(this is Problem 7.6 from Binney & Merrifield's "Galactic Astronomy", on reserve in the library)

Suppose that a series of four different standard candles are used to step out along the cosmic distance ladder as far as the Hubble flow, and that the calibration of each standard candle carries an uncertainty of 0.2 magnitudes. Show that, by changing the calibration for each step within the range allowed by its uncertainty, it is possible to derive values for the Hubble constant that lie anywhere between ~ 0.7 and ~ 1.4 of the nominal value.

(problem courtesy Heather Morrison)

In order to give you a feel for the problems associated with using galaxies which are not distant enough to be in the Hubble flow for deriving H0, here is a slice of the "Virgo consortium universe". These data come from a massive simulation of a cube of the universe measuring 150 Mpc on a side. The data give the x, y, and z coordinates [in Mpc] of each galaxy in the simulation, their line-of-sight velocity [in km/s], and their star formation rate [in Msun/yr]. The slice has been taken by restricting the x coordinates of the galaxies, so plot y vs z to see the large scale structure in the simulation slice.

Assume that the Sun is at the coordinate (50,0,0), and calculate the inferred Hubble constant from each of the following samples:

galaxies closer than 20 Mpc from the Sun,
galaxies between 25 and 75 Mpc from the Sun, and
galaxies further than 100 Mpc from the Sun

To do this, use the known distance of the galaxies (calculated from the coordinates) and the line-of-sight velocity. What do you estimate for the value of the Hubble constant used to produce the simulation (include an errorbar!)?

Comment on the accuracy of using the two relatively nearby samples: how much of an error do the peculiar velocities of galaxies add?

Now repeat this using only elliptical galaxies (star formation rate = 0). Are your results different? Why?

Here are Fundamental Plane datasets for two galaxy clusters:

Coma (cz=7008 km/s): Jorgensen et al (1993)
S639 (cz=6545 km/s): Jorgensen & Jonch-Sorensen (1998)

Using the Coma data given in Table 1 of Jorgensen et al (1993), derive the zeropoint of the B-band Fundamental Plane: log(re) = 1.24*log(sigma) - 0.82*log<I> + ZP. To do this, adopt a Hubble constant of 72 km/s/Mpc, and assume the Coma cluster has no peculiar motion. Also note that log<I>=-0.4*(<mu>-26.4).
Then use the S639 data along with your Fundamental Plane fit to get a Fundamental Plane distance to S639. Note that the S639 data has surface brightness in r mags, not B mags. Convert those surface brightnesses to B by adopting a B-r color of 1.1 for the galaxies, and that way they'll match the magnitude system of the Coma data.
Combine your FP distance to S639 with its redshift to calculate its peculiar velocity.

The Mice are a pair of interacting galaxies. Their properties are:

NGC 4676A: cz=6680 km/s, mB=14.1
NGC 4676B: cz=6510 km/s, mB=14.7
their seperation is 35 arcseconds on the sky

What is the luminosity of each member (in solar luminosities)? What is the physical (projected) seperation? (assume H0=72)

For an OmegaM=1, OmegaL=0 universe, at what redshift would they have the smallest seperation, and what would that be (in arcseconds)? At this redshift what will the TOTAL apparent magnitude of the pair be?

Astr/Phys 328/428 Homework #3 (due Oct 25)