Summer School on Gravitational-Wave Astronomy
Course Plan

The astrophysics of neutron stars and binaries

Topics: Stellar Hydrostatic Equilibrium (in General Relativity, with and without spin), Ultradense matter (Expected properties, equation of state and uncertainties), Formation and structure of Neutron Stars (including interior composition, superfluidity and superconductivity), Radiation from isolated Neutron Stars (Thermal and magnetospheric origin, pulsars and magnetars), Evolution of binary stars and formation of compact star binaries (Roche potential, mass exchange, stellar evolution with varying mass, orbital evolution with mass transfer, orbital evolution with angular momentum loss - gravitational waves and magnetic braking), Accreting Neutron Stars (Physical processes in X-ray binaries, constraints on mass and radius, spin evolution, r-mode instability and gravitational waves), Relativistic Neutron Star Binaries (Double Neutron Star and Neutron Star-Black Hole systems, relativistic orbital parameters and the measurement of masses, long-term orbital evolution leading to merger), Gamma Ray Bursts, Kilonovae and Gravitational Waves from Neutron Star mergers.

References: 

  • Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects, S.L. Shapiro, S.A. Teukolsky, Wiley (1984)
  • Rapidly Rotating Neutron Stars in General Relativity: Realistic Equations of State, G.B. Cook, S.L. Shapiro, S.A. Teukolsky, Astrophysical Journal, 424, 823 (1994)
  • First Multimessenger Observations of a Neutron Star Merger, R. Margutti, R. Chornok, Annual Reviews of Astronomy and Astrophysics, 59, 155 (2021)
  • Physics of Binary Star Evolution - from stars to X-ray binaries and Gravitational Wave Sources, T.M. Tauris, E.P.J. van den Heuvel, Princeton Series in Astrophysics (2023)

Preparatory reading: 

  • Masses, Radii and the Equation of State of Neutron Stars, F. Ozel, P. Freire, Annual Reviews of Astronomy and Astrophysics, 54, 401 (2016)
  • The formation and evolution of binary and millisecond pulsars, D. Bhattacharya and E.P.J. van den Heuvel, Physics Reports, 203, 1 (1991)
  • Whispers from the edge of physics, N. Andersson, Journal of Astrophysics and Astronomy, 38, 0058 (2017)

Ultralight boson clouds around black holes 

Topics: Kerr black holes (Ergoregion, black hole thermodynamics, Penrose process), superradiance instability (scalar test-field equations, Hydrogen-like solution, instability rates, scalar fluxes across horizon), instability saturation (adiabatic linear evolution, cloud energy, gravitational waves saturation), Gravitational wave emission (linearized Einstein equations with sources, Teukolsky formalism, radiation in non-relativistic limit), Beyond the Standard Model motivation and constraints (proposed scalar, vector, and spin-2 particles, gravitational wave search strategies, current constraints)

References: 

  1. A Relativist’s Toolkit, Eric Poisson, Cambridge University Press (2004)
  2. General Relativity, Robert Wald, The University of Chicago Press (1984)
  3. Superradiance, Richard Brito, Vitor Cardoso, and Paolo Pani, Lecture Notes in Physics (Springer), 2020 (see also arXiv version: 1501.06570)

Preparatory reading: 
Chapters 5.3.1—5.3.5 and 5.3.12–5.3.13 in [1] (see also chapter 5.5 in [1] and chapters 12.4–12.5 in [2] for those that want to see more details). For those that want to see a preview of what’s to come, see chapters 4.7.1–4.7.3, as well as 5.6.2 in [3].

Rapidly spinning neutron stars and emission mechanisms 

Topics: 

  • Brief review of NS basics (birth, EOS variations, exotic matter), rotational effects on mass / stability, mass-shedding spin frequency, actual distribution of pulsar frequencies, magnetic fields (origin, burial, reemergence, energy content)
  • Known pulsar population (discovery, models, wavelengths), timing, barycentering, stability, timing noise, young vs millisecond pulsars, P-Pdot diagram, magnetars, Taylor-Hulse, GW170817,  pulsar timing arrays. 
  • GW radiation - formulae, braking indices, mountains, B-field non-axisymmetry, accretion, r-modes, torque-balance, Sco X-1, timing fluctuations
  • Other NS GWs (glitches - bursts/CW), millisecond magnetars & post-merger remnants (X-ray evidence, energetics). Lamppost topics: boson clouds, Sun objects, ultralight PBHs etc, dark photon dark matter. 

References:

  1. Searches for continuous-wave gravitational radiation, K. Riles, Living Reviews in Relativity 26, 3 (2023).
  2. Handbook of Pulsar Astronomy, D.R. Lorimer and M. Kramer, Cambridge University Press, 2005.
  3. Gravitational-Wave Astronomy: Exploring the Dark Side of the Universe, N. Andersson, Oxford University Press, 2020

Preparatory reading: 

  1. Reference [1]: Sections 1-2 
  2. Reference [2]: Chapters 1-3
  3. Reference [3]: Chapters / Sections 1, 3, 6, 13.1-13.5, 13.8, 14.1-14.2, 14.6-14.7 and 15.1-15.3
  4. Black Holes, White Dwarfs and Neutron Stars -- The Physics of Compact Objects, S.L. Shapiro and S.A. Teukolsky (Chapters 1, 9, 10, 15 and 16) [Dated but still informative]
  5. Reference [3]: Sections 14.3, 14.8-14.13, 15.4-15.7,  21.1-21.3, 22.7 [Deeper dives]
  6. The Physics and Astrophysics of Neutron Stars, Eds. L. Rezzolla, P. Pizzochero, D.I. Jones, N. Rea and I. Vidana, Springer, 2018 (Chapters 1, 2, 7, 8  and 12) [Deeper dives]

Searches for continuous GWs: Methods and results

Topics: 

  1. Noise characterization, production of simulated gw noise, SFTs
  2. CW signals and parameter space. Different type of searches and associated computational cost
  3. Examples of: Time-domain bayesian search; Frequency domain F-statistics. Semi-coherent methods and hierarchical approaches.
  4. Post-processing of data: Vetoes, clustering, follow-up . Setting upper limits
  5. Review of the LVK results obtained on O3 data.

References: 

  1. K. Riles, Searches for continuous-wave gravitational radiation, Living Rev. Rel. 26, 3 (2023), arXiv:2206.06447 [astro-ph.HE].
  2. R. Tenorio, D. Keitel, and A. M. Sintes, Search Methods for Continuous Gravitational-Wave Signals from Unknown Sources in the Advanced-Detector Era, Universe 7, 474 (2021), arXiv:2111.12575 [gr-qc].
  3. K. Wette, Searches for continuous gravitational waves from neutron stars: A twenty-year retrospective, Astropart. Phys. 153, 102880 (2023), arXiv:2305.07106843 [gr-qc].
  4. Ornella Juliana Piccinni, Status and perspectives of Continuous Gravitational Wave searches, Galaxies 2022, 10(3), 72; arXiv:2202.01088 [gr-qc]
  5. Magdalena Sieniawska and Michał Bejger, Continuous gravitational waves from neutron stars: current status and prospects, Universe 2019, 5(11), 217, arXiv:1909.12600 [astro-ph.HE]
  6. D. Keitel, R. Tenorio, G. Ashton, and R. Prix, PyFstat: a Python package for continuous gravitational-wave data analysis, J. Open Source Softw. 6, 3000 (2021) arXiv:2101.10915 [gr-qc].
  7. P. Jaranowski, A. Królak, and B. F. Schutz, Data analysis of gravitational-wave signals from spinning neutron stars: The signal and its detection, Phys. Rev. D 58, 063001939 (1998).
  8. B. Krishnan, A. M. Sintes, M. A. Papa, B. F. Schutz, S. Frasca, and C. Palomba, The Hough transform search for continuous gravitational waves, Phys. Rev. D 70, 082001 (2004), arXiv:gr-qc/0407001.
  9. R. Tenorio and L. Mirasola, Towards a computationally-efficient follow-up pipeline for blind continuous gravitational-wave searches, (2024), LIGO-P2400221