Nonparametric Prediction and the Exoplanet Mass-Radius Relationship Bo Ning 1 with Angie Wolfgang 2 , 3 and Sujit Ghosh 1 , 4 1 North Carolina State University 2 Pennsylvania State University 3 NSF Astronomy & Astrophysics Postdoctoral Fellow 4 Statistical and Applied Mathematical Sciences Institute May 8, 2017
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Collaborators Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 2
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Outline Background 1 Model 2 Estimating Mass-Radius Relations 3 4 Future work Concluding remarks 5 Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 3
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Section 1 Background 1 Model 2 3 Estimating Mass-Radius Relations Future work 4 Concluding remarks 5 Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 4
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Introduction Since 1992, astronomers have discovered thousands of exoplanets Mass or Radius can be measured for those discovered exoplanets Measuring Mass and Radius is important because they tell us about the planets’ compositions. Measuring mass: radial velocity Measuring radius: transits Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 5
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Introduction Since 1992, astronomers have discovered thousands of exoplanets Mass or Radius can be measured for those discovered exoplanets Measuring Mass and Radius is important because they tell us about the planets’ compositions. Measuring mass: radial velocity Measuring radius: transits Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 5
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Introduction Since 1992, astronomers have discovered thousands of exoplanets Mass or Radius can be measured for those discovered exoplanets Measuring Mass and Radius is important because they tell us about the planets’ compositions. Measuring mass: radial velocity Measuring radius: transits Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 5
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Introduction Since 1992, astronomers have discovered thousands of exoplanets Mass or Radius can be measured for those discovered exoplanets Measuring Mass and Radius is important because they tell us about the planets’ compositions. Measuring mass: radial velocity Measuring radius: transits Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 5
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Introduction Since 1992, astronomers have discovered thousands of exoplanets Mass or Radius can be measured for those discovered exoplanets Measuring Mass and Radius is important because they tell us about the planets’ compositions. Measuring mass: radial velocity Measuring radius: transits Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 5
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Measuring mass and radius Photo credit: Leslie Rogers Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 6
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Kepler planet candidates Photo credit: Angie Wolfgang Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 7
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Goal Most planets only have either a mass or a radius measurement, very few have both Measurements for planets radius are more precise Goal: To create a statistical tool for predicting planets mass given their radii. Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 8
Background Model Estimating Mass-Radius Relations Future work Concluding remarks Section 2 Background 1 Model 2 3 Estimating Mass-Radius Relations Future work 4 Concluding remarks 5 Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 9
Background Model Estimating Mass-Radius Relations Future work Concluding remarks A hierarchical Bayesian power-law model HBM [Wolfgang, Rogers and Ford, 2016]: M obs ∼ N ( M i , σ obs M , i ) , i R obs ∼ N ( R i , σ obs R , i ) , i M i | R i , C , γ, σ M ∼ N ( CR γ i , σ M ) M i is the planet mass divided by the Earth’s mass, R i is the planet radius divided by the Earth’s radius. RV only < 4 R ⊕ : M i | R i ∼ N ( 2 . 7 R 1 . 3 , 1 . 9 ) i RV only < 8 R ⊕ : M i | R i ∼ N ( 1 . 6 R 1 . 8 , 2 . 9 ) ( Data: NASA Exoplanet Archive ) i Why is intrinsic scatter normally distributed? Why is intrinsic scatter a constant, not σ M ( R i ) ? � σ 2 σ = M + β ( R i − 1 ) [WRF16] Why use a power law? Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 10
Background Model Estimating Mass-Radius Relations Future work Concluding remarks A hierarchical Bayesian power-law model HBM [Wolfgang, Rogers and Ford, 2016]: M obs ∼ N ( M i , σ obs M , i ) , i R obs ∼ N ( R i , σ obs R , i ) , i M i | R i , C , γ, σ M ∼ N ( CR γ i , σ M ) M i is the planet mass divided by the Earth’s mass, R i is the planet radius divided by the Earth’s radius. RV only < 4 R ⊕ : M i | R i ∼ N ( 2 . 7 R 1 . 3 , 1 . 9 ) i RV only < 8 R ⊕ : M i | R i ∼ N ( 1 . 6 R 1 . 8 , 2 . 9 ) ( Data: NASA Exoplanet Archive ) i Why is intrinsic scatter normally distributed? Why is intrinsic scatter a constant, not σ M ( R i ) ? � σ 2 σ = M + β ( R i − 1 ) [WRF16] Why use a power law? Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 10
Background Model Estimating Mass-Radius Relations Future work Concluding remarks A hierarchical Bayesian power-law model HBM [Wolfgang, Rogers and Ford, 2016]: M obs ∼ N ( M i , σ obs M , i ) , i R obs ∼ N ( R i , σ obs R , i ) , i M i | R i , C , γ, σ M ∼ N ( CR γ i , σ M ) M i is the planet mass divided by the Earth’s mass, R i is the planet radius divided by the Earth’s radius. RV only < 4 R ⊕ : M i | R i ∼ N ( 2 . 7 R 1 . 3 , 1 . 9 ) i RV only < 8 R ⊕ : M i | R i ∼ N ( 1 . 6 R 1 . 8 , 2 . 9 ) ( Data: NASA Exoplanet Archive ) i Why is intrinsic scatter normally distributed? Why is intrinsic scatter a constant, not σ M ( R i ) ? � σ 2 σ = M + β ( R i − 1 ) [WRF16] Why use a power law? Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 10
Background Model Estimating Mass-Radius Relations Future work Concluding remarks A hierarchical Bayesian power-law model HBM [Wolfgang, Rogers and Ford, 2016]: M obs ∼ N ( M i , σ obs M , i ) , i R obs ∼ N ( R i , σ obs R , i ) , i M i | R i , C , γ, σ M ∼ N ( CR γ i , σ M ) M i is the planet mass divided by the Earth’s mass, R i is the planet radius divided by the Earth’s radius. RV only < 4 R ⊕ : M i | R i ∼ N ( 2 . 7 R 1 . 3 , 1 . 9 ) i RV only < 8 R ⊕ : M i | R i ∼ N ( 1 . 6 R 1 . 8 , 2 . 9 ) ( Data: NASA Exoplanet Archive ) i Why is intrinsic scatter normally distributed? Why is intrinsic scatter a constant, not σ M ( R i ) ? � σ 2 σ = M + β ( R i − 1 ) [WRF16] Why use a power law? Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 10
Background Model Estimating Mass-Radius Relations Future work Concluding remarks A hierarchical Bayesian power-law model HBM [Wolfgang, Rogers and Ford, 2016]: M obs ∼ N ( M i , σ obs M , i ) , i R obs ∼ N ( R i , σ obs R , i ) , i M i | R i , C , γ, σ M ∼ N ( CR γ i , σ M ) M i is the planet mass divided by the Earth’s mass, R i is the planet radius divided by the Earth’s radius. RV only < 4 R ⊕ : M i | R i ∼ N ( 2 . 7 R 1 . 3 , 1 . 9 ) i RV only < 8 R ⊕ : M i | R i ∼ N ( 1 . 6 R 1 . 8 , 2 . 9 ) ( Data: NASA Exoplanet Archive ) i Why is intrinsic scatter normally distributed? Why is intrinsic scatter a constant, not σ M ( R i ) ? � σ 2 σ = M + β ( R i − 1 ) [WRF16] Why use a power law? Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 10
Background Model Estimating Mass-Radius Relations Future work Concluding remarks A hierarchical Bayesian power-law model HBM [Wolfgang, Rogers and Ford, 2016]: M obs ∼ N ( M i , σ obs M , i ) , i R obs ∼ N ( R i , σ obs R , i ) , i M i | R i , C , γ, σ M ∼ N ( CR γ i , σ M ) M i is the planet mass divided by the Earth’s mass, R i is the planet radius divided by the Earth’s radius. RV only < 4 R ⊕ : M i | R i ∼ N ( 2 . 7 R 1 . 3 , 1 . 9 ) i RV only < 8 R ⊕ : M i | R i ∼ N ( 1 . 6 R 1 . 8 , 2 . 9 ) ( Data: NASA Exoplanet Archive ) i Why is intrinsic scatter normally distributed? Why is intrinsic scatter a constant, not σ M ( R i ) ? � σ 2 σ = M + β ( R i − 1 ) [WRF16] Why use a power law? Bo Ning — Nonparametric Prediction and the Exoplanet Mass-Radius Relationship 10
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