Gamma Radiation from PSR B1055-52

THE ASTROPHYSICAL JOURNAL, 516 :297È306, 1999 May 11999. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

GAMMA RADIATION FROM PSR B1055[52

D. J. THOMPSON,1,2 M. BAILES,3 D. L. BERTSCH,1 J. CORDES,4 N. DÏAMICO,5 J. A. ESPOSITO,1,6 J. FINLEY,7 R. C. HARTMAN,1W. HERMSEN,8 G. KANBACH,9 V. M. KASPI,10 D. A. KNIFFEN,11 L. KUIPER,8 Y. C. LIN,12 A. LYNE,13 R. MANCHESTER,14

S. M. MATZ,15 H. A. MAYER-HASSELWANDER,9 P. F. MICHELSON,12 P. L. NOLAN,12 M. POHL,17H. O� GELMAN,16P. V RAMANAMURTHY,1,18 P. SREEKUMAR,2 O. REIMER,9 J. H. TAYLOR,19 AND M. ULMER15

Received 1998 June 12 ; accepted 1998 December 7

ABSTRACTThe telescopes on the Compton Gamma Ray Observatory (CGRO) have observed PSR B1055[52 a

number of times between 1991 and 1998. From these data a more detailed picture of the gamma radi-ation from this source has been developed, showing several characteristics that distinguish this pulsar :the light curve is complex ; there is no detectable unpulsed emission ; the energy spectrum is Ñat, with noevidence of a sharp high-energy cuto† up to greater than 4 GeV. Comparisons of the gamma-ray datawith observations at longer wavelengths show that no two of the known gamma-ray pulsars have quitethe same characteristics ; this diversity makes interpretation in terms of theoretical models difficult.Subject headings : gamma rays : observations È pulsars : individual (PSR B1055[52)

1. INTRODUCTION

The Compton Gamma Ray Observatory (CGRO) tele-scopes have detected pulsed gamma radiation from at leastseven spin-powered pulsars : Crab, Vela, Geminga, PSRB1509[58, PSR B1706[44 PSR B1951]32, and PSRB1055[52, with some evidence for an eighth, PSRB0656]14. For a summary of CGRO pulsar results, seeUlmer (1994) and Thompson et al. (1997). Upper limits havebeen calculated for selected samples of radio pulsars(Thompson et al. 1994 ; Fierro et al. 1995 ; etCarramin8 anaal. 1995 ; Schroeder et al. 1995) and for all cataloged pulsars(Nel et al. 1996).

The present work is a detailed analysis of the gamma-rayobservations of PSR B1055[52, based on repeated obser-vations during 1991È1998 that have nearly tripled the

1 Code 661, Laboratory for High Energy Astrophysics, NASA GoddardSpace Flight Center, Greenbelt, MD 20771.

2 djt=egret.gsfc.nasa.gov.3 Astrophysics and Supercomputing, Mail No. 31, Swinburne Univ. of

Technology, PO Box 218, Hawthorn Victoria 3122, Australia.4 Physics Department, Cornell University, Ithaca, NY.5 Osservatorio Astronomico di Bologna, via Zamboni 33, I-40126

Bologna.6 USRA Research Associate.7 Physics Dept., Purdue University, Lafayette, IN.8 SRON/Utrecht, Sorbonnelaan 2, 3584 CA Utrecht, the Netherlands.9 Max-Planck-Institut Extraterrestrische Physik, Giessenbachstr D-fu� r

85748, Garching, FRG.10 Physics Department, MIT, Cambridge, MA.11 Department of Physics, Hampden-Sydney College, Hampden-

Sydney, VA 23943.12 W. W. Hansen Experimental Physics Laboratory and Department of

Physics, Stanford University, Stanford CA 94305.13 Nuffield Radio Astronomy Laboratories, Jodrell Bank, University of

Manchester, MacclesÐeld, Cheshire SK11 9DL, UK.14 ATNF, CSIRO, Australia.15 Physics Dept., Northwestern University, Evanston, IL.16 Physics Dept., University of Wisconsin, Madison, WI.17 Danish Space Research Institute, 2100 Copenhagen O, Denmark.18 National Academy of Sciences-National Research Council Senior

Research Associate. Present address : S. T. E. Laboratory, Nagoya Uni-versity, Nagoya, Japan.

19 Physics Department, Princeton University, Princeton, NJ.

source exposure time compared to the discovery data(Fierro et al. 1993). The gamma-ray observations of this andother pulsars are shown in a multiwavelength context.Comparison of the multiwavelength properties of pulsars isimportant in attempting to construct models for theseobjects.

Using ROSAT , & Finley (1993) found pulsedO� gelmanX-rays from PSR B1055[52, with a pulse that changedboth shape and phase at photon energy about 0.5 keV. TheX-ray energy spectrum requires at least two components,one thought to be emission from the hot neutron starsurface and the other likely to be from the pulsar magneto-sphere (see also Greiveldinger et al. 1996, and Wang et al.1998).

Mignani, Caraveo, & Bignami (1997) have found evi-dence based on positional coincidence for an opticalcounterpart of PSR B1055[52 using the Hubble SpaceT elescope (HST ) Faint Object Camera. In the absence of afast photometer on HST and the presence of a nearbybright star, Ðnding optical pulsations will be difficult, asnoted by the authors.

2. RADIO OBSERVATIONS

The basic pulsar parameters (Taylor, Manchester, &Lyne 1993), derived from radio observations, are shown inTable 1.

PSR B1055[52 was on the list of nearly 300 pulsarsmonitored regularly by radio astronomers to assistgamma-ray telescopes on the CGRO (Kaspi 1994 ;Arzoumanian et al. 1994 ; Johnston et al. 1995 ; DÏAmico etal. 1996). High-energy gamma-ray data are sparse ; weak,short-period gamma-ray pulsars are detectable only if thetiming parameters are determined independently of thegamma-ray data. In the case of PSR B1055[52, thismonitoring, carried out at Parkes, has continued. Thepulsar exhibits considerable timing noise. For this reason,the timing solutions used for the gamma-ray analysis weredeveloped piecewise over time intervals for which the pulsephase could be adequately modeled using only a simple

297

298 THOMPSON ET AL. Vol. 516

TABLE 1

BASIC DATA

Parameter Value

Names . . . . . . . . . . . . . . . . . . . . . . . . . . . PSR B1055[52, PSR J1057[5226Period P . . . . . . . . . . . . . . . . . . . . . . . . 0.1971 sPeriod Derivative P0 . . . . . . . . . . . 5.8 ] 10~15 s s~1Timing Age q . . . . . . . . . . . . . . . . . . . 537,000 yrSpin-down luminosity E0 . . . . . . 3.0] 1034 ergs s~1Magnetic Field B . . . . . . . . . . . . . . 1.1 ] 1012 gauss

spin-down law in terms of l, and Table 2 lists thel5 , l� .solutions relevant to the CGRO viewings, given in terms offrequency l and its derivatives instead of period, and validat time T0.20

3. GAMMA-RAY OBSERVATIONS

All the telescopes on the CGRO have pulsar timing capa-bility. Time in universal coordinated time (UTC) is carriedon board the spacecraft to an accuracy of better than 100km. The conversion of gamma-ray arrival time at the loca-tion of the CGRO to pulsar phase is carried out using amodiÐcation of the TEMPO timing program (Taylor &Weisberg 1989) and the Jet Propulsion Laboratory DE200ephemeris.

EGRET is the high-energy gamma-ray telescope onCGRO (Thompson et al. 1993), operating from about 30MeV to over 20 GeV. The Ðeld of view mapped by EGRETextends to more than 30¡ from the instrument axis. PSRB1055[52 was within 30¡ of the telescope axis during 24 ofthe CGRO viewing intervals to date. No additional EGRETobservations of this pulsar are scheduled. PSR B1055[52 isnot a particularly bright source compared to many othersseen by EGRET (see the second EGRET catalog, Thomp-son et al. 1995). Its gamma-ray count rate is low, about 4photons (E[ 100 MeV) per day when the source is within10¡ of the EGRET axis. Data processing for EGRET relieson two principal methods : timing analysis and spatialanalysis. The spatial analysis compares the observedgamma-ray map to that expected from a model of thedi†use Galactic and extragalactic radiation (Hunter et al.1997 ; Sreekumar et al. 1998). Source location and Ñux as afunction of energy are determined using a maximum likeli-

20 These timing solutions are from the database maintained at Prin-ceton University (anonymous FTP: ftp ://puppsr.princeton.edu/gro) withthe addition of recent timing solutions from Parkes (http ://wwwatnf.atnf.csiro.au/research/pulsar/psr/archive).

hood method (Mattox et al. 1996). The timing and spatialapproaches can also be combined to produce phase-resolved maps and energy spectra.

COMPTEL, the Imaging Compton Telescope, is anotherof the CGRO telescopes, operating in the energy range0.75È30 MeV et al. 1993). Like EGRET,(Scho� nfelderCOMPTEL uses both spatial and timing analysis, andbecause the COMPTEL Ðeld of view is larger thanEGRETÏs and the two telescopes are co-aligned on thespacecraft, PSR B1055[52 was viewed by COMPTEL atthe same times as by EGRET.

OSSE, the Oriented Scintillation Spectrometer Experi-ment, is a third of the CGRO telescopes, operating in theenergy range 0.05È10 MeV (Johnson et al. 1993). LikeEGRET and COMPTEL, OSSE uses both spatial andtiming analysis, with the spatial analysis coming from anon-source/o†-source analysis. Because of its smaller Ðeld ofview, OSSE observes individual targets. PSR B1055[52was observed by OSSE and simultaneously by EGRET andCOMPTEL 1997 September 2È9 and 1997 September 23ÈOctober 7.

4. RESULTS

4.1. L ight CurvesFigure 1 shows the EGRET light curve for PSR

B1055[52 combining data from all 24 viewings, derived intwo di†erent ways : (T op) The gamma-ray selection wasbased on maximizing the signiÐcance of the pulsed signal inthe light curve, as characterized by the (binned) s2 or(unbinned) H-test value (De Jager, Swanepoel, & Rauben-heimer 1978). The strongest signal was obtained for energiesabove 240 MeV with gamma rays selected within of the1¡.7known pulsar position. As found by Ramanamurthy et al.(1995a) for PSR B1951]32, a Ðxed cone can produce animproved signal to background for relatively weak signals,because the Ðxed cone selects photons from the narrowcomponent of the point-spread function of the EGRETinstrument (Thompson et al. 1993) for this energy range,eliminating the broad wings that contribute to the standardenergy-dependent event selection. The optimization wasdone iteratively on angle and energy, involving about 20trials ; (Bottom) The alternate gamma-ray selection usedphotons selected within an energy-dependent cone of radius

h ¹ 5¡.85(Ec/100 MeV)~0.534 , (1)

with respect to the pulsar position in MeV). This choice(Ecrepresents the 67% containment angular resolution of theEGRET instrument (Thompson et al. 1993), including bothnarrow and broad components. In this case the strongestsignal was obtained for photon energies greater than 600MeV. For both light curves, the phase is the same, refer-

TABLE 2

RADIO TIMING PARAMETERS FOR PSR B1055[52

T 0 l l5 l�Valid Dates (MJD) (s~1) (10~13 s~2) (10~24 s~3)

1991 Sep 13È1992 Oct 1 . . . . . . . 48704 5.0733041127598 [1.50169 0.001991 Feb 9È1994 Jan 21 . . . . . . . 48834 5.0733024258637 [1.50152 8] 10~61993 Aug 26È1995 Jan 21 . . . . . . 49481 5.0732940338018 [1.50096 3] 10~51995 May 6È1995 Oct 3 . . . . . . . 49918 5.0732883705741 [1.50189 5.041996 Feb 1È1996 Nov 12 . . . . . . 50256 5.0732839892859 [1.50195 3] 10~51997 Jan 12È1998 Apr 24 . . . . . . 50693 5.0732783214141 [1.50110 17.2

No. 1, 1999 GAMMA RADIATION FROM PSR B1055[52 299

FIG. 1.ÈHigh-energy gamma-ray light curve for PSR B1055[52. The197 ms period is divided into 30 phase bins. The double radio pulse haspeaks with centroids at phases 0.43 (short-dashed vertical line) and 0.0(long-dashed vertical line). T op : gamma rays above 240 MeV selected froma Ðxed cone with radius bottom : gamma rays above 600 MeV selected1¡.7 ;from an energy-dependent cone, as described in the text.

enced to one of the two radio pulses that deÐnes phase 0(long-dashed line). The centroid of the second radio pulse isat phase 0.43 (see, e.g., Biggs 1990), indicated in the Ðgure bya short-dashed line.

The two gamma-ray light curves are not independent.Most of the 146 photons in the lower light curve are alsocontained in the 328 photon upper curve. Nevertheless, thesimilarity of the light curve shapes shows that the featuresare not the result of a particular selection technique. Thelight curve is di†erent from those of the Crab, Vela,Geminga and PSR B1951]32, all of which show twonarrow peaks separated by 0.4È0.5 in phase. PSRB1055[52 more closely resembles PSR B1706[44(Thompson et al. 1996) in having a broad phase range ofemission. Between phases 0.7 and 1.1, PSR B1055[52shows evidence of two peaks. The upper, higher statisticslight curve, is reasonably well Ðtted by two Gaussians plus aconstant term (reduced s2\ 1.2, 23 degrees of freedom,probability 0.25) but not well by a single Gaussian plus aconstant (reduced s2\ 2.2, 26 degrees of freedom, probabil-ity \0.001) or by a square pulse (reduced s2\ 2.1, similarto the single Gaussian). Adding the second peak increasesthe F-test statistic from 20.7 to 43.7, a marked improve-ment. The best Ðt is obtained with the following param-eters : peak 1 phase 0.75, (4.5 ms) ; peak 2 phasep1\ 0.020.95, (14.2 ms). In light of the limited statistics,p2\ 0.07

details of the pulse shape cannot be considered well deÐned.The signiÐcance of the small peak near phase 0.52 can beassessed by calculating the Poisson probability of Ðndingone bin out of 18 in the o†-pulse region with 13 or morecounts when the average in this phase region is 5.33 countsper bin. The resulting 6% probability indicates that none ofthe features in the 0.1È0.7 phase range is statistically signiÐ-cant.

Timing analysis of the COMPTEL data produced nostatistically signiÐcant detection of pulsed emission in anyof the bands 0.75È1, 1È3, 3È10, or 10È30 MeV. Each of thebands and the summed COMPTEL light curve do,however, show a low-signiÐcance peak at phase D0.73 con-sistent in phase with the narrower of the two EGRETpeaks. Taking the EGRET pulse as a reference to deÐne apreferred phase, the statistical signiÐcance of the peak in thesummed COMPTEL light curve for a single trial is 3.5 p,with a probability of chance occurrence less than 0.001.Although the EGRET statistics do not warrant a detailedspectral analysis for the two pulses separately, it is notedthat the narrow pulse does not appear above 2 GeV whilethe broad pulse extends to more than 4 GeV, suggestingthat the narrow pulse may have a softer spectrum than thebroad pulse, consistent with the peak seen by COMPTELand the peak seen in hard X-rays. The COMPTEL lightcurve is shown in Figure 2, along with light curves fromother wavelengths. The vertical dashed line marks the refer-ence radio peak, deÐning phase 0 in Figure 1.

Timing analysis of the OSSE data produced no evidenceof pulsed emission, even taking into account the constraintsof assuming the same light-curve shape at seen at the higherenergies. The 95% conÐdence upper limit in the energyrange 50È200 keV is 2.1] 10~4 ph cm~2 s~1 MeV~1. TheOSSE light curve is also shown in Figure 2.

4.2. Search for Unpulsed Emission and Source V ariabilityIn the region of sky mapped by EGRET around the

pulsar, each photonÏs arrival time is converted to pulsarphase, whether or not this photon is likely to have comefrom the pulsar itself. Phase-resolved maps of the sky arethen constructed ; the spatial analysis using maximum likeli-hood (Mattox et al. 1996) is used to assess the statisticalsigniÐcance of a source at the pulsar location. The likeli-hood ratio test is used to determine the signiÐcance of pointsources. The likelihood ratio test statistic is T S 4 2( ln L 1where is the log of the likelihood of the data[ ln L 0), ln L 1if a point source is included in the model, and is log ofln L 0the likelihood of the data without a point source. For posi-tive values of T S, the analysis gives the most likely gamma-ray Ñux of a source at the pulsar location. The pulsar isdetected with high signiÐcance between phases 0.7 and 1.1.Based on the summed map for all observations, the time-averaged Ñux above 100 MeV for this phase range is(2.5^ 0.2)] 10~7 ph cm~2 s~1, and the statistical signiÐ-cance of the detection is 13.6 p. The Ñux is consistent withthe value of (2.2 ^ 0.4)] 10~7 in the second EGRETcatalog (Thompson et al. 1995). Analysis of the o†-pulsephase range 0.1È0.7 yields an excess with a statistical signiÐ-cance of 1.9 p, too small to claim a detection. The upperlimit (95% conÐdence) is 1.2] 10~7 ph cm~2 s~1. Above100 MeV, any unpulsed component is therefore less than50% of the pulsed emission.

In a search for time variability, we examined the E[ 100MeV observations of the PSR B1055[52 Ñux as a function


FIG. 2.ÈMultiwavelength light curves for PSR B1055[52. The spec-tral band and intensity units are as follows : (a) radio, 1520 MHz, relativeintensity ; (b) ROSAT X-rays less than 0.5 keV & Finley 1993) ;(O� gelman(c) ROSAT X-rays greater than 0.5 keV & Finley 1993) ; (d)(O� gelmanOSSE gamma rays, 48È184 keV photons s~1 detector~1 ; (e) COMPTELgamma rays 0.75È30 MeV; ( f ) EGRET gamma rays [ 240 MeV. Twocomplete cycles are shown. The radio reference is shown by a verticaldashed line.

of time, from 1991 to 1997, for those 10 observations whenthe pulsar was within 20¡ of the EGRET axis, based on themaps of phase range 0.7È1.1. As seen for the Crab,Geminga, and Vela pulsars (Ramanamurthy et al. 1995b),and PSR B1706[44 (Thompson et al. 1996), the high-energy gamma radiation from PSR B1055[52 appears tobe steady. The s2 is 13.9 for 13 degrees of freedom.

4.3. Energy SpectrumBecause there is no substantial evidence for unpulsed

emission (phase 0.1È0.7), the energy spectrum of the pulsarcan be derived by analyzing the 0.7È1.1 phase map in eachof 10 energy bands, using the maximum likelihood methodas described above. Including the few excess photons fromthe unpulsed region (less than 15% increase in statistics) hasno signiÐcant inÑuence on the spectrum. Nearby sourcesfrom the third EGRET catalog (Hartman et al. 1998) areincluded in the analysis, because the point-spread functionsfor these sources overlap that of the pulsar, especially at thelower energies. The excesses in each band are then com-pared to model spectra forward-folded through the EGRETenergy response function, as described by Nolan et al.(1993). Pulsed emission is detected from 70 MeV to morethan 4 GeV. The EGRET spectrum, shown in Figure 3 as aphase-averaged photon number spectrum, can be represent-

FIG. 3.ÈPhase-averaged gamma-ray energy spectrum of PSRB1055[52. The Ðts in the energy range 70 MeVÈ10000 MeV to a powerlaw and a power law with a break at 1000 MeV are described in the text,with extrapolations to lower energies shown as dotted and dashed linesrespectively. The uncertainties shown are statistical only.


ed by a power law

dNdE

\ (7.67^ 0.70)] 10~11A E541 MeV

B~1.73B0.08

photons cm~2 s~1 MeV~1 . (2)

The reduced s2 for this Ðt is 1.19. Alternately, the spec-trum can be Ðt as a broken power law, with a spectral breakat D1000 MeV, similar to the spectrum for PSR B1706[44(Thompson et al. 1996)

dNdE

\ (3.22^ 0.59)] 10~11A E1000 MeV

Ba

photons cm~2 s~1 MeV~1 , (3)

where

a \G[1.58^ 0.15E¹ 1000 MeV

[ 2.04^ 0.30Eº 1000 MeV.(4)

The reduced s2 for this Ðt is 1.17 ; therefore, this is not asigniÐcantly better Ðt. The reason for favoring the brokenpower law rather than the single power law in the EGRETenergy range is that the single power law is marginallyinconsistent with the upper limit from OSSE. We conserva-tively treat the COMPTEL results as upper limits ; if theevidence for the narrow pulse were treated as a detection(which would be a Ñux of (6.3^ 1.8)] 10~7 ph cm~2 s~1 inthe energy range 0.75È30 MeV), then a spectral break wouldbe required in or just below the COMPTEL energy range inorder to match the OSSE upper limit. An extrapolation ofthe two-component spectrum back to the X-ray band isconsistent with the Ñux seen in the 1È2 keV range, suggest-ing that the spectrum could be continuous across Ðvedecades in energy.

Integrating either equation (2) or (3) gives a photon Ñuxabove 100 MeV of (1.9^ 0.2)] 10~7 ph cm~2 s~1, wherethe errors are statistical only. The di†erence between thisvalue and the value in ° 4.2 gives a measure of the system-atic uncertainty that can be introduced by the two di†erentanalysis methods. The spectrum derived here is signiÐcantlysteeper than that found in the original detection of thispulsar by Fierro et al. (1993), which had a power law indexof 1.18 ^ 0.16 between 100 MeV and 4 GeV, based on justÐve broad energy bands. The di†erence appears to arisefrom the increase in statistics, already noted by Fierro(1995). In particular, the spectrum is now seen down to 70MeV and up past 4 GeV with no indication of a high-energyspectral break. The 4È10 GeV band represents an excess ofÐve photons, none of which exceed 7 GeV. This data pointdoes not, therefore, constrain the spectral shape, whichcould have either a sharp cuto†, a gradual cuto†, or nocuto† below 10 GeV. The lack of pulsed emission in theTeV range as seen by CANGAROO (Susukita 1997)requires a steepening in the spectrum at some energy abovethe range detected by EGRET.

5. DISCUSSION

5.1. L ight CurveThe overall gamma-ray light curve for PSR B1055[52

di†ers from those of most of the other gamma-ray pulsars.The Crab, Vela, Geminga, and PSR B1951]32 light curvesare all characterized by two narrow pulses separated by0.4È0.5 in phase. PSR B1509[58 (detected up to 10 MeV,Kuiper et al. 1998) has a well-deÐned single pulse. PSR

B1055[52 shows two broader pulses with a phase separa-tion of about 0.2, similar to PSR B1706[44. What iscommon to all the pulsars seen above 100 MeV is thedouble pulse shape, suggestive of a hollow cone or similargeometry and consistent with the idea that these relativelyyoung pulsars radiate primarily from the magnetosphericregion associated with one magnetic pole of the neutronstar (e.g., Manchester 1996).

Comparison with the pulsar light curves at lower fre-quencies, Figure 2, shows that the emission is quite compli-cated. The broad hard X-ray pulse coincides approximatelyin phase but not in shape with the high-energy gamma-raylight curve, and neither of these light curves resembles thatseen in soft X-rays or radio. One component of the softX-ray pulse is aligned with one of the radio pulses, but it hasbeen argued based on radio polarization studies that theother radio pulse is the one that deÐnes the closestapproach to the magnetic pole (Lyne & Manchester 1988).With pulsed emission at some wavelength seen during morethan half the rotation of the neutron star, it would seemdifficult to have all these components originating in oneregion of the magnetosphere.

5.2. DistanceThe distance determined from the dispersion measure

30.1 cm~3 pc (Taylor & Cordes 1993) is 1.5 (^0.4) kpc.Independent distance limits derived from H I absorption orother indicators are not available for this pulsar (Taylor,Manchester, & Lyne 1993). In their analysis of the ROSATX-ray data, & Finley (1993) found that a distanceO� gelmanof 500 pc would produce a more realistic estimate of theneutron star radius (15 km compared to 30 km for the 1.5kpc distance estimate), although Greiveldinger et al. (1996)derived an estimate of km assuming a distance of 118~4`15kpc. Combi, Romero, & (1997) derive a distanceAzca� rateestimate of 700 pc from a study of the extended nonthermalradio source around the pulsar. For this work, we use the1.5 kpc distance derived from the dispersion measure, rec-ognizing that the pulsar may be somewhat closer.

5.3. L uminosity and BeamingIn terms of the observed energy Ñux the luminosity ofF

E,

a pulsar is

L c \ 4nfFED2 , (5)

where f is the fraction of the sky into which the pulsarradiates and D is the distance to the pulsar. This beamingfraction f is uncertain. In a nearly aligned rotator model,Sturner & Dermer (1994) Ðnd a beaming fraction of lessthan 0.1, while an outer-gap model (Yadigaroglu & Romani1995) suggests a value of 0.18. In comparing the EGRET-detected pulsars, Thompson et al. (1994) adopted a value of1/4n.

The observed energy Ñux obtained by integrating equa-tion (3) in the range 70È10 GeV is (1.9^ 0.2)] 10~10 ergscm2 s~1. For a distance of 1.5 (^0.4) kpc, the gamma-rayluminosity of PSR B1055[52 is then (4 ^ 2)] 1033 ] 4n fergs s~1. Unless the beaming fraction is extremely small(compared to the assumed value of 1) or the distance is lessthan 1 kpc, the observed gamma radiation represents about6%È13% of the spin-down luminosity, ergE0 \ 3 ] 1034s~1. In light of the fact that the pulsar is not seen at TeVenergies (Susukita 1997), the spectrum must show a furthersteepening somewhere above the EGRET range, and the


luminosity is dominated by the radiation observed in thegamma-ray band. Extrapolating equation (3) to cover theentire range 1 keV to 30 GeV produces an energy Ñux andcorresponding luminosity just 50% larger than that actuallymeasured by EGRET in the 70È10,000 MeV range.

5.4. Pulsar ModelsTwo general classes of models have been proposed for

high-energy pulsars. In polar cap models (recent examples :Daugherty & Harding 1994, 1996 ; Sturner & Dermer 1994 ;Usov & Melrose 1996 ; Rudak & Dyks 1998), the particleacceleration and gamma-ray production take place in theopen Ðeld line region above the magnetic pole of theneutron star. In outer gap models (recent examples :Romani & Yadigaroglu 1995 ; Zhang & Cheng 1997 ; Wanget al. 1998), the interaction region lies in the outer magneto-sphere in vacuum gaps associated with the last open Ðeldline. Other models include a hybrid model (Kamae & Seki-moto 1995) and a Deutsch Ðeld model (Higgins & Henrik-sen 1997, 1998). Romero (1998) discusses current models inlight of the PSR B1055[52 observations.

Because all these models can be viewed as having ahollow surface geometry, a double pulse has a straightfor-ward explanation. The observerÏs line of sight cuts acrossthe edge of the cone at two places. Although the speciÐcdetails depend on the size of the beam and its relationshipto the rotation axis and the observerÏs line of sight, in thecase of PSR B1055[52, one possibility is that the line ofsight is closer to the edge of the cone than for the pulsarswith two widely spaced light curve peaks. The fact that thepeaks are broader for PSR B1055[52 is also consistentwith this geometric picture, because the line of sight crossesthe cone at a shallower angle.

In the polar cap models, a sharp turnover is expected inthe few to 10 GeV energy range owing to attenuation of thegamma ray Ñux in the magnetic Ðeld (Daugherty & Harding1994). The outer gap model predicts a more gradual turn-over in the same energy range (Romani 1996). The presentobservations do not conÑict with either model.

6. PSR B1055[52 IN COMPARISON TO OTHER

GAMMA-RAY PULSARS

In addition to the CGRO, other space- and ground-basedobservatories have provided a wide range of results onpulsars. Multiwavelength energy spectra provide one usefulway of comparing di†erent pulsars across the electromag-netic spectrum. In particular, such spectra can address suchquestions as the number of di†erent emission componentsrequired. Figure 4 shows the broadband energy spectra ofthe seven known gamma-ray pulsars. The format is a orlFlE2] Flux spectrum, showing the observed power perlogarithmic energy interval. What is shown is emission fromclose to the neutron star itself, either pulsed or seen as aspatially pointlike source. Although likely to be powered bythe pulsar, any nebular emission is excluded. References forthis Ðgure are given in Table 3. An earlier version of thisÐgure was given by Thompson (1996).

These multiwavelength spectra have some common fea-tures :

1. The radio emission appears to be distinct from thehigher energy emission. In most cases, the radio spectrashow decreasing power at higher frequencies. The high-energy radiation power rises from the optical to the X-rayband. It has long been thought that the radio is a coherent

process, while the high-energy radiation results from inco-herent physical processes.

2. In all cases, the maximum observed energy output is inthe gamma ray band. The peak ranges from photon ener-gies of about 100 keV for the Crab to photon energies above10 GeV for PSR B1951]32. This feature emphasizes thatthese pulsars are principally nonthermal sources with par-ticles being accelerated to very high energies.

3. All these spectra have a high-energy cuto† or break.For PSR B1509[58, it occurs not far above 10 MeVphoton energy (Kuiper et al. 1999) ; for PSR B1951]32 itmust lie somewhere above 10 GeV, between the highestenergy EGRET point and the TeV upper limit. As discussedabove, the origin of this break can be explained in di†erentways by di†erent models.

Based on their known timing ages and spectral features,these seven pulsars can be divided into two groups : theyoung (D1000 yr old) pulsars, and the older pulsars. With atiming age of about half a million years, PSR B1055[52 isthe oldest of the gamma-ray pulsars.

6.1. Y oung PulsarsBoth the Crab and PSR B1509[58 have high-energy

spectra that could be continuous from the optical to thehigh-energy gamma-ray range. In particular, neither showsevidence of thermal emission from the neutron star surfaceor atmosphere (see Becker & 1997 for a summaryTru� mperof soft X-ray properties of neutron stars), although theseyoung neutron stars are expected to be hot ([106 K; seePage & Sarmiento 1996, for a summary). The magneto-spheric emission from accelerated particles strongly domi-nates the observed radiation, even in the soft X-ray band.

In the case of PSR B1509[58, the high-energy emissionis only observed with certainty from the soft X-ray tomedium gamma-ray energy ranges. There is a candidateoptical counterpart (Caraveo, Mereghetti, & Bignami 1994),but the absence of pulsations and the possibility of a chancecoincidence leave some doubt that it is actually the pulsar(Chakrabarty & Kaspi 1998 ; Shearer et al. 1998a) ; hence weshow the counterpart as an upper limit. Additionally, all thepoints above 5 MeV (about 1021 Hz) are upper limits,although detection by COMPTEL is now reported up to 10MeV (Kuiper et al. 1999). In particular, the EGRET limits(Brazier et al. 1994 ; Nel et al. 1996), compared with theOSSE (Matz et al. 1994) and COMPTEL (W. Hermsen1997, private communication) detections show that thespectrum must bend between 10 and 100 MeV. This spec-tral feature in the MeV range is unlike those seen in any ofthe other gamma-ray pulsars and is probably attributableto the high magnetic Ðeld of PSR B1509[58 (e.g., Harding,Baring, & Gonthier 1997)

6.2. Older PulsarsAll Ðve older gamma-ray pulsars share the spectral

feature of having their maximum luminosity in the high-energy gamma-ray regime. In the case of PSRs B1951]32and B1055[52, the actual peak luminosity lies near orbeyond the highest energy EGRET detection of the pulsars,although the TeV limits require a turnover in the 10È300GeV range. The two brightest and closest of these pulsars,Vela and Geminga, show relatively sharp spectral turnoversin the few GeV energy range. PSR B1706[44 is welldescribed by two power laws, with a spectral slope change


FIG. 4.ÈMultiwavelength energy spectra for the known gamma-ray pulsars. References for this Ðgure are given in Table 3.

(*a^ 1) at 1 GeV. As discussed above, PSR B1055[52 isconsistent with also having a spectral change at 1 GeV,although smaller in magnitude than that seen in PSRB1706[44.

The three older gamma-ray pulsars that are the strongestX-ray sources (Vela, Geminga, and PSR B1055[52) allshow evidence of thermal emission (as does PSRB0656]14, a possible eighth gamma-ray pulsar) consistentwith emission from near the neutron star surface. This com-ponent of the emission is clearly distinct from the non-thermal hard X-rays and gamma-rays. Whether the hardX-ray component seen in these pulsars extends to gamma-ray energies is problematic. In the case of Geminga, thehard component appears to extrapolate below the EGRETobservations (Halpern & Wang 1997).

6.3. High-Energy L uminosityExcept for the thermal peak seen in three of the pulsars of

Figure 4, the optical through gamma-ray spectra are fairlycontinuous, suggesting an origin in a single population ofaccelerated particles, though perhaps with two or moreemission mechanisms. The broadband spectra can be usedto derive a high-energy luminosity, for these pulsars,L HE,including all the observed radiation. Integrating theobserved spectra to derive the energy Ñux is a Ðrst step,F

Ealthough some assumptions must be made for bands wherethe pulsars are not seen. In most cases, the luminosity isdominated by the energy range around the peak in the lFlspectrum, as noted for PSR B1055[52 (so that the thermalpeaks seen for Vela, Geminga, and PSR B1055[52 make

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GAMMA RADIATION FROM PSR B1055[52 305

no signiÐcant contribution). Only in the case of the Crab isit necessary to include all the radiation from optical to high-energy gamma rays in order to estimate the luminosity. Inthe cases of PSR B1509[58 and PSR B1951]32, the shapeof the spectrum above the peak is unknown. We haveassumed a spectral slope change of *a\ 1.5, a valuebetween the sharp turnover seen for Vela and Geminga andthe shallower slope change for PSR B1055[52 and PSRB1706[44.

As discussed above, there are two signiÐcant uncer-tainties in converting from into high-energy luminosity :F

Ethe beaming fraction and the distance. For the distance, wetake the radio measurements and include a 25% uncer-tainty, the typical value estimated by Taylor & Cordes(1993) for these pulsars. The beaming fraction is modeldependent, but cannot exceed 1. The fact that the high-energy pulses are typically broad suggests, but does notprove, that the beam is not tiny. We therefore adopt a valueof 1/4n, assuming radiation into 1 sr, as an intermediatevalue, easily scaled for comparison with models. In mostX-ray papers, luminosity is calculated assuming radiationinto 4n. If this same assumption were made for PSRB1055[52, the gamma rays would represent 160% of thespin-down luminosity for the nominal distance of 1.5 kpc,E0or 80% for a distance of 1 kpc. The rotational energy loss ofthe neutron star, as the energy source, must Ðrst accelerateparticles that then radiate gamma rays. It seems highlyunlikely for such processes to take place with approx-imately 100% efficiency. The smaller assumed beaming frac-tion in this work should be taken into account whencomparing with X-ray luminosities such as those in thesummary of Becker & (1997). Because the distanceTru� mperenters the luminosity calculation as the second power, itsuncertainty is likely to dominate.

Table 4 summarizes some observed and derived proper-ties of the seven gamma-ray pulsars, including the inte-grated energy Ñux and high-energy (optical and above)luminosities calculated here. The efficiency g is the ratio ofthe high-energy luminosity to the total spin-down lumi-nosity. Rudak & Dyks (1998) Ðnd similar numbers in theirsummary of published gamma-ray pulsar results.

Figure 5 shows the high-energy luminosity, integratedover photon energies above 1 eV under the above assump-tions, as a function of the Goldreich-Julian current N0 ^ 1.7

particles s~1(Goldreich & Julian 1969 ;] 1038P0 1@2P~3@2Harding 1981), which is also proportional to the open Ðeldline voltage volts (D B/P2, where BV ^ 4 ] 1020P0 1@2P~3@2is the surface magnetic Ðeld ; Ruderman & Sutherland1975). Both V and are proportional to (see Fig. 7 ofN0 E0 1@2Arons 1996 and Figure 2 of Rudak & Dyks 1998). Althoughnot a perfect Ðt, this relationship is a reasonable approx-

FIG. 5.ÈPulsar luminosities, integrated over photon energies above 1eV, assuming radiation into one sr, vs, Goldreich-Julian current .N0 DE0 1@2

imation extending for more than 2 orders of magnitude.This proportionality would be expected if either (1) allpulsars accelerate particles to the same energy but the parti-cle current di†ers from pulsar to pulsar or (2) the particleÑow is constant, with di†erent pulsars accelerating particlesto di†erent energies (Thompson et al. 1997). As noted byArons (1996), this simple trend cannot extend to muchlower values of V or because more than 100% efficiencyN0 ,for conversion of spin-down luminosity would be implied.Nevertheless, Figure 5 shows a useful parameterization ofhigh-energy pulsar properties with straightforward (thoughnot unique) physical interpretations. As noted by Goldoni& Musso (1996), other simple parameters are not well corre-lated with the observed properties of these pulsars. TheÐgure is similar to a pattern seen in 0.1È2.4 keV X-rays byBecker & (1997). The slope of the line in Figure 5Tru� mperis Ñatter than the one found by Becker & (1997),Tru� mperbecause the integrated luminosity is dominated by thegamma rays, and the pulsars with smaller are also theE0older pulsars that have Ñatter energy spectra.

7. SUMMARY

PSR B1055[52 is one of at least seven spin-poweredpulsars seen at gamma-ray energies. Observations fromtelescopes on the CGRO between 1991 and 1998 have pro-vided new details of the gamma radiation :

1. The light curve has two peaks separated by about 0.2in phase. Only PSR B1706[44 shows a similar light curve.

2. There is no detectable unpulsed gamma radiationfrom the pulsar.

TABLE 4

SUMMARY PROPERTIES OF THE KNOWN GAMMA-RAY PULSARS

P q E0 FE

d L HE gName (s) (y) (erg s~1) (erg cm~2 s~1) (kpc) (erg s~1) (E[ 1 eV)

Crab . . . . . . . . . . . . 0.033 1300 4.5 ] 1038 1.3] 10~8 2.0 5.0] 1035 0.001B1509[58 . . . . . . 0.150 1500 1.8 ] 1037 8.8] 10~10 4.4 1.6] 1035 0.009Vela . . . . . . . . . . . . . 0.089 11,000 7.0] 1036 9.9] 10~9 0.5 2.4] 1034 0.003B1706[44 . . . . . . 0.102 17,000 3.4] 1036 1.3] 10~9 2.4 6.9] 1034 0.020B1951]32 . . . . . . 0.040 110,000 3.7] 1036 4.3] 10~10 2.5 2.5] 1034 0.007Geminga . . . . . . . . 0.237 340,000 3.3] 1034 3.9] 10~9 0.16 9.6] 1032 0.029B1055[52 . . . . . . 0.197 530,000 3.0] 1034 2.9] 10~10 1.5 6.2] 1033 0.207

306 THOMPSON ET AL.

3. There is no evidence that the gamma-ray Ñux from thepulsar varies on long timescales.

4. The gamma-ray energy spectrum above 70 MeV canbe represented by a power law with photon index [1.73.There may be a break in the spectrum at D1000 MeV.

5. The maximum observable power from the pulsar is inthe gamma-ray energy range.

6. The observed gamma radiation represents about6%È13% of the spin-down luminosity of the pulsar,although the unknown beaming geometry and distanceuncertainty make this estimate rather uncertain. Themaximum observable power from the pulsar is in thegamma-ray energy range.

7. A comparison of PSR B1055[52 with the othergamma-ray pulsars shows that this is the oldest and mostefficient in converting spin-down luminosity into high-energy radiation.

The EGRET team gratefully acknowledges support fromthe following : Bundesministerium fur Forschung und Tech-nologie, Grant 50 QV 9095 (Max-Planck-Institut Extra-fu� rterrestrische Physik authors), and NASA GrantNAG5-1742 (Hampden-Sydney College) ; NASA GrantNAG5-1605 (Stanford University).

REFERENCESArons, J. 1996, A&AS, 120, 49Arzoumanian, Z., Nice, D. J., Taylor, J. H., Thorsett, S. E. 1994, ApJ, 422,

671Becker, W., & J. 1997, A&A, 326, 682Tru� mper,Bennett, K., et al. 1993, Proc. 23rd Int. Cosmic-Ray Conf. (Calgary), 1, 172Biggs, J. D. 1990, MNRAS, 246, 341Brazier, K. T. S., et al. 1994 MNRAS, 268, 517Caraveo, P. A., Mereghetti, S., & Bignami, G. F. 1994 ApJ, 423, L125

A. et al. 1995, A&A, 304, 258Carramin8 ana,Chadwick, P. M. et al. 1997, Proc. 25th Int. Cosmic-Ray Conf. (Durban), 3,

189Chakrabarty, D. & Kaspi, V. M. 1998, ApJ, 498, L37Chang, H.-K., & Ho, C. 1997, ApJ, 479, L125Combi, J. A., Romero, G. E., & I. N. 1997, ApSS, 250, 1Azca� rate,DÏAmico, N. et al. 1996 ApJS, 106, 611Daugherty, J. K., & Harding, A. K. 1994, ApJ, 429, 325ÈÈÈ. 1996, ApJ, 458, 278Davidson, K., et al. 1982 ApJ, 253, 696De Jager, O. C., Swanepoel, J. W. H., & Raubenheimer, B. C. 1978 A&A,

221, 180Downs, G. S., Reichley, P. E., & Morris, G. A. 1973, ApJ, 181, L143Fegan, D. J., et al. 1993, in AIP Conf. Proc. 280, Compton Gamma Ray

Observatory, ed. Friedlander, M., Gehrels, N., & Macomb, D. J. (NewYork : AIP), 223

Fierro, J. M. 1995, Ph.D. thesis, StanfordFierro, J. M., et al. 1993, ApJ,413, L27ÈÈÈ. 1995, ApJ, 447, 807Fierro, J. M., Michelson, P. F., Nolan, P. L., Thompson, D. J. 1998, ApJ,

494, 734Finley, J. P., et al. 1998, ApJ, 493, 884Goldoni, P., & Musso, C. 1996, A&AS, 120, 103Goldreich, P., & Julian, W. H. 1969 ApJ, 157, 869Greiveldinger, C., et al. 1996, ApJ, 465, L35Halpern, J. P., & Ruderman, M. 1993, ApJ, 415, 286Halpern, J. P., & Wang, F. Y.-H. 1997, ApJ, 477, 905Harding, A. K. 1981, ApJ, 245, 267Harding, A. K., Baring, M., & Gonthier, P. L. 1997, ApJ, 476, 246Harnden, F. R., Jr., & Seward, F. D. 1984, ApJ, 283, 279Hartman, R. C. 1998, ApJS, submittedHermsen, W. et al. 1993, in AIP Conf. Proc. 280, Compton Gamma Ray

Observatory, ed. Friedlander, M., Gehrels, N., & Macomb, D. J. (NewYork : AIP), 204

Higgins, M. G., & Henriksen, R. N. 1997, MNRAS, 292, 934ÈÈÈ. 1998, MNRAS, 295, 188Hunter, S. D., et al. 1997, ApJ, 481, 205Johnston, S., et al. 1992, MNRAS, 255, 401Johnston, S., Manchester, R. M., Lyne, A. G., Kaspi, V. M., DÏAmico, N.

1995, A&A, 293, 795Johnson, W. N., et al. 1993 ApJS, 86, 693Kamae, T. & Sekimoto, Y. 1995, ApJ, 443, 780Kanbach, G., et al. 1994, A&A, 289, 855Kaspi, V. M. 1994, Ph.D. thesis, PrincetonKawai, N., Okayasu, R., & Sekimoto, Y. 1993, in AIP Conf. Proc. 280,

Compton Gamma Ray Observatory, ed. Friedlander, M., Gehrels, N., &Macomb, D. J. (New York : AIP), 213

Knight, F. K. 1982, ApJ, 260, 538Kuiper, L., et al. 1998, A&A, 337, 421Kuiper, L., et al. 1999, A&A, in preparationKulkarni, S. R., et al. 1988, Nature, 331, 50Kuzmin, A. D., & Losovsky, B. Ya. 1997, Russian Astr. Lett., 23, 341Lyne, A. G., & Manchester, R. N. 1988, MNRAS, 234, 477Mahoney, W. A., Ling, J. C., & Jacobson, A. S. 1984, ApJ, 278, 784Manchester, R. N. 1971, ApJ, 163, L61Manchester, R. N. 1996, in ASP Conf. Ser. 105, Pulsars : Problems and

Progress, ed. M. Bailes, S. Johnston, M. Walker (San Francisco 105), 193

Manchester, R. N., Wallace, P. T., Peterson, B. A., & Elliott, K. H. 1980,MNRAS, 190, 9P

Mattox, J. R., et al. 1996 ApJ, 461, 396Matz, S. M., et al. 1994, ApJ, 434, 288Mayer-Hasselwander, H. A., et al. 1994 ApJ, 421, 276Middleditch, J., Pennypacker, C., & Burns, M. S. 1983, ApJ, 273, 261Mignani, R., Caraveo, P. A., & Bignami, G. F. 1997, ApJ, 474, L51Much, R., et al. 1995, A&A, 299, 435Nel, H. I., et al. 1993, ApJ, 418, 836ÈÈÈ. 1996, ApJ, 465, 898Nolan, P. L., et al. 1993, ApJ, 409, 697

H. B., & Finley, J. P. 1993, ApJ, 413, L31O� gelman,Finley, J. P., & Zimmerman, H. U. 1993, Nature, 361, 136O� gelman,

Oke, L. B. 1969, ApJ, 156, L49Page, D., & Sarmiento, A. 1996, ApJ, 473, 1067Percival, J. W., et al. 1993, ApJ, 407, 276Pravdo, S. H., & Serlemitsos, P. J. 1981, ApJ, 246, 484Ramanamurthy, P. V., et al. 1995a, ApJ, 447, L109ÈÈÈ. 1995b, ApJ, 450, 791ÈÈÈ. 1996, ApJ, 458, 755Rankin, J. M., & Sutton, D. H. 1970, Nature, 226, 69Ray, A., Harding, A. K., & Strickman, M. 1999, ApJ, 513, 919Rickett, B. J., & Seiradakis, J. H. 1982, ApJ, 256, 612Romani, R. W., & Yadigaroglu, I. -A. 1995, ApJ, 438, 314Romani, R. W. 1996, ApJ, 470, 469Romero, G. E. 1998, Revista Mexicana de y 34, 29Astronom•� a Astrof•� sica,Rudak, B., & Dyks, J. 1998, MNRAS, 295, 337Ruderman, M., & Sutherland, P. 1975, ApJ, 199, 51SaÐ-Harb, S., H. B., & Finley, J. P. 1995, ApJ, 439, 722O� gelman,

V., et al. 1993 ApJS, 86, 657Scho� nfelder,Schroeder, P. C., et al. 1995, ApJ, 450, 784Seiradakis, J. H. 1992, IAU Circ. 5532Seward, F. D., Harnden, F. R., Szymkowiak, A., & Swank, J. 1984, ApJ,

281, 650Shearer, A., et al. 1998a, A&A, 333, L16ÈÈÈ. 1998b, A&A, 335, L21Shitov, Yu. P., & Pugachev, V. D. 1998, NewA 3, 101Sreekumar, P., et al. 1998, ApJ, 494, 523Srinvasen, R., et al. 1977, ApJ, 489, 170Strickman, M. S., et al. 1993, in AIP Conf. Proc 280, Compton Gamma

Ray Observatory, ed. Friedlander, M., Gehrels, N., & Macomb, D. J.(New York : AIP), 209

Sturner, S. J., & Dermer, C. D. 1994, ApJ, 420, L79Susukita, R. 1997, Ph.D. thesis, Inst. Physical and Chemical Research,

Wako, JapanTaylor, J. H., & Cordes, J. M. 1993, ApJ, 411, 674Taylor, J. H., & Weisberg, J. M. 1989, ApJ, 345, 434Taylor, J. H., Manchester, R. N., & Lyne, A. G. 1993, ApJS, 88, 529Thompson, D. J. 1996, in ASP Conf. Ser. 105, Pulsars : Problems and

Progress, ed. M. Bailes, S. Johnston, & M. Walker (San Francisco : ASP),307

Thompson, D. J., et al. 1993 ApJS, 86, 629ÈÈÈ. 1994, ApJ, 436, 229ÈÈÈ. 1995, ApJS, 101, 259ÈÈÈ. 1996, ApJ, 465, 385ÈÈÈ. 1997, in AIP Conf. Proc. 410, Proc. Fourth Compton Symp., ed. C.

D. Dermer, M. S. Strickman, & J. D. Kurfess (New York : AIP), p. 39Ulmer, M. P. 1994, ApJS, 90, 789Ulmer, M. P. et al. 1993, ApJ, 413, 738Usov, V. V., & Melrose, D. B. 1996, ApJ, 464, 306Wang, F. Y.-H., Ruderman, M., Halpern, J. P., & Zhu, T. 1998, ApJ, 498,

373Yadigaroglu, I. -A., & Romani, R. W. 1995, ApJ, 449, 211Yoshikoshi, T., et al. 1997 ApJ, 487, L65Zhang, L., & Cheng, K. S. 1997 ApJ, 487, 370

Gamma Radiation from PSR B1055-52

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