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Solar-like oscillations are oscillations in distant stars that are excited in the same way as those in the Sun, namely by turbulent convection in its outer layers. Stars that show solar-like oscillations are called solar-like oscillators. The oscillations are standing pressure and mixed pressure-gravity modes that are excited over a range in frequency, with the amplitudes roughly following a bell-shaped distribution. Unlike opacity-driven oscillators, all the modes in the frequency range are excited, making the oscillations relatively easy to identify. The surface convection also damps the modes, and each is well-approximated in frequency space by a Lorentzian curve, the width of which corresponds to the lifetime of the mode: the faster it decays, the broader is the Lorentzian. All stars with surface convection zones are expected to show solar-like oscillations, including cool main-sequence stars (up to surface temperatures of about 7000K), subgiants and red giants. Because of the small amplitudes of the oscillations, their study has advanced tremendously thanks to space-based missions[1] (mainly COROT and Kepler).

Solar-like oscillations have been used, among other things, to precisely determine the masses and radii of planet-hosting stars and thus improve the measurements of the planets' masses and radii.[2][3]

In red giants, mixed modes are observed, which are in part directly sensitive to the core properties of the star. These have been used to distinguish red giants burning helium in their cores from those that are still only burning hydrogen in a shell,[4] to show that the cores of red giants are rotating more slowly than models predict[5] and to constrain the internal magnetic fields of the cores[6]

Echelle diagrams
An echelle diagram for the Sun, using data for low-angular-degree modes from the Birmingham Solar Oscillations Network (BiSON).[7][8] Modes of the same angular degree \( \ell \) form roughly vertical lines at high frequencies, as expected from the asymptotic behaviour of the mode frequencies.

The peak of the oscillation power roughly corresponds to lower frequencies and radial orders for larger stars. For the Sun, the highest amplitude modes occur around a frequency of 3 mHz with order \( {\displaystyle n_{\mathrm {max} }\approx 20} \), and no mixed modes are observed. For more massive and more evolved stars, the modes are of lower radial order and overall lower frequencies. Mixed modes can be seen in the evolved stars. In principle, such mixed modes may also be present in main-sequence stars but they are at too low frequency to be excited to observable amplitudes. High-order pressure modes of a given angular degree ℓ {\displaystyle \ell } \ell are expected to be roughly evenly-spaced in frequency, with a characteristic spacing known as the large separation Δ ν {\displaystyle \Delta \nu } \Delta\nu.[9] This motivates the echelle diagram, in which the mode frequencies are plotted as a function of the frequency modulo the large separation, and modes of a particular angular degree form roughly vertical ridges.
Scaling relations

The frequency of maximum oscillation power is accepted[10] to vary roughly with the acoustic cut-off frequency, above which waves can propagate in the stellar atmosphere, and thus are not trapped and do not contribute to standing modes. This gives

\( {\displaystyle \nu _{\mathrm {max} }\propto {\frac {g}{\sqrt {T_{\mathrm {eff} }}}}} \)

Similarly, the large frequency separation \( \Delta\nu \) is known to be roughly proportional to the square root of the density:

\( {\displaystyle \Delta \nu \propto {\sqrt {\frac {M}{R^{3}}}}} \)

When combined with an estimate of the effective temperature, this allows one to solve directly for the mass and radius of the star, basing the constants of proportionality on the known values for the Sun. These are known as the scaling relations:

\( {\displaystyle M\propto {\frac {\nu _{\mathrm {max} }^{3}}{\Delta \nu ^{4}}}T_{\mathrm {eff} }^{3/2}} \)
\( {\displaystyle R\propto {\frac {\nu _{\mathrm {max} }}{\Delta \nu ^{2}}}T_{\mathrm {eff} }^{1/2}} \)

Equivalently, if one knows the star's luminosity, then the temperature can be replaced via the blackbody luminosity relationship \( {\displaystyle L\propto R^{2}T_{\mathrm {eff} }^{4}} \) , which gives

\( {\displaystyle M\propto {\frac {\nu _{\mathrm {max} }^{12/5}}{\Delta \nu ^{14/5}}}L^{3/10}} \)
\( {\displaystyle R\propto {\frac {\nu _{\mathrm {max} }^{4/5}}{\Delta \nu ^{8/5}}}L^{1/10}} \)

See also

Asteroseismology
Helioseismology
Variable stars

Some bright solar-like oscillators

Procyon
Alpha Centauri A and B
Mu Herculis

References

Chaplin, W. J.; Miglio, A. (2013). "Asteroseismology of Solar-Type and Red-Giant Stars". Annual Review of Astronomy and Astrophysics. 51: 353–392.arXiv:1303.1957. Bibcode:2013ARA&A..51..353C. doi:10.1146/annurev-astro-082812-140938.
Davies, G. R.; et al. (2016). "Oscillation frequencies for 35 Kepler solar-type planet-hosting stars using Bayesian techniques and machine learning". Monthly Notices of the Royal Astronomical Society. 456 (2): 2183–2195.arXiv:1511.02105. Bibcode:2016MNRAS.456.2183D. doi:10.1093/mnras/stv2593.
Silva Aguirre, V.; et al. (2015). "Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology". Monthly Notices of the Royal Astronomical Society. 452 (2): 2127–2148.arXiv:1504.07992. Bibcode:2015MNRAS.452.2127S. doi:10.1093/mnras/stv1388.
Bedding, Timothy R.; et al. (2011). "Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars". Nature. 471 (7340): 608–11.arXiv:1103.5805. Bibcode:2011Natur.471..608B. doi:10.1038/nature09935. PMID 21455175.
Beck, Paul G.; et al. (2012). "Fast core rotation in red-giant stars as revealed by gravity-dominated mixed modes". Nature. 481 (7379): 55–7.arXiv:1112.2825. Bibcode:2012Natur.481...55B. doi:10.1038/nature10612. PMID 22158105.
Fuller, J.; Cantiello, M.; Stello, D.; Garcia, R. A.; Bildsten, L. (2015). "Asteroseismology can reveal strong internal magnetic fields in red giant stars". Science. 350 (6259): 423–426.arXiv:1510.06960. Bibcode:2015Sci...350..423F. doi:10.1126/science.aac6933. PMID 26494754.
Broomhall, A.-M.; et al. (2009). "Definitive Sun-as-a-star p-mode frequencies: 23 years of BiSON observations". Monthly Notices of the Royal Astronomical Society. 396: L100.arXiv:0903.5219. Bibcode:2009MNRAS.396L.100B. doi:10.1111/j.1745-3933.2009.00672.x.
Davies, G. R.; Chaplin, W. J.; Elsworth, Y.; Hale, S. J. (2014). "BiSON data preparation: a correction for differential extinction and the weighted averaging of contemporaneous data". Monthly Notices of the Royal Astronomical Society. 441 (4): 3009–3017.arXiv:1405.0160. Bibcode:2014MNRAS.441.3009D. doi:10.1093/mnras/stu803.
Tassoul, M. (1980). "Asymptotic approximations for stellar nonradial pulsations". The Astrophysical Journal Supplement Series. 43: 469. Bibcode:1980ApJS...43..469T. doi:10.1086/190678.

Kjeldsen, H.; Bedding, T. R. (1995). "Amplitudes of stellar oscillations: the implications for asteroseismology". Astronomy and Astrophysics. 293: 87.arXiv:astro-ph/9403015. Bibcode:1995A&A...293...87K.

External links

Lecture Notes on Stellar Oscillations published by J. Christensen-Dalsgaard (Aarhus University, Denmark)

vte

Stars
Formation

Accretion Molecular cloud Bok globule Young stellar object
Protostar Pre-main-sequence Herbig Ae/Be T Tauri FU Orionis Herbig–Haro object Hayashi track Henyey track

Evolution

Main sequence Red-giant branch Horizontal branch
Red clump Asymptotic giant branch
super-AGB Blue loop Protoplanetary nebula Planetary nebula PG1159 Dredge-up OH/IR Instability strip Luminous blue variable Blue straggler Stellar population Supernova Superluminous supernova / Hypernova

Spectral classification

Early Late Main sequence
O B A F G K M Brown dwarf WR OB Subdwarf
O B Subgiant Giant
Blue Red Yellow Bright giant Supergiant
Blue Red Yellow Hypergiant
Yellow Carbon
S CN CH White dwarf Chemically peculiar
Am Ap/Bp HgMn Helium-weak Barium Extreme helium Lambda Boötis Lead Technetium Be
Shell B[e]

Remnants

White dwarf
Helium planet Black dwarf Neutron
Radio-quiet Pulsar
Binary X-ray Magnetar Stellar black hole X-ray binary
Burster

Hypothetical

Blue dwarf Green Black dwarf Exotic
Boson Electroweak Strange Preon Planck Dark Dark-energy Quark Q Black Gravastar Frozen Quasi-star Thorne–Żytkow object Iron Blitzar

Stellar nucleosynthesis

Deuterium burning Lithium burning Proton–proton chain CNO cycle Helium flash Triple-alpha process Alpha process Carbon burning Neon burning Oxygen burning Silicon burning S-process R-process Fusor Nova
Symbiotic Remnant Luminous red nova

Structure

Core Convection zone
Microturbulence Oscillations Radiation zone Atmosphere
Photosphere Starspot Chromosphere Stellar corona Stellar wind
Bubble Bipolar outflow Accretion disk Asteroseismology
Helioseismology Eddington luminosity Kelvin–Helmholtz mechanism

Properties

Designation Dynamics Effective temperature Luminosity Kinematics Magnetic field Absolute magnitude Mass Metallicity Rotation Starlight Variable Photometric system Color index Hertzsprung–Russell diagram Color–color diagram

Star systems

Binary
Contact Common envelope Eclipsing Symbiotic Multiple Cluster
Open Globular Super Planetary system

Earth-centric
observations

Sun
Solar System Sunlight Pole star Circumpolar Constellation Asterism Magnitude
Apparent Extinction Photographic Radial velocity Proper motion Parallax Photometric-standard

Lists

Proper names
Arabic Chinese Extremes Most massive Highest temperature Lowest temperature Largest volume Smallest volume Brightest
Historical Most luminous Nearest
Nearest bright With exoplanets Brown dwarfs White dwarfs Milky Way novae Supernovae
Candidates Remnants Planetary nebulae Timeline of stellar astronomy

Related articles

Substellar object
Brown dwarf Sub-brown dwarf Planet Galactic year Galaxy Guest Gravity Intergalactic Planet-hosting stars Tidal disruption event

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