Recent Measurements of Millisecond Pulsar Masses

Recent Measurements of Millisecond Pulsar Masses

Recent Measurements of Millisecond Pulsar Masses

Recent Measurements of Millisecond Pulsar Masses Paulo C. C. Freire Arecibo Observatory / Cornell University Physics Department / West Virginia University

Recent Measurements of Millisecond Pulsar Masses
  • In this talk...
  • Normal Pulsars and Millisecond Pulsars.
  • How to Measure Pulsar Masses.
  • Why look in globular clusters?
  • Mass measurements in globular clusters: The early years.
  • Some late surprises!
  • Measuring the mass of the PSR J1903+0327 (Parts I & II)
Recent Measurements of Millisecond Pulsar Masses
  • Normal Pulsars and Millisecond Pulsars
  • The main difference between normal and recycled pulsars is not merely the spin period, which is faster for the second class. Recycled pulsars also spin down much more slowly.
  • Furthermore, many more of them are in binary systems!
  • The fast-spinning objects (P < 8 ms) - the millisecond pulsars (MSPs) are either isolated or have light white dwarf companions and low-eccentricity orbits.
  • Some of the slower-spinning recycled pulsars (8 < P < 110 ms) are either isolated, or they have a massive white dwarf or a neutron star companion. The orbits for these systems are generally eccentric!
Recent Measurements of Millisecond Pulsar Masses
  • Normal Pulsars and Millisecond Pulsars
  • The differences among the recycled pulsars reflect different evolution scenarios!
  • If the companion is massive, accretion won’t last long - mildly recycled pulsar. The massive companion then goes supernova, producing a double neutron star system (DNS).
  • If companion is not so massive, it will evolve to a white dwarf. In this case, accretion lasts much longer! Resulting pulsar should spin much faster and it should be much more massive. From: Duncan Lorimer’s Living Review on Binary and Millisecond Pulsars
Recent Measurements of Millisecond Pulsar Masses
  • Summary
  • Pulsars in double neutron star systems are mildly recycled (or not at all for their companions)
  • Their orbits are eccentric.
  • Millisecond pulsars in binary systems have white dwarf companions.
  • Their orbits are circular.
  • They could be more massive than members of DNSs.
Recent Measurements of Millisecond Pulsar Masses
  • How to Measure Pulsar Masses
  • Five Keplerian parameters can normally be measured from fitting the velocity (or, preferably, the delay) curves: orbital period (Pb), projected size of the orbit, in light seconds (x), eccentricity (e), longitude of periastron (ω) and time of passage through periastron (T0). A non-changing Keplerian orbit is exactly what is predicted by Newtonian gravity.
  • Without access to information on transverse velocities, the individual masses of the components (m1 and m2) and the inclination of the system (i) cannot be measured, but...
  • The mass function, a relation between these three quantities, can be measured to excellent precision, as it depends on two observable parameters:
Recent Measurements of Millisecond Pulsar Masses
  • How to Measure Pulsar Masses
  • According to general relativity, these quantities depend on the known Keplerian parameters and the masses of the two components of the binary.
  • We now have three equation for three unknowns! We can determine the masses of the components and the inclination.
Recent Measurements of Millisecond Pulsar Masses

  • How to Measure Pulsar Masses
  • An excellent example is “the” (first) binary pulsar, PSR B1913+16, discovered at the Arecibo Observatory by Russell Hulse and Joe Taylor.
  • Mass determination lead to prediction of the orbital decay due to emission of gravitational waves: the orbital period should getting 75.8 microseconds shorter every year. From: Weisberg and Taylor, ASP Conf. Series vol. 302, p. 93, 2003

Recent Measurements of Millisecond Pulsar Masses
  • Neutron Star Masses
  • Several neutron star masses have been measured precisely. Almost all of these are in DNS systems, like PSR B1913+16 or PSR J0737-3039. This happens because they have eccentric orbits, where more relativistic effects can be measured. Their masses range from 1.25 to 1.44 solar masses.
  • Because of prolonged accretion, MSPs could be a lot more massive. But are they?
  • MSP masses are difficult to determine – in the Galaxy, the orbits are very circular, so normally no relativistic effects can be used to provide extra equations to solve for m1, m2, i, as for the DNS.
  • A precise measurement of the mass of a MSP (PSR J1909–3744, Jacoby et al. 2005) based on the Shapiro delay yielded a pulsar mass of 1.47 solar masses (Hotan, Bailes and Ord 2006).
  • However, there have been claims of more massive MSPs! Unfortunately, no other MSP masses can be precisely determined for the Galactic systems!
Recent Measurements of Millisecond Pulsar Masses
  • Neutron Star Masses
  • One of the best diagnostics of the EOS for super-dense cold matter is finding the upper limit for NS masses.
  • The existence of massive neutron stars would indicate that matter is highly incompressible. From: Lattimer and Prakash, 2007, Phys. Rep. 442, 109
  • Why Look for MSPs in Globular Clusters?
  • MSPs in globular clusters can be particularly useful to this experiment:
  • There are twice as many MSPs known in globular clusters as in the Galactic Disk.
  • MSPs in globular clusters can be in eccentric orbits, because of:
  • Perturbations from passing stars
  • Exchange interactions
  • Eccentric orbits allow the measurement of post-Keplerian effects; like the precession of periastron and (much later) the Einstein delay.
  • These, in turn, allow the measurement of MSP masses!
  • Why Look for MSPs in Globular Clusters?
  • So, the question is, How Massive are MSPs in Globular Clusters?
  • Let’s first find them, and then time them - and hopefully, in a few cases, find their masses!
  • Millisecond Pulsars in 47 Tucanae
  • We (Paulo Freire, Duncan Lorimer, Michael Kramer, Fernando Camilo, Andrew Lyne, Richard Manchester and Nicolo D’Amico) used the Parkes Multibeam system to search for new pulsars in 47 Tucanae.
  • We found eleven new MSPs! (Camilo et al. 2000, ApJ, 535, 975, Freire et al. 2009, MNRAS, in preparation)
  • We also used these observations to determine the orbit and timing solution of PSR J0024-7204H, one of the 11 previously known pulsars (Manchester et al., 1991, Nature, 352, 219).


  • Millisecond Pulsars in 47 Tucanae
  • PSR J0024-7204H is a 3.21-ms pulsar with an orbital period of 2.350 days and an orbital eccentricity of 0.0705.
  • Assuming a pulsar mass of 1.4 solar masses, the companion has a minimum possible mass of 0.19 solar masses. Cover of the ASP proceedings of the “Radio Pulsars” conference (ASP 302), ed. M .Bailes, D. Nice, D. and S. E. Thorsett. Optical image of 47 Tucanae: AAT

  • Millisecond Pulsars in 47 Tucanae
  • The rate of advance of periastron allows an estimate of the total system mass for PSR J0024-7204H: (1.61±0.04) solar masses (Freire et al. 2003, MNRAS, 340, 1359).
  • The pulsar mass can not be larger than 1.52 solar masses, the companion has a mass larger than 0.16 solar masses.
  • This was (as far as I know) the first measurement shows that the recycling of a MSP can be accomplished with ~0.1 solar masses.
  • Is this the case for all MSPs? From: Freire et al., 2003, MNRAS. 340, 1359
  • A Millisecond Pulsar in NGC 1851
  • In 2003, we (Paulo Freire, Yashwant Gupta and Scott Ransom) used the GMRT to search for pulsars in 11 GCs.
  • One pulsar was found: PSR J0514–4002A, in NGC 1851. This object has a spin period of 4.99 ms (Freire et al. 2004, ApJL, 606, 53).
  • Previously, nearly all known MSPs had low-eccentricity orbits. NGC 1851A has an orbital eccentricity of 0.89, the highest known at the time!
  • This violates the normal rules of stellar evolution! From: Freire et al. 2004, ApJ Lett., 606. 53
  • A Millisecond Pulsar in NGC 1851
  • This system was probably formed by an exchange interaction. These are only likely to happen in environments with very high stellar densities, like globular clusters.
  • The same mechanism could also form a MSP-MSP system or a MSP-BH system! Such systems would be the ultimate probes of GR, particularly if they could be timed with the SKA!
  • The high eccentricity allows a measurement of the periastron advance, indicating a total system mass of 2.453(14) solar masses.

The pulsar has a maximum mass of 1.5 solar masses (Freire, Ransom and Gupta, 2007, ApJ, 662, 1177). Again, not significantly larger than previous neutron star mass measurements! From: Freire, Ransom and Gupta, 2007, ApJ 662, 1177

  • PSR J1911-5958A
  • This 3.27-ms pulsar was discovered in 2001, in the Southern globular cluster NGC 6752 (D’Amico et al. 2001, ApJ, 548, 171)
  • It has a ~0.2-solar mass companion in a 0.837-day orbit. The eccentricity is < 10–5.
  • Bassa et al. (2006, A&A, 456, 295) have estimated the mass of the companion from its observed optical spectrum and estimated (cluster) distance: 0.175 ± 0.010 solar masses.
  • From the orbital variations in the Doppler shift, they could also estimate the mass ratio for this binary: MPSR/MWD = 7.36 ± 0.25.
  • From this, they derive a pulsar mass of 1.34 ± 0.08 solar masses.
  • This is consistent with a similar mass determination made by Cocozza et al. (2006, ApJ, 641, 129)
  • These highly recycled MSPs seem to have masses similar to those of neutron stars in DNS systems!!!
  • Accretion can definitely be achieved with very small amounts of matter, confirming the result of PSR J1909–3744!
  • Is this the case for all MSPs? All we can do is to keep searching for more eccentric binaries, measure any PK parameters we can, and see what we find.
  • A Search for Millisecond Pulsars in Terzan 5
  • In 2004, we (Scott Ransom, Jason Hessels, Ingrid Stairs, Paulo Freire, Vicky Kaspi, Fernando Camilo and David Kaplan) used the S-Band receiver of the Green Bank Telescope and the pulsar spigot to find 30 new MSPs in the globular cluster Terzan 5 (Ransom et al. 2005, Science, 307, 892). All of these have timing solutions now! Picture Above courtesy of Scott M. Ransom NRAO
  • A Search for Millisecond Pulsars in Terzan 5
  • Terzan 5 has five of the ten fastest known millisecond pulsars anywhere, including the fastest: PSR J1748-2446ad (rotating 716 times per second)!
  • Six of the new systems in Terzan 5 (I, J, Q, U, X and Z) have orbital eccentricities above 0.3!
  • Terzan 5 I is a 9.57-ms pulsar in a 1.33-day orbit with a 0.24-solar mass companion. The orbital eccentricity of this system is 0.43.
  • Terzan 5 J is a 80.3-ms pulsar in a 1.10-day orbit with a 0.39-solar mass companion. The orbital eccentricity is 0.35.

The compactness of these orbits allowed the measurement of the rate of advance of periastron for these two binaries by 2005: they have total masses of 2.17(2) and 2.20(4) solar masses respectively.

  • A Search for Millisecond Pulsars in Terzan 5
  • If this effect is fully relativistic, two systems (I and J) could host massive pulsars: their median masses are 1.86 and 1.76 solar masses.
  • There is a 95% probability that one of them is more massive than 1.68 solar masses.
  • Still, it is possible that these are being seen at low inclination! From: Ransom et al., 2005, Science, 307, 892
  • Arecibo Timing of M5B
  • Discovered by A. Wolszczan in 1989 using the Arecibo telescope, PSR B1516+02B was one of the first MSPs to be found in a globular cluster (NGC 5904, or M5), for that reason it is also known as M5B.
  • Timing solution found by Anderson et al. (1997, ApJ, 482, 870). It is a 7.95-ms pulsar in a 6.85-day orbit with a 0.13-solar mass companion. The orbital eccentricity is 0.14, the highest known at the time for a MSP.
  • Precession of periastron was detected, but no astrophysically useful mass limits were derived! NAIC / Arecibo Observatory
  • Arecibo Timing of M5B
  • The Arecibo upgrade, in the late 1990s, has allowed the use of much higher frequencies and increased bandwidths.
  • An Arecibo L-band globular cluster survey started in 2001, this discovered a total of 13 new MSPs in several globular clusters in the Arecibo Sky (Hessels et al. 2007, ApJ, 670, 363).
  • This found 3 new pulsars in M5. These were timed until the present (Stairs et al., in preparation)
  • Data was also used to time previously known pulsars, PSR B1516+02A and B at L-band.

The rate of advance of periastron is now determined with high significance!

  • Arecibo Timing of M5B
  • The total mass of the system is remarkably similar to the total masses of Terzan 5 I and J: 2.29(17) solar masses.
  • Pulsar mass: 2.08+0.18 –0.19 solar masses. There is a 0.77% probability that the mass of the neutron star is “normal”.
  • Pulsar mass is similar to Terzan 5 I and J. There is a 95% probability that it is more massive than 1.72 solar masses. (Freire et al. 2008b, ApJ,679, 1433) From: Freire et al. 2008b, ApJ, 679, 1433
  • Arecibo Timing of M5B
  • HST archival images of the position of M5B don’t show any companions down to magnitude 26.5.
  • This implies that, if companion is a MS star, its mass is below 0.25 solar masses.
  • Otherwise, it is a white dwarf.
  • In either case, rotational effects are likely to be negligible! The periastron advance is therefore very likely to be relativistic. From: Freire et al. 2008b, ApJ, 679, 1433 (2008)
  • New Globular Cluster Searches: 35 New MSPs!
  • Motivated by the spectacular Terzan 5 results (30 new MSPs to date!), we decided to use the same observing system to search for pulsars in other globular clusters.
  • So far we have found 35 new MSPs in other globular clusters!
  • Eleven of these were found in the globular cluster NGC 6626, or M28 (Steve Bégin, M.Sc. Thesis, Begin et al. 2009, ApJ., in preparation)
  • Two of them are in eccentric orbits: PSR J1824–2452C and PSR J1824–2452D.
  • PSR J1824–2452C is a 4.159 ms pulsar in a 8.0-day orbit with a 0.25-solar mass companion. The orbital eccentricity is 0.85! Maximum possible mass: 1.35 solar masses!

PSR J1824–2452D is a 79.8-ms pulsar in a 30-day orbit with a 0.37-solar mass companion. The orbital eccentricity is 0.78!

  • NGC 6440B
  • The same GBT/S-band/SPIGOT survey has also found 8 new MSPs in NGC 6440 and NGC 6441 (Freire et al. 2008a, ApJ, 675, 670). AAT
  • NGC 6440B
  • One of the new discoveries is PSR J1748-2021B, or NGC 6440B. It is a 16.7-ms pulsar in an eccentric (e = 0.57) 20.5-day orbit with a ~0.1 solar mass companion. Image courtesy of Scott M. Ransom
  • NGC 6440B
  • After ~1 year timing this pulsar, we have obtained a good measurement of the rate of advance of periastron. If fully relativistic, this implies a total system mass of ~2.92 ± 0.25 solar masses. It could be a double neutron star system!
  • The companion has only ~0.1 solar masses. Median of probability for pulsar mass is 2.74 solar masses.
  • There is a 99% probability of mass being larger than 2 solar masses, 0.1% probability of having a “normal” mass.
  • Is this a super-massive neutron star? From: Freire et al. (2008a), ApJ 675, 670
  • NGC 6440B
  • If it is a DNS binary, there is a 1% chance of finding such a low inclination among the known DNSs.
  • Another possibility is that this is a 2.1-solar mass pulsar like M5B with a massive companion seen at low inclination! Perhaps a better alternative than new physics!
  • We will only know the real masses over the next few years, with increases in the precision of the advance of periastron, measurements of the relativistic gamma and multi-wavelength studies of the companion star.
  • Hubble Space Telescope time already approved to look for the companion star. If it is a MS star (a possible origin of a classical contribution), it should be readily detectable in HST images.This will allow a verification on whether periastron advance is relativistic.
  • Ongoing surveys are finding more MSPs, and more objects with eccentric orbits!
  • Therefore, next few years are going to be a lot of fun for our group!!!
  • NGC 6440B
  • Confirmation of a very high pulsar mass would have revolutionary implications for the study of the EOS. It would imply that matter at the center of neutron stars can propagate sound waves at nearly the speed of light! This would exclude most known models for the behavior of matter at supra-nuclear densities!
  • MSP Ensemble
  • If the masses of M5B and NGC 6440B are confirmed, that will also mean that millisecond pulsars have a much broader mass range than previously thought - by a factor of two!
  • This is much wider than observed for the neutron stars in double neutron star systems.
  • The likely reason for this is the accretion of material into the neutron star that was needed to recycle it into a millisecond pulsar.
  • Strange new trend: more massive objects have much smaller spin frequencies! M5B NGC 6440B 0 0.5 1 1.5 2 2.5 3 3.5 4 Pulsar Mass (Solar Masses) Probability density From: Freire et al. 2008b, ApJ, 679, 1433
  • Summary
  • Over the last 20 years, many MSPs were found in globular clusters. Their number quadrupled in the last 10 years, with the discovery of more than 100 new objects.
  • An increasing number of MSPs is being found in eccentric binary systems.
  • Timing campaigns are now determining post-Keplerian parameters for some of these orbits, constraining the masses of the components in these binaries.
  • Many of these are indistinguishable from the masses of mildly recycled NS, indicating that accretion does not necessarily add much mass to the NS. However, some MSPs seem to be significantly more massive than 1.44 solar masses i.e., the range of masses observed for MSPs appears to be much wider than what is observed for normal NSs.
  • Over the next few years, real masses will be measured with much better precision.
  • Some of these high masses might pose extreme constraints on the EOS for dense matter.

Measuring the Mass of PSR J1903+0327 Collaborators: Scott Ransom (NRAO), David Champion (ATNF), Patrick Lazarus (McGill), Fernando Camilo (Columbia), Victoria Kaspi (McGill), David Nice (Bryn Mawr), Ingrid Stairs (UBC), Ben Stappers (University of Manchester), Julia Deneva (Cornell) and James Cordes (Cornell)

The PSR J1903+0327 Binary System With a spin period of 2.15 ms, PSR J1903 +0327 was the first millisecond pulsar (MSP) discovered in Arecibo’s ALFA pulsar survey.

It is in a 95-day binary system. Its mc ~ 1.0 Msun companion is by far the most massive of any MSP with a similar spin period. It is the first millisecond pulsar in the disk of the Galaxy to have an eccentric orbit: e = 0.44. All other MSPs in binary systems have e < 0.002 (Champion et al., Science, 320, 1309). It is very difficult to explain the formation of such a binary system with previous stellar evolution theory.

From: Champion et al., Science, 320, 1309 (2008)

The PSR J1903+0327 Binary System The system is even harder to explain if the companion turns out to be a main sequence (MS) star as suggested by the presence of a source with a coincident position in optical observations! No previously known MSP in the Galactic disk has a MS companion. Champion et al. (2008) estimate a 2.6% probability of a chance alignment. Follow-up at optical wavelengths will verify this possibility, and possibly allow an estimate of the mass ratio. From: Champion et al., Science, 320, 1309 (2008)

From: NRAO / Cornell University Press Release

Measuring the Mass of PSR J1903+0327: Part I Apart from presenting an evolutionary puzzle, the unusual characteristics of this binary system are interesting because they allow the measurement of postKeplerian orbital parameters that lead to a precise determination of the masses of the components of the system. The eccentricity of this binary system allowed a measurement of the apsidal motion even in the early GBT timing. Assuming GR is correct, this gives us the total mass of the system. The large companion mass, coupled with the good timing precision, allow a measurement of the Shapiro delay.

This is a truly unusual set of circumstances for a MSP binary system! From: Champion et al., Science, 320, 1309 (2008)

Measuring the Mass of PSR J1903+0327: Part I In Champion et al. (2008), only the “Shape” of the Shapiro delay (s) was measured with any degree of confidence. In most theories of gravitation, this measures the sine of the orbital inclination. Nevertheless, combining the early apsidal motion and the measured s, Champion et al. derived a pulsar mass of 1.74 +/- 0.04 solar masses, and a companion mass of 1.07 +/- 0.02 solar masses! This is potentially interesting for studies of the EOS for dense matter! From: Champion et al., Science, 320, 1309 (2008), on-line additional reference material

Measuring the Mass of PSR J1903+0327: Part I Caveats: If the companion is indeed a MS star...

and it is rotating fast, then it could add a classical term to the observed apsidal motion (Dicke’s condition). In that case, we can’t estimate the total mass of the system from this effect. ... and has a strong wind, there might be increases in the delay near superior conjunction due to propagational effects in the companion’s wind. These would contribute to the Shapiro delay. The GBT measurements do not show this effect within measurement accuracy.

Image courtesy: Ransom, Camilo (2008)

Measuring the Mass of PSR J1903+0327: Part II To eliminate (or confirm) these pesky possibilities, and improve the precision on the PK parameters, we started timing the pulsar regularly at Arecibo at several frequencies: At 2.0 - 2.4 GHz we can achieve a precision of 0.55 us every 500 seconds for a total bandwidth of 200 MHz. Pulsar is joining the array being used for detection of gravitational waves. This has improved significantly the measurement of the apsidal motion (86.58 +/- 0.25 arcseconds per century), of s (0.977 +/- 0.002, implying an orbital inclination of about 78 degrees) and now allows a measurement of the “range parameter” (r) of the Shapiro delay.

In general relativity, this parameter is proportional to the companion mass. This is very important to confirm whether (or not!) the apsidal motion is fully relativistic. Multi-frequency observations (to be obtained around June 2009) at 1.5 and 3.5 GHz will produce much improved limits on the extra electron column density at superior conjunction. These measurements can rule out (or not!) any significant contributions to the timing of the extra gas near superior conjunction.

Results The improvement in the apsidal motion and the Shapiro s now leads to a pulsar mass of 1.67 +/- 0.01 solar masses. This is 1.75-sigma lower that the measurement in Champion et al. (2008), the variation is probably caused by correlations with other parameters. The mass measurement has became very stable after 1 year of S-band Arecibo data. These parameters predict a companion mass of 1.028 +/- 0.004 solar masses. The companion mass derived from Shapiro r is 1.00 +/- 0.04 solar masses. The predicted value is 0.7 sigma above this - not statistically different. From: Freire et al., 2009 (in preparation)

Results The mass predicted from the Shapiro r and s is 1.58 +/- 0.12 solar masses, i.e., we can’t exclude a “normal” mass of 1.4 solar masses based on the Shapiro effect alone. But likewise, we can’t exclude from the Shapiro effect alone the possibility that the apsidal motion and s are giving us the real pulsar mass. More measurements will improve r and disentangle it better from astrometric and other orbital effects. We hope to decide conclusively for either possibility based on the Shapiro effect alone.

The proper motion already affects the apsidal motion at a level similar to its present measurement uncertainty.

From: Freire et al., 2009 (in preparation)

Summary Combining the apsidal motion and the Shapiro s, we obtain a pulsar mass of 1.67 +/- 0.01 solar masses. A precise measurement of the Shapiro r has not contradicted the assertion that the apsidal motion is relativistic! This is the most precise mass ever derived for a millisecond pulsar. This is also the largest pulsar mass that has ever been precisely measured. It is also the only one that is backed up with extra PK parameters. It shows that during accretion, millisecond pulsars can become more massive than “normal” pulsars. More measurements will improve all the PK parameters and show whether the Shapiro delays are contaminated by dispersive delays or not.

If companion is optically detected, we might measure the mass ratio and test GR precisely in a system with two components of very different degree of compactness. Although not spectacular, this is a very solid constraint on the EOS.

  • Thank you for your time!
  • For questions, comments, discussion, contact me at:, or visit my website at
  • For an up-to-date list of pulsars in globular clusters, check GCpsr.html The National Astronomy and Ionosphere Center is operated by Cornell University, under a cooperative agreement with the National Science Foundation. The National Radio Astronomy Observatory is a Facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Incorporated. The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by the CSIRO.

India’s Giant Metrewave Radio Telescope is run by the National Center for Radio Astrophysics of the Tata Institute of Fundamental Research

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