1. High-Energy & Radio Pulsar Population Modeling (++) Maura McLaughlin & Jim Cordes Jodrell Bank Observatory Cornell University December 11, 2001

2. Modeling the  -ray pulsar population Comparison w/ radio luminosity law The giant-pulse/  -ray connection New distance model (real soon) Arecibo multibeam pulsar surveys

3. Modeling the  -ray pulsar population McLaughlin & Cordes 2000, ApJ, 538, 818 McLaughlin PhD Thesis, Cornell 2001 Likelihood Analysis and Results Predictions for GLAST New Pulsars/Unidentified EGRET Sources Comparison with Other Models

4. Things we hope to learn from modelling of the  -ray pulsar population include What is the scaling law for the gamma-ray luminosity? How many unidentified EGRET sources are pulsars? Which pulsars are likely to be detectable at high energies? How much of the  -ray background is attributable to unresolved pulsars? What will next-generation  -ray telescopes detect?

5. 7 detected pulsars, 349 upper limits, & 3 diffuse background measurements Available Data: Vela 89 36.9 Geminga 237 34.5 Crab 33 38.7 B1706–44 102 36.5 B1055–52 197 34.5 B1046–58 124 36.3 B1951+21 40 36.6 Name P (ms) E (ergs/s). Detected EGRET pulsars (in order of decreasing EGRET flux) R1 R2 2 1 3 2 1 3 4 5 39 29 9 9 6 13 E/D 2. L/D 2 Ranks

6. The Model: Given a simple luminosity model we can calculate a predicted flux for each pulsar as and a population-averaged  -ray pulsar luminosity as

7. We need a spatial distribution for the pulsar population. Our model consists of a Gaussian disk of radius r g with exponential scale height h plus a molecular ring of width w r at radius r r. PDF for distance D from the Sun for the model used for this analysis: r g = 6 kpc h = 0.5 kpc r r = 4 kpc w r = 1.5 kpc

8. Other assumptions: Constant birthrate of 1/100 yr -1. Galaxy is 10 10 years old. Beam solid angle of 2 . Maximum pulsar efficiency is 1/2. Pulsars may contribute up to 1/2 of the diffuse flux. We fit for: , , , n, P 0, and B 12

9. We construct a likelihood function using detections, upper limits & diffuse background measurements where Black line shows where model-predicted flux equals measured flux, upper limit, or ½ of diffuse background measurement.

10. Best-fit luminosity law for EGRET data is Contours of log likelihood vs pairs of parameters

11. Diffuse flux measurements do not significantly constrain the model. Pulsars likely do not contribute more than a few percent to the diffuse flux. Percent diffuse flux due to pulsars for a range of parameter values. Pulsars should not contribute significantly to the GLAST diffuse flux

12. Predicted Flux Distributions of Gamma-Ray Pulsars 1043 pulsars included

13. Predicted Flux Distributions of Gamma-Ray Pulsars Vela Crab Geminga J1357–6435 J1740+1000 B1929+10 J1124–5916 J2229+6114 B0656+14 B1509–58 B1706–44 J0631+1036

14. Predicted Flux Distributions of Gamma-Ray Pulsars For the best-fit luminosity law and assuming n = 2.5 P 0 = 15 ms B 12 = 1

15. Predicted Flux Distributions of Gamma-Ray Pulsars EGRET should detect 20 pulsars as point sources. There are 47 non-variable unidentified sources.

16. Predicted Flux Distributions of Gamma-Ray Pulsars GLAST should detect 750 pulsars as point sources. This includes only 120 known radio pulsars.

17. Predicted Flux Distributions of Gamma-Ray Pulsars GLAST could detect 140 pulsars in blind periodicity searches.

18. Notable associations between pulsars with high predicted  -ray fluxes and unidentified EGRET sources. J2229+6114 33.1 3EG J2227+6122 0.194 J1420–6048 32.2 3EG J1420–6038 1.144 J1015–5719 32.1 3EG J1014–5705 0.549 J1837–0604 32.0 3EG J1837–0606 2.811 J1637–4642 31.9 3EG J1639–4702 1.884 J1016–5857 31.8 3EG J1013–5915 0.154 Pulsar Log(F p ) Unidentified Source Variability Have searched for pulsations from these unidentified sources over a range of periods and period derivatives with no success. ID of unidentified sources with these pulsars will likely have to wait for GLAST. New variability indices have been calculated for all 3EG sources. pulsars = 0.62, agn = 5.1, unidentified = 3.12

19. Model Comparison: 2) Yadigaroglu & Romani (1995) assume outer gap geometry dependent on radio pulsar beamwidths and luminosities use Monte Carlo techniques to estimate that - EGRET should have detected 5 radio pulsars - EGRET should have detected 17 radio-quiet pulsars - 5% of the EGRET diffuse background due to pulsars 1) McLaughlin & Cordes (2000) assume no specific geometry no dependence on radio pulsar beamwidths or luminosities use likelihood analysis to estimate that - EGRET should have detected 20 pulsars - <5% of EGRET diffuse background due to pulsars

20. Model Comparison: 2) Gonthier et al. (2001) assume polar cap geometry use Monte Carlo techniques to estimate that - EGRET should have detected 7 radio pulsars - EGRET should have detected 1 radio-quiet pulsar - GLAST should detect 76 radio pulsars, 74 radio-quiet pulsars as point sources and 7 radio-quiet pulsars as pulsed sources - with B-field decay, GLAST should detect 90, 101, and 9 radio pulsars, radio-quiet pulsars as point sources and radio-quiet pulsars as pulsed sources 1) McLaughlin & Cordes (2000) assume no specific geometry use likelihood analysis to estimate that - EGRET should have detected 20 pulsars - GLAST should detect 750 pulsars as point sources and 140 pulsars as pulsed sources

21. Comparison of Luminosity Laws Luminosity lawP, B dependence L  Edot P -4 B 2 L  voltage drop P -2 B OSSE best fit P -8.3 B 7.6 EGRET best fit P -1.8 B 1.5 Radio best fit P -1.7 B 0.8 Arzoumanian, Chernoff & Cordes, in press

22. Moffett & Hankins ‘96 Extra, bandlimited pulse components Giant pulses only in MP, IP components IPMP Crab Pulsar

23. Giant pulse phenomenology 3 objects (Crab, 2 MSPs) (only ~ 50 well studied) GPs occur in pulse components with high-energy counterparts; power-law PDF; up to 1000x mean. B @ light cylinder ~ 10 6 Gauss Strong, stochastic circular polarization in B1937+21 (Cognard et al.) No high energy GP counterparts (Lundgren et al. 1995; J. Fierro PhD thesis) But … GP components all have high-energy counterparts

24. Extremely Model Dependent Analysis of the Crab Pulsar JMC & Mal Ruderman (based on previous work of MR with K.S. Cheng) Radio precursor = polar cap ion beam MP, IP = inward, outward going outer-gap beams (not all possible polar-cap/outer-gap beams are active or seen) Reflection of low-f precursor radiation from outside LC illuminates the outer-gap beams;  frequency boosting by  || 2 to produce radio MP,IP. Cyclotron maser amplification produces giant pulses occurs in outer gap beams  GPs in MP, IP only Reflections of radio emission at ion gyroresonances produce extra, bandlimited radio components (~10 6 G) reflection of MP,IP radio beams occurs from closed magnetosphere Polarization is a consequence of reflections, adiabatic walking, and maser amplification.

25. Millisecond Pulsars Two-sided beams from polar caps (with highly offset dipole axis) Strong gravitational bending for large dipole offsets Cyclotron maser amplification produces giant pulses (need synchrotron lifetime long enough) Maser amplification is sporadic, exponentiating in one or the other circular polarization. Frequency matching implies 10 6 G

26. Implications Gamma-ray beaming fraction < ½ (beams are narrow) (assuming outer gap emission only) Radio-gamma-ray correlations: –Radio & gamma-ray beams are not always aligned –Reflection components in radio have no gamma-ray counterparts –May be radio-frequency dependent –Some but not all objects may show giant pulses B0540-69:broad radio pulse, no GPs (unpublished Parkes data) Geminga: no, no giant pulses (McLaughlin et al.) Predictions of gamma-ray yield obviously model dependent; current models suggest possible yields & correlations. GLAST + radio (+IR etc) studies are likely to help determine magnetospheric structure & activity (find the currents)

27. Parkes MB Feeds Arecibo Multibeam Surveys

28. I. Arecibo Galactic-Plane Survey |b| < 5 deg, 32 deg < l < 80 deg 1.5 GHz total bandwidth = 300 MHz digital correlator backend (1024 channels) (1st quadrant available = WAPP) multibeam system (7 feeds) ~300 s integrations, 3000 hours total Can see 2.5 to 5 times further than Parkes (period dependent) Expect ~500 to 1000 new pulsars

29. Surveys with Parkes, Arecibo & GBT. Simulated & actual Yield ~ 1000 pulsars.

30. II. High Galactic Latitude Survey Millisecond pulsars (z scale height ~ 0.5 kpc) High-velocity pulsars (50% escape) (scale height =  ) NS-NS binaries (typical z ~ 5 kpc) NS-BH binaries (typical z ~ few kpc ?) Search for:

31. NE2001 = New Model Cordes & Lazio (to be submitted [in 2001]) x2 more lines of sight (D,DM,SM) [114, 931, 471 data points] Local ISM component (new) [12 parameters] Thin & thick disk components (as in TC93) [8 parameters] Spiral arms (revised from TC93) [21 parameters] Galactic center component (new) [3 parameters] (+auxiliary VLA/VLBA data ; Lazio & Cordes 1998) Individual `clumps’ of enhanced DM/SM (new) [3 parameters x 20 LOS] Improved fitting method (iterative likelihood analysis) penalty if distance or SM is not predicted to within the errors

32. NE2001 Spiral Arms Electron density (log gray scale to enhance local ISM)

33. Summary Current models ok for getting rough estimates of the pulsar yield from GLAST GLAST detections and  -ray/radio correlations will allow identification of accelerators in magnetospheres Giant radio pulse/  -ray objects are possible rosetta stones; need radio GP survey in advance of GLAST Arecibo Multibeam surveys will ~ double the number of radio pulsars w/ many young objects deep in the Galactic plane (GBT too, but later) Distance models will improve significantly with VLBI astrometry over next 5 years

34. The Model: Given a simple luminosity model

35. The Model: Given a simple luminosity model we can calculate a predicted flux for each pulsar as

36. Other assumptions: Constant birthrate of 1/100 yr -1. Galaxy is 10 10 years old. Beam solid angle of 2 . Maximum pulsar efficiency is 1/2. Pulsars may contribute up to 1/2 of the diffuse flux.