Q&A: General Astronomy and Space Science

Q:
In reference to this article, I am surprised that trigonometry can be used for such purposes. I was always taught that stars and galaxies are so far away they can be regarded as point sources ("PSF" - coming from image processing point of view). That is how I do deconvolution to "un-blur" images taken from CCD camera on telescopes. If they are indeed point sources of light, I supposed that trigonometry as practised by the author would be impossible - correct?

A:
Stars are so far away that they are effectively point sources. But even this comes with a caveat: with a good enough telescope this is no longer true. Hubble has resolved Betelgeuse, for example. See
http://antwrp.gsfc.nasa.gov/apod/ap970216.html

Nearby galaxies are certainly *not* effectively point sources; you can see that the Andromeda Galaxy (M31) is extended with binoculars, for example. In fact, if one makes the assumption that M31 is a circular disk if viewed face-on, then one could use trigonometry and exactly the same exercise I outlined for the Crab ring to figure out the inclination angle for M31. The fact that we can see structure (and lots of it!) in the Crab image tells you that it isn't effectively a point source.

The confusion in terms of PSF corrections to images comes about because that process isn't really treating each object in the field as a point source. What it is doing is taking the image distribution that would be obtained by a point source viewed through a particular telescope (i.e. a slightly blurry distribution) and saying "Ok, if each pinpoint of light is getting blurred out by this distribution, I can un-blur the image - even of an extended object like M31 - by backing out that blur component for each piece of the image."

Q:
Also, the author mentioned that the Crab Nebula is moving across the sky. How does one ensures that the "proper motion" is measured? And measured, relative to what? All the stars and galaxies move as well, so how sure are we to say that the Crab Nebula is moving at X km/sec in direction Y? Perhaps it might be the background stars are moving 180 degrees from the Crab Nebula and the Crab itself is stationary.

A:
The motions of stars are tiny; they are so far away that we really don't even have good proper motions for most of them. That means that you can typically find a good set of reference stars in the field with which to compare the position of the object of interest. Since pulsars have a higher velocity distribution than the stars in general (presumably from "kicks" during the explosions in which they form), if you take a pulsar that is somewhat nearby and can find 4 or 5 stars (best if they are more distant) then measuring the pulsar motion relative to the average of that ensemble gives a pretty solid measurement of the pulsar's motion. The more stars the better, obviously, and if one can actually use background galaxies or AGN it is much better because the angular motion of those across the sky is tiny (for example, at a redshift of 0.1 - where a typical magnitude might be about 15 - if the velocity of the AGN is several thousand km/s as is typical of galaxies in clusters, the motion across the sky would be a paltry 0.001 milliarcsec/year). So, although things are moving everywhere, they are also far away and thus, for most, their angular motion on the sky is negligible. We are thus able to establish a reasonable reference frame with which to measure the motions of faster moving objects.