THE LUMINOSITY FUNCTION AND STELLAR EVOLUTION
Edwin E. Salpeter
The luminosity function for main-sequence stars in the solar neighborhood is studied.
The rate of star formation as a function of stellar mass is calculated.
Studies of stellar evolution has been a growing field.
A lot has been learned by studying Population II systems.
For studying Population II stars:
Particularly, studies of globular clusters H-R diagrams, that suggest that most of the stars in a cluster are formed around the same time.
magnitudes brighter than 3.5 there are basically no stars in the H-R diagram,
and by estimating the time that it takes for a star (with
For studying Population I stars:
Studies of the solar neighborhood.
Stars have larger range of masses.
Using large data of the solar neighborhood stars, the luminosity function can be calculated to an acceptable accuracy.
The luminosity function depends on three factors:
- rate of creation of stars as a function of time since the formation of our galaxy
- evolution of stars of different masses after they have burned out an appreciable fraction of their hydrogen mass and have left the main sequence
Since they cannot derive these factors from the luminosity function, then what the author can do is test that the assumptions they are taking, are actually compatible with the observed luminosity function:
- SFR in the solar neighborhood has remained the same since the beginning of the galaxy
- Stars do not change their mass (just in last stages)
- Most stars are poorly mixed and move off the MS when 12% of their mass has burned into helium.
- OBSERVATIONAL DATA
The luminosity function gives the number of stars (or galaxies) per luminosity interval. – Given a luminosity as input, the luminosity function essentially returns the abundance of objects with that luminosity (specifically, number density per luminosity interval).
(stars per pc3) of stars with absolute visual magnitude
Salpeter is only
considering the luminosity function in the range
is not considering the detailed luminosity-spectral type function,
Table 1, basically shows the fraction of stars of each spectral class that are MS stars.
defines the luminosity function for the MS alone as
they need values for the average mass
- THE “ORIGINAL MASS FUNCTION”
In Figure 1, the luminosity function values (shown in Table 2) are plotted.
There is a significant change in the slope of the function, being steeper in the brighter end.
This change is more significant for the MS stars.
change occurs somewhere between
change in slope for population I star may be explained similarly to the
globular cluster HR diagram: there are no stars older than
the “original mass function”,
the initial mass function (IMF) is an empirical function that describes the initial distribution of masses for a population of stars.
corresponding “original luminosity function”,
The “original” functions correspond to what we would observe if stars where to stay on the MS forever.
Considering a MS
star with absolute visual magnitude
The relation between the original luminosity function and the observed one is
Because the data is not very accurate to determine the value of the limiting magnitude, Salpeter uses the turning point for the globular clusters HR diagrams: +3.5
value, and the observed luminosity function, and so on… they derive
Left side: total
mass per pc3 of all stars created at any time since the origin of
the galaxy, with
total mass per pc3 contained in all stars with
the total mass which has been in the form of main- sequence stars once but has taken on different form by now is of the same order of magnitude as the total mass of present stars
Left side: total number of burned-out stars
Right side: total number of MS stars
roughly 10 per cent of existing stars should be white dwarfs, which agrees well with observational estimates of the abundance of white dwarfs
If the hypotheses that the author stated from section 1, turn out to be true, it would be logic to think that an appreciable fraction of the interstellar gas has been in the interior of stars at some point.
However, there are many sources of error for the calculations.