An Eccentric Binary Millisecond Pulsar in the Galactic Plane
D. J. Champion, S. M. Ransom, P. Lazarus, F. Camilo, C. Bassa, V. M. Kaspi, D. J. Nice, P. C. C. Freire, I. H. Stairs, J. van Leeuwen, B. W. Stappers, J. M. Cordes, J. W. T. Hessels, D. R. Lorimer, Z. Arzoumanian, D. C. Backer, N. D. R. Bhat, S. Chatterjee, I. Cognard, J. S. Deneva, C.-A. Faucher-Giguere, B. M. Gaensler, J. L. Han, F. A. Jenet, L. Kasian, V. I. Kondratiev, M. Kramer, J. Lazio, M. A. McLaughlin, A. Venkataraman, W. Vlemmings
aa r X i v : . [ a s t r o - ph ] M a y An Eccentric Binary Millisecond Pulsar in the Galactic Plane
David J. Champion , ∗ , Scott M. Ransom , Patrick Lazarus , Fernando Camilo , Cees Bassa ,Victoria M. Kaspi , David J. Nice , Paulo C. C. Freire , Ingrid H. Stairs , Joeri van Leeuwen ,Ben W. Stappers , James M. Cordes , Jason W. T. Hessels , Duncan R. Lorimer ,Zaven Arzoumanian , Don C. Backer , N. D. Ramesh Bhat , Shami Chatterjee ,Isma¨el Cognard , Julia S. Deneva , Claude-Andr´e Faucher-Gigu`ere , Bryan M. Gaensler ,JinLin Han , Fredrick A. Jenet , Laura Kasian , Vlad I. Kondratiev , Michael Kramer ,Joseph Lazio , Maura A. McLaughlin , Arun Venkataraman & Wouter Vlemmings Dept. of Physics, McGill Univ., Montreal, QC H3A 2T8, Canada ATNF-CSIRO, PO Box 76, Epping NSW 1710, Australia NRAO, 520 Edgemont Rd., Charlottesville, VA 22903, USA Columbia Astrophysics Laboratory, Columbia Univ., 550 West 120th St., New York, NY 10027, USA Physics Dept., Bryn Mawr College, Bryn Mawr, PA 19010, USA NAIC, Arecibo Observatory, HC03 Box 53995, PR 00612, USA Dept. of Physics and Astronomy, Univ. of British Columbia, 6224 Agricultural Rd., Vancouver, BC V6T 1Z1, Canada Astronomy Dept., 441 Campbell Hall, Univ. of California at Berkeley, Berkeley, CA 94720, USA Jodrell Bank Observatory, Manchester Univ., Macclesfield, Cheshire SK11 9DL, UK Astronomy Dept., Cornell Univ., Ithaca, NY 14853, USA Astronomical Institute “Anton Pannekoek,” Univ. of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands Dept. of Physics, West Virginia Univ., Morgantown, WV 26506, USA CRESST and X-ray Astrophysics Laboratory, NASA-GSFC, Code 662, Greenbelt, MD 20771, USA Swinburne Univ. of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia School of Physics, The Univ. of Sydney, NSW 2006 Australia LPCE / CNRS, UMR 6115 3A, Av de la Recherche Scientifique, F-45071 Orleans Cedex 2, France Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS-10, Cambridge, MA 02138, USA National Astronomical Observatories, CAS, Jia-20 DaTun Rd., Chaoyang Dist., Beijing 100012, China Center for Gravitational Wave Astronomy, Univ. of Texas at Brownsville, TX 78520, USA Naval Research Laboratory, 4555 Overlook Ave. SW, Washington, DC 20375, USA Argelander-Institut f¨ur Astronomie, University of Bonn, Auf dem H¨ugel 71, 53121 Bonn, Germany ∗ To whom correspondence should be addressed; E-mail: [email protected] inary pulsar systems are superb probes of stellar and binary evolution andthe physics of extreme environments. In a survey with the Arecibo telescope,we have found PSR J1903 + e = 0 . ) 95-day orbit around a solar mass com-panion. Infrared observations identify a possible main-sequence companionstar. Conventional binary stellar evolution models predict neither large orbitaleccentricities nor main-sequence companions around millisecond pulsars. Al-ternative formation scenarios involve recycling a neutron star in a globularcluster then ejecting it into the Galactic disk or membership in a hierarchicaltriple system. A relativistic analysis of timing observations of the pulsar findsits mass to be 1.74 ± ⊙ , an unusually high value. The population of binary and millisecond pulsars in the disk of our Galaxy is thought tohave two main formation mechanisms ( ). Most pulsars with spin periods of tens of millisec-onds have neutron star (NS) companions in orbits of high eccentricity caused by the near dis-ruption of the system by a supernova explosion. In contrast, pulsars with spin periods less thanabout 10 ms (i.e. “millisecond pulsars” or MSPs) have white dwarf (WD) companions in orbitsmade highly circular (orbital eccentricities e < . ) by tidal effects during the recycling pro-cess. The combination of rapid spin rates and circular orbits is considered vital evidence thatMSPs achieve their short periods via accretion of mass and angular momentum from binarycompanion stars ( ). Here we report the discovery of an unprecedented MSP that requires adifferent formation mechanism and whose potentially large mass may play an important role inconstraining the equation of state of matter at supra-nuclear density ( ).2 iscovery and Follow-up Observations We are conducting a pulsar survey of the Galactic plane using the Arecibo L-band Feed Array(ALFA) receiver on the 305-m Arecibo radio telescope in Puerto Rico ( ). The large collectingarea of Arecibo, the rapid sampling rate (every 64 µ s), and the high spectral resolution (256channels over 100 MHz, which minimizes the dispersive smearing due to free electrons alongthe line of sight) provides sensitivity to MSPs over a much larger volume of the Galactic diskthan any previous pulsar survey.The 2.15-ms pulsar J1903 +
5, 6 ). It was detected as a highly significant signal with a largedispersion measure (DM) of 297 pc cm − in data taken in October 2005. Follow-up timingobservations using Arecibo, the Green Bank Telescope, and the Westerbork Synthesis RadioTelescope revealed the binary orbit of the pulsar to be highly eccentric (Fig. 1). The Keplerianorbital parameters give a minimum companion mass of 0.85 − ⊙ (for pulsar masses of1.3 − ⊙ ). Additional constraints come from the extensive timing of the pulsar, includinga general relativistic interpretation of the measurement of the advance of periastron, ˙ ω , and adetection of the Shapiro delay. As described in the supplementary online material, and in thecaption to Table 1, the best model fit to the pulse times of arrival indicates that the companionhas a mass of . M ⊙ and that the pulsar has a mass of . M ⊙ . It should be notedthat these masses are based on ∼ − ⊙ seen in most double neutron star (DNS) sys-tems ( ) it is comparable to the inferred masses of several recently detected pulsars in eccentricbinaries in globular clusters (
7, 8, 9 ), at least one other Galactic MSP ( ), and the X-ray pulsarVela X-1 ( ). If the large pulsar mass is confirmed in future observations, it will constrain the3quation of state of matter at supra-nuclear density and potentially rule-out certain ‘soft’ equa-tions of state ( ). The companion mass is compatible with those of a NS, WD, or main-sequence(MS) companion. Although the spin parameters of PSR J1903 + ∼ µ Jy for a period of2 ms and ∼ µ Jy for a period of 200 ms assuming a pulse duty cycle of 30% of the pulse period.To search for a MS companion, we obtained images of the pulsar field with the Gemini Northtelescope on July 24, 2007. The total exposure times were 10 min in the infrared J, H and K S bands (1.27, 1.67 and 2.22 µ m, respectively). After calibrating the astrometry and photometryof the images against the 2MASS catalog, we find a single star within the 0.13 ′′ σ frame-tieerror circle at the position of the pulsar (Fig. 3). It has J = 19 . , H = 18 . and K S = 18 . magnitudes. Given the density of stars in this field, we estimate the probabilityof finding a star in the error circle by chance is 2.6%. Using MS star models ( ) and estimatingthe reddening with red clump stars ( ) at the ∼ ), we find that a 0.9 M ⊙ star of age 10 Gyr would have similar magnitudes to those observed.The uncertainties in the distance and reddening measurements also allow for a 1.05 M ⊙ star ofage 1–5 Gyr making it possible that this (likely) MS star is a companion to PSR J1903 + < − . If4he companion of PSR J1903 + ∼ ⊙ main-sequence star with Solar-like winds,we would expect an additional DM contribution of order 10 − pc cm − near conjunction ( ).Strong irradiation of the companion by the pulsar’s relativistic wind, however, could lead to asubstantially larger mass loss. Our DM variation limit argues against such a large mass loss.For a system like PSR J1903 + ) that would contribute to the measured ˙ ω = 2 . × − deg yr − . If the companion star is a WD rotating near breakup velocity,the classical contribution would typically be of order 10 − deg yr − , but could be more thanan order of magnitude larger for specific but unlikely system orientations. If the companionis a 1 − ⊙ main-sequence star with a typical rotational period of 8 −
10 days ( ),the classical contribution would be 2 × − deg yr − for most system orientations. Such a starwould need a rotational period between 1.3 and 1.5 days and/or an unlikely system orientationto account for ∼
10% of the measured ˙ ω , or a rotational period < ˙ ω is dominated by general relativistic effects and,given the high quality of the fit, that the use of the relativistic timing model is well justified. Formation Mechanisms
What is the origin of this unique system with a short spin period, large orbital eccentricity, andpossible MS companion? According to conventional evolutionary scenarios ( ), binary pulsarsthat have been recycled down to millisecond periods should always appear in circularized orbits.In contrast, pulsars in eccentric systems should be only mildly recycled or not recycled at all.Since PSR J1903 + × G). First, there are no pulsars likeJ1903 + ). Second, a “born-fast” scenario for PSR J1903 + ). Third, magneticfields in young pulsars likely originate either from dynamo action in the proto-NS ( ) or viacompression of ‘frozen-in’ fields of the progenitor star during collapse ( ). If compression isthe correct mechanism, then young pulsars with magnetic fields < G are rare, as we knowof none. Alternatively, the dynamo model actually requires rapidly spinning systems to havestrong magnetic fields. While core-collapse born-fast mechanisms seem to be ruled out, theaccretion induced collapse of massive and rapidly rotating WDs to NSs might form MSPs ( ).This collapse may be able to produce the observed orbital parameters, but the large observedpulsar mass would require the collapsing WD to be well above the Chandrasekhar mass, andwould also suggest that the companion should be evolved.Globular clusters (GCs) are known to be efficient producers of MSPs, including those ineccentric binaries, due to interactions between NSs and other stars or binaries in their highdensity cores. Of the ∼
130 known GC pulsars ( ), more than 10% are in highly eccentric( e > . ) orbits. These numbers, combined with the known populations of NSs in GCs and theGalaxy, and the respective masses of GCs and the Galaxy, imply that GCs produce eccentricbinary pulsars at least 1000 times more efficiently per unit mass than the Galactic disk. Further-6ore, stellar interactions and exchanges can provide MS companions for MSPs, although thosecompanions should be less massive than the most evolved MS stars currently observed in GCs( ∼ − ⊙ ).Although GCs seem a natural formation ground for PSR J1903 + + ), the Spitzer
GLIMPSE survey data ( ), or in our Gemini observa-tions. An intriguing possibility is that PSR J1903 + ∼ − ∼
50% of recycled NSs are ejected within the ∼
10 Gyr lifetimes of theGCs ( ). Once the pulsar has left the cluster it drifts far away from its parent cluster on10 − year timescales. Alternatively, the cluster could have been disrupted during orbitalpassages through the Galactic disk and bulge within the past ∼ ). Rough estimatesbased on the masses and densities of the GC system and the Galactic disk suggest (see thesupporting online material) a 1 −
10% chance that PSR J1903 + ∼ + − ⊙ ) WD in a wide circular orbit, although nosuch borderline systems have been observed to date. In this scenario the WD is the companion7een in the timing. The third star in the system, now the MS star that we detect as the infraredcounterpart, is in a much wider and highly inclined orbit around the inner binary. Secularperturbations in such a system can cause large oscillations of the inner-binary eccentricity andthe outer-orbit inclination (so-called Kozai cycles) ( ). Especially for a cycle period resonantwith the inner-binary relativistic periastron advance at ∼ × yrs, a 0.9 M ⊙ MS star ∼
120 AUout in a highly-inclined ∼ yr orbit can induce large inner-binary eccentricities ( ). Initialestimates (see the supporting online material) for the formation and survival probability of sucha triple system suggest that a few percent of observed NS–WD binaries could be members ofhierarchical triples. As such, it seems plausible that after finding ∼
50 pulsar–WD binaries, wehave now found the first in an hierarchical stellar triple.A related scenario that avoids the need for formation of both a fully recycled MSP anda high-mass WD companion (which has never been observed before) has PSR J1903 + +
47 ( ). The MSP then ablated away its WD companion and was leftin a 95-day eccentric orbit around the MS star we now observe.Further observations of PSR J1903 + > − ), vialong-term timing or Very Long Baseline Interferometry astrometry, might reflect a cluster origingiven the high velocities of most GCs. Spectroscopic observations of the MS star will revealits spectral type and metallicity, both possible indicators for or against a GC origin, and willshow whether it exhibits the 95-day orbital motion of the pulsar. If the star is the companion,the radial-velocity curve will further constrain the masses of both the pulsar and the companion.Additionally, if the MS companion is confirmed to be more massive than ∼ ⊙ , it will likelyrule out a GC origin as MS stars of that mass in clusters have already left the MS. Finally,long-term and higher-precision timing of the pulsar will dramatically improve the relativistic8arameters of the system (and therefore the derived masses) and will reveal secular changes inthe spin and orbital parameters caused by the presence of a third star or by classical effects fromthe rotation of a MS companion. References and Notes
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Astrophys. J. , 434 (1989).33. We thank the staff at NAIC and ATNF for developing ALFA and its associated data acqui-sition systems. This work was supported by the NSF through a cooperative agreement withCornell University to operate the Arecibo Observatory. The National Radio AstronomyObservatory is a facility of the National Science Foundation operated under cooperativeagreement by Associated Universities, Inc. Pulsar research at Cornell is supported by NSFgrants AST 0507747 and CISE/RI 040330 and by the Center for Advanced Computing. TheMcGill pulsar group Beowulf computer cluster used for this work was funded by the CanadaFoundation for Innovation. Pulsar research at Bryn Mawr College is funded by NSF grantAST 0647820. Basic research in radio astronomy at NRL is supported by 6.1 Base funding.Pulsar research at Columbia University is supported by NSF grant AST 0507376. Pulsarresearch at UBC is supported by an NSERC Discovery Grant. V. M. K. holds a CanadaResearch Chair and the Lorne Trottier Chair and acknowledges support from an NSERCDiscovery Grant, CIFAR, and FQRNT. J. W. T. H. holds an NSERC Postdoctoral Fellowshipand CSA supplement. L. K. holds an NSERC CGS-D fellowship. J. v. L. is a Niels StensenFellow. Pulsar research at the University of Texas at Brownsville is funded by NSF grantAST 0545837. We thank O. Pols, D. Fabrycky and G. Duchˆene for helpful discussions.11iming Parameters Assuming General RelativityRight Ascension (J2000) . . . . . . . . . . . . . . . . . . . . . 19 h m . s ◦ ′ . ′′ × − Dispersion Measure (pc cm − ) . . . . . . . . . . . . . . . . 297.537(7)Epoch of Period (MJD) . . . . . . . . . . . . . . . . . . . . . . 54280.0Orbital Period (days) . . . . . . . . . . . . . . . . . . . . . . . . 95.1741176(2)Projected Semi-Major Axis (lt-s) . . . . . . . . . . . . . 105.60585(11)Eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.436678411(12)Longitude of Periastron . . . . . . . . . . . . . . . . . . . . . . 141.65779(4) ◦ Epoch of Periastron (MJD) . . . . . . . . . . . . . . . . . . . 54063.8402308(5)Total System Mass, M tot (M ⊙ ) . . . . . . . . . . . . . . . 2.79(5)Companion Mass, M (M ⊙ ) . . . . . . . . . . . . . . . . . . 1.051(15)Other ParametersScattering Time at 1.4 GHz (ms) . . . . . . . . . . . . . . 0.126(1)1.4-GHz Flux Density (mJy) . . . . . . . . . . . . . . . . . 1.3(4)2-GHz Flux Density (mJy) . . . . . . . . . . . . . . . . . . . 0.62(5)5-GHz Flux Density (mJy) . . . . . . . . . . . . . . . . . . . 0.09(2)Spectral Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -2.1(2)Derived ParametersGalactic Longitude (J2000) . . . . . . . . . . . . . . . . . . 37 . ◦ − . ◦ ⊙ ) . . . . . . . . . . . . . . . . . . . . . . . . . 0.1396076(2)Distance (kpc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ∼ × Characteristic Age (Gyr) . . . . . . . . . . . . . . . . . . . . . 1.8Spin-down Luminosity (ergs s − ) . . . . . . . . . . . . . 7.5 × Advance of Periastron (deg yr − ) . . . . . . . . . . . . . 2.46(2) × − Orbital inclination . . . . . . . . . . . . . . . . . . . . . . . . . . . 78(2) ◦ Pulsar Mass, M (M ⊙ ) . . . . . . . . . . . . . . . . . . . . . . . 1.74(4)Table 1: Measured and derived parameters for PSR J1903 + ) and the “DDGR” timing modelwhich assumes that general relativity fully describes the parameters of the binary system ( ).A total of 342 pulse arrival times measured between MJDs 53990 and 54568 were fit. Thenumbers in parentheses are twice the TEMPO-reported 1- σ uncertainties in the least significantdigit or digits quoted as determined by a bootstrap error analysis. The distance is inferredfrom the NE2001 free electron density model ( ). Ensemble distance measurements using thismodel have an estimated error of 25%, although errors for individual pulsars may be larger.12igure 1: Residual pulse arrival times as a function of orbital phase (mean anomaly) forPSR J1903 + Top
The measured timing residuals if no orbit is accounted for. The result-ing curve is the Roemer delay (i.e. the light-travel time across the orbit) and its non-sinusoidalshape shows the large eccentricity ( e = 0 . ) of PSR J1903 + . Middle
The same residuals as in the top panel but with the Roemer delay and all generalrelativistic delays except for Shapiro delay from the timing solution in Table 1 removed.
Bottom
The timing residuals for the full “DDGR” timing model described in Table 1 which assumesthat general relativity fully describes the parameters of the binary system ( ). The weightedroot-mean-square timing residual shown here is 1.9 µ s.13igure 2: Rotation periods, period derivatives, and orbital eccentricities (for binary pulsars)of pulsars in the disk of the Galaxy. The bottom face of the cube shows a plot of rotationperiod versus rotation period derivative for all Galactic pulsars. Colored points show the binarypulsars, projected upward from the bottom face in proportion to their orbital eccentricities.Square blue points are double neutron star systems, triangular green points are pulsars withmain-sequence or massive companions, circular yellow points are pulsars with white dwarf orsub-dwarf companions, and the red star is PSR J1903+0327, which occupies a unique place inthe diagram. 14igure 3: A K S -band image of the PSR J1903 + − ′′ ) with the Gemini North telescope. The red circle shows the 2- σ error circle,with radius 0 . ′′
32 (produced by the frame-tie uncertaities in right ascension and declination), forthe position of the pulsar based on astrometric calibrations made with the 2MASS catalog. Thestar within the error circle is the possible main-sequence companion to the pulsar.15 aterials and methods
In the following, we describe several details of the discovery and follow-up observations ofPSR J1903 + Discovery
The survey ( S1 ) collects data during 5-min pointings for each of seven positions on the skyusing the Arecibo L-band Feed Array (ALFA) receiver and digital spectrometers covering 100-MHz of bandwidth centered at 1400 MHz. The recorded data have 256 frequency channels anda time resolution of 64 µ s. We initially detected PSR J1903 + S2, S3 ). The basic stepsof the pipeline are similar to those of the “quicklook pipeline” ( S1 ), except that we process thedata at full resolution in both time and radio frequency, we perform extensive radio-frequencyinterference excision in the time and frequency domains, and we look specifically for compactbinary pulsars using linear “acceleration” searches ( S4 ). To remove the dispersive effects of theinterstellar medium, the data were first dedispersed for 1272 trial dispersion measures (DMs)between 0 − − . The DM trial values are spaced such that the pulse smearing dueto interstellar dispersion is < <
600 pc cm − , thereby giving us unprecedentedsensitivity to millisecond pulsars (MSPs) in the disk of our Galaxy. We conduct standard period-icity and acceleration searches by taking the Fast Fourier Transform (FFT) of each dedispersedtime series using incoherent harmonic summing of up to 16 harmonics. In addition, single-pulsesearches of the data were carried out which were sensitive to transient events in the time domainwith widths in the range 64 µ s to 0.1 s 16 iming Once a pulsar is discovered it is characterized by its position, spin parameters and any orbitalparameters. Using the search data these parameters are poorly constrained, but they can bemeasured to much greater levels of precision by fitting a timing model of the pulsar’s rotationto the data. Integer numbers of pulsar rotations are fitted between the times-of-arrival of theobserved pulses; in such a “phase connected solution” every rotation of the pulsar is accountedfor. Follow-up timing observations were carried out with Arecibo at ∼ ∼ ∼ ∼ S5 ), a digital correlator which synthesized either 768 or 1536 frequency chan-nels covering 600 MHz of bandwidth and sampled every 81.92 µ s. Individual GBT observationswere made at 5 and 9 GHz with the Spigot in a mode with 1024 frequency channels recordedover 800 MHz of bandwidth and sampled every 81.92 µ s. WSRT observations used the PUMaII data acquisition system ( S6 ) to record eight 20 MHz wide dual polarization bands. Each bandwas subsequently analyzed offline by forming a 64-channel coherent filterbank leading to a finaltime resolution of 16.8 µ s.The timing model parameters shown in Table 1 of the main article were derived from thebest-fit model to the pulse arrival times we obtained with the above telescopes and instru-mentation. A timing model using a simple Keplerian orbit provides a very poor fit to thedata (reduced- χ of 29.5 for 327 degrees of freedom [DOF]). The addition of an orbital pe-17iastron advance ( ˙ ω ) dramatically improves the fit (reduced- χ of 2.12 for 326 DOF), giving ˙ ω = 2 . × − deg yr − , but systematic trends remain in the timing residuals. Given theorientation of the orbit, these remaining trends are most likely explained by the Shapiro delay:the delay should have an amplitude of tens of µ s, an order of magnitude larger than our arrivaltime measurement precision, even though most of that signal will be covariant with the pro-jected semi-major axis, a sin i . Using the “DDGR” model ( S7, S8 ), which assumes that generalrelativity correctly describes the dynamics of the system with Keplerian orbit parameters plusthe total system mass M tot and the mass of the companion star M , the fit is further improved(reduced- χ = 1.13 for 325 DOF) and results in no visible systematics in the residuals (Fig. 1).In Fig. S1, we show a χ contour map of the mass constraints from the DDGR model.In order to confirm that this timing is consistent with general relativity, the “DD” model ( S9,S8 ), a theory independent relativistic description of the orbital parameters, was used separatelyfitting for the orbital periastron advance, the companion mass and sine of the inclination angle( sin i). In this fit (reduced- χ = 1.12 for 324 DOF) all of the post-Keplerian parameters whichare not specific to general relativity are consistent with the parameters from the general relativityspecific DDGR model at the 1-2 σ level. The timing model parameters for the DD model areshow in Table S1. Search for a pulsar companion
Given the possibility that this is a double neutron star system, and that the companion is po-tentially a pulsar, we searched for pulsations from the companion using several of the earlyobservations of the system taken at Arecibo. As well as searching each observation indepen-dently, we summed power spectra from the individual observations to increase sensitivity. Wededispersed each observation at the known DM of PSR J1903 + + ◦ . The only unknown parameter in this calculation isthe ratio of the semi-major axes of the pulsar and companion which is the inverse of the ratioof their masses. A search over a series of trial projected semi-major axes for the companionwas therefore used, ranging from 60 to 185 light-seconds. This encompasses the range of well-measured neutron star masses ( S10 ). Finally the summed FFT was searched for candidatesusing the techniques described above. The search yielded no significant candidates.We set an upper limit on pulsed emission at 1.4 GHz of 20 µ Jy for a period of 2 ms and 9 µ Jyfor a period of 200 ms, both at a DM of 297 pc cm − . These upper limits correspond to 1.4 GHzradio luminosities of 0.8 and 0.4 mJy kpc respectively. Only two percent of all radio pulsarscurrently known have luminosities below the latter value. Our non-detection therefore excludesmost of the observable radio pulsar population as a companion, but does not of course rule outa neutron star that is unfavorably beamed away from our line of sight or rotating too slowly tobe observed as a pulsar. Optical and infra-red analysis
The field of PSR J1903+0327 was observed with the Near InfraRed Imager (NIRI) on the Gem-ini North telescope on July 24, 2007. Dithered series of 6 second exposures were obtained in the J , H and K S filters, amounting to a total exposure time of 10 minutes in each filter. All imageswere corrected for dark current and flatfielded using skyflats. The non-uniform sky distributionwas removed by substracting a sky frame constructed of the unregistered science images to re-move the contributions of stars. After these corrections, the images taken with the same filterwere registered and averaged.Astrometry was done relative to the 2MASS catalogue ( S11 ), as the small field of view of19IRI ( ′ × ′ ) contains no astrometric standards from the UCAC2 catalogue ( S12 ). A total of 712MASS stars coincided with the registered and average K S -band image and 51 of these werenot saturated and appeared steller and unblended. After iteratively removing 9 outliers, the finalastrometric calibration has rms residuals of . ′′ in right ascension and . ′′ in declination.A comparison of the positions of 281 UCAC2 standards coinciding with 2MASS stars within ′ from the position of PSR J1903+0327 shows no significant shift between the positions inboth catalogues.Taking the rms uncertainty on both coordinates as a measure for the 1- σ uncertainty in theastrometric calibration, we find a single star inside the . ′′ error circle on the pulsar position at α J2000 = 19 h m . s and δ J2000 = 03 ◦ ′ . ′′ , where the uncertainty on the positionis the quadratic sum of the uncertainty in the astrometry and the intrinsic positional uncertaintyof the star in the image ( . ′′ in each coordinate). This position if offset from the pulsar positionby . ′′ in right ascension and . ′′ in declination.Photometry was also done relative to the 2MASS catalogue. Magnitude offsets were deter-mined and outliers were iteratively removed, leaving 30 to 40 stars for the photometric calibra-tion. The calibrations showed no significant dependence with star color. We find that the objectin the error circle has J = 19 . , H = 18 . and K S = 18 . .To estimate the reddening towards PSR J1903+0327, we used red clump stars to trace thereddening as a function of distance ( S13 ). Again using the 2MASS catalogue, we selected 1400stars within ′ from PSR J1903+0327 and determined the J − K S colour of the red clump stars atdifferent K S magnitudes using the formalism of ( S14 ). At the DM-distance of PSR J1903+0327, d = 6 . kpc (assuming a 25% uncertainty), we constrain the reddening at A V = 4 . .For this distance and reddening, the intrinsic magnitudes of the star inside the error circle are M J = 3 . , M H = 3 . and M K S = 3 . .Though the metallicity and age of the star are unknown, stars of solar metallicity, ages of20 Gyr or less and masses between approximately 0.8 and 1.3 M ⊙ will have similar absolute mag-nitudes ( S15 ). Stars older than 1 Gyr will have evolved and will match the absolute magnitudesfor lower masses. At 10 Gyr and solar metallicity the mass range decreases to approximately0.75 to 1.1 M ⊙ . For a mass of 1.05 M ⊙ as determined from the radio timing, a solar metallicitystar will match the observed absolute magnitudes if the age is less than 6 Gyr.At the apparent magnitudes, the star is bright enough for optical or infrared spectroscopy todetermine radial velocity variations which would unambiguously confirm the star as the binarycompanion to PSR J1903+0327. Globular cluster calculations
While PSR J1903 + ∼
100 times that in the disk (
S16, S17 ).PSR J1903 + ∼ yr ago such that they are no longer in the same part of the sky. Many GCsmay have been completely disrupted via gravitational interactions with the disk and bulge overthe course of many orbits in the Galactic potential. As a result, their stars become part of theGalactic spheroid population (an approximately spherical distribution of older stars distributedin an extension of the central Galactic bulge, with a diameter of ∼
10 kpc). Estimates suggestthat over half the spheroid mass could have come from such disrupted GCs (
S18 ). Such dis-ruption should require several Galactic orbits of the GC, the periods of which are ∼ − + S4 ), any model involving GC disruption requires a recycled pulsarto exchange its companion and acquire an eccentric orbit and its parent GC to then be totally21isrupted in less than ∼ + S19 ) and disk (
S20 ) populations, we find ρ spheroid /ρ disk = 4 . × − M ⊙ pc − / . × − M ⊙ pc − ∼ × − . Assuming that half of the spheroid mass originated in disrupted GCs, the < ∼ + < ∼
20% of that mass could have come from GCs disrupted sincethe recycling of the pulsar. Furthermore, if we assume that those GCs produced highly eccentricbinary MSPs ∼ times more efficiently per unit mass than the disk, we can crudely estimatethat the probability that PSR J1903 + < ∼ + + M ⊙ ) to the disk mass (10 M ⊙ ) times the 10 formation efficiencyfactor for highly eccentric binary MSPs times the ∼
50% fraction of pulsars which are eventuallyejected from GCs (
S21 ). The resulting ∼
5% probability again indicates that some GC formationmechanism for PSR J1903 + Hierarchical triple system calculations
Hierarchical stellar triple systems are common, and such a system may explain the eccentricitywe observe in PSR J1903 + ∼ ⊙ companionseen in timing at the 95-day orbit) with a third object orbiting at greater distance (in this case,the main sequence star observed in the infra-red). Here we assess the plausibility of formingsuch an end state.Constraints on the formation of the inner binary are: (i) to form a 2.15-ms MSP there must22ave been a long period of stable mass transfer to spin up the neutron star; (ii) to produce thewide 95-day orbit the white dwarf progenitor cannot be too massive, to avoid common-envelope(CE) evolution and spiral-in; (iii) the star must have been massive enough to leave a ∼ ⊙ white dwarf after final mass transfer ( S22 ). We therefore consider an initial system containinga central binary formed by a 8 M ⊙ primary; a secondary that is just below CE mass, we shallhere assume 3 M ⊙ ; and a 0.9 M ⊙ third star.A survey of the multiplicity of massive stars in the Orion Nebula ( S23 ) suggests that 80%of spectroscopic binaries with OB-star primaries have a third visual companion. These systemsmust survive the supernova that creates the pulsar: the inner binary will remain bound givensuitable mass-loss and kick parameters (
S24 ). The outer companion can remain bound (
S25 )if its orbital velocity is comparable to the new system velocity of the inner binary (a few tensof km s − , ( S26 )). The multiplicity survey (
S23 ) finds ∼ S27 ). In thishierarchical triple the outer companion cannot unbind the inner binary, but its orbit evolvestowards a Kozai-cycle resonance with the inner-binary relativistic periastron advance period(
S28 ). Our above rough estimates of the various fractions combine to a roughly 4% chance thata given evolved NS-WD binary is part of a hierarchical triple. As there are currently ∼
50 NS-WD systems known in Galactic-disk binaries, this simple estimate is consistent with the ideathat PSR J1903 + ⊙ , a relativelyhigh inclination of the third star’s orbit i > ◦ and some eccentricity in the outer orbit, the23nner-binary eccentricity is higher than e = 0 . for about 20% of the oscillation time ( S28 ).Second, for the line-of-sight acceleration from the third star to be less than our measured ˙ P thisthird star must currently be close to plane of the sky, the a priori probability of which is ∼ References and Notes
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A&A , 1165 (2004). 26iming Parameters Using the DD ModelRight Ascension (J2000) . . . . . . . 19 h m . s ◦ ′ . ′′ × − Dispersion Measure (pc cm − ) . . 297.537(7)Epoch of Period (MJD) . . . . . . . . 54280.0Orbital Period (days) . . . . . . . . . . . 95.1741176(2)Projected Semi-Major Axis (lt-s) 105.593459(8)Eccentricity . . . . . . . . . . . . . . . . . . . 0.43667838(5)Longitude of Periastron . . . . . . . . 141.652477(3) ◦ Epoch of Periastron (MJD) . . . . . 54063.8402310(6)Advance of Periastron (deg yr − ) 2.46(3) × − Sine of Orbital Inclination . . . . . . 0.966(10)Companion Mass, M (M ⊙ ) . . . . 1.3(2)Table S1: Measured and derived parameters for PSR J1903 + S29 ) and the “DD” timing modelwhich uses a theory independent relativisitc model to describe the parameters of the binarysystem (
S9, S8 ). A total of 342 pulse arrival times measured between MJDs 53990 and 54568were fit. The numbers in parentheses are twice the TEMPO-reported 1- σ uncertainties in theleast significant digit or digits quoted as determined by a bootstrap error analysis.27igure S1: A χ -map showing the 1 and 2- σ confidence regions for the total system mass (M tot )and companion mass (M ) based on the timing solution presented in Table 1 after doubling thenominal TEMPO errors. Those errors were within 20% of the bootstrap error estimates. Thegrey region in the lower right portion of the figure is excluded by the mass function. The greylines show inclinations i of 70, 75, 80, and 85 ◦ . For PSR J1903 + tot is best constrainedfrom the measurement of the relativistic advance of periastron ˙ ω while M is constrained by ameasurement of sin ii