The Star Mass Project

(c) 2022 by Barton Paul Levenson

It has become a truism that stellar properties measured inaccurately are of little use, following the classic statement by Andersen (1991) that "few useful results... can be extracted from masses and radii with uncertainties of even ± 5%." But to take this guideline over-literally would be to throw out data which, if not precise on a case-by-case basis, may still be useful en masse, on the principle that a great many measurements of some phenomenon must be more precise than a single individual measurement. Consider for example the standard error of the mean from statistics:

sμ = s / √N

(1)

where N observations x_i are drawn from a sample with standard deviation s. Thus, for example, single thermometers at meteorological stations may have a standard deviation as high as 1 K, but if there are 1,000 thermometers in the network, their mean measurement only has a standard error of 0.0316 K. Thus it is easily possible to discern trends in global mean temperature.

It is also well known that tables of stellar properties, based on different samples taken at different times, sometimes give very different values for a given spectral type. The mean mass of an O5V star, for example, is given as 40 M_☉ by Allen (1973, p. 209), but 60 M_☉ by Schmidt-Kaler (1982). At the other end, these two authorities give a type M8V star a mean mass of 0.10 and 0.06 M_☉, respectively, while Mamajek (2015, 2021) makes it 0.085 M_☉. The first pair is discrepant by a factor of 1.5, the latter trio by a factor of 1.7.

But a great number of binaries have been examined since 1973, 1982, or even 2015. I have started a project to collect all known masses for main sequence stars. I include only directly measured masses, for the sun, visual binaries, or detached eclipsing binaries. Close binaries with volume distortion were excluded, as there might be mass transfer through the Roche lobe. Measurements were excluded from papers that did not publish errors on the mass figures they found.

Some spectral types were inferred from temperatures--if the spectral type in the "raw data" file has a question mark after it, I inferred the type using Mamajek's temperature scale. Mass measurements of any magnitude of probable error were allowed.

Probable errors were then translated to standard deviations using the simple relation derived from the normal distribution, γ = 0.6745 σ, and the weighted mean taken for each spectral class. This ensured that measurements with wide error bars were systematically given less weight. The equation for the weighted mean is:

μw = (Σ wi xi) / (Σ wi)

(2)

where w_i is the weight for each point i. When it is desirable to give lesser weight to figures of lesser accuracy, the most satisfactory weighting is by the inverse square of the reported standard deviation (the standard deviation, not the probable error) of each measurement:

wi = 1 / si2

(3)

The variance of the weighted mean is then:

sμ2 = [N / (N - 1)] [Σ wi (xi - μw)2 / Σ wi]

(4)

Standard deviations for each weighted mean were then translated back to probable errors using the same ratio cited above.

The point of all this is to be able to accurately answer questions such as "What is the average mass of a type K0V star?" The sad fact is that after nearly two centuries of measurements of star masses, we still don't have a big enough database to do this. We have several hundred figures. We need several thousand.

But here's hoping. Links to the files for this project follow.

If you'd like to contribute to this project, please send any direct mass determinations you can find in the literature--please include the star designation, the spectral type (main sequence only), the mass found (with probable error), and a complete citation, or at least enough to find the paper on the internet. More detailed data on what I want can be found on the Desired Data page. You can send me email by clicking this link. Be sure to check the database here to see if I already have the star in question, although if you have a more recent study than the one I cite, that's useful as well. Thanks!

P.S. Here are some main sequences published by various people on the internet:

David Jeffery (University of Nevada at Las Vegas) gives an abbreviated O5-M8 table.

Lumen Learning gives a very abbreviated O5-M0 table.

Erik Mamajek (University of Rochester) gives a very comprehensive O7-L2 table.

Siobhan Morgan (University of Northern Iowa) gives a long but not comprehensive O5-T8 table, and I'm very suspicious of the high masses she attributes to brown dwarfs.

Wikipedia* gives an abbreviated O2-L1 table.

*Cites Zombeck, M.V. 1990. Handbook of Space Astronomy and Astrophysics (2nd ed). Cambridge, UK: Cambridge Univ. Press.

As of 04/22/2022, the database includes 1,029 main sequence stars (at least I hope they're all main sequence) in 104 different spectral types.