CALCULATING DISTANCES. Cepheids and RR Lyrae India Jackson-Henry

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1 CALCULATING DISTANCES Cepheids and RR Lyrae India Jackson-Henry

2 What are Cepheids and RR Lyrae Stars As stars evolve, their atmospheres become unstable and the star becomes intrinsically variable. Two special classes of variable stars are used to determine distances within our galaxy and distances to neighboring galaxies. Cepheid variables have periods that range from a few days to a few hundred days. They are evolved Population I stars and lie within the spiral arms of a galaxy. RR Lyrae stars (named after the prototype star RR in the constellation Lyra) are evolved population II stars and can be seen in the halos of galaxies, especially in globular clusters. Periods of RR Lyrae stars are typically 0.5 to 1 day, making it possible to see one or more periods in a single night of observations.

3

4 Henrietta Leavitt Leavitt: found a relationship between period and luminosity (apparent magnitude) in cepheid variables in LMC. Since all the stars are in the LMC, and are at the same distance from us, the apparent magnitudes are an accurate measure of the true relative luminosities of the stars.

5 Hubble Used Cepheids as standard candles Was the first to measure distances to spiral nebulae Found that a galaxy's redshift and distance are related! = # $ %

6 Why not just uses parallax? The only directly measurable distances in astronomy are those made by trigonometric parallax such as stars on the main sequence. However, Cepheids are not main sequence stars. Once you get to a certain distance the parallax technique is null. Some galactic Cepheids are found in clusters of stars. Like the stars in the LMC, all the stars in these clusters are at the same distance from us. One can use the spectroscopic parallax of the main sequence stars in the cluster to determine the distance to the cluster, and the Cepheid. The distance and observed magnitude then directly give the luminosity of the Cepheid, and a calibration of the period-luminosity relation.

7 Basic Technique Determine the period, and observe the mean magnitude m. Find the absolute magnitude M that corresponds to that period:! " = 2.76 )*+, **Hubble Space Telescope:! / = 2.43 ± 0.12 )*+, 1 (4.05 ± 0.02) The difference between the apparent and absolute magnitudes, m-m, known as the distance modulus, is equal to 5 log(d) -5, where the distance is in parsecs: 6! = 5 log : 5 6! + 5 = 5 log : 6! + 5 = log : 5 : = 10 A

8 Examples & Range of Relevant Distances!"# 6822: ( = 10,-./0 0 = /0 0 = :

9 Potential Problems There are of course many complications, most of which are beyond the scope of this introduction. However, there is one very important caveat. The galactic calibration of the Cepheids is inapplicable to the LMC Cepheids. This is because there is a large difference in mean metallicity between the two galaxies: stars in the LMC are metal-deficient relative to our Galaxy. This affects the opacity, and the periods. Population I consists of metal-rich stars, including the Sun. Population II is metal poor, representing a population of stars that formed from a less enriched interstellar medium. At a given period, W Vir stars are less luminous than are classical Cepheids. Inadvertent application of the classical Cepheid P-L relation to W Vir stars leads to a to a large overestimate of the distances.

10 Recent Results The Next Generation Virgo Cluster Survey (NGVS). XVIII. Measurement and Calibration of Surface Brightness Fluctuation Distances for Bright Galaxies in Virgo (and Beyond) Michele Cantiello, Published 2018 March The American Astronomical Society Hubble Space Telescope Trigonometric Parallax of Polaris B, Companion of the Nearest Cepheid *. Howard E. Bond 1,2,6, Edmund P. Nelan 2, Nancy Remage Evans 3, Gail H. Schaefer 4, and Dianne Harmer 5 P.2018 January 23

11 References Benedict, G. Fritz; (2002). "Astrometry with the Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator δ Cephei". The Astronomical Journal. 124(3): Periods of 25 Variable Stars in the Small Magellanic Cloud, Harvard College Observatory Circular 173, 1912, Edward C. Pickering

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