# Gyrochronology

Gyrochronology is a method for estimating the age of a low-mass star like the Sun from its rotation period. The term is derived from the Greek words gyros, chronos and logos, roughly translated as rotation, age, and study respectively. It was coined in 2003 by Sydney Barnes[1] to describe the associated procedure for deriving stellar ages, and developed extensively in empirical form in 2007.[2]

The technique builds on an insight of Andrew Skumanich,[3] who realized that another measure of stellar rotation (v sin i) declined steadily with stellar age. Gyrochronology uses the rotation period P of the star instead of the doubly ambiguous v sin i, which depends on the unknown inclination of the star's axis of rotation, i. In particular, the technique accounts for the substantial mass dependence of stellar rotation, as exemplified by early rotation-period work on the Hyades open cluster.[4] These two improvements are largely responsible for the precision in the ages provided by gyrochronology. The associated age estimate for a star is known as the gyrochronological age.

The basic idea underlying gyrochronology is that the rotation period P, of a main-sequence cool star is a deterministic function of its age t and its mass M (or a suitable proxy such as color). The detailed dependencies of rotation are such that the periods converge rapidly to a certain function of age and mass, mathematically denoted by P = P (t, M), even though stars have a range of allowed initial periods. Consequently, cool stars do not occupy the entire 3-dimensional parameter space of (mass, age, period), but instead define a 2-dimensional surface in this space. Therefore, measuring two of these variables yields the third. Of these quantities, the mass (or a proxy such as color) and the rotation period are the easier variables to measure, providing access to the star's age, otherwise difficult to obtain.

Defining a star as "Sun-like" is very difficult, because to be Sun-like the star should have a mass, radius, age, temperature metallicity, and spectral type that is similar to the Sun's. Measuring most of these factors is difficult, and determining the age of a star is extremely difficult, so astronomers tend to ignore it when deciding if a star is Sun-like or not. However, this is not ideal, because the Sun, and all stars change over time. If a star's rotation period is less than 25 days, the star can be determined as being younger than the Sun, if the rotation rate is longer, the star can be determined as being older than the Sun.[original research?]

The relationship between rotation and age was initially discovered by Soren Meibom and colleagues by measuring the period of rotation of stars in a billion-year-old cluster. Because the ages of the stars were already known, the researchers could discover a relationship between a star's age and its rotation period.[5] A study of 30 cool stars in the 2.5-billion-year-old cluster NGC 6819 allowed to estimate the age–period relationship for older stars. Using these results, the ages of a large number of cool galactic field stars can be derived with 10% precision.[6]

## References

1. ^ Barnes, Sydney (March 2003). "On the rotational evolution of Solar- and Late-Type Stars, Its Magnetic Origins, and the Possibility of Stellar Gyrochronology". The Astrophysical Journal. 586 (1): 464–479. arXiv:astro-ph/0303631. Bibcode:2003ApJ...586..464B. doi:10.1086/367639.
2. ^ Barnes, Sydney (November 2007). "Ages for Illustrative Field Stars Using Gyrochronology: Viability, Limitations, and Errors". The Astrophysical Journal. 669 (2): 1167–1189. arXiv:0704.3068. Bibcode:2007ApJ...669.1167B. doi:10.1086/519295.
3. ^ Skumanich, Andrew (February 1972). "Time Scales for CA II Emission Decay, Rotational Braking, and Lithium Depletion". The Astrophysical Journal. 171: 565. Bibcode:1972ApJ...171..565S. doi:10.1086/151310.
4. ^ Radick, Richard; Thompson, D. T.; Lockwood, G. W.; Duncan, D. K.; Baggett, W. E. (October 1987). "The activity, variability, and rotation of lower main-sequence Hyades stars". The Astrophysical Journal. 321: 459–472. Bibcode:1987ApJ...321..459R. doi:10.1086/165645.
5. ^ Hall, Shannon. "'Gyrochronology' Allows Astronomers to Find True Sun-like Stars". Universe Today. The Astrophysical Journal Letters. Retrieved 2 January 2015.
6. ^ Meibom, Søren; Barnes, Sydney A.; Platais, Imants; Gilliland, Ronald L.; Latham, David W.; Mathieu, Robert D. (5 January 2015). "A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster". Nature. 517: 589–591. arXiv:1501.05651. Bibcode:2015Natur.517..589M. doi:10.1038/nature14118. PMID 25539085.