TTVFaster

First order eccentricity transit timing variations (TTVs) computed in Agol & Deck (2015)

This implements equation (33) from that paper by computing the Laplace coefficients using a series solution due to Jack Wisdom, computing the $f_{1,j}^{(\pm k)}$ coefficients given in equation (34) using the functions $u$ and $v_{\pm}$ with coefficients given in Table 1.

You can install the registered TTVFaster repo as a Julia package with the Pkg manager.

• the repo from the package registry has been tested on Julia v1.6.0

julia> using Pkg Pkg.add("TTVFaster.jl")

In its current state, the package computes the TTVs of a multi-transiting planetary system where at least 2 planets are observed to be transiting. If you intend to modify the source code for any reason, please create a GitHub fork to develop your own version.

• make sure to replace your-GitHub-username with your actual GitHub username in the code below

julia> Pkg.develop(PackageSpec(url="git@github.com:your-GitHub-username/TTVFaster.jl.git"))

TTVFaster computes TTVs with respect to 5 properties for each planet: $\mu$, $T_0$ , $P$, $e \cos(\omega)$ , $e \sin(\omega)$; where $\mu$ is the mass ratio of the planet to the star ($m_p/M_{\star}$), $T_0$ is the initial transit time (of the averaged orbit), $P$ is the mean orbital period, $e$ is the eccentricity, and $\omega$ is the longitude of periastron.

The file kepler62ef_planets.txt in the examples/ directory contains a comma-separated set of 10 parameters that describe a system with two planets similar to Kepler-62e/f.

julia> using TTVFaster,DelimitedFiles

julia> data=readdlm("kepler62ef_planets.txt",',',Float64)  
1x10 Array{Float64,2}:
 3.02306e-5  122.386  -16.5926  -0.00127324  0.0026446  1.67874e-5  267.307  155.466  -0.0025544  0.00117917

julia> include("test_ttv.jl")  
test_ttv (generic function with 4 methods)

julia> @time ttv1,ttv2=test_ttv(5,40,20,data);  # inputs are jmax,ntrans1,ntrans2,data
  0.982326 seconds (2.04 M allocations: 98.466 MiB, 12.08% gc time)
julia> @time ttv1,ttv2=test_ttv(5,40,20,data);  
  0.001171 seconds (331 allocations: 21.922 KiB)

This computes the TTVs and writes them to the files inner_ttv.txt and outer_ttv.txt in the examples/ directory. Note that the TTVs are stored in the variables ttv1 and ttv2, as well. The test_ttv.jl routine accepts jmax (the maximum $j$ to sum to, in this example 5), ntrans1 (number of transits of the inner planet), ntrans2 (the number of transits of the outer planet), and data which contains the parameters of both planets.