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 you are
using distances measured this way to derive the Hubble constant. Assume
also that
the calibration of each of the four standard candles being used carries
an uncertainty of 0.2
magnitudes. What is the fractional uncertainty in the Hubble
constant you would derive?

2. The Difference between "Near" and "Far"

(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 H

First, make a plot of y vs z to see the large scale structure in the simulation.

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

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?

3. The Peculiar Velocity of S639

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(r
_{e}) = 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. You must also include a
quantitative uncertainty estimate and an explanation of how you derived
it. 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.

- Plot
the data for each cluster on a Fundamental Plane plot, along with a
line showing the Fundamental Plane with your fitted zeropoints.

- Combine your FP distance to S639 with its redshift to calculate its peculiar velocity.

4. Stickman and Voids

Here is a dataset from the CfA redshift survey,
containing coordinates (RA and dec), B magnitudes, and redshifts (cz,
in km/s) for a sample of galaxies. Use it to recreate the "Stickman"
figure shown in class. It's easiest to convert the angular coordinates
and redshift (RA, dec, cz) into cartesian X,Y coordinates with units
km/s. Since the data was taken in a slice of declination, all
declination values are roughly the same, and you can just use the RA as
your main angular coordinate.

_{0}])? Show how
both your answers depend on the Hubble Constant (in other words, if you
decided to use a different value for the Hubble constant, how do your
answers change?). Is my idea of galaxy formation in voids any good?

Note on coordinates:

- Right ascension: an angular coordinate in units of time: hours, minutes of time, seconds of time. To convert to degrees, first convert to decimal hours, then remember that there are 15 degrees in an hour.
- Declination: an angular coordinate in units of degrees, minutes of arc, seconds of arc.

5. ASTR 428: Project

I want
a thorough, well researched outline of your project, along with a quality reference list.
Let's say that I was doing a project about using the Sunyaev-Zeldovich Effect to get H_{0}. Here are
examples of outlines: