TRAPPIST-1 and Proxima Centauri habitability analysis

Since the advent of space exploration, we’ve discovered an astounding number of celestial structures that wasn’t even known to us a couple decades ago. Exoplanets are one them, those newly discovered planets are light-years away from us, which we might never be able to reach them.

But what if we could live on one, could we ?

What ? Exoplanet ?

You might or not have heard the term. In short, an exoplanet is a planet that resides outside of our solar system, orbiting another sun and having it’s own structure. Some of them are really (really) hot, burning at high temperatures others are freezing at extremely low temperatures. We can find a wide variety of exoplanets in space. Like KELT-9b, which is the hottest extrasolar planet ever discovered. Having twice the size of Jupiter, it has an incredible day-side temperature of 4600K(4326°C), which makes it hotter than most stars ! It’s so close to its host star KELT-9 that it orbits every 1½ days. Other planets like 2MASS J2126−8140 orbits its host star each 900 thousand years, which is quite amazing !

Planetary Habitability

Here we won’t focus on those insanely hot and dangerously toxic planets. For a planet to be habitable, it has to possess some important features similar to Earth’s. As we can only use our own planet as a basis of comparison because you are actually alive and reading this article. There are multiple factors in play when considering a planets habitability. It’s surface temperature or it’s average temperature is one that quickly comes up to mind. It has to be in the habitable zone, we don’t want to die of extreme cold nor die in high temperatures melting away, we are looking for something not too hot, not too cold. Another important one is mass, since the determining factor for gravity is mass, the more mass, the stronger the gravitational field, that’s usually the case. But keep in mind that mass is not the only factor affecting gravitational attraction. There many more aspects to consider when assessing habitability on an alien planet, like it’s distance from its host star, its eccentricity, its atmospheric composition and much more.

Here in our analysis our main focus will be on the surface temperature and the planetary mass. Since both of them are important factors when evaluating habitableness. We will also be exploring other features like the exoplanet’s distance from its star and much more.

 

A quick introduction to the planetary features we will be exploring

 

Surface Temperature

The surface temperature here will be calculated in Kelvins, which is an absolute thermometric scale used in astrophysics and in other physical sciences. 0 Kelvin is equivalent to −273.15 °C (−459.67 °F) which is when thermal motion ceases. In astronomy, when calculating a distant planet’s temperature we use a concept called the planetary equilibrium temperature or the equivalent blackbody temperature which is a theoretical temperature which the planet is at when considering it as a black body being heated only by its main star. The presence of an atmosphere isn’t taken into consideration here, therefore no greenhouse effect.

Planetary Mass

The planetary mass will be calculated in Jupiter mass MJpt, which is the mass relative to Jupiter’s mass. Jupiter is 1 MJpt, Earth is 0.00315 MJpt and Mars is 0.00034 MJpt.

Distance

The distance  from our Sun to other stars  is calculated in Parsec(pc), one pc is approximately 3.26 light-years. It is a pretty sophisticated method of calculating astronomical distances, so i won’t get into too much details. 

paralax

Period

The period is how long an astronomical object takes to complete one orbit around another object. Here the period will be in days, Earth’s orbital period around the Sun is 365 days.

Semi-major axis

The semi-major axis is defined as the radius of an orbit at the two most distant points. It is calculated in astronomical unit or AU, which is the distance from Earth to the Sun. 1 AU is approximately 150 million kilometers.

smi

Our data

We’ll be exploring the Open Exoplanet Catalogue  inside Jupyter Notebook for our research, as the names says it, it’s an open catalogue of all discovered exoplanets. Filled with useful and interesting information regarding extra-solar planets.

 

Surface temperature and planetary mass relation

Our main focus will be on the surface temperature and the planet’s mass, but first let’s see how both of those variables interact in the data set.

 

Complete data set

 

meansmediancomplete
Means and medians that are too far away tells us that there are outliers present in our dataset
corr
We got a correlation coefficient of 0.11(11%), which indicates that both variables tend to have a positive relation

 

completedateset
Here we can see some outliers at the extremes.

 

surfacedistrib
Surface temperature distribution
planetmassdistrib
Planetary mass distribution

 

datadist
Data distribution (SurfaceTempK and PlanetaryMassJpt)

 

pearson1
We got a PCC(Correlation) of 0.11 and a p-value of 0.0036, we also got a positive relation, which indicates that planets having a higher mass tend to be slightly hotter. Here though we got a huge confidence interval(95%) gap(blue translucent around the line) at the end of our regression line. Which means that there’s 95% chance that new unseen data will be in that gap. Which is why we must not jump to any conclusion yet even though our p-value is really low (i.e strong evidence against the null-hypothesis).

 

Cleaned data set SurfaceTempK(0-2000), PlanetaryMassJpt(0-10)

 

Let’s contain all the data between 0 and 2000 on the X-axis(SurfaceTempK) and 0 and 10 on the Y-axis(PlanetaryMassJpt). So now we’ll gather all the exoplanets having a surface temperature in the interval of 0 and 2000 Kelvin and a planetary mass between the interval of 0 and 10 Mjpt.

Interestingly (and obviously), we now get a different correlation score

negative corr
Now we got a negative correlation coefficient of -0.09(9%), which is a clear indication of outliers at the extremes
meansmedianclean
Our means and medians are a lot closer which indicates that we’ve eliminated some outliers

 

complete clean
We still got some outliers but they have a relatively lesser effect on our data as a whole

 

datadist_2

 

pearson2
We got a PCC(Correlation) of -0.097 and a p-value of 0.015. With a pretty small 95% CI at the ends of the regression line

 

Cleaned data set SurfaceTempK(0-2000), PlanetaryMassJpt(0-2)

 

Here we’ll reduce the interval and gather all the exoplanets having a planetary mass(PlanetaryMassJpt) between 0 and 2 Mjpt. Surface temperature stays at the same interval of 0 and 2000 Kelvin.

2_
Now we got a correlation coefficient of 0.07(7%), which is positive
meansmedianendclean
Now our mean/median gap is even smaller

 

 

2_
We can still see some outliers, but the variables are closer to the mean/median

 

datadistfinal
Our data distribution after containing PlanetaryMassJpt (0-2)

 

pearson3
We end up with a PCC of 0.073 and a p-value of 0.11. But we got a bigger 95% CI gap at the ends

(A p-value of 0.11 basically means that if our null-hypothesis(i.e no correlation between surface temperature and planetary mass) is true we would’ve get the observed effect or more (i.e surface temperature and planetary mass correlation) at a rate of 11 % in the population of exoplanets, which is a little too high. We would need a p-value low as 0.05 to really say that there’s a correlation between surface temperature and planetary mass.)

 

Data of interest

allexo
Here for the planetary mass  and the surface temperature, we’ll gather all the planets having a Mjpt greater than 0.0003(>0.0003) and lesser than 0.1(<0.1), and for the surface temperature we’ll gather the ones that are greater than 192(>192) and lesser than 320 (<320)

 

plots
Planets with MJpt (> 0.0003 < 0.1) and surface temperature (> 192 < 320)

 

pairs
Planets and exoplanets pairplots with MJpt (> 0.0003 < 0.1) and surface temperature (> 192 < 320)

 

We can see a bunch of them that are relatively similar to Earth in terms of temperature and mass.

We won’t go though each one them, we’ll be focusing only on the TRAPPIST-1 exoplanets and Proxima Centauri b.

 

TRAPPIST-1

We’ve got some interesting exoplanets from the TRAPPITS-1 system showing up on the plot. Which are TRAPPIST-1 d, TRAPPIST-1 e, TRAPPIST-1 f and TRAPPIST-1 g.

trapearth

Let’s take a closer look at the TRAPPIST-1 system.

TRAPPIST-1 is an ultracool dwarf star which has a temperature of less than 2,700 Kelvin and a solar mass of 0.0802, which is a pretty low temperature and mass for a star. TRAPPIST-1 is 12.1 Parsec away from us, which is around 40 light-years away from our Sun, in the constellation of Aquarius. (That would take us 40 years traveling at the speed of light to get us there)

There are seven planets that have been detected so far orbiting the star. There is evidence of water being present on them due to a trail of hydrogen left by the closer orbiting planets when they transit in front of TRAPPIST-1. The planets that are farther away from the main star have a low equilibrium temperature, which helps in maintaining water at the surface.

TRAPPIST-1 planets are orbiting closely to one another which makes them more likely to be impacted by UV irradiation, this radiation causes water molecules to break down, producing hydrogen and oxygen. A significant amount of hydrogen could therefor be present system wide indicating a history of water loss from the planets. Each one of them would have lost water at a different rate due to the runaway greenhouse effect, which ultimately led to water boiling away.

(Hydrogen being present system-wide is due to the high levels of  XUV radiation hitting the water molecules present on the exoplanets, which breaks up water molecules by a process called “ionizing radiation”.)

 

Trappist system

It is also highly likely that each of TRAPPIST-1 orbiting exoplanets are in a tidally locked orbit, having one side of their hemispheres constantly facing their parent star with one side getting light and the other shrouded in darkness. If that hypothesis was to be true, that would imply that between those two extremes there would be what we call a terminator line, which is the limit between light and complete darkness, that delimiting area would have a stable temperature suitable for liquid water to exist.

Another thing to keep in mind is that some of those planets weren’t always in the habitable zone.

 

TRAPPIST-1 d

d
TRAPPIST-1 d shares some similarities with Earth in terms of mass and temperature. With a equilibrium temperature of 288 Kelvin which is approximately 15 ℃. With a mass of 0.001290 Mjup, which is one of the smallest in the TRAPPIST-1 system. The planet is situated in the inner part of the habitable zone of its parent start with a semi-major axis of 0.02817AU which is a pretty close orbit compared to Earth and with a orbital period of 4 days. With the correct conditions water could exist somewhere on its surface. But due to its closeness to its star it could have lost a substantial amount of its water content. If we consider that the water loss only occurs during the runaway phase, TRAPPIST-1 d might have lost less than 4 earth oceans before reaching the habitable zone. The hemisphere facing TRAPPIST-1 would be highly irradiated by XUV(extreme ultraviolet) radiation, the main reason behind the water loss.

 

TRAPPIST-1 e

e
Still orbiting TRAPPIST-1, we’ve got TRAPPIST-1 e which is in the habitable zone, likely rocky and Earth-sized in terms of mass and radius. A semi-major axis of 0.02817 AU with a orbiting period of 6 days, it has a blackbody temperature of251.3 Kelvin which is  equivalent to -22 ℃, and with a planetary mass of 0.001950 Mjup which is slightly smaller than that of Earth. Similarly to TRAPPIST-1 d, it lost less than 4 earth oceans before reaching the HZ. Water might still be present in large amounts on its surface. Even though TRAPPIST-1 e seems to be right in the middle of the HZ, XUV radiation would still be pretty high on the planet.

 

TRAPPIST-1 f

f
Then we got TRAPPIST-1 f, the surface temperature is at 219 Kelvin which is −54 °C. A semi-major axis of 0.0371 AU which is a bit  more than one third of the distance between Earth and the Sun, it has a orbital period of 9 days. Its surface is pretty cold compared to d and e, similarly to TRAPPIST-1 d and TRAPPIST-1 e it lost approximately the same amount of water. With a planetary mass of 0.002139 Mjup, slightly more massive than TRAPPIST-1 e. Situated in the outer part of the HZ, a substantial amount of water could be on the surface. Being one of the farthest away exoplanet, it is less influenced by the XUV irradiation coming from its star due to the interstellar medium’s absorption.

 

TRAPPIST-1 g

g
At last we got TRAPPIST-1 g, one of the farthest away with a surface temperature of 198.6 Kelvin which is approximately -74.55 °C. With a planetary mass of 0.004215 Mjup, which is twice as massive as TRAPPIST-1 f and slightly bigger than Earth’s mass which is at 0.003146 Mjup. TRAPPIST-1 g is outside of the HZ with a semi-major axis of 0.0451 AU a little less than half of the distance between Earth and the Sun, it also has a orbital period of 12 days. Ultraviolet light is largely absorbed by the ISM before reaching the planet at that distance.

 

Earth’s and TRAPPIST’s variables and correlations

 

summary
Earth and TRAPPIST’s varibles

 

trapcorrelate
We can see how they correlate to each other, TRAPPIST-1 g having the highest correlation with Earth.

 

That’s for the TRAPPIST-1 exoplanets ! Like i said in the beginning there are many factors in play when we look into habitability. Not considering the existence of a suitable atmosphere with the right properties is pretty dangerous. Even though TRAPPIST-1 habitable zone seems to be “habitable”, if the star isn’t calm and quiescent, excessive ultraviolet light could pretty much kill any living thing on those planets.

Another important aspect to consider is the distance separating us from TRAPPIST-1, the star is 12.1 Parsec away from our Sun, that’s almost 40 light-years away ! Unless we find a way to distort space-time or get to find a wormhole (A wormhole is basically a compact region in space-time which reduces time to travel between two points), traveling to TRAPPIST-1 is physically impossible.

 

Proxima Centauri

At last we got Proxima Centauri b

 

prixomaearth

Proxima Centauri which means in latin “nearest (star) of centaurus”, a red dwarf low-mass star, it is 4.25 light-years away from our Sun, it is 10 times less massive than our sun with a temperature about half of our Sun.

It is loosely orbiting the Alpha Centauri(Alpha Centauri A and Alpha Centauri B) binary star. In 2016, the European Southern Observatory (ESO) announced the presence of an Earth-like exoplanet orbiting Proxima Centauri, Proxima Centauri b.

 

Proxima Centauri b

proxima

Proxima Centauri b is one of the closest Earth-like exoplanet ever discovered to this date. Orbiting its sun in the habitable zone, it is highly likely that water is present on its surface. Having a surface temperature of approximately -39.15 °C with a planetary mass of 0.004089 Mjup which makes it a great candidate for a habitable planet. It has a semi-major axis of  0.0485, orbiting closely its main star. Above all, it is pretty “close” to us at 1.295 Parsec from us, that’s approximately 4.22 light-years away from our Sun. The planet also receives 30 times more XUV radiation than Earth and 250 times more X-rays.

 

Earth’s and Proxima’s variables and correlations

 

proximacomparing
Earth and Proxima variables, they are pretty close to each other

 

correlation proxima
It has a correlation coefficient of 0.35(35%).

 

(According to some researchers Proxima Centauri b might have been hit by ‘superflares’ coming from its main star that made the planet uninhabitable long time ago.)

 

Conclusion

The TRAPPIST-1 exoplanets might be habitable in theory, but not knowing the planets exact atmospheric properties and irradiation levels opens a wide gap of uncertainty. Similarly, Proxima Centauri b atmospheric properties aren’t known, which is a crucial aspect when assessing habitability.

Our best bet would be Proxima Centauri b and TRAPPIST-1 g if we ignore the fact that those exoplanets might be highly irradiated due to the closeness to their main stars, they still share some important similarities with Earth. With a acceptable surface temperature and planetary mass. Proxima Centauri b is relatively close to us at a distance of 4.22 light-years. Unless we find a wormhole, we won’t be able to go anywhere close to it during our lifetime.

XUV radiation carry enough energy to break up electrons from atoms, high levels of radiation can break up water molecules which in turn destroys any life prospects. Which is why it is a major factor when looking for life-sustaining planets.

Looking for a new home in space isn’t that simple.

I would also like to point out that all the data we have about those extrasolar planets is largely based on theoretical assumptions and not on hard facts.

 

Github: https://github.com/alitanweer/oecanalysis

Sources:

 

 

 

 

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