# Regarding binary systems (with pulsars)

Are binary systems (in case of stars and other celestial bodies) more favorable than independent existence? I've been going through an article regarding pulsars, where it was stated that 'many pulsars are found in binary systems.The companion of pulsars have been found to be normal stars, planets, white dwarf stars, neutron stars and even another pulsar.

So what are the criteria to form binary systems ? I know that their sizes should be comparable, and that leads to the equilibrium of the gravitational attraction between the bodies, etc. As it is a known fact that neutron stars and pulsars are quite heavy and dense, how are they able to co-exist as binary systems with other stars, planets, etc.? Search this @ http://outreach.atnf.csiro.au/education/everyone/pulsars/

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What exactly are you asking regarding it being more "favorable"? The simple answer is that 3-body systems are unstable, 2-body stems can exist stably, and they do. Are you interested in the astronomic prevalence of binary systems versus independent systems? This would be an astronomy question of a statistical nature (naturally, one that can't be 100% answered either). Lastly, how did you establish the intuition that pulsars would have any problem existing in orbit with other gravitational bodies? I am sure it is a bad intuition. You need to articulate it so people can tell you why not. –  Alan Rominger Jun 14 '12 at 14:28
Actually I have a doubt regarding the fact that neutron stars and pulsars are massively heavy, so how does a binary system of a neutron star or a pulsar along with planets co-exist ? Why doesn't the planet submerges into the strong attractive pull of them? –  stp30 Jun 14 '12 at 17:10

It's hard to get exact figures for how many star systems are binaries, but in our galaxy observations suggest that at least a third of all star systems are binaries, i.e. at least half of all stars are in binaries.

So observation suggests that formation of binary systems as roughly as likely as formation of single star systems. There has been a lot of effort put into modelling star formation (see http://arxiv.org/abs/1109.3740 for a recent review) and the most likely cause of binary formation appears to be an instability developing in the protostellar disk that leads to fragmentation of the disk. The fragments then form separate stars.

I'm not sure if you're asking whether pulsars are more likely to be in binary systems. I couldn't find any stats on this, but it seems plausible. Pulsars result from supernova explosions and in a binary the heavier star can increase its mass, and thereby become a supernova by, taking matter from its companion star. This would make pulsars more likely to be in binary systems.

Response to comment: The Sun is a million times heavier than the Earth, but it doesn't gulp it down (just as well really :-). A binary system is perfectly stable no matter how different the masses are.

There's a big difference between a neutron star binary and a pulsar binary. A neutron star can form in a relatively peaceful way. The original star will burn out and collapse to form the neutron star, but will probably leave it's companion star and at least outer planets relatively unscathed.

However a pulsar is formed from a supernova. While the companion star may (just) survive being so close to a supernova it's extremely unlikely that any planets would. Where you have a binary pulsar with planets one possibility is that new planets formed from the debris left behind by the supernova.

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Thanks for the answer.But please help me clarify my doubt regarding the co-existence of a neutron star with a planet or something else in a binary system. Doesn't the neutron star gulp down its binary companion ? Clarify also for the case of pulsars. –  stp30 Jun 15 '12 at 3:41
@Stp30: I've amended my answer to address your comment. –  John Rennie Jun 15 '12 at 6:06

Neutron stars form in core collapse supernovae, and have progenitors that are of at least $8M_{\odot}$.

Stars like the Sun are found in binary systems about half of the time - to be more precise, if you look at Sun-like stars it turns out that about 50% of the time you are looking at a multiple system, where the Sun-like star is the most massive component. Another statistic that can be quoted is that 2/3 of Sun-like stars are in some sort of multiple system with another star. But more massive stars are found more frequently in binary or multiple systems. The literature is reviewed by Duchene & Kraus (2013); they conclude that an early-B or O-star ($>8M_{\odot}$) is born (on average) with $\geq 1$ companions, and some have argued that O-stars are always born in binary/multiple systems.

In terms of what the companion masses are, the review of Duchene & Kraus concludes that the distribution of mass ratios $f(q)$ is flat (ie. all masses are equally probable), or possibly favours lower mass ratios ($q<0.5$). The frequency of $q<0.1$ companions is still unconstrained, because it is difficult to find/study them.

So to answer the main part of your question - yes it does appear to be more favourable to form stars as part of binary or multiple systems and this is especially true of the progenitors of neutron stars (and black holes). The reasons for this are as yet unclear, not least because the formation of massive stars is still an unsolved problem.

Note that the fraction of pulsars that are part of binary systems would be expected to be lower than the birth binarity frequency of their progenitors. The supernova explosion that produces the pulsar can disrupt the binary system in many cases, as evidenced by the high velocity dispersion of the known young pulsars ( http://arxiv.org/abs/astro-ph/0402282 ) . In addition, about 20% of high mass stars are seen as "runaways" from star forming regions, probably ejected from multiple systems ( e.g. http://adsabs.harvard.edu/abs/2011Sci...334.1380F ), and will presumably form isolated neutron stars in the future. On the other hand it is also clear that multiple systems containing pulsars or neutron stars frequently survive the supernova explosion, presumably because the mass and momentum loss is highly symmetric or the binary system is very close and strongly bound.

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