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--- song_science [2023/08/04 20:08] – [How asteroseismology works] jasonj
+++ song_science [2023/08/05 14:43] (current) – [How asteroseismology works] jasonj
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 ===== How asteroseismology works =====
-{{ :science:four_modes.gif?direct|}}
 We focus on stars that pulsate like our Sun in what follows, both for simplicity and because the interpretation of the data is much more advanced than for other types of pulsators. Such solar-like oscillators need not be solar-type, main-sequence stars at all; for example, almost all red giants, such as the bright Aldebaran {[farr2018]}, display solar-like oscillations. They are the result of acoustic pressure waves that are excited to small, yet observable amplitudes by near-surface turbulent convection {[goldreich1977]}.  These stars, therefore,  must have an outer convection zone, with effective (surface) temperature below about 7000K, corresponding to an upper mass of about 1.5 solar masses on the main sequence and spectral types later than mid-F. For evolved  subgiants and giants, G, K, and M stars are most typical (and masses can exceed 1.5 solar masses).
-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.
+{{ :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 (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]}
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 All of the above may be considered as a broad application of asteroseismic analysis of global observables. SONG will go much further than applying the scaling relations. It will provide very precise individual mode frequencies for more modes than space photometry can, including mixed modes, L=3 modes, and modes split into multiplets by internal rotation.  In fact, the relative amplitudes of the frequency multiplets can be used to measure the inclination of the stellar rotation axis {[gizon2003]}. In any case, the measured frequencies can then be confronted with the frequencies predicted from sophisticated numerical models. The result is a deeper understanding of all of the interior stellar properties and evolutionary state of stars.
-===== SONG project status =====
-{{ :wiki:song_network.png?direct&500}}
-SONG is planned as a network of eight fully-robotic 1-m telescopes that will carry out near-continuous, high-precision radial-velocity  measurements of bright stars. The telescopes are to be equipped with nearly identical optical spectrographs capable of reaching a  precision of 1 m/s per exposure on stars down to a visible magnitude of M_V=6. The nodes in the network are  distributed in longitude to be able to continuously monitor stars and avoid the day/night cycle. The figure highlights the site locations.  SONG is modeled  after the the six-station Birmingham Solar Oscillations Network (BISON) and the Global Oscillation Network Group (GONG), which have both very successfully studied the Sun with helioseismology for over 25 years {[hale2016,kiefer2021]}. SONG is a highly cost-effective and innovative next step forward for asteroseismology.
-SONG was conceived and is led by collaborators in the Department of Physics and Astronomy at Aarhus University in Denmark. That group spearheaded the development of the high-precision spectrograph instrumention, which was ultimately realized at the prototype facility at the Observatorio del Teide in the Canary Islands on  Tenerife, Spain. SONG-Tenerife has been operating since 2014 and consists of the Hertzsprung-SONG Telescope. A second node has recently been built at the Mt. Kent Observatory in Queensland, Australia and is undergoing commissioning as of January 2022. A third node is under construction at a new observatory in Lenghu, China, and is scheduled to be operational by  2024. As the figure demonstrates, SONG in New Mexico will be a crucial bridge for the global network, providing required longitudinal coverage to continuously monitor stars.
+===== Why do we need a global network?  =====
+Asteroseismology is a time-domain science and data analysis is carried out in  the temporal frequency (Fourier) domain. Analysis is most successful when the power spectrum of the time series shows oscillation modes at distinct frequencies that can be identified (guided by models or empirical relations) according to their radial order and spherical harmonic degree. This requires sufficient duration to resolve the modes in frequency space, as well as ample sampling to capture the highest frequencies: both of these criteria are straightforward to meet in practice, even from a single location.
+However, regular gaps in the data (such as from the day/night cycle) cannot be overcome by simply observing longer or more often, and lead to a sampling (window) function that is not optimal. The Fourier transform of this function is known as the spectral window. The power spectrum of the target star is thus effectively a convolution of this spectral window and the true underlying oscillation spectrum. For gapped data, the spectral window introduces alias frequencies into the power spectrum that do not correspond to real frequencies, wreaking havoc with the analysis. That is why, before SONG, solar-like oscillations had only been detected in a handful of stars from the ground using ad-hoc networks or large telescopes, and Herculean analysis efforts {[bedding2007,arentoft2008,bedding2008]}.
+{{ :science:window_effect.png?direct |}}
+The figure above demonstrates this issue by contrasting observations from idealized  two- or three-site networks. Space-based Sun-as-a-star velocity data (for which we have very long,  uninterrupted time series), mimicking a distant pulsating star,  were used to construct a one-month long time series with a one-minute sampling.  Regular gaps of 8 hours were introduced every 24 hours to simulate a network of two sites, while no  regular gaps are present in the idealized three-site network. The resulting power spectra and spectral windows are shown in the figure. Since the two-site spectral window has aliasing frequencies at 1 cycle/day =11.57 μHz and its overtones (right panel), each peak in the corresponding power spectrum is surrounded by false peaks. These peaks can interfere with neighboring modes, causing contamination {[arentoft2014]}. This is clearly evident in the inset panel. Furthermore, the amplitudes of the modes are altered by the contamination.
+The introduction of false frequencies that overlap and interfere with real ones can be absolutely detrimental  to the interpretation and analysis of the oscillation spectra -- this is the prime motivation for establishing a global network {[jain2021]}. We recognize that continuous coverage for long periods will still be limited by weather conditions, but the presence of //random// gaps has significantly less effect than the //regular// gaps that arise from a lack of full longitudinal coverage.