Rung 4: Period-Luminosity Relation for Variable Stars Continuing outward you find Cepheids and/or RR-Lyrae in stars clusters with a distance known through main sequence fitting. Or you can employ the more direct ``Baade-Wesselink method'' that uses the observed expansion speed of the variable star along the line of sight from the doppler shifts in conjunction with the observed angular expansion rate perpendicular to the line of sight. Since the linear expansion rate depends on the angular expansion rate and the distance of the star, the measurement of the linear expansion rate and angular expansion rate will give you the distance of the variable star. RR-Lyrae have the same time-averaged luminosity (about 49 solar luminosities or an absolute magnitude M V = +0.6). They pulsate with periods < 1 day. Cepheids pulsate with periods > 1 day. The longer the pulsation, the more luminous they are. There are two types of Cepheids: classical (brighter, type I) and W Virginis (fainter, type II). They have different light curve shapes. The
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