Astr/Phys 328/428 Homework #3
1. Distance ladder
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
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:
- 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. 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
are Fundamental Plane datasets for two galaxy clusters:
- 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).
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.
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.
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.
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
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: