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RE: Red dwarf Exoplanets
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NASA Finds Planets of Red Dwarf Stars May Face Oxygen Loss in Habitable Zones

The search for life beyond Earth starts in habitable zones, the regions around stars where conditions could potentially allow liquid water - which is essential for life as we know it - to pool on a planet's surface. New NASA research suggests some of these zones might not actually be able to support life due to frequent stellar eruptions - which spew huge amounts of stellar material and radiation out into space - from young red dwarf stars.
Now, an interdisciplinary team of NASA scientists wants to expand how habitable zones are defined, taking into account the impact of stellar activity, which can threaten an exoplanet's atmosphere with oxygen loss.

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Every red dwarf star has at least one planet

Three new planets classified as habitable-zone super-Earths are amongst eight new planets discovered orbiting nearby red dwarf stars by an international team of astronomers from the UK and Chile. The study identifies that virtually all red dwarfs, which make up at least three quarters of the stars in the Universe, have planets orbiting them.
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Small Star Exoplanets
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Title: The Occurrence Rate of Small Planets around Small Stars
Authors: Courtney D. Dressing, David Charbonneau

We use the optical and near-infrared photometry from the Kepler Input Catalogue to provide improved estimates of the stellar characteristics of the smallest stars in the Kepler target list. We find 3897 dwarfs with temperatures below 4000K, including 64 planet candidate host stars orbited by 95 transiting planet candidates. We refit the transit events in the Kepler light curves for these planet candidates and combine the revised planet/star radius ratios with our improved stellar radii to revise the radii of the planet candidates orbiting the cool target stars. We then compare the number of observed planet candidates to the number of stars around which such planets could have been detected in order to estimate the planet occurrence rate around cool stars. We find that the occurrence rate of 0.5-4 Earth radius planets with orbital periods shorter than 50 days is 0.86 (+0.04/-0.03) planets per star. The occurrence rate of Earth-size (0.5-1.4 Earth radius) planets is constant across the temperature range of our sample at 0.47 (+0.06/-0.05) Earth-size planets per star, but the occurrence of 1.4-4 Earth radius planets decreases significantly at cooler temperatures. Our sample includes 2 Earth-size planet candidates in the habitable zone, allowing us to estimate that the mean number of Earth-size planets in the habitable zone is 0.06 (+0.06/-0.03) planets per cool star. Our 95% confidence lower limit on the occurrence rate of Earth-size planets in the habitable zones of cool stars is 0.015 planets per star. With 95% confidence, the nearest transiting Earth-size planet in the habitable zone of a cool star is within 29 pc. Moreover, the nearest non-transiting planet in the habitable zone is within 7 pc with 95% confidence.

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Red dwarf Exoplanets
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Exoplanets near red dwarfs suggest another Earth nearer

The nearest habitable, Earth-sized planet could be just 13 light-years away, research suggests.
An analysis of small, dim "red dwarf" stars - which make up a majority of stars in our galaxy - shows that 6% of them host such a planet.
The results will appear in Astrophysical Journal.
 
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