The Hertzsprung-Russell diagram and star clusters
There are few direct tests of stellar structure models. However, they can be
generalized to models of stellar evolution (later). There are many tests of these.
Some derive from applications to star clusters and their H.-R. diagrams. The primary
reason for their use in this context is not that cluster stars are gravitationally bound,
but that they are thought to be all born at more or less the same time.
Stars and clusters are traditionally displayed and compared graphically in the (2-d)
Hertzsprung-Russell Diagram. There are many variations for observations and
model calculations:
x-axis
Observational
color, spectral type
Theoretical
Teff, (mass)
y-axis
MV, Mbol, (lum. class)
Luminosity
Sample H-R diagram
from Wikipedia.org
Features of the general H-R diagram
The Main Sequence: (discovered independently by H&R in 19131915.) Diagonal band (one-parameter family) of stars with mass increasing
towards upper left. 90% of all stars are on the main sequence.
The Giants: Located in the upper right part of the diagram, i.e. high L,
low T --> enormous R (> 100 Rsolar!). Rare numerically, but prominant.
White Dwarfs: In lower left part of the diagram, i.e. very low L, despite
high T --> very small radii, R < 0.01Rsolar ≈ REarth.
Many varieties of HR diagram: nearest stars, brightest stars, galactic (open)
clusters, globular clusters,.... but beware sanitized HR diagrams.
More H-R diagrams
Two MW globular clusters from
Catelan et al. (2006) ApJ 651, L133
2 old open clusters from
Wikipedia.org
Globular cluster in M33 from Barker
et al. (2007) ApJ 133, 1125
The first feature of stellar evolution theory that clusters confirm is that massive
stars have much shorter main sequence lifetimes than low mass stars.
Conversely, the main sequence turnoff provides a primary indicator of cluster age.
There are several other age indicators, though most are less accurate. More details
later.
Initial Mass Functions (IMF) and luminosity functions.
- The IMF is a distribution function giving the relative number of stars born in
different mass ranges - φ(m) ∝ dN/dm
- It is often assumed to have an approximate power-law form dN ∝ φ(m) dm = m-α dm.
α = 2.35 is the most famous example, first proposed by Salpeter in 1955, and
still found to be a good approximation in many cases.
- In a cluster with a finite number of stars, a power-law distribution cannot
continue indefinitely. There must be cut-offs or ‘turn-overs’, especially at the
low mass end.
- Luminosity functions for clusters or groups of stars are the observational
equivalent of an IMF. To go from an observed LF to an IMF usually requires a
number of corrections, especially for age effects.
- Like HR diagrams there are many versions of these.
From the review article of Bonnell, Larson, & Zinnecker, 2006 (astro-ph 0603447)
A question of active research is whether the IMF is universal, I.e., the same in all
star forming environments, to within stochastic variations. There is quite good
evidence that is generally so, though there continue to be studies claiming to
show variations in extreme environments.
Another active research area concerns the exact nature of the origin of the IMF in
turbulent star-forming clouds. Numerical simulations have gotten quite
sophisticated, but there is no concensus on the dominant physical processes.
We will talk more about star formation later, in connection with galaxies.
From the review article of Bonnell, Larson, & Zinnecker, 2006 (astro-ph 0603447)