Spotting corpses using stopwatches

Using pulsar timings to detect compact stellar remnants.

Transcript

1. spotting corpses using stopwatches Using Pulsar Timings to Detect Compact Stellar Remants Daniel Williams Supervisors: Prof Graham Woan & Dr Norman Gray June 27 2015 School of Physics and Astronomy University of Glasgow
2. direct detection Neutron Stars ∙ Black body radiation Black Holes ∙ Hawking radiation Both black holes and neutron stars produce black body radiation: both have some form of temperature, but both have low luminosity. 1
3. indirect methods Pulsar Timing Shapiro delay Einstein delay Gravitational Lensing Photometric Astrometric Gravitational Interaction Orbits Accretion Magnetic Interaction ISM Shock wave 2
4. pulsar timing N(t) = νt + 1 2 ˙ νt2 Time 3
5. pulsar timing N(t) = νt + 1 2 ˙ νt2 + ϵ Time 4
6. a light excursion with gravity ∙ Light travels along “straight lines” (null geodesics) in spacetime. ∙ Massive objects bend spacetime (increases the length of light’s path) 5
7. shapiro delay 6
8. shapiro delay Path in flat space Path with gravitational potential 7
9. shapiro delay 40 20 0 20 40 Angular separation [as] 0 20000 40000 60000 80000 100000 120000 Total delay [ns] Delay from a solar mass object 1 pc from the Earth 8
10. shapiro delay 0° 45° 90° 135° 180° 225° 270° 315° Angle from line of sight (α) 0.5 1.0 1.5 2.0 Distance [pc] 25 50 75 100 125 150 175 200 Total delay [µs] 9
11. shapiro delay Added geometry = added travel time = additive time delay 10
12. a bit more time with gravity ∙ Massive objects bend spacetime ∙ Cause time dilation within their gravitational potential—causes clocks to run slow. 11
13. einstein delay 12
14. einstein delay 0° 45° 90° 135° 180° 225° 270° 315° Angle from line of sight (α) 0.5 1.0 1.5 2.0 Distance [pc] 50 100 150 500 1000 Total delay [µs] 13
15. einstein delay Time dilation = cumulative time delay 14
16. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Distance to neutron star [pc] 100 200 300 400 500 600 700 800 900 1000 Neutron star velocity [km/s] 20 y 30 y 40 y 50 y 60 y 70 y 80 y 90 y Figure 1: Contours of the detection times (in years) using the residual flatness method. The pulsar parameters used to generate the times-of-arrival in the simulation were consistent with a millisecond pulsar, with ν = 641 , and ˙ ν = −1.05 × 10−19 s−1, while the simulated timing errors had a standard deviation of 80 , with observations made at equal time intervals twelve times per year. 15
17. 0.0 0.2 0.4 0.6 0.8 1.0 Distance to neutron star [pc] 0 200 400 600 800 1000 Neutron star velocity [km/s] 25y 35y 45y 55y 65y 75y 85y 95y Figure 2: A contour plot of the detection times (in years) using a Bayesian inference method, taking an odds ratio of 100 or greater to constitute support for a third-order fit. 16
18. Spotting corpses … with other corpses? 17
19. combined delay equation t′ = t ( 1 − GM D ) + r1 c − 2GM c3 [ log (√ D2 − D cos(α) ) − log (√ 2r1 D cos(α) + D2 + r2 1 − D cos(α) )] 18