# Solar binary

This composite image shows an exoplanet (2M1207b, the red spot on the lower left), orbiting the brown dwarf 2M1207 (centre). 2M1207b is a Jupiter-like planet. It orbits the brown dwarf at a distance nearly twice as far as Neptune is from the Sun. Credit: ESO.
 Completion status: Been started, but most of the work is still to be done.

A solar binary of the Sun and Jupiter may serve to establish an upper limit for interstellar cometary capture. The basic problem even with a passage through a molecular cloud of some 10 million years is the low relative velocity (~0.5 km s-1) required between the solar system and the cometary medium. Some of the captured bodies may localize in the Oort cloud, while others localize near the Sun or Jupiter.

 Educational level: this is a secondary education resource.

As stars often occur as binaries or multiple star systems, it is likely that the Sun may have been a member of a binary system or even a multiple star system at some time in the past.

 Educational level: this is a tertiary (university) resource.
 Educational level: this is a research resource.
 Resource type: this resource is an article.
 Resource type: this resource contains a lecture or lecture notes.
 Subject classification: this is an astrophysics resource.

## Notation

Notation: let the symbol Def. indicate that a definition is following.

Notation: let the symbols between [ and ] be replacement for that portion of a quoted text.

## Universals

To help with definitions, their meanings and intents, there is the learning resource theory of definition.

Def. evidence that demonstrates that a concept is possible is called proof of concept.

The proof-of-concept structure consists of

1. background,
2. procedures,
3. findings, and
4. interpretation.[1]

The findings demonstrate a statistically systematic change from the status quo or the control group.

For a solar binary, proof of concept is that the Sun and Jupiter together can act in some way like a stellar binary.

## Binary star

Def. "[t]wo stars that appear to be one when seen with the naked eye, either because they orbit one another (binary stars) or happen to be in the same line of sight even though they are separated by a great distance"[2] is called a double star.

Def. "[a] star that appears as a double due to an optical illusion; in reality, the stars may be far apart from each other"[3] is called an optical double.

Def. "[t]wo stars which form a stellar system, such that they orbit the point of equilibrium of their gravitational fields"[2] is called a double star.

Def. "[a] stellar system that has two stars orbiting around each other"[4] is called a binary star.

“A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, ... or secondary. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known.”[5]

Def. "[a] binary star whose components can be visually resolved"[6] is called a visual binary.

### Astrometric binaries

"Astrometric binaries are relatively nearby stars which can be seen to wobble around a point in space, with no visible companion. The same mathematics used for ordinary binaries can be applied to infer the mass of the missing companion. The companion could be very dim, so that it is currently undetectable or masked by the glare of its primary, or it could be an object that emits little or no electromagnetic radiation"[5].

"The visible star's position is carefully measured and detected to vary, due to the gravitational influence from its counterpart. The position of the star is repeatedly measured relative to more distant stars, and then checked for periodic shifts in position. Typically this type of measurement can only be performed on nearby stars, such as those within 10 parsecs. Nearby stars often have a relatively high proper motion, so astrometric binaries will appear to follow a sinusoidal path across the sky."[5]

### Spectroscopic binaries

"Sometimes, the only evidence of a binary star comes from the Doppler effect on its emitted light. In these cases, the binary consists of a pair of stars where the spectral lines in the light emitted from each star shifts first toward the blue, then toward the red, as each moves first toward us, and then away from us, during its motion about their common center of mass, with the period of their common orbit."[5]

"In these systems, the separation between the stars is usually very small, and the orbital velocity very high. Unless the plane of the orbit happens to be perpendicular to the line of sight, the orbital velocities will have components in the line of sight and the observed radial velocity of the system will vary periodically. Since radial velocity can be measured with a spectrometer by observing the Doppler shift of the stars' spectral lines, the binaries detected in this manner are known as spectroscopic binaries. Most of these cannot be resolved as a visual binary, even with telescopes of the highest existing resolving power."[5]

### Eclipsing binaries

An eclipsing binary is shown with an indication of the variation in intensity.[7][8] Credit: .

"An eclipsing binary star is a binary star in which the orbit plane of the two stars lies so nearly in the line of sight of the observer that the components undergo mutual eclipses. In the case where the binary is also a spectroscopic binary and the parallax of the system is known, the binary is quite valuable for stellar analysis.[9] Algol is the best-known example of an eclipsing binary.[9]"[5]

### Eclipsing binary with matter transfer

This animation is for an eclipsing binary with matter (gas + plasma) transfer like beta Lyrae. Credit: Stanlekub.

"[M]atter [may] transfer from one star to another through a process known as Roche Lobe overflow (RLOF) ... through an accretion disc. The mathematical point through which this transfer happens is called the first Lagrangian point.[10] It is not uncommon that the accretion disc is the brightest (and thus sometimes the only visible) element of a binary star."[5]

### Detached binaries

For detached binaries “each component is within its Roche lobe, i.e. the area where the gravitational pull of the star itself is larger than that of the other component. The stars have no major effect on each other, and essentially evolve separately. Most binaries belong to this class.”[5]

### Semidetached binaries

A semidetached binary has “one of the components [filling] the binary star's Roche lobe and the other does not. Gas from the surface of the Roche-lobe-filling component (donor) is transferred to the other, accreting star. The mass transfer dominates the evolution of the system. In many cases, the inflowing gas forms an accretion disc around the accretor.”[5]

### Contact binaries

In a contact binary both components fill their Roche lobes; i.e., they “are so close that they touch each other or have merged to share their gaseous envelopes.” after the Wikipedia article on a contact binary. When stars share an envelope the pair may be called an overcontact binary.[11][12][13] “As the friction of the envelope brakes the orbital motion, the stars may eventually merge.[14] [A contact binary is] a stable configuration [where the two stars touch,] with a typical lifetime of millions to billions of years ... Almost all known contact binary systems are eclipsing binaries[15][16].

### Common envelope binaries

A common envelope (CE) binary “refers to a short-lived (months to years) phase in the evolution of a binary star in which the largest of the two stars (the donor star) has initiated unstable mass transfer to its companion star. ... This [may become a run-away process in which] the [donor star’s] envelope [expands to] engulf the companion star. ... The [loss] of orbital energy [may] heat up and expand the envelope ... [T]he whole common-envelope phase ends when either the envelope is expelled into space, or the two objects inside the envelope merge and no more energy is available to expand or even expel the envelope. This phase of the shrinking of the orbit inside the common envelope is known as a spiral-in.”[17]

## Chaos assisted capture

In a mechanism of chaos assisted capture (CAC), particles such as comets or those of sizes in the range of the irregular moons of Jupiter become entangled in chaotic layers which temporarily “extend the lifetimes of [these] particles within the Hill sphere, thereby providing the breathing space necessary for relatively weak dissipative forces (eg gas-drag) to effect permanent capture.”[18] These objects of the Sun-Jupiter binary system may localize near Jupiter and become satellites, specifically the irregular moons.[18]

## Solar antapex

In 1917 the solar antapex has an equatorial location of right ascension (RA) 6h declination (Dec) -34°.[19]

## Star fission

“Zero-age contact must be a consequence of star fission under critical angular momentum.”[20] When the angular momentum is too large, the star brakes into a detached binary.[20] When the angular momentum is too small, the star remains as a single star.[20] BH Centauri and V1010 Ophiuchi have zero-age radii and are zero-age contact systems.[20] BH Centauri is an overcontact system.[20]

Fragmentation of the molecular cloud during the formation of protostars is an acceptable explanation for the formation of a binary or multiple star system.[21][22]

With respect to low-mass star formation, "fragmentation to form a binary star [may be] most simply achieved if collapse is initiated by an external impulse."[23] "On its own, [the] process under which a dense molecular cloud core can collapse to form a binary, or multiple, star system would produce wide binaries".[23] "[C]lose binaries [may be] formed because of mutual interactions between the protostellar discs surrounding the various fragments."[23] "[T]he most likely collision which has an effect on the core is the one for which [the velocity change imparted by the impulse,] Δv ~ cs [(the internal sound speed),] induced by a clump of mass ~0.1Mʘ."[23] "[T]he impulsive collapse of the cloud cores [requires] that they are not primarily magnetically supported in their central regions."[23]

## Sun-Jupiter binary

The Sun-Jupiter binary may serve to establish an upper limit for interstellar cometary capture when three bodies are extremely unequal in mass, such as the Sun, Jupiter, and a third body (potential comet) at a large distance from the binary.[24] The basic problem with a capture scenario even from passage through “a cloud of some 10 million years, or from a medium enveloping the solar system, is the low relative velocity [~0.5 km s-1] required between the solar system and the cometary medium.”[25] The capture of interstellar comets by Saturn, Uranus, and Neptune together cause about as many captures as Jupiter alone.[25]

## References

1. Ginger Lehrman and Ian B Hogue, Sarah Palmer, Cheryl Jennings, Celsa A Spina, Ann Wiegand, Alan L Landay, Robert W Coombs, Douglas D Richman, John W Mellors, John M Coffin, Ronald J Bosch, David M Margolis (August 13, 2005). "Depletion of latent HIV-1 infection in vivo: a proof-of-concept study". Lancet 366 (9485): 549-55. doi:10.1016/S0140-6736(05)67098-5. Retrieved on 2012-05-09.
2. (July 30, 2010) "double star". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
3. (March 7, 2011) "optical double". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
4. (October 21, 2010) "binary star". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
5. (July 8, 2012) "Binary star". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
6. (August 1, 2010) "visual binary". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
7. D. Gossman (October 1989). "Light Curves and Their Secrets". Sky & Telescope.
8. Script error
9. Script error
10. Script error
11. contact binary, David Darling, The Internet Encyclopedia of Science. Accessed on line November 4, 2007.
12. overcontact binary, David Darling, The Internet Encyclopedia of Science. Accessed on line November 4, 2007.
13. pp. 51–53, An Introduction to Astrophysical Fluid Dynamics, Michael J. Thompson, London: Imperial College Press, 2006. ISBN 1-86094-615-1.
14. R. Voss, T.M. Tauris (2003). "Galactic distribution of merging neutron stars and black holes". Monthly Notices of the Royal Astronomical Society 342 (4): 1169–84. doi:10.1046/j.1365-8711.2003.06616.x. Bibcode2003MNRAS.342.1169V.
15. p. 231, Stellar Rotation, Jean Louis Tassoul, Andrew King, Douglas Lin, Stephen P. Maran, Jim Pringle, and Martin Ward, Cambridge, UK, New York: Cambridge University Press, 2000. ISBN 0-521-77218-4.
16. (March 28, 2012) "Contact binary". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
17. (June 29, 2012) "Common envelope". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-10.
18. Sergey A. Astakhov and David Farrelly (November 2004). "Capture and escape in the elliptic restricted three?body problem". Monthly Notices of the Royal Astronomical Society 354 (4): 971-9. doi:10.1111/j.1365-2966.2004.08280.x. Bibcode2004MNRAS.354..971A. Retrieved on 2012-03-12.
19. Oliver Justin Lee (1917). Yerkes Observatory. ed. Zone +45° of Kapteyn’s Selected Areas: Parallaxes and Proper Motions of 1041 Stars, In: Publications of the Yerkes observatory of the University of Chicago, Volume 4 Part IV. Chicago, Illinois: University of Chicago Press. pp. 123-89. Retrieved 2012-07-10.
20. Kam-Ching Leung and Donald P. Schneider (February 1977). "Eclipsing systems in star clusters. III. Early-type contact system BH Centauri.". The Astrophysical Journal 211 (2): 844-52. doi:10.1086/154993. Bibcode1977ApJ...211..844L.
21. A.P. Boss (1992). J. Sahade, G.E. McCluskey, Yoji Kondo. ed. Formation of Binary Stars, In: The Realm of Interacting Binary Stars. Dordrecht: Kluwer Academic. pp. 355. ISBN 0-7923-1675-4.
22. J.E. Tohline, J.E. Cazes, H.S. Cohl. The Formation of Common-Envelope, Pre-Main-Sequence Binary Stars. Louisiana State University.
23. J. E. Pringle (July 1989). "On the formation of binary stars". Royal Astronomical Society, Monthly Notices 239 (7): 361-70. Bibcode1989MNRAS.239..361P. Retrieved on 2012-03-24.
24. MJ Valtonen (February 1983). "On the capture of comets into the Solar System". The Observatory 103 (2): 1-4. Bibcode1983Obs...103....1V. Retrieved on 2012-03-12.
25. M. J. Valtonen; K. A. Innanen (April 1982). "The capture of interstellar comets". The Astrophysical Journal 255 (4): 307-15. doi:10.1086/159830. Bibcode1982ApJ...255..307V. Retrieved on 2012-03-12.