## Cepheid Pulsation: An Idealized Thought Experiment## Compiled by Grady Owens## Based on a problem presented in |

For this experiment, consider a highly unrealistic model of a
pulsating star consisting of a central point mass equal to the entire
mass of the star,
The left-hand side of this equation represents the total force on the system, or the equilibrium state; the right side sums the force upon the gas shell due to the gravitational influence of the central mass and the shell's own mass, and the force upon the shell's internal surface area applied by the internal massless gas. Assuming the expansion and contraction of the gas are adiabatic and
using the definition of velocity, it is possible to find the velocity of
the outer shell, its radius, and the pressure of the inner massless gas
after an interval of time Δ In this example, we are going to assume that
^{10} mv = 0 m s_{i}^{-1}P = 5.6 × 10_{i}^{4} N m^{-2}using a time interval of Δ
Using the values for the radius
Using Figure 2 as a reference, we can see that ^{10}
m; using this, we can calculate that the period of this oscillation is
roughly 5.28 days. The period for this oscillation is observed in δ
Cephei to be roughly 5.37 days. Considering the highly idealized nature
of this experiment, the obtained value for this is remarkable, and
tells us something of the inner workings of the Cepheid class of
variable stars. |