Binary mass function: Difference between revisions

Revision as of 20:52, 27 April 2016

Revision as of 11:51, 29 April 2016

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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> But because the true orbital velocity cannot be determined generally, this information is limited.<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=http://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=

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The binary mass function <math>f</math> (with [[Units of measurement|unit]] of mass) is<ref name="bailes">{{cite journal|doi=10.1126/science.1208890|title=Transformation of a Star into a Planet in a Millisecond Pulsar Binary|year=2011|last1=Bailes|first1=M.|author1-link=Matthew Bailes|last2=Bates|first2=S. D.|last3=Bhalerao|first3=V.|last4=Bhat|first4=N. D. R.|last5=Burgay|first5=M.|last6=Burke-Spolaor|first6=S.|last7=d'Amico|first7=N.|last8=Johnston|first8=S.|last9=Keith|first9=M. J.|last10=Kramer|first10=M.|last11=Kulkarni|first11=S. R.|last12=Levin|first12=L.|last13=Lyne|first13=A. G.|last14=Milia|first14=S.|last15=Possenti|first15=A.|last16=Spitler|first16=L.|last17=Stappers|first17=B.|last18=Van Straten|first18=W.|journal=[[Science (journal)|Science]]|bibcode = 2011Sci...333.1717B|pmid=21868629|volume=333|issue=6050|pages=1717–1720|arxiv = 1108.5201 |display-authors=8}}</ref><ref name="tauris" /><ref name="podsiadlowski" /><ref name="kerkwijk">{{cite journal|doi=10.1088/0004-637X/728/2/95|title=Evidence for a Massive Neutron Star from a Radial-velocity Study of the Companion to the [[Black-widow Pulsar]] PSR B1957+20|year=2011|last1=

van Kerkwijk|first1=M. H.|last2=Breton|first2=M. P.|last3=Kulkarni|first3=S. R.|author3-link=Shrinivas Kulkarni|journal=[[The Astrophysical Journal]]|bibcode = 2011ApJ...728...95V|volume=728|issue=2|pages=95|arxiv = 1009.5427}}</ref><ref name="karttunen" /><ref name="larson" /><ref>{{cite web |url=http://astronomy.swin.edu.au/cms/astro/cosmos/b/Binary+Mass+Function |title=Binary Mass Function |publisher=COSMOS -– The SAO Encyclopedia of Astronomy, [[Swinburne University of Technology]] |access-date=April 20, 2016 }}</ref>

<math>f = \frac{M_{2}^{3}\ \mathrm{sin}^{3}i }{(M_{1} + M_{2})^{2}} = \frac{P_\mathrm{orb}\ K^{3}}{2 \pi G}.</math>

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=== X-ray binaries ===

If the accretor in an [[X-ray binary]] has a minimum mass that significantly exceeds the [[Tolman–Oppenheimer–Volkoff limit]] (the maximum possible mass for a [[neutron star]]), it is expected to be a black hole. This is the case in [[Cygnus X-1]], for example, where the radial velocity of the companion star has been measured.<ref>{{citation | last=Mauder | first=H. | date=1973 | title=On the Mass Limit of the X-ray Source in Cygnus X-1 | bibcode=1973A&A....28..473M | journal=[[Astronomy and Astrophysics]] | volume=28 | pages=473–475}}</ref><ref>[http://imagine.gsfc.nasa.gov/features/yba/cyg-X1-mass/mass-solution3.html NASA -– Imagine the Universe! Partial Solution for Mass of Cyg X-1]</ref>

=== Exoplanets ===

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== References ==

{{Reflist|30em}}

[[Category:Binary stars]]