On November 1, 2011, the formula for estimating the abundance of extraterrestrial life in our galaxy – Drake equation – celebrated its 50th birthday.

In its original terms the Drake equation states that:

N=R* x fp x ne x f x fi x fc x fl

where:

N = the number of civilizations in our galaxy with whom we might establish communication;

and

R* = the average rate of star formation per year in our galaxy;

fp = the fraction of those stars that have planets;

ne = the average number of planets that can potentially support life per star that has planets;

f = the fraction of the above that actually go on to develop life at some point;

fi = the fraction of the above that actually go on to develop intelligent life;

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into spac;

fl = the length of time for which such civilizations release detectable signals into space.

The following values were used by Drake and his colleagues in this historical day of November 1st, 1961

  • R* = 10/year (10 stars formed per year, on the average over the life of the galaxy)
  • fp = 0.5 (half of all stars formed will have planets)
  • ne = 2 (stars with planets will have 2 planets capable of developing life)
  • fl = 1 (100% of these planets will develop life)
  • fi = 0.01 (1% of which will be intelligent life)
  • fc = 0.01 (1% of which will be able to communicate)
  • L = 10,000 years (which will last 10,000 years)

Which produced N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 10,000 = 10.

So, we suppose to have at least 9 neighbor civilizations that will be willing and able to communicate with us.

Where are you, our cosmic brothers?

Here I would like to evaluate the first 4 parameters from the Drake equation.

Let’s look to the first parameter R*

Its approximate value can be easy derived from the large amount of astronomical data gathered by the Earth’s civilizations during the last 5 000 years (or even more), so the estimate of 10 stars per year considered fair.

However, I think it makes sense to change the R* parameter from original Drake Equation to the number that represents a rate of star formation that happened several billion years ago, when life first appears in a particular galaxy. That makes a perfect sense because life needs time to develop to civilization,  and civilization, in turn, needs time to develop to a state when it will able and willing to communicate. And this time is in average (given Earth civilizations) several billion years, so the rate of star formation can differ during this time-span.

The alternative is to use instead of R* a number of stars in the galaxy N* multiplied to the age of a galaxy  Tg.  However, this estimate also assumes that the star formation rate is constant over the life of the our galaxy. That gives N*=R*x Tg.

Milky Way is estimated to have from 200 to 400 billion stars. Its age is estimated to be between 12.6 and 16 Ga.

That gives R* range 12-30, so 10 is still a good number for R*.

To be continued …

References:

Extrasolar planets: More giants in focus, http://www.nature.com/nature/journal/v467/n7314/full/467405a.html

Habitable planets around the star Gliese 581? http://www.aanda.org/index.php?option=com_article&access=doi&doi=10.1051/0004-6361:20078091&Itemid=129

Extrasolar planets on Wikipedia http://en.wikipedia.org/wiki/Kepler_%28spacecraft%29#Extrasolar_planets_detected

NASA Staff (2 February 2011). “NASA Finds Earth-size Planet Candidates in Habitable Zone, Six Planet System”. NASA. http://kepler.nasa.gov/news/nasakeplernews/index.cfm?FuseAction=ShowNews&NewsID=98. Retrieved 2011-04-24.

Overbye, Dennis (2 February 2011). “Kepler Planet Hunter Finds 1,200 Possibilities”. New York Times. http://www.nytimes.com/2011/02/03/science/03planet.html. Retrieved 2011-04-24.

Borenstein, Seth (19 February 2011). “Cosmic census finds crowd of planets in our galaxy”. Associated Press. http://apnews.excite.com/article/20110219/D9LG45NO0.html.

Cumming, A. et al. Publ. Astron. Soc. Pacif. 120, 531–554 (2008).

Gould, A. et al. Astrophys. J. 720 , 1073–1089 (2010).

Schneider, Jean (10 September 2011). “Interactive Extra-solar Planets Catalog”. The Extrasolar Planets Encyclopedia. http://exoplanet.eu/catalog.php

Borucki et al: Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data , Fed 01, 2011, arXiv:1102.0541v1 [astro-ph.EP]

Selsis F., J. F.Kasting, B. Levrard, J. Paillet, I. Ribas, and X. Delfosse,  Habitable planets around the star Gliese 581?, A&A 476, 1373–1387 (2007), DOI: 10.1051/0004-6361:20078091