Subject: Re: Hipparcos Parallax query

From: Jonathan Thornburg <[email-masked]>
Date: 14 Jul 1997 16:31:59 GMT

In article <[email-masked]>, Harvey Taylor asks
some questions about the Hipparcos parallax catalog:

|         This leaves only the question of the negative angles.  
|         Does anybody happen to know exactly how these arose?

These are due to observational errors (statistical fluctuations
>from Hipparcos only observing a finite number of photons from the
star, unmodelled thermal distortions of the Hipparcos optical bench,
noise in the detectors, etc etc).  That is, for any star we can
write

	observed parallax = true parallax + observational error

True parallaxes are always positive, but observational errors may
be either positive or negative.  If a particular star happens to
have a negative observational error larger in magnitude than its
true parallax, then its observed parallax (= the number in the
Hipparcos catalog) will be negative.

In the distant past (pre-1900), people often replaced negative
observed parallaxes by zero, or omitted negative-observed-parallax
stars from catalogs.  However, early in this century it was realised
that this is a very bad thing to do -- the negative observed parallaxes
still carry statistical information about both the observational
errors and about the statistical distribution of true parallaxes.
So the modern approach is to simply leave them in the catalog.

|         I have been comparing the Gliese3 and the Hipparcos
|         preliminary data files.
| 
| 	[...]
| 
|         I am trying to get a handle on the relative completeness
|         of these catalogues.  If Hipparcos shows N stars within 
|         M lightyears, what proportion of the actual number of 
|         stars is this likely to be?  

Only a tiny proportion of the actual stars near our Sun are in the
Hipparcos catalog.  Due to the design of the Hipparcos satellite,
the stars to be observed (i.e. the stars in the catalog) all had
to be chosen _ahead_of_time_, *before* the satellite was launched.
The main Hipparcos catalog was limited to around 100,000 stars, and
the experimental design also placed various limits on how the catalog
stars could be distributed over the sky.  For example, the satellite
couldn't accurately measure star positions if more than 5 or 6
sufficiently bright stars (whether in the catalog or not) stars
were present within an approximately 30 arcsecond circle.  And it
couldn't accurate measure star positions for too-faint stars.  And
these restrictions also depended on position in the sky.

The Hipparcos consortium obviously wanted to maximize the scientific
return from the mission.  Since some stars are of more scientific
interest than others, the consortium spent a lot of time and effort
trying to maximize the "total interest" of catalog stars.  (They put
out a number of public calls to astronomers as a whole for suggestions
of "interesting" stars to be included in the catalog, then winnowed
their preliminary catalog down based on the experimental constraints
and the various stars' degree of scientific interest.)

The net result is that the Hipparcos stars are a highly selective and
non-random sample of all the stars within (say) 1000 light years of us.
You can't easily make any inferences at all about "all nearby stars"
>from the Hipparcos data by itself.  (Of course, combining the Hipparcos
data with other astronomical data can tell you a lot more.)

In practice, the Hipparcos catalog is probably complete only out to
at most 10 light years or so, and maybe less than that.  Indeed, it's
not unlikely that there are some stars (say) 15-20 light years from
here, which haven't even been discovered yet!

|         What I wonder is if Tycho includes higher magnitude stars, 
|         what percentage will be high magnitude because of distance 
|         and what percentage will be high magnitude because they 
|         are intrinsically dim? 

Mostly the former.

|         Related to this is another question.  I have read in a 
|         pre-Hipparcos text that trigonometric parallax measurements
|         are useful only up to about 50 million AUs (ie. ~800 LYs).
|         Is this rule of thumb out the window with the presumably 
|         more accurate measurements of Hipparcos?

It's a matter of degree.

Hipparcos's original design goal was parallaxes with a standard
deviation of 2 to 5 milliarcseconds, depending on brightness and
position on the sky.

If you want the relative error of the observed parallax
(i.e. the ratio   observational error / observed parallax )
to be (say) 10%, then that means (taking the 2 milliarcsecond figure
for purposes of discussion) Hipparcos parallaxes are good down
to 20 milliarcseconds, i.e. out to 50 parsecs (= 165 light years)
distance.  On the other hand, if you can live with 20% relative
errors, then the parallaxes are good down to 10 milliarcseconds,
i.e. 100 parsecs (= 325 light years) distance.  Or if you need
1% relative errors, then they're only good down to 200 milliarcseconds,
i.e. out to 5 parsecs (= 16 light years) distance.  Etc etc.

So the only good answer to your question is, "it depends".

|         BTW Hipparcos shows ~80,000 stars within 1000 lightyears.
|         Any guesses how many Tycho shows?

The original design goal was for Tycho to cover 400,000 stars
around magnitude 9-10, with the possibility of considerably-
-poorer-quality data for another 800,000 stars of magnitude 10-12.

Unfortunately, due to a rocket failure, Hipparcos didn't make it
into its planned orbit, but was stuck in a scientifically-inferior
"parking" orbit.  This meant that a considerable part of the data
had to be discarded due to noise from the Earth's Van Allen radiation
belts.  ESA (= European Space Agency = the people who ran Hipparcos)
was able to partially work the problem, but I don't know how the
final performance compared to the original design plans.

Reference (technical discussion of the original mission design):

	M A C Perryman & T. D. Guyenne
	"The Scientific Aspects of the Hipparcos
	 Space Astrometry Mission"
	ESA SP-177, May 1982

-- 
-- Jonathan Thornburg <[email-masked]> (personal E-mail)
   U of British Columbia / Physics Dept / <[email-masked]>
   "The 1980s were the go-go junk-bond days of early-universe cosmology"
						       - Michael S. Turner