Tully–Fisher relation

Tully–Fisher relation is an empirical correlation in astronomy between the intrinsic luminosity of a spiral galaxy and its rotational velocity. First published in 1977 by astronomers R. Brent Tully and J. Richard Fisher, it serves as a crucial tool for determining extragalactic distances. The relation posits that more luminous galaxies rotate faster, providing a standard candle for measuring cosmic distances independent of traditional methods like Cepheid variable stars. Its discovery significantly advanced the field of observational cosmology and the study of large-scale structure in the universe.

Definition and basic principle

The core principle states that the total absolute magnitude, or luminosity, of a spiral galaxy is tightly correlated with the amplitude of its rotation curve. This is typically quantified by measuring the width of the galaxy's integrated hydrogen 21 cm line emission or optical emission lines like H-alpha from regions such as H II regions. The broader the spectral line width, the higher the maximum rotational velocity, which corresponds to a more massive and luminous system. This empirical law is analogous to the Faber–Jackson relation for elliptical galaxies and forms part of the broader suite of scaling relations describing galaxy formation. The initial work by R. Brent Tully and J. Richard Fisher utilized observations from instruments like the Arecibo Observatory to establish this foundational correlation.

Observational methodology

Measuring the relation requires precise determinations of a galaxy's rotational velocity and its apparent brightness. Astronomers typically use radio telescopes, such as those at the Green Bank Observatory or the Karl G. Jansky Very Large Array, to observe the neutral hydrogen 21 cm line. Alternatively, optical spectrographs on facilities like the Keck Observatory or the Hubble Space Telescope measure Doppler broadening from ionized gas. The observed line width is corrected for the galaxy's inclination relative to Earth, derived from imaging data often obtained by the Sloan Digital Sky Survey. The apparent magnitude is measured through photometric filters, corrected for effects like interstellar extinction and redshift, to eventually compute the absolute luminosity and calibrate the distance.

Physical interpretation and theoretical basis

The physical foundation lies in the link between a galaxy's mass, its luminosity, and the depth of its gravitational potential well. Within the framework of Newtonian dynamics, the rotational velocity traces the total mass, including both luminous baryonic matter and dark matter. The baryonic Tully–Fisher relation suggests a direct connection between the galaxy's stellar mass and its rotation speed, implicating processes of galaxy formation and evolution. Theoretical models, including those based on Modified Newtonian dynamics (MOND) and ΛCDM simulations, attempt to explain the remarkable tightness of the correlation. Research by institutions like the Max Planck Institute for Astrophysics explores how feedback mechanisms from supernovae and active galactic nuclei regulate this scaling law.

Applications in cosmology

Its primary application is as a powerful distance indicator for establishing the extragalactic distance scale and measuring the Hubble constant. By comparing the intrinsic luminosity inferred from the rotation speed to the observed apparent magnitude, astronomers derive the galaxy's distance, independent of the cosmic distance ladder rungs like Cepheid variables. This method has been instrumental in mapping the velocity field of the local universe, revealing structures like the Virgo Cluster, the Great Attractor, and the Laniakea Supercluster. Large surveys, such as those conducted with the Australia Telescope Compact Array and the Spitzer Space Telescope, have used it to study large-scale structure and constrain parameters like the density of dark energy.

Limitations and ongoing research

Key limitations include sensitivity to galaxy morphology, inclination measurement errors, and the effects of internal extinction, particularly in dusty systems. The relation also shows scatter due to variations in star formation history, gas fraction, and the presence of bulges or bars. Ongoing research by teams using the Atacama Large Millimeter Array and the upcoming Nancy Grace Roman Space Telescope aims to refine the calibration across different wavelengths and environments. Investigations into the relation for dwarf galaxies and its evolution at high redshift, studied with the James Webb Space Telescope, test galaxy formation models. Discrepancies in Hubble constant measurements from different methods, including those from the Planck mission, motivate continued scrutiny of its systematic uncertainties.

Category:Empirical astronomical laws Category:Galaxy scaling relations Category:Observational cosmology Category:Astronomical distance measurements