Improved Constraints for the XUV Luminosity Evolution of Trappist-1
Jessica Birky, Rory Barnes, David P. Fleming
Abstract
Abstract We re-examine the XUV luminosity evolution of TRAPPIST-1 utilizing new observational constraints (XUV and bolometric luminosity) from multi-epoch X-ray/UV photometry. Following the formalism presented in Fleming et al., we infer that TRAPPIST-1 maintained a saturated XUV luminosity, relative to the bolometric luminosity, of log 10 ( L XUV / L bol ) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>3.03</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.23</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.25</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> at early times for a period of t sat <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>3.14</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.46</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>2.22</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> Gyr. After the saturation phase, we find L XUV decayed over time by an exponential rate of β XUV <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.17</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.28</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.27</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . Compared to our inferred age of the system, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>age</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>7.96</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.87</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.78</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> Gyr, our result for t sat suggests that there is only a ∼4% chance that TRAPPIST-1 still remains in the saturated phase today, which is significantly lower than the previous estimate of 40%. Despite this reduction in t sat , our results remain consistent in the conclusion that the TRAPPIST-1 planets likely received an extreme amount XUV energy—an estimated integrated XUV energy of ∼10 30 –10 32 erg over the star’s lifetime.