TOI-1416: A system with a super-Earth planet with a 1.07d period

TOI 1416 (BD+42 2504, HIP 70705) is a V=10 late G or early K-type dwarf star with transits detected by TESS. Radial velocities verify the presence of the transiting planet TOI-1416 b, with a period of 1.07d, a mass of $3.48 M_{Earth}$ and a radius of $1.62 R_{Earth}$, implying a slightly sub-Earth density of $4.50$ g cm$^{-3}$. The RV data also further indicate a tentative planet c with a period of 27.4 or 29.5 days, whose nature cannot be verified due to strong suspicions about contamination by a signal related to the Moon's synodic period of 29.53 days. The near-USP (Ultra Short Period) planet TOI-1416 b is a typical representative of a short-period and hot ($T_{eq} \approx$ 1570 K) super-Earth like planet. A planet model of an interior of molten magma containing a significant fraction of dissolved water provides a plausible explanation for its composition, and its atmosphere could be suitable for transmission spectroscopy with JWST. The position of TOI-1416 b within the radius-period distribution corroborates that USPs with periods of less than one day do not form any special group of planets. Rather, this implies that USPs belong to a continuous distribution of super-Earth like planets with periods ranging from the shortest known ones up to ~ 30 days, whose period-radius distribution is delimitated against larger radii by the Neptune desert and by the period-radius valley that separates super-Earths from sub-Neptune planets. In the abundance of small-short periodic planets against period, a plateau between periods of 0.6 to 1.4 days has however become notable that is compatible with the low-eccentricity formation channel. For the Neptune desert, its lower limits required a revision due to the increasing population of short period planets and new limits are provided. These limits are also given in terms of the planets' insolation and effective temperatures.