NS masses from radio timing: Past, present and future

Paul Demorest (NRAO)Symposium on Neutron Stars, Ohio U., May 2016

Overview

Review of how to measure neutron star masses via radio pulsar timing.

Summary of recent (and not-so-recent) influential results.

Progress in data analysis methods.

Future instrumentation for radio searching and timing.

… and associated challenges.

Neutron star interior

(Watts et al 2015)

Equation of state; Mass/radius plot

(Watts et al 2015)

EOS implies certain track in Mass-Radius plot. Maximum observed NS mass can rule out specific models.

Pulsar timing

PNS are visible as radio pulsars – we can track phase of pulse train over many years or decades. MSPs have P ~ few ms.

Fluctuations in pulse arrival times are a direct measurement of variations in Earth—PSR distance (light travel time); 1 us → 0.3 km

For pulsars in binary systems, measures projected orbital motion – in most cases is many times pulse period!

(plot: S. Ransom)

Characterizing binary pulsar orbits

Besides the normal 5 “Keplerian” parameters (Porb, e, asin(i)/c, T0, ω), post-Keplerian orbital effects are measurable:

where: T⊙ GM⊙/c3 = 4.925490947 μs, M = m1 + m2

In general relativity, these are only functions of:- the precisely known Keplerian orbital parameters P

b, e, asin(i)

- the mass of the pulsar m1 and the mass of the companion m

2

Mass-mass diagram

(PSR B1913+16; plot: Will, 2014)

The original binary pulsar: PSR B1913+16

(Figures and masses: Weisberg et al 2010)

The first binary pulsar, discovered in 1974 Arecibo pulsar survey.

~7-hour orbit, 60-ms pulse period, companion is another NS.

Measured change in orbital period exactly matches GR prediction for emission of GW → 1993 Nobel prize in physics for Hulse and Taylor. First evidence for GW!

Also provided accurate masses for both stars:

M1 = 1.4398(2) M

sun

M2 = 1.3886(2) M

Sun

Three PKparamsmeasured

J0737—3039: A double pulsar system

Discovered in 2003 in Parkes multibeam survey.

Extreme NS-NS binary: 2.4-hr orbit, 22-ms period, viewed nearly edge-on (allows Shapiro delay). Excellent GR test!

Only such system where both stars are (were) visible as pulsars.

M1 = 1.3381(7) M

sun

M2 = 1.2489(7) M

Sun

May eventually provide moment of inertia via spin-orbit effects. (Kramer et al. 2006)

Masses from Shapiro delay

Long-term, eccentric orbit

Eccentric orbit

Long-term, compact orbit

Short-term, geometry

Orbital evolution needs eccentric, compact orbit → mainly possible in DNS systems. NS-WD binaries tend to have very circular orbits.

Other non-GR effects (tidal effects, galactic acceleration) can contribute systematic errors to mass measurements.

Shapiro delay avoids both issues, but is a smaller-amplitude effect, so harder to detect. Main requirement is ideal alignment of orbit wrt Earth.

Shapiro delay

General relativistic time delay from propagation through curved spacetime. First detected in solar system radar experiments.

Shapiro delay in pulsar binariesFirst SD detection in a pulsar binary system: PSR B1855+09 (Ryba & Taylor, 1991)

NRAO / Bill Saxton

MPSR

= 1.27(20) Msun

i = 88.3(7) deg

Shapiro delay in pulsar binaries

Shape and amplitude of signal highly dependent on orbital inclination – “edge on” (i = 90 deg) gives sharp peak, stronger signal.

3-ms pulsar in an 8.7-day orbit with a WD.

Marginal Shapiro delay after ~7 years of GBT timing with older generation of backend instruments (Spigot, BCPM, GUPPI-1, etc):

PSR J1614-2230

Orbital inclination = 89.17(2) deg!

Companion mass = 0.500(6) solar!

Pulsar mass = 1.97(4) solar!

Improved instrument (better BW, time resolution) plus lots of telescope time → dramatically improved data quality.

… ~1 week of dense timing observations with upgraded GUPPI:

(Demorest et al, 2010)

Extremely compact NS-WD binary (Antoniadis et al 2013)

WD optical radial velocity + PSR radio timing → Mass ratio

Mass ratio + WD spectrum → MPSR

= 2.01(4) Msun

Mass ratio + orbital period derivative + GR → MPSR

= 2.07(20) Msun

Radio plus optical: PSR J0348+0423

Mass-radius plot with observations

(Figure: N. Wex)

Black widow pulsar systems

PSR in binary with low-mass, “puffy” companion. Often show ecplises.

Are being discovered in greater numbers via Fermi source followup.

“Messy” binary does not permit GR-based mass measurement.

Radio timing plus optical obs and companion modeling give intriguingly high masses!

B1957+20: MPSR

~ 2.4 Msun

(van Kerkwijk et al

2011)

J1311-3430: MPSR

~ 2.1 to 2.7 Msun

(Romani et

al 2012)

(See R. Romani talk later this session for more!)

(van Kerkwijk et al 2011)

NS mass compilation

(Watts et al 2015; AASKA)

LMXB Optical DNS MSP

Statistical analysis – NS mass distribution

(Watts et al 2015)

(Ozel et al 2012)

Growing total number of measurements.

Eventually may be able to statistically constrain maximum mass.

LMXB Opt DNS MSP

Somehwat unclear whether statistical maximum mass determination will tell us more about physics or astrophysics.

(See also Ozel et al 2012, Kiziltan et al 2010, …)

Statistical analysis – orbital inclination distribution

(Sanpa-arsa, Ransom et al)

Assuming Pb – M

c relation (Tauris & Savonije 1999) and NS mass

distribution (Ozel et al 2012), can test distribution of cos(i).

Does not directly use detected Shapiro delay or other PK params.

Shows either inconsistency with “flat cos(i)” or wrong assumption.

Non-flat cos(i) could be due to PSR beaming direction effects.

Fourier decomposition of Shapiro delay

H1

Full

H3+

H2

H3

H4

Introduced by Freire & Wex (2010).

First two harmonics (H1, H2) totally covariant with other basic orbital params.

“Unabsorbed” (ie, detectable) Shapiro signal encoded in H3 and higher harmonics.

Fourier decomposition of Shapiro delay

(Freire & Wex 2010)

Provides better parameterization than traditional (r,s) – especially for low-i or low-significance detections. If used consistently may help inform statistical population analyses; this is now beginning to be done (e.g. Fonseca et al. NANOGrav binary analysis).

Noise modeling and Bayesian analysis

Recent work in PTA/GW context has provided tools for advanced noise analysis and Bayesian parameter estimation (Ellis, van Haasteren, et al) → will lead to more robust mass measurements from timing.

(plots: J. Ellis)

Noise modeling and Bayesian analysis

(NANOGrav, Arzoumanian et al 2015)

Pulsar timing arrays

Large ongoing effort worldwide to detect nHz-frequency GW using MSP timing.

(IPTA 2014 meeting, Banff, Canada)

Pulsar timing arrays

(NANOGrav 9-year data; plot D. Nice)

PTA projects are conducting regular observations of many MSPs (~50 in upcoming NANOGrav 11-year data set). ~70% are in binary systems.

Data are taken long-term using very consistent observational setup/procedures; analyzed using consistent methodologies.

Data volume results in more NS mass measurements; consistency may also help provide a relatively unbiased data set for statistical population analysis.

(See next talk by E. Fonseca for binaries in the NANOGrav 9-year data set!)

The future – improving NS mass measurements

Conceptually easy:

Surveys to increase number known MSPs; small fraction will be suitable for mass measurement or otherwise exotic.

Improve instrumentation for better timing precision on known pulsars; detect smaller timing effects.

Upcoming instrumental improvements on current telescopes:

“Backend” (digital) development – mostly done.

“Ultra-wide band” receiver systems for improved timing.

Multi-pixel feeds for better survey speed.

New (larger) telescopes.

“Ultra-wideband” receiver systems

Standard receivers have octave (2:1) BW. New quad-ridge designs go up to ~6:1. Could improve S/N and DM estimation; however likely noise penalty. Ongoing developments at Effelsberg, Parkes, FAST, etc.

Telescopes for searching and timing

Current US pulsar telescopes:

Green Bank Telescope: 100-m single steerable dish

Arecibo: 305-m fixed reflector

Other upcoming GHz-freq telescopes:

FAST (China): 500-m, Arecibo-like; ~2016-2017

MeerKAT (SA): 64 x 13.5-m; 2017

SKA1-Mid (SA): 133 x 15-m + MeerKAT; ~2020

Lower-freq instruments: LOFAR, MWA, CHIME, SKA1-Low, …

Complementary searches and ISM monitoring.

Further off (~2030s): SKA2, next-gen VLA, … ?

Future telescopes – FAST (China)

500-m “Arecibo-style” fixed reflector; 40 deg zenith angle range; currently under construction, first light expected this year, drift-scan mode for at least first ~year. Sensitivity should be ~2x Arecibo.

Future telescopes – MeerKAT (South Africa)

64-element array of 13.5-m dishes; under construction. 16-element array this year, full array mid-2017.

Sensitivity ~ GBT; southern hemisphere location ideal for pulsar observing.

SKA pulsar searches

(Keane et al, AASKA14)

Searches with SKA telescopes should increase total known pulsar population by a factor of ~2—5.

SKA2 should find majority of detectable pulsars in the galaxy.

Shapiro delay detectability

Improved timing precision → higher fraction of systems with detectable Shapiro delay. ~80% of orientations have > 50 ns signal (assuming “flat cos(i)” distribution).

(Watts et al 2015)

Challenges – Pulsar searches with arrays

(Plot: S. Ransom)

Challenges – ISM timing effects

Wavelength-dependent timing effects due to multi-path propagation through ISM. Influences optimal frequency choice for PTA and other timing projects (higher freq → less ISM influence but PSRs are fainter).

(NANOGrav, Arzoumanian, et al 2015)

Challenges – Intrinsic pulse jitter

Extreme example, individual pulses from magnetar J1745–2900:

(Bower et al. 2014)

Jitter averages down over time but not over BW or collecting area.MSPs likely show similar behavior, only detectable statistically (e.g., Shannon et al 2014; Dolch et al 2014)

Summary

Radio timing of MSPs offers a number of direct measurements of NS mass

In recent years, measurements of several ~2-solar-mass NS.

PTA projects currently motivating advances in timing data analysis and observations.

Moving into regime of large numbers of masses, allows statistical analysis.

Many future telescopes planned and under construction will perform radio pulsar searches and timing over the next 10 – 20 years.

Will increase number of measured masses by at least factor of several.