We may be measuring planetary temperatures with less than optimum tools. Calling it a “new phenomenon,” Cornell University’s Nikole Lewis described the background of a just published paper looking into hot Jupiter temperatures. Lewis had been increasingly puzzled by earlier work on the matter, which produced temperatures colder than scientists expected. The deputy director of the Carl Sagan Institute, Lewis joined colleagues Ryan MacDonald and Jayesh Goyal in looking for the reason, reporting their results in Astrophysical Journal Letters.
What emerged was the need to fine-tune our analysis of exoplanet atmospheres, as delivered by the technique called transmission spectroscopy, in which the light of a parent star is filtered through a planetary atmosphere during a transit. Have a look, for example, at an illustration of the hot-Jupiter WASP-43b as it transits its star. Scientists have been able to construct temperature maps for the planet as well as probing its atmosphere to understand the molecular chemistry within. But the data on atmospheric composition have to be interpreted correctly.
Image: In this artist’s illustration the Jupiter-sized planet WASP-43b orbits its parent star with a year lasting just 19 hours. The planet is tidally locked, meaning it keeps one hemisphere facing the star, just as the Moon keeps one face toward Earth. The color scale on the planet represents the temperature across its atmosphere. This is based on data from a 2014 study (not the Lewis paper) that mapped the temperature of WASP-43b in more detail than had been done for any other exoplanet at that time. Credit: NASA, ESA, and Z. Levay (STScI).
Hot Jupiters orbit close enough to their star to become tidally locked, while the intense gravitational forces at work can cause the planet to bulge, making it egg-shaped. What we would expect is a wide range of temperatures, varying by thousands of degrees, between the blistering ‘day’ side of the star and the frigid side turned away from the star. Averaging temperatures like these can be a problem, according to the Cornell researchers, and the range of temperatures likewise can promote entirely different chemistry between the two sides.
“When you treat a planet in only one dimension, you see a planet’s properties – such as temperature – incorrectly,” Lewis said. “You end up with biases. We knew the 1,000-degree differences were not correct, but we didn’t have a better tool. Now, we do.”
Let’s dig into this. We have over 40 examples of hot Jupiters with transmission spectra, meaning that the science of exoplanet atmospheres is becoming established — eventually, we’ll drill down to smaller rocky worlds to learn about possible biosignatures, but for now, we’re detecting various atoms and molecules in the atmospheres of close-in gas giants. Observations of high enough precision can use transmission spectroscopy to learn about temperatures at the terminator, the zone where day meets night and the temperature contrast can be huge.
Both optical and near-infrared data are needed to draw accurate conclusions. The anomaly that the authors are addressing is that almost all of the retrieved temperatures for hot Jupiters are cooler than planetary equilibrium temperatures derived for the planet. In fact, the retrieved temperatures for most hot Jupiters are between 200 and 600 K cooler than the equilibrium temperature ought to be. The equilibrium temperature is the point at which the planet emits as much thermal energy as it receives from the star. It is commonly denoted as Teq.
The authors propose that the colder temperatures being found via transmission spectra are the result of the use of 1-dimensional models. The atmosphere at the terminator is more complex than the 1D model can show. They call for more complex 3D general circulation models (GCM) to replace them. Sets of differential equations are put to work in a GCM, with the planet divided into a 3-dimensional grid and analyzed in terms of winds, heat transfer, radiation and other factors, taking into account their interactions with other parts of the grid. The difference is striking, as the image below, drawn from the paper, demonstrates.
Image: This is Figure 1 from the paper. Caption: Schematic explanation of the cold retrieved temperatures of exoplanet terminators. Left: a transiting exoplanet with a morning-evening temperature difference (observer’s perspective). Differing temperature and abundance profiles encode into the planet’s transmission spectrum. Right: the observed spectrum is analysed by retrieval techniques assuming a uniform terminator. The retrieved 1D temperature profile required to fit the observations is biased to colder temperatures. Credit: MacDonald et al.
Thus the earlier models bias the results toward colder temperatures. And this can be significant in our evaluation of planetary atmospheres, as the paper notes:
Those [chemical] species exhibiting compositional differences have retrieved 1D abundances biased lower than the true terminator-averaged values. Even species uniform around the terminator (here, H2O) are biased, though to higher abundances. Compositional biases become more severe as the retrieved P-T profile deviates further from the true terminator temperature. In the most extreme case, the retrieved H2O abundance is biased by over an order of magnitude, such that one would incorrectly believe a solar-metallicity atmosphere was 15 × super-solar at > 3σ confidence.
We need to resolve this matter, then, to conduct more accurate atmospheric work. The paper continues:
The retrieved cold temperatures of exoplanet terminators in the literature can be explained by inhomogenous morning-evening terminator compositions. The inferred temperatures arise from retrievals assuming uniform terminator properties. We have demonstrated analytically that the transit depth of a planet with different morning and evening terminator compositions, when equated to a 1D transit depth, results in a substantially colder temperature than the true average terminator temperature. This also holds for state-of-the-art retrieval codes, with the added complication that retrieved chemical abundances can also be significantly biased.
Using the older models has meant that the temperatures of hot Jupiters thus far measured may be biased by hundreds of degrees below their true value. The figure reaches 1000 K in the case of ultra-hot Jupiters. An implication here is that the chemistry derived from the older models is less reliable. The authors call for the use of more sophisticated retrieval tools, acknowledging the increased computer overhead involved with 3D approaches but arguing that such models will produce more accurate data on atmospheric temperatures and composition.
The paper is MacDonald et al., “Why Is it So Cold in Here? Explaining the Cold Temperatures Retrieved from Transmission Spectra of Exoplanet Atmospheres,” Astrophysical Journal Letters Vol. 893, No. 2 (23 April 2020). Abstract / preprint.
I don’t think that it matters if the exoplanet is Asymmetric or off center or symmetric or center since a transmission spectra is the star light passing through the atmosphere where light from the star is absorbed and re emitted by the atmosphere. Consequently, the atmosphere of a hot Jupiter is a black body radiator in the infra red spectrum, so the brightness in infra red is what determines the temperature which is isotropic radiation and based on the thermal motion or rotation and vibration of the molecules and atoms.
Transmission spectra are sensitive to starlight which is absorbed, but not that which is re-emitted. Imagine a beam of starlight going through an exoplanet atmosphere towards our telescopes. If photons are absorbed and then re-emitted, they travel in all directions and very few will be re-emitted in the original direction of the beam. Transmission spectra are therefore sensitive to any process which removes photons, but not to what happens to the removed photons. The consequence of this is that any asymmetries in the way different regions of the planet absorb (e.g. changing chemical composition in different regions) imprints into the spectra we observe.
This looks like a very complicated problem. Both planetary atmospheres trade in the notion of “optical depth”, but where I have encountered it, the assumption was usually a simple up and down and extinction – with depth. On the other hand, radio occultation has been applied in flyby of planets and satellites to assess their atmospheric profiles, but it was more like shining a beam through the increasingly
dense atmospheric medium to a terrestrial receiver, until it was stopped by falling below a solid horizon. In this case you are dealing with a situation where both the light source and the occulting object have considerable dimensions which effect the simple models described earlier. It would be bad enough if the atmospheric medium were inert
and not circulating. But some assumptions have to be made about how all this is affected by leading edge and poles. …
Considering that a hot jupiter might be so close to primary, would it not be possible to get some reflectance from it prior and after its transit?
The geometry we are dealing with here is close to the radio occultation geometry you mentioned, but in this case we have an extended source sending beams through all parts of the day-night planetary boundary at once. This geometry results in much greater optical depths than what would be seen by a spacecraft observing a planet vertically – one of the reasons why we are quite sensitive to clouds in transiting planet atmospheres.
We can’t observe reflected light just before or after transit, as the planetary nightside faces the observer during transit. But if you wait half an orbit and observe just before the planet passes *behind* its star, you can indeed observe reflected light. We have done this for a few hot Jupiters already, allowing us to measure what colour they would appear to the human eye (dark charcoal blue, sometimes green).
This is interesting. With so many hot Jupiters, there may be some that end up being flung into space via orbital instability. These planets would have a lot of residual heat from the host star(s) and may benefit from colocation of radioactive isotopes near their cores. So they might be conducive for providing warmth to planetary moons or serve as an infrared warming source for space colonies that might eventually be established in orbits around these hot planets.
It is an interesting analysis. I had to look at the paper to understand the figure used in the post. Luckily we have powerful computers to do the needed modeling to get the better analysis that is needed to understand their atmospheres better.
Interestingly enough, the rate limiting step at the moment is developing the algorithms which can explore all the possible 3D models. Essentially, this boils down to ‘mapping’ a high-dimensional space of possible atmospheres (where each dimension is an atmospheric property, say, the temperature at a given location or the abundance of one molecule) to find the regions consistent with our observations. We are certainly working on developing codes to do this!
How would you eliminate false positives? By chance alone among a quantity of models there will be statistically significant matches. Offhand this seems to be a high risk approach.
Great question Ron. There always is a range of solutions which can fit a given dataset within the error bars – we call these ‘degenerate solutions’. One common example is cloud-chemistry degeneracies (e.g. a high-altitude cloud deck with lots of H2O above it can produce a similar spectrum to a lower cloud deck with less H2O per unit volume). The key is that these degeneracies are not exact symmetries, so we can always narrow down the solutions to a finite range of possibilities.
For example, when we say “we have measured how much H2O there is in planet XYZ to a factor of 2”, what we actually mean is “accounting for all potential alternative explanations within our model, the amount of H2O must lie within a factor of 2 of the best-fitting value to be able to fit the observations”. The mathematical framework used to do this is called ‘Bayesian marginalisation’.
Thanks for the response, Ryan. My main concern is with “all potential alternative explanations”. I am wondering at how complete the set of hypotheses can be since there is so much about exoplanet atmospheres we don’t yet know.
Of course I understand constraints on the possibilities must be constrained as well as we can, and that is what you must work with. I have some familiarity with Bayesian hypothesis evaluation and comparison techniques but not for astronomy.
I’ve downloaded the preprint and will try to find some time to read it.
We tend to be reasonably agnostic when exploring alternative explanations. Typically, we consider the abundances of some 20 gases (ranging from 10^-10 to 100% of the atmosphere), a flexible vertical temperature structure, various cloud and haze properties etc. So the solution space considered is a quite broad ~30 dimensional parameter space. Of course, we can always think of new complexity to add to our models, and investigating how much complexity is needed is one of my main focuses prior to James Webb’s first observations.
What astonished me here is that you can have morning on a planet where the sun never rises! They do address this:
“Consider a transiting exoplanet with a temperature difference between its morning and evening terminators… For tidally locked planets, this can arise from various circulation regimes between the dayside and nightside. A temperature difference can in turn induce a compositional difference – by equilibrium or disequilibrium mechanisms – and hence an opacity difference around the terminator.
Think of it. These clever people have a way to measure the *wind* on a planet that never steps out of the same pixel as its star, and can even measure *chemical changes* in that wind – chemical changes that could point at a means by which energy from the day side can be absorbed and stored so that it could be available to some unimagined form of life that may exist in the night.
(Lead author of the study here)
Great article, thanks Paul. Happy to answer any questions that your readers may have, feel free to reply here or drop me an email!
Very pleased to have you here, Dr. MacDonald! Any readers with questions should feel free to post them here for Dr. MacDonald’s perusal.
I don’t understand much of https://arxiv.org/pdf/2001.03668.pdf … but it is intriguing! You examine a network of provocative organic chemicals, observe chemical changes of up to 10^12, see large changes in the amount of water at low mbar values … if someone observed any one of these things on Mars, I know what the press would be printing. It’s one of the craziest planets in the cosmos to ask this about (always a good sign) … how much free energy would become available for the use of a hypothetical nightside organism that would catalyze a reaction from one of the chemical disequilibria that you have observed? What sort of temperatures do you expect would be present at 0.02 bar or so on the night side? Is there anything clearly preventing the small organic compounds you’ve studied from forming larger, more complicated molecules capable of developing the characteristics of life?
A related question: do you know how uniform the “morning” and “evening” terminators really are? Could there be some bands of winds running in opposite directions like on Saturn? Sorry, I want to give my pets a way to hide in the dark. :)
The nightside temperature of the ultra-hot Jupiter HAT-P-7b in our models at 0.02 bar was ~1000 K, so I wouldn’t recommend it for your pets!
The morning and evening terminators will probably also be quite non-uniform. We don’t expect to see bands like Jupiter and Saturn (tidal-locking radically changes the circulation pattern), but we do expect different winds at the poles vs. the equator. We do already have some wind measurements for some of these hot Jupiters (~ 2 km/s), and there is ongoing work trying to resolve this into winds at different locations around the planet.
VERY impressive that you can deduce this much – even if it dashes my daydreams. Anything is possible in biology … chemistry is another matter. This is fairly near the temperature for pyrolysis… on Earth such a reaction could break down most organic compounds and produce carbon/PAH soot particles. I see you already were looking for soot and haze, and didn’t see much, perhaps because in the lower layers of the dayside atmosphere even that will break apart.
I guess that GCMs ( be it “Generalised circulation model” or “global climate model ” ) are opaque to most non specialists. I’m a lay person with only a vague grasp of the various 0-D , 1-D, 2-D and 3-D ( GCM) climate models available – with increasing sophistication and related computational processing power requirement .
A brief overview of this subject and its huge relevance would be welcome. I read a review by Shields last August in Astro-ph , though this focused more on climate modelling for putative habitable zone terrestrial planets – which are still well out of reach data wise. ( clouds not withstanding)
Your work here is seminal. A real breakthrough.
As I understand it however sophisticated a simulation is ( and the various GCMs certainly qualify for that ) it can only be as good as the available data that informs it. It’s great that there is now enough real transmission spectroscopy data ( no small feat in itself !) to recognise the discrepancy in pre-existing GCMs . Then to both explain and amend it. Not just relying on data originally derived from Earth or theory.
The first time for any non solar system planet and certainly for ANY exoplanet type .
A real step forward in the characterisation of all exoplanet atmospheres .
Many congratulations.
Just to be clear, this terminator effect applies to hot planets, primarily the hot Jupiters. where the temperature differences between morning and evening terminators, when averaged, result in incorrect calculations for the planet’s atmospheric composition.
At this point is there any way to verify this analysis with observations, or is the resolution needed to obtain separate transmission spectra much too high to allow this?
Secondly, it seems that the discrepancies are very much temperature-dependent. For worlds in the HZ, when we eventually can detect their transmission spectra, this will not be a problem for temperate worlds. Is this a valid assumption?
We found that it was the averaging of different compositions on the morning and evening terminators that caused biased inferences. Though the differing compositions do indeed tend to arise from differing temperatures.
There are many ways to verify this with observations. One way would be observe the first part of an exoplanet transit (ingress) with high time sampling, in which only the morning terminator occults the star. You can then do the same towards the end of the transit (egress) to probe the evening terminator. These are challenging observations to make, but James Webb will be able to do this routinely. The first analysis of this kind was recently actually recently published in Nature, revealing a difference in how much Fe each side of the hot Jupiter WASP-76b contains: https://www.nature.com/articles/s41586-020-2107-1
Planets in the HZ around M stars, of the kind we will probe with James Webb, will still be tidally locked and hence experience temperature and chemistry differences. These will not be as extreme as for hot Jupiters, but the atmosphere of Earth certainly isn’t uniform ;)
Going from one pixel per planet to two is definitely a step in the right direction! :) I wonder how long it will be before someone is able to model the position of a starspot and measure the light they don’t see when it passes beneath the exoplanet’s atmosphere…
Ryan Mcdonald, the infra red temperature can be used to make a map also. https://www.nasa.gov/mission_pages/spitzer/news/spitzer-20070509.html One uses a continuous spectrum to get the temperature. The brightest part of the spectrum is in the infra red since a hot Jupiter gets very hot due to its closeness to the star so it should be a black body radiator or bright in the infra red which is independent of the chemistry. Hot Jupiter’s are easy to detect in the infra red.
It’s actually the total infra red light gathered from the hot exoplanet which is independent of spectral lines or chemistry.
I get the idea of the difference in chemistry from the day to night side with the iron rain on the night side and condensation, etc. Shouldn’t the morning and evening terminators be the same temperature?