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‎docs/tutorials/astrometric.ipynb‎

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"cells": [
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"(astrometric)=\n",
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"cell_type": "markdown",
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"In this case study we'll walk through the simplest astrometric example with `exoplanet` and then explain how to build up a more complicated example with parallax measurements. For our dataset, we'll use astrometric and radial velocity observations of a binary star system.\n",
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"Many of these measurements in this heterogeneous dataset do not have reported error measurements. For these, we assume a modest uncertainty of $1^\\circ$ in position angle and $0.01^{\\prime\\prime}$ in separation for the sake of specifying something, but we'll include a jitter term for both of these measurements as well. The scatter in points around the final solution will be a decent guide of what the measurement uncertainties actually were."
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"cell_type": "markdown",
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"## Astrometric conventions\n",
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"The plot on the sky is helpful to look at, but the \"raw\" measurements are the values of $\\rho$ (separation) and $\\theta$ (also called P.A., position angle) that we listed in our data table, and that the measurement uncertainties live on these values as nice Gaussians. So, to visualize this space more clearly, we can plot $\\rho$ vs. time and P.A. vs. time."
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"## Fitting the astrometric orbit with *exoplanet*\n",
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".. note:: Orbits in *exoplanet* generally specify the semi-major axis in units of solar radii `R_sun`. For transits and RV orbits, you usually have enough external information (e.g., estimate of stellar mass from spectral type) to put a physical scale onto the orbit. For the most basic of astrometric orbits without parallax information, however, this information can be lacking and thus it makes sense to fit for the semi-major axis in units of `arcseconds`. But, `exoplanet` is modeling a real orbit (where semi-major axis is in units of `R_sun`), so we do need to at least provide a fake parallax to convert from arcseconds to `R_sun.`"
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"Now that we have an initial orbit, we can set the model up using PyMC3 to do inference."
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"Now that we have a maximum a posteriori estimate of the parameters, let's take a look at the results to make sure that they seem reasonable."
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"Now let's sample the posterior."
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"First we can check the convergence for some of the key parameters."
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"That looks pretty good.\n",
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"Finally, we can plot the posterior constraints on $\\rho$ and $\\theta$.\n",
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"As we can see from the narrow range of orbits (the orange swath appears like a thin line), the orbit is actually highly constrained by the astrometry.\n",
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"## Including parallax\n",
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"Check the convergence diagnostics."
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"And make the corner plot for the physical parameters."
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"## Citations\n",
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