If H escape is assumed to be limited by its diffusion through the homopause

If h escape is assumed to be limited by its diffusion

This preview shows page 4 - 6 out of 48 pages.

If H escape is assumed to be limited by its diffusion through the homopause, which is the fastest possible escape rate per unit area ( φ (cm - 2 s - 1 )) at these concentrations, then φ = b H a f H 2 (4) Here, fH 2 is the total H 2 mixing ratio at the homopause (~2 × 10 - 3 for the moist greenhouse), H a is the atmospheric scale height, and b is a constant the describes how H 2 diffuses through a background atmosphere. For Earth, the quantity b/H a is ~3.3 × 10 13 given H a = 7.5 × 10 5 cm and assuming b = 2.5 × 10 19 cm - 2 s - 1 [ 23 ]. This yields an escape rate per unit area of ~6.6 × 10 10 molecules/cm 2 /s. The Earth’s surface area is ~5.1 × 10 18 cm 2 , resulting in an H escape rate of ~3.4 × 10 29 molecules/s. The mass of H 2 in Earth’s oceans is ~(1/9) × 1.4 × 10 21 kg or 1.56 × 10 20 kg (~4.7 × 10 46 molecules). Thus, it takes ~(4.7 × 10 46 /3.4 × 10 29 ) 1.4 × 10 17 s (~4.5 billion years) for all of the H molecules in Earth’s oceans to escape to space, as mentioned above. Planetary atmospheres with even higher non-condensable inventories than the Earth are diluted with respect to their water vapor concentrations, requiring that the moist greenhouse be triggered at even higher mean surface temperatures. The opposite is true for worlds with lower non-condensable inventories [ 1 , 24 ]. A more optimistic inner edge is located even closer to the star, commencing when the net absorbed stellar flux exceeds the net outgoing radiation at the top of the atmosphere, which triggers a rapid and uncontrollable runaway greenhouse that can desiccate the planet on shorter (~thousand to million year) timescales. In our solar system, this “runaway greenhouse limit” occurs at ~0.95 AU according to models (e.g., [ 25 ]). Previous work had suggested that the runaway greenhouse on a planet with an Earth-like surface water inventory occurs at the critical point for water (i.e., mean surface temperature
Image of page 4
Geosciences 2018 , 8 , 280 5 of 48 of 647 K and surface pressure above ~220 bars) [ 1 , 26 ]. However, recent calculations find that once the net absorbed solar flux exceeds the thermal infrared flux, radiative energy balance is no longer possible and the runaway greenhouse gets triggered at temperatures well below 400 K (e.g., [ 13 , 25 , 27 ]). Such temperatures are potentially consistent with suggested upper limits for life on Earth [ 11 ]. Again, on a planet with a smaller water inventory than our planet, the runaway greenhouse can be triggered at even lower surface temperatures (e.g., [ 1 ]). This is because less solar energy would be needed to devolatilize the surface. Nevertheless, the exact conditions under which a moist greenhouse may occur are currently under debate and further modeling will be needed. Leconte et al. [ 25 ] had found that the moist greenhouse is bypassed in atmospheres that become steadily warmer, immediately transitioning to the runaway greenhouse state instead (see below). In contrast, subsequent calculations find a moist greenhouse state before initiation of the full runaway [ 28 , 29 ].
Image of page 5
Image of page 6

You've reached the end of your free preview.

Want to read all 48 pages?

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes