ASTR 498N Lecture 4 The Stellar Menagerie Part 2
(online at www.astro.umd.edu/~drabin/)
The truth is still out there.
Hertzsprung-Russell
redux
(O&C §8.2)
Let’s return to Russell’s diagram.
He drew a diagonal band to indicate that most of the plotted stars fall
within a main sequence. This name is suggestive in
two ways: first, that one independent
parameter governs the position of a star on the main sequencethis turns out to be true, as we’ll see; second, that
the main sequence is an evolutionary sequence, so that stars evolve along it in
time
a false idea which nevertheless influenced early
thinking on stellar evolution.
Russell’s “primitive” diagram deserves still a bit more attention. We should ask:
· Is the main sequence truly a band of finite width, or could it represent a strict relationship that is broadened by observational errors in both axes?
· More plotted stars are on the main sequence than off it; but, even on the sequence, the number of stars per logarithmic luminosity (or temperature) interval varies widely.
· Is the distribution of stars off the main sequence also non-random?
· Is there any information in the number of stars per luminosity or temperature interval? (The luminosity function, rather than the temperature function, turns out to be of central importance).
· How were the plotted stars selected? Do they come from a particular part of the sky, or a particular volume in space, or a complete sample of stars in some range of absolute magnitude? As we’ll see below, these are not minor details (the truth is out there, but it matters where you look).
Russell plotted absolute photographic magnitude against spectral type. The “physical” HR diagram instead plots bolometric luminosity against effective temperature. We can overlay one relationship on the physical HR diagram from the outset.
Recall the Stefan-Boltzmann law in the form that defines effective
temperature, . We may write this in normalized form as
which shows that lines of constant radius have slope in the physical HR diagram.
We’re ready to stroll through …
A Gallery of HR Diagrams
Stars within about 5 pc of Earth.
The 100 brightest stars as seen from Earth.
Spectral luminosity classes.
A schematic HR diagram that represents types of stars rather than a particular sample.
(MHp, V-I) diagram for the 41453 single stars from the Hipparcos Catalogue with relative distance precision σπ /π less than 0.2 and σV-I less than 0.05 mag (π is parallax). Colors indicate number of stars in a cell of 0.01 mag in V-I and 0.05 mag in MHp
Schematic diagram for open clusters of different ages.
A globular cluster.
Two globular clusters in the V, VI observational plane.
Variability in the HR diagram. The horizontal axis is the V-I color index and the vertical axis is the absolute magnitude. Blus indicates little or no variability and red indicates 100% of the objects are variable.
The location of some types of variable stars in the HR diagram. Only Beta Cephei stars on the high mass end of the main sequence and flare stars on the low mass end are relatively close to the main sequence. T Tauri stars are pre-main sequence objects, but all remaining types are in advanced stages of evolution.
Schematic evolutionary tracks.
Evolutionary tracks in the HR diagram, for the composition [Z=0.0004,
Y=0.23]. For most tracks of low-mass stars up to the RGB-tip (panel a),
and intermediate-mass ones up to the TP-AGB (panel b), the stellar mass (in M)
is indicated at the initial point of the evolution. For the low-mass tracks
from the ZAHB up to the TP-AGB (panels c and d), we indicate the complete range
of stellar masses in the upper part of the plots.
Evolution of a star
of mass 5 M and Population I composition. From Iben (1967).
Tracks in the HR diagram of theoretical model stars of low
(1 M),
intermediate (5 M
),
and high (25 M
)
mass. Nuclear burning on a long time
scale occurs along the heavy portions of each track. The places where first and second dredge-up episodes occur are
indicated, as are the places along the AGB where thermal pulses begin. The third dredge-up process occurs during
the thermal pulse phase, and it is here where one may expect the formation of
carbon stars and ZrO-rich stars. The
luminosity where a given track turns off from the AGB is a conjecture based on
comparison with the observations. From
Iben (1985).
Theoretical isochrones in the HR diagram, for the
compositions [Z=0.0004, Y=0.230] (panel a), and [Z=0.030, Y=0.300]
(panel b). The age range goes from log(t/yr) = 7.8 to 10.2, at equally spaced
intervals of Δlog
t = 0.3. In both cases, the main sequence is complete down to 0.15 M.
Luminosity and Mass Functions
The luminosity function (L) gives the number of stars per unit volume
with luminosity in the interval L to
L+dL. Similar,
the mass function ξ(M) gives the number of stars with mass in
the interval M to
M+dM. As these are both number density functions
of the same thing (stars), they satisfy
. The mass function that applies to a
particular stellar population before any evolution has occurred is called the initial mass function
and is of great interest for a theory of star formation.
Sandquist et al. find an excess of M5 giants above the RGB bump in both their B-band and I-band luminosity functions. There are unexpectedly large numbers of stars between apparent magnitudes of about 15.4 and 14.3 in the B band and 13.1 and 11.4 in the I band. The remainder of the stars fit the theoretical luminosity function for the RGB quite well, including a "bump."
Empirical mass-luminosity relation for main sequence stars.
Roughly,
Note that this relationship is remarkably tight.
Three determinations of the initial mass function (Salpeter 1955, Miller and Scalo 1979, Scalo 1986).
The classical “Salpeter” slope is .