transit valuations
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Discoveries relating to transiting extrasolar planets often make the news. This is in keeping both with the wide public interest in extrasolar planets, as well as the effectiveness of the media-relations arms of the agencies, organizations, and universities that facilitate research on planets. I therefore think that funding support for research into extrasolar planets in general, and transiting planets in particular, is likely to be maintained, even in the face of budget cuts in other areas of astronomy and physics. There’s an article in Saturday’s New York Times which talks about impending layoffs at Fermilab, where the yearly budget has just been cut from $342 million to $320 million. It’s often not easy to evaluate how much a particular scientific result is “worth” in terms of a dollar price tag paid by the public, and Sean Carroll over at Cosmic Variance has a good post on this topic.
For the past two years, the comments sections for my oklo.org posts have presented a rather staid, low-traffic forum of discussion. That suddenly changed with Thursday’s post. The discussion suddenly heated up, with some of the readers suggesting that the CoRoT press releases are hyped up in relation to the importance of their underlying scientific announcements.
How much, actually, do transit discoveries cost? Overall, of order a billion dollars has been committed to transit detection, with most of this money going to CoRoT and Kepler. If we ignore the two spacecraft and look at the planets found to date, then this sum drops to something like 25 million dollars. (Feel free to weigh in with your own estimate and your pricing logic if you think this is off base.)
The relative value of a transit depends on a number of factors. After some revisions and typos (see comment section for this post) I’m suggesting the following valuation formula for the cost, C, of a transit:
The terms here are slightly subjective, but I think that the overall multiplicative effect comes pretty close to the truth.
The normalization factor of 580 million out front allows the total value of transits discovered to date to sum to 25 million dollars. The exponential term gives weight to early discoveries. It’s a simple fact that were HD 209458 b discovered today, nobody would party like its 1999 — I’ve accounted for this with an e-folding time of 5 years in the valuation.
Bright transits are better. Each magnitude in V means a factor of 2.5x more photons. My initial inclination was to make transit value proportional to stellar flux (and I still think this is a reasonable metric). The effect on the dimmer stars, though was simply overwhelming. Of order 6 million dollars worth of HST time was spent to find the SWEEPS transits, and with transit value proportional to stellar flux, this assigned a value of two dollars to SWEEPS-11. That seems a little harsh. Also, noise goes as root N.
Longer period transits are much harder to detect, and hence more valuable. Pushing into the habitable zone also seems like the direction that people are interested in going, and so I’ve assigned value in proportion to the square root of the orbital period. (One could alternately drop the square root.)
Eccentricity is a good thing. Planets on eccentric orbits can’t be stuck in synchronous rotation, and so their atmospheric dynamics, and the opportunities they present for interesting follow-up studies make them worth more when they transit.
Less massive planets are certainly better. I’ve assigned value in inverse proportion to mass.
Finally, small stars are better. A small star means a larger transit depth for a planet of given size, which is undeniably valuable. I’ve assigned value in proportion to transit depth, and I’ve also added a term, Np^2, that accounts for the fact that a transiting planet in a multiple-planet system is much sought-after. Np is the number of known planets in the system. Here are the results:
| Planet | Value |
| CoRoT-Exo-1 b | $86,472 |
| CoRoT-Exo-2 b | $53,274 |
| Gliese 436 b | $4,356,408 |
| HAT-P-1 b | $969,483 |
| HAT-P-2 b | $85,507 |
| HAT-P-3 b | $285,768 |
| HAT-P-4 b | $189,636 |
| HAT-P-5 b | $146,178 |
| HAT-P-6 b | $245,873 |
| HD 149026 b | $792,760 |
| HD 17156 b | $953,665 |
| HD 189733 b | $2,665,371 |
| HD 209458 b | $11,084,661 |
| Lupus TR 3 b | $19,186 |
| OGLE TR 10 b | $66,112 |
| OGLE TR 111 b | $81,761 |
| OGLE TR 113 b | $40,153 |
| OGLE TR 132 b | $13,523 |
| OGLE TR 182 b | $16,743 |
| OGLE TR 211 b | $20,465 |
| OGLE TR 56 b | $21,680 |
| SWEEPS 04 | $2,004 |
| SWEEPS 11 | $211 |
| TrES-1 | $610,330 |
| TrES-2 | $124,021 |
| TrES-3 | $102,051 |
| TrES-4 | $225,464 |
| WASP-1 | $209,041 |
| WASP-2 | $207,305 |
| WASP-3 | $115,508 |
| WASP-4 | $114,737 |
| WASP-5 | $72,328 |
| XO-1 | $478,924 |
| XO-2 | $506,778 |
| XO-3 | $36,607 |
HD 209458 b is the big winner, as well it should be. The discovery papers for this planet are scoring hundreds of citations per year. It essentially launched the whole field. The STIS lightcurve is an absolute classic. Also highly valued are Gliese 436b, and HD 189733b. No arguing with those calls.
Only two planets seem obviously mispriced. Surely, it can’t be true that HAT-P-1 b is 10 times more valuable than HAT-P-2b? I’d gladly pay $85,507 for HAT-P-2b, and I’d happily sell HAT-P-1b for $969,483 and invest the proceeds in the John Deere and Apple Computer corporations.
Jocularity aside, a possible conclusion is that you should detect your transits from the ground and do your follow up from space — at least until you get down to R<2 Earth radii. At that point, I think a different formula applies.
Note: I see that the XO planets somehow didn’t make the list! I’ll add them, re-run the code shortly, and correct for this oversight. They’ll likely be similar to the WASPs in value. Also, “V” on the left is the value, and “V” on the right is V-magnitude. I’ll also fix this notation oversight shortly…
I wouldn’t write off space-based transit detection so quickly. CoRoT still has at least three years to pay for itself, and you’d expect it to report more valuable (longer period) planets later in its mission.
I’m not writing off space-based detection. I just didn’t think it was fair to include the cost of the space missions in the formula because, as you say, the majority of their results are still to come. It’ll be interesting to revisit this analysis after Kepler and CoRoT are completed. (On re-reading what I wrote, I’ve edited the last paragraph of the post to put it more in line with the point I wanted to make).
Again by the COROT mission statement their sensitivity is optimized to long period planets of a maximum of 50 days! Closer than Mercury is to the sun.
It is pretty clear they are not optimized for the detection of rocky planets yet their recent statements completely ignore this. To wit..
“CoRoT is discovering exo-planets at a rate only set by the available resources to follow up the detections” (2/11/2007) This is simply not true. The rate of discovery is severely constrained by the design of the instruments. Why not make this clear.
Or
“The data of the first exoplanet discovered by Corot (Corot-Exo-1b) has a precision of 3 parts in 10 000 (3 x 10-4) for one
hour observation. This means that when all the corrections are applied to the light-curves, photometry at the level of 1
part in 20 000 will be reached (5x 10-5). The precision can even reach 1 part in 50 000 (2 x10-5) if the number of the
observed transits is larger than 25. The implications are that very small exoplanets similar to Earth are within the grasp
of Corot, and that variations of the stellar reflected light by the planet may be observable (depending on its reflectance),
giving indication on its chemical composition.” (May/03/2007) Is this not disingenuous. Earths indeed.
There is a under current of scientific competition here with the COROT folks trying to underplay the significance of the Kepler mission, that is starting to get unsavory. In the beginning it was little things, now it is huge whoppers.
You also missed Hat-P-6b. I’m having trouble replicating the dollar values your formula gives. For starters, should the magnitude term read sqrt(2.5^(-(V-7.0))) ? Or does V mean something different? Maybe you could write how the terms work out for an example…
Hi tfisher98,
Thanks for pointing that out. I did indeed have a typo in the latexed eqn. I also had an earlier version of the table. The equation and the table should now be in agreement, and all the planets are now added.
Greg
I’m still having trouble getting the numbers to match your table. Taking CoRoT-Exo-2 b as an example, I use the following (from exoplanet encyclopedia):
scaling factor 7.46e6
ty = 2007 :: discovery factor 0.2466
P = 1.7429964 d :: period factor 0.7057
V = 12.57 :: brightness factor 0.0779
M = 3.53 MJ :: mass factor 0.2833
e = 0 :: eccentricity factor 1.0
Rplanet = 1.429 RJ ~~~ Rpl = 0.147 Rsun
Rstar = 0.941 Rsun :: transit depth factor 0.156
Npl = 1 :: multi-planet factor 1.0
Multiplied together, I get arount $4470 for this planet, compared to $123000 in the table. Am I still doing something wrong?
Hi tfisher98
Thanks again. It was getting late last night when I checked the consistency between my program and the latex eqn. They had both gone through many versions as I worked out the metric.
Now I *think* I’m happy
There was still a typo in the posted equation (now fixed). It should have (Rp/Rstar)^2, since we’re valuing according to transit depth.
In my program, I was using Jovian radii and solar radii, and so my 7.46e+6 normalization to 25mil only made sense in those mixed units. Using the same units for planet and star requires a nomalization factor of 5.8e+8
And I was also taking the root of the mass factor as per an earlier version of the eqn. I think it’s better to have the planets valued in inverse proportion to mass. I’ve updated the numbers to account for this.
Regarding the COROT releases, it might be better if they didn’t release any info until the actual papers are out, rather than saying they are making groundbreaking discoveries then releasing what seem like fairly run-of-the-mill candidates in press releases.
Continuing with that 1995 feeling, I was amused to note that TIME pegged the recent SuperWASP planets (total value of all three in current version of table is about $300,000) in their top 10 scientific discoveries, ahead of results like Gliese 436b, HD 17156b (or even Gliese 581)… gosh! wow! Hot Jupiters, who knew, eh?
Hi Andy,
Thanks for the link to the TIME article. With regards to editorializing on that particular call, I think I’ll just remind myself that discretion is the better part of valor :)
Greg
I agree with Andy …
I just have a related philosophical thought:
- What is a scientific announcement?
The somewhat vague definition of announcement
from a Thesaurus is:
“A message that is stated or declared; a communication (oral or written) setting forth particulars or facts etc”
In science, the facts and particulars should be clearly spelled out. What if crucial and basic parameters are missing from the ‘announcement’, such as coordinates, period, identification?
Maybe an announcement in science is something others can independently confirm? (or at least comment on, should the announcement be on a unique natural phenomena that happened only once)?
The XO team just made the XO-3b preprint vailable.
http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.4283v1.pdf
This is an interesting one sitting right on the edge of the deuterium burning limit. It also shows the urgent need for an astrometric mission follow up of Hipparcos as the physical characteristics of the host stars are the main limiting factors in deducing the corresponding figures for the planets.
Happy New Year,
Luis
Well, GAIA is that follow-up. We all must wait just a few years more…
XO-3b seems to be a very interesting object which is rather undervalued by the formula in this post. I wonder how much the ranking would change if superjovians (which seem to be rather rare in short-period orbits) as well as low-mass planets get increased values.
Looks like Setiawan et al. hit a jackpot — a massive hot Jupiter in a 8-10 million years old system TW Hydrae. The system is so young that the protoplanetary disk is still there. Even more intriguing, there seems to be evidence of orbital clearing as the planet migrated inwards.
abstract — http://www.nature.com/nature/journal/v451/n7174/abs/nature06426.html