# How are SIMBAD's parallaxes calculated?

I've been trying to figure out how to convert parallax information from SIMBAD's database into parsecs. Looking at Wikipedia as well as many other sources, parallax is calculated as follows:

distance in parsecs = 1 / parallax


Given the nature of reciprocals, we can inverse this relationship:

parallax = 1 / distance in parsecs


The thing is, all stars I've looked up in SIMBAD do not match other sources using these methods.

For example:

• Rigel, according to sky-map.org is 236.967 parsecs away (0.0042p | ~773 ly). Wikipedia places it at 260 parsecs. SIMBAD has nothing even close to these numbers.
• Betelgeuse, according to sky-map.org is 131.062 parsecs away (0.0076p | ~427 ly). Wikipedia places it at 168.1 parsecs. Again, SIMBAD has completely different numbers.

I've checked a few other stars from SIMBAD as well and the parallaxes seem to be following some other format. They have a description of measurement types page, but it does not seem to indicate how these values are to be interpreted.

How does one actually interpret SIMBAD parallaxes, and how can they be converted to distance in parsecs?

Trigonometric parallaxes are measured, not calculated.

Simbad reports the source of its parallax measurements if you look carefully. For example, Simbad reports Rigel's parallax as $$3.78\pm 0.34$$ milli-arcsecs, which comes from the revised Hipparcos catalogue of van Leeuwen et al. (2007) (which will be the case for many bright stars that do not feature in the Gaia catalogue).

A parallax in arcseconds can be reciprocated to give a distance in parsecs. However, if the parallax has a significant uncertainty (say greater than about 10%), then simply reciprocating the parallax is not a correct procedure, because the uncertainty in distance has an asymmetric distribution. In addition, there are various biases to do with the number of stars as a function of distance, which means the likelihood distribution of the distance is biased towards larger values (it is more likely to find a more distant star scattering into a volume, than a closer star scattering out of that volume). This is thoroughly discussed in Luri et al. (2018) along with (non-trivial) methods for correctly calculating a distance from a parallax (and uncertainty).

Just doing the naive reciprocation of Rigel's parallax gives a distance of 265 pc, with an uncertainty of just under 10%. I'm not sure why you say this is nothing like the other numbers quoted.

Simbad and sky-map.org are not primary sources of parallax or distance information. You should always try to find the primary source.

Betelgeuse has a very uncertain parallax because its angular size on the sky is comparable with its parallax and it has shifting surface brightness inhomogeneities. There are several questions on this site about that. See for example What will it finally take to accurately measure the distance to Betelgeuse? and linked questions.

• Thank you for the detailed answer! I think half the problem was that I didn't realise things would be provided in milli-arcseconds, and that [0.34] represents uncertainty. It makes a lot more sense now Sep 26 at 20:19