abj2016 - Convert parallaxes to distances like Astraatmadja & Bailer-Jones (2016)

HOWTO

This simple python module lets you infer stellar distances from measured parallaxes. It basically implements the formalism of Astraatmadja & Bailer-Jones (2016). This is how it works. Easiest thing is to download the abj2016.py and copy it into your project. Then

import abj2016
import numpy as np

Now, let's imagine an array of stellar distances (in kiloparsecs), between 0.05 and 4 kpc. We measure the parallax for each star with an uncertainty of about 0.04 milliarcsec (vamos, a typical Gaia DR2 value). Then we have

true_dists = np.linspace(0.05, 4., 100)
measured_parallaxes = 1. / true_dists + np.random.normal(loc=0.0, scale=0.04, size=100)

If we, in turn, want to infer the stellar distances from the measured parallaxes, that's not as easy, as explained in e.g. Bailer-Jones (2015). Especially in the presence of large fractional parallax uncertainties, you shouldn't just do d = 1/measured_parallax... Instead, you want to compute statistics of the posterior distance PDF (given parallax and parallax uncertainty):

distpdf = abj2016.distpdf(measured_parallaxes, 0.04)   # Initiates the distpdf object
modedists = distpdf.modedist
meandists = distpdf.meandist
sigdists  = distpdf.diststd

This also works if the parallax uncertainties are given as an array. Or if the measured parallax is a scalar.

You can also specify the space density prior by adding e.g. priors="uniform_density". Currently, only the three isotropic density priors presented by Astraatmadja & Bailer-Jones (2016) are supported (default:priors="exponential"). You can also specify the resolution of the distance posterior PDF (default: resolution=10000), and the minimum and maximum allowed distances in kiloparsec (default: min_dist=0 and max_dist=30).

You can also get the posterior PDF itself, via e.g.:

pi, sigma_pi = 0.3, 0.1 # measured parallax and uncertainty in mas 
distpdf = abj2016.distpdf(pi, sigma_pi, min_dist=0., max_dist=10., resolution=100000, priors="uniform_distance")
array, pdf = distpdf.distarray, distpdf.distpdf

Have fun and give a shout if you find a bug or have a question: fanders*ät*aip*dot*de.