Parameter Estimation

During early in the mission of Gaia, BP/RP spectra would not be available but only integrated flux will be available. Thus estimating extinction, A₀, and T_eff using the BP/RP flux is very useful early in the mission. Figure 1 shows relationship between astrophysical parameters (APs) and colors.

[ Figure 1. AP and Gaia colors. Clear degeneracy can be seen. ]

I developed Priam (Photometric Estimation of Astrophysical Parameters) using colors, G_Mag - G_BP and G_Mag - G_RP. I used two machine learning methods to train regression models, each of which is Support Vector Machine (SVM) and Gaussian Process (GP). We confirmed GP estimates APs a bit more accurately than SVM, but the differences are not significant (Table 1). Given that we used only two colors, the AP estimation results is quite good (Figure 2).

[ Table 1. Priam AP estimation quality ]

[ Figure 2. AP estimation results. Note that we used only two colors to train regression models. ]

Nevertheless, in the case of insufficient input data such as Priam, proper selection of priors could improve results. Thus we employed Bayesian analysis to improve Priam AP estimations. We used the extinction map (Arenou+ 1992) and the Gaia Universe Model Statistics (GUMS) v1.0 to create realistic priors for A₀ and T_eff. Figure 3 shows the two priors.

[ Figure 3. Realistic A₀ and T_eff Priors ]

Using the priors, and likelihood derived from the Priam, we produce posterior shown in Figure 4.

[ Figure 4. Posterior probability derived using Priam ]

Priam is implemented into the Apsis chain (Bailer-Jones+ 2013). For details about Priam, see GAIA-C8-TN-MPIA-DWK-001.