Eclipsing star

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Animation of an eclipsing double star with resulting light curve.

An eclipsing variable star or photometric binary star is a binary star system , whose orbit is so in space, the two that star from the earth periodically seen hide .

The prototype of these double stars is Algol (β Persei) in the constellation Perseus , which the Arabs called the Devil's Star in the Middle Ages . Its variability was already noted in antiquity and its exact periodicity was published by John Goodricke in the Philosophical Transactions in 1783/84 . Algol's brightness drops to a third every 2.87 days and shows a small secondary minimum in half the period.

Analysis of the light curve

The following parameters can be derived from the light curve , the change in the brightness of the unresolved binary star system during an orbit around the common center of gravity :

  • The period of rotation
  • The duration of the major and minor minimum
  • The possible minimum downtime in the case of total coverage
  • The amplitudes of the minima
  • The course of brightness in the decrease and increase of the minima

From this data, conclusions can be drawn about the surface brightness of the stars, the relative radii , the orbital inclination , the edge darkening , the gravitational darkening , the deviation from the spherical shape due to centrifugal forces and the relative distance. If the observation is carried out in a photometric system in several wavelengths, conclusions can also be drawn about the surface temperature of the stars. Since stars can only assume a limited range of state variables , a determination of the absolute parameters such as luminosity and of geometric parameters, e.g. B. star radii, possible.

If the course of the radial velocity is determined by means of the Doppler effect , the masses of the stars and the orbital eccentricity can also be calculated. Since the orbital inclination of a binary star system that cannot be optically resolved into its components can only be determined with eclipsing stars, they are the most important source for determining stellar masses.

Classification

There are two main classifications for coverage variables based on the light curve and the geometric relationships:

Light curve

  • Algol stars show an almost constant brightness between the minima
  • In Beta-Lyrae stars , the light change is continuously variable with rounded maxima, but minima of different depths. The period of rotation is between one and up to 20 days.
  • The W-Ursae Majoris stars are similar to the Beta Lyrae stars without standstills, with the minima being approximately the same depth. The period of rotation is less than a day.

Geometric relationships

  • Separate systems that show no exchange of material between the components.
  • Semi-separated systems in which one component has taken the maximum extent in the binary star system. With any further expansion of this component, matter would flow to the companion.
  • In contact systems, each component has assumed its maximum expansion and there is a constant exchange of matter between the two stars.

  • Detached binary: Double stars orbit each other, but do not influence each other so much that they cross the Roche limit.

  • Semidetached binary: Double stars influence each other so much that the Roche limit is exceeded.

  • Contact binary: double stars in physical contact. They may even form a common shell.

Special forms

In addition to stars, non-luminous companions can also cause obscuration. These include exoplanets , brown dwarfs, and dust discs as in the case of Epsilon Aurigae . Because these objects do not shine themselves, only a decrease in brightness is observed with one coverage variable per revolution. Planets and brown dwarfs have a much smaller diameter than stars and therefore the minimum change in brightness is small. The necessary measurement accuracy can be achieved outside of the earth's atmosphere with significantly fewer instruments, especially with the simultaneous and long-term monitoring of a large number of stars to search for such minima. For example, the primary goals of the Kepler and COROT satellite missions are to search for exoplanets using the transit method .

There are also triple coverage systems such as KOI-126. Here a star orbits a close binary star system in an eccentric orbit, whereby both stars of the narrow system can be covered by the extended companion. The light curve appears irregularly variable due to the superposition of the minima.

Use for astrophysics

Artist's impression of a binary star system. A compact star accretes gas in its partner's atmosphere.

The astrophysical benefit of this class of stars is the possibility of measuring the orbit data and physical state variables of the stars in the binary star system by measuring the light curve . With the help of the new generation of large telescopes, it is possible to find and examine eclipsing stars within the local group . By deriving the luminosity from the light curve, the distances to the Magellanic Clouds , the Andromeda Nebula , the Triangle Nebula and some dwarf galaxies of the local group could be determined with an accuracy of up to 6%.

Eclipsing variables also allow the spatial resolution of structures on or near the stars of the binary system. This includes:

The observation of an apsidal rotation of the path of an eclipse variable is relatively easy, since in this case the position of the main and the secondary minima change relative to one another. Since the apsidic rotation is also dependent on the structure of the stars in the binary system, eclipse variables can also be used to verify models of the internal structure of stars. However, the rotation parameters and the alignment of the axes must be known for this, as in the case of DI Herculis . The apsidal precession can also lead to falsification of alternative theories of gravity are used. With these hypotheses, the observed deviations in the rotation curves of galaxies, the dynamic stability of galaxy clusters and the gravitational lenses through galaxies or clusters can be explained just as well as through the assumption of dark matter . The observed apsidal rotations in eclipsed stars with a large orbital eccentricity should deviate in a few years from the values ​​calculated according to the theory of relativity and should enable a differentiation.

Since the probability of a mutual occultation of the stars also decreases with the distance, most of the eclipsing variables have short periods and therefore a small orbit half-axis in relation to the star radii. As a result, the development of stars in binary systems can deviate from that of single stars due to mass exchange between the components, accelerated rotation and magnetic activity.

Period changes

Changes in the total angular momentum of the binary star system or in the distribution of the angular momentum should lead to a shift in the time of minimum brightness. Since the change accumulates with each orbit, the smallest deviations can be measured and observations show that the orbital times of many eclipsing stars are not constant. The following phenomena are known that can trigger or simulate a change in period:

  • Apse rotation
  • With the time-of-flight effect , a third body orbits the binary star system and thus shifts the center of gravity around which the two stars of the eclipsing variable move. Due to the finiteness of the speed of light, this shifts the time of minimum brightness.
  • Mass exchange between the components
  • Loss of mass from the binary star system z. B. by stellar winds
  • Radiation of gravitational waves
  • The loss of magnetic angular momentum occurs when a star loses ionized gas along the star's magnetic field lines . The gas is frozen in the magnetic field lines up to the radius at which the magnetic field rotates at the speed of light. The result is a decrease in the star's speed of rotation and thus a loss of angular momentum in the binary star system.
  • In the Applegate mechanism, angular momentum is redistributed between the inner and outer convection zones of a star in the course of a magnetic cycle . This leads to a change in the rotational flattening and thus indirectly also the period of rotation, which can both increase and decrease. According to observations, cyclical period increases and decreases occur almost exclusively only in eclipsed stars in which at least one component shows magnetic activity.
  • An asymmetrical distribution of brightness on the hemisphere to be covered by star spots
  • Pulsations caused by tidal forces , which are often in resonance with the orbital period of the double star.

Most of the observed period changes in eclipsing stars are attributed to the mass exchange between the components of the binary star systems. However, the cause of many cyclical period changes is not known.

Change of the light curve

If a third star runs around the common center of mass and its orbit is not in the plane of the eclipsing variable, this leads to a precession of the orbit of the narrow binary star system. As a result, the inclination of the orbit changes and thus also the depth of the minima. Overall, only a small number of triple systems are known with a variable depth of the minima due to the gravitational influence of a third body. These stars include Algol and HS Hydrae.

In addition, the normal brightness can fluctuate due to changes in the surface of one or both components of the variable coverage. The most famous examples include the RS Canum Venaticorum stars . Star spots with a radius of up to 20 ° and a temperature that is around 1500 K below the undisturbed star surface form on the surface of a late giant . This leads to depressions in the light curves that migrate through the light curve over the course of months to years. In the case of coverage variables, due to the bound rotation, the rotation period is identical to the orbit period. The slow migration of the star spots across the surface is therefore the result of a differential rotation in the late giants. Also eclipsing BY Draconis star show a similar modulation of the light curve. This class of stars are late dwarfs with star spots on their surfaces.

Artist's impression of the dust cloud emanating from the planet KIC 12557548b

When a planet gets too close to its central star, it heats up to such an extent that parts of its surface evaporate and the matter can leave the gravitational field of the Super Mercury . When the orbit of the planet passes in front of the star when viewed from the earth, the depth and duration of the minimum eclipse can vary. The period of rotation is constant as in the case of KIC 12557548, where the depth of the minima fluctuates between 0.2% and 1.2%. The vaporized matter condenses back to dust at a distance from the star and absorbs the star light very effectively. The cover light curve is asymmetrical and, as with all planetary transits, the secondary minimum is missing.

Web links

  • Hagen Observatory - interactive Java applet to illustrate the geometry and the resulting light curves (along with theoretical treatment).

Individual evidence

  1. ↑ z. B. Zdenek Kopal: Dynamics of Close Binary Systems. 1978 (1914), p. 3 below ; The Philosophical Transactions of the Royal Society of London, from Their Commencement in 1665 to the Year 1800. published 1809, pp. 456ff
  2. ↑ W. Strohmeier: Variable stars . Treugesell-Verlag, Düsseldorf 1974.
  3. ^ John R. Percy: Understanding Variable Stars . Cambridge University Press, Cambridge 2007, ISBN 978-0-521-23253-1 .
  4. ^ Alfred Weigert , Heinrich Johannes Wendker , Lutz Wisotzki: Astronomy and Astrophysics. A basic course.
  5. ↑ Joshua A. Carter et al .: KOI-126: A Triply-Eclipsing Hierarchical Triple with Two Low-Mass Stars . In: Astrophysics. Solar and Stellar Astrophysics . 2011, arxiv : 1102.0562v1 .
  6. ↑ Alceste Z. Bonanos: Eclipsing Binaries: Tools for Calibrating the Extragalactic Distance Scale . In: Binary Stars as Critical Tools and Tests in Contemporary Astrophysics, International Astronomical Union. Symposium no.240, held August 22-25, 2006 in Prague, Czech Republic, S240, # 008 . 2006. arxiv : astro-ph / 0610923 .
  7. ^ P. Zasche: On the apsidal-motion of thirteen eclipsing binaries . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1204.5578v1 .
  8. ^ S. Albrecht, S. Reffert, I. Snellen: Misaligned spin and orbital axes cause the anomalous precession of DI Herculis . In: Nature . tape 461 , 2009, p. 373–376 , doi : 10.1038 / nature08408 .
  9. ^ M. De Laurentis, R. De Rosa, F. Garufi, L. Milano: Testing gravitational theories using Eccentric Eclipsing Detached Binaries . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1207.5410v1 .
  10. ^ Cuno Hoffmeister , G. Richter, W. Wenzel: Veränderliche Sterne . JA Barth Verlag, Leipzig 1990, ISBN 3-335-00224-5 .
  11. Jump up ↑ DR Gies, SJ Williams, RA Matson, Z. Guo, SM Thomas: A Search for Hierarchical Triples using Kepler Eclipse Timing . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1204.0030v1 .
  12. ↑ Jetsu, L., Porceddu, S., Lyytinen, J., Kajatkari, P., Lehtinen, J., Markkanen, T, Toivari-Viitala, J .: Did the Ancient Egyptians Record the Period of the Eclipsing Binary Algol - The Raging One? . In: The Astrophysical Journal . 773, No. 1, 2013, p. A1 (14pp). bibcode : 2013ApJ ... 773 .... 1J . doi : 10.1088 / 0004-637X / 773/1/1 .
  13. ↑ P. Zasche and A. Paschke: HS Hydrae about to turn off its eclipses . In: Astronomy & Astrophysics . tape 542 , 2012, p. L23 , doi : 10.1051 / 0004-6361 / 201219392 .
  14. ↑ Arnold, CN, Montle, RE, Stuhlinger, TW, & Hall, DS: UBV photometry and light curve solution of the eclipsing binary RS CVn SS Cam . In: Acta Astronomica . tape 29 , 1979, pp. 243-258 .
  15. ^ J. MacDonald and DJ Mullan: Precision modeling of M dwarf stars: the magnetic components of CM Draconis . In: Astrophysics. Solar and Stellar Astrophysics . 2011, arxiv : 1106.1452v1 .
  16. ↑ M. Brogi, CU Keller, M. de Juan Ovelar, MA Kenworthy, RJ de Kok, M. Min, IAG Snellen: Evidence for the disintegration of KIC 12557548 b . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1208.2988 .