The β Pictoris b Hill Sphere Transit Campaign II. Searching for the signatures of the β Pictoris exoplanets through time delay analysis of the δ Scuti pulsations

Context. The β Pictoris system is the closest known stellar system with directly imaged gas giant planets, with the inner planet, β Pictoris c also indirectly detected with radial velocity, an edge-on circumstellar disk, and evidence for falling evaporating bodies and transiting exocomets. The star is a known δ 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 these pulsations due to a varying light travel time. Aims. We search for phase shifts in the δ Scuti pulsations consistent with the known planets β Pictoris b and c and carry out an analysis of the stellar pulsations within β Pictoris over a multi-year timescale. Methods. We use the photometric data collected by the BRITE-Constellation, bRing, ASTEP and TESS to derive a list of the strongest significant δ Scuti pulsations. We carry out an analysis with the open-source python package maelstrom to study the stability of the pulsational modes of β Pictoris to determine the long term trends in the pulsations seen. Results. We do not detect the expected signal for β Pictoris b or β Pictoris c. The expected time delay is 6 seconds for β Pictoris c and 24 seconds for β Pictoris b. In the absence of systematic drifts of pulsational modes in the star, our combined sensitivity is SZ: XXX seconds. CHECK With simulations we determine that the photometric noise in all the combined data sets cannot reach the sensitivity needed to detect the expected timing drift. An analysis of the pulsational modes of β Pictoris using maelstrom shows that the modes themselves drift on a timescale of a year, fundamentally limiting our ability to detect exoplanets around β Pictoris using the pulsation drift technique.