VO Tools: Data Registry(ies), TOPCAT, VOPlot
Background: A classic problem in galactic astronomy has been to determine the motion of the sun with respect to the various populations of stars in the local neighborhood. This is one step in determining the motion of the sun in our galaxy. We are presuming that the motion of any star can be described by a bulk motion component and a peculiar motion component. By looking at an ensemble of stars of similar spectral type, all within a modest spatial volume near the sun, we can determine the peculiar motion of the sun by assuming that the mean peculiar motion of the ensemble is zero with respect to the bulk motion (or Local Standard or Rest).
In this exercise, we use the measured proper motions (angular motions in the plane of the sky) of a set of stars to determine the direction of the sun's peculiar velocity with respect to the local standard of rest. If we know the distance to all these stars, we can determine the magnitude of the solar peculiar motion as well (which is a problem for another day).
1) First we generate a list of lines of sight around which we will sample the proper motions of the stars.
- ra = {1, 3, 5, ..., 23} hours
- dec = {-80,-60, ..., 80} degrees
- centers = [ra x dec] (cross product of the two lists, for 9 x 12 = 108 pointings)
cat /dev/null > ctrlist
@ _r = 1
while ( $_r < 24 )
@ _d = -80
while ($_d < 90)
echo $_r $_d | \
awk '{v1=sprintf("%2d 00 00 %3d 00 00 , rm=60",$1,$2); \
print v1}' >> ctrlist
@ _d += 20
end
@ _r += 2
end
Leaving a new file called ctrlist.)
The positions can be given in either sexigesimal hours/degrees or decimal degrees/degrees. We select an extraction cone 1 degree in radius. A typical line will look like:
- 03 00 00 +20 00 00 , rm=60
(We have specified the search radius as rm=radius in arcminutes, which is the form that Vizier expects.)
2) If we did not know what catalogues contained appropriate proper motion (and possibly also parallax) data, we would next query one of the NVO Data Registries at either with keywords such as:
- proper motion
- parallax
3) We will use the Tycho-2 catalogue. Go to Vizier at CDS
and under Direct access to Catalogues, enter Tycho and hit Find Catalogue On the results page, click on I/259/tyc2 to get to direct access to the Tycho2 catalogue
Go to the bottom of the page, and in the Adapt Form box, click on the LIST of Targets button. To ease later steps, set the the Output layout to XML - VOTable (DTD) to get back VOTable results we can use with TOPCAT and/or VOPlot. Then after the window updates, you can Choose File, and submit your file of positions.
4) Once you have retrieved the output, start up TOPCAT and read in the results. There should be a set for each (RA,DEC) direction. From each set, we wish to determine the mean proper motion of the set.
For each pointing, we will do the following:
4-a) Since we would like to determine the solar motion with respect a particular stellar population, we need someway to separate the spectral types. In this case, we can use color as a rough analogue for spectral type. The color is defined as the difference between two different passband magnitudes, in this case B and V. Within each data block, select a modest range of B-V, by making a Row Subset.
- Subset Name: red stars
- Expression: BTmag - VTmag > 0.8 && BTmag - VTmag < 1.2
4-b) Select this new subset, and request the Statistics operation, which will give the mean proper motions in both RA and DEC. Save the mean RA, DEC, MURA and MUDEC.
(Since we have in fact retrieved all the Tycho-2 stars within each region, we could set up other color selection and figure out the motion of the Sun with respect to other stellar populations.)
5) Concatenate the list of Region Centers and respective mean proper motions values into a file.
6) Now, in your favorite plotting package, plot up a vector flow diagram. At each point in (RA, DEC)_i, you plot a small arrow in the direction (MURA, MUDEC)_i (where i=1,...,N), where the arrow length is proportional to the total velocity.
The apex of the solar motion will be the in the direction where (MURA,MUDEC) is zero (or close to it), and the proper motion vectors are pointing AWAY from this low point (ie it looks like a source). The Antipex will be the other zero point, where the vectors appear to be converging on the zero (it looks like a sink).