Stellar Structure and Evolution pp 398-406 | Cite as

# Adiabatic Spherical Pulsations

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## Abstract

The functions where the subscript 1 indicates the perturbations for which we have made a separation ansatz with an exponential time dependence [as in (25.17)]. The relative perturbations

*P*_{0}(*m*),*r*_{0}(*m*), and*ϱ*_{0}(*m*) are supposed to belong to a solution of the stellar-structure equations (9.1–4) for the case of complete equilibrium. Let us assume that we perturb the hydrostatic equilibrium, say by compressing the star slightly and releasing it again suddenly. It will expand and owing to inertia overshoot the equilibrium state: the star starts to oscillate. The analogy to the oscillating piston model (see §6.6) is obvious. More precisely we assume the initial displacement of the mass elements to be only radially directed (*dϑ*=*dϕ*= 0) and of constant absolute value on concentric spheres. This leads to purely*radial oscillations*(or radial pulsations) during which the star remains spherically symmetric all time. For the perturbed variables at time*t*we write$$ \begin{gathered} P(m,t) = {P_0}(m) + {P_1}(m,t) = {P_0}(m)\left[ {1 + p(m){e^{{i\omega t}}}} \right], \hfill \\ r(m,t) = {r_0}(m) + {r_1}(m,t) = {r_0}(m)\left[ {1 + x(m){e^{{i\omega t}}}} \right], \hfill \\ \varrho (m,t) = {\varrho_0}(m) + {\varrho_1}(m,t) = {\varrho_0}(m)\left[ {1 + d(m){e^{{i\omega t}}}} \right] \hfill \\ \end{gathered} $$

(38.1)

*p, x, d*are assumed to be ≪ 1.## Keywords

Radiation Pressure Hydrostatic Equilibrium Radial Oscillation Polytropic Index Outer Boundary Condition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1990