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--- song_science [2023/08/04 21:01] – [How asteroseismology works] jasonj
+++ song_science [2023/08/05 14:43] (current) – [How asteroseismology works] jasonj
@@ Line 37: / Line 37: @@
 {{ :science:four_modes.gif?direct|}}
-The oscillations are global modes in a star, which distort the stellar surface with a spatial pattern that can usually be described by spherical harmonics, resulting in luminosity and radial-velocity variations. The figure shows 4 examples, where the red and blue denote the distortion of the particular part of the surface, and white are nodes (no distortion). Cancellation effects due to the point-source nature of distant stars only allow for observations of the lowest spherical harmonic degrees (L=0 - 3). In the figure, the top 2 animations are for L=1 and L=3, which would be observable. The other two (L=6 and L=10, would not be). Power spectra of a time series of a solar-like oscillator show a comb-like structure of peaks within a broad acoustic mode envelope that has a maximum amplitude at some temporal frequency. This can range from about 20 μHz (half a day period) for evolved giants to a few thousand μHz (periods of minutes) for dwarfs.  The comb pattern has peaks that are evenly spaced in frequency, whereby frequency differences between modes of consecutive radial order n and the same spherical degree L are known as the large frequency spacing.
+The oscillations are global modes in a star, which distort the stellar surface with a spatial pattern that can usually be described by spherical harmonics, resulting in luminosity and radial-velocity variations. The figure shows 4 examples, where the red and blue denote the (highly exaggerated) distortion of the particular part of the surface, and white are nodes (no distortion). Cancellation effects due to the point-source nature of distant stars only allow for observations of the lowest spherical harmonic degrees (L=0 - 3). In the figure, the top 2 animations are for L=1 and L=3, which would be observable. The other two (L=6 and L=10, would not be). Power spectra of a time series of a solar-like oscillator show a comb-like structure of peaks within a broad acoustic mode envelope that has a maximum amplitude at some temporal frequency. This can range from about 20 μHz (half a day period) for evolved giants to a few thousand μHz (periods of minutes) for dwarfs.  The comb pattern has peaks that are evenly spaced in frequency, whereby frequency differences between modes of consecutive radial order n and the same spherical degree L are known as the large frequency spacing.
 These observed modal properties are often interpreted in terms of the asymptotic theory of stellar oscillations {[tassoul1980]}. In this case, the large frequency spacing is related to the sound crossing time of an acoustic wave across the star, and therefore scales with the mean density. An empirically-motivated relationship connects the frequenc of maximum power with the surface gravity and effective temperature {[brown1991]}. When these two relations are combined, scaling relations for a star's mass and radius can be derived {[kjeldsen1995]}