Planets Across Space and Time (PAST). IV. The Occurrence and Architecture of Kepler Planetary Systems as a Function of Kinematic Age Revealed by the LAMOST–Gaia–Kepler Sample

Abstract

Abstract One of the fundamental questions in astronomy is how planetary systems form and evolve. Measuring the planetary occurrence and architecture as a function of time directly addresses this question. In the fourth paper of the Planets Across Space and Time series, we investigate the occurrence and architecture of Kepler planetary systems as a function of kinematic age by using the LAMOST–Gaia–Kepler sample. To isolate the age effect, other stellar properties (e.g., metallicity) have been controlled. We find the following results. (1) The fraction of stars with Kepler-like planets ( F Kep ) is about 50% for all stars; no significant trend is found between F Kep and age. (2) The average planet multiplicity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) exhibits a decreasing trend (∼2 σ significance) with age. It decreases from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:math> ∼ 3 for stars younger than 1 Gyr to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:math> ∼ 1.8 for stars of about 8 Gyr. (3) The number of planets per star ( η = F Kep × <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) also shows a decreasing trend (∼2 σ –3 σ significance). It decreases from η ∼ 1.6–1.7 for young stars to η ∼ 1.0 for old stars. (4) The mutual orbital inclination of the planets ( σ i , k ) increases from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>.°</mml:mo> </mml:mrow> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.4</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo>.°</mml:mo> </mml:mrow> <mml:msubsup> <mml:mrow> <mml:mn>5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>8.1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> as the stars age from 0.5 to 8 Gyr with a best fit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>0.4</mml:mn> <mml:mo>×</mml:mo> <mml:mi>log</mml:mi> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:mi>Age</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>Gyr</mml:mi> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:math> . Interestingly, the solar system also fits such a trend. The fact that F Kep remains relatively constant at approximately ∼ 50% across different ages suggests the robustness of planet for

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