Markov chain Monte Carlo population synthesis of single radio - - PowerPoint PPT Presentation

Markov chain Monte Carlo population synthesis of single radio pulsars in the Galaxy

Marek Cieślar1, Tomasz Bulik1, Stefan Osłowski2,3,4

1. Astronomical Observatory, Univeristy of Warsaw

• Al. Ujazdowskie 4 00-478 Warsaw, Poland

2. Centre for Astrophysics and Supercomputing Swinburne University of Technology Hawthorn,Victoria 3122, Australia 3. Fakultat fur Physik, Universitat Bielefeld Postfach 100131, 33501 Bielefeld, Germany 4. Max-Planck-Intitut fur Radioastronomie Auf dem Hugel 69, 53121 Bonn, Germany

Motivation for the project

• Replication of the Faucher-Giguere, Kaspi 2006

with enhancements.

• Markov chain Monte Carlo probing of the

parameter space (initial conditions, magnetic field decay, radio-luminosity law).

• A general purpose population generator.

An arbitrary large set of pulsars with statistical properties similar to observed sample.

Model Components Overview

Dynamics Physics Observations

• Galactic potential
• Kicks
• Initial position in

the Arms

• P,Pdot,B evolution

(lighthouse model)

• B Decay

(exponential)

• Death lines/area
• Luminosity model
• Minimal observable

flux (survey-wise)

• DM (YMW16)
• Beaming fraction
• Survey coverage

Initial position and kicks

• The position in arms adopted after

Faucher-Giguere&Kaspi

• Hobbs2005 kicks 1D Maxwellian

distribution with RMS 265 km/s

• Integration with the Position Verlet

method (leap-frog family)

B Field Decay P-Pdot-B

• B decay formula
• Dipole model
• P(t)

Luminosity models

• Narayan (as a reference)
• Rotational model

(proportional to ~Lrot)

• Power-law model
• 400Mhz→1400Mhz

Death Area

Death lines after Rudak and Ritter, 1994 Psi = 0.2

Parkes Multibeam Survey

The ATNF cut

• Parkes Multibeam Survey
• Parkes window (GalL, GalB)
• Not MSP (B >= 1e10 G)
• All fields present (P,Pdot,S1400,GalL,GalB,B,DM)

→ 970 PSRs

Dispersion measure – YMW16 model

• Difference with NE2001 – considerable more computational time
• Less numerical artefacts

Dispersion measure – YMW16 model

• Difference with NE2001 – considerable more computational time
• Less numerical artefacts

Markov chain Monte Carlo computation

Dynamics Physics Observations

• Galactic potential
• Kicks
• Initial position in

the Arms

• P,Pdot,B evolution

(lighthouse model)

• B Decay

(exponential)

• Death lines/area
• Luminosity model
• Minimal observable

flux (survey-wise)

• DM (YMW16)
• Beaming fraction
• Survey coverage

the main bottleneck

Density of a PSRs

• Density at a given point is a given by a Gaussian average:
• From a regular grid of points in the P-Pdot-S comparison

space, a set of 700 location in the vicinity of observed PSRs is chosen.

• Normalization to 1.

Likelihood of a model

• The Probability of making a measurement of a particular density
• f modeled PSRs equal ‘m’, given that the density of the
• bserved PSR is equal ‘o’, is described by a normal distribution:
• Then the likelihood statistic is computed
• Which allows to compare two models with different set of

parameters

Power-law

Power-law model

Rotational

Rotational model

Rotational Power-law

Power-law

Rotational

SKA predictions

Estimated number of detected PSRs

Rotational Power-law SKA-1-Mid-B ~1200 SKA-1-Mid ~2300 Rotational

The Indri code

The code can be obtained from the github site: https://github.com/cieslar/indri

Summary

• The MCMC can be used for pulsar population

synthesis (never done before)

• The preferred magnetic decay scale is ~4Myr
• The correlation in luminosity parameters and

magnetic decay scale implicate degenerate model

• r over-parametrization
• Estimated increase of PSRs for the SKA is between

23 − 137% compared to Parkes Multibeam Survey