a r X i v :a s t r o -p h /0506419v 1 17 J u n 2005To appear in ApJLPreprint typeset using L A T E X style emulateapj v.6/22/04A COHERENT TIMING SOLUTION FOR THE NEARBY ISOLATED NEUTRON STAR RX J0720.4−3125D.L.Kaplan 1,2and M.H.van Kerkwijk 3To appear in ApJLABSTRACTWe present the results of a dedicated effort to measure the spin-down rate of the nearby isolated neutron star RX J0720.4−paring arrival times of the 8.39-sec pulsations for data from Chandra we derive an unambiguous timing solution for RX J0720.4−3125that is accurate to <0.1cycles over >5years.Adding data from XMM and ROSAT ,the final solution yields ˙P=(6.98±0.02)×10−14s s −1;for dipole spin-down,this implies a characteristic age of 2Myr and a magnetic field strength of 2.4×1013G.The phase residuals are somewhat larger than those for purely regular spin-down,but do not show conclusive evidence for higher-order terms or a glitch.From our timing solution as well as recent X-ray spectroscopy,we concur with recent suggestions that RX J0720.4−3125is most likely an off-beam radio pulsar with a moderately high magnetic field.Subject headings:pulsars:individual (RX J0720.4−3125)—stars:neutron —X-rays:stars1.INTRODUCTIONOne of the interesting results from ROSAT All-Sky Survey (Voges et al.1996)was the discovery of seven ob-jects that appear to be nearby,thermally-emitting neu-tron stars that have little if any magnetospheric emis-sion (see Haberl 2004for a review).These objects,known most commonly as “isolated neutron stars,”are distinguished by their long periods ( 3s,when mea-sured),largely thermal spectra with cool temperatures (kT 100eV),faint optical counterparts (when de-tected),and lack of radio emission.It is not yet clear what sets the isolated neutron stars apart from the nearby,relatively young rotation-powered pulsars that also have cool thermal emission —sources like PSR B0656+14and PSR B1055−52—which tend to have short (<1s)spin periods,∼1012-G magnetic fields,non-thermal (i.e.power-law)components in their X-ray spectra,and radio pulsations (e.g.,Pavlov &Zavlin 2003;Kaplan 2004).The isolated neutron stars are known to have longer periods,but their spin-down rates (and hence magnetic fields )are unknown,largely be-cause it has not yet been possible to determine a reliable,coherent timing solution (Kaplan et al.2002,hereafter Paper I;Zane et al.2002).In this Letter we report a new analysis of the varia-tions of the 8.39-s period of the second brightest source of the group,RX J0720.4−3125(Haberl et al.1997).We describe our analysis of Chandra data obtained specifically for timing purposes,as well as archival ROSAT ,Chandra ,and XMM data,in §2.In §3,we show that with the new data,we can avoid the pitfalls of the previous phase-coherent timing analyses and obtain a reliable timing solution.We discuss possible timing noise in §4and the implications of our result in §5.1Pappalardo Fellow2Center for Space Research,Massachusetts Institute of Technol-ogy,77Massachusetts Avenue,37-664D,Cambridge,MA 02139,USA;dlk@3Department of Astronomy and Astrophysics,University of Toronto,60St.George Street,Toronto,ON M5S 3H8,Canada;mhvk@astro.utoronto.ca2.OBSERVATIONSOur primary data were eight observations with the Advanced CCD Imaging Spectrometer (ACIS;Garmire et al.2003)aboard the Chandra X-ray Observa-tory (CXO ;Weisskopf et al.2000).These were designed for timing accuracy,consisting of two sets of four expo-sures geometrically spaced over a period of about two weeks and separated by about half a year.We combined these with data from other Chandra observations,as well as from observations with XMM-Newton (Jansen et al.2001)and ROSAT (Tr¨u mper 1993).A log of all obser-vations is given in Table 1.For the Chandra data,we processed the level-1event lists to the level-2stage following standard procedures and the latest calibration set (CALDB version 3.0.0).For the ACIS continuous-clocking data,this includes correcting the recorded event times for readout,dither,and spacecraft motion —corrections that used to re-quire additional steps (Zavlin et al.2000).We ex-tracted events within 1′′of the source,and then ap-plied a clock correction of 284.7µs to the arrival times (Davis,Holmes,&Myers 2003);the arrival times should now be accurate to 6µs.For the HRC-S/LETG data,we extracted zeroth-order events from a circle with ra-dius 10pixels (1.′′3),and first-order events using the stan-dard LETG spectral extraction windows,but limited to 10≤λ≤65˚A .Finally,we used the axbary program to barycenter all of the events (using the optical po-sition:αJ2000=07h 20m 24.s 96,δJ2000=−31◦25′50.′′2;Kaplan et al.2003)For the XMM data,we used the standard procedures emchain and epchain (XMMSAS version 6.1.0)to repro-cess the observations.One additional step was necessary for the PN data set 622-U2,for which we found a small number of duplicate events (frames 963685–963719);we removed these before processing.Next,we extracted all single-pixel events within 37.′′5of the source position,and used barycen to convert the arrival times to the solar-system barycenter 4.4Some portions of the 2000and 2002XMM /PN ob-servations were affected by a known processing problem2Kaplan&van KerkwijkTABLE1Log of Observations and Times of ArrivalInstrument a ID b Date Exp.Counts TOA c(ks)(MJD)PSPC......3381993-09-27 3.2580049257.2547031(25)HRI........8841996-11-0333.71266250391.3006530(16)HRI........9441998-04-208.1307450925.6881172(36)HRC........3682000-02-01 5.4347251575.3026910(46)HRC........7452000-02-0226.11514951576.2804856(27)HRC........3692000-02-04 6.1366751578.7722735(65)PN/ff/thin..78-S32000-05-1321.114410451677.2260789(5)MOS2/thin.78-S22000-05-1343.97391551677.4127431(7)PN/ff/med.175-S32000-11-2125.715303751869.8413358(14)MOS1/open175-U22000-11-21 6.81776251869.8433759(14)MOS2/open175-U22000-11-217.22108451869.9571032(6)ACIS-CC...27742001-12-0415.0318*******.7881789(11)ACIS-CC...27732001-12-0510.62284752248.2835843(13)ACIS-CC...27722001-12-06 4.1879052249.6286894(26)PN/ff/thin..533-S32002-11-0628.319984152584.9260561(5)PN/ff/thin..534-S32002-11-0830.221217752587.0013053(4)MOS1/open622-U22003-05-027.61762952761.6222174(14)MOS2/open622-U22003-05-027.51878852761.6226056(12)PN/sw/thick622-U22003-05-0272.821016052761.9950589(5)PN/sw/thin711-S72003-10-2718.111287652939.8228751(9)PN/sw/thick711-S82003-10-2725.013868952939.8228774(8)MOS1/open711-U22003-10-2713.83332352939.8506513(5)MOS2/open711-U22003-10-2713.83563652940.1162720(5)ACIS-CC...46662004-01-0610.11904853010.2635608(14)ACIS-CC...46672004-01-07 4.8893853011.2639869(20)ACIS-CC...46682004-01-11 5.2933453015.5407400(19)ACIS-CC...46692004-01-19 5.2939153023.1274147(23)HRC........53052004-02-2735.72159753062.4142490(27)PN/ff/thin..815-S12004-05-2231.621985553147.6811948(4)ACIS-CC...46702004-08-0310.11743253220.9975987(14)ACIS-CC...46712004-08-05 5.1805153222.2171299(21)ACIS-CC...46722004-08-09 5.1855653226.2443808(25)ACIS-CC...46732004-08-23 5.1713353240.1824669(24)HRC........55812005-01-2367.74480153393.6657119(18)a PSPC:Position Sensitive Proportional Counter(Briel&Pfeffermann1995)aboard ROSAT.HRI:High-Resolution Imager(Zombeck et al.1995)aboardROSAT.HRC:High-Resolution Camera for spectroscopy aboard Chandra(HRC-S;Kraft et al.1997),used with the Low-Energy Transmission Grat-ing.ACIS:Chandra’s Advanced CCD Imaging Spectrometer(Garmire et al.2003),used in continuous clocking mode.EPIC-pn:XMM’s European Pho-ton Imaging Camera with PN detectors(Str¨u der et al.2001),used in full-frame(ff)or small window(sw)mode,with thin,medium,or thickfilter.EPIC-MOS1/2:European Photon Imaging Cameras with MOS detectorsaboard XMM(Turner et al.2001),used in small-window mode with thin orno(open)filter.b Observation identifier(CXO,ROSAT)or revolution number and exposureidentifier(XMM).c The TOA is defined as the time of maximum light closest to the middle ofeach observation,and is given with1-σuncertainties.The reduction of the ROSAT data followed that inPaper I,except that we properly corrected the eventtimes to the Barycentric Dynamical Time(TDB)sys-tem instead of the Coordinated Universal Time(UTC)system returned by the FTOOLS barycentering tasks(seeCropper et al.2004).We used the corrections suppliedin Cox(2000,p.14).that rejected significant portions of the observations;seehttp://xmm.vilspa.esa.es/sas/documentation/watchout/lost_events.shtml. This should not introduce any systematic error,though it meansthat our TOAs for these observations are not as precise as possiblewith all events.However,since the present TOA uncertaintiesare smaller than the timing noise(§4),we decided not to try toremedy this problem.3.TIMING ANALYSISOur goal was to use times-of-arrival(TOAs)to infer a phase-coherent timing solution involving the spin period and its derivative,where each cycle of the source was counted.To measure TOAs we needed an initial refer-ence period,something which we determined using a Z21 test(Rayleigh statistic;Buccheri et al.1983)on the com-bined2004January ACIS and2004February HRC data. Wefind P=8.3911159(10)s(here and below,numbers in parentheses indicate twice the formal1-σuncertain-ties in the last digit unless otherwise indicated),which is consistent with our earlier value(Paper I)but much more accurate because we could coherently connect ob-servations over a much longer(52day)time span. Using this period,we constructed binned light curvesA Timing Solution for RX J0720.4−31253Fig. 1.—Phase residuals for RX J0720.4−3125.The top panelshows the residuals for each TOA compared to a linear(˙ν=0)model.The solid curve gives the best-fit quadratic(˙ν=0,¨ν=0)ephemeris for all data(Tab.2,with a0.27-s systematic uncertaintyadded in quadrature).The vertical dashed line indicates the ref-erence time t0.The bottom panel shows the residuals relative tothe quadratic model.We also show a best-fit cubic model(¨ν=0;dotted line)and a model that includes a glitch in frequency nearMJD52800(∆f≈1×10−9;dashed curve).(with16phase bins)and determined the TOAs byfittinga sinusoid(appropriate for the sinusoidal pulsations ofRX J0720.4−3125;Haberl et al.1997);the uncertaintieswere calculated from the uncertainties in the phases ofthefitted sinusoids(we verified that we obtain consistentresults if we change the binning or measure TOAs usingcross-correlation instead).Here,the TOA is defined asthe time of maximum light closest to the middle of theobservation,a choice which minimizes co-variance withsmall changes in period.We present TOAs for all of thedata in Table1.We then determined a timing solution for only theChandra data using an iterative procedure.Wefirst usedthe reference period to determine cycle counts for thefiveabove-mentioned observations,as well as the next obser-vation closest in time.Wefit these cycle counts toφ(t)=φ0+ν(t−t0)+16¨ν(t−t0)3...,(1)whereφ0is the cycle count plus phase at reference time t0,νis the spin-frequency,˙νis its derivative,¨νis the second derivative.We then iterated,using the improved solution to determine the cycle count for the next ob-servation,etc.We started with˙ν=¨ν=0,but left˙νfree once that significantly improved thefit;¨νwas not required(cf.,§4below).Thefinal ephemeris listed in Table2has small,≤0.1cycle,residuals,andfits the Chandra data well:χ2ν≡χ2/N dof=1.06(with N dof=13degrees of free-dom).To test the uniqueness of our ephemeris,we tried changing the cycle counts(adding or subtracting one or more cycles)at the least unambiguous points,but found that the resulting solutions were very poor(e.g.,alter-ing the cycles between the2001ACIS and2000HRC observations gaveχ2ν=89.26).To improve and extend the ephemeris,we added the XMM and ROSAT data into the solution(see Table2). As for the Chandra data alone,the cycle counts are unambiguous and,as can be seen in Fig.1,the resid-TABLE2X-ray Timing Ephemerides for RX J0720.4−3125 Quantity a CXO only All data b Dates(MJD)51575–5339449257–53394t0(MJD)....53010.2635605(18)53010.2635637(24)ν(Hz)......0.11917366926(46)0.11917366908(38)˙ν(Hz s−1)..−9.97(11)×10−16−9.918(30)×10−16 TOA rms(s)0.180.31χ2/DOF....13.8/13=1.0630.7/31=0.99P(s)........8.391115305(32)8.391115532(26)˙P(s s−1)....7.019(80)×10−146.983(22)×10−14˙E(erg s−1)..4.7×10304.7×1030B dip(G)....2.5×10132.4×1013τchar(yr)....1.9×1061.9×106Note.—Uncertainties quoted are twice the formal1-σuncertainties in thefit.a˙E=1045I454π2ν˙νis the spin-down luminosity(with I=1045I45g cm2the moment of inertia);B dip=3.2×10194Kaplan&van Kerkwijkbyfitting the phase residuals with a third-order(¨ν=0) solution like that shown in Fig.1.This does in fact im-prove thefit—givingχ2ν=6.02for N dof=30with an rms of0.32s—though it is still formally unacceptable. Wefind¨ν≈2.4(4)×10−25Hz s−2(this also changes ˙νby3%from the value in Tab.2),giving a timing noise measurement of∆8≡log10(|¨ν|(108)3/6ν)=−0.5. This value is on the high side of,but not outside the range expected from relations between˙P and∆8found for radio pulsars(Arzoumanian et al.1994)and mag-netars(Woods et al.2000;Gavriil&Kaspi2002).We do not believe it is likely that the third-order solution represents a real long-term change in˙ν,since the value of¨νchanges significantly if one uses just the Chan-dra,Chandra+XMM,or all of the data5[8(6),18(4), or2.4(4)×10−25Hz s−2,withχ2ν=0.64,2.81,or6.02 respectively].A second possibility is a sudden change in rota-tion—a glitch,as proposed(and largely rejected)by de Vries et al.(2004)to account for variations in spec-tral shape(differences of10%in the inferred temper-ature)and pulse shape(changes of50–100%in pulsed fraction)observed between2000and2003.The system-atic increase in the residuals after MJD53000in Fig-ure1might indeed indicate a glitch.We triedfitting a simple glitch model,in which we assumed that only the frequency changed,that the recovery time was longer than the span of our observations,and that the glitch occurred on2003July1(MJD52821),in between the two XMM observations that showed the largest spec-tral change(de Vries et al.2004).Wefind a reasonable fit for a glitch with∆f=1.3×10−9Hz and a recov-ery time>3yr,givingχ2ν=7.7(see Fig.1).This would be a small glitch,with∆f/f=1.1×10−8com-pared to values of10−9to10−6for radio pulsars(with smaller values more typical for larger magneticfields; Lyne,Shemar,&Smith2000).It also implies that ener-getically,the putative glitch would be insignificant:the change in kinetic energy of∼1036ergs(van Riper et al. 1991)would only be noticeable if dissipated in<1day given the bolometric luminosity of RX J0720.4−3125of 2×1032d2300ergs s−1(where d=300d300pc is the dis-tance to RX J0720.4−3125;Kaplan et al.2003).In prin-ciple,however,it could still have altered the light curve and spectrum of RX J0720.4−3125through realignment of the magneticfield relative to the spin axis. Finally,a more mundane explanation for the rela-tively poorfit is that the data are from different instru-ments with different energy responses(even among a sin-gle instrument aboard XMM,the changingfilters alter the response).The pulse profile of RX J0720.4−3125 is known to depend on energy(Cropper et al.2001; Paper I;Haberl et al.2004)and to change over time (de Vries et al.2004).While the changes to the shape are small,some systematic offsets are expected between the pulse profiles as measured by different instruments or at different times.We hope to investigate this in more detail in the near future.At present,we cannot distinguish between the various5From Fig.1,it may appear that one could obtain a betterfit by reducing the cycle count for the1998HRI point by one;however, doing that,the other ROSAT points cannot be reproduced any more.possibilities for the relatively poorfits.The predicted future behavior is different,however,and thus further observations of RX J0720.4−3125(some of which are in progress)should be able to distinguish between these models.5.DISCUSSION&CONCLUSIONSFrom our timing solution,we infer a spin-down rate ˙P=6.98(2)×10−14s s−1.This is consistent with the limits derived in Paper I and by Zane et al.(2002),but inconsistent with the tentative solution of Cropper et al. (2004),who found˙P=(1.4±0.6)×10−13s s−1at99% confidence(but who noted that elements of their solution were inconsistent with each other and that their analy-sis was subject to confusing aliases).In Table2,we list derived parameters—rotational energy loss rate,mag-neticfield,and characteristic age(the latter two under the assumption of magnetic dipole spin-down).The values of P and˙P place RX J0720.4−3125well above above most of the radio-pulsar“death-lines”pro-posed so far(e.g.,Young,Manchester,&Johnston1999) and in a region populated by radio pulsars in P-˙P diagrams like that in Paper I(its parameters are ap-proximately between those of PSR J1830−1135,with P=6.2s,˙P=5×10−14s s−1,and PSR J1847−0130, with P=6.7s,˙P=1.3×10−12s s−1).Hence, RX J0720.4−3125may well be a radio pulsar itself,but one whose radio beam(s)do not intersect our line of sight. Its inferred magneticfield,B=2.4×1013G,is not excep-tional;the Parkes Multi-beam Survey(Manchester et al. 2001)in particular has discovered a fair number of ra-dio pulsars with B 1013G(e.g.,Camilo et al.2000; Morris et al.2002;McLaughlin et al.2003),and it is now clear the distribution of magneticfields isflatter than previously assumed(Vranesevic et al.2004).With˙E=4.7×1030ergs s−1,RX J0720.4−3125is not expected to have much non-thermal X-ray emis-sion:from the relation of Becker&Tr¨u mper(1997), one estimates L X,non−th∼10−3˙E≃5×1027ergs s−1, much smaller than the thermal emission,L X,therm≃2×1032d300ergs s−1.This is consistent with lim-its from Chandra and XMM(Paerels et al.2001; Pavlov,Zavlin,&Sanwal2002;Kaplan et al.2003). What is somewhat puzzling is the inferred age of2Myr. Tracing RX J0720.4−3125back to OB associations where it might have been born put it close to the Trumpler10 association∼0.7Myr ago(Motch,Zavlin,&Haberl 2003;Kaplan2004).Similarly,based on its estimated temperature and luminosity,most standard cooling mod-els(modified URCA for1.4M⊙neutron stars)put RX J0720.4−3125at 1Myr(Heyl&Hernquist1998; Paper I;Cropper et al.2004).It is of course possible that RX J0720.4−3125was born with a long period and/or had significantly non-dipole braking,such that the spin-down age is not a good es-timate of its true age.However,no case with as long a birth period as would be required for RX J0720.4−3125 is known among radio pulsars(cf.Kramer et al.2003; Gavriil et al.2004).Another possible explanation is that RX J0720.4−3125 was ejected from a binary system with a massive com-panion∼0.7Myr ago,either when the companion un-derwent a supernova or during a binary exchange inter-A Timing Solution for RX J0720.4−31255action.In this case,a relatively long period is expected: if the neutron star accreted matter from its compan-ion,its spin period would have tended toward the equi-librium period,P eq≈5s(B/1013G)6/7(˙M/˙M Edd)−3/7 (where˙M is the accretion rate and˙M Edd is the Edding-ton rate).A relatively short cooling age would also be consistent with this model:the accretion and accompa-nying steady hydrogen burning could reheat the neutron star(or keep it hot).Of course,it remains to be seen that a suitable evolutionary scenario can be found.In any case,the prediction for the model with two supernovae is that there may well be another 1Myr old neutron star whose proper motion traces back to the same origin as RX J0720.4−3125(cf.Vlemmings et al.2004). Finally,we can compare the magneticfield strength of 2.4×1013G with what is inferred from the broad absorp-tion feature in the spectrum(observed to be at0.3keV, which corresponds to0.39keV at the surface for a grav-itational redshift of0.3;Haberl et al.2004;Vink et al. 2004).If due to a proton cyclotron line,one infers B≃6×1013G(Haberl et al.2004),which is substan-tially larger than inferred from the spin-down.This may simply reflect the inadequacy of the dipole spin-down model,or the presence of higher order multipoles.On the other hand,based on a comparison with other sources, van Kerkwijk et al.(2004)suggested that the absorption feature was due to the transition from the ground state to the second excited tightly bound state of neutral hydro-gen,which would require B≃2×1013G and matches the spin-down value nicely.If that is the case,higher signal-to-noise spectra should reveal the transition to thefirst excited state at∼0.15keV.We thank an anonymous referee for useful comments, and Kaya Mori,George Pavlov,Saul Rappaport,Deepto Chakrabarty,and Peter Woods for helpful discussions. 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