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Lyman-$\alpha$ transits have been detected from several nearby exoplanets and are one of our best insights into the atmospheric escape process. However, due to ISM absorption, we typically only observe the transit signature in the blue-wing, making them challenging to interpret. This challenge has been recently highlighted by non-detections from planets thought to be undergoing vigorous escape. Pioneering 3D simulations have shown that escaping hydrogen is shaped into a cometary tail receding from the planet. Motivated by this work, we develop a simple model to interpret Lyman-$\alpha$ transits. Using this framework, we show that the Lyman-$\alpha$ transit depth is primarily controlled by the properties of the stellar tidal field rather than details of the escape process. Instead, the transit duration provides a direct measurement of the velocity of the planetary outflow. This result arises because the underlying physics is the distance a neutral hydrogen atom can travel before it is photoionized in the outflow. Thus, higher irradiation levels, expected to drive more powerful outflows, produce weaker, shorter Lyman-$\alpha$ transits because the outflowing gas is ionized more quickly. Our framework suggests that the generation of energetic neutral atoms may dominate the transit signature early, but the acceleration of planetary material produces long tails. Thus, Lyman-$\alpha$ transits do not primarily probe the mass-loss rates. Instead, they inform us about the velocity at which the escape mechanism is ejecting material from the planet, providing a clean test of predictions from atmospheric escape models., Comment: Accepted for publication in MNRAS

(abridged) We present an analysis of high resolution optical spectra for a sample of very young, mid- to late M, low-mass stellar and substellar objects in Upper Sco and Taurus. Effective temperatures (T_eff) and surface gravities are derived from a multi-feature spectral analysis using TiO, NaI and KI, through comparison with the latest synthetic spectra. In combination, they allow us to determine T_eff to within 50K and gravity to within 0.25 dex. Our high-resolution analysis does not require extinction estimates. Moroever, it yields T_eff and gravities independent of theoretical evolutionary models. We find that our gravities for most of the sample agree remarkably well with the isochrone predictions for the likely cluster ages. However, discrepancies appear in our coolest targets: these appear to have significantly lower gravity (by up to 0.75 dex) than our hotter objects, even though our entire sample covers a relatively narrow range in T_eff (about 300K). This drop in gravity is also implied by inter-comparisons of the data alone, without recourse to synthetic spectra. We consider, and argue against, dust opacity, cool stellar spots or metallicity differences leading to the observed spectral effects; a real decline in gravity is strongly indicated. Such gravity variations are contrary to the predictions of the evolutionary tracks, causing improbably low ages to be inferred from the tracks for our coolest targets. We venture that these results may arise from evolutionary model uncertainties related to accretion, deuterium-burning and/or convection effects. Finally, when combined with photometry and distances, our technique for deriving gravities and temperatures provides a way of obtaining masses and radii for substellar objects independent of evolutionary models, as presented in Paper II., 74 pages, incl. 11 figures, accepted ApJ

Young stars surrounded by disks with very low mass accretion rates are likely in the final stages of inner disk evolution and therefore particularly interesting to study. We present ultraviolet (UV) observations of the ~5-9 Myr old stars RECX-1 and RECX-11, obtained with the Cosmic Origins Spectrograph and Space Telescope Imaging Spectrograph on the Hubble Space Telescope, as well as optical and near-infrared spectroscopic observations. The two stars have similar levels of near-UV emission, although spectroscopic evidence indicates that RECX-11 is accreting and RECX-1 is not. The line profiles of Hα and He I λ10830 in RECX-11 show both broad and narrow redshifted absorption components that vary with time, revealing the complexity of the accretion flows. We show that accretion indicators commonly used to measure mass accretion rates, e.g., U-band excess luminosity or the Ca II triplet line luminosity, are unreliable for low accretors, at least in the middle K spectral range. Using RECX-1 as a template for the intrinsic level of photospheric and chromospheric emission, we determine an upper limit of 3 × 10^(–10) M_☉ yr–1 for RECX-11. At this low accretion rate, recent photoevaporation models predict that an inner hole should have developed in the disk. However, the spectral energy distribution of RECX-11 shows fluxes comparable to the median of Taurus in the near-infrared, indicating that substantial dust remains. Fluorescent H2 emission lines formed in the innermost disk are observed in RECX-11, showing that gas is present in the inner disk, along with the dust.