Gravitational Influence from Planets on the Measured Rates of Period Change of Pulsating White Dwarfs

Abstract The measured rates of period change, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> , in the signals of pulsating white dwarf stars are often interpreted as direct detections of structural changes from secular cooling. Due to the intrinsic nature of this quantity, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> analysis has been used to probe fundamental physics, such as constraining the mass of hypothetical axion particles. However, most white dwarfs are expected to host planets that could induce an external source of period change, caused by the light travel time variations from reflex motion about the system barycenter. Assuming a plausible distribution of planets that could orbit white dwarf stars, we quantify the amount of reflex motion expected from undiscovered planets as an important source of extrinsic error in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> analyses. While the median error from reflex motion is ∼10 −15 s s −1 (similar to the secular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> rates expected for cool DAV pulsators), individual close-in planets could cause <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> errors as large as 10 −11 s s −1 .