## Probabilities in the Galaxy A Distribution Model for habitable Planets Copyright © Klaus Piontzik

 German Version

## 10.2 - The extended Seager-Equation

 The Seager equation treats only a certain amount of red dwarf stars, ie stars of the spectral class M, namely only stars that can be detected by the JWST telescope. The Seager equation can also be extended to all red dwarf stars, in the galaxy.

N* = NRZ = A·FRZ is the number of M stars (Red Dwarfs) present in the galaxy with FRZ = 0.7 and A = 200-300 billion stars.

fQ stands for the proportion of quiet M-stars, which account for about 80 %

fHZ = Fph = Fp·Fh is the proportion of those M stars, which have a planet first and secondly it is in the habitable zone.Fp = 201:14,000 and Fh = 10:603 with Fph = 1:4,200.

fO quantifies the proportion of those planets that are visible at the star for the JWST.(0.01 x 0.1= 0.001)

fL = FL is the fraction of animated planets, with FL = 1:9.

fS stands for an intelligence which leaves a measurable biosignature in the atmosphere, ie a technological civilization, with: fS = Fi·Fz = 1:14
· 1:7,943 = 1:111.203

This results in:

 10.2.1 Equation N = A · FRZ · fQ · Fph · fO · FL · Fi · Fz N = A · FRZ · fQ · Fph · fO · FLiz

Substituting the values into equation10.2.1 yields:

N = (100-300)·109 · 0.7 · 0.8 · 0.001 · 1:4200 · 1:1001
N = 14 – 40 technological civilizations

According to Theorem 6.4.1, there are 10 – 290 technological civilizations, in sun-like star systems, in our galaxy.
This results in a much smaller number of civilizations, with red dwarfs as central stars, than in sun-like systems.

 10.2.2 Equation NS > NRZ

Comment:
A biosignature means certain signs in the atmosphere of an exoplanet, such as the existence of certain gases (such as CO2 and CFCs) that indicate the presence of a technological civilization.

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