Binary mass function: Difference between revisions

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Because the orbital period and orbital velocities in the binary system are related to the masses of the binary components, measuring these parameters provides some information about the masses of one or both components.<ref name="podsiadlowski">{{cite web |url=http://www-astro.physics.ox.ac.uk/~podsi/binaries.pdf |title=The Evolution of Binary Systems, in Accretion Processes in Astrophysics |first1=Philipp |last1=Podsiadlowski |publisher=[[Cambridge University Press]] |access-date=April 20, 2016 }}</ref> However, the true orbital velocity is often unknown, because velocities in the plane of the sky are much more difficult to determine than velocities along the line of sight.<ref name="karttunen" />

Radial velocity is the velocity component of orbital velocity in the line of sight of the observer. Unlike true orbital velocity, radial velocity can be determined from [[Doppler spectroscopy]] of [[spectral line]]s in the light of a star,<ref name="radial">{{cite web |url=http://www.planetary.org/explore/space-topics/exoplanets/radial-velocity.html |title=Radial Velocity – The First Method that Worked |publisher=[[The Planetary Society]] |access-date=April 20, 2016 }}</ref> or from [[pulsar timing|variations in the arrival times]] of pulses from a [[radio pulsar]].<ref name="cornell">{{cite web |url=httphttps://www.astro.cornell.edu/academics/courses/astro201/psr1913.htm |title=The Binary Pulsar PSR 1913+16 |publisher=[[Cornell University]] |access-date=April 26, 2016 }}</ref> A binary system is called a single-lined spectroscopic binary if the radial motion of only one of the two binary components can be measured. In this case, a lower limit on the mass of the other, unseen component can be determined.<ref name="karttunen" />

The true mass and true orbital velocity cannot be determined from the radial velocity because the [[orbital inclination]] is generally unknown. (The inclination is the orientation of the orbit from the point of view of the observer, and relates true and radial velocity.<ref name="karttunen" />) This causes a degeneracy between mass and inclination.<ref name="brown">{{cite journal|doi=10.1088/0004-637X/805/2/188|title=True Masses of Radial-Velocity Exoplanets|year=2015|last1= Brown| first1=Robert A.| journal=[[The Astrophysical Journal]]|bibcode = 2015ApJ...805..188B|volume=805|issue=2|pages=188|arxiv = 1501.02673|s2cid=119294767}}</ref><ref name="larson">{{cite web |url=http://www.physics.usu.edu/shane/classes/astrophysics/lectures/lec08_binaries.pdf |title=Binary Stars |first1=Shane |last1=Larson |publisher=[[Utah State University]] |access-date=April 26, 2016 |url-status=dead |archive-url=https://web.archive.org/web/20150412200552/http://www.physics.usu.edu/shane/classes/astrophysics/lectures/lec08_binaries.pdf |archive-date=April 12, 2015 }}</ref> For example, if the measured radial velocity is low, this can mean that the true orbital velocity is low (implying low mass objects) and the inclination high (the orbit is seen edge-on), or that the true velocity is high (implying high mass objects) but the inclination low (the orbit is seen face-on).

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=== Exoplanets ===

An [[exoplanet]] causes its host star to move in a small orbit around the center of mass of the star-planet system. This 'wobble' can be observed if the radial velocity of the star is sufficiently high. This is the [[Methods of detecting exoplanets|radial velocity method]] of detecting exoplanets.<ref name="brown" /><ref name="radial" /> Using the mass function and the radial velocity of the host star, the minimum mass of an exoplanet can be determined.<ref>{{cite web |url=http://exoplanets.org/methodology.html |title=Documentation and Methodology |publisher=[[Exoplanet Data Explorer]] |access-date=April 25, 2016 }}</ref><ref>{{cite journal|doi=10.1086/504701|title=Catalog of Nearby Exoplanets | year=2006 | last1=Butler|first1=R.P.|author1-link=R. Paul Butler|last2=Wright|first2=J. T.|last3=Marcy|first3=G. W.|author3-link=Geoffrey Marcy|last4=Fischer|first4=D. A.|author4-link=Debra Fischer|last5=Vogt|first5=S. S.|author5-link=Steven S. Vogt|last6=Tinney|first6=C. G.|last7= Jones|first7=H. R. A.|last8= Carter|first8=B. D.|last9=Johnson|first9=J. A.| last10=McCarthy|first10=C.|last11=Penny|first11=A. J.|journal=[[The Astrophysical Journal]]|bibcode = 2006ApJ...646..505B | volume=646|issue=1|pages=505–522|arxiv = astro-ph/0607493 |s2cid=119067572|display-authors=8}}</ref>{{rp|p=9}}<ref name="boffin" /><ref>{{cite web |url=http://www.phy.duke.edu/~kolena/invisible.html |title=Detecting Invisible Objects: a guide to the discovery of Extrasolar Planets and Black Holes |first1=John |last1=Kolena |publisher=[[Duke University]] |access-date=April 25, 2016 }}</ref> Applying this method on [[Proxima Centauri]], the closest star to the [[Solar System]], led to the discovery of [[Proxima Centauri b]], a [[terrestrial planet]] with a minimum mass of {{Earth mass|sym=y|1.27}}.<ref name="proxima b discovery paper">{{cite journal

| bibcode = 2016Natur.536..437A

| title = A terrestrial planet candidate in a temperate orbit around Proxima Centauri