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Prospects of observing pulsed radiation from gamma-ray pulsars with H.E.S.S

a r X i v :a s t r o -p h /0010179v 1 10 O c t 2000

Prospects of observing pulsed radiation from gamma-ray pulsars with H.E.S.S.

O.C.de Jager 1,A.Konopelko 2,B.C.Raubenheimer 1and

B.Visser 1

1Unit for Space Physics,Potchefstroom University,Potchefstroom,2520,South Africa 2

Max Planck Institut f¨u r Kernphysik,Postfach 103980,D-69029Heidelberg,Germany

Abstract.Observations and theoretical studies have demonstrated that the pulsed spectra of all gamma-ray pulsars terminate at energies below a few hundred GeV.In most cases we expect this cuto?energy E o to be around 10GeV.Only with next-generation ground-based γ-ray telescopes,which are expected to have non-zero trigger probabilities near 10GeV,can we expect to detect pulsations.The large γ-ray ?uxes below E o ,together with the associated sharp pulse pro?les,compensate for the lack of imaging capability near threshold.For H.E.S.S.we ?nd that the pulsed component of PSR B1706-44should be detectable near threshold,whereas the unidenti?ed GeV EGRET sources should be detectable if the superexponential cuto?energy is larger than ~30GeV for relatively hard pulsar photon spectra (~E ?1.5).

A Introduction

Whereas gamma-ray pulsars are known to count amongst the brightest sources in the 1-30GeV range (Lamb &Macomb,1997),only their plerions,supernova shells and extragalactic sources appear to be visible at TeV energies.This is not unexpected,since pulsed γ-rays are known to be created in strong magnetic ?elds and magnetic pair production results in a superexponential cuto?above a charac-teristic energy E o .Simulations of pair cascades have shown that E o is usually in the 10GeV region (Daugherty &Harding,1996),but this cuto?depends on several parameters,such as the altitude of γ-ray production above the polar cap,the ob-server’s viewing angle relative to the spin axis,and the magnetic inclination angle relative to the spin axis.A γ-ray/e +/?cascade develops and those photons which escape pair creation (with E

dN γ/dE =k (E/E n )?g exp (?(E/E o )b ).

(1)

Whereas pulsar photon spectral indices between g=1.4and2.1are observed, harder spectra are theoretically possible(A.K.Harding,2000,personal communi-cation to O.C.de Jager).The constant k represents the monochromatic?ux at the normalising energy E n?E o.We will normalise spectra at E n=1GeV.

In the case of the outergap model for pulsars(Cheng,Ho,&Ruderman1996),γ-ray production is expected to occur near the pulsar light cylinder,and the cuto?is expected to result from energetics arguments,rather than from magnetic pair production.In this case a larger E o may be observable.Ground-based TeVγ-ray observations however provide?rm upper limits on E o.(Nel et al.(1993)gave a detailed discussion on this topic;see also Catanese&Weekes1999.)

B Gamma-Ray Pulsar Spectral Parameters above1GeV Table1shows the parameter results of a?t to the total pulsed spectra of the six brightest EGRETγ-ray pulsars.These spectral parameters reproduce the EGRET ?ux up to30GeV,and are consistent with the TeV pulsed limits.They also reproduce the GeV source catalog?ux(Lamb&Macomb1997).In the case of Vela and Geminga the cuto?s are well de?ned by the EGRET data and the errors on E o are relatively small(~20%).In the case of Crab and PSR B1055-52,some evidence of a turnover is seen in the spectra above10GeV,although it is di?cult to obtain reliable measures of E o and b.In the case of PSR B1951+32and PSR B1706-44we see no evidence of a turnover up to30GeV,and a minimum value of E o=40GeV(consistent with EGRET)was selected.This value is conservative with respect to the H.E.S.S.response.For those cases where E o is not well de?ned, we have selected b=2(a value typical for a spectrum attenuated by magnetic pair production)to give conservative H.E.S.S.rates.

Using the H.E.S.S.collection area vs.energy A(E)for any2-telescope triggers (Konopelko2000),we were able to calculate the expected rates R p for pulsedγ-rays by integrating the product of A(E)dNγ/dE over all energies.The results for the six EGRET pulsars are shown in Table1(indicated by“R p”).It is clear that the rate for PSR B1706-44is the largest of all pulsars if E o is not smaller than40GeV.

C H.E.S.S.Sensitivity for Pulsedγ-Ray Mission

It was shown by de Jager,Swanepoel&Raubenheimer(1987)and de Jager

(1994)that the basic scaling parameter for any test for uniformity on the circle

(given a test period)is given by x=p

TABLE1.Gamma-ray spectral parameters above1GeV and corresponding H.E.S.S.rates and observation time for detection.Spectral references from Macomb&Gehrels(1999).

Crab24.0 2.0830*******

Vela138 1.628.0 1.71488400 Geminga73.0 1.42 5.0 2.276?1-

PSR B1951+32 3.80 1.74402 4.91801

PSR B1055-52 4.00 1.80202 4.58420 PSR B1706-4420.5 2.10402202401 FWHM(single peak),if B is taken as the Z2m test statistic with m=10harmonics (see e.g.de Jager,Swanepoel&Raubenheimer1987).In this case c=20.

A value of x=3would introduce a~3σDC excess in a spatial analysis,but assuming that we have no imaging capability for E o near the detection threshold, we have to rely on a timing analysis,which would give Z210~73,or a chance probability of7×10?8if the period is known,but0.03after multiplying with the

number of trials for a6hour observation if searching for periods as short as50ms.

A con?rming run(e.g.on a second night)should always be made to see if one of the few most signi?cant periods from the previous run have repeated itself-in this case at the~10?7level.

Using an additional topological software trigger,and selecting events by image size and angular shape,we were able to reject~99.2%of the triggered background events,while retaining95%of the source events.From a total background rate of 1kHz(Konopelko2000),we get R b=8Hz.This allows us to calculate detection sensitivities for periodicities:

From the GeV source catalogue,we?nd that the galactic unidenti?ed EGRET source(some may be pulsars-Lamb&Macomb1997)?uxes range from F(> 1GeV)=1to25×10?8cm?2s?1.Figures1and2give the H.E.S.S.sensitivity for a wide range of possible pulsar photon spectral indices between1and2,and requiring a marginal detection within T=3to6hours(assuming a minimum“DC signi?cance”of x=3):Figures1and2respectively show E o and T vs k,with the latter within the EGRET range as discussed above.Table1also shows T calculated in the same way,but assuming the spectral parameters of individual pulsars.

D Conclusions

It is clear that H.E.S.S.can only detect pulsars if E o exceeds~30GeV.Even weak EGRET sources may be detectable if the spectra are as hard as E?1,provided that E o exceeds the levels prescribed by Figure1.PSR B1706-44(for which E o is known to be at least as large as~40GeV)should be a H.E.S.S.candidate and

Prospects of observing pulsed radiation from gamma-ray pulsars with H.E.S.S

other similar pulsars(such as PSR B1951+32)may be similarly detectable within one night.If one cannot detect a clear signal within a single night,an exact timing solution would be required to do a coherent analysis over a long period of time. Whereas we have addressed the conservative polar cap model,any outergap com-ponent is expected to give a large value for E o(which is no challenge for H.E.S.S.), but k may be small for such pulsars.This will be treated in a separate paper.

References

Beran,R.J.1969,Ann.Math.Statist.,40,1196.

Catanese,M.&Weekes,T.C.1999,PASP,111(764),1193.

Cheng,K.S.,Ho,C.&Ruderman,M.A.1986,ApJ,300,500.

Daugherty,J.K.&Harding,A.K.1996,ApJ,458,278.

de Jager,O.C.,Swanepoel,J.W.H.&Raubenheimer,B.C.1986,A&A,170,187. de Jager,O.C.1994,ApJ,436,239.

Konopelko,A.2000,these proceedings.

Lamb,R.C.&Macomb,D.J.,1997,ApJ,488,872

Macomb,D.J.&Gehrels,N.1999,ApJ Suppl,120,335.

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