CS 670: Data Science Course Project

Exploring the NASA Exoplanet Archive

Shistata Subedi & Cory Johns

Introduction

The field of exoplanet research has advanced significantly over the past few decades, driven by improvements in observational techniques and data collection methods. The NASA Exoplanet Archive provides a structured dataset of confirmed exoplanets, capturing their physical and orbital characteristics and details about their host stars. In this project, we aim to perform a comprehensive data-driven analysis to identify trends, correlations, and distributions of exoplanets based on factors such as mass, radius, orbital properties, and their relationship with host stars.

1. Data Selection and Overview

  • Source: NASA Exoplanet Archive: NASA Exoplanets
  • Creator & Purpose: This dataset originates from NASA’s Exoplanet Archive, which compiles confirmed exoplanet discoveries from space missions (Kepler, TESS, etc.), ground-based observatories, and other studies. It is used to analyze exoplanet properties and distributions.
  • Collection Method: Data was scraped from NASA’s website using a Python script with Selenium (for automation) and BeautifulSoup (for parsing), followed by preprocessing and cleaning.
  • Attributes: The dataset (5,250 entries) includes:
    • name, discovery_year, detection_method (Identification & source)
    • distance, stellar_magnitude (Host star brightness)
    • planet_type, mass, radius, orbital_radius, orbital_period, eccentricity (Planet characteristics, with mass/radius relative to Jupiter or Earth)
  • Representation Decisions & Impact:
    • Standardized Units: Mass and radius are scaled relative to Jupiter/Earth, aiding comparison but requiring conversion for other analyses.
    • Missing Values: Attributes like distance and stellar magnitude have gaps, which may limit specific analyses.
    • Categorical Variables: Planet_type and detection_method require encoding for machine learning models.
    • Data Source Variability: Differences in observational methods may introduce inconsistencies.

This dataset is valuable for studying exoplanet trends, planetary system formation, and predictive modeling.

2. Research Questions

2.1. What are the different types of exoplanets present in the dataset?

Analysis:

Exoplanets were categorized based on mass and radius into Terrestrial, Super-Earth, Gas Giant, Neptune-like, Super-Neptune, and Inflatable Planets.

2.1.1. Visualization

The dataset was explored using various visualization techniques in R, leveraging the ggplot2 package. The visualizations generated include:

Bar Chart of Exoplanet Classification

# Bar chart showing the distribution of exoplanet types
ggplot(data, aes(x = category, fill = category)) +
   geom_bar() +
   labs(title = "Distribution of Exoplanet Types",
        x = "Exoplanet Type",
        y = "Count") +
   theme_minimal() +
   theme(axis.text.x = element_text(angle = 45, hjust = 1))


This bar chart shows how exoplanets are categorized based on mass and radius.

Scatter plot: Mass vs. radius distribution.

# Scatter plot of Mass vs. Radius, colored by exoplanet type
ggplot(data, aes(x = radius, y = mass_earth, color = category)) +
   geom_jitter(alpha = 0.5, size = 1, width = 0.1, height = 0.1) +
   labs(title = "Mass vs. Radius of Exoplanets",
        x = "Radius (Earth radii)",
        y = "Mass (Earth masses)") +
   theme_minimal()


A scatter plot visualizing the relationship between mass and radius, categorized by exoplanet type. This scatter plot visualizes how exoplanet mass and radius are related, showing that larger planets tend to be more massive.

Density Plot of Orbital Radius Distribution

# Density plot for orbital radius distribution by planet type
ggplot(data, aes(x = orbital_radius, color = category)) +
   geom_density(alpha = 0.7) +
   scale_x_log10() +  # Log scale for better visualization
   labs(title = "Orbital Radius Distribution by Exoplanet Type",
        x = "Orbital Radius (AU)",
        y = "Density") +
   theme_minimal()


This plot shows how different types of exoplanets are distributed in terms of orbital distance. It provides insights into whether certain planet types are more common at specific distances.

2.1.2. Models
  • Feature Engineering: The code processes the dataset by converting Jupiter-based mass and radius values to Earth-based equivalents.
  • Categorization of Exoplanets: Based on their mass and radius, exoplanets were classified as terrestrial, super-Earth, Neptune-like, gas giant, super-Neptune, and inflatable planet.
  • Handling Missing Values: Median imputation was used to fill in the missing values for mass_multiplier, radius_multiplier, and orbital_radius.

2.2. Is there a relationship between an exoplanet’s properties and its host star?

Analysis:

  • Examined correlations between stellar magnitude and planetary characteristics.
  • Applied Pearson correlation and regression models to check dependencies.
2.2.1 Visualization

Scatter plot: Stellar Magnitude vs. Exoplanet Mass

# Scatter plot: Stellar Magnitude vs. Exoplanet Mass
ggplot(data, aes(x = stellar_magnitude, y = mass_earth)) +
  geom_point(alpha = 0.5, color = "blue") +
  geom_smooth(method = "lm", color = "red", se = TRUE) +
  labs(title = "Stellar Magnitude vs. Exoplanet Mass",
       x = "Stellar Magnitude",
       y = "Mass (Earth masses)") +
  theme_minimal()


This graph shows how a star’s brightness (stellar magnitude) relates to the mass of its exoplanets. There is a weak negative correlation (R2=0.012R^2 = 0.012R2=0.012), meaning stellar brightness alone does not strongly influence exoplanet mass.

Scatter plot: Stellar Magnitude vs. Exoplanet Radius (Log Scale)

# Scatter plot: Stellar Magnitude vs. Exoplanet Radius
ggplot(data, aes(x = stellar_magnitude, y = radius)) +
   geom_point(alpha = 0.5, color = "blue") +
   geom_smooth(method = "lm", color = "red", se = TRUE) +
   scale_y_log10() +  # Log scale for better visualization
   labs(title = "Stellar Magnitude vs. Exoplanet Radius (Log Scale)",
        x = "Stellar Magnitude",
        y = "Radius (Earth radii, log scale)") +
   theme_minimal()
# `geom_smooth()` using formula = 'y ~ x'


This graph examines how a star’s brightness relates to the size of its exoplanets.

Scatter plot: Stellar Magnitude vs. Orbital Radius (Log Scale)

# Scatter plot: Stellar Magnitude vs. Orbital Radius
ggplot(data, aes(x = stellar_magnitude, y = orbital_radius)) +
   geom_point(alpha = 0.5, color = "blue") +
   geom_smooth(method = "lm", color = "red", se = TRUE) +
   scale_y_log10() +  # Log scale to manage extreme values
   labs(title = "Stellar Magnitude vs. Orbital Radius (Log Scale)",
        x = "Stellar Magnitude",
        y = "Orbital Radius (AU, log scale)") +
   theme_minimal()
# `geom_smooth()` using formula = 'y ~ x'


This graph checks whether stellar brightness influences how far planets orbit from their host star. The correlation is weak, suggesting that the brightness of a star does not strongly impact the distance of planetary orbits.

2.2.2. Models

Regression Model Results & Interpretation

Predictor (X) Response (Y) Coefficient R² p-value Interpretation
Stellar Magnitude Exoplanet Mass -134.2 0.012 1.656e-15 (***) It’s a weak negative relationship, but stellar mass likely matters more.
Stellar Magnitude Exoplanet Radius -0.816 0.2215 <2.2e-16 (***) Moderate negative correlation; larger planets found around brighter stars.
Stellar Magnitude Orbital Radius -0.64 0.0002 0.292 (NS) No significant correlation; planetary orbits depend on other factors.

Multiple Linear Regression Model

In order to further investigate the relationship between exoplanet properties and their host stars a multiple linear regression model was fit to the data using 10-fold cross-validation.

Model: Stellar Magnitude ~ Exoplanet Mass + Exoplanet Radius + Orbital Period + Orbital Radius + Eccentricity

R² : 0.3513

Predictor (X) Coefficient p-value Interpretation
(Intercept) 1.445e+01 <2e-16 (***) Stellar magnitude starts at about 14 for this model, though, only exccentricity can be expected to be near 0.
Exoplanet Mass 3.453e-05 0.000512 (***) Similar to the univariate linear regression case.
Exoplanet Radius -2.384e-01 <2e-16 (***) Similar to the univariate linear regression case.
Orbital Period 4.534e-06 0.512100 Period was not significant.
Orbital Radius -3.798e-04 0.660614 Even less significant then with ULR.
Eccentricity -7.064e+00 <2e-16 (***) Strong negative correlation, non-circular orbits impliy brighter stars.


Plot shows the prediction accuracy of the MLR model. Density lines have been added to mitigate overplotting, and a perfect predication accuracy reference line of y=x was also added. Points above this line are an overestimate and points below the line are an underestimate.

2.2.3. Results, Analysis, and Discussion
  • Findings:
    • Exoplanet radius is the most strongly correlated with stellar magnitude, likely due to the link between stellar mass and planet formation.
    • Exoplanet mass shows a weak correlation, meaning stellar brightness alone is not a good predictor.
    • The orbital radius does not show any meaningful correlation with stellar magnitude.
  • Limitations
    • Selection Bias: The dataset contains exoplanets detected via different methods (e.g., transit, radial velocity), which may introduce observational bias.
    • Missing Key Variables: Stellar magnitude does not fully capture important host star properties. A better analysis can include:
      • Stellar Mass: Directly impacts planetary formation.
      • Spectral Type: Determines the star’s temperature, affecting habitable zones.
      • Metallicity: High-metallicity stars tend to form gas giants more frequently.
  • Future Work:
    • Alternative Methods: Future studies should explore multivariate regression models incorporating stellar mass, radius, and luminosity to get a clearer picture.
    • Better Visualizations: Plotting exoplanet mass/radius against stellar mass instead of using stellar magnitude may reveal stronger correlations.

2.3. How do exoplanet mass distributions vary, and what insights can we gain about planetary formation, detection biases, and their comparison with the Solar System?

Examined the distribution of exoplanet masses to identify trends, detect biases in observational methods, and compare findings with known planetary formation models.

  • Used histograms and density plots (linear and log scale) to explore exoplanet mass distributions.
  • Conducted correlation analysis to investigate the relationship between mass and radius.
  • Applied k-means clustering to identify mass-based groupings of exoplanets.
  • Analyzed detection biases using ANOVA and Tukey HSD tests to examine how different detection methods influence mass distributions.
  • Created boxplots and scatter plots to visualize exoplanet mass trends by detection method.
2.3.1. Visualization
2.3.1.1. Exoplanet Mass vs. Radius Analysis


Description: This scatter plot shows the relationship between exoplanet mass and radius on a log scale. The red line represents a regression fit.

Interpretation: Mass and radius have a positive correlation—larger planets tend to have higher masses. The log-log transformation makes it easier to visualize this relationship, highlighting a power-law dependence.

Mass-Radius Relationship with Power-Law Fit


Description: This plot extends the previous one by applying a power-law fit to the data.

Interpretation: The power-law fit suggests that planetary radii increase at a decreasing rate with mass, meaning that adding more mass results in proportionally smaller increases in radius.

2.3.1.2. Exoplanet Mass Distribution

Histogram of Log-Transformed Exoplanet Mass Distribution – Addressing skewness.


Description: A histogram of exoplanet masses using a log transformation.

Interpretation: Unlike the linear-scale histogram, this shows a more normal-like distribution, indicating that planetary mass follows a power-law distribution.

Density Plot of Exoplanet Masses (Log Scale) – Better view of mass spread.


Description: A density plot showing mass distribution on a logarithmic scale.

Interpretation: This plot further confirms the skewed nature of the mass distribution, revealing clusters of planets with distinct masses.

2.3.1.3. Clustering Analysis of Exoplanets

K-Means Clustering of Exoplanets – Scatter plot with three clusters.


Description: This scatter plot divides exoplanets into three clusters based on mass and radius.

Interpretation: The three clusters likely represent different planet types, such as terrestrial planets, gas giants, and super-Earths.

Clusters vs. Solar System Planets – Comparison of exoplanet clusters with known planets.


Description: This figure compares exoplanet clusters with known Solar System planets.

Interpretation: The clustering method groups planets similarly to how terrestrial planets (red), ice giants (blue), and gas giants (green) are classified.

2.3.1.4. Exoplanet Detection Methods

Exoplanet Mass Distribution by Detection Method – Boxplot comparing mass across different detection techniques.


Description: A box plot showing mass distributions for different detection methods.

Interpretation: Different detection methods favor different types of planets. For example, radial velocity tends to detect higher-mass planets, while transit favors smaller ones.

Tukey HSD Result Plot – Multiple comparison test for mass variation across detection methods.


This Tukey HSD analysis helps determine which detection methods are statistically different in their ability to detect exoplanet masses.

If detection methods lead to biases in mass distribution, conclusions about exoplanet populations may be skewed.

2.3.2. Models

The analysis involves fitting multiple models to understand the relationships between exoplanet mass, radius, and detection methods. Several statistical techniques, including correlation analysis, linear regression, and clustering, were applied to identify patterns in the data.

Correlation Analysis

A Pearson correlation test examined the relationship between mass and radius.

  • Pearson’s r = 0.94 indicates a strong positive correlation between mass and radius.
  • P-value < 2.2e-16: This confirms that the relationship is highly statistically significant, meaning that as mass increases, the radius also increases significantly.

Linear Regression Model

A linear regression model was used to quantify the relationship between mass and radius on a log-log scale.

  • Intercept = -0.00976: The base value of the radius when mass is at its minimum.
  • Slope (log_mass coefficient) = 0.4817: This suggests that radius increases with mass but not in a 1:1 ratio.
  • R-squared = 0.8842: Indicates that 88.42% of the variation in radius can be explained by mass.
  • P-value < 2.2e-16: Confirms statistical significance.

Clustering Analysis

K-Means clustering was applied to log-transformed mass and radius values to identify distinct groups of exoplanets.

  • The Elbow Method determined the optimal number of clusters to be three.
  • Cluster summaries showed meaningful groupings:
    • Cluster 1 (Lower mass, more minor radius planets)
    • Cluster 2 (Higher mass, larger radius planets)
    • Cluster 3 (Intermediate mass and radius planets)

Tukey’s HSD Test

Tukey’s Honest Significant Difference (HSD) test was used to compare detection methods and determine whether they significantly differ in the types of exoplanets they detect.

Key Findings:

Statistically Significant Differences (p < 0.05):

  • Gravitational Microlensing vs. Orbital Brightness Modulation (p = 0.027)
    • Microlensing detects significantly more massive exoplanets than brightness modulation.
  • Gravitational Microlensing vs. Pulsar Timing (p = 0.0018)
    • Microlensing detects heavier planets compared to Pulsar Timing.
  • Transit vs. Gravitational Microlensing (p < 0.0001)
    • The transit method detects significantly lighter planets than Microlensing.
  • Radial Velocity vs. Pulsar Timing (p = 0.0078)
    • Radial Velocity detects significantly heavier exoplanets than Pulsar Timing.
  • Transit vs. Radial Velocity (p < 0.0001)
    • Transit detects lighter exoplanets compared to Radial Velocity.

Non-Significant Differences (p > 0.05):

  • Direct Imaging does not show significant mass differences with most methods.
  • Most other methods do not significantly differ in the masses of detected exoplanets.
2.3.3. Results, Analysis, and Discussion

The results confirm that exoplanet mass and radius are strongly correlated, with the log-transformed regression model capturing nearly 88.42% of the variance. The clustering analysis identified three main groups of exoplanets, indicating natural groupings based on size and mass. The Tukey HSD test also highlighted how different detection methods preferentially identify exoplanets of varying masses.

The analysis reveals that:

  • Transit and Radial Velocity methods primarily detect more minor, less massive planets.
  • Microlensing and Radial Velocity methods tend to detect more significant and more massive exoplanets.
  • Direct Imaging does not show a significant difference in detecting planets of varying masses compared to other methods.
2.3.3.1. Limitations
  • The dataset primarily contains exoplanets detected using methods that favor large planets, leading to potential bias.
  • Orbital parameters such as eccentricity and period were not fully integrated into the analysis, which might impact classification.
  • More advanced models, such as non-linear regression or machine learning techniques.
2.3.3.2. Future Data Collection

To enhance the robustness of this analysis, additional data could include:

  • More detailed composition analysis of exoplanets.
  • Integration of stellar properties (e.g., metallicity, age, and temperature) to refine models.
  • Expanding the dataset with newly discovered exoplanets from recent missions.

2.4. How are detected exoplanets distributed in the galaxy?

The Kaggle database was combined with position data obtained from the Sesame Name Resolver to explore how these exoplanets were distributed in the galaxy. This new data was not formatted in a database, so the information was copied, and a simple Python program was written to extract the relevant lines. The output of the Python program was reformatted to a CSV format and merged with the Kaggle database with R. This did not yield position data for all the exoplanets in the Kaggle database (4917 of the 5250 entries), so the above process was repeated for the missing entries by using the name of the star instead of the exoplanet (these have the exact coordinates; the star name is the same as the exoplanet but lacks the lowercase letter at the end). This yielded an additional 110 positions. After this data was integrated, position data was available for 5027/5250 entries (223 missing positions). This position data was formatted in J2000 (J2K) Earth-centered inertial coordinates and was converted to Cartesian coordinates for graphing. Any differences between origins and orientations in right ascension and J2K systems were ignored. The differences in origin are negligible between solar-system-centered and Earth-centered origins compared to interstellar distances. The conversion for J2K coordinates to Cartesian was done as follows:

Step 1) Convert J2K to radians:

\[ (\frac{j.hr}{24} + \frac{j.m}{24 * 60} + \frac{j.s}{24 * 3600}) * 2 \pi \]
Where j.hr, j.m, j.s is the J2K hours, minutes, and seconds respectively.

Step 2) Convert right ascension to radians:

\[ d.sign*(\frac{d.deg}{360} + \frac{d.m}{24*60} + \frac{d.s}{24*3600})*2 \pi \]
Where d.deg is the declination degrees, d.sign is the sign (+-) of the declination, and d.m, d.s are the declination minutes and seconds, respectively.

Step 3) Convert the spherical coordinates to rectangular coordinates.

Typical conversions between spherical and Cartesian coordinates are well known. However, declination is measured from the equator, not the pole, so the following conversion was derived:

\[ x = r*cos(γ)*cos(θ) \] \[ y = r*cos(γ)*sin(θ) \] \[ z = r*sin(γ)\ \]
Where r is the distance to the exoplanet, γ is the declination in radians, and θ is the right ascension.

Finally, to ease data analysis further, columns were added based on the existing columns:

  1. The star names were added as a column.
  2. Several stars had more than one exoplanet, so a new column was added to count the number of exoplanets in the system.
    1. data <- merge(as.data.frame(table(star.name)), data)
    2. The new ‘Freq’ column was then renamed to ‘num.exoplanets’
  3. The Kaggle database reported exoplanet mass and radius in a relative to Jupiter/Earth manner; this was converted to mass [10^24 kg] and radius [km] and added as new columns mass.10.24.kg and radius.km. This data was found on the NASA website.
2.4.1. Visualization
library(data.table)
data <- fread("data.csv")
attach(data)
library(plotly)

# set the axis ranges and ticks
axx <- list(nticks=10, range=c(-5000,5000))
axy <- list(nticks=35, range=c(-25000,10000))
axz <- list(nticks=25, range=c(-15000,10000))
# normalize the z and y-axis scale using the x-axis as a reference
x.r <- 10000
y.r <- 35000
z.r <- 25000

# rotate the plot's x-y plane to match the galaxy's plane. This is done by swapping z with -x, and x with z.
fig <- data %>% plot_ly(x=~z.pos, y=~y.pos, z=~I(-1*x.pos), color=~planet_type, size=~num.exoplanets, text=~star.name, opacity = 0.5)
# also swap the axis range and aspect ratio
fig <- fig %>% layout(scene=list(xaxis=axz, yaxis=axy, zaxis=axx, aspectmode='manual', aspectratio=list(x=z.r/x.r, y=y.r/x.r, z=1)))
# fig <- fig %>% layout(scene=list(aspectmode='manual', aspectratio=list(x=1, y=y.r/x.r, z=z.r/x.r)))
fig <- fig %>% add_markers()
fig  # run plot

Rough estimate of exoplanet locations in the Galaxy

2.4.2. Analysis, and Discussion
2.4.2.1. Analysis

Two additional data points were added to the database to better line up the 3D plot with a NASA galaxy map. These two entries were Sagittarius A* and Cygnus OB2. Sagittarius A* is the black hole at the center of the Milky Way, and its location is well known. The data also shows that the farthest detected exoplanet in the database was at a distance of ~27000 light years, almost the same as Sagittarius A*, and most of the gravitational microlensing observations that had position data fit on a line between Earth and this farthest exoplanet. Once Sagittarius A* was plotted, it was in the same direction as this exoplanet. Cygnus OB2 was picked for three reasons: 3 points are needed to define a plane (Earth, Cygnus OB2, Sagittarius A*), the Kepler Telescope pointed in the direction of the Cygnus constellation, and Cygnus OB2 was marked on the NASA Milky Way map.

The Kepler observations are distributed in a flattened cone. The cone part is expected since this was the telescope’s field of view, but the flattened nature of the data is unexpected. This is likely an error, but it is lined up with the galactic plane, which could be related to the galaxy’s rotation.

KST field of view

2.4.2.2. Limitations
  • The exoplanet data is extremely sparse, with the observations confined to limited areas.
  • The detection methods have strong bias to particular types of exoplanets.
  • Detection becomes harder as the objects get farther from Earth due to the inverse square law.

2.5. What kinds of observations didn’t get position data resolved?

Position data was not found for over 200 exoplanets. Most of the missing data was from gravitational microlensing detections. This is likely because the Sesame Name Resolver did not have these surveys in their database, or Kaggle named these exoplanets differently. However, this was only about 3.8% of the exoplanets.

2.5.1. Visualization
attach(data)

ref.stars <- subset(data, data$num.exoplanets == 0)
na.data <- subset(data, is.na(data$x.pos))
t1 <- as.data.frame(table(na.data$detection_method, na.data$planet_type))
colnames(t1)[colnames(t1) == 'Freq'] <- 'Frequency'
colnames(t1)[colnames(t1) == 'Var1'] <- 'Detection.Method'
colnames(t1)[colnames(t1) == 'Var2'] <- 'Planet.Type'

t1 %>%
        ggplot(aes(x=Planet.Type, y=Frequency, fill=Detection.Method))+
        geom_bar(stat="identity", position= "dodge", width = 0.5)+
        labs(title="NA Position Data",
             x="Planet Type",
             fill="Detection Method")+
        theme_bw()

Plot of exoplanets with empty position data

2.6. How much has the Kepler Space Telescope impacted exoplanet data?

The Kepler Space Telescope is responsible for about half of all exoplanet discoveries and most of the diversity in exoplanet types. Most of the non-Kepler discoveries are of the Gas Giant type; most of these are likely “Hot Jupiters” (gas giants with orbits close to their host star).

2.6.1. Visualization
no.ref.data <- subset(data, data$num.exoplanets != 0)
kepler.data <- no.ref.data[grep("epler", no.ref.data$star.name)]
non.kepler.data <- no.ref.data[!grep("epler", no.ref.data$star.name)]
k1 <- as.data.frame(table(kepler.data$planet_type))
colnames(k1)[colnames(k1) == 'Freq'] <- 'Kepler.Data'
colnames(k1)[colnames(k1) == 'Var1'] <- 'Planet.Type'
k2 <- as.data.frame(table(non.kepler.data$planet_type))
colnames(k2)[colnames(k2) == 'Freq'] <- 'Non.Kepler.Data'
colnames(k2)[colnames(k2) == 'Var1'] <- 'Planet.Type'
k.data <- merge(k1, k2)
rm(k1, k2)

k.data %>% pivot_longer(cols=c('Kepler.Data', 'Non.Kepler.Data'), names_to="Subset", values_to="Number") %>%
        ggplot(aes(x=Planet.Type, y=Number, fill=Subset))+
        geom_bar(stat="identity", position= "dodge", width = 0.5)+
        labs(title="Kepler Data Vs Non-Kepler Data",
             x="Planet Type",
             fill="Set")+
        theme_bw()

Plot of comparing KST data vs non-KST data

2.7. How does Kepler’s Data differ from other sources?

The Kepler Space Telescope (KST) used the transit technique to detect exoplanets as opposed to the traditional method of radial velocity. This means that KST is not biased to massive planets with a short orbital period. The properties of the detected exoplanets should be different between the KST observations and the non-KST observations.

2.7.1. Visualization
kepler.set = (no.ref.data$star.name %like% "epler")
no.ref.data %>%
        ggplot(aes(x=mass.10.24.kg, y=orbital_radius, colour=kepler.set))+
        geom_point(alpha=0.4)+
        labs(title="Mass Vs Orbital Radius",
             x="Mass (10^24 kg) [log10]",
             y="Orbital Radius (AU) [log10]",
             fill="Set")+
        scale_y_continuous(trans='log10')+
        scale_x_continuous(trans='log10')+
        facet_wrap(vars(planet_type))+
        theme_bw()

Distribution of Mass vs orbital radius for different exoplanet types

2.8. Are there differences in exoplanet type distribution in systems with more than one exoplanet?

Systems with multiple exoplanets were pervasive in the dataset but were not visible in the 3D plot (but shown as larger dots) since each planet in a multi-planet system has the exact same coordinates.

2.8.1. Visualization
no.ref.data <- subset(data, data$num.exoplanets != 0)
x2 <- as.data.frame(table(no.ref.data$planet_type, no.ref.data$num.exoplanets))
colnames(x2)[colnames(x2) == 'Var1'] <- 'planet.type'
colnames(x2)[colnames(x2) == 'Var2'] <- 'num.exoplanets'

#### figure 6
x2 %>%
        ggplot(aes(x=num.exoplanets, y=Freq, fill=planet.type))+
        geom_bar(stat="identity", position= "dodge", width = 0.5)+
        theme_bw()+
        labs(title="Number of Exoplanets in System Vs Type",
        x="Number of Exoplanets in System",
        y="Frequency",
        fill="Exoplanet Type")

Rough estimate of exoplanet locations in the Galaxy

2.8.2. Analysis

The figure above shows that the distribution of exoplanet type is roughly the same in systems with more than one exoplanet.

3. Impact

The classification of exoplanets is crucial in identifying potentially habitable planets and refining criteria for exoplanet research. This study reveals key insights, such as the tendency of more minor planets to orbit fainter stars, which has implications for planetary formation theories. Additionally, the findings highlight the influence of different detection methods on exoplanet discovery, guiding future telescope designs and improving target selection for habitability studies. Understanding these relationships can help prioritize observations, reduce detection biases, and refine planetary classification models. However, inaccuracies in these models could lead to misinterpretations about exoplanet prevalence. Further analysis, including regression and clustering and advancements in detection techniques, will enhance our ability to predict planetary characteristics and improve the search for Earth-like worlds.

4. Project Summary

This project addressed 8 questions:

1 - What are the different types of exoplanets present in the dataset?

There were 5 types of exoplanets categorized in the dataset: Gas Giant, Neptune-like, Super Earth, Terrestrial, and Unknown. These categories were further divided based off of mass and radius into: Terrestrial, Super-Earth, Gas Giant, Neptune-like, Super-Neptune, and Inflatable Planets. Of these Super-Earths and Gas Giants were found to be the most common.

2 - Is there a relationship between an exoplanet’s properties and its host star?

We explored several models to relate exoplanets to their host star (stellar magnitude). While many of the models had highly significant coefficients none of them produced R2 values greater then 0.5.

3 - How do exoplanet mass distributions vary, and what insights can we gain about planetary formation, detection biases, and their comparison with the Solar System?

The models explored in this section produced much better results then the last one. The results confirmed that exoplanet mass and radius are strongly correlated, with the log-transformed regression model capturing nearly 88.42% of the variance. The clustering analysis identified three main groups of exoplanets, indicating natural groupings based on size and mass. The Tukey HSD test also highlighted how different detection methods preferentially identify exoplanets of varying masses.

4 - How are detected exoplanets distributed in the galaxy?

Known Exoplanets were found to be distributed in 3 major patterns:

  1. A spherical distribution centered on Earth with decreasing density as distance increases. The decrease in density is expected because of dimming due to the inverse square law. The spherical distribution is interesting as it, combined with point 2, implies that almost every star has at least one planet.
  2. A dense cone pointed in the direction of Cygnus constellation due to the Kepler Space Telescope. The density of exoplanets discovered by Kepler is impressive considering its detection method requires both the exoplanet’s orbital plane to be almost perfectly lined up with Earth and the exoplanet to pass in front of its star during the time Kepler was active.
  3. A sparse line of observations spanning to the center of the galaxy due mostly to gravitational microlensing observations. This is likely because there are a lot of stars rapidly orbiting the black hole at the center of the galaxy and these stars could be used as the back-end of the gravitational microlensing method without requiring the exoplanet (to be detected) to move as much as with the transit approach.

5 - What kinds of observations didn’t get position data resolved?

The data with unresolved position was mostly gravitational microlesing observations. Since this technique relies on a transient change in brightness of a reference star due to an object passing in front of it, it stands to reason that obtaining the position of the object might be harder. Or perhaps a different naming convention was used that didn’t get added to the Sesame Name Resolver database.

6 - How much has the Kepler Space Telescope impacted exoplanet data? 7 - How does Kepler’s Data differ from other sources?

The Kepler Space Telescope had a massive impact on the exoplanet data, being responsible for about half of all known exoplanets and most of the diversity in exoplanet type. Most of the data that is not from Kepler was from radial velocity, which has a strong bias to massive objects with short orbital periods. By using the transit method, the Kepler Space Telescope was not biased in the same way, but it likely still has some bias to short orbital periods, as these will be closer to their star and pass in front of them more often.

8 - Are there differences in exoplanet type distribution in systems with more than one exoplanet?

Interestingly no notable difference was found with multi-planet systems compared to single planet systems. This may be because if a system has one planet it is likely to have others.

5. References

  1. Gebru et al. (2018). “Datasheets for Datasets.” [arXiv:1803.09010](https://arxiv.org/abs/1803.09010)
  2. NASA Exoplanet Archive: <https://exoplanetarchive.ipac.caltech.edu>
  3. Sesame Name Resolver: <https://cds.unistra.fr/cgi-bin/Sesame>
  4. Jupiter/Earth Data: <https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html>
  5. Kepler Telescope Field of View: <https://d1jqu7g1y74ds1.cloudfront.net/wp-content/uploads/2013/04/kepler_field_of_view.png>
  6. Star Map of Milky Way: “By Kevin Jardine at galaxymap.org. See the README pdf at File:Map production details, Kevin Jardine (2022) for more details. - Main page: https://gruze.org/posters_dr3/Data sources and blog pages: http://galaxymap.org/drupal/node/265, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=139524709”