M-dwarf Planetary Relations️

In v1.1 we also include a pre-conditioned M-dwarf sample fit consisting of 88 planets with precise (> 3-sigma) masses and radii, and stellar effective temperatures < 4200 K. We perform three fits of increasing complexity on this dataset in 2-D, 3-D and 4-D as follows. This is to account for the effect of stellar mass, insolation (in addition to planetary radius) to the planetary mass as shown in Figure 6 from Kanodia et al. (2023) Though the example shown here is only for an M-dwarf planet sample, in principle, the same can be performed on any sample.

2D Distributions — f(m|r)

This is the traditional mass-radius fit in 2D, similar to that performed in Kanodia et al. (2019) , but on an updated sample of 88 planets compared to the 24 there. The joint distribution for this fit is shown below and utilizes a grid of 60 x 60 weights.

Figure 1: M-dwarf 2D mass-radius joint distribution.

While users can use the inference examples here to perform any inference of their choice, we also include an in-built function to infer planetary mass from radius. This can be called as follows -

from mrexo.predict_nd import Mdwarf_InferPlMass_FromPlRadius
# To infer the planetary mass for three planets with radii as 8, 10, and 12 earth radius,
# with an output in earth masses
print(Mdwarf_InferPlMass_FromPlRadius(pl_rade = [8, 10, 12]))

The sample script for this is included in the Mdwarf prediction functions .

3D Distributions — f(m|r, stm)

As an improvement to the previous 2D relation, the user can also infer from a 3D relationship, where the planetary mass is conditioned in planetary radius and the stellar mass. This can be done with the in-built function as follows.

from mrexo.predict_nd import Mdwarf_InferPlMass_FromPlRadiusStMass
# To infer the planetary mass for a grid of planets with radii as 8, 10, and 12 earth radius,
# and stellar masses as 0.4, 0.5 and 0.6 sol mass. The output is in earth masses
print(Mdwarf_InferPlMass_FromPlRadiusStMass(pl_rade=[8, 10, 12],  st_mass=[0.4, 0.5, 0.6]))

The sample script for this is included in the Mdwarf prediction functions .

4D Distributions — f(m|r, insol, stm)

As an improvement to the previous 3D relation, the user can also infer from a 4D relationship, where the planetary mass is conditioned in planetary radius, stellar mass and insolation flux. This can be done with the in-built function as follows.

from mrexo.predict_nd import Mdwarf_InferPlMass_FromPlRadiusInsolStMass
# To infer the planetary mass for a grid of planets with radii as 8, 10, and 12 earth radius,
#and stellar masses as 0.4, 0.5 and 0.6 sol mass, and insolation fluxes of 100 and 500 Searth. The output is in earth masses
print(Mdwarf_InferPlMass_FromPlRadiusInsolStMass(pl_rade=[8, 10, 12], pl_insol=[100, 500], st_mass=[0.4, 0.5, 0.6]))

# The user can also do this for a single planet as follows
print(Mdwarf_InferPlMass_FromPlRadiusInsolStMass(pl_rade=10, pl_insol=100, st_mass=0.5))

The sample script for this is included in the Mdwarf prediction functions .