Revisiting the HIP41378 system with K2 and Spitzer

We present new observations of the multi-planet system HIP~41378, a bright star ($V$ = 8.9, $K_s$ = 7.7) with five known transiting planets. Observations in Campaign 5 of the K2 mission showed multiple transits of two Neptune-sized bodies and single transits of three larger planets ($R_P= 0.33R_J, 0.47R_J, 0.88 R_J$). K2 recently observed the system again in Campaign 18. We observe one new transit each of two of the larger planets, HIP41378~d and~f, giving maximal possible orbital periods of 1114 and 1084 days, respectively. Other possible periods include integer divisions of these maximum values down to a lower limit of about 50 days. We use all available photometry to determine the eccentricity distributions of HIP41378~d \& f, finding that periods $\lesssim$300 days require non-zero eccentricity. We also perform a stability analysis on the orbits of planets d and f to assess the likelihood of their different possible periods, finding that short periods (P $<$ 300 days) are disfavored. In addition, we observe transits of the inner two planets b and c with Spitzer/IRAC, which we combine with the new K2 observations of these planets to search for transit timing variations (TTVs). We find a linear ephemeris for planet b, but see a significant TTV signal for planet c that could be induced by planet d, e, or f. The ability to recover the two smaller planets with Spitzer shows that the several planets in this fascinating system will continue to be detectable with Spitzer, CHEOPS, TESS, and other observatories. This will allow us to precisely determine the periods of d and f, characterize the TTVs of planet~c, recover the transits of planet~e, and further enhance our view of this remarkable dynamical laboratory.