1. Neutron Star (Mostly Pulsar) Masses Ingrid Stairs UBC Vancouver CAWONAPS TRIUMF Dec. 9, 2010

2. Pulsars are one manifestation of neutron stars: spin periods ~1.4 ms to 8.5 seconds, magnetic fields ~10 8 to ~5 x10 13 G. Low fluxes mean large radio telescopes are needed to detect them.

3. Modern observing systems use the coherent dedispersion technique over hundreds of MHz of bandwidth. Result: sharp profile features are resolved, leading to more precise pulse Times of Arrival (TOAs). The wide bandwidths increase the signal-to-noise ratio and therefore also TOA precision. Build up a “standard profile” over hours/days of observing.

4. Standard profile Observed profile Measure offset Pulsar Timing in a Nutshell Record the start time of the observation with the observatory clock (typically a maser). The offset gives us a Time of Arrival (TOA) for the observed pulse. Then transform to Solar System Barycentre, enumerate pulses and fit the timing model.

5. Timing Residuals: Actual TOAs – Predicted Gaussian residuals imply a good ephemeris. PSR J1751-2857 – Stairs et al. (2005)

6. The Pulsar Population

7. Binary Pulsars Doppler shift in period is quickly obvious. All systems: fit basic Keplerian parameters: P b, ecc, asini = x, ω and T 0.

8. The 5 Keplerian parameters leave the two masses and the orbital inclination angle i unknown. These are related by the mass function:... but there are still two unknowns.

9. Mass function: So measuring masses is difficult! It's only possible when we can measure “post-Keplerian” (PK) parameters: advance of periastron, time dilation/redshift, orbital period decay and/or Shapiro delay.

10. Assuming general relativity (GR) is the correct theory of gravity, we can get the masses from the PK parameters:

11. The mass constraints are easily understood via a mass-mass diagram. Nice, Stairs & Kasian, “40 Years of Pulsars” proceedings (2007) J0621+1002: advance of periastron measured; limit on Shapiro delay Pulsar mass: 1.70 +0.10 -0.17 M ʘ

12. Shapiro Delay Timing signature can be partly absorbed into Keplerian parameters for circular orbits -- unless the orbit is nearly edge-on to the line of sight. 1802-2124: WD: 0.78 ± 0.04M ʘ NS: 1.24 ± 0.11 M ʘ Ferdman et al. 2010

13. Shapiro delay in PSR J1713+0747 Also other constraints on the inclination angle via geometric effects. Splaver et al., ApJ 620, 405 (2005).

14. PSR J0751+1807: Shapiro delay and orbital decay This was “the 2.1 M ʘ pulsar.” Early data was folded with a bad ephemeris, distorting the profiles, and this turns out to have corrupted the measurement.

15. Nice, Stairs & Kasian, “40 Years of Pulsars” proceedings (2007). PSR J0751+1807: Shapiro delay and orbital decay This was “the 2.1 M ʘ pulsar.” Early data was folded with a bad ephemeris, distorting the profiles, and this turns out to have corrupted the measurement. Pulsar mass is now 1.26 ± 0.14 M ʘ at 68% confidence.

16. More PK params in double-NS binaries PSR B1534+12 (Stairs et al, unpublished) 5 PK parameters including Shapiro delay ⇒ masses precisely measured PLUS self-consistency tests of GR or other theories of strong-field gravity.

17. The double pulsar J0737-3039A/B 5 PK params plus the mass ratio! (Therefore even more tests of strong-field gravity.) Kramer et al., 2006.

18. Well-measured masses for X-ray binaries can be found in Lattimer 2010 review in Ap&SS. Here are masses for radio pulsars. Are the differences significant? due to evolution?

19. There are also several eccentric systems in globular clusters for which we have measured. M28 and Ter5 numbers still preliminary -- do not quote! About half of these are pointing to highish pulsar masses – if is purely due to GR with no mass-quadrupole effects. Not sure what is going on with these! Note also several low-mass pulsars.

20. Future Prospects for Mass Measurements J1614-2230 and J1903+0327: starting to put useful constraints on the NS equation of state. J0737-3039: advance of periastron is so precisely measured that we may be able to measure the contribution from spin-orbit coupling and get the moment of inertia of pulsar A. Requires measuring s and very precisely. Hope to clear up masses in those eccentric globular-cluster systems, by measuring time dilation (γ) in some cases. Wide-band observing systems should lead to new results for more pulsars. Long-term: stay tuned for results from the SKA!