Methodology

In this analysis, I define a binary outcome for orbital eccentricity and use a small set of stellar and system-level features to prepare a simple classification task. The goal is to build a clean training and testing split so the model can later be fit and evaluated on whether a planet is more likely to be in an eccentric versus circular orbit.

This logistic regression model was fit on the training set to estimate how the selected stellar and system features relate to the probability that a planet is eccentric. In plain terms, it helps answer: which star-system characteristics are most useful for separating likely eccentric orbits from likely circular ones.

The predictors are chosen because they reflect physically meaningful properties of the host star and its planetary system. Stellar metallicity traces the abundance of elements heavier than hydrogen and helium, which can affect the amount of solid material available for planet formation and the architecture of the resulting planetary system. Stellar mass and effective temperature describe the star’s gravitational and radiative environment, while surface gravity measures how strongly the stellar photosphere is bound to the star and captures information about the star’s compactness and internal structure.

The model can be written as:

\[ \operatorname{logit}(p_i)=\beta_0+\beta_1\,\text{st\_met}_i+\beta_2\,\text{st\_mass}_i+\beta_3\,\text{st\_teff}_i+\beta_4\,\text{st\_logg}_i+\beta_5\,\text{sy\_pnum}_i, \]

Each covariate carries a distinct astrophysical interpretation. Stellar metallicity is a proxy for the chemical enrichment of the protoplanetary disk. Stellar mass sets the star’s scale and evolutionary context. Effective temperature reflects the star’s radiative output and the thermal environment of the system. Surface gravity tracks the star’s compactness and internal structure, while the number of planets in the system captures the possibility that multiplicity and dynamical interactions may help shape orbital eccentricity.

Data preparation

This step creates the modeling dataset by converting orbital eccentricity into a binary response and selecting the predictors used in the model. The outcome is coded as 1 when the orbital eccentricity is at least 0.1 and 0 as otherwise.

Train-test split

The data were split into training and testing sets so the model could be fit and then evaluated on unseen observations. This helps reduce the risk of overfitting and provides a more realistic check on predictive performance.

Set Rows Eccentric Circular
Training 4102 941 3161
Testing 1026 238 788

Logistic regression model

A logistic regression model was fitted to estimate how the selected predictors relate to the probability that an orbit is eccentric.

  • The model turns each system’s measurements into a probability between 0 and 1.
  • That makes results easier to use than a strict yes/no label when deciding which systems to prioritize for follow-up.

Model summary

The table below is the model’s technical report card for each predictor.

  • It shows the direction of each effect (pushes predictions up or down) and how stable that effect looks in this sample.
  • More stable effects are generally more trustworthy as signals for future screening decisions.
term estimate std_error z_value p_value odds_ratio
(Intercept) 5.3060 0.6173 8.5959 0.0000 201.5366
st_met 0.8567 0.2136 4.0115 0.0001 2.3553
st_mass -0.2250 0.1674 -1.3439 0.1790 0.7985
st_teff -0.0002 0.0001 -2.9725 0.0030 0.9998
st_logg -1.2154 0.1204 -10.0952 0.0000 0.2966
sy_pnum -0.0642 0.0340 -1.8869 0.0592 0.9379

Odds ratios with confidence intervals

The table below translates model effects into easier-to-read multipliers.

  • Values above 1 suggest a predictor is linked to higher odds of eccentricity, while values below 1 suggest lower odds.
  • This makes it easier to compare which predictors have stronger practical influence.
  • The confidence interval gives a plausible range for the effect size; narrower ranges suggest greater precision.
term OR 2.5 % 97.5 %
(Intercept) 201.5366 61.3989 694.0948
st_met 2.3553 1.5515 3.5843
st_mass 0.7985 0.5687 1.1217
st_teff 0.9998 0.9997 0.9999
st_logg 0.2966 0.2329 0.3743
sy_pnum 0.9379 0.8765 1.0016