Astr/Phys 328/428 Homework #3

1. Distance ladder

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 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.

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:
To do this, use the known distance of the galaxies (calculated from the coordinates) and the line-of-sight velocity. For each sample, make a Hubble plot (velocity versus distance) and plot your derived Hubble law on the data.

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:
  1. 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).
  2. 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.
  3. Plot the data for each cluster on a Fundamental Plane plot, along with a line showing the Fundamental Plane with your fitted zeropoints.
  4. 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.

Note on coordinates:
Estimate the size of the voids (underneath Stickman's armpits), in both km/s and Mpc. Let's say that I told you that galaxies formed in the voids early on in the Universe, but have since moved out due to peculiar velocities. If typical peculiar velocities are ~ 600 km/s (like that of our galaxy with respect to the CMB), how long would it take for galaxies to clear the void (express your answer both in years and in terms of the Hubble time [defined as 1/H0])? 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?


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 H0. Here are examples of outlines: