tokens: from the singlet ground state (1 1 S) because radiative transitions between them are strongly suppressed. Due to relativistic and finite-wavelength corrections to the magnetic dipole transition formula, the 2 3 S triplet helium can radiatively decay into the singlet ground state with an exceptionally long lifetime of 2.2 hr (Drake 1971 ). The 2 3 S state can be populated by recombination 4 4 Around 75% of helium recombinations result in the triplet configuration (Osterbrock Ferland 2006 ). or by collisional excitation from the ground state (see Figure 1 ). Depopulation of this state progresses slowly making it metastable, and hence a promising origin of absorption lines. The resonance scattering from the metastable state to the 2 3 P state produces an absorption line at 10830 Å. This transition consists of three lines, two of which—at 10830.34 Å and 10830.25 Å—are practically indistinguishable, whereas the third component is at 10829.09 Å. Figure 1. Atomic structure of the helium atom, indicating the radiative and collisional transitions included in our analysis. The transition shown in red depicts the 10830 Å absorption line. The helium 10830 Å line has been used to probe the dynamics of stellar winds (e.g., Dupree et al. 1992 ; Edwards et al. 2003 ) and outflows from active galactic nuclei (e.g., Leighly et al. 2011 ), as well as the structure of the solar chromosphere and transition region (Avrett et al. 1994 ; Andretta Jones 1997 ; Mauas et al. 2005 ). Even though this line has been identified as one of the most promising spectral signatures of exoplanet atmospheres (Seager Sasselov 2000 ), no firm detections have been reported thus far (see, e.g., Moutou et al. 2003 ). Most previous models of escaping atmospheres have focused on hydrogen or tracked helium only in terms of neutrals and ions, without modeling the metastable state. Turner et al. ( 2016 ) used cloudy to compile a list of ∼60 potentially interesting absorption lines for probing upper exoplanet atmospheres, including the 10830 Å line. 3. Methods and Results 3.1. Isothermal Parker Wind Our model is based on the assumption that upper layers of a hydrodynamically escaping atmosphere can be described by an isothermal Parker wind driven by gas pressure (Parker 1958 ; Watson et al. 1981 ). Winds in which heating and cooling are due to radiative processes are close to being isothermal (Lamers Cassinelli 1999 ). If the radiative heating/cooling processes operate on short timescales compared to the dynamical time of the system, the gas can self-regulate at a constant temperature. A time-independent and spherically symmetric wind has a constant mass-loss rate determined by the equation of mass conservation:For an isothermal wind, the energy equation iswhereas the momentum equation is given byWe ignore the gravitational influence of the star and the Coriolis force. The momentum equation has a singularity at the so-called critical point, which in our case coincides with the sonic point,
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O