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In my previous post about Drake equation, I tried to calculate R* – = the average rate of star formation per year in our galaxy.

I ended up with R* between 12 and 30, which is a think in good agreement with 10 – the original Drake estimate.

fp stays for a fraction of stars that have planets. The Drake estimate for this parameter was fp=0.5. Which means that 50% of stars in Milky Way may have planets. In its modern estimate fp ~ 0.4 (Marcy et al , 2005), however this number can become much higher with developing more precise techniques for planet detection.

Where this number come from?

The problem with detecting planets is that they are small, even giant gaseous planets like Jupiter are still much smaller that stars. So we have to use a very precise technique to detect such a relatively small mass.

Let me first give a quick overview of methods used to detect extra solar planets

The most of extrasolar planets have been found by using one of the following methods:

    • The new microlensing technique (Gould et al., 2011) based on a property of mass to act as a gravitational lens.
    • The Doppler velocity technique (Cumming, A. et al., 2008) measures small shifts in the radial velocity of a star due the gravitational pull of its orbiting planet.
    • Properties of millisecond pulsars combined with Doppler velocity technique can be used to probe their environments for object as small as asteroids.


  • The transit technique based on the Doppler velocity technique (employed by Kepler) detects periodic variations in a star’s brightness while a planet passes in front of it (between the star and the observer) and in its back.

The microlensing technique (Gould et al., 2011; see the figure below) is a relatively new technique that uses the approach, based on a property of mass to act as a gravitational lens. If a relatively faint star is passing in front of a distant bright star, it acts as a gravitational lens, causing light from a distant bright star to brighten and fade with a characteristic ‘light curve’ over a period of several weeks. If this faint nearer star possesses a planet (and/or planetary system, or some objects orbiting the star), it too acts as a gravitational lens, altering the light curve. This alteration can be large enough to be measured even for an Earth-mass planet. However, this deviation is hard to detect because it lasts for only several hours.

Figure courtesy  Gould et al. 2011.

Microlensing technique

From Gould et al. 2011: “(a) When a faint star (red) passes in front of a more distant bright star (yellow), it focuses light from the distant object, causing it to brighten and fade over several weeks with a characteristic ‘light curve’. (b) The presence of a planet (brown) orbiting the nearer star causes additional brightness variations on a timescale of hours. Continual monitoring of a microlensing event can determine whether planets are present, and yields their mass and orbital separation from the parent star.”

The above technique used by Gould et al (2011) found that in observed 13 such events, 5 resulted in planetary detections.

Other microlensing surveys (Chambers J. 2011) found planets in about 1/3 of systems examined, which makes a lower limit of fp ~ 0.3.

Millisecond pulsars can be timed with high precision which makes them very sensitive probes of their environments. For example, any object placed in orbit around them causes periodic Doppler shifts in their pulses’ arrival times on Earth. These maesurements can then be analyzed to reveal the presence of the companion and, with enough data, provide precise measurements of the orbit and the object’s mass.

The first confirmed exoplanets were actually found in orbit around a millisecond pulsar, PSR B1257+12. However, I doubt that life can exist on these planets.

Doppler velocity technique

According to estimate produced by Mayor et all (2011), based on Doppler velocity technique, more than 50% of solar type stars in Milky Way have at least 1 planet of any mass and it has an orbital period of more than 100 days. On the other hand, Cumming, A. et al (2008) analyzing data from a large Doppler velocity survey proposed that about 10% of solar-mass stars possess a planet at least as massive as Saturn, orbiting within 3 AU. So where are Saturns, there could be Earths.

As of November 4, 2011, 695 extra solar planets (in 571 planetary systems and 81 multiple-planet systems) have been identified. See, Schneider (10 September 2011).

The transit technique

On February 2, 2011, the Kepler team released a list of 1235 extrasolar planet candidates, including 54 that may be in the habitable zone. These findings are based on the results of observations conducted for 128 days (May 12 to Sept. 17, 2009), of more than 156,000 stars in Kepler’s field of view, which covers approximately 1/400 of the sky.

The selection of target stars done by Kepler team was purposefully skewed to enhance the detectability of Earth-size planets by choosing those stars with an effective temperature and magnitude (those that have temperatures between 4000 and 6500 K and of late F, G and K spectral types). That choice maximized the transit signal-to-noise ratio (SNR).

This population of target stars has the following frequencies of planets detection (Borucki et al, 2011):

6.1% for Earth-size,
6.7% for super-Earth-size,
17.2% for Neptune-size,
4.1% for Jupiter-size,
and 0.02% for very-large candidates

This makes 6.1+6.7+17.2+4.1+0.2=34.3

So the current value of fp according to above data is somewhere between 0.3 and 0.34.

And I wonder if it is possible to combine the current techniques used by Kepler with microlensing technique to check the results?


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

Borucki et al (2011). Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data arxiv.org DOI: arXiv:1102.0541v1


Chambers J (2010). Extrasolar planets: More giants in focus. Nature, 467 (7314), 405-6 PMID: 20864987

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


Goud et al (2010). Frequency of Solar-Like Systems and of Ice and Gas Giants Beyond the Snow Line from High-Magnification Microlensing Events in 2005-2008 Astrophysics Earth and Planetary Astrophysics DOI: arXiv:1001.0572

Marcy, G.; Butler, R.; Fischer, D.; Vogt, Steven et al. (2005). “Observed Properties of Exoplanets: Masses, Orbits and Metallicities”. Progress of Theoretical Physics Supplement 158: 24–42. arXiv:astro-ph/0505003. Bibcode 2005PThPS.158…24M. doi:10.1143/PTPS.158.24.

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