the pulsar mass distribution

The Pulsar Mass DistributionJohn Antoniadis

Marcel Grossmann Meeting, Rome July 13th

NS mass measurements - Overview

• Information on masses for about 70 binary systems• Excluding marginal detections, strongly model-dependent measurements, probabilistic arguments,

then we have 35 precision measurements, all of them for DNS and millisecond binary pulsars• 10 additional systems with constraints on the total mass• Only few extrema, recent measurements

Trip

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Pulsar Timing Measurements

TOA residual

model

fold fold

Session i Session j

KP: Orbital Period Eccentricity Inclination

Epoch of periastron Longitude of periastron Longitude of ascension Projected semi-major axis

PK: Precession of periastron ‘‘Einstein” delay Shapiro-delay “range”

Shapiro-delay “shape” Spin precession Orbital decay

D. Champion

Pulsar Timing Measurements

PK = f(K;mp,mc)

Parametrized post-Keplerian formalism

For a wide class of gravity theories:

(Damour 1988, Damour & Taylor 1992 )

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r = T�mc s = sin i

In General Relativity:

Caveats• Highest precision achieved for millisecond pulsars, but those are found in binaries

with extremely small eccentricity• Impossible to measure precession of periastron, thus mass measurements possible

only through Shapiro delay in high inclination systems

Optical Spectroscopy to the Rescue!!!

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JA et al. 2012

ExtremaPSR J1614-2230

Demorest et al. 2010

• Binary MSP with 8.7 days orbital period• Edge on inclination• Pulsar mass 1.97(4) solar masses

Revised value based on the 9-year NanoGrav dataset:(Arzurmanian et al. 2015; Arxiv:1505.07540)

1.928(17) Solar Masses

ExtremaPSR J0348+0432

• Relativistic binary MSP system with 2.5 hours orbital period• Low Mass White-Dwarf Companion• Pulsar mass 2.01(4) solar masses based on optical spectroscopy

MWD MWD

P.b

P.b qq

JA et al. 2013

ExtremaPSR J0348+0432

JA et al. 2013

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MWD MWD

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PSR J0348+0432

April 2014

• Relativistic binary MSP system with 2.5 hours orbital period• Low Mass White-Dwarf Companion• Pulsar mass 2.01(4) solar masses based on optical spectroscopy

Potential Extrema

• Example I: PSR J1748-2021B - GC MSP in eccentric orbit around low-mass companion. Total mass of the system 2.92(20) Solar Masses

• Example II: PSR J1012+0537 - Estimate based on revised WD models: 1.83(11) Msol• Example III: B1957+20 - MPSR = 2.40(12) Msol

Constraints on the EoS

Courtesy: N. Wex

Possible Complementary ConstraintsEccentric Millisecond Pulsars: A new class of binaries

Pulsar P (ms) Porb [days] Mc [Msol] eccentricity Companion Ref.

J1946+3417 3.1 27 0.24 0.13 ? Barr et al. 2013

J2234+0611 3.6 32 0.23 0.13 WD Deneva et al. 2013

J1950+2414 4.3 32 0.24 0.08 ? Knispel et al.

J1618-3921 12 23 0.20 0.027 ? Bailes et al. 2010

Scenario A (exciting!)Rotationally-delayed Accretion Induced Collapse of a Massive WD (Freire & Tauris 2014)

Eccentric MSPS: Possible Formation Scenarios

If correct, then all MSPs should have masses very close to the Chandrasekhar mass

…but mass measurements give a direct constraint on the gravitational binding energy

Scenario Β (exciting!)Phase transition from neutron star to strange quark star (Long et al. 2015)


Core Density in LMXBs reaches threshold for quark deconfinement -> Transformation to Strange Quark Star

Again similar masses(?) Constraints on binding energy

Scenario C (boring…)Interaction of the proto-WD with a circumbinary disk (JA, 2014, ApJL)


Mass distribution should be identical to those of regular MSPs


• White Dwarf has been detected in optical for PSR J2234+0611

• Measurement of the advance of periastron (+ Shapiro delay or optical) will

yield very precise masses for all of these systems

• At least one of them is massive ( > 1.85 Solar Masses), making A unlikely :-(

The MSP mass distribution• ~15% of MSPs are massive

• Past studies infer a normal distribution for MSPs with M~1.45 and ΔΜ~0.2 Solar Masses

(or less than 2% of MSPs above 1.9 Solar Masses)

• Distribution highly skewed or bimodal

Massive Pulsars May Not Be Outliers After All!!!

Ozel et al. 2012 Pulsar Mass [Solar Masses]

The MSP mass distributionEvidence for Bimodality

• Binormal distribution is highly favoured compared to alternatives (e.g. comparing in terms of a penalized likelihood, > 95% more likely)

• Peaks at m1,2 =1.4, 1.8 solar masses with Δm1 = 0.08, Δm2 = 0.2

• Expected from stellar evolution if there is a difference between stars burning carbon radiatively/convectively (Timmes et al. 1996)

350 MSPs

3σ

2σ

1σ

500 MSPs

3σ

2σ1σ

Implications for EoS constraintsThe MSP mass distribution

At least 350 MSP masses in the future with SKA phase-II, GAIA, LSST…

Summary

So far 20 precision mass measurements for MSPs of which 4 have a mass > 1.8 Msol

There seem to be clear ways to distinguish between AIC, strange stars and “normal” NSs in (some) binary systems

Massive Neutron Stars are not as rare as previously thought [15-20% are massive]

Millisecond Pulsar Mass Distribution is most likely bimodal

Strong constraints on the EoS, Mmax > 1.94 Msol (99.9% CL), but we will do better in the future

Double NS mass distribution (not discussed) also extremely interesting (check talk by Joey Martinez at BN3)

the pulsar mass distribution

Science