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Neutron Star (Mostly Pulsar) Masses

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

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Neutron Star (Mostly Pulsar) Masses

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  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 ~108 to ~5 x1013 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. Pulsar Timing in a Nutshell Standard profile Measure offset Observed profile 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 PSR J1751-2857 – Stairs et al. (2005) Gaussian residuals imply a good ephemeris.

  6. The Pulsar Population

  7. Binary Pulsars Doppler shift in period is quickly obvious. All systems: fit basic Keplerian parameters: Pb, ecc, asini = x, ω and T0.

  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 Mʘ

  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 ± 0.04Mʘ NS:1.24 ± 0.11 Mʘ 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 Mʘ pulsar.” Early data was folded with a bad ephemeris, distorting the profiles, and this turns out to have corrupted the measurement.

  15. PSR J0751+1807: Shapiro delay and orbital decay This was “the 2.1 Mʘ 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 Mʘ at 68% confidence. Nice, Stairs & Kasian, “40 Years of Pulsars” proceedings (2007).

  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 binariescan be found in Lattimer2010 review in Ap&SS.Here are massesfor radio pulsars. Are the differences significant? due to evolution?

  19. There are also several eccentric systems in globular clusters for which we have measured . 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. M28 and Ter5 numbers still preliminary -- do not quote!

  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!

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