LOWER LIMITS ON PULSAR PAIR PRODUCTION MULTIPLICITIES FROM H.E.S.S. OBSERVATIONS OF PULSAR WIND NEBULAE

The Astrophysical Journal, 658:1177Y1182, 2007 April 1 # 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A. LOWER LIMITS ON PULSAR PAIR PRODUCTION MULTIPLICITIES FROM H.E.S.S. OBSERVATIONS OF PULSAR WIND NEBULAE O. C. de Jager 1 Unit for Space Physics, North-West University, Potchefstroom Campus, Potchefstroom 2520, South Africa; fskocdj@puk.ac.za Received 2006 September 16; accepted 2006 December 13 ABSTRACT One of the most fundamental questions in pulsar physics is the generation of pair cascading to explain radio through -ray pulsed emission. In this paper we derive the pair production multiplicity for pulsars from the very high energy (VHE) -ray spectra of their pulsar wind nebulae (PWNs), as measured by H.E.S.S., since the IC-generated -ray spectra are free from assumptions of the associated nebular magnetic field strength. Most VHE PWNs have been resolved by H.E.S.S., and since the VHE size is already consistent with the maximal expected PWN size of the sources considered in this paper, the age of the VHE emitting electrons must at least be comparable to the age of the pulsar. This allows us to integrate the Goldreich-Julian current over the lifetime of the pulsar, resulting in time averages higreater that 2000 and 500 for PSR B1509 58 and PSR B1823 13, respectively, whereas the H.E.S.S. data alone for Vela X indicate an anomalously low value, less than unity. The extreme brightness of Vela X in radio, however, indicates that most of the electrons from the pulsar have been reprocessed into the radio synchrotron domain, leading to an upper limit of hi < 4 ; 10 5, if we assume the minimal field strength of 1.7 Gderivedfroma comparison of H.E.S.S. and ASCA/ROSAT data of Vela X. Similar (large) numbers are, however, derived for PSR B1823 13 and PSR B1509 58 if we extrapolate the H.E.S.S.-derived electron spectra into the uncooled domain toward the unseen radio nebular domain. Such divergent limits on hi can be resolved by adding forthcoming GLAST data to H.E.S.S. information. Subject headings: ISM: jets and outflows pulsars: general pulsars: individual (PSR B1509 58, PSR B1823 13, PSR B0833 45) 1 Visiting scientist at the APC, Collège de France, 75231 Paris Cedex 05, France. 1177 1. INTRODUCTION Pair production has been central to the theory of pulsars that has been developed over the past 35 years (Goldreich & Julian 1969; Sturrock 1971; Arons & Scharlemann 1979; Daugherty & Harding 1982; Harding & Muslimov 1998; Hibschmann & Arons 2001b). Termination or severe inhibition of pair production also then defines the radio pulsar death line on the Ṗ-P diagram (Hibschmann & Arons 2001a; Harding et al. 2002) for radio pulsars. Models for nonthermal pulsar magnetospheric emission will always have the pair production multiplicity as fundamental output, but unless such models can predict the required pairs to explain both the observed radio pulse and the X-ray and -ray pulse intensity/spectrum/profile, they cannot be self-consistent. Such models may also then be of limited use in providing the necessary particle input in pulsar wind nebula ( PWN) models to predict the bolometric radio through X-ray and very high energy (VHE) -ray nebular fluxes. Furthermore, we know that the steep radio pulse spectra do not connect to the typical hard X-ray/ -ray pulsed spectra of pulsars. Even though the radiation mechanisms are completely different, this may imply that if we assume that the (lowest energy) radio-emitting electrons in the PWNs were previously associated with the ( lowest energy) radio pulsed emission before transport through the light cylinder into the nebula, whereas the ( highest energy) X-ray emitting nebular electrons were previously associated with the (highest energy) -ray pulsed emission in the pulsar magnetosphere, then the nebular radio and X-ray spectra may not connect smoothly. Although electrons suffer severe energy losses before escaping through the light cylinder, it is still conceivable to postulate two particle populations escaping through the light cylinder because, as we show in this paper, radio and High Energy Stereoscopic System ( H.E.S.S.) observations of Vela X support such a discontinuous distribution of nebular electrons, but we have to count electrons from both populations to measure correctly. The total numbers should remain conserved even though electron energies are significantly redistributed beyond the light cylinder, so that it is valid to measure from nebular observations. In de Jager et al. (1995) and du Plessis et al. (1995), we were probably the first to point out that Galactic pulsar wind nebulae (PWNs) in general (excluding the Crab Nebula) would be potentially detectable via the inverse Compton (IC) scattering of PWN electrons on the cosmic microwave background radiation (CMBR) and possibly via far-infrared photons from galactic dust. In de Jager et al. (1995) we derived analytical expressions for the expected VHE spectra based on the basic expressions of Blumenthal & Gould (1970) and for the measured X-ray spectral parameters of the PWN. These first calculations were crude, since they depended on pre-röntgensatellit (ROSAT ) X-ray fluxes and spectra derived from earlier primitive X-ray detectors. Our basic message, however, still holds; the nebular field strengths in these evolved post-crab nebulae would be smaller than the Crab nebular field strength, which allows relic VHE emitting electrons to accumulate over the pulsar lifetime while surviving synchrotron losses in the weaker (compared to Crab) nebular field strengths. Furthermore, the IC flux also does not depend on the nebular field strength, so that the number of electrons can be directly derived from observed nebular -ray spectra. It was, however, only recently that H.E.S.S. discovered a growing population of such post-crab PWNs. See, e.g., de Jager (2005) for

1178 DE JAGER Vol. 658 a review of the first few H.E.S.S. PWNs and Aharonian et al. (2006c) for additional candidate H.E.S.S. detections from the galactic plane scan. More candidates are now added on a frequent basis. We introduce a measurement of the time-averaged pair production multiplicity hi, defined as the ratio of the total amount of electrons and positrons escaping through the light cylinder since the birth of the pulsar (as introduced by Rees & Gunn 1974), relative to the total time-integrated Goldreich-Julian current (as suggested by J. Arons 2006, private communication). In the latter case, the birth period and the pulsar braking index (if not measured) enter as unknowns. The H.E.S.S. observations lead to a firm lower limit on the total number of electrons in the nebula, and by integrating the Goldreich-Julian current over the expected PWN lifetime, we can derive a lower limit on the hi. If the PWNs also reveal a radio synchrotron component, the true value of himay be much larger, since the number of radio-emitting electrons may exceed the corresponding number of VHE emitting electrons by far. We use VHE -ray observations of PWNs by H.E.S.S. to determine the time-averaged for (1) PSR B1509 58 in G320.0-1.2 (Aharonian et al. 2005a), (2) HESS J1825 137 associated with G18.0-0.7 and PSR B1823 13 (Aharonian et al. 2005b, 2006a), and (3) Vela X associated with the Vela pulsar (Aharonian et al. 2006b). Only in the latter case is a clear radio nebula associated with Vela X, and we also give a firm upper limit for hi. We also review evidence for an electron (and hence IC) or hadronic origin for the -rays from these PWNs. 2. MEASURING THE ELECTRON SPECTRA OF PWNs VIA -RAY OBSERVATIONS As an alternative to inverse Compton scattering in PWNs, Bednarek & Bartosik (2003) suggested nucleonic interactions to explain any observable VHE -ray signal from the jetlike PWN of PSR B1509 58. Since the northern jet interacts with the dense nebula RCW 89 (Gaensler et al. 2002; Dubner et al. 2002), Bednarek & Bartosik (2003) were tempted to invoke a nucleonic rather than an electron IC prediction for this PWN, as originally proposed by us in du Plessis et al. (1995). In their model, the VHE signal from PSR B1509 58 should come from RCW 89, given their assumption that nuclei from the PWN jet would interact with dense material in this thermal nebula and produce -rays via 0 decay. However, H.E.S.S. observations of this PWN (Aharonian et al. 2005a) confirmed the jetlike feature, as seen in the lowdensity region below RCW 89 in X-rays, with no VHE emission from RCW 89 itself (Aharonian et al. 2005a). It is therefore clear that our original approach in du Plessis et al. (1995) for an IC origin was correct. Following the suggestion of a possible association of HESS J1825 137 (Aharonian et al. 2005b) with the PWN G18.0 0.7, more H.E.S.S. observations of this PWN have proven that the VHE PWN exhibits an energy-dependent morphology, with the size of the nebula shrinking toward increasing energies (converging toward the pulsar), while the photon index steepens by an amount of 0.5, which is expected for typical E 2 electron cooling due to synchrotron and/or IC losses (Aharonian et al. 2006a). H.E.S.S. detected a clear maximum in the spectral energy distribution from the cocoon of the Vela X PWN (Aharonian et al. 2006b). Even though the latter authors proposed a leptonic IC interpretation, Horns et al. (2006) proposed a nucleonic interpretation for the H.E.S.S. signal. Variability on the ion cyclotron wave timescale in a PWN shock can be taken as evidence of the existence of such ions (Amato & Arons 2006), and in the case of the Vela PWN we do see 1 month variability at the location of the PWN shock (Helfand et al. 2001). Horns et al. (2006) invoked a field strength of B 10 G in the cocoon to reduce the amount of IC scattering in favor of a hadronic signal, but ignored three aspects: 1. The X-ray and H.E.S.S. signals from the cocoon represent emission from mixed gasses of adiabatic indices ¼ 4/3 and 5/3 when the reverse shock of the Vela supernova remnant (SNR) pushed the PWN toward the south (Blondin et al. 2001). According to the latter authors, the crushing started 3000 years after the birth of the Vela SNR, whereas further two-dimensional magnetohydrodynamic (MHD) simulations show that the reverse shock for Vela (given a 4 forward shock radius) would have reached the center of the SNR (in the absence of the counterpressure of a PWN) after 5000 years (S. E. S. Ferreira & O. C. de Jager 2007, in preparation). The crushing process itself takes a few kyr to complete (Blondin et al. 2001). The southern region of the cocoon therefore represents the oldest electrons removed from the replenishing pulsar, with (E X ) ¼ (1:2 kyr)b 3/2 5 E 1/2 kev being the synchrotron lifetime of these electrons, of which the minimum should be comparable to the crushing timescale. Inserting a field strength of 10 G (i.e., B 5 ¼ 1), we get a lifetime of 400 yr for 10 kev emitting electrons, which represent the highest energy electrons from Figure 2 of Horns et al. (2006; labeled 60 0 TeV plerion ). This timescale is an order of magnitude smaller than the expected crushing timescales, but by reducing the field strength to 3 G, we get a more reasonable lifetime of 2.3 kyr, which would account for the displacement of the cocoon to the present southern position. 2. The total size of Vela X at 2.3 GHz is 3 ; 2,asderived from the Hartebeesthoek Radio Astronomy Observatory (HartRAO) wide field of view (FOV) sky map provided by J. Jonas (2006, private communication), whereas the H.E.S.S. cocoon size is 1 ; 0:72, giving a total Vela XYtoYcocoon volume ratio of 20. With the high required ion energy budget of 10 48 ergs (iron) to 10 49 ergs (protons), the authors invoked the early epoch of pulsar output to account for the observed -ray flux. However, protons ejected during such early epochs (and convected by the pulsar wind) should fill the total (old) radioemitting Vela X PWN and not just the smaller (and younger) cocoon. Thus, the total energy budget in Vela X implied by the H.E.S.S. detection will then be (to first order) 2 ; 10 49 ergs (for iron) to 2 ; 10 50 ergs (for protons). Furthermore, van der Swaluw & Wu (2001) estimated a birth period of P 0 40 ms for the Vela pulsar to account for the observed classical ratio of PWN radius to SNR radius of 0.25. The total integrated kinetic energy provided by the pulsar since birth is then 0:5I 2 0 ¼ 1:2 ; 10 49 ergs, which means that we may have a conversion efficiency of >100% of spin down power to ions in Vela X. 3. Another reason Horns et al. (2006) introduced the hadronic component for the signal is to account for the apparent low conversion efficiency of spin down power to leptons in the cocoon. Once again, to get the total energy in leptons, we have to take the bolometric spectrum from the total Vela X, which is one of the brightest radio sources in the sky. In x 4 (and Fig. 2, below) wefindthatthetotalleptonenergyintheradionebulaisw e ¼ 6:2 ; 10 47 ergs (for B ¼ 10 G) or 3:8 ; 10 48 ergs (B ¼ 3 G), giving respective conversion efficiencies of W e /(0:5I 2 0 ) ¼ 5% and 30% for the above-mentioned birth period of 40 ms. Thus, there does not appear to be a missing leptonic component, and it is clear is that most energy has been processed in the low-energy

No. 2, 2007 PAIR PRODUCTION MULTIPLICITIES FROM H.E.S.S. 1179 TABLE 1 Pulsar (ATNF Parkes Catalog) and PWN Parameters Name Period (s) Age Distance ( yr) Braking Index a ( pc) F(E ¼ 1 TeV) b c e d E 1 e (erg) N e f PSR B1509 58... 0.151 1550 2.84 5.1 5.7 ; 10 12 2.3 3.0 0.5 2.4 ; 10 48 PSR B1823 13... 0.101 21400 2.0 3.5 4.6 ; 10 12 2.3 3.0 0.3 2.5 ; 10 48 PSR B0833 45... 0.089 11300 3.0 0.29 6.4 ; 10 12 1.5 2.0 0.5 1.4 ; 10 45 a See text for the assumed braking index. b Monochromatic flux at 1 TeV (cm 2 s 1 TeV 1 ). c Average photon spectral index. d Average electron spectral index. e Minimum electron energy corresponding to the H.E.S.S. range. f Total number of electrons derived from the H.E.S.S. range. leptonic domain. However, there are also observational lower limits to the Vela X averaged field strength; using EGRET upper limits, de Jager et al. (1996) have shown that we can already constrain the volume-averaged field strength to hbi> (4 G)( b /10 11 Hz) 0:4,where b is the unknown radio spectral break frequency. GLAST LAT observations should either detect this radio counterpart of Vela X, or provide more stringent lower limits on hbi. This also calls for a separate study on variations in B; how does B in the cocoon differ relative to hbi,giventhe presence of filaments in the PWN, which would then introduce a filling factor for the PWN? Note that whereas point (3) shows that there is no missing leptonic energy component in Vela X, it does not disprove a nucleonic interpretation. Similarly, we may also invoke pathological SNR/pulsar/interstellar medium (ISM) parameters to get around point (2) in favor of a nucleonic interpretation, but point (1) offers a hard defense of a nucleonic interpretation; if the cocoon field strength is 10 G, Advanced Satellite for Cosmology and Astrophysics (ASCA) should not have seen nonthermal X-rays from the southern regions, where the electrons are no longer replenished by the pulsar during the postcrushing, offset PWN era. The problem can be further traced back to Figure 2 of Horns et al. (2006), where the physics discussion related to the cutoff at 20 kev in the 60 0 TeV plerion was ignored. This spectrum cannot be treated with simplistic assumptions and is expected to be the result of a two-stage process: pulsar injection during the precrushing phase and synchroton burn-off during the post crushing phase [source function Q(E ) ¼ 0], leading to the present day cutoff at 10Y20 kev. Thus, based on the previous arguments, we prefer to invoke a leptonic inverse Compton interpretation for the H.E.S.S. detection of Vela X, and we restore the following consistencies. The prebreak/cutoff electron spectral index (2.0) in the VHE domain (Aharonian et al. 2006b) would be perfectly consistent with the 2.0 spectral index of the uncooled electrons in the torus/jet region near the pulsar (within 1 0 ), as derived from the compact nebular photon index of 1.5 (Mangano et al. 2005). This electron index of 2.0 is indeed the uncooled spectral index, since further away from the pulsar (i.e., 15 0 ), the photon index steepens by 0.5 to 2.0, as expected for synchroton cooling, which corresponds to an electron spectral index of 3.0, as seen in X-rays, but only marginally by H.E.S.S., where most of the lower energy electrons contributing to the H.E.S.S. detection appear to be confined to the uncooled domain. However, care should be taken when attempting to model the southern tip of the cocoon because of the above-mentioned two-stage process. 3. PAIR PRODUCTION MULTIPLICITIES We take the total nebular VHE -ray spectra of PSR B1509 58, HESS J1825 137, and Vela X as measured by H.E.S.S. and find the electron spectra corresponding to the VHE -ray spectral band. If we were to use only the CMBR, the total number of observed electrons N e (obs) would be larger than estimates thereof if IC scattering on far-infrared photons due to the 25 K Galactic dust component is included. Approximations for these energy densities are given by GALPROP (Strong et al. 2000; Aharonian et al. 2005a), which indicates radiation energy densities for the starlight and 25 K dust component of the order of 1 ev cm 3 for sources at the positions of PSR B1509 58 and PSR B1823 13, whereas these numbers are comparable to the 0.25 ev cm 3 energy density for the CMBR in the solar neighborhood where Vela X is located. To obtain the total number of electrons/positrons in the nebula, we derive the electron spectra corresponding to the H.E.S.S. spectra above the minimum electron energies E 1 shown in Table 1. These threshold energies correspond to the -ray threshold energy, which is slightly different for each observed source. This table also lists the electron spectral index e that would reproduce the observed VHE -ray spectral indices as seen by H.E.S.S. Note that target photon fields, such as the galactic farinfrared and starlight photon fields, also tend to steepen the observed photon index to some degree (relative to the CMBR alone) because of Klein-Nishina cross section effects. The total number of electrons N e (obs) (for electron energies above E 1 ) contributing to the total H.E.S.S. flux for each source is listed in Table 1. The normalization constant for the total number of electrons was obtained after taking the dilution effect 4D 2 into account, with the assumed distances D for each source listed in Table 1 and references to these distances in the respective H.E.S.S. source papers. The Goldreich-Julian (GJ) current defines the rate at which electrons are stripped from the stellar surface of each polar cap. We calculate the expected total amount of GJ electrons from the pulsar by taking the reversed time integral over this current, integrated from the present time (t ¼ 0) into the past [t ¼ T(P 0 )] to give N GJ ¼ Z t¼ T ð P0 Þ t¼0 1=2 6cĖðÞ t e ð dtþ: ð1þ The time-dependent spin down power Ė(t) varies only with spin frequency (for a given pulsar braking index n) if we assume that the magnetic dipole moment remains constant over the lifetime

1180 DE JAGER Vol. 658 of H.E.S.S. emitting electrons (which can be as large as 50 kyr), so that Ėt ðþ ¼ I ¼ K nþ1 ; ð2þ with K a constant. The reverse-order time integral is obtained by working from the presently measured pulsar parameters and, as well as the pulsar braking index n, as obtained either from spin down measurements, or from SNR age constraints. In the latter case, van der Swaluw & Wu (2001) calculated the required initial spin period P 0 of several PWNs/SNRs to reproduce the observed forward shock radius of the SNR relative to its PWN outer radius. The average pair production multiplicity hi for electrons and positrons is then obtained from the ratio hi ¼ N e(obs) ; ð3þ 2N GJ Fig. 1. Plots of the time-averaged pair production multiplicity hirelative to the Goldreich-Julian current from two polar caps. The lines marked (i) refer to the minimal values of hias derived from H.E.S.S. data alone. Lines (ii) and (iii) refer to maximal values of hiarising from the addition of the radio-emitting component of Vela X, with (ii) corresponding to 8 G and (iii) to 1.7 G. with the factor 2 taking the two electron species (e )intoaccount. We obtain such a time-averaged value of for each pulsar. We remark first that this multiplicity is indicated as a lower limit, since we did not count those electrons with energies below the H.E.S.S. range. Second, even if the lifetime of H.E.S.S. emitting electrons is less than the true age T(P 0 ), this calculation of hi min would still represent a true lower limit, provided that we did not select T(P 0 ) too small (or P 0 too large). We do expect, however, that the H.E.S.S. emitting electrons lifetimes are comparable to or longer than the corresponding true ages, but this treatment is beyond the scope of this paper. Figure 1 plots the minimal pair production multiplicities for the three selected PWNs, as constrained by H.E.S.S. observations. Van der Swaluw & Wu (2001) obtained a birth period around 40 ms for most PWNs, where the ratio of the PWN radius R PWN to the SNR forward shock radius R 1 is of the order of 0.25. This ratio of 0.25 is observed and predicted for those PWNs for which the reverse shock has already returned to the PWN (van der Swaluw & Wu 2001). For PSR B1509 58, van der Swaluw & Wu (2001) inferred a ratio of R PWN /R 1 ¼ 0:17 and an expected birth period of 0.07 s, but note that the shape of the PWN is jetlike rather than spherical, so that we may expect large uncertainties for this pulsar birth period. For HESS J1825 137, de Jager et al. (2005) have shown that a ratio of R PWN /R 1 < 0:25 would imply a too large SNR forward shock radius, and we were forced to assume a braking index of n ¼ 2 to double the age of the SNR to 42 kyr, which would allow the SNR sufficient time to evolve to its expected present (but unseen) size of 4 times the size of HESS J1825 137. In de Jager et al. (2005) we even had to assume a low-density environment in the hot phase of the ISM to get to the required large size for the SNR forward shock. In Figure 1 we see that the time-averaged minimal values of hiare 500 for PSR B1823 13 and 2000 for PSR B1509 58 at P 0 ¼ 40 ms. The former two agree with the theoretical calculations of Hibschmann & Arons (2001b). Unfortunately, the PWN of PSR B1509 58 and PSR B1823 13 are not detectable in radio (Gaensler et al. 2000; Dubner et al. 2002), leaving the true lower limit on the electron energy weakly constrained, so that hishown in Figure 1 (derived from the H.E.S.S. minimum E 1 in Table 1) can be considered as a true lower limit (provided we can select a birth period with confidence). However, since further H.E.S.S. observations of HESS J1825 137 showed a gradual hardening of the electron spectrum toward lower energies and closer to the pulsar (Aharonian et al. 2006a), as expected for moving over a cooling break toward the uncooled domain, the electron spectral index below 0.3 ergs is expected to converge toward 2.0, given that the index of 3.0 in Table 1 represents the cooled index in the H.E.S.S. range. We can then extrapolate the electron spectrum toward lower energies to find a much higher value of hi ¼ 2 ; 10 5 1GeV E 0 ; ð4þ where E 0 1 GeV (i.e., well below E 1 in Table 1) is the assumed absolute (but unknown) minimum electron energy in the PWN. This extrapolation effectively takes care of the unseen radio component. Note that the hardening in the spectrum already becomes apparent at energies below 1 TeV, so that the above-mentioned number represents an upper limit, given our assumption of a spectral break at 0.3 TeV. However, future GLAST observations should show if the electron spectral index of HESS J1825 137 (associated with PSR B1823 13) finally converges toward an E 2 spectrum at -ray energies well below E 1 ¼ 300 GeV, giving us a more accurate measure of from lower energy data. 4. VELA X AND THE VELA PULSAR: A CASE FOR TWO ELECTRON SPECTRAL COMPONENTS From Figure 1 we see that the H.E.S.S. observations imply hi min 0:5 for the Vela pulsar as derived from the cocoon region. This low value for Vela is quite a surprise, given that Vela is the brightest radio pulsar in the sky, at 400 MHz (Australia Telescope National Facility [ATNF] Pulsar catalog, Parkes Radio Telescope), and it is also one of the most luminous -ray pulsars above 100 MeV, which certainly (qualitatively) requires the participation of significant amounts of electrons/positrons in the pulsar magnetosphere. In fact, in Sefako & de Jager (2003) we also introduced a new way of measuring by using the multiwavelength spectrum at the pulsar wind shock radius r s. The reason for this choice is that the spectrum at the shock represents the location where the accelerated electrons are injected into the nebula, and since they escape relatively fast downstream (with post shocked velocity V c/3), we basically measure the steady state spectrum N(E ) ¼ Q(E )r s /V with slight modifications due to adiabatic losses. Taking into account that IC observations

No. 2, 2007 PAIR PRODUCTION MULTIPLICITIES FROM H.E.S.S. 1181 Fig. 2. Electron spectra of Vela X as derived from H.E.S.S. and radio observations. The thick solid lines represent the electron energy ranges that contribute to the observed radio synchrotron emission between 30 MHz and 8.5 GHz for the two field strengths of 1.7 and 8 G indicated and IC scattering (for H.E.S.S.) of VHE electrons mostly on the CMBR. The two H.E.S.S. lines correspond to the two possible spectral fits discussed by Aharonian et al. (2006b), with ¼ 2:0 and 2.4 representing the two possible electron spectral indices. cannot distinguish between electrons and positrons, the measurement of Sefako & de Jager (2003) implies a present day value of 200Y300, but this value should be revised given the new compact nebular radio observations by Hales et al. (2004). If we rescale the H.E.S.S. measurement of hifor Vela X to electron energies as low as 1 GeVas required by radio data, the electron spectrum (Table 1) would allow us to scale this Ee 2 anomalously low average value up to a higher value of hi ¼ 0:5(0:3 TeV/1GeV) 150, which is still small compared to the extrapolated value of PSR B1823 13, as discussed previously. We already get a hint that should be much larger than implied by H.E.S.S. observations, since the Vela X radio nebula is quite bright (see Alvarez et al. 2001, and references therein), so that we can obtain an upper limit on the time-averaged from radio synchrotron observations if we assume a reliable lower limit on the nebular field strength. Although a lower limit of B 2 G was discussed by Aharonian et al. (2006b), a slightly lower value of B ¼ 1:7 G gives a good fit between the H.E.S.S. and ROSAT/ASCA spectra of Vela X if we assume that the Vela X H.E.S.S. spectrum steepens due to cooling rather than cuts off above 13 TeV. It is, however, important to map the full TeV cocoon area in X-rays before a final matching field strength between the H.E.S.S. and X-ray signals can be derived. The two possible electron spectra of Vela X (assuming an IC origin) as measured by H.E.S.S. (Aharonian et al. 2006b) are shown in Figure 2. In this figure we also add the electron spectrum corresponding to the bright Vela X radio nebula. By calculating the electron spectrum that would reproduce the observed Vela X radio spectrum of F 540(/8:5 GHz) Jy, with the radio spectral index ¼ 0:39 (Alvarez et al. 2001), we obtain an electron spectral index of e ¼ 1:78 in the radio domain. We assume two levels corresponding to the minimal and maximal field strengths of 1.7 and 8 G, respectively, leading to the electron spectra as indicated in Figure 2; since we are more interested in the number of electrons, rather than energetics, we have plotted the number spectrum E(dN/dE) ofvelaxusing the measured radio spectrum between 30 MHz and 8.5 GHz, with the corresponding electron energy range shown by thick solid lines marked radio. The normalization constants of the two lines corresponds to 1.7 and 8 G, as indicated on the figure. It is clear that an extrapolation of the electron spectrum corresponding to the radio component does not steepen sufficiently to meet the softer electron spectrum corresponding to the H.E.S.S. energy range, but if we have to force these two electron spectra to meet, we have to increase the average magnetic field strength of Vela X to hbi > 8 G. This then raises the interesting question of whether there are significant variations between B in the cocoon relative to the average nebular value, as discussed briefly in x 2. From Figure 1 we see that the time-averaged pair production multiplicity of Vela can be as large as hi max ¼ 5 ; 10 5 if we assume B ¼ 1:7 G as a lower limit on the Vela X nebular field strength. However, this would already violate the EGRET upper limit of Vela X as discussed by de Jager et al. (1996), and with a future GLAST measurement of hbi, we should be able to measure down to relatively low electron energies, giving hi ¼ 2:5 ; 10 5 3 G B h i : ð5þ This number is several orders of magnitude larger than inferred from H.E.S.S. data alone, but is, however, consistent with the extrapolated value of hi corresponding to the other Vela-like pulsar PSR B1823 13 discussed earlier. 5. CONCLUSION We have exploited the fact that IC observations of PWNs in the VHE -ray domain give us a measurement of the electron spectrum, independent of the nebular magnetic field strength. By counting the total number of electrons corresponding to the H.E.S.S. range, we could obtain lower limits on the total number of electrons. This represents a strict lower limit, since electrons with lower energies, not seen by H.E.S.S., may contribute significantly to the total. The fact that the PWNs of PSR B1509 58 and PSR B1823 13 are intrinsically luminous in the VHE domain resulted in lower limits on the time-averaged pair production multiplicity of 2000 and 500, respectively. These lower limits are already consistent with the theoretical estimates of for such relatively young canonical pulsars (Hibschmann & Arons 2001b), but the addition of electrons corresponding to the unseen radio component (if it does exist) would increase even further; extrapolating the fully justified uncooled electron spectrum of HESS J1825 137 down to E 0 ¼ 1 GeV (the unseen radio domain) gives a much higher average pair production multiplicity of hi 2 ; 10 5 (1 GeV/E 0 ), which is comparable to that of Vela. Furthermore, making the conservative assumption that the spectral hardening for the PWN of PSR B1509 58 from e ¼ 3 to 2 is just below the H.E.S.S. range, we would obtain a rescaled value (as for PSR B1823 13) of hi 7 ; 10 5 (1 GeV/E 0 ). Note that this pulsar has a relatively large surface field strength, with pulsed -ray spectral cutoff in the MeVrange, which hints at significant pair creation. This multiplicity (for E 0 ¼ 1 GeV) already implies a total rate of more than 10 40 leptons s 1 injected over the lifetime of the pulsar, which is comparable to that of the Crab pulsar (Rees & Gunn 1974). The extrapolation down to E 0 ¼ 1 GeV is also justified, since this approximate minimum lepton energy is required to explain the minimum synchrotron frequency of 30 MHz detected from the Vela X PWN.

1182 DE JAGER Whereas the lower limits of pair production multiplicities derived from H.E.S.S. data are already interesting, we also obtained extrapolated multiplicities below the H.E.S.S. energy range by surfing along the uncooled (due to synchrotron radiation) E 2 electron spectra toward energies as low as E 0 ¼ 1 GeV, leading to values of that are already well above the predictions of pulsar theorists (see e.g., Hibschmann & Arons 2001b). Such extrapolations can be further tested with future GLAST observations of PWNs, since we should then be able to measure the spectral turnovers in the sub-tev range more accurately, while also probing the low-energy particle spectra down to -ray energies corresponding to 100 MeV, leading to the relatively high values of hi. In general, such studies should force us to review our understanding of how pairs are created in pulsars, since current theories seem to underpredict the actual pair production rates. O. C. de Jager would like to thank J. Arons for stressing the importance to measure for pulsars in general, Yves Gallant for a critical reading of the manuscript, and Arache Djannati-Ataï for his hospitality at the College de France. Aharonian, F., et al. 2005a, A&A, 435, L17. 2005b, A&A, 442, L25. 2006a, A&A, 460, 365. 2006b, A&A, 448, L43. 2006c, ApJ, 636, 777 Alvarez, H., Aparici, J., May, J., & Reich, P. 2001, A&A, 372, 636 Amato, E., & Arons, J. 2006, ApJ, 653, 325 Arons, J., & Scharlemann, E. T. 1979, ApJ, 231, 854 Bednarek, W., & Bartosik, M. 2003, A&A, 405, 689 Blondin, J. M., Chevalier, R. A., & Frierson, D. M. 2001, ApJ, 563, 806 Blumenthal, G. R., & Gould, R. J. 1970, Rev. Mod. Phys., 42, 237 Daugherty, J. K., & Harding, A. K. 1982, ApJ, 252, 337 de Jager, O. C. 2005, in AIP Conf. Proc. 801, Astrophysical Sources of High Energy Particles and Radiation, ed. M. M. Shapiro, T. Stanev, & J. P. Wefel ( New York: AIP), 298 de Jager, O. C., Funk, S., & Hinton, J. 2005, Proc. 29th Int. Cosm. Ray Conf., Vol. 4, ed. B. S. Acharya, et al. ( Mumbai: Tata Institute of Fundamental Research), 239 de Jager, O. C., Harding, A. K., Baring, M. G., & Mastichiadis, A. 1995, Proc. 24th Int. Cosm. Ray Conf., Vol. 2, ed. N. Iucci & E. Lamanna (Rome: ICRC), 528 de Jager, O. C., Harding, A. K., Sreekumar, P., & Strickman, M. 1996, A&AS, 120, 441 Dubner, G. M., Gaensler, B. M., Giacani, E. B., Goss, W. M., & Green, A. J. 2002, AJ, 123, 337 REFERENCES du Plessis, I., de Jager, O. C., Buchner, S., Nel, H. I., North, A. R., Raubenheimer, B. C., & van der Walt, D. J. 1995, ApJ, 453, 746 Gaensler, B. M., Arons, J., Kaspi, V. M., Pivovaroff, M. J., Kawai, N., & Tamura, K. 2002, ApJ, 569, 878 Gaensler, B. M., Stappers, B. W., Frail, D. A., Moffet, D. A., Johnston, S., & Chatterjee, S. 2000, MNRAS, 318, 58 Goldreich, P., & Julian, W. H. 1969, ApJ, 157, 869 Hales, A. S., et al. 2004, ApJ, 613, 977 Harding, A. K., & Muslimov, A. G. 1998, ApJ, 508, 328 Harding, A. K., Muslimov, A. G., & Zhang, B. 2002, ApJ, 576, 366 Helfand, D. J., Gotthelf, E. V., & Halpern, J. P. 2001, ApJ, 556, 380 Hibschmann, J. A., & Arons, J. 2001a, ApJ, 554, 624. 2001b, ApJ, 560, 871 Horns, D., Aharonian, F., Santangelo, A., Hoffmann, A. I. D., & Masterson, C. 2006, A&A, 451, L51 Mangano, V., Massaro, E., Bocchino, F., Mineo, T., & Cusumano, G. 2005, A&A, 436, 917 Rees, M. J., & Gunn, J. E. 1974, MNRAS, 167, 1 Sefako, R. R., & de Jager, O. C. 2003, ApJ, 593, 1013 Strong, A. W., Moskalenko, I. V., & Reimer, O. 2000, ApJ, 537, 763 Sturrock, P. A., 1971, ApJ, 164, 529 van der Swaluw, E., & Wu, Y. 2001, ApJ, 555, L49