Definitions and Abbreviations

Abbreviations

  • AGN: Active Galactic Nucleus, an accreting massive black hole that produced observable EM emission (radio, optical, X-ray, etc). Generally used synonymously with “Quasar” which is traditionally a very bright AGN, produced by an MBH accreting at a very high rate.

  • BH: Black Hole

  • CBD: Circum-Binary Disk, an accretion disk surrounding both components of a binary system.

  • CSD: Circum-Single Disk, an accretion disk surrounding a single component of a binary system.

  • CW: Continuous Wave, as in Continuous Wave GW source

  • DF: Dynamical Friction, the drag force experienced by a massive object moving in a gravitating background.

  • EM: Electromagnetic, traditional radiation produced by moving charges (from the radio to optical to gamma-ray).

  • GR: General relativity.

  • GPF: Galaxy Pair Fraction, the fraction of galaxies in galaxy pairs.

  • GMR: Galaxy Merger Rate, the specific rate of galaxy mergers (i.e. the rate of mergers per galaxy).

  • GMT: Galaxy Merger Time, the characteristic duration that a galaxy merger takes. This is typically defined observationally, i.e. the duration of time over which a galaxy merger could be identified in an imaging survey.

  • GSMF: Galaxy Stellar-Mass Function, the number-density of galaxies as a function of their stellar mass.

  • GW/GWB: Gravitational Waves / Gravitational Wave Background

  • ISCO: Inner-most Stable Circular Orbit, the radius or location within which no object can maintain a stable orbit around a black hole. The radius is dependent on the spin of the black hole, but equal to 3 times the Schwarzschild radius for a non-spinning (\(a=0\)) black hole.

  • LISA: Laser Interferometer Space Antenna, future space-based GW detector

  • MBH: Massive Black-Hole, usually treated interchangeably with ‘SMBH’ (super-massive black-hole)

  • MBHB: Massive Black-Hole Binary, also referred to as BSMBH, SMBHB, …

  • NFW: Navarro-Frenk-White dark matter radial-density profile for a dark-matter halo.

  • PTA: Pulsar Timing Array.

  • QLF: Quasar Luminosity Function. The number-density of quasars/AGN as a function of their brightness.

  • SAM: Semi-Analytic Models. (Grey area relative to SEMs).

  • SEM: Semi-Empirical Models. (Grey area relative to SAMs).

  • TOA: Time of Arrival, the specific measured time at which a pulsar’s radio bursts are measured by the observer.

Symbols

  • \(a\):

      1. binary orbital semi-major axis (i.e. separation).

      1. the scale-factor of the universe at a given redshift, \(a = 1 / (1+z)\).

  • \(d_c\): Comoving Distance, the distance to a location in the Universe that, for zero relative velocity, remains invariant as a function of redshift. Related to luminosity distance as, \(d_c = d_L / (1+z)\).

  • \(d_L\): Luminosity Distance, the effective distance to a source in the Universe determining its EM brightness or GW amplitude. Related to comoving distance as, \(d_L = d_c \, (1+z)\).

  • \(\mathcal{M}`\): Chirp-mass

  • \(M\): Mass, or total-mass (\(M=m_1 + M_2\)) in the context of a binary.

  • \(q\): Mass-ratio of a binary, defined to be less-than or equal to unity, \(q\equiv m_2/m_1\), where the more massive primary is \(m_1\).

  • \(z\): (Cosmological) redshift, a proxy for the distance to a source/location in the Universe, and also a proxy for the age of the Universe at that time. Related to the scale-factor as \(z = (1/a) - 1\).

Terminology

  • AGN/Quasar: There is a long and convoluted history of terms for different types of EM-bright astronomical sources that are now all believed to be produced by accreting massive black holes. ‘Active galactic nuclei’ is perhaps the most generic term for any accreting MBH which is then producing EM emission. Formally ‘quasars’ are relatively massive MBHs that are accreting at very high rates, and are thus very bright. Often ‘quasar’ is used relatively interchangeably with AGN (for instance in ‘Quasar Luminosity Function’).

  • Hardening: the shrinking of the semi-major axis of a binary system by extracting energy and angular momentum. This term is also often used to simply mean the process of bringing two bodies (i.e. MBHs) closer together, even if they are not formally a gravitational-bound binary. ‘Hardening’ is typically due to either GW emission, or interactions between the binary and the surrounding environment. More generally, the “hardness” of a binary refers to how its binding energy compares to the kinetic energy of the surrounding environment (typically stars). If the binding energy is larger, then the binary is said to be ‘hard’; if the binding energy is less, it is said to be ‘soft’. The “Heggie Law” or the “Heggie-Hills Law” states that hard binaries tend to harden further, and soft binaries tend to soften further, both based on interactions with the surrounding medium. This is based on a pair of papers: [Heggie1975] and [Hills1975].

  • M-Mbulge: the \(M_{bh} - M_\textrm{bulge}\) relation, whereby the mass of MBHs is closely correlated with the mass of the stellar bulge of their host galaxy.

  • Stellar Bulge