High-Energy & Radio Pulsar Population Modeling (++)

Maura McLaughlin & Jim Cordes

Jodrell Bank Observatory Cornell University

December 11, 2001

• Modeling the -ray pulsar population

• Comparison w/ radio luminosity law

• The giant-pulse/-ray connection

• New distance model (real soon)

• Arecibo multibeam pulsar surveys

Modeling the -ray pulsar population

McLaughlin & Cordes 2000, ApJ, 538, 818McLaughlin PhD Thesis, Cornell 2001

• Likelihood Analysis and Results• Predictions for GLAST• New Pulsars/Unidentified EGRET Sources• Comparison with Other Models

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?

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/D2.

L/D2

Ranks

The Model:

Given a simple luminosity model

12BPL

we can calculate a predicted flux for each pulsar as

2D

LF

and a population-averaged -ray pulsar luminosity as

1

2

02

122

012 11

2

2|

ng

g

T

P

BPBL

index braking -

down time-spin initial -

at periodpulsar -

Galaxy theof age -

periodspin initial -

distancepulsar -

angle solid beam -

field magnetic -

period -

0

0

12

n

TP

T

P

D

B

P

gg

g

We need a spatial distribution for the pulsar population.

Our model consists of a Gaussian disk of radius rg with exponential scale height h plus a molecular ring of width wr at radius rr.

PDF for distance D fromthe Sun for the model used for this analysis:

rg = 6 kpch = 0.5 kpcrr = 4 kpcwr = 1.5 kpc

Other assumptions:

•Constant birthrate of 1/100 yr-1.•Galaxy is 1010 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, P0, and B12

We construct a likelihood function using detections, upper limits & diffuse background measurements

bgupdettot LL LL where

Black line shows where model-predicted flux equals measured flux, upper limit, or ½ ofdiffuse background measurement.

)detections (for det,1

di

N

iN

d

LL

Best-fit luminosity law for EGRET data is

Contours of log likelihood vs pairs of parameters

ergs/s 10 5.112

8.10.32 BPL

Diffuse flux measurements do not significantly constrain

the model. Pulsars likely do not contribute more than a

few percent to the diffuse flux.

Percent diffuseflux due to pulsars for a range of parameter values.

Pulsars should not contribute significantly to the GLAST diffuse flux

Predicted Flux Distributions of Gamma-Ray Pulsars

1043 pulsarsincluded

5.112

8.10.3210 BPL

Predicted Flux Distributions of Gamma-Ray Pulsars

Vela

CrabGeminga

J1357–6435J1740+1000B1929+10J1124–5916J2229+6114B0656+14B1509–58B1706–44J0631+1036

Predicted Flux Distributions of Gamma-Ray Pulsars

For the best-fitluminosity lawand assuming

n = 2.5 P0 = 15 ms B12 = 1

Predicted Flux Distributions of Gamma-Ray Pulsars

EGRET shoulddetect 20 pulsarsas point sources.

There are 47non-variableunidentified sources.

Predicted Flux Distributions of Gamma-Ray Pulsars

GLAST shoulddetect 750 pulsarsas point sources.

This includes only120 known radiopulsars.

Predicted Flux Distributions of Gamma-Ray Pulsars

GLAST could detect 140 pulsarsin blind periodicity searches.

Notable associations between pulsars with high predicted-ray fluxes and unidentified EGRET sources.

J2229+6114 33.1 3EG J2227+6122 0.194J1420–6048 32.2 3EG J1420–6038 1.144J1015–5719 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(Fp) Unidentified Source Variability

Have searched for pulsations from these unidentified sources over arange of periods and period derivatives with no success. ID of unidentified sources with these pulsars will likely have to wait forGLAST.

New variability indices have been calculated for all 3EG sources.<V>pulsars = 0.62, <V>agn = 5.1, <V>unidentified = 3.12

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

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

Comparison of Luminosity Laws

Luminosity law P, B dependence

L Edot P-4 B2

L voltage drop P-2B

OSSE best fit P-8.3 B7.6

EGRET best fit P-1.8 B1.5

Radio best fit P-1.7 B0.8

Arzoumanian, Chernoff & Cordes, in press

Moffett & Hankins ‘96

Extra, bandlimited pulse components

Giant pulses only in MP, IP components

IPMP

Crab Pulsar

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 ~ 106 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

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 (~106 G)

reflection of MP,IP radio beams occurs from closed magnetosphere

• Polarization is a consequence of reflections, adiabatic walking, and maser amplification.

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 106 G

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 <radio>, 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)

Parkes MB Feeds

Arecibo Multibeam Surveys

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

Surveys Surveys with Parkes, with Parkes, Arecibo & Arecibo & GBT.GBT.

Simulated & Simulated & actualactual

Yield ~ 1000 Yield ~ 1000 pulsars.pulsars.

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:

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

NE2001 Spiral Arms

Electron density (log gray scale to enhance local ISM)

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

The Model:

Given a simple luminosity model

12BPL

index braking -

down time-spin initial -

at periodpulsar -

Galaxy theof age -

periodspin initial -

distancepulsar -

angle solid beam -

field magnetic -

period -

0

0

12

n

TP

T

P

D

B

P

gg

g

The Model:

Given a simple luminosity model

12BPL

we can calculate a predicted flux for each pulsar as

2D

LF

index braking -

down time-spin initial -

at periodpulsar -

Galaxy theof age -

periodspin initial -

distancepulsar -

angle solid beam -

field magnetic -

period -

0

0

12

n

TP

T

P

D

B

P

gg

g

Other assumptions:

•Constant birthrate of 1/100 yr-1.•Galaxy is 1010 years old.•Beam solid angle of 2.•Maximum pulsar efficiency is 1/2.•Pulsars may contribute up to 1/2 of the diffuse flux.