Saturday, November 09, 2013

Earth size planets and MaxHELP

Back from a flying visit to San Francisco and LA. Stayed with one of our dearest and most delightful friends who lives in Silicon Valley, then to LA for meetings and back (on an A380 - excellent) for a dinner party for 12 at home - the oldest guest was 50 years older than the youngest and it was a terrific evening, but I'm glad I was on LA time not Beijing!

Fig 1 from Petugura et al, showing observed planets
and calculated survey completeness.
Just before I left on Mon news broke of Petigura et al's PNAS paper "Prevalence of Earth-size planets orbiting Sun-like stars"  This suggests that the fraction of Sun-like stars which harbor an Earth-size planet with orbital periods of 200–400 days is about 6%. They also make somewhat more speculative arguments for a 22% occurrence rate of Earth-size planets in habitable zones of Sun-like stars.

Of course an earth-sized planet with a reasonable level of energy flux doesn't make it a Habitable Earth-like Planet within my definition, since we need sufficient stability (amongst other things) which almost certainly requires a Jupiter-style planet and a Moon-sized moon. Petigura et al suggest that only 1.6 ± 0.4% of Sun-like stars harbour a Jupiter-size (8− 16 R⊕) planet with P = 5–100 d and given that there seems to be a log-linear distribution of orbital period. Jupiter has an orbital period of over 4,000d and if we assume that the Jupiter-sized planet needs to have an orbital period of say 500-10,000 d in order to induce the necessary stability then perhaps about 0.2% of these stars will have Jupiters. And no-one quite knows how the Earth got such a large moon let alone what the prevalence was. Nevertheless it is at least suggestive of support for MaxHELP.

I sent a short email to Don Page and Martin Rees and this triggered a fascinating series of emails between them with additional contributions from Bill Unruh and Andrei Linde.  I need to reflect on these fascinating ideas.

I did need to point out respectfully that my hypothesis relates to Habitable Earth-like planets. I suggested that this might entail:
  1. stable average temperatures somewhere between say 280-350K
  2. Not too much ionising radiation or
  3. bombardment by large meteors
  4. M/MEarth greater than 0.1 and stability for at least (say) 2bnYr, and
  5. an abundance of key elements (esp H,O,C,N) within a factor of 2 of their observed values.
I suspect that (3) may require a Jupiter-sized planet with a relatively long orbital period, an a large enough Moon. This makes the hypothesis a bit less falsifiable than simply counting Earth-like planets in the sense of Petigura et al.

I agree of course that the hypothesis may well be false but I hope it is sufficiently interesting to warrant further investigation. Certainly if we knew enough to calculate the partial derivatives of E[HELP] wrt each of the fundamental parameters we would know an enormous amount about solar system formation than we do at present!

Maybe by 2015 there would be some point in having a seminar to explore this? In the meantime much would be learned from any comments they can give.

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