Chapter 2: First Steps with PDL
Page 12
We work out the area by simply summing up the 0,1 pixels in the mask image. The answer is the
bulge has about 7 times the surface brightness than the disk - something we might have guessed
from looking at the above figure, which tells astronomers its stellar density is much higher.
Of course PDL being so powerful, we could have figured this out in one line:
pdl> print ( avg($gal->where(rvals($gal)<50)) /
avg($gal->where(rvals($gal)>=50)) )
6.56590509414673
Twinkle, twinkle, little star
Let's look at something else, we'll zoom in on a small piece of the image:
pdl> $section = $gal(337:357,178:198);
pdl> imag $section; # the bright star
Here we are introducing something new - we can see that PDL supports extensions to the Perl
syntax. We can say $var(a:b,c:d...) to specify multidimensional slices. In this case we have
produced a sub-image ranging from pixel 337 to 357 along the first dimension, and 178 through 198
along the second. Remember pdl data dimension indexes start from zero. We'll talk some more about
slicing and dicing later on. This sub-image happens to contain a bright star.
At this point you will probably be able to work out for yourself the amount of light coming from this
star, compared to the whole galaxy. (Answer: about 2%) But let's look at something more involved:
the radial profile of the star. Since stars are a long way away they are almost point sources, but our
camera will blur them out into little disks, and for our analysis we might want an exact figure for this
blurring.
We want to plot all the brightness of all the pixels in this section, against the distance from the centre.
(We've chosen the section to be conveniently centered on the star, you could think if you want about
how you might determine the centroid automatically using the xvals and yvals functions). Well it is
simple enough to get the distance from the centre:
pdl> $r = rvals $section;
But to produce a one-dimensional plot of one against the other we need to reduce the 2D data arrays
to one dimension. (i.e our 21 by 21 image section becomes a 441 element vector). This can be done
using the PDL clump function, which 'clumps' together an arbitrary number of dimensions:
pdl> $rr = $r->clump(2); # Clump first two dimensions
pdl> $sec = $section->clump(2);
pdl> points $rr, $sec; # Radial plot
You should see a nice graph with points like those in the figure below showing the drop-off from the
bright centre of the star. The blurring is usually measured by the 'Full Width Half Maximum' (FWHM) -
or in plain terms how fat the profile is across when it drops by half. Looking at the plot it looks like this
is about 2-3 pixels - pretty compact!
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