The Hertzsprung-Russell Diagram

Abstract

PLACEHOLDER - NOT A COMPLETE PAGE. Notes about the HRD.

Keywords: Hertzsprung-Russell diagram, colour-magnitude diagram, stellar magnitudes, stellar temperatures

Introduction

Once a system of spectral classification had been conceived, and many thousands of stars classified accordingly by Cannon and her Harvard colleagues, it became possible for the first time to consider their properties en masse. In 1913, Ejnar Hertzsprung (a Dane) and Henry Norris Russell (American) independently discovered that the absolute luminosity of most stars is very strongly correlated with their temperature. When colour index is plotted against absolute luminosity, the majority of stars fall into a narrow band known as “the main sequence.”

H-ZAMS and He-ZAMS

The properties and behaviours of the objects we wish to study in this article are constrained by exotic physical processes which are only becoming understood today. They manifest themselves on the H-R Diagram as a group of limits and zones which one seldom encounters in the ‘amateur’ literature, so a brief survey is given here.

The Eddington Limit

The atoms and ions in a stellar atmosphere are constantly subjected to bombardment by photons, each of which accelerates the particle in the direction the photon was travelling. Although the photons will come from all directions, there will be a net outflow away from the centre of the star and therefore a net outwards acceleration applied to the atmospheric particles. By calculating the values at which these radiative forces become strong enough to destroy the whole star, Eddington determined the maximum possible luminosity a star might possess. Beyond the Eddington Limit, stars would fly apart under their own radiative pressure alone.

For a star of 1 M_¤, the maximum possible luminosity is about 5 x 10⁴ L_¤ or about M_bol = -7.0. For a star of 40 M_¤, M_bol ≈ -11.0 and, in fact, we do not observe stars much brighter than this. At M_bol ≈ -11.6, Eta Carinae is one of the most luminous stellar objects of our Galaxy. This is a star having a serious confrontation with the Eddington Limit.

The Humphreys-Davidson Limit

As further data for stars near the top of the HR diagram accumulated towards the end of the 1970s, it became apparent that the upper luminosity limit varies with temperature for hot stars as reported by, for example, Hutchings (1976) who may have been among the first to document this phenomenon. Credit is generally given to Humphreys and Davidson (1979), however, who further noted that the decrease stops at an effective temperature of about 10⁴ K, the maximum luminosity remaining more or less constant for cooler stars, and suggested that an instability leading to rapid and unsteady mass loss set in there. The observed boundary could, in principle, be explained by steady mass loss, but only if the loss were much higher than that which is actually observed for objects near the boundary (typically 10^-5 M_¤ per year), so it is the sporadic eruptions which are considered to be of foremost importance.

“A stability limit, probably caused by radiation pressure, is a possibility, but the classical Eddington luminosity limit did not show the observed dependence on temperature for the hot stars. However, as temperatures decrease below about 30,000 K, opacity tends to increase as low-level ions such as HI, FeII, et al., begin to appear; so we can imagine a modified Eddington luminosity limit which decreases with decreasing temperature, like the observed limit” Humphreys 1989, p. 3.

There are still problems with this explanation, however, and the suggestion is still an active area of research.

Rotational Instability

Langer’s paper …

The Hyashi Line and Forbidden Zone

Interpretation

High mass stars (greater than about 3 solar masses) have a much shorter main sequence lifetime than stars with less mass. They burn their hydrogen into helium after only a few millions of years, much more quickly than lower mass stars. After a high mass star burns through all of the hydrogen in its core, its internal changes place it along the supergiant branch. Eventually, the core of the star will run out of fusible material. At this point, the star comprises a central core surrounded by concentric layers of different elements.

	Cool Red Giants	Sun	O-Type Star	LBV	W-R
M dot (M yr-1)	10-8 to 10-5	10-14	10-6	10-4	10-5 to 10-4
Lifetime (yr)			106	105
Teff (K)		5800	30,000	20,000	30,000
Mbol

References

Humphreys R. M.; Davidson K. 1979: Studies of luminous stars in nearby galaxies. III. Comments on the evolution of the most massive stars in the Milky Way and the Large Magellanic Cloud. ApJ 232: 409-420.

Humphreys, R.M. 1989: What are LBVs? - Their characteristics and role in the upper H-R diagram. In Davidson, K.; Moffat, A.F.J.; Lamers, H.J.G.L.M. (ed.) 1989: Physics of Luminous Blue Variables. Kluwer Academic Publishers : 3-12.

Hutchings, J.B. 1976: Stellar winds from hot supergiants. Astrophysical Journal 203: 438-447.