The $\beta$ Pictoris b Hill sphere transit campaign. Paper II: Searching for the signatures of the $\beta$ Pictoris exoplanets through time delay analysis of the $\delta$ Scuti pulsations

TL;DR

This study investigates the potential to detect exoplanets around $eta$ Pictoris by analyzing pulsation phase shifts in its $ ext{delta}$ Scuti stars, but finds current data sensitivity insufficient for detection.

Contribution

It demonstrates the limitations of using long-term pulsation stability for exoplanet detection in $eta$ Pictoris with existing photometric data.

Findings

No detection of expected time delays for $eta$ Pictoris b and c.

Photometric noise prevents detection of predicted timing drifts.

Pulsation modes drift on a yearly timescale, hindering exoplanet detection.

Abstract

The $\beta$ Pictoris system is the closest known stellar system with directly detected gas giant planets, an edge-on circumstellar disc, and evidence of falling sublimating bodies and transiting exocomets. The inner planet, $\beta$ Pictoris c, has also been indirectly detected with radial velocity (RV) measurements. The star is a known $\delta$ Scuti pulsator, and the long-term stability of these pulsations opens up the possibility of indirectly detecting the gas giant planets through time delays of the pulsations due to a varying light travel time. We search for phase shifts in the $\delta$ Scuti pulsations consistent with the known planets $\beta$ Pictoris b and c and carry out an analysis of the stellar pulsations of $\beta$ Pictoris over a multi-year timescale. We used photometric data collected by the BRITE-Constellation, bRing, ASTEP, and TESS to derive a list of the strongest and most significant $\delta$ Scuti pulsations. We carried out an analysis with the open-source python package maelstrom to study the stability of the pulsation modes of $\beta$ Pictoris in order to determine the long-term trends in the observed pulsations. We did not detect the expected signal for $\beta$ Pictoris b or $\beta$ Pictoris c. The expected time delay is 6 seconds for $\beta$ Pictoris c and 24 seconds for $\beta$ Pictoris b. With simulations, we determined that the photometric noise in all the combined data sets cannot reach the sensitivity needed to detect the expected timing drifts. An analysis of the pulsational modes of $\beta$ Pictoris using maelstrom showed that the modes themselves drift on the timescale of a year, fundamentally limiting our ability to detect exoplanets around $\beta$ Pictoris via pulsation timing.