Plotting MCMC results from VFTS 243
In this example we produce corner plots from the results of VFTS 243 that were stored from the previous example. We start by loading up
using CairoMakie
using SideKicks
using CornerPlotting
using Distributions
results, observations, priors, metadata = SideKicks.ExtractResults("vfts243_results.hdf5")4-element Vector{Any}:
Dict{Any, Any}(:P_f => [899631.9031002622 899128.2365316936 899567.7176608172 899274.2186061341; 897420.9590948492 898364.0776499602 899280.8119107054 898661.5158801406; … ; 899853.3482188154 902558.2047020107 898875.7129623046 896802.1472756597; 899667.0430973007 897347.7153521972 898940.5618871566 907406.0788773461], :venv_N => [1.3876483202127969e7 1.2621530687144091e7 1.4068447071361382e7 1.2572763598337747e7; 1.4297599649547035e7 1.2681803314372845e7 1.4013590948218038e7 1.5102794465687463e7; … ; 1.5956360603457477e7 1.7627150018358894e7 1.2305354307782372e7 9.722302898470417e6; 1.4216782827237887e7 1.7964819484936602e7 1.393845812017831e7 9.90533834806879e6], :ϕ => [1.1855987607820342 0.34423732021334685 0.22719236136917054 6.059693841940314; 1.1800452040065998 0.2710937181347743 4.247340964941075 4.9401887733347305; … ; 2.4468645221823544 2.295664622174951 1.2973145884130466 0.6384852168876669; 2.107615085076962 2.131552186127755 1.6707341096559 0.6983512516108324], :vsys => [2.4459897203830904e6 4.74591727359189e6 810096.3371508452 164273.80881000054; 2.252121160849232e6 4.598989648369307e6 466188.0807210991 1.0971275371248862e6; … ; 2.1120811611542227e6 3.5189278072270844e6 2.4411074574470157e6 1.7674036107103191e6; 1.7807666745114257e6 3.206321547812187e6 1.4435516203253793e6 1.8567173424360012e6], :a_f => [3.974197911516519e12 4.3219480324469956e12 5.336350505940822e12 4.187743135025976e12; 4.07599781431358e12 4.2924732257835117e12 4.449246065584152e12 4.2589297315169077e12; … ; 3.9624942503117715e12 4.527507089729218e12 4.925581015847777e12 4.752289113594853e12; 4.418765925615615e12 4.49279148936757e12 3.917708057959593e12 4.866225974013546e12], :m2_i => [4.5420429663070215e33 1.0255206550372551e34 6.529789111609211e34 9.055041353242428e33; 4.472022577130002e33 9.72492981954303e33 1.8589692075620655e34 4.613751095292726e33; … ; 5.375767771195607e33 2.112189025645653e34 2.853017619425047e34 3.222067675326792e34; 5.501945541574509e33 1.9356664733722574e34 1.6782648171627284e34 3.581508898025151e34], :m2_f => [3.658346955348851e32 1.0189180748545276e34 6.006584974215178e34 8.982047826105577e33; 3.4680697658736314e32 9.639946375569758e33 1.7325265225037192e34 2.4240092352998267e33; … ; 1.6777356685227182e33 1.7502680402613544e34 2.845474641511032e34 2.685617910056339e34; 1.664468978164774e33 1.6287018641077607e34 1.5345771063226315e34 2.9765933782810635e34], :e_i => [0.003283606870221012 0.0015448147167173942 0.00238191766586427 0.0019022910718393565; 0.003370977828596793 0.0017171465728704183 0.007984786172564953 0.00876975643743151; … ; 0.0079152573677324 0.006566989623737115 0.007984928979181561 0.001226729868378267; 0.007824588410649536 0.006410373704541231 0.0026614356894650287 0.00279881089829437], :vsys_r => [-1.114922850497939e6 -1.2981358022188311e6 -62372.49692616431 -10262.22165019547; -805673.2861609499 -1.6713906647240615e6 -79873.29706496377 -367949.3551159365; … ; -532037.7174065365 -1.8906511514613263e6 -1.6932254290861562e6 -913211.4145697725; -421278.13856933184 -1.521111855904251e6 -861526.348945061 -964913.2511110031], :K2 => [1.830420922286099e7 3.800748217623164e7 7.439969989771869e6 2.3018731464705925e7; 2.1233625634853058e7 3.7718798881862886e7 2.223512577914477e7 2.0512358588310216e7; … ; 9.9445515838298e6 2.4050177549604084e7 1.7427862623049874e7 1.5631269031815333e7; 1.1236761356232785e7 2.419777516199235e7 1.5328656177662924e7 1.4676130614657408e7]…)
SideKicks.Observations([:P_f, :e_f, :m1_f, :K1, :v_N, :v_E, :v_r, :ω_f], [10.4031, 0.017, 25.0, 81.4, 138.8, 409.3, 261.5, 66.0], [0.01, 0.012, 2.3, 1.3, 7.6, 9.3, 0.42, 53.0], [86400.0, 1.0, 1.9884098706980504e33, 100000.0, 100000.0, 100000.0, 100000.0, 0.017453292519943295])
SideKicks.Priors(Distributions.Uniform{Float64}(a=0.1, b=3.0), Distributions.Uniform{Float64}(a=0.1, b=3.0), Distributions.Uniform{Float64}(a=-1.0, b=3.0), Distributions.Uniform{Float64}(a=0.0, b=4.0), Distributions.Uniform{Float64}(a=0.0, b=1.0), Distributions.Uniform{Float64}(a=0.0, b=0.01), Distributions.Normal{Float64}(μ=1.46, σ=0.4), Distributions.Normal{Float64}(μ=3.93, σ=0.42), Distributions.Normal{Float64}(μ=2.7030000000000003, σ=0.111), missing, missing, missing, missing)
HDF5.Group: /metadata (file: vfts243_results.hdf5)As an initial check, we can plot the quantities that were used as observations. A basic consistency check is to verify these are consistent with the MCMC samples.
names = [:m1_f, :P_f, :e_f, :K1]
scaling = Dict( :m1_f => m_sun,
:P_f => day,
:e_f => 1,
:K1 => km_per_s
)
labels = Dict( :m1_f => L"M_{1f}\;[M_{\odot}]",
:P_f => L"P_f\;[\mathrm{days}]",
:e_f => L"e_f",
:K1 => L"K_1 \;[\mathrm{km s}^{-1}]",
)
set_theme!(CornerPlotting.default_theme())
cp = CornerPlotting.CornerPlot(results, names, scaling=scaling, labels=labels)
CornerPlotting.plot_extra_1D_distribution(cp, :m1_f, Normal(25.0,2.3))
CornerPlotting.plot_extra_1D_distribution(cp, :e_f, Normal(0.017,0.012))
CornerPlotting.plot_extra_1D_distribution(cp, :K1, Normal(81.4, 1.3))
CornerPlotting.plot_extra_1D_distribution(cp, :P_f, Normal(10.4031, 0.01))
save("vfts243_observables.png", cp.fig)
cp.fig
And, after verifying the samples do correspond to our observational constraints, we can analyze the consequences for explosion itself.
names = [:m2_i, :dm2, :P_i, :vkick, :vsys]
scaling = Dict( :m2_i => m_sun,
:dm2 => m_sun,
:P_i => day,
:vkick => km_per_s,
:vsys => km_per_s,
)
labels = Dict( :m2_i => L"M_{2f}\;[M_{\odot}]",
:dm2 => L"ΔM_2 \;[M_{\odot}]",
:P_i => L"P_i \;[\mathrm{days}]",
:vkick => L"v_{kick} \;[\mathrm{km s}^{-1}]",
:vsys => L"v_{\mathrm{sys}} \;[\mathrm{km s}^{-1}]",
)
set_theme!(CornerPlotting.default_theme())
cp = CornerPlotting.CornerPlot(results, names, scaling=scaling, labels=labels)
save("vfts243_derived.png", cp.fig)
cp.fig
As you might see, the results are not very flattering, but this is a consequence of the very small number of samples used.
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