Spin dynamics of a millisecond pulsar around a massive black hole - - PowerPoint PPT Presentation

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Spin dynamics of a millisecond pulsar around a massive black hole - - PowerPoint PPT Presentation

Jun 03, 2023 35 likes •269 views

Spin dynamics of a millisecond pulsar around a massive black hole Jiale Kaye Li (Physics Department, The Chinese University of Hong Kong) Collaborator: Prof Kinwah Wu (Mullard Space Science Laboratory, University College London, UK)

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Spin dynamics of a millisecond pulsar around a massive black hole

Jiale Kaye Li (Physics Department, The Chinese University of Hong Kong)

Collaborator: Prof Kinwah Wu (Mullard Space Science Laboratory, University College London, UK)

2018-02-06, Kyoto Gravity and cosmology, 2018

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Simulation and interesting results Theory

Mathisson–Papapetrou–Dixon (MPD) formulation

Pulsar observation Gravitational wave

spin precession

  • rbital precession

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Outline

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SLIDE 3

Motion of test particle

  • Non-spinning object – geodesic equation

The world line of a freely falling test body is independent of its composition or structure.

  • Weak Equivalence Principle

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Motion of extended body

  • Spinning object – Mathisson-Papapetrou-Dixon equations

Spin-curvature coupling and spin-orbit coupling Precession of spin axis Hidden momentum

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SLIDE 5

EMRI binary system

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Simulation and interesting results Theory

Mathisson–Papapetrou–Dixon (MPD) formulation

Pulsar observation Gravitational wave

spin precession

  • rbital precession

5

Outline

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SLIDE 7

Precession of the NS orbit

Geodesics precession Corrections due to spin

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Non-planar orbital motion

The precession of the

  • rbital plane
  • 30
  • 20
  • 10

10 20 30

  • 20
  • 15
  • 10
  • 5

5 10 15 20 z [km] x [M] a/M=-0.99 (λ=1)

(Singh, Wu, and Sarty, 2014)

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10 10 20 30 40 50 60 70 80 90 100 t [sec]

  • 8
  • 6
  • 4
  • 2

2 4 6 8 10 20 30 40 50 60 70 80 90 100 t [sec] a/M=-0.99 (λ=1)

  • 30
  • 20
  • 10

10 20 30

  • 15
  • 10
  • 5

5 10 15 z [km] x [M] a/M=0.99 (λ=1)

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Deviation from the geodesics

low eccentricity (quasi-circular) eccentric

5 10 15 20

t(s)

10 20 30 40 50 60

r(km)

retrograde prograde

e=0.10 e=0.20 e=0.30

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Precession of spinning-axis

Black hole

(image credit: H. Sulzer)

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Precession of spinning-axis

time

Pulses received by distance observer

ü Pulse profile changes or even disappears when the spinning-axis wobbles around ü Assume a conal emission ~10o , the time shifts by about and .

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Nutation of spinning-axis

(image credit: H. Sulzer)

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Gravitational lensing effect

  • A small perturbation ~10$% rad becomes up to ~ 0.1 rad due to lensing
  • f the black hole

Red solid lines: photon paths with different impact parameter Colorful lines: photon paths with perturbed initial velocity

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Simulation and interesting results Theory

Mathisson–Papapetrou–Dixon (MPD) formulation

Pulsar observation Gravitational wave

spin precession

  • rbital precession

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Outline

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SLIDE 15

ü Pulse time shift: ü Pulse profile shift:

magnetic field axis

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Spin-axis wobbling effect

spin axis

(Rafikov and Lai 2008)

period spin axis wobbling

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Temporal dispersion of pulse signals

ü Pulse arrival time dispersion in the presence of line-of-sight plasma ü Pulse emission in all frequencies follow the same trajectory but will arrive at different time

(Lorimer, D Ross, and M Kramer)

Flat space-time with plasma

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Frequency dependent spatial dispersion of emission

ü Emission of different frequencies have different paths under the gravity of a rotating black hole

(Kimpson, Wu and Zane 2018)

Curved space-time with plasma

non-rotating black hole rotating black hole

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SLIDE 18

Simulation and interesting results Theory

Mathisson–Papapetrou–Dixon (MPD) formulation

Pulsar observation Gravitational wave

spin precession

  • rbital precession

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Outline

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LISA band

(image credit: Moore, Cole and Berry)

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LISA band

(Peters, P 1963)

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The definition of orbital plane, inclination angle, etc…

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Summary

1. Spin-curvature coupling:

  • Non-geodesic motion
  • Precession and nutation of pulsar’s spin axis

2. Implication on pulsar observation:

  • Orbital precession would shift the arrival time of pulses
  • Spin precession would distort the pulse profile and even lead to

the disappearance of pulses

  • Emission with different frequencies have spatial and temporary

dispersion 3. Gravitational wave:

  • Corrections to phase to gravitational wave and distortion of the

waveform

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Reference

ü Singh, Dinesh, Kinwah Wu, and Gordon E. Sarty. "Fast spinning pulsars as probes of massive black holes’ gravity." Monthly Notices of the Royal Astronomical Society 441.1 (2014): 800-808. ü Peters, P. (n.d.). Gravitational Radiation from Point Masses in a Keplerian Orbit. ü Kramer, Michael, et al. "Tests of general relativity from timing the double pulsar." Science 314.5796 (2006): 97-102. ü Lorimer, Duncan R. "Binary and millisecond pulsars." Living reviews in relativity 11.1 (2008): 8. ü Rafikov, Roman R., and Dong Lai. "Effects of Pulsar Rotation on Timing Measurements of the Double Pulsar System J0737–3039." The Astrophysical Journal 641.1 (2006): 438. ü Lorimer, Duncan Ross, and Michael Kramer. Handbook of pulsar astronomy. Vol. 4. Cambridge university press, 2005.

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Acknowledgement

I would like to thank Prof Kinwah Wu and Dr Leung Po Kin for useful discussion and suggestions on the project. I thank Otto, Adrian C, Adrian L for suggestions on the slide and presentation. I thank the Physics department and Tjonnie Li for funding my visit to Kyoto.

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