Astronomy 250Problem Set Number 8Solutions

1) (Worth 4 points) A galaxy has a mass of 1010 Msun. Suppose that this galaxy is comprised only of stars. What is the maximum luminosity that this galaxy could have if powered by main sequence stars? What would the maximum luminosity be if it were constrained to have equal numbers of each spectral type of star on the main sequence (you may assume that the galaxy is very young and that no stars have evolved off the main sequence)?

From the Lecture Notes on starburst galaxies (or from examining data tables such as the one in the appendix of the text), the lowest M/L ratio and hence maximum luminosity per unit mass occurs for early O stars. The M/L for such stars in solar units is .0001. If the entire galaxy were comprised of such stars

Looking at a slightly more realistic case with equal numbers of each spectral type with Nstar being the number of each type of star:

Compute the galaxy luminosity by multiplying Nstars by Lsun for each spectral type and summing to get 3.02x1013 Lsun.

Sp.Type / M(Msun) / L(Lsun) / Lstars
O / 20 / 1.00E+05 / 2.93E+13
B / 8 / 3000 / 8.79E+11
A / 3 / 75 / 2.20E+10
F / 1.5 / 4 / 1.17E+09
G / 1 / 1.5 / 4.40E+08
K / 0.5 / 0.1 / 2.93E+07
M / 0.1 / 0.005 / 1.47E+06
Sum / 34.1
Nstars= / 2.93E+08 / Lgalaxy= / 3.02E+13

Notice that the luminosity in this case is less than that of the previous case; since no real galaxy has been observed with such a high luminosity, we can conclude that real galaxies have larger fractions of low mass stars than the equal number assumption implies. Also, O stars are usually very minor contributors to a galaxy's output because of their very short main sequence lifetimes.

3) (Worth 3 points) The synchrotron source in problem 2 is observed to produce a flux of 15.3 Jy at a frequency of 5 GHz (1 GHz = 109 Hz). If it has a typical distribution of electron energies, what will the flux be at a frequency of 25 GHz?

For a typical distribution of electron energies

4) (Worth 7 points) Examine the figure below. The upper spectrum is the spectrum from which the redshift of 3C273 was first measured. It is shown as a negative image so emission lines appear dark. The spectrum beneath that of the QSO is from a comparison lamp situated at the telescope and recorded at the same time as the QSO’s spectrum. Conveniently the locations of three hydrogen lines, (H, H, and H) have been marked in both the lamp spectrum and in the QSO’s spectrum. You may assume rest wavelengths of 486.1 nm, 434.0 nm,, and 410.2 nm for these lines respectively. Use a ruler to measure the redshift of 3C273 from each of lines and average the three results together. Using Ho=75km/sec/Mpc, compute the distance to 3C273. The V magnitude of 3C273 is 12.6. What is its MV and what is its V luminosity in terms of Lsun?

(I am not showing steps in measuring the wavelengths off the spectrum provided)

This redshift is just high enough that the relativistic form for the Doppler shift needs to be used.

5) (Worth 7 points) Estimates for the qo, the deceleration parameter, lie around a value of 0.1. A galaxy is observed to have a redshift of 55,000 km/sec. How long ago did the light being observed today leave this galaxy? If stars of spectral type G3V are at the tip of the main sequence in similar galaxies nearby, what type of star would lie at the tip of the main sequence in this galaxy? Would you expect this galaxy to have a lower or higher luminosity than a nearby galaxy of the same type?

Since q0 < 0.5, use the open Universe equations for computing lookback time:

Recall the expression for the lifetime of a star:

Since a G3V star is very close to the Sun, we shall assume its mass is equal to that of the Sun. We can then compute the mass of a star at the tip of the main sequence in the distant galaxy:

So the galaxy should appear noticeably brighter than a nearby galaxy of the same type.