03-exoplanets.jl

### A Pluto.jl notebook ###
# v0.20.4

using Markdown
using InteractiveUtils

# ╔═╡ 0837dd0b-64b6-47cb-851f-af90948e8b2b
using PlutoUI; TableOfContents()

# ╔═╡ a480e429-6c46-44b0-a7f3-c1ef8a799a82
begin
	ENV["DATADEPS_ALWAYS_ACCEPT"] = true
	using Octofitter, OctofitterRadialVelocity, Distributions, Pigeons, CairoMakie, PairPlots, HypertextLiteral
end

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md"""
# (Re-)Discovering the GJ876 Planets

In this tutorial, we will cover or revisit:

* Loading data from CSVs
* Basic plotting with Makie
* Creating Lomb-Scargle Periodograms
* Fitting an RV model with 1-4 planets
* Using a Bayesian model comparison to determine the number of planets supported by our data
"""

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html"""<style>
	main {
    	max-width: 1000px;
	}
"""

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md"""
# Loading the data
In this section, we will load RV data from an online database, and plot it.

```julia
	rv_data = OctofitterRadialVelocity.HARPS_RVBank_rvs("GJ876")
```
"""

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md"""
We can access each column by name:

```julia
	rv_data.epoch
```
"""

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md"""
## Plotting data
We can plot the data using Makie

```julia
	let
		fig = Figure()
		ax = Axis(fig[1,1], xlabel="epoch [MJD]", ylabel="RV [m/s]")
		scatter!(ax, rv_data.epoch, rv_data.rv, rv_data.σ_rv)
		fig
	end
```
"""

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md"""
To analyse this RV data, we start by creating a periodogram:

```julia
	using LombScargle
```
"""

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md"""
```julia
	pgram = lombscargle(
		rv_data.epoch,
		rv_data.rv,
		rv_data.σ_rv # typed: \sigma + TAB)
```
"""

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md"""
```julia
	let
		fig = Figure()
		per, pow = LombScargle.periodpower(pgram)
		ax = Axis(
			fig[1,1],
			xlabel="period",
			ylabel="power",
		)
		lines!(ax, per, pow, color=:black)
		xlims!(ax, low=0, high=200)
		# vlines!(ax, [30,61,123])
		fig
	end
```
"""

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md"""
## Orbit Model (1 planet)

We now fit a one-planet model to the data.
"""

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md"""
Create a "radial velocity" object to hold our observations
"""

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md"""
```julia
	rv_likelihood = MarginalizedStarAbsoluteRVLikelihood(
		rv_data,
		instrument_name="HARPS",
		jitter=:jit1,)
```
"""

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md"""
We start by defining a probabilistic model with priors:

```julia
	@planet b RadialVelocityOrbit begin
		e = 0.0
		ω = 0.0

		# We set a prior on period in years
		P ~ Uniform((61.1057 - 5)/Octofitter.julian_year, (61.1057 + 5)/Octofitter.julian_year)
		a = cbrt(system.M * b.P^2)

		τ ~ Uniform(0,2pi)
		tp = b.τ*b.P*365.256360417 + 55000 # reference epoch for τ. Choose an MJD date near your data.

		# minimum planet mass [jupiter masses]. really m*sin(i)
		mass ~ LogUniform(0.001, 10)
	end;
```
"""

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md"""
```julia
	@system GL876_one_planet begin
		# total mass [solar masses]
		M ~ truncated(Normal(0.346,0.007),lower=0.1)

		jit1 ~ LogUniform(0.1, 100)
	end rv_likelihood b;
```
"""

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md"""
We now compile our model to efficient machine code, with derivatives

```julia
	model_one_planet = Octofitter.LogDensityModel(GL876_one_planet)
```
"""

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md"""
We can now sample from the model using Pigeons:
```julia
	chain_one_planet,pt_one_planet = octofit_pigeons(model_one_planet,n_rounds=10)
```
"""

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md"""
We can examine the results

```julia
	display(chain_one_planet)
```
"""

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md"""
```julia
	Octofitter.rvpostplot(model_one_planet, chain_one_planet, show_summary=true)
```
"""

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md"""
## Excercise: One Planet Model with Eccentricity

Try modifying the code above to allow non-zero eccentricity (say, between 0 and 0.5).
"""

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md"""
## Two Planet Model

There is still quite a bit of variance in that data. Maybe a second planet can explain it!

```julia
	@planet c RadialVelocityOrbit begin
		e ~ Uniform(0, 0.7)
		ω ~ Uniform(0, 2pi)

		# We set a prior on period in years
		P ~ Uniform((30 - 5)/Octofitter.julian_year, (30 + 5)/Octofitter.julian_year)
		a = cbrt(system.M * c.P^2) # note the equals sign.

		τ ~ Uniform(0,2pi)
		tp = c.τ*c.P*365.256360417 + 55000

		# minimum planet mass [jupiter masses]. really m*sin(i)
		mass ~ LogUniform(0.001, 10)
	end;
```
"""

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md"""
```julia
	@system GL876_two_planet begin
		# total mass [solar masses]
		M ~ truncated(Normal(0.346,0.007),lower=0.1)

		jit1 ~ LogUniform(0.1, 100)
	end rv_likelihood b c;
```
"""

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# ╔═╡ 5d5b1c8f-c903-41fd-b206-18e0cf015c0b
md"""
```julia
	model_two_planet = Octofitter.LogDensityModel(GL876_two_planet)
```
"""

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md"""
```julia
	chain_two_planet,pt_two_planet = octofit_pigeons(model_two_planet,n_rounds=10)
```
"""

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md"""
```julia
	display(chain_one_planet)
```
"""

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md"""
```julia
	Octofitter.rvpostplot(model_two_planet, chain_two_planet, show_summary=true)
```
"""

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md"""
## Model Comparison

Should we prefer the one, or two planet models? We can answer this by performing a model comparison.

We will use the log Bayesian evidence, calculated directly using Pigeons. This is one of the most robust ways to compare Bayesian models, if you are able to calculate it.

```julia
	stepping_stone(pt_one_planet)
```
"""

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md"""
```julia
	stepping_stone(pt_two_planet)
```
"""

# ╔═╡ 4f3191a3-a1ec-44d2-a59d-b5d9199f25a1


# ╔═╡ ff7b5daf-eb51-4dfb-b7ab-7d25a1dc112b
md"""
```julia
	stepping_stone(pt_two_planet) - stepping_stone(pt_one_planet)
```
"""

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md"""
This difference is **overwhelming**. The additional complexity of the increased paramters is more than justified by its improved ability to model the data.

```julia
	octocorner(model_one_planet,chain_one_planet, chain_two_planet,small=true)
```
"""

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md"""
Finally, we can see how adding an extra planet affects the parameters of the first planet
"""

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md"""

We find that adding a second planet does significantly impact the derived parameters of planet b.


We can plot the final two planet model parameters in a corner plot, to examine the covariance.

```julia
	octocorner(model_two_planet, chain_two_planet, small=true)
```
"""

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md"""
## Excercise! Try adding a third planet!
"""

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[[deps.ZygoteRules]]
deps = ["ChainRulesCore", "MacroTools"]
git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.5"

[[deps.isoband_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.3+0"

[[deps.libaec_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "46bf7be2917b59b761247be3f317ddf75e50e997"
uuid = "477f73a3-ac25-53e9-8cc3-50b2fa2566f0"
version = "1.1.2+2"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "522c1df09d05a71785765d19c9524661234738e9"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.11.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.2+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.3+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "b7bfd3ab9d2c58c3829684142f5804e4c6499abc"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.45+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "libpng_jll"]
git-tree-sha1 = "1e53ffe8941ee486739f3c0cf11208c26637becd"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.4+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.libwebp_jll]]
deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"]
git-tree-sha1 = "d2408cac540942921e7bd77272c32e58c33d8a77"
uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2"
version = "1.5.0+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "dcc541bb19ed5b0ede95581fb2e41ecf179527d2"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.6.0+0"
"""

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