Occurrence and core-envelope structure of 1-4× Earth-size planets around Sun-like stars

Small planets, 1-4× the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R_⊕ planets with orbital periods under 100 d, and 11% have 1-2 R_⊕ planets that receive 1-4× the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 the Earth-Sun distance, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R_⊕ show that the smallest of them, R < 1.5 R_⊕, have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: <mml:math id="i1"><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>=</mml:mo><mml:mn>2.32</mml:mn><mml:mo>+</mml:mo><mml:mrow><mml:mrow><mml:mn>3.19</mml:mn><mml:mi>R</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mo>⊕</mml:mo></mml:msub></mml:mrow></mml:mrow><mml:mo> </mml:mo><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">g cm</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math>. Larger planets, in the radius range 1.5-4.0 R_⊕, have densities that decline with increasing radius, revealing increasing amounts of low-density material (H and He or ices) in an envelope surrounding a rocky core, befitting the appellation ''mini-Neptunes.'' The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of life's biochemical origins.