Uncertainty in data from star databases

Question

I have students who are pulling data from various astronomical databases like SIMBAD or the Binary Star Database and then using that data to determine correlations between certain properties. My question is how do you factor in uncertainty when using those databases. For instance, you can calculate the mass of a star in a binary system through various methods, but that calculation should have an uncertainty that I can't seem to find. I would imagine each binary star would have a different absolute/relative uncertainty. Does it require backtracking through the databases and the calculations to individually calculate uncertainty? Do astronomy papers not focus on individual uncertainties but focus on statistical uncertainty with large sets of data?

Just background info: I'm a high school IB Physics instructor. I'm not well versed in astronomy.

Answer 1

In general it depends on the calculation to be done. The databases should give uncertainties on measured quantities, such as the brightness in some bandpass (usually given in magnitudes). In some calculations the uncertainties can be propagated analytically, e.g. when multiplying two quantities the relative uncertainty on the product is the sum in quadrature of the relative uncertainties of the factors.

In other cases the propagation is impossible, or at least very impractical, to carry out "by hand". Often a reasonable approach is to generate a new realisation of the data by sampling a value from the uncertainty distribution of every value involved in the calculation. For instance, perhaps every quantity had a Gaussian-distributed random error. You would generate a new set of values by drawing a Gaussian-distributed random number from each distribution. You can then repeat the calculation of the quantity of interest with the new realisation, and record the result. By repeating this process many times (with independent random draws each time, of course), the ensemble of values recorded approximate the distribution of possible values for the quantity of interest. This is called "bootstrap resampling".

There are many other possible sources of uncertainty besides random errors on measurements (e.g. what can be broadly described as systematic errors); in general how these can be estimated varies wildly depending on the problem at hand. If you can be more specific in your question, I might be able to be more specific in my answer.