Multiple Star-system percentages

Question

What are the percentages of systems that have x number of stars in them?

What I have found thus far is something like:

• Single Star Sytems = 69%
• Double Star Systems = ~10%
• Triple Star Systems = <20%
• Quadruple Star Systems = ???
• Quintuple Star Systems = ???
• Sextuple Star Systems = ???
• Septuple Star Systems = ???

Also... Is there any way to get these percentages for systems that have primaries that are Giants (more than 2 Solar Masses) Major Stars (0.5 to 2 Solar Masses), and Minor Stars (0.5 Solar Masses... red dwarfs)

I have found an article that says...

Giant Stars = 80% have companions
Major Stars = 50% have companions
Minor Stars = 25% have companions

Sources:
http://www.space.com/1995-astronomers-wrong-stars-single.html
http://boards.straightdope.com/sdmb/showthread.php?t=499261
http://www.skyandtelescope.com/astronomy-news/surprise-most-star-systems-are-single/

Answer 1

Your best bet for finding relevant information on this is to look up actual published papers. I'll walk you through my research process to help in the future, as well as provide the results I found.

Step 1: Google Scholar is your friend

I start out using Google Scholar. This is much like Google, but rather than returning any old website, it specifically returns published papers and other scholarly articles. Part of this magic is of course knowing what to search. I went with "multiplicity of stellar systems". Immediately I found two sources which seemed promising.

Stellar Multiplicity and the Initial Mass Function: Most Stars Are Single (Lada 2006)

A Catalogue of Multiplicity Among Bright Stellar Systems (Eggleton & Tokovinin 2008)

I've lucked out because both articles happen to be free so I can see the full contents!

Step 2: NASA ADS

NASA Astrophysics Data System is a very large catalogue of just about every astronomy (and some physics) related paper published in any journal. What's even more amazing, very often the papers here are free, even if they aren't free on the journal's actual web page. If you ever run into a paper from a journal that only gives you an abstract, try looking for the paper here.

It was already free on the journal's webpage, but I was able to look up and find the Lada paper I cited above.

I specifically point you towards ADS for a few reasons.

1. It has a large collection of free papers.
2. You may have heard of or even use arxiv, which is a great resource, but very often the papers on arxiv are versions which are pre-publication and not the officially peer-reviewed and published papers. ADS usually has the official published papers (and links to arxiv versions!).
3. ADS has another hugely important feature. It lists article citations and articles which have cited that article.

Step 3: Backtracking and Forwardtracking

Once you've found a good source (such as the two papers above), you don't want to stop there. There's likely more or better papers and you can use the papers you have to find new ones. What you want to do now is take a look at all the papers your current source has cited, and look at all the papers which cite your current source. ADS very conveniently gives you all this information.

The Lada 2006 source is 10 years old at this point so I wanted to see if there was anything more recent. I was able to click on the "Citations to the Article" link on ADS for that article, and found the list of 217, more recent papers which cited the Lada paper. Scanning through this list I found two promising papers:

Stellar Multiplicity of the Open Cluster ASCC 113 (Guerrero et al. 2014)

An Adaptive Optics Multiplicity Census of Young Stars in Upper Scorpius (Lafrenière et al. 2014)

From here, just rinse and repeat until you've got the information you want.

Results

I found four papers which appear to give some or all of the information you want.

1. Lada 2006 - This paper is more or less a conglomeration of past research on the fraction of stars which are single star systems. It focused on lower mass stars (G to M) and found that the fraction of single star systems ranged from ~43% for G type stars to ~75% for M type stars (which are the most populous type).

2. Eggleton & Tokovinin 2008 - I think that this is the best source for your particular question. Within their abstract they state

   We identify 4559 such bright systems (including the Sun), and the frequencies of multiplicities 1, 2,..., 7 are found to be 2718, 1437, 285, 86, 20, 11 and 2.

   This implies the fraction of multiplicities is: 59.62%, 31.52%, 6.25%, 1.88%, 0.44%, 0.24%, and 0.04%. However, note they say their measurements have "substantial" uncertainties which they describe.

3. Guerrero et al. 2014 - This group looked at and around a specific cluster and found

   a ratio of the number of single to binary stars to be 27:7

   within the cluster itself. Including stars around the cluster, the following multiplicities were found (ranging from 1 to 8 companions)

   125:27:4:1:0:0:0:1

   These two sets of ratios indicate that within the cluster they saw 79% single star systems and 21% binary star systems. Overall they saw multiplicity fractions of 79.1%, 17.1%, 2.5%, 0.6%, 0%, 0%, 0%, and 0.6%, respectively.

4. Lafrenière et al. 2014 - A study that looked at 91 stars and found 57 single stars (63%), 29 binaries (32%), and 5 triple systems (5.5%).

What this suggests is that the multiplicity of stars is highly variable, still somewhat unknown, and that it depends on the environment you look at (and I found a few papers discussing this very point). The Eggleton paper had the largest sample and so may be the most trustworthy in regards to a true average, but make sure to understand what their uncertainties are.

Answer 2

The answers are out there. The problem with your question is that the answer is highly mass-dependent. The mass dependence is also somewhat uncertain, with the best empirical knowledge for solar-type stars, with rather more uncertain values and smaller statistical numbers for more and less massive stars.

The best contemporary review of binarity for main sequence stars like the Sun of spectral types F6-K3 (and the one everyone uses) is that of Raghavan et al (2010). Their study deals with binaries over the full range of possible separations and attempts to deal with the complex selection effects of different surveys and observation techniques. The answer you want is directly in the abstract of the paper: $56\pm 2$% single, $33\pm 2$% binary, $8 \pm 1$% triple, $3 \pm 1$% higher order multiples.

The best overall review of binary statistics (in my opinion) is that of Duchene & Kraus (2013). This deals quite well with the mass-dependence of the multiplicity frequency, which clearly declines with mass. The overall multiplicity fraction for solar-type stars is 44% (see above), but this becomes more like 30% for M-dwarfs and perhaps as low as 20% for stars/brown dwarfs with $M<0.1M_{\odot}$, though this latter number has an uncertainty of at least 5%. The fraction of multiple systems that feature $>2$ stars is probably quite similar to solar type stars (i.e. about a quarter of multiple systems are more than binaries).

For higher mass stars the multiplicity is also higher. It is at least 50% for stars between 1.5-5 solar masses and probably approaches 100% ($>80$%) for O-stars.

The overall results are summarised in Table 1 of the review. This is a highly cited and respectable source.