Solar-like oscillations

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

Bison echelle
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 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 , 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 are expected to be roughly evenly-spaced in frequency, with a characteristic spacing known as the large separation .[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

Similarly, the large frequency separation is known to be roughly proportional to the square root of the density:

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:

Equivalently, if one knows the star's luminosity, then the temperature can be replaced via the blackbody luminosity relationship , which gives

See also

Some bright solar-like oscillators


  1. ^ 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.
  2. ^ 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.
  3. ^ 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ 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.
  7. ^ 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.
  8. ^ 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.
  9. ^ Tassoul, M. (1980). "Asymptotic approximations for stellar nonradial pulsations". The Astrophysical Journal Supplement Series. 43: 469. Bibcode:1980ApJS...43..469T. doi:10.1086/190678.
  10. ^ 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

32 Aquarii

32 Aquarii is a binary star system in the zodiac constellation of Aquarius. 32 Aquarii is its Flamsteed designation. It is visible to the naked eye as a dim, white-hued star with an apparent visual magnitude of 5.29. This system is moving away from the Earth with a heliocentric radial velocity of +19 km/s, and is a possible member of the corona of the Ursa Major flow.This is a single-lined spectroscopic binary with an (assumed) circular orbit having a period of only 7.8 days. It has an a sin i value of 0.777 Gm (0.00519 AU), where a is the semimajor axis and i is the orbital inclination. Since the sine function can be no larger than one, this provides a lower bound on the true semimajor axis of their orbit.

The primary component is an metallic-line (Am) star with the calcium K line of an A3 star, the hydrogen lines of an F1 star, and the metal lines of an F2 star. It is a sharp-lined, slowly rotating star with a projected rotational velocity of 9.6 km/s and is about 465 million years old. The star has 1.69 times the mass of the Sun and three times the Sun's radius. It is radiating 29 times the luminosity of the Sun from its photosphere at an effective temperature of 7,976 K.


Asteroseismology or astroseismology is the study of oscillations in stars. Because a star's different oscillation modes are sensitive to different parts of the star, they inform astronomers about the internal structure of the star, which is otherwise not directly possible from overall properties like brightness and surface temperature. Asteroseismology is closely related to helioseismology, the study of stellar oscillations specifically in the Sun. Though both are based on the same underlying physics, more and qualitatively different information is available for the Sun because its surface can be resolved.

Beta Virginis

Beta Virginis (β Virginis, abbreviated Beta Vir, β Vir), formally named Zavijava , is (despite its designation 'beta') the fifth-brightest star in the constellation of Virgo. Larger and more massive than the Sun, it is comparatively metal-rich (that is, it has a higher preponderance of elements heavier than helium).It is 0.69 degrees north of the ecliptic, so it can be occulted by the Moon and (rarely) by planets. The next planetary occultation of Zavijava will take place on 11 August 2069, by Venus.


CoRoT (French: Convection, Rotation et Transits planétaires; English: Convection, Rotation and planetary Transits) was a space telescope mission which operated from 2006 to 2013. The mission's two objectives were to search for extrasolar planets with short orbital periods, particularly those of large terrestrial size, and to perform asteroseismology by measuring solar-like oscillations in stars. The mission was led by the French Space Agency (CNES) in conjunction with the European Space Agency (ESA) and other international partners.

Among the notable discoveries was COROT-7b, discovered in 2009 which became the first exoplanet shown to have a rock or metal-dominated composition.

CoRoT was launched at 14:28:00 UTC on 27 December 2006, atop a Soyuz 2.1b rocket, reporting first light on 18 January 2007. Subsequently, the probe started to collect science data on 2 February 2007. CoRoT was the first spacecraft dedicated to the detection of transiting extrasolar planets, opening the way for more advanced probes such as Kepler and TESS. It detected its first extrasolar planet, COROT-1b, in May 2007, just 3 months after the start of the observations. Mission flight operations were originally scheduled to end 2.5 years from launch but operations were extended to 2013. On 2 November 2012, CoRoT suffered a computer failure that made it impossible to retrieve any data from its telescope. Repair attempts were unsuccessful, so on 24 June 2013 it was announced that CoRoT has been retired and would be decommissioned; lowered in orbit to allow it to burn up in the atmosphere.

Delta1 Tauri

Delta¹ Tauri (δ¹ Tauri, abbreviated Delta¹ Tau, δ¹ Tau) is a double star in the zodiac constellation of Taurus. Based upon an annual parallax shift of 20.96 mas as seen from Earth, it is located roughly 156 light-years distant from the Sun. The system is faintly visible to the naked eye with a combined apparent visual magnitude of +3.772. It is considered a member of the Hyades cluster.The two constituents are designated δ¹ Tauri A and B. A is itself a binary star with components designated δ¹ Tauri Aa (officially named Secunda Hyadum , the traditional name for the entire system) and Ab.

Eta Serpentis

Eta Serpentis (η Ser, η Serpentis) is a star in the constellation Serpens. In particular, it lies in Serpens Cauda, the snake's tail. The star has an apparent visual magnitude of 3.260, making it visible to the naked eye. Parallax measurements give a distance estimate of 60.5 light-years (18.5 parsecs) from the Earth.This star is larger than the Sun, with twice the mass and almost six times the radius. The spectrum matches a stellar classification of K0 III-IV, with the luminosity class of III-IV corresponding to an evolved star that lies between the subgiant and giant stages. The expanded outer envelope star is radiating about 19 times the luminosity of the Sun at an effective temperature of 4,890 K. At this temperature, it has an orange hue typical of a K-type star. Eta Serpentis displays solar-like oscillations with a period of 0.09 days.Eta Serpentis was previously classified as a carbon star, which would have made it the brightest carbon star in the sky, although this classification was since found to be erroneous.Eta Serpentis is currently 1.6 light years away from Gliese 710.

HD 89345 b

HD 89345 b is a Neptune-like exoplanet that orbits a G-type star. It is also called K2-234b. Its mass is 35.7 Earths, it takes 11.8 days to complete one orbit of its star, and is 0.105 AU from its star. It was discovered by 43 astrophysicists, one which is V. Van Eylen, and is announced in 2018.


Kepler-444 (or KOI-3158, KIC 6278762, 2MASS J19190052+4138043, BD+41 3306) is a star, estimated to be 11.2 billion years old (more than 80% of the age of the universe), approximately 116 light-years (36 pc) away from Earth in the constellation Lyra. On 27 January 2015, the Kepler spacecraft is reported to have confirmed the detection of five sub-Earth-sized rocky exoplanets orbiting the main star.

. According to NASA, no life as we know it could exist on these hot exoplanets, due to their close orbital distances to the host star.

Kepler space telescope

Kepler space telescope is a retired space telescope launched by NASA to discover Earth-size planets orbiting other stars. Named after astronomer Johannes Kepler, the spacecraft was launched on March 7, 2009, into an Earth-trailing heliocentric orbit. The principal investigator was William J. Borucki. After nine years of operation, the telescope's reaction control system fuel was depleted, and NASA announced its retirement on October 30, 2018.Designed to survey a portion of Earth's region of the Milky Way to discover Earth-size exoplanets in or near habitable zones and estimate how many of the billions of stars in the Milky Way have such planets, Kepler's sole scientific instrument is a photometer that continually monitored the brightness of approximately 150,000 main sequence stars in a fixed field of view. These data are transmitted to Earth, then analyzed to detect periodic dimming caused by exoplanets that cross in front of their host star. Only planets whose orbits are seen edge-on from Earth can be detected. During its over nine and a half years of service, Kepler observed 530,506 stars and detected 2,662 planets.

New Technology Telescope

The New Technology Telescope or NTT is an Alt-Az, 3.58-metre Ritchey–Chrétien telescope part of the European Southern Observatory and began operations in 1989. It is located in Chile at the La Silla Observatory and was an early pioneer in the use of active optics. The telescope and its enclosure developed a revolutionary design for optimal image quality.

Outline of astronomy

The following outline is provided as an overview of and topical guide to astronomy:

Astronomy – studies the universe beyond Earth, including its formation and development, and the evolution, physics, chemistry, meteorology, and motion of celestial objects (such as galaxies, planets, etc.) and phenomena that originate outside the atmosphere of Earth (such as the cosmic background radiation).


Procyon is the brightest object in the constellation of Canis Minor and usually the eighth-brightest star in the night sky with a visual apparent magnitude of 0.34. It has the Bayer designation α Canis Minoris, which is Latinised to Alpha Canis Minoris, and abbreviated α CMi or Alpha CMi, respectively. As determined by the European Space Agency Hipparcos astrometry satellite, this system lies at a distance of just 11.46 light-years (3.51 parsecs), and is therefore one of Earth's nearest stellar neighbours.

A binary star system, Procyon consists of a white-hued main-sequence star of spectral type F5 IV–V, designated component A, in orbit with a faint white dwarf companion of spectral type DQZ, named Procyon B. The pair orbit each other with a period of 40.8 years and an eccentricity of 0.4.

Red-giant branch

The red-giant branch (RGB), sometimes called the first giant branch, is the portion of the giant branch before helium ignition occurs in the course of stellar evolution. It is a stage that follows the main sequence for low- to intermediate-mass stars. Red-giant-branch stars have an inert helium core surrounded by a shell of hydrogen fusing via the CNO cycle. They are K- and M-class stars much larger and more luminous than main-sequence stars of the same temperature.


Serpens ("the Serpent", Greek Ὄφις) is a constellation of the northern hemisphere. One of the 48 constellations listed by the 2nd-century astronomer Ptolemy, it remains one of the 88 modern constellations defined by the International Astronomical Union. It is unique among the modern constellations in being split into two non-contiguous parts, Serpens Caput (Serpent Head) to the west and Serpens Cauda (Serpent Tail) to the east. Between these two halves lies the constellation of Ophiuchus, the "Serpent-Bearer". In figurative representations, the body of the serpent is represented as passing behind Ophiuchus between Mu Serpentis in Serpens Caput and Nu Serpentis in Serpens Cauda.

The brightest star in Serpens is the red giant star Alpha Serpentis, or Unukalhai, in Serpens Caput, with an apparent magnitude of 2.63. Also located in Serpens Caput are the naked-eye globular cluster Messier 5 and the naked-eye variables R Serpentis and Tau4 Serpentis. Notable extragalactic objects include Seyfert's Sextet, one of the densest galaxy clusters known; Arp 220, the prototypical ultraluminous infrared galaxy; and Hoag's Object, the most famous of the very rare class of galaxies known as ring galaxies.

Part of the Milky Way's galactic plane passes through Serpens Cauda, which is therefore rich in galactic deep-sky objects, such as the Eagle Nebula (IC 4703) and its associated star cluster Messier 16. The nebula measures 70 light-years by 50 light-years and contains the Pillars of Creation, three dust clouds that became famous for the image taken by the Hubble Space Telescope. Other striking objects include the Red Square Nebula, one of the few objects in astronomy to take on a square shape; and Westerhout 40, a massive nearby star-forming region consisting of a molecular cloud and an H II region.

Tau Ceti

Tau Ceti, Latinized from τ Ceti, is a single star in the constellation Cetus that is spectrally similar to the Sun, although it has only about 78% of the Sun's mass. At a distance of just under 12 light-years (3.7 parsecs) from the Solar System, it is a relatively nearby star and the closest solitary G-class star. The star appears stable, with little stellar variation, and is metal-deficient.

Observations have detected more than ten times as much dust surrounding Tau Ceti as is present in the Solar System. Since December 2012, there has been evidence of possibly five planets orbiting Tau Ceti, with two of these being potentially in the habitable zone. Because of its debris disk, any planet orbiting Tau Ceti would face far more impact events than Earth. Despite this hurdle to habitability, its solar analog (Sun-like) characteristics have led to widespread interest in the star. Given its stability, similarity and relative proximity to the Sun, Tau Ceti is consistently listed as a target for the Search for Extra-Terrestrial Intelligence (SETI) and appears in some science fiction literature.It can be seen with the unaided eye as a third-magnitude star. As seen from Tau Ceti, the Sun would be a third-magnitude star in the northern hemisphere constellation Boötes.

Theta Cygni

Theta Cygni (θ Cygni, θ Cyg) is a star in the northern constellation of Cygnus. It has an apparent visual magnitude of 4.5, so it can be seen from the northern hemisphere with the naked eye in sufficiently dark skies. Based upon parallax measurements, it is at a distance of about 59.8 light-years (18.3 parsecs) from the Earth. It is suspected of hosting an extrasolar planet.

Tim Bedding

Timothy R. Bedding (born 21 July 1966) is an Australian astronomer

known for his work on asteroseismology, the study of stellar oscillations. In particular, he contributed to the first detections of solar-like oscillations in stars such as eta Bootis, beta Hydri and alpha Centauri. He also led the discovery, using data from the Kepler space telescope, that red giants oscillate in mixed modes that are directly sensitive to the core properties of the star and can be used to distinguish red giants burning helium in their cores from those that are still only burning hydrogen in a shell.Bedding has worked in the School of Physics at the University of Sydney since 1995 and was Head of School from 2012 to 2018.

He received the University's Excellence in Teaching Award in 1999 and was appointed as a Payne Scott Professor in 2019.In 2007 the asteroid 231470 Bedding was named in his honour.

Bedding was a member of the Australian Ultimate Frisbee team and participated in the 1990 World Championships held in Oslo, Norway.

Variable star

A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.

This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:

Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.

Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle.

Xi Hydrae

Xi Hydrae, Latinized from ξ Hydrae, is a solitary star in the equatorial constellation of Hydra. It was also given the Flamsteed designation 19 Crateris. This magnitude 3.54 star is situated 130 light-years from Earth and has a radius about 10 times that of the Sun. It is radiating 58 times as much luminosity as the Sun.Flamsteed gave Xi Hydrae the designation 19 Crateris. He included a number of stars now within the IAU boundaries of Hydra as part of a Hydra & Crater constellation overlapping parts of both modern constellations.The star Xi Hydrae is particularly interesting in the field of asteroseismology since it shows solar-like oscillations. Multiple frequency oscillations are found with periods between 2.0 and 5.5 hours.Xi Hydrae has left the main sequence, having exhausted the supply of hydrogen in its core. Its spectrum is that of a red giant. Modelling its physical properties against theoretical evolutionary tracks shows that it has just reached the foot of the red giant branch for a star with an initial mass around 3 M☉. This puts its age at about 510 myr.

Star systems
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