Q&A: General Astronomy and Space Science
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?
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
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."
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.
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