Talk presented at the MG14 meeting in Rome

1. The Pulsar Mass Distribution
John Antoniadis
Marcel Grossmann Meeting, Rome July 13th

2. 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
Triple
MSCompanion
WDCompanion
NSCompanion
Eclipsing
XBs

3. 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

4. Pulsar Timing Measurements
PK = f(K; mp, mc)
Parametrized post-Keplerian formalism
For a wide class of gravity theories:
(Damour 1988, Damour & Taylor 1992 )
˙!
E
˙Pb
˙! = 3
✓
Pb
2⇡
◆ 5/3
(T M)2/3
(1 e2
) 1
E = e
✓
Pb
2⇡
◆1/3
T
2/3
M 4/3
mc(mp + 2mc)
˙Pb =
192⇡
5
✓
1 +
73
24
e2
+
37
96
e4
◆
(1 e2
) 7/2
T
5/3
mpmcM 1/3
r = T mc s = sin i
In General Relativity:

5. 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!!!
mc
Pb
.
Pb
.
mc
qq
JA et al. 2012

6. Extrema
PSR 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

7. Extrema
PSR 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

8. Extrema
PSR J0348+0432
JA et al. 2013
P
.
bP
.
b
MWD MWD
q q
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

9. 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

10. Constraints on the EoS
Courtesy: N. Wex

11. Possible Complementary Constraints
Eccentric 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

12. 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

13. Scenario Β (exciting!)
Phase transition from neutron star to strange quark star (Long et al. 2015)
Eccentric MSPS: Possible Formation Scenarios
Core Density in LMXBs reaches
threshold for quark
deconfinement ->
Transformation to Strange Quark
Star
Again similar masses(?)
Constraints on binding energy

14. Scenario C (boring…)
Interaction of the proto-WD with a circumbinary disk (JA, 2014, ApJL)
Eccentric MSPS: Possible Formation Scenarios
Mass distribution should be identical to those of regular MSPs

15. Eccentric MSPS: Possible Formation Scenarios
• 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 :-(

16. 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]

17. The MSP mass distribution
Evidence 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)

18. 350 MSPs
3σ
2σ
1σ
500 MSPs
3σ
2σ
1σ
Implications for EoS constraints
The MSP mass distribution
At least 350 MSP masses in the future
with SKA phase-II, GAIA, LSST…

19. 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)