1608-52 620 why the maximum spin frequency known for accretingneutron stars is 619 Hz (Hartman et al. 2003). Hesselset al. (2006) discovered the fastest known radio millisec-ond pulsar, that spins at 716 Hz, surprisingly close to thecut-off spin limit of 730 Hz. If I repeat the calculationof the spin distribution cutoff as done by Chakrabarty etal. (2003), with a sample size which has doubled in themeanwhile (from 11 to 23 known accreting neutron starspins, see Table 7)
I still find a cutoff of 730 Hz, but witha higher confidence level of 99% .IGR J00291 is the third fastest known accreting neu-tron star and among the fastest neutron stars known. Itis therefore at the upper end of the spin distribution ofaccreting neutron stars, which is plotted in Figure 5 (seeWatts et al. 2008,Markwardt et al. 2007 and Gallowayet al. 2010 for references). If the spin evolution of thissource is representative of the behavior of AMXPs, thenit explains the existence of a cutoff of 730 Hz in the spindistribution of accreting pulsars.Several mechanisms have been proposed to explain thelack of sub-millisecond pulsars, but what appears cer-tainly true is that these spin frequencies are not limitedby the break-up frequency of neutron stars, which setsin when the centrifugal force exceeds the gravitationalpull. The break-up frequency depends on the equationof state of ultra-dense matter, and its determination istherefore of fundamental importance to understand theground state of matter (Weber 2005). Basically all equa-tion of states allow a much higher break-up frequencythan 730 Hz. Alternative models to explain the lack ofsub-millisecond accreting neutron stars have been pro-posed, including loss of angular momentum due to emis-sion of gravitational radiation and the existence of mag-netic spin equilibrium.In the former case, a train of gravitational waves isemitted as soon as the neutron star develops a significantquadrupole moment. The angular momentum broughtaway by the gravitational waves slows down the pul- N u m be r o f sys t e m s Spin Frequency [Hz]Nuclear-powered PulsarsAccretion-powered Pulsars
Fig. 5.—
Spin frequency distribution. The red bars represent10 nuclear powered pulsars whose spin frequency is measured viaburst oscillations during thermonuclear bursts. The 13 accretionpowered pulsars are identified by blue bars, and no accreting pulsarwith spin below 100 Hz is counted in the sample, according to thedefinition of millisecond pulsar. Note that the red and the bluehistograms are not overlapped, but they are added. If a pulsar isboth accretion powered and nuclear powered, I have counted it asan accretion powered. The total number of neutron stars in thesample (accretion plus nuclear powered) is 23. sar rotational period, thus preventing accreting neutronstars to reach sub-millisecond periods. The gravitationalwave torque is proportional to ν s , so its effect greatly in-creases at high rotational frequencies. This can producethe sharp cutoff in the spin distribution (see Chakrabarty2008 for further discussions of the problem). A loss ofangular momentum via gravitational radiation is still anopen possibility, but the good agreement between themagnetic field determination via accretion torques andvia magneto dipole spin down seems to suggest a sim-pler (and in this sense more likely) explanation for theexistence of a 730 Hz cutoff.If the timescale for the spin-up in IGR J00291 is ofthe order of 7 Gyr (see Section 5.2), then a plausible ex-planation for the 730 Hz cutoff is that accreting neutronstars reach the spin equilibrium earlier than it is requiredto reach sub-millisecond periods. In this sense, the rea-son why there are no observed sub-ms pulsars might bea simple consequence of binary and magnetic field evolu-tion (see also Lamb & Yu 2005 and Lamb & Boutloukos2008b).It is possible to compare this behavior with the onlyother AMXPs with a measured spin down in quiescence:SAX J1808.4-3658 (Hartman et al. 2008, Hartman et al.2009, Patruno et al. 2009a). The overall long term spinfrequency in SAX J1808.4-3658 is decreasing over an ob-served baseline of ∼
10 years, suggesting that no sig-nificant accretion torque operates during the outbursts.Therefore also this pulsar will not significantly move inthe spin distribution diagram on a timescale compara-ble with the Hubble time. Unless the neutron star wasborn with a spin already in the millisecond range, strongaccretion torques must have spun up the pulsar in thepast. Its current magnetic field and average mass accre-tion rate might be instead too small to allow a significantspin up during the outbursts. Therefore the spin evolu-tion of these two AMXPs is compatible with a scenarioin which AMXPs evolve close to the spin equilibrium ona timescale shorter than it is required to spin up to thepin evolution of IGR J00291 11sub-millisecond range.Before drawing a firm conclusion it is important toinvestigate the spin evolution of more accreting neu-tron stars, but it seems justified here to propose that,given the observed spin evolution of IGR J00291 andSAX J1808, sub-millisecond pulsars might be, at best,extremely rare. SUMMARY IN THE FRAMEWORK OF THE RECYCLINGSCENARIO
A first achievement for the recycling theory arrivedwith the discovery of the first Accreting Millisecond X-ray Pulsar in 1998 (Wijnands & van der Klis 1998). An-other fundamental step has been the recent detection ofa millisecond radio pulsar in a position coincident with aa previously known quiescent neutron star X-ray binary(Archibald et al. 2009, Homer et al. 2006). This was afurther evidence that accreting millisecond pulsars mightindeed turn on as millisecond radio pulsars.However, there was still a missing test that needed tobe performed before the recycling scenario could be ac-cepted as the correct theory of accreting neutron stars:the accreting pulsar is spun up, so it must be possible toobserve accretion torques in the process of acceleratingthe neutron star rotation and spin down during quies-cence due to magneto dipole torques. Many claims havebeen made for a detection of an accretion torque in ac-creting millisecond pulsars, but none of these has beenbroadly accepted until now because of the presence oftiming noise that affects the determination of spin andaccretion torques when using a standard coherent timinganalysis.The results presented here show that accretion torquesare present in IGR J00291, and the spin evolution over4 years is entirely consistent with the prediction of the recycling scenario . The gas is channeled along the weakmagnetic field lines very close to the neutron star sur-face, at a distance of less than 24 km from the neutronstar center. Furthermore, a slow spin down is detected when the accretion halts (or is strongly reduced), whichI ascribe to magnetic dipole spin down as observed inradio pulsars. This allows the measurement of the mag-netic field of the neutron star, which I determine to be1 . × G < ∼ B < ∼ × ± . . × G. This value is consis-tent with that inferred from the accretion torques duringthe 2004 outburst. Given the large uncertainties in theanalysis discussed in Section 5, it is still premature tostate that the results reported in this paper finally con-firm the recycling scenario. However, it has been shownhere that there is no need for new physics to explainthe results reported. For example, there is no evidencefor a spin down mechanism other than magneto dipoletorques.There is instead strong evidence for an ordered pro-cess that is always present in all observed outbursts thatmight be ascribed to a motion of the hot spot on theneutron star surface. Finally, I find evidence for IGRJ00291 being very close to the spin equilibrium, with thepulsar spin evolving on timescales of ∼ REFERENCESAlpar, M. A., Cheng, A. F., Ruderman, M. A., & Shaham, J. 1982,Nature, 300, 728Archibald, A. M., et al. 2009, Science, 324, 1411Cognard, I., & Backer, D. C. 2004, ApJ, 612, L125Bachetti, M., Romanova, M. 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