# Atmosphere of habitable world around K-type star

I'm trying to work out the parameters of my planet, using the spreadsheets that Artifexian has developed (particularly this Planet Calculator and this Atmosphere Calculator) as a guide. In order for this planet to have liquid water at the surface, it requires its atmosphere to provide twice the insulation of Earth's atmosphere; that is, the atmosphere needs to raise the surface temperature by ~65 K instead of the ~33 K that the Earth's atmosphere does.

What kind of atmospheric composition could achieve this?

At the moment I've got an atmosphere comprising 2.349% Ne, 73.446% N2, 16.344% O2, 7.574% Ar, and 0.215% CO2 by unit volume of dry air. Water vapour content sits at around 0.8–1% averaged over the entire atmosphere. This atmospheric composition is approximately 0.1% denser than Earth's, but I essentially pulled these numbers out of a hat and I'd like to do slightly better than that. Ideally the air pressure at sea level would be no more than about 1.4 Earth's.

Other system details:

• Sun is a K1.2V
• Planet orbits its sun at a distance of 0.871 AU
• Planet radius, mass, and density are 0.956, 0.862 and 0.986 of Earth

## Short Answer: It's Complicated

Greenhouse effect calculations have some serious math behind them. There are positive and negative feedback loops, variations in albedo due to changing cloud patterns ocean ice, growing deserts... Then the variation of the stars spectral class makes all the empirical data from the Sol system inaccurate due to its different Black body radiation curve and the shifting importance of different absorbtion spectra of greenhouse gasses. Nothing short of a physics simulation will give you a perfect answer.

## Long Answer: I got a Workaround. Sort of.

Having encountered this problem during worldbuilding myself, I developed a workaround using linear model based on data from the solar system. Be aware that this is just a "good enough" approach and it is tuned to a G type star. Yet it served my purposes well and I never got crazy values out of it. Be aware that as soon as your planets temperature exceeds 230 Kelvin or 47 degrees Celsius Oceans will start to boil away in a runaway greenhouse effect. This is what happened to Venus in the past and will happen to Earth in about a billion years.

Greenhouse Gas List

$$CO2 = 514 K/atm /// 1378 K/atm$$ (if under 0.005 atm)

$$HO2 = 677 K/atm$$

$$CH4 = 404 K/atm /// 1466666 K/atm$$

(if under 0.00005 atm)

$$SO2 = 501 K/atm$$

$$O3 =19600000 K/atm$$

For a realistic atmosphere you'll need CO2, but do not exceed 0.02 atm (0.005 atm for comfort) or the atmosphere won't be breathable for humans. Water Vapor is also a must have, as it is the most important greenhouse gas. Ozone requires Oxygen (keep it between 0.16 and 0.5 atm for human survivability and don't have it exceed 35 % of the atmosphere, as it will burn out at higher concentrations) and should be kept under 0.0000001 atm for comfort. Methane requires biological processes and shouldn't exceed 0.05 atm. Sulfur dioxide is optional and would be a indicator of strong vulcanic activity. Keep it below 0.000005 atm.

## Your Atmosphäre

Looking at your atmosphere the high concentrations on Ar and Ne will need a special explanations.The lack of O3, H2O and CH4 is a bit on the oid side as well. My quick and dirty method tells me that you only get 2,96356 K out of your current atmosphere.

My suggestion

Go for 0,0045 atm CO2, add 0.05 atm H2O, 0.0000007 atm O3 and 0.0000075 atm CH4. Remove some of the noble gasses to make room and add some mire O2 and N2. This will get you to 64,771 K.

Now this still ignores the feedback loops, but should you feel fancy guesstimating the albedo of the planet for a given temperature is doable. Run the calculation and guesstimation several times and you should reach an acceptable equilibrium.

• Can you provide more details on how your calculations work? This seems to be the right kind of approach, and it might be able to be generalised to extend the atmosphere spreadsheet. Commented Apr 23, 2019 at 11:19
• How they work? As in how to use them or as in how did I come up with them? Commented Apr 23, 2019 at 11:47
• A little bit of both. I added another column using the numbers you provided, and ended up with a much lower value than what you did. Commented Apr 23, 2019 at 11:50
• I guess that you did not use a conditional function in Exel. For CH4 and CO2 I did provide two values and which one to use depends on the ammount of the gas. Since CH4 did provide a lot of heat, my guess is that you used the wrong value. Commented Apr 23, 2019 at 13:10
• How I came up with is simple, I looked up values and used the rule of proportion. There is no high art there tose values are just crude approximations. Commented Apr 23, 2019 at 13:13

To increase the temperature of the atmosphere, you need to trap more IR radiation.

If you want to increase the atmospheric capability of keeping IR radiation, you need to increase the content of greenhouse gases, like $$CO_2$$, $$CH_4$$, $$H_2O$$.

Those gases block the IR emitted from the surface, thus increasing the atmosphere temperature.