The Salpeter IMF is
with a = 2.35 from Mlow = 0.1 to Mup = 120 Mo.
Assume that main sequence stars obey a mass-luminosity relation of the form
in solar units. Ignore other branches of the HR diagram.
The Salpeter IMF is often used as a fiducial by which other IMF's are measured.
when you integrate up the two IMFs,
normalized so that both produce the same number of stars.
It is OK that Mup and Mlow differ for the two IMFs - that is part of what makes this interesting.
Use the data of Verheijen (table 5 of his thesis chapter 5*) to determine the distance to the UMa cluster of galaxies.
Do this for both the I-band and K'-band** data,
for the calibration of Pierce & Tully given by Binney & Merrifield and
for the HST Key Project calibration given by
Sakai et al.
Be sure to include a plot of the data with calibration lines overlaid.
Assuming the recession velocity of the Ursa Major cluster is 1088 km/s, what Hubble constant(s) do you find? How does this compare to the value given by Sakai et al.?
* Note that in this table, Verheijen gives absolute magnitudes for a presumed distance of 15.5 Mpc.
** For the K'-band data, use the H-band calibrations assuming H-K = 0.25.