Science Applications 3: Local Analysis
Science With the Virtual Observatory
2006 Summer School

Local Analysis Example:

Students will use results from resources such as the Registry and ConeSearch to access astronomcal data on galaxies including magnitudes and HI widths and analyze it using local tools. Participants will be able to download relevant data and construct a Tully-Fisher relation from data queries.

Tully-Fisher relation

The Tully-Fisher relation is a correlation the luminosity and maximum rotation velocity of a spiral galaxy. A simple analytical derivation (ala Carroll and Ostlie) is as follows. Beyond several kiloparsecs, spiral galaxies have a flat rotation curve. For mass contained within an entire galaxy of radius R, we have from basic dynamics:

and

We can make two assumptions about the physical properties of spiral galaxies. One property of spiral galaxies (Roberts 1969 and Tully & Fisher 1977) is that the total mass to light ratio is approximately constant. We can therefore substitute Luminosity for Mass (within a constant)

The second assumption is that the surface brightness is the same for spiral galaxies.

Substituting for the galaxy radius, and collecting constants, we arrive at the proporionality

Converting from magnitude to luminosities using the distance modulus:

In this exercise, we will use several resources to build a Tully-Fisher relation with data from an archive of HI (neutral hydrogen) detections and the Sloan Digital Sky Survey. We will perform the appropriate inclination correction to the HI width with ellipsoidal fits to the galaxies in SDSS images. If we assume an edge-on spiral has an axial ratio (r0) of ~0.2, then from geometry we can determine the inclination from:

We will only use galaxies with cz measurements greater than 3000 km/s so that we are removed from peculiar velocity corrections that arise in the local universe. Note that all the data collected below will be collected for analysis in a XML/VOTable file.

Data from the Digital HI Archive

We can use HI data query form from the digital HI archive located here. In this exercise, we will focus on Sa type galaxies. We will select the coordinates RA/Dec, velocity (for distances based on pure Hubble flow), and the parameter WF50 for HI widths (hold the control key to select multiple parameters. Our query parameters will be to select galaxies with a velocity greater than 3000 km/s and a RC3 morphological type of 1 (Sa spirals). Submit the query.

Getting some useful optical data using the SDSS Upload tool

Matches for the galaxies with HI profiles can be found using the SDSS Upload tool. We have 3 preceding data columns - the name, width and velocity. This particular form requires that the ra and dec come last. You can copy the text file we will use here. We also want to return some extra parameters and therefore will add to the default SQL query, displayed below. Note than any parameters we put into the upload list will be returned in the table, with the exception of our input ra/dec(which we return with the parameters u.up_ra and u.up_dec. Data are extracted from the derived table PhotoTag(a listing of commonly used photometric parameters), but we will also need other parameters from the main table PhotoObjAll. 


SELECT 
   p.objID, p.ra, p.dec, u.up_ra, u.up_dec,
   p.modelMag_u, p.modelMag_g, p.modelMag_r, p.modelMag_i, p.modelMag_z,
   k.isoA_u,k.isoA_g,k.isoA_r,k.isoA_i,k.isoA_z,
   k.isoB_u,k.isoB_g,k.isoB_r,k.isoB_i,k.isoB_z,
   k.expAB_u, k.expAB_g, k.expAB_r,k.expAB_i,  k.expAB_z
FROM #x x, #upload u, PhotoTag p, PhotoObjAll k
WHERE u.up_id = x.up_id and x.objID=p.objID and x.objID=k.objID and p.type=3
ORDER BY x.up_id

The parameters are described in the SDSS Table Schema here. The expAB parameters are useful because it saves on the (trivial) step of determining the axial ratio.

Paste the above code and view the output in HTML form - we get a nice reference table with links to images.

Doing analysis on the data locally

We will pick just one photometric band to focus on in this exercise and choose i-band because their is less extinction. The SQL query we will use is as follows:


SELECT 
   p.objID, p.ra, p.dec, u.up_ra, u.up_dec,
    p.modelMag_i, k.expAB_i, (u.up_ra-p.ra)*3600.0
FROM #x x, #upload u, PhotoTag p, PhotoObjAll k
WHERE u.up_id = x.up_id and x.objID=p.objID and x.objID=k.objID and p.type=3
ORDER BY u.up_id

The resulting data can be found here in an XML/VOTable format. Save the file to your disk, and open it in VOPlot with the command (in the $NVOSS_HOME/bin directory) 


voplot

Navigate to where you saved your file and open it. Let's examine the sky distribution and select RA for the x-axis and DEC for the y-axis. We can add the following columns to our table


Name:        cossqi
Expression:  ($11*$11-0.04)/(0.96)



Name:        inclination
Expression:  acos(sqrt($12))



Name:        logcorWidth
Expression:  log($5/sin($13))

We will not correct for any peculiar velocities or distance models, and assume pure Hubble flow with Ho=70 km/s/Mpc.


Name:        distance
Expression:  $4/70.0



Name:        absMag
Expression:  $10-5*log($15*1000000/10.0)

You now have the columns required to plot a (very) simple Tully-Fisher. A file with all of the created columns can be found here. Plot the absMag vs. logcorWdith. We have not corrected for extinction, and unfortunately there is a lot of scatter in the plot. VOPlot does not allow for regression, but one can save the new VOTable file and use the VOStat web page to determine a slope and intercept. 


Slope:       13.92
x-intercept: -2.54

Further exercises (projects?)

The NVO Summer School is made possible through the support of the National Science Foundation and the National Aeronautics and Space Administration.