## The Motion of the Milky Way

This project is aimed at detecting (or trying to!) the motion of the Milky Way and/or the Local Group of galaxies with respect to various sets objects with measured distances. It is all about reference frames.

We will look at several different data sets:

• Type I Supernovae with measured distances
• Nearby Galaxies with measured distances
• and perhaps others such as

• Galaxy Clusters with distance estimates
• The object of the game is essentially to look at the differences in a parameter like the Hubble Constant (the ratio between apparent velocity and distance) as a function of direction on the sky. You will need to plot the objects on a map of the sky as a function of this ratio or something like it and then you will need to calculate the average value for H0 in different areas of the sky. For this, I might start with just quadrants.

You will need to think about coordinate systems. We usually use two different ones, celestial (Right Ascension and Declination, which are like Longitude and Latitude only set to the sky) and Galactic (Galactic Longitude and Galactic Latitude). To understand these better, look at almost any introductory astronomy book in the library.

An example of a skymap showing our survey of the local supercluster is

This is an Aitoff equal area projection in celestial (RA,Dec) coordinates. I can provide a version of this program to you, but it accepts specific input formats only, so you will either have to modify it or the input data.

You will also need to do coordinate conversions. There are a number of ways to do this, perhaps the easiest is to use the converter in NED:

• NED
• But you can also use one of my programs by typing:

• /home/huchra/library/coord
• from a CfA unix machine or a login to one from your home computer.

Part of the exercise will be to understand the coordinate systems and the difference between redshift and velocity and distance. Remember, redshift is the wavelength or frequency shift in the observed spectrum of an object caused by the combination of

• Cosmological Expansion + Gravity Induced Motion
• and its the "gravity induced motion" of the milky way with respect to the set of objects in any given sample that we are going to study.

The raw data sets I have are linked below. Note each comes with a description of the columns and each is in a coordinate reference system . So you'll need to do the conversions to make them work! You should also remember the appropriate velocity reference frames:

• Heliocentric <--> Galactocentric <--> Local Group Centric <--> CMB Frame
• 270 Supernovae Distances
• Nearby Galaxy Distances

The velocities given for the nearby galaxies are explicitly heliocentric . Those for the SN are in a different frame, the CMB frame, so you should transform accordingly or look up the heliocentric or localgroupocentric velocities.

Here also is a whole-sky catalog of galaxies with just redshifts and magnitudes.

• All Sky IR Catalog

Unlike the first two catalogs, this catalog cannot be used to look at the Hubble Constant (distance vs redshift) relation in different directions but can be used to see if there is a dipole magnitude shift in shells at constant redshift (or conversely, a redshift dipole in shells of constant magnitude). There are over 13,000 galaxies in this sample, so it provides you with better sky coverage statistics --- but magnitiude is by no means as good a distance indicator as the distances in the first two tables.

And here is a little program for reading the nearby galaxy distances and putting their ``pecliar velocities'' into zcat format for use later witht he mapping program:

• read.f

I will work on getting those velocities for you in the next few weeks, but you might get them yourselves. For this exercise, I believe we want to work in the heliocentric frame for the nearby galaxies and in the centroid of the Local Group for the distant SN.

Here's the mapping program:

• Fortran file of map.f
• or run this link from a CF machine:
• /home/huchra/z/map
• Remember that the data file for this program must be in zcat format unless you recompile the program.

There are some primers for using CfA computer system utitlities on the Seminar home-page.

Good Luck!

John