A Coherent Timing Solution for the Nearby, Thermally Emitting Isolated Neutron Star RX J0420.0-5022
aa r X i v : . [ a s t r o - ph . H E ] S e p ApJL, in press
Preprint typeset using L A TEX style emulateapj v. 5/2/11
A COHERENT TIMING SOLUTION FOR THE NEARBY, THERMALLY EMITTING ISOLATED NEUTRONSTAR RX J0420.0 − D. L. Kaplan and M. H. van Kerkwijk ApJL, in press
ABSTRACTWe present a phase-coherent timing solution for RX J0420.0 − kT ≃
45 eV) andfastest-spinning ( P = 3 .
45 s) of the seven so-called isolated neutron stars (INSs). Using 14 observationswith the
XMM-Newton spacecraft in 2010–2011, we were able to measure a spin-down rate ˙ ν =( − . ± . × − Hz s − ( ˙ P = (2 . ± . × − s s − ), from which we infer a dipolar magneticfield of 1 . × G. With reasonable confidence we were able to extend the timing solution backto archival
XMM-Newton from 2002 and 2003, giving the same solution but with considerably moreprecision. This gives RX J0420.0 − Subject headings: stars: individual (RX J0420.0 − INTRODUCTION
The so-called isolated neutron stars (INSs; see Haberl2007 and Kaplan 2008 for reviews) are a group ofseven nearby ( . ∼ erg s − ) X-ray luminosities and long (3–10 s) spin pe-riods (Kaplan & van Kerkwijk 2009b). They are uniquein that the X-ray emission likely comes from a largefraction of the neutron stars’ surfaces, and is not in-fluenced by accretion (as in the case of X-ray binaries)or non-thermal magnetospheric emission (as in the caseof rotation-powered pulsars); the INSs are also radio-quiet (e.g., Kondratiev et al. 2009). The INSs then havethe potential to help understand neutron star radii andcooling via measurements of their emission areas andluminosities, but this is made difficult by our inabilityto realistically model the X-ray, ultra-violet, and op-tical emission from these objects (e.g., Ho et al. 2007;Kaplan et al. 2011).Recently it was proposed (Kaplan & van Kerkwijk2009b; Pons, Miralles, & Geppert 2009; Popov et al.2010) that the current temperatures and magnetic fieldsof the INSs reflect non-thermal, coupled evolution, wherethe magnetic field has decayed in strength, heating theneutron-star surface. Testing this hypothesis is an impor-tant step to using the INSs to constrain the overall cool-ing history of neutron stars, and through it probe theirinner structure and composition (Yakovlev & Pethick2004). To constrain evolutionary models, measure-ments of the current magnetic fields and temperaturesof the INSs are required. Similarly, to understand Physics Dept., U. of Wisconsin - Milwaukee, Milwaukee WI53211, USA; [email protected] Department of Astronomy and Astrophysics, University ofToronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada;[email protected] the broad absorption features seen at energies of 0.2–0.75 keV in the spectra of almost all INSs (Haberl 2007;van Kerkwijk & Kaplan 2007), also requires knowledgeof the magnetic fields, as at these field strengths the as-sumed transition energies are field-dependent. There-fore, we have undertaken systematic measurements ofthe dipole magnetic fields for the INSs through phase-coherent X-ray timing using the
Chandra and
XMM-Newton spacecraft (Kaplan & van Kerkwijk 2005a,b;van Kerkwijk & Kaplan 2008; Kaplan & van Kerkwijk2009a,b, hereafter KvK05a; KvK05b; vKK08; KvK09;KvK09b).Here we measure the spin-down of the INSRX J0420.0 − ROSAT observations showed a verysoft thermal spectrum and yielded an improved posi-tion, both of which led to its classification as a neutronstar. While initially a 22.7-s period was suggested, ob-servations with
XMM found a period of 3.45 s instead,the shortest among all INSs (Haberl et al. 2004, here-after H+04); the same observations also showed thatRX J0420 was the coolest INS, with kT ≃
45 eV. OBSERVATIONS & ANALYSIS
We observed RX J0420 fourteen times with
XMM (Jansen et al. 2001) in 2010 and 2011, and focus hereon the data taken with the European Photon ImagingCamera (EPIC) with pn and MOS detectors, all used insmall window mode with thin filters (Table 1). We re-processed our observations with SAS version 11.0.0 andcalibration files current as of 2011 May 25. We also re-processed the pn data from H+04, which are taken with Kaplan & van Kerkwijk
TABLE 1Log of Observations and Times of Arrival
Exp. a f bga TOA b Rev. Date (ks) Counts a (%) (MJD TDB)560 2002 Dec 30 20,047 4,201 10.0 52638.2855519(12)561 2002 Dec 31 20,048 4,593 11.7 52640.0466236(12)570 2003 Jan 19 20,547 4,647 11.6 52658.8319656(8)664 2003 Jul 25 20,036 4,384 11.8 52846.0226435(10)1887 2010 Mar 30 7,472 2,062 41.2 55285.5413317(17)1890 2010 Apr 04 9,072 2,679 45.8 55290.8432112(23)1892 2010 Apr 09 7,772 2,049 35.4 55295.4037368(11)1913 2010 May 21 5,471 1,462 32.1 55337.2761247(20)1948 2010 Jul 29 6,472 1,626 37.2 55406.6382597(30)1975 2010 Sep 21 9,872 2,372 38.2 55460.4233059(20)1981 2010 Oct 02 11,672 2,980 34.8 55472.0349984(22)1981 2010 Oct 03 12,972 3,064 38.6 55472.8839787(11)1981 2010 Oct 04 16,871 4,465 40.2 55473.3194015(13)1983 2010 Oct 06 10,471 2,586 36.9 55476.0218532(19)2008 2010 Nov 26 5,471 1,339 35.2 55526.4316848(19)2032 2011 Jan 13 15,471 4,223 44.5 55575.0260821(17)2071 2011 Mar 31 7,018 1,577 38.2 55651.9068660(24)2076 2011 Apr 11 5,471 1,248 32.2 55662.3338203(19) Note . — All observations used the small window mode and thinfilter for both EPIC-pn and EPIC-MOS1/2, except for Revs. 560,561, 570, 664, in which the full window mode was used (whichmeant that only the EPIC-pn data were suitable for timing). a The exposure time, number of counts, and estimated fraction ofevents due to background f bg given here are for EPIC-pn only. b The TOA is defined as the time of maximum light of the fun-damental closest to the middle of each observation computed fromthe combined EPIC-pn and EPIC-MOS1/2 datasets, and is givenwith 1- σ uncertainties. the same filter, but with the full window mode instead(we did not use their full-frame MOS data, since thesedo not resolve the pulsations). We used epchain and emchain and selected source events from a circular re-gion of 37 . ′′ Chandra X-ray Observatory posi-tion from H+04: α = 04 h m . s
95 and δ = − ◦ ′ . ′′ RAWY coordinate, as recommended by theSAS User Guide. For MOS1/2, the small-window modedoes not permit such large background areas, but weused several smaller areas to compensate.
Timing Analysis
Our timing analysis largely follows the procedure de-scribed in KvK05a. As a starting place, we first de-termined the frequency that maximized the power ina Z periodogram for the EPIC-pn data from the See http://xmm.esac.esa.int/external/xmm_user_support/documentation/sas_usg/USG/node64.html . −50 0 φ − φ li n ( c y c . ) φ − φ q u a d ( c y c . ) MJD-50,000 (days) C oun t R a t e ( k s − ) Fig. 1.—
Phase residuals for RX J0420. In the top panel, we showthe residuals relative to a linear model ( ˙ ν = 0). The line showsthe best-fit quadratic solution. Residuals relative to the quadraticsolution are shown in the bottom panel. Inset: pulse profile forRX J0420, based on a combination of all of the 2010–2011 datafolded according to the ephemeris in Tables 2 and corrected for thebackground. The blue curve is the best-fit sinusoidal profile. longest observation in Rev. 1981. We then expandedthe periodogram to include data from all observationsin Revs. 1981 and 1983, finding a best-fit frequency of ν = 0 . ± . Z power is 33.8, while Z = 34 . Z = 35 .
2, both of which are consistent with the ad-ditional power of 1 expected for noise. We also checkedto see if the true period was in fact 6.9 s (closer to thatof the other INSs), but the pulse shape, hardness ratio,and median energy were all consistent with no variationbetween the first and second halves of the pulse (with 16bins the lightcurve variation between the first and sec-ond halves has χ = 10 . /
8, while the hardness ratiovariation has χ = 4 . / ± . ± . χ for the fit to the composite profilewas good, 14.4 for 13 dof.Using our TOAs, we were able to identify a reasonablyunambiguous coherent timing solution. This was possibleas we restricted solutions to have | ˙ ν | < × − Hz s − or B dip < × G (based on the incoherent limitsset by Haberl 2007). Among those, the solution pre-sented in Table 2 was the best, yielding χ = 19 . χ = 25 . B dip = 1 . × G), χ = 37 . B dip = 7 × G),and χ = 38 . ν > ± − TABLE 2Measured and Derived Timing Parameters forRX J0420.0 − Quantity Value2010–2011 2002–2011Dates (MJD) . . 55,286–55,662 52,638–55,662 t (MJD) . . . . . . . 55,430.6001387(6) 55430.6001387(6) ν (Hz) . . . . . . . . . 0.2896029061(12) 0.2896029058(10)˙ ν (10 − Hz s − ) − . − . χ /DOF . . . . . . . 19.9/11 24.8/15 P (s) . . . . . . . . . . . 3.453004024(14) 3.453004027(12)˙ P (10 − s s − ) . 2.8(3) 2.759(10) τ char (Myr) . . . . . 2.0 2.0 B dip (10 G) . . 1.0 1.0˙ E (10 erg s − ) 2.7 2.7 Note . — Quantities in parentheses are the formal 1- σ uncer-tainties on the last digit. τ char = P/ P is the characteristic age,assuming an initial spin period P ≪ P and a constant magneticfield; B dip = 3 . × p P ˙ P G is the magnetic field inferred as-suming spin-down by dipole radiation; ˙ E = 3 . × ν ˙ ν erg s − isthe spin-down luminosity. densely sampled Rev. 1981–1983 group and the next clos-est observation, Rev. 1975, and is close to the limit fromHaberl (2007); we will return to this alias shortly. Wewere able to identify the same solution using a single co-herent Z ( ν, ˙ ν ) periodogram (as in vKK08). Spin-downis well-detected, at ∼ σ . The reduced χ is somewhathigh, but even adjusting our uncertainties to allow foran reduced χ of 1 will still give an 8 σ detection of spin-down. The implied magnetic field is well within the rangeof other detections for the INSs (KvK09b).We can confirm and improve our solution by extrapo-lating it back to the older data from 2002–2003. Thetime difference is roughly 2600 days and our ˙ ν uncer-tainty gives a formal cycle-count uncertainty of ± χ = 24 . χ . However, the alter-nate solutions either have nearly the same implied spin-down rate but differ slightly in the cycle counts betweenthe 2002–2003 and 2010–2011 observations (and the low-est of those has χ = 33 . χ ( χ = 45 . ν > B dip = 1 . × G solution from abovedoes not extrapolate well to the older data, allowing us toexclude it. Overall, the older data thus allow us to con-fidently select the correct solution to the new data, andselect a reasonably secure overall solution (∆ χ = 8 . Spectroscopic Analysis
We examined all EPIC-pn spectra of RX J0420. (Afull spectral analysis, including the EPIC-MOS and RGSdata and a phase-resolved analysis, is in progress.) Weused the same source and background extraction regionsas for the timing analysis, created appropriate response −2 −1 C oun t s ( s − k e V − ) R e s i d . −0.200.2 B G Fig. 2.—
Blackbody fits to the merged EPIC-pn data ofRX J0420, from 2002–2003 (blue circles) and 2010–2011 (redsquares). The model is the thick black line. The middle panelshows the backgrounds used, and highlights the background struc-ture seen at low energies in the 2010–2011 data. The bottom panelshows the residuals. files, and binned the spectral files such that the numberof source plus background counts was at least 25 and thebin width was at least 30 eV (so that there are roughly2 bins per EPIC-pn resolution element).We first compared the raw EPIC-pn spectra of all ofthe observations against each other. This did not includeany response files or calibration corrections, but even sothe binned pn spectra were generally consistent with eachother, implying no spectral change (Fig. 2). There aresmall deviations at low energies (0.2–0.4 keV) and we willreturn to these below, but the 2010-2011 data did notshow any appreciable variability.We fit the pn data using sherpa (Refsdal et al. 2009).To aid in fitting we merged the event and response filesinto two groups: one for 2002-2003 (full-frame data, alsofit by H+04) and one for 2010-2011 (small-window data).While not perfect, we found that an absorbed blackbodyprovided a reasonable fit, with N H < × cm − , kT ∞ = 47 . ± . R ∞ = 12 . ± . − (formal 1- σ uncertainties; χ = 73 . ). Hence, it is difficult to interpret anyresidual structure there with respect to a blackbody. DISCUSSION & CONCLUSIONS
We have determined a reliable, statistically significantcoherent spin-down solution for RX J0420. With this, See . Kaplan & van Kerkwijkonly RX J1605.3+3249, which as yet has only a ten-tative detection of a periodicity, lacks a coherent solu-tion (although in the cases of RX J2143.0+0654 andRX J0806.4 − E , characteristic age) of RX J0420 place it wellwithin the INSs, RX J0420 has the shortest period bymore than a factor of 2. In the context of the magneto-thermal evolution model, this could be a consequenceof a lower initial magnetic field, and thus less dramaticearly spin-down. RX J0420 also has the lowest currentfield, although it is not clear whether there is a goodcorrelation between current magnetic field and period:RX J0806.4 − − − . × G), while appearing the younger one bykinematic age (Kaplan, van Kerkwijk, & Anderson 2007;Tetzlaff et al. 2010, 2011). It would be interesting tomeasure the kinematic age of RX J0420 to compare itwith the rest of the population.To view the evidence for field decay in a different way,we show in Figure 3 the blackbody temperature ver-sus characteristic age for pulsars and the INSs (see alsoZhu et al. 2011). It is quite clear that the INSs are sys-tematically a factor of 5–10 older in characteristic age forthe same temperature. If instead one uses the kinematicage, however, one sees that the difference is much smaller(for the two sources for which kinematic ages are avail-able). In the context of a picture in which the fields ofINSs decayed, the main difference with pulsars inducedby the initially much stronger field is thus that it leadsto rapid initial spin down and long present periods (andthus long characteristic ages); the current temperaturesare not as strongly affected. Indeed, in the models ofPons et al. (2009), the heat generated by field decay islost fairly rapidly.Third, given both the low temperature and low mag-netic field, RX J0420 largely follows the empiricaltemperature-magnetic field correlation from KvK09. Asdiscussed there, the origin of this relation (evolution-ary vs. surface physics) or even its overall integrity inthe face of new data are not clear. It does seem toform an upper limit to the possible magnetic field ofan INS, and even the rotating radio transient (RRAT)J1819 − E as well) seems to roughly agree (based B ( G )
50 100 150 200 250 Characteristic Age (yr) D o m i n a n t B l ac kbody T e m p e r a t u r e ( e V ) INSPulsar
Fig. 3.—
Blackbody temperature (measured at infinity) ver-sus characteristic age for the INSs (circles) and rotation-poweredpulsars (squares and upper limits); for all objects the color indi-cates the dipole magnetic field according to the scale at the right.The pulsars included here are both those that are visible in the
ROSAT
All-Sky Survey and those with dipole fields ≥ Gthat have X-ray measurements. See Zhu et al. (2011) for a sim-ilar plot, although there they emphasize the variation among radiopulsars as a function of magnetic field, while here we emphasizeprimarily the distinction between pulsars and INSs. The data aretaken from Kaplan & van Kerkwijk (2009b), with the addition ofPSR B1916+14 (Zhu et al. 2009), PSR J1734 − − −
19 (Zhu et al. 2011, inprep), PSR J0726 − − R BB > kT . The horizontal lines extending to the left ofRX J1856.5 − − on McLaughlin et al. 2007).Fourth, we did not confirm the tentative absorp-tion feature found by H+04, although problems withthe background subtraction meant we cannot refute itwith confidence either. If it is true that RX J0420has no broad X-ray absorption feature, it would joinRX J1856.5 − assuming it emits like a blackbody, it isdifficult to set confident limits). These are the two INSswith the lowest temperatures and the lowest magneticfields, suggesting some relation between the presence ofabsorption features (or their energy) and either tem-perature or field strength (although a direct correlationof energy with field strength seems excluded; KvK09).RX J0420 is also similar to RX J1856.5 − − − XMM-Newton , this researchhas made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO andSherpa., this researchhas made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO andSherpa.