Perform a 4-star fit using a fully optimized approach

Introduction

This tutorial shows a 4-star fit with an MCMC. The script should be easy to adapt to a 3-star fit. The driver of a 2 vs. 3 vs. 4-star fit is the number of initial parameters provided (and the ndim value).

Before starting, make sure you have all the material. To save space, some files common to the previous tutorials are not duplicated. We assume that you did a copy of the files,

• image.fits and
• image.psf

in the current directory of this tutorial.

Step 1: save image in a binary file for fast and multiple access

It is the exact same as for a 2-star fit. Please have a look to Tutorial 3, step 1.

Step 2: perform a 2-star MCMC fit using multiprocessing

The additional two stars require six new parameters compared to a 2-star fit:

# Initial positions if new run (will be used to initialize MCMC chains)
# If you select flag_continue=True below, then these values are not used.
x3fg, y3fg = 1093.820, 1171.420
x4fg, y4fg = 1108.780, 1167.000
flux_ratio13_fg = 0.173373372520  # flux ratio between star 1 and 3
flux_ratio14_fg = 0.058225386230  # flux ratio between star 1 and 4

# Increase the size of the fitting box to include the PSF of 4 stars
# Not necessary essential as the code is supposed to do it automatically.
box_xmin, box_xmax, box_ymin, box_ymax = 1080, 1133, 1157, 1203

ndim = 11  # Number of fit variables
nwalkers = 22  # Number of chains (should be at least 2 x ndim)

You can then run:

$ python Step2.py

Step 3: monitor and analyze the results

It is the exact same step as Tutorial 3, step 3. The output should look like:

Autocorrelations
    Shape: (20000, 22, 11)
   [101.6255145   95.70460545 125.99204653 166.84592421 123.05689724
 130.29826304 149.23861903 186.21687404 118.76941755 102.53530003
 161.3323406 ]

Best-fit:
                x1           y1          x2          y2  ...  flux_ratio14    FTOTAL        chi2  dchi2
48900  1112.541611  1183.238107  1112.36045  1190.00736  ...      0.058326  1.124251  2524.23871    0.0

[3 rows x 14 columns]
Reduced chi-square: 0.999303
Each sub-plot must be 5.553in x 5.553in to have a figure of 6.614in. Okay! I'm using it!

The resulting star centroids are shown in magenta, and the fitting box in white in the picture below:

Beside, the chi-square regions look like that (a longer MCMC would be required to derive an accurate posterior distribution).