Period-luminosity relation

Period-luminosity relation[edit]

Period-Luminosity Relation for Cepheids

A classical Cepheid's luminosity is directly related to its period of variation. The longer the pulsation period, the more luminous the star. The period-luminosity relation for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds.^[20] She published it in 1912^[21] with further evidence. Once the period-luminosity relationship is calibrated, the luminosity of a given Cepheid whose period is known can be established. Their distance is then found from their apparent brightness. The period-luminosity relationship has been calibrated by many astronomers throughout the twentieth century, beginning with Hertzsprung.^[22] Calibrating the period-luminosity relation has been problematic; however, a firm Galactic calibration was established by Benedict et al. 2007 using precise HST parallaxes for 10 nearby classical Cepheids.^[23] Also, in 2008, ESO astronomers estimated with a precision within 1% the distance to the Cepheid RS Puppis, using light echos from a nebula in which it is embedded.^[24] However, that latter finding has been actively debated in the literature.^[25]

The following relationship between a Population I Cepheid's period P and its mean absolute magnitude M_v was established from Hubble Space Telescope trigonometric parallaxes for 10 nearby Cepheids:

${\displaystyle M_{\mathrm {v} }=(-2.43\pm 0.12)\left(\log _{10}P-1\right)-(4.05\pm 0.02)\,}$

with P measured in days. ^[19][23] The following relations can also be used to calculate the distance d to classical Cepheids:

${\displaystyle 5\log _{10}{d}=V+3.34\log _{10}{P}-2.45(V-I)+7.52\,.}$^[23]

or

${\displaystyle 5\log _{10}{d}=V+3.37\log _{10}{P}-2.55(V-I)+7.48\,.}$^[26]

I and V represent near infrared and visual apparent mean magnitudes, respectively.