Estimates for Very High Energy Gamma Rays from Globular Cluster Pulsars

arXiv:0903.3047v2 [astro-ph.HE] 21 Sep 2009 Estimates for Very High Energy Gamma Rays from Globular Cluster Pulsars C. VENTER∗,† and O.C. DE JAGER∗,∗∗ ∗Unit for Space Physics, North-West University, Potchefstroom Campus, Private Bag X6001, Potchefstroom 2520, South Africa †The Centre for High Performance Computing, CSIR Campus, 15 Lower Hope Street, Rosebank, Cape Town, South Africa ∗∗South African Department of Science and Technology, and National Research Foundation Research Chair: Astrophysics and Space Science Abstract. Low-Mass X-ray Binaries (LMXRBs), believed to be the progenitors of recycled millisecond pulsars (MSPs), occur abundantly in globular clusters (GCs). GCs are therefore expected to host large numbers of MSPs. This is also confirmed observationally. The MSPs continuously inject relativistic electrons into the ambient region beyond their light cylinders, and these relativistic particles produce unpulsed radiation via the synchrotron and inverse Compton (IC) processes. It is thus possible, in the context of General Relativistic (GR) frame-dragging MSP models, to predict unpulsed very high energy radiation expected from nearby GCs. We use a period-derivative cleaned sample of MSPs in 47 Tucanae, where the effects of the cluster potential on the individual period derivatives have been removed. This MSP population is likely to have significant pair production inhibition, so that slot gaps and outer gaps are not expected to form in the pulsar magnetospheres. The utilisation of unscreened pulsar potentials is therefore justified, and fundamental tests for the predicted average single pulsar gamma-ray luminosities and associated particle acceleration are simplified. Using a Monte Carlo process to include effects of pulsar geometry, we obtain average injection spectra (with relatively small errors) of particles leaving the MSPs. These spectra are next used to predict cumulative synchrotron and IC spectra expected from 47 Tucanae, which is a lower limit, as no reacceleration is assumed. We find that the IC radiation from 47 Tucanae may be visible for H.E.S.S., depending on the nebular field B as well as the number of MSPs N in the GC. Telescopes such as Chandra and Hubble may find it difficult to test the SR component prediction of diffuse radiation if there are many unresolved sources in the field of view. These results may be rescaled for other GCs where less information is available, assuming universal GC MSP characteristics. Keywords: Pulsars, Globular clusters in the Milky Way, Radiation mechanisms PACS: 97.60.Gb, 98.20.Gm, 95.30.Gv INTRODUCTION A total of 137 globular cluster (GC) pulsars have been discovered in 25 GCs1, following the discovery of the first GC millisecond pulsar (MSP) in M28 [1]. Low-Mass X-ray Binaries (LMXRBs), believed to be the progeni- tors of recycled MSPs [2], occur abundantly in GCs. GCs are therefore expected to host large numbers of MSPs, up to ∼200 MSPs or more [3, 4]. Indeed, GC MSP spin properties seem consistent with the recycling scenario [5]. Terzan 5, 47 Tucanae, and M28 collectively contain nearly half of all GC pulsars, housing 33, 23, and 11 pul- sars respectively [5]. GC MSPs are sources of relativistic electrons, which are continuously being injected into the ambient region beyond the MSPs’ light cylinders. These relativistic particles produce high-energy emission via synchrotron radiation (SR) and inverse Compton scatter- ing (ICS) on bright starlight photons as well as on the 1 http://www.naic.edu/∼pfreireGCpsr.html cosmic microwave background (CMB). In this paper, we calculate the cumulative injection spectrum and resulting unpulsed SR and ICS fluxes, us- ing a population of 13 MSPs in 47 Tucanae, with cor- rected values of their period-derivatives [6]. GC gamma- ray visibility is also discussed. We use a more refined injection spectrum, originating from a General Relativis- tic (GR) frame-dragging MSP model (e.g. [7, 8, 9]), than that assumed by [4], and our calculations are comple- mentary to pulsed gamma-ray flux predicted by [10]. As we only consider particles originating from MSP magne- tospheres, with no further acceleration, our calculations should be viewed as lower limits to the expected TeV flux. INJECTION SPECTRUM CALCULATION As in [10, 11], we use a population of 13 MSPs in 47 Tu- canae, with corrected values of their period-derivatives ˙P [6]. We calculate the injection spectrum Qi of elec- FIGURE 1. Loss timescales (left panel for B = 1µG, right panel for B = 10µG). Solid lines represent Z = 0, dashed lines Z = 1, thin lines τrad, intermediate straight lines τesc, and thick lines τeff (see text for details). trons leaving each MSP i, with i = 1,···,13, by bin- ning the number of primary electrons leaving a stellar surface patch and moving along a B-line according to ELC e ≡γLCmec2, the residual electron energy at the light cylinder, divided by energy bin size. We next randomly choose N = 100 MSPs (with ran- dom inclination angles χ), and sum their pa

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