How Heavy Can a Star Get?

By Tim Hunter

Stellar mass is the most important attribute of a star. It determines a star’s luminosity, its physical size, and its ultimate fate (Kaler, 2001; Philips 1999). The most massive stars are the brightest, and they are known as “Supergiants” because of their large size and their enormous luminosity compared to most other stars (Moore, 2002). Supergiants have a mass greater than 10 times that of the Sun, and the most massive of them are known as Hypergiants (Kaler, 2001). These stars lie above the Main Sequence of the Hertzsprung-Russell Diagram and are often unstable with unpredictable variations in their luminosities. They occur with spectral types O to M.

An observational upper limit to stellar luminosity has been found in the Milky Way and the Local Group of galaxies, the Humphreys-Davidson limit (Lamers, 1988). It is somehow related to how massive a star can become. The Eddington limit is a theoretical upper limit to the ratio of luminosity to mass for a star. At the Eddington limit, the outward pressure of a star’s energy from its central nuclear processes exceeds its inward gravitational pull. At this point, a more massive star could not hold itself together with a resultant outflow of stellar material and mass loss (Kaler, 2001; Moore, 2002). This limit has been variously estimated as 60-440 Solar masses (Moore, 2002).

Measured stellar masses range from 0.08 Solar masses to observational claims of stellar masses as large as 150 Solar masses (Weidner, 2004). It is difficult to directly measure the mass of most large, luminous stars, because they are often not part of a binary system. While it is possible to estimate stellar mass based on a star’s effective temperature and luminosity, this is not necessarily accurate for massive stars that are no longer on the Main Sequence. Simply stated, the upper limit for stellar mass is unknown. The most massive stars are hydrogen burning O stars. Only a very small fraction (10^-7) of the stars in the Galaxy are more massive than 20 Solar masses. Since massive stars are so uncommon, the upper limit for their mass is unknown. The observed limit of 150 Solar masses may reflect either a fundamental mass limit, or it may merely reflect an observational limitation of the data (Weidner, 2004).

“There is a significant (factor 2!) discrepancy between the masses predicted by stellar evolutionary models and stellar atmosphere models…” (Massey, 1999). Some stellar formation models suggest a limit of 100 Solar masses as a finite upper limit for stellar mass, while other models allow for larger mass limits through disk-accretion and escape of thermal radiation pole-ward (Weidner, 2004).

Stars with a mass greater than 100 Solar masses do not have their maximum luminosity in the optical bands, which makes photometry of these stars difficult. Indirect photometric and spectroscopic examination of the massive young star cluster R136 in the Large Magellanic Cloud finds stars with masses as great as 140-155 Solar masses (Massey, 1997; Weidner 2004). Direct measurement of massive stars is rare. However, combined radial velocity and photometry for massive spectroscopic binaries in the R136 cluster has found one primary star with a directly computed mass of 57 Solar masses and “…comparison of …masses with those derived from standard evolutionary tracks shows excellent agreement” (Penny, 2001). Thus, we can infer that determination of stellar mass for massive stars using indirect photometric and spectroscopic methods is reasonably accurate (Massey, 1999).

Stellar birth is defined as when nuclear fission begins in a star’s core. Salpeter in 1955 introduced the concept of initial mass function (IMF), which represents the number of stars with a given mass M at stellar birth per unit volume of space (Salpeter, 1955; Moore, 2002). The IMF is assumed to be a power law in the form:

IMF (M) = cM^-(1+x) , where x is the parameter of the power law. Salpeter set x at 1.35. In the Solar neighborhood the IMF = M^-2.35 (Moore, 2002). This means that low mass stars are much more likely to form than high mass stars.

The exact nature of the Salpeter constant [x] remains a subject of much investigation, especially for massive stars (Kroupa, 2004). A massive star often has more than one companion which constrains their formation, and a significant fraction of all massive OB stars are found far from their probable birth site, presumably because they were ejected from cores of binary-rich star systems (Kroupa, 2004).

There are theoretical considerations and some observational evidence to suggest star formation in higher metallicity environments appears to produce more low mass stars (Kropa, 2001). Thus, we might postulate that earlier generations of massive stars, such as the purported very early Population III stars, were truly massive compared to the largest Supergiant stars we see today, because, in general, star formation today takes place in the presence of a higher metal content than in earlier epochs of star formation (Mackey, 2003).

Unfortunately, there is no strong data thus far to support this conclusion. It appears that the IMF is very uniform over a wide variety of conditions from the formation of low mass brown dwarf stars to very massive stars. According to Kroupa (2004): “This general insight appears to hold for populations including present-day star formation in small molecular clouds, rich and dense massive star-clusters forming in giant clouds, through to ancient and metal-poor exotic stellar populations that may be dominated by dark matter. This apparent universality of the IMF is a challenge for star formation theory, because elementary considerations suggest that the IMF ought to systematically vary with star-forming regions.” Recent work has also shown no deficiency of massive stars at high metallicity (Schaerer, 2003).

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