Fitting Interferometric Observables
In this tutorial, we fit a planet & orbit model to a sequence of interferometric observations. Closure phases and squared visibilities are supported.
We load the observations in OI-FITS format and model them as a point source orbiting a star.
Interferometer modelling is supported in Octofitter via the extension package OctofitterInterferometry. To install it, run pkg> add http://github.com/sefffal/Octofitter.jl:OctofitterInterferometry
using Octofitter
using OctofitterInterferometry
using Distributions
using CairoMakie
using PairPlots
┌ Warning: Module Octofitter with build ID ffffffff-ffff-ffff-0000-00a6ce1adcbe is missing from the cache.
│ This may mean Octofitter [daf3887e-d01a-44a1-9d7e-98f15c5d69c9] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:1948
Download simulated JWST AMI observations from our examples folder on GitHub:
download("https://github.com/sefffal/Octofitter.jl/raw/main/examples/AMI_data/Sim_data_2023_1_.oifits", "Sim_data_2023_1_.oifits")
download("https://github.com/sefffal/Octofitter.jl/raw/main/examples/AMI_data/Sim_data_2023_2_.oifits", "Sim_data_2023_2_.oifits")
download("https://github.com/sefffal/Octofitter.jl/raw/main/examples/AMI_data/Sim_data_2024_1_.oifits", "Sim_data_2024_1_.oifits")
"Sim_data_2024_1_.oifits"
Create the likelihood object:
vis_like = InterferometryLikelihood(
(; filename="Sim_data_2023_1_.oifits", epoch=mjd("2023-06-01"), spectrum_var=:contrast_F480M, use_vis2=false),
(; filename="Sim_data_2023_2_.oifits", epoch=mjd("2023-08-15"), spectrum_var=:contrast_F480M, use_vis2=false),
(; filename="Sim_data_2024_1_.oifits", epoch=mjd("2024-06-01"), spectrum_var=:contrast_F480M, use_vis2=false),
)
OctofitterInterferometry.InterferometryLikelihood Table with 14 columns and 3 rows:
filename epoch spectrum_var use_vis2 ⋯
┌───────────────────────────────────────────────────────────
1 │ Sim_data_2023_1_.oi… 60096.0 contrast_F480M false ⋯
2 │ Sim_data_2023_2_.oi… 60171.0 contrast_F480M false ⋯
3 │ Sim_data_2024_1_.oi… 60462.0 contrast_F480M false ⋯
Plot the closure phases:
fig = Makie.Figure()
ax = Axis(
fig[1,1],
xlabel="index",
ylabel="closure phase",
)
Makie.stem!(
vis_like.table.cps_data[1][:],
label="epoch 1",
)
Makie.stem!(
vis_like.table.cps_data[2][:],
label="epoch 2"
)
Makie.stem!(
vis_like.table.cps_data[3][:],
label="epoch 3"
)
Makie.Legend(fig[1,2], ax)
fig
![Example block output](85236a3a.png)
@planet b Visual{KepOrbit} begin
a ~ truncated(Normal(2,0.1), lower=0)
e ~ truncated(Normal(0, 0.05),lower=0, upper=0.90)
i ~ Sine()
ω ~ UniformCircular()
Ω ~ UniformCircular()
# Our prior on the planet's photometry
# 0 +- 10% of stars brightness (assuming this is unit of data files)
contrast_F480M ~ truncated(Normal(0, 0.1),lower=0)
θ ~ UniformCircular()
tp = θ_at_epoch_to_tperi(system,b,60171) # reference epoch for θ. Choose an MJD date near your data.
end
@system Tutoria begin
M ~ truncated(Normal(1.5, 0.01), lower=0)
plx ~ truncated(Normal(100., 0.1), lower=0)
end vis_like b
System model Tutoria
Derived:
Priors:
M Truncated(Distributions.Normal{Float64}(μ=1.5, σ=0.01); lower=0.0)
plx Truncated(Distributions.Normal{Float64}(μ=100.0, σ=0.1); lower=0.0)
Planet b
Derived:
ω, Ω, θ, tp,
Priors:
a Truncated(Distributions.Normal{Float64}(μ=2.0, σ=0.1); lower=0.0)
e Truncated(Distributions.Normal{Float64}(μ=0.0, σ=0.05); lower=0.0, upper=0.9)
i Sine()
ωy Distributions.Normal{Float64}(μ=0.0, σ=1.0)
ωx Distributions.Normal{Float64}(μ=0.0, σ=1.0)
Ωy Distributions.Normal{Float64}(μ=0.0, σ=1.0)
Ωx Distributions.Normal{Float64}(μ=0.0, σ=1.0)
contrast_F480M Truncated(Distributions.Normal{Float64}(μ=0.0, σ=0.1); lower=0.0)
θy Distributions.Normal{Float64}(μ=0.0, σ=1.0)
θx Distributions.Normal{Float64}(μ=0.0, σ=1.0)
Octofitter.UnitLengthPrior{:ωy, :ωx}: √(ωy^2+ωx^2) ~ LogNormal(log(1), 0.02)
Octofitter.UnitLengthPrior{:Ωy, :Ωx}: √(Ωy^2+Ωx^2) ~ LogNormal(log(1), 0.02)
Octofitter.UnitLengthPrior{:θy, :θx}: √(θy^2+θx^2) ~ LogNormal(log(1), 0.02)
OctofitterInterferometry.InterferometryLikelihood Table with 14 columns and 3 rows:
filename epoch spectrum_var use_vis2 ⋯
┌───────────────────────────────────────────────────────────
1 │ Sim_data_2023_1_.oi… 60096.0 contrast_F480M false ⋯
2 │ Sim_data_2023_2_.oi… 60171.0 contrast_F480M false ⋯
3 │ Sim_data_2024_1_.oi… 60462.0 contrast_F480M false ⋯
Create the model object and run octofit_pigeons
:
model = Octofitter.LogDensityModel(Tutoria)
using Pigeons
results,pt = octofit_pigeons(model, n_rounds=10);
[ Info: Determining initial positions and metric using pathfinder
┌ Info: Found a sample of initial positions
└ initial_logpost_range = (161.61990614922573, 178.21820663016962)
────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
scans restarts Λ Λ_var time(s) allc(B) log(Z₁/Z₀) min(α) mean(α) min(αₑ) mean(αₑ)
────────── ────────── ────────── ────────── ────────── ────────── ────────── ────────── ────────── ────────── ──────────
2 0 4.6 4.94 6.69 1.3e+09 -1.72e+03 0 0.692 0.939 0.965
4 0 4.3 4.95 1.61 1.47e+09 -326 0 0.701 0.894 0.927
8 0 4.83 4.38 2.36 2.37e+09 -65.5 2.16e-211 0.703 0.907 0.928
16 0 5.66 5.6 4.73 4.76e+09 173 8.91e-24 0.637 0.889 0.917
32 0 6.1 6.28 9.5 9.57e+09 178 0.00356 0.601 0.902 0.918
64 7 6.31 2.55 20.9 2.01e+10 176 0.143 0.714 0.907 0.923
128 12 6.48 2.61 39.7 3.98e+10 176 0.0997 0.707 0.908 0.923
256 25 6.71 2.62 78.2 7.82e+10 176 0.288 0.699 0.91 0.921
512 63 6.95 2.73 156 1.57e+11 176 0.452 0.688 0.908 0.92
1.02e+03 148 6.77 2.66 317 3.16e+11 176 0.518 0.696 0.909 0.92
────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Note that we use Pigeons paralell tempered sampling (octofit_pigeons
) instead of HMC (octofit
) because interferometry data is almost always multi-modal (or more precisely non-convex, there is often still a single mode that dominates).
Examine the recovered photometry posterior:
hist(results[:b_contrast_F480M][:], axis=(;xlabel="F480M"))
![Example block output](840cf1db.png)
Determine the significance of the detection:
using Statistics
phot = results[:b_contrast_F480M][:]
snr = mean(phot)/std(phot)
7.276898550901578
Plot the resulting orbit:
octoplot(model, results)
![Example block output](238fdc5d.png)
Plot only the position at each epoch:
using PlanetOrbits
els = Octofitter.construct_elements(results,:b,:);
fig = Makie.Figure()
ax = Makie.Axis(
fig[1,1],
autolimitaspect = 1,
xreversed=true,
xlabel="ΔR.A. (mas)",
ylabel="ΔDec. (mas)",
)
for epoch in vis_like.table.epoch
Makie.scatter!(
ax,
raoff.(els, epoch)[:],
decoff.(els, epoch)[:],
label=string(mjd2date(epoch)),
markersize=1.5,
)
end
Makie.Legend(fig[1,2], ax, "date")
fig
![Example block output](57fdda9e.png)
Finally we can examine the joint photometry and orbit posterior as a corner plot:
using PairPlots
using CairoMakie: Makie
octocorner(model, results)
![Example block output](53528092.png)