Millisecond-Pulsar Population Synthesis

PsrPopPy

PsrPopPy (https://github.com/samb8s/PsrPopPy) is a Python software package capable of simulating a galactic population of pulsars [1]. It extrapolates parameters of the observed population informed by various surveys to the entire galaxy. PsrPopPy has two modes: "snapshot" (psrpoppy.populate), which randomly draws pulsar attributes from empirical distributions for the population at this point in time; and "evolve" (psrpoppy.evolve) which evolves pulsar intial conditions through the galacic potential. Given that lifetimes of millisecond pulsars are much longer than canonical pulsars, the snapshot method is more appropriate for simulating a galaxy of MSPs. The number of MSPs detected in a list of pulsar surveys provides the overall normalization of population. Each generated pulsar is checked whether or not it would be detected by each survey in the list according to DEC limits, survey sensitivity, etc. Pulsars cease to be generated by the software when the number of simulated detections matches the actual sum total of all MSPs detected by the provided surveys.

Snapshot MSP Model

I have generated a snapshot model of the galactic MSP population containing 38475 MSPs. The population is normalized by the 28 MSPs detected by the Parkes Multibeam Pulsar Survey [2]. Dispersion measure and scattering timescales are calculated using the NE2001 electron density model [3]. The following distributions were used to generate the population:

log-normal luminosity with $\mu = -1.1 \log_{10}(\mathrm{mJy\ kpc^2})$, $\sigma = 0.9 \log_{10}(\mathrm{mJy\ kpc^2})$ [1]
log-normal period with $\mu = 1.5\ \mathrm{ms}$, $\sigma = 0.58\ \mathrm{ms}$ [4]
gaussian radius with $\mu = 0\ \mathrm{kpc}$, $\sigma = 7.5\ \mathrm{kpc}$ [1]
exponential scale height with $\mu = 0.5\ \mathrm{kpc}$ [1]
gaussian spectral index with $\mu = -1.6$, $\sigma = 0.35$ [1]
pulse widths calculated using a simple duty cycle with log-normal scatter determined by a K-S test with simulated NANOGrav Detection Working Group RMSs for $ \sigma_\mathrm{TOA} \le 400\ \mathrm{ns}$
$\mu = \overline{\log(W)} = \log\left(0.04 P^{\:0.9}\right)$, $\sigma = 0.3$
log-normal $\dot{P}$ with $\mu = -19.9$, $\sigma = 0.5$ computed by fitting ATNF Pulsar Catalog distribution of (non-GC/SNR) MSP $\dot{P}$s and assumes $P$ and $\dot{P}$ are uncorrelated. (I am currently exploring whether this assumption is a good one, which is why $\dot{P}$s are not implemented in psrpoppy.populate.)
time of arrival uncertainties ($\sigma_\mathrm{TOA}$) computed from the quadrature sum of radiometer noise ($\sigma_\mathrm{RN}$) using scattered pulse widths and jitter noise ($\sigma_\mathrm{J}$)[5] at 1.4 GHz: $$\sigma_\mathrm{RN} = {W_\mathrm{scat} \over S/N} = {W_\mathrm{scat}S_\mathrm{sys} \over S_\mathrm{mean} \sqrt{n_\mathrm{pol}t_\mathrm{int}\Delta f}} \sqrt{W_\mathrm{scat} \over P - W_\mathrm{scat}}$$ where $ W_\mathrm{scat} = \sqrt{W_\mathrm{intrinsic}^2 + t_\mathrm{scatter}^2}$. $$ \sigma_\mathrm{J} = {W_\mathrm{intrinsic} \over \sqrt{N}} = {W_\mathrm{intrinsic} \over \sqrt{t_\mathrm{int}/P}}$$ where $N$ is the number of pulses and $t_\mathrm{int}$ is the integration time per epoch.

Download the Model

ASCII

Pickled psrpoppy.population object (Does not include TOA uncertainties)

Period_ms: Pulse period in ms
Pdot: Pulse period derivative
DM: Dispersion measure from NE2001 in pc cm$^{-3}$
t_scatter: Scattering timescale in ms
Width_ms: Intrinsic pulse width in ms
GL: Galactic latitude in degrees
GB: Galactic longitude in degrees
S_1400: Flux at 1.4 GHz in mJy
L_1400: Luminosity at 1.4 GHz in mJy kpc$^2$
SPINDEX: Spectral index
DTRUE: True distance from radius and scale height
X, Y, Z: Galactic position in cartesian coords

Frequency-Dependent Timing Precision

For the same population described above, I have computed the infinity-frequency TOA uncertainty with consideration for the frequency dependent effects of DM dispersion, interstellar scintillation and scattering, and telescope sensitivity using FrequencyOptimizer. The TOA uncertainty referenced at infinite frequency is given by $$\sigma_\mathrm{TOA} = \sqrt{\sigma_\mathrm{W}^2 + \sigma_{\delta\mathrm{DM}}^2 + \sigma_\mathrm{tel}^2}$$ where $\sigma_\mathrm{W}$ are the white noise errors, $\sigma_{\delta\mathrm{DM}}$ is the DM estimation error, and $\sigma_\mathrm{tel}$ are the remaining telescope errors including noise from RFI, gain calibration, and circular polarization. $\sigma_\mathrm{W}$ is comprised of three components which add in quadrature: the the template-fitting error $\sigma_\mathrm{S/N}$ (radiometer noise), the jitter error $\sigma_\mathrm{J}$, and the scintillation error $\sigma_\mathrm{DISS}$ [6].

I simulate pulsar timing campaigns with a variety of telescope configurations. Each MSP in the population is tested at Arecibo at L-band for 30 minutes to get an upper-limit on the $S/N$ (ignoring the effects of scatter-broadening). If $S/N < 5$ or the intrinsic pulse width is greater than the period, it is ignored. MSPs outside of the declination limits of the timing telescope are not timed. For the remaining MSPs, $\sigma_\mathrm{TOA}$, $\sigma_\mathrm{W}$, $\sigma_{\delta\mathrm{DM}}$, and $\sigma_\mathrm{tel}$ are computed. Additionally, if the telescope is a dish array and $\sigma_\mathrm{J} > \sigma_{S/N}$ the pulsar is considered for timing with a subarray.

Simulated Timing Programs by Telescope

Each file below contains the full population of 38475 MSPs with the additional parameters:

sigma_toa: Total TOA uncertainty $\sigma_\mathrm{TOA}$ in us
sigma_tel: Telescope noise errors $\sigma_\mathrm{tel}$ in us
sigma_dm: DM estimation uncertainty $\sigma_{\delta\mathrm{DM}}$ in us
sigma_w: Total white noise errors $\sigma_\mathrm{W}$ in us
subarray: Should the MSP be considered for subarraying?

If the MSP is too dim or smeared out to be timed, the TOA errors are set to -1. If the MSP is outside of the telescope's sky, the TOA errors are set to -2.

DSA2000

I consider three possible frequency ranges: 0.5-2 GHz, 0.7-2 GHz, and 1-4 GHz. For the 0.7-2 GHz configuration, I also consider a halved-subarray DSA2000 and a quarter-subarray DSA2000, to be used for optimizing integration time per MSP. Each MSP is timed for 30 minutes / epoch.

0.5-2 GHz (ASCII)

0.7-2 GHz full array (ASCII)

0.7-2 GHz half array (ASCII)

0.7-2 GHz quarter array (ASCII)

1-4 GHz (ASCII)

Current Arecibo Program

Simulated campaign with Arecibo 430 and L-wide for 30 minutes / pulsar / epoch considering frequency-dependent receiver temps and gains

Arecibo 430/L-wide (ASCII)

Current GBT Program

Simulated campaign with Green Bank Rcvr_800 and Rcvr_1_2 for 30 minutes / pulsar / epoch considering frequency-dependent receiver temps and gains

GBT 800/1200 MHz (ASCII)

GBT Ultra-wideband Receiver

Simulated campaigns with Green Bank UWBR (0.7-4 GHz) for 15 minutes / pulsar / epoch considering frequency-dependent receiver temps and gains with and without Cyclic Spectroscopy mode ($\tau_\mathrm{scatter}=0$). Also included are S/N values for the population measured with the UWBR at the center of the band.

GBT UWBR (ASCII)

GBT UWBR (CySpec) (ASCII)

GBT UWBR S/N (ASCII)

VLA

30 minutes / pulsar / epoch at L and S band at the VLA

VLA L/S-band (ASCII)

next generation VLA

Simulated timing campaign with ngVLA based on the straw-man program in http://arxiv.org/abs/1810.06594. 20% subarray and 30 minutes integration / pulsar in Band 1 (1.2-3.5 GHz) and Band 2 (3.5-12.3 GHz)

ngVLA Bands 1 & 2 (ASCII)