The

_{ }period-luminosity relationship for classical Cepheid variable stars is_{ }log( L / L _{sun}) 1.15 · log ( P / 1 day ) + 2.47^{ }Use

_{ }this and the absolute visual magnitude_{ }of the Sun (+4.83) to derive a_{ }relation between the absolute_{ }visual magnitude M_{V}and period P of a Cepheid._{ }Use

_{ }the distance modulus to derive the relation_{ }between the distance (in pc)_{ }and the apparent visual magnitude m_{v}and period P._{ }Polaris

_{ }has an apparent visual magnitude of m_{v}= 2.3 and is a Cepheid with a period_{ }of P=13 days. What is the absolute_{ }visual magnitude of Polaris, and what is its approximate_{ }distance in parsecs?_{ }Consider

_{ }a set of two Cepheid variable stars, with masses, radii, and absolute visual magnitudes as given below:_{ }M / M _{sun}^{ }R / R _{sun}^{ }M _{V}^{ }P (days) _{ }^{ }5 ^{ }_{ }36.3 ^{ }_{ }-3.1 ^{ }_{ }10 ^{ }_{ }195.0 ^{ }_{ }-5.9 ^{ }_{ }Use

_{ }the period vs. density relationship for pulsating starsP _{ }= [ 3/ (2G) ]^{1/2}with

_{ }= 4/3,_{ }to calculate the expected periods_{ }(in days) and fill in the table._{ }Assume

_{ }that Cepheids follow a relationship of the formM _{V}= a · log( P / 1 day ) + band

_{ }solve for the constants a and b using our_{ }calibrator stars given above._{ }(Note that this relation may be different_{ }than the one given above!)We

_{ }observe a Cepheid variable with a period of 20 days_{ }and an apparent visual magnitude of m_{v}= 10.4. What is the distance to_{ }the star in parsecs?_{ }The star Mira is a long-period variable (LPV) star with a

_{ }period of 400 days._{ }The average absolute bolometric of Mira_{ }magnitude is M_{bol}= -5, and the average temperature is 2300 K. What_{ }is the radius of Mira (in Rsun)?_{ }Where (what branch or sequence) in the H-R diagram_{ }does Mira lie? (Note: M_{bol,Sun}= +4.75.)During its 400 day period,

_{ }Mira brightens by 5.1 magnitudes while at the same time its_{ }temperature goes from 2000_{ }K to 2600_{ }K. What ratio of maximum to minimum_{ }radius does this imply for a radial pulsation?Consider stars with all the same luminosity L distributed

^{ }uniformly through space.^{ }Show that the number-flux counts follow^{ }the relation^{ }N( > f ) f ^{-3/2}where N( > f )

^{ }represents the number of stars visible^{ }in the sky with an apparent flux greater or^{ }equal to f.The

_{ }circular rotation velocity of the disk of our galaxy_{ }is approximately constant at 220_{ }km/s. Use simple power-law scaling_{ }arguments to derive the mass density_{ }law (r) implied by this_{ }constant rotation velocity with radius from the galactic center._{ }What is the scaling for the enclosed_{ }mass M( < r )?

*smyers@nrao.edu*
*Steven T. Myers*