Although traditional definitions of the habitable zone assume that carbon dioxide and water vapor are the most important greenhouse gases (as they are on the Earth), a study led by Ramses Ramirez and co-author Lisa Kaltenegger has shown that the size of the habitable zone is greatly increased if prodigious volcanic outgassing of hydrogen is also included along with the carbon dioxide and water vapor. The outer edge in the Solar System would extend out as far as 2.4 AU in that case. Similar increases in the size of the habitable zone were computed for other stellar systems. An earlier study by Ray Pierrehumbert and Eric Gaidos had eliminated the CO2-H2O concept entirely, arguing that young planets could accrete many tens to hundreds of bars of hydrogen from the protoplanetary disc, providing enough of a greenhouse effect to extend the solar system outer edge to 10 AU. In this case, though, the hydrogen is not continuously replenished by volcanism and is lost within millions to tens-of-millions of years.