Main Sequence K Type Stars - Habitable Simulation

The K-Type Stars described here are Main Sequence Stars on The H-R Diagram. They are dimmer then our sun, Sol and are subdivided from K0 to K9. Some scientists believe that K - type stars offer the best conditions for an Earth-Like Planet. So, studying them is very important. This article is based on data available from [www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt here]. Additional parameters are calculated using the black body radiation formulas available at Math And Terraforming.

It is very important to remember that stars don't behave exactly as shown in the table. Each star has its own variations. Also, my calculations are based on the black body radiation formulas and they do not include flares and the Stellar Wind.

For each star model, parameters are compared to our own sun, Sol.

This article is dedicated for sci-fi writers, to have a better and close-up idea if a planet around a certain star can indeed be terraformed or not and at what cost. Please don't take it as a scientific work, it is just a simulation made with values that are much more easy to understand then dedicated scientific papers.

About the values[]

For all stars, the following parameters are calculated:

Main parameters:

Temperature (in degrees K, for our Sun, Sol it is 5778 K).
Mass: given in Solar masses
Radius: given in Solar radii
Bolometric Magnitude: includes all star's radiation, for Sol it is 4.81.
Visual magnitude: includes only visual light, for Sol it is 4.81.

Spectral parameters:

Main light spectra (for Sol, it is 577 nm). It helps us see if most light is emitted in red, blue, infrared or ultraviolet spectra.

Solar Constant - total energy output of the star: (Sol = 1)
Infrared light: (Sol = 1)
Red light: (Sol = 1)
Visible light: (Sol = 1)
Blue light: (Sol = 1)
Ultraviolet light: (Sol = 1)
Far UV light: (Sol = 1)

Habitable zone, based on light emissions:

Calculating the habitable zone, one must include four parameters:

Roche limit - below it, a star's gravity would tear apart any planet;
Solar constant - depends on distance from the star. For Earth, it is 1. Using Greenhouse Gases, it is possible to terraform a planet with a solar constant of 1/1000. By using Anti-Greenhouse Technology, it might be possible to terraform a planet with a solar constant of 20.
Light spectra - Plants on New Worlds need both red and blue light, which must be at least 1/1000 of what is on Earth. If either red or blue light fall below this limit, plants will not survive.
Toxic radiation include UV (especially far UV), X, gamma rays and ionized particle from the Stellar Wind. If toxic radiation is over 100 times higher then on Earth, Earth-like life is seriously threatened and atmosphere becomes too ionized and might be blown into space.

Further parameters:

Extended habitable zone (for Sol 0.223 to 31.6 AU): After applying all these constrains, one can determine the extended Habitable Zone, where greenhouse gasses or anti-greenhouse technology can bring temperature within acceptable boundaries, plants have enough red and blue light and toxic UV radiation is within acceptable limits.
Earth-like planet orbit: The distance of a Habitable Zone Planet or Earth-Like Planet (for Sol, 1 AU) is where a planet can exist without greenhouse gasses or anti greenhouse technology. It is listed if it fits within the extended habitable zone.
Tidal index: The star's tidal force on a planet in the extended habitable zone.
Orbital period: the orbital period of a star within the extended habitable zone.
Angular size: the size of the star as viewed from a planet in the habitable zone (Sol from Earth: 9.34). To see yourself how large a star would be as seen from a planet, draw a circle with the listed size in millimetres and look at it from a distance of one metre.

K0 Star[]

Main parameters:

Temperature: 5270
Mass: 0.88
Radius: 0.813
Bolometric magnitude: 5.59
Visual magnitude: 5.78

Spectral parameters:

Main light spectra: 603 (orange)

Solar constant: 0.502
Infrared light: 0.582
Red light: 0.506
Visible light: 0.473
Blue light: 0.425
Ultraviolet light: 0.189
Far UV light: 0.00127

Habitable zone, based on light emissions:

Solar constant = 20: 0.158 AU
Solar constant = 1: 0.708 AU
Solar constant = 1/1000: 22.4 AU
Minimum red light: 22.5 AU
Minimum blue light: 20.6 AU
Roche limit: 0.00011 AU

Further parameters:

Extended habitable zone: 0.158 - 20.6 AU
Earth-like planet orbit: 0.708 AU
Tidal index: 0.00207 - 35.1
Tidal index for Earth-like planet: 1.755
Orbit period (days): 24.5 - 36400 (100 years)
Orbital period for Earth-like planet: 232 (0.6 years)
Angular size: 0.37 to 48.0
Angular size for Earth-like planet: 10.73.

K0 stars are about half as luminous as the Sun and orange. Their habitable zones are smaller as these stars are dimmer.

K1 Star[]

Main parameters:

Temperature: 5170
Mass: 0.86
Radius: 0.797
Bolometric magnitude: 5.72
Visual magnitude: 5.95

Spectral parameters:

Main light spectra: 614 (orange)

Solar constant: 0.455
Infrared light: 0.545
Red light: 0.458
Visible light: 0.422
Blue light: 0.371
Ultraviolet light: 0.138
Far UV light: 0.000310

Habitable zone, based on light emissions:

Solar constant = 20: 0.151 AU
Solar constant = 1: 0.675 AU
Solar constant = 1/1000: 21.3 AU
Minimum red light: 21.4 AU
Minimum blue light: 19.3 AU
Roche limit: 0.00011 AU

Further parameters:

Extended habitable zone: 0.151 - 19.26 AU
Earth-like planet orbit: 0.675 AU
Tidal index: 0.00232 - 37.8
Tidal index for Earth-like planet: 1.890
Orbit period (days): 23.1 - 33300 (91 years)
Orbital period for Earth-like planet: 218 (0.6 years)
Angular size: 0.39 to 49.4
Angular size for Earth-like planet: 11.04.

K1 stars are about half as luminous as the Sun and orange. Their habitable zones are smaller as these stars are dimmer.

K2 Star[]

Main parameters:

Temperature: 5100
Mass: 0.82
Radius: 0.783
Bolometric magnitude: 5.81
Visual magnitude: 6.07

Spectral parameters:

Main light spectra: 623 (orange)

Solar constant: 0.422
Infrared light: 0.516
Red light: 0.424
Visible light: 0.387
Blue light: 0.334
Ultraviolet light: 0.109
Far UV light: 0.0001105

Habitable zone, based on light emissions:

Solar constant = 20: 0.1452 AU
Solar constant = 1: 0.649 AU
Solar constant = 1/1000: 20.5 AU
Minimum red light: 20.6 AU
Minimum blue light: 18.3 AU
Roche limit: 0.00010 AU

Further parameters:

Extended habitable zone: 0.145 - 18.27 AU
Earth-like planet orbit: 0.649 AU
Tidal index: 0.00246 - 38.9
Tidal index for Earth-like planet: 1.944
Orbit period (days): 22.3 - 31500 (86 years)
Orbital period for Earth-like planet: 211 (0.6 years)
Angular size: 0.40 to 50.4
Angular size for Earth-like planet: 11.27.

K2 stars are about half as luminous as the Sun and orange. Their habitable zones are smaller as these stars are dimmer. These stars produce slightly more red then blue light.

K3 Star[]

Main parameters:

Temperature: 4830
Mass: 0.78
Radius: 0.755
Bolometric magnitude: 6.13
Visual magnitude: 6.55

Spectral parameters:

Main light spectra: 658 (orange)

Solar constant: 0.333
Infrared light: 0.444
Red light: 0.332
Visible light: 0.289
Blue light: 0.232
Ultraviolet light: 0.0447
Far UV light: 0.000001691

Habitable zone, based on light emissions:

Solar constant = 20: 0.1290 AU
Solar constant = 1: 0.577 AU
Solar constant = 1/1000: 18.25 AU
Minimum red light: 18.22 AU
Minimum blue light: 15.24 AU
Roche limit: 0.00010 AU

Further parameters:

Extended habitable zone: 0.129 - 15.24 AU
Earth-like planet orbit: 0.577 AU
Tidal index: 0.00336 - 46.9
Tidal index for Earth-like planet: 2.34
Orbit period (days): 19.15 - 24600 (67 years)
Orbital period for Earth-like planet: 181.2 (0.5 years)
Angular size: 0.46 to 54.7
Angular size for Earth-like planet: 12.23.

Compared to the Sun, K3 stars are clearly redder. The lack of blue light means that some far outer planets cannot support plant life. A habitable planet would experience shorter seasons then Earth. Because of higher tidal forces, such a planet would have longer days then Earth does.

K4 Star[]

Main parameters:

Temperature: 4600
Mass: 0.73
Radius: 0.713
Bolometric magnitude: 6.46
Visual magnitude: 6.98

Spectral parameters:

Main light spectra: 690 (orange)

Solar constant: 0.257
Infrared light: 0.369
Red light: 0.252
Visible light: 0.210
Blue light: 0.1578
Ultraviolet light: 0.01835
Far UV light: 3.12E-08

Habitable zone, based on light emissions:

Solar constant = 20: 0.1133 AU
Solar constant = 1: 0.506 AU
Solar constant = 1/1000: 16.12 AU
Minimum red light: 15.87 AU
Minimum blue light: 12.56 AU
Roche limit: 0.000095 AU

Further parameters:

Extended habitable zone: 0.113 - 12.56 AU
Earth-like planet orbit: 0.506 AU
Tidal index: 0.00462 - 56.9
Tidal index for Earth-like planet: 2.85
Orbit period (days): 16.28 - 19020 (52 years)
Orbital period for Earth-like planet: 154.0
Angular size: 0.53 to 58.8
Angular size for Earth-like planet: 13.15.

As one can see, around K4 stars infrared light becomes significantly stronger, while blue light is dimmer. The ultraviolet part of the spectra is becoming negligible. The far UV emissions assuming the black body model are so weak that they don't affect life and habitability in any way. At this point, a star releases far more of its far UV and X part of the spectra through stellar flares and coronal mass ejections then through radiation from the stellar body. Therefore, for next categories of stars, the far UV emission will no longer be displayed.

K5 Star[]

Main parameters:

Temperature: 4440
Mass: 0.7
Radius: 0.701
Bolometric magnitude: 6.65
Visual magnitude: 7.28

Spectral parameters:

Main light spectra: 715 (red)

Solar constant: 0.223
Infrared light: 0.338
Red light: 0.215
Visible light: 0.1740
Blue light: 0.1241
Ultraviolet light: 0.00986

Habitable zone, based on light emissions:

Solar constant = 20: 0.1056 AU
Solar constant = 1: 0.472 AU
Solar constant = 1/1000: 14.93 AU
Minimum red light: 14.68 AU
Minimum blue light: 11.14 AU
Roche limit: 0.000094 AU

Further parameters:

Extended habitable zone: 0.1056 - 11.14 AU
Earth-like planet orbit: 0.472 AU
Tidal index: 0.00564 - 62.8
Tidal index for Earth-like planet: 3.14
Orbit period (days): 14.97 - 16220 (44 years)
Orbital period for Earth-like planet: 141.6
Angular size: 0.59 to 62.0
Angular size for Earth-like planet: 13.9.

Around K5 stars, light is orange. A habitable zone planet would experience significant tidal stress to be forced into a synchronous rotation period or would experience strong volcanism.

K6 Star[]

Main parameters:

Temperature: 4300
Mass: 0.69
Radius: 0.669
Bolometric magnitude: 6.89
Visual magnitude: 7.64

Spectral parameters:

Main light spectra: 739 (red)

Solar constant: 0.1845
Infrared light: 0.294
Red light: 0.1752
Visible light: 0.1371
Blue light: 0.0932
Ultraviolet light: 0.00519

Habitable zone, based on light emissions:

Solar constant = 20: 0.0960 AU
Solar constant = 1: 0.429 AU
Solar constant = 1/1000: 13.58 AU
Minimum red light: 13.23 AU
Minimum blue light: 9.66 AU
Roche limit: 0.000094 AU

Further parameters:

Extended habitable zone: 0.0960 - 9.66 AU
Earth-like planet orbit: 0.429 AU
Tidal index: 0.00740 - 74.8
Tidal index for Earth-like planet: 3.74
Orbit period (days): 13.08 - 13180 (36 years)
Orbital period for Earth-like planet: 141.6
Angular size: 0.65 to 65.1
Angular size for Earth-like planet: 14.5.

Compared to the Sun, K6 stars offer a much more inner habitable zone, with the best condition for habitability found around the orbit of Mercury.

K7 Star[]

Main parameters:

Temperature: 4100
Mass: 0.64
Radius: 0.63
Bolometric magnitude: 7.23
Visual magnitude: 8.16

Spectral parameters:

Main light spectra: 775 (red edge)

Solar constant: 0.1418
Infrared light: 0.242
Red light: 0.1304
Visible light: 0.0973
Blue light: 0.0613
Ultraviolet light: 0.001695

Habitable zone, based on light emissions:

Solar constant = 20: 0.0842 AU
Solar constant = 1: 0.377 AU
Solar constant = 1/1000: 11.91 AU
Minimum red light: 11.42 AU
Minimum blue light: 7.83 AU
Roche limit: 0.000090 AU

Further parameters:

Extended habitable zone: 0.0842 - 7.83 AU
Earth-like planet orbit: 0.377 AU
Tidal index: 0.01043 - 90.3
Tidal index for Earth-like planet: 4.51
Orbit period (days): 11.15 - 10000 (27 years)
Orbital period for Earth-like planet: 105.4
Angular size: 0.75 to 69.9
Angular size for Earth-like planet: 15.63.

Compared to the Sun, K7 stars offer a much more inner habitable zone, with the best condition for habitability found around the orbit of Mercury.

K8 Star[]

Main parameters:

Temperature: 3990
Mass: 0.62
Radius: 0.615
Bolometric magnitude: 7.4
Visual magnitude: 8.43

Spectral parameters:

Main light spectra: 796 (red edge-infrared)

Solar constant: 0.1245
Infrared light: 0.222
Red light: 0.1121
Visible light: 0.0812
Blue light: 0.0490
Ultraviolet light: 0.001131

Habitable zone, based on light emissions:

Solar constant = 20: 0.0789 AU
Solar constant = 1: 0.353 AU
Solar constant = 1/1000: 11.16 AU
Minimum red light: 10.59 AU
Minimum blue light: 7.00 AU
Roche limit: 0.000089 AU

Further parameters:

Extended habitable zone: 0.0789 - 7.00 AU
Earth-like planet orbit: 0.353 AU
Tidal index: 0.01265 - 99.6
Tidal index for Earth-like planet: 4.98
Orbit period (days): 10.28 - 8590 (24 years)
Orbital period for Earth-like planet: 97.2
Angular size: 0.82 to 72.8
Angular size for Earth-like planet: 16.28.

Compared to the Sun, K8 stars offer a much more inner habitable zone, with the best condition for habitability found around the orbit of Mercury. The lack of blue light significantly reduces the outer limit of their habitable zone.

K9 Star[]

Main parameters:

Temperature: 3930
Mass: 0.59
Radius: 0.608
Bolometric magnitude: 7.49
Visual magnitude: 8.56

Spectral parameters:

Main light spectra: 808 (infrared)

Solar constant: 0.1163
Infrared light: 0.212
Red light: 0.1033
Visible light: 0.0736
Blue light: 0.0433
Ultraviolet light: 0.000830

Habitable zone, based on light emissions:

Solar constant = 20: 0.0763 AU
Solar constant = 1: 0.341 AU
Solar constant = 1/1000: 10.79 AU
Minimum red light: 10.16 AU
Minimum blue light: 6.58 AU
Roche limit: 0.000087 AU

Further parameters:

Extended habitable zone: 0.0763 - 6.58 AU
Earth-like planet orbit: 0.341 AU
Tidal index: 0.01362 - 101.4
Tidal index for Earth-like planet: 5.07
Orbit period (days): 10.01 - 8020 (22 years)
Orbital period for Earth-like planet: 94.7
Angular size: 0.86 to 74.5
Angular size for Earth-like planet: 16.66.

There is a habitable zone around K9 stars, limited outside by the lack of blue light. Any inner planet would be tidal locked, any Earth-like planet would also likely be tidal locked or be a Low-Spinning Planet.

Conclusion[]

K - type stars vary significantly from the heaviest K0 to the lightest K9. All these stars offer habitable zones. Many scientists consider these stars as life sanctuaries, as they offer somehow similar conditions to Sol, are far more common in the Universe and have long life spans.

The fact is that K - type stars offer narrower habitable zones then the Sun, exposed to stronger tidal forces and with shorter seasons.