Juliette Becker
Exoplanetary System Dynamical Considerations for NASA Missions

All right.
Hello everyone.
My name is Juliette Becker and I'm an assistant professor at the University of Wisconsin, Madison.
And I'm a part of WCOR, the Wisconsin Center for Origins Research.
It's a new center at the University of Wisconsin where we're trying to understand the origins of life and what makes planets habitable.
And in fact, that is exactly what I'm going to talk to you about today. So to start with the kind of schematic clip art of what we hope Habitable Worlds Observatory will someday see.
So this in the middle it's a star.
It's a host star around that. I've a green banded zone. The habitable zone right now the main way we define the habitable zone is it's something where we think there's the possibility of surface water being liquid.
There's some nuances in the literature.
Some people are more optimistic about what types of atmospheres will allow habitability, but in any case there's some habitable zone based on the effective temperature of the planet. And then here.
The goal eventually of habitable worlds is going to be to find these earth like planets in the tank spectroscopy.
Learn more about their atmospheres.
This is a great goal.
There are a lot of dynamical considerations that go into planetary habitability beyond just.
It's mean effective temperature, or it's instantaneous orbit?
So today I'm going to talk a little bit about those considerations and then I'm going to end with talking about what we should be doing now to prepare for these eventual observations and set us up for success in the 20 fourties when habitable worlds finally finds these plan.
That we're looking for how we'll actually be able to confirm that they're not just, maybe, possibly habitable planets, but really concretely have.
A well determined system architecture that allows us to confirm they probably are habitable.
So to start with, again, if you have just a single planet in a system and you have the planet starts in the habitable zone, then by Kepler's laws you might expect for this planet to just stay in the habitable zone with time.
Have a pretty constant effective temperature, but if there's anything that we've learned from Kepler and Tess and so much of the other work done from the ground and in space so far is that planetary systems are never this simple.
So I'm going to start by just kind of a toy schematic where we add one additional companion plant to the system.
And exterior perturbing Jupiter mass companion.
And this companion could do a few things to the planet.
So I'll start with an animation that's maybe more similar to our own solar system.
Where the Jupiter light companion isn't going to do too much to the earth like planet.
So if you look at just the orbit of the Earth in this animation, it's not too different than it was in the previous case where it was the only Lonely Planet in the system.
However, this is with maybe a solar system like Jupiter. We also know from again years of radial velocity surveys that Jupiter's.
Arrive in a or exist in a variety of orbital eccentricities in a large variety of orbits.
So if we slightly perturb the orbit and give it some eccentricity for the Jupiter, then all of a sudden we've created a system geometry that's not going to be as amenable to habitability for the earth like planet in the habitable zone. And the reason for that is that.
The planet's passing close together is not going to be good for the long term stability of the system.
Both orbital stability and also climate stability.
Now this animation is limited by how many PNG images I can stitch together on my laptop.
So it's not really good for looking at the long term habitability of a system.
So let's change the dimensions that were looking at. Instead of looking at just kind of the schematic of what habitable World's Observatory will see, let's look at how the orbital elements of the system change over long time scales.
So this is an animation showing the eccentricity of the two planets in black. You have the eccentricity of that Earth.
Planet that we're hoping is habitable then in red its companion the the Jupiter perturber, and for this particular geometry with a little bit of a higher eccentricity companion, the eccentricity of the potentially habitable Earth planet is going to vary over huge ranges over even just thousands or T.
Of thousands of years.
So there's two different things that this can mean.
The first potential option is a dynamical instability where a planet is lost from the system, so the earth like planet.
Comes so close to the Jupiter at some point that it's orbital velocity is accelerated.
Goes above the escape velocity lost entirely from the system, so there's already been some good work in the community to characterize of the habitable world's observatory target stars.
Which of these are most susceptible to having this happen?
So here's an example from a paper from last year by Stephen Kane where he went through and looked at the systems that we know that could be habitable worlds targets and given the planets we currently know about in the systems. What?
Could you put a earth like planet in the habitable zone?
So on the Y axis we have the simulation survival percentage, so something down at the bottom of the plot means that if you had a planet there would not survive, it would be lost from the system.
And this is a kind of pretty typical system HD 10647 has.
A little bit larger than Jupiter companion at about two astronomical units, but you'll notice is that even with just that limited information, we know about this system, that there's one Jovian companion.
There's a huge range of parameter space for habitable planets cannot reside, so this is the first potential danger to habitable planets. Is the fact that if the perturbing influences of other planets in the system are strong enough, they might be lost entirely.
The second potential danger to planets is if you have perturbations that are not strong enough to lose the planet entirely, but strong enough to alter the orbit of the habitable planet, then this could also potentially be detrimental to habitability.
So we again have been using the planetary effective temperature as a kind of measure of how habitable we think it is.
But if you have an orbit where the planet's orbital elements are changing with time, then the averaged flux that the planet gets over time will also change.
So this is a pretty commonly used equation for the surface flux that a planet gets due to a star with some luminosity.
Big as the albedo, little as the semi major axis.
There's this extra factor in here, dependent on the eccentricity that people don't usually think about, but for eccentric orbits, the average flux the planet is going to get over its orbit is going to change due to the fact that instead of existing stably, it's constant value of some.
Major axis it passes closer to the star at its per Astron distance and then further away at App Astron.
So this is an example for the previous animation. We were just looking at what the surface flux of that planet over time is going to look like.
And you get here a little bit over 50 watts per meter squared of surface flux variability over again 10s of thousands of years timescale.
So this could paint the picture of a planet that looks very different from our planet, which has relatively constant overall bulk solar flux with time.
And this is going to be compounded on top of the fact 'cause this is not something that happened significantly for Earth.
On earth.
What drives climate variability over seasonal time scales is.
Seller obliquity, so this is going to compound with additional effects from the obliquity or planetary obliquity.
So this is going to compound with effects from the planetary obliquity.
So the effects of the planetary obliquity are probably most commonly known by average scientist via the Milankovitch cycles, which are the cycles in Earth's own obliquidats tilt and its eccentricity over time.
So we have 3 animations showing the pieces of Earth's tilt, its procession rate, and then its ecentricity the shape of its orbits orbit the parameter. We're just looking at.
The three panels on the right here show how those parameters change with time and the changes with time are driven by Planet planet interactions.
So this is a cycle that we know very well for Earth based on not only numerical simulations of orbital dynamics, but also geologists can look in the rock records and test these results and show how the.
Planetary obliquity has been changing with time, but on exoplanet systems we can't generalize this.
We have to redo this calculation for each individual system and to do it right, we have to know all the components in the system. If you don't know about the planet's that are perturbing.
Planet. Then you won't be able to know how its obliquity is changing with time.
So we have these two factors.
Planetary eccentricity planetary obliquity, which are going to change the amount of surface flux you get at the planet over time, which would potentially take something that you normally would think would be habitable and move it out of the habitable regime.
But there's another factor that must be considered for.
Habitability in Multi Planet Systems and that is the dynamical effect of giant perturbers like Jupiter in terms of both protecting or potentially increasing their rate of impacts.
So there's a long dialogue in the planetary science literature about what Jupiter does to the impact rate of asteroids and comets on Earth, and the one thing that everyone agrees on is that Jupiter effects this rate. Some people think it decreases the rate and that Jupiter is a.
Protective influence. Saving the earth from collisions.
That was kind of the idea throughout the 1990s. In the early 2000s.
More recently, people have started do some calculations that show that Jupiter can actually.
Sometimes increase the rate of collisions on Earth's surface, but since planetary impacts can be so destructive for habitability both in terms of resurfacing a planet, but also in terms of stripping an atmosphere like high enough, collisions could strip a planetary atmosphere.
And then what?
We'll see with Habitable Worlds, Observatory will be just a flat line of nothing of rock.
So to understand the prospects of habitability, you need to not only model processes that affect weather.
Planets can exist.
Such as have the planets been dynamically ejected because they're an unstable parameter spaces?
Or can they be the right temperature for life due to their eccentricity and obliquity variations?
But also how other objects in the system such as Jupiter's, could affect their long term viability.
So what do we wanna do?
The road map to maximizing the potential impact of habitable worlds in a couple decades.
First, obviously, we're gonna want to identify the planets that are candidates to be habitable.
We wanna be able to characterize them in detail and when I say them, I mean not just the planets themselves. Like. Yes, we wanna know their atmospheric chemistry, which we should be able to get with HWO. We wanna know their orbital dynamics, an orbit we can.
Probably also fit with Hwo data.
But we really need to understand the entire architecture of the system in which they're living, to know if their entire environment is amenable to habitability or not.
And then finally more generally, not just for hwo targets, but these are going to be some really great ones we can study in depth.
We want to investigate their formation histories and try to understand how these fit into our global picture of planet formation.
So for identifying planets, this is something that hwo will hopefully will do.
We'll hopefully find some good targets in the habitable zone that could potentially be habitable, be good targets for spectroscopy, but these last two bullet points we actually don't need to wait for habitable worlds observatory to be built so we can start characterizing the systems that are on the.
Target stars list and we can start thinking about their formation histories and whether the systems would be expected to even host habitable planets or not.
We can do both of those things right now. So last thing I'm going to talk through today.
Is a few examples from the literature of how we can set the stage for these future missions.
So the type of work that we should be doing now to characterize these systems and come into hwos lifetime with the best possible pre knowledge of both which hwo target stars are most likely to be fruitful targets for Earth searches, but also having decades worth of pre stud.
On the architecture of the systems will set us up to really understand what's going on in these systems.
So here's another animation.
I've added some more planets to remind you guys that even though I was talking mostly about a single Jovian perturbing planet before.
The dynamics that a habitable earth are going to be subject to are going to be a consequence of everything in the system, so it's not enough to find like one single planet, the lowest hanging fruit in a target world and think OK, we understand the system in reality.
We wouldn't understand Earth's solar cycles from simulations unless we knew about the terrestrial planets.
So we need to go as deep as we can in each of these target systems and try to understand their full geometries.
Additionally, we need to parameterize or we need to measure as many orbital parameters of the systems as we can.
So here is an example of two sets of simulations where we started with an earth like planet in the habitable zone, and then we put in an additional single Jupiter companion. So the orbital period of the earth like planet is on the X axis and the eccentricity of.
The companion is on the Y axis.
Don't need to worry about the details with the big picture here.
Is that the only difference between these two panels is the coplanarity of the companion to the potentially habitable Earth.
So in the panel on the left it's called planar with an earth like planet.
And then the other one, it's 10ø misaligned.
So there's a difference here, even with very slight alterations to the planet properties in the system of exactly how we habitable we expect.
These planets to be, and this is not an easy mapping.
It's one that needs to be done independently and individually for each system, because very slight alterations in period ratios or inclinations can change the entire phase space of where you expect planets to be habitable.
So things we should be doing now are trying to characterize what else is in these habitable worlds observatory target systems.
So here's a few examples of what we should be doing.
So first I want to highlight some work led by Katie Painter, who's a PhD student at the University of Texas.
So she's been digging back into hippocross.
Combined with Gaia data release three data to try and get astrometric constraints on where planets could be in hwo target stars.
So here is a couple examples of the types of constraints that she can get. So each of these panels is for one particular hwo target star and in her paper she has all of them.
But this method using.
Long term astroometric acceleration.
Allows her to detect roughly Jupiter mass planets out to about 10 astronomical units in these systems, which is exactly the type of companion that could be either increasing or decreasing the impact rate and potentially perturbing habitable planet out of the habitable zone.
So these are exactly the kind that we need to know about.
Next up here is a submitted paper by Harada et al. So this paper also uses long term measurements from high res.
You can see the X axis here.
These R vs for this particular target star start before the year 2000 and come up to nearly the present day and again long term radial velocities are another way to get kind of large Jovian mass planets in the intermediate ranges of these systems.
And then finally, another different and complementary method that I wanna highlight. That's pretty new and hasn't been done too much yet. I think actually this is the only paper I know of that's done it exactly this way is a imaging using Miri on JW St. which allows.
Cold planets up to a much larger range than a couple previous slides.
Up to hundreds or even 1000 AU to be detected. So as far as I know, this method hasn't been applied to habitable worlds. Observatory target stars, yeah.
But it has the potential to teach us about the outer part of the system that the astrometric accelerations and R vs may not be able to detect.
OK, so to end off there are kind of a few main conclusions that I would hope everyone would take away from this.
1st is that secular cycles, which is just the change in orbital elements over time due to planet interactions are going to orbit or change the orbital parameters of our potentially habitable Earth like planets over time.
This could lead to dynamical instability or heat budget alterations.
But if you're really thinking about the long term habitability of a planet and not just its instantaneous snapshot, then these are all parameters that you need to include in your model.
Next, the exoplanet sample we know from tests and Kepler work that's still ongoing as people discover more and more tightly packed systems.
It's very more densely, dynamically packed as compared to the solar system, and so this means that there's no reason that we shouldn't expect for multi planet dynamics to be very relevant in hwo target systems.
So Giant planet companions in these systems.
Could provide a stabilizing or a destabilizing influence.
And that's something that we need to do the work to figure out which that's going to be finally.
Hwo alone cannot capture the full range of constraints that we need to characterize these systems and the time to start collecting data to characterize these systems in a really detailed way and understand their full geometries and their full census of planets is now. If we are being opt.
Then we might say that Habitable Worlds Observatory could be launched in 15 years, maybe 20-40 if we're being realistic, then maybe it's going to be more like 20 to 25 years.
I won't be pessimistic, so I'll just stop there.
But if we think about what was happening 15 years ago in the field, that was the launch of Kepler. If we think about what was happening 20 to 25 years on the field that was on that RV plot I showed, that was the earliest points on the.
Plot so there is a lot of time beforehand is going to fly.
And we can do a lot of work in the meantime, building up these data sets and getting to the point where for some of these target stars, we could have up to 40 to 45 years of data by the time hwo starts finding potentially habitable Earths, so.
The time to start or the time to continue getting this data and to start thinking about how detailed of architectures we can construct for these target stars is now. With that I feel like we really haven't seen this plot enough of orbital period versus planet mass. So I.
Just put it up and.
Ask for questions.
Thank you all so much.
Really, we have time for one quick question.
Yeah, Charles Bichman NExScI.
So thanks for a very, very timely presentation.
One of the concerns that we started, I started 1/2 after seeing Stephen Kane's paper was he went down to a certain level of math for which the data are available in terms of known RV planets as you go to lower masses, we know less.
But we do know that.
Smaller classes, smaller planets are more abundant than large ones, and their hill radius only decreases like the one third power.
So where do you see?
Sort of. The low mass cut off of where you have to worry about your habitable zone being impinged upon?
Yeah, that's a good question.
So I think in terms of we know from Kepler and Tess that multi planet systems with spacings about 8:00 to 10:00.
Hill radii are not only possible, but they're also like one of the dominant outcomes of planet formation.
What we don't have is we don't really have an understanding of what those geometries look at look like further out at like 1 AU around G Type stars, which is where a lot of the HWO targets are going to be.
So I think I'm glad that we have 15 more years to think about this, but I I do think that a lot of the interesting parameter space of like low mass planet planet interactions of like.
An analogous like analogous Venus in an exoplanet system.
I think we're probably gonna be able to detect most of those, so hopefully we can get the Jupiters and the saturns and then we'll see about the Neptunes and below.
Unfortunately, that's all the time we have, but I encourage you to continue the conversation online.
Let's thank Juliet again.