On the abundance of extraterrestrial life after the Kepler mission

Abstract

The data recently accumulated by the Kepler mission have demonstrated that
small planets are quite common and that a significant fraction of all stars may
have an Earth-like planet within their Habitable Zone. These results are
combined with a Drake-equation formalism to derive the space density of biotic
planets as a function of the relatively modest uncertainty in the astronomical
data and of the (yet unknown) probability for the evolution of biotic life, Fb.
I suggest that Fb may be estimated by future spectral observations of exoplanet
biomarkers. If Fb is in the range 0.001 -- 1 then a biotic planet may be
expected within 10 -- 100 light years from Earth. Extending the biotic results
to advanced life I derive expressions for the distance to putative
civilizations in terms of two additional Drake parameters - the probability for
evolution of a civilization, Fc, and its average longevity. For instance,
assuming optimistic probability values (Fb Fc 1) and a broadcasting longevity
of a few thousand years, the likely distance to the nearest civilizations
detectable by SETI is of the order of a few thousand light years. The
probability of detecting intelligent signals with present and future radio
telescopes is calculated as a function of the Drake parameters. Finally, I
describe how the detection of intelligent signals would constrain the Drake
parameters.

Full text

Accepted for publication in the Internationa l Journal of Astrobiology
On the abundance of extraterrestrial life after the Kepler mission
Amri Wandel, Racah Inst. of Physics, The Hebrew University of Jerusalem
E-mail: amri@huji.ac.il
Abstract
The data recently accumulated by the Kepler mission have demonstrated that small
planets are quite common and that a significant fraction of all stars may have an
Earth-like planet within their Habitable Zone. These results are combined with a
Drake-equation formalism to derive the space density of biotic planets as a function of
the relatively modest uncertainty in the astronomical data and of the (yet unknown)
probability for the evolution of biotic life, Fb. I suggest that Fb may be estimated by
future spectral observations of exoplanet biomarkers. If Fb is in the range 0.001 -- 1
then a biotic planet may be expected within 10 -- 100 light years from Earth.
Extending the biotic results to advanced life I derive expressions for the distance to
putative civilizations in terms of two additional Drake parameters - the probability for
evolution of a civilization, Fc, and its average longevity. For instance, assuming
optimistic probability values (Fb~Fc~1) and a broadcasting longevity of a few
thousand years, the likely distance to the nearest civilizations detectable by SETI is of
the order of a few thousand light years. The probability of detecting intelligent signals
with present and future radio telescopes is calculated as a function of the Drake
parameters. Finally, I describe how the detection of intelligent signals would constrain
the Drake parameters.
Keywords: Kepler mission – exoplanets – biotic planets – SETI – Drake equation
Introduction
An important yet until recently poorly known factor, required for estimating the
abundance of extraterrestrial life is the fraction of stars with planets, in particular
Earth-like planets within the Habitable Zone. The recent findings of the Kepler
mission unveiled much of the uncertainty about extra-solar planets (exoplanets),
reducing the uncertainty in estimating the abundance of extraterrestrial life. One of
the unknown "astronomical" parameters in the Drake Equation has been the fraction
of stars with planets, and in particular Earth-like planets. As this work applies the
recent exoplanet findings to the abundance of biotic planets and the Drake equation,
a few exoplanet key results should be reviewed. In the past decade planets have been
discovered around hundreds of nearby stars [Fridlund et al. 2010]. However, until
the Kepler mission the main method to detect exoplanets has been the Doppler
(radial motion) method, which is strongly biased towards massive planets. Of some
400 exoplanets found until 2010 almost all have been Jupiter-sized. The data
released by the Kepler mission revealed over 2000 exoplanet candidates, most of
which are smaller than Neptune and their planet mass histogram is peaked towards
the smaller end of a few Earth masses [Borucki et al 2011a,b; Batalha et al., 2012].
Small planets have been shown to be abundant [Buchhave et al., 2012] and likely

found in the habitable zone [Traub, 2011]. Recent analyses of the Kepler statistics
showed that about 20% of all Sun-like stars have Earth-sized planets orbiting within
the habitable zone [Petigura, Howard and Marcy 2014]. These results are confirmed
by observations other than Kepler. The HARPS team estimated that more than 50%
of solar-type stars harbor at least one planet, with the mass distribution increasing
toward the lower mass end (<15 Earth masses) [Mayoret al., 2011]. Using micro-
lensing observations it has been estimated that on average there is at least one planet
per star in the Galaxy [Cassan et al., 2012]. These findings demonstrate that Earth-
like planets are probably quite common, enhancing the probability to find planets
with conditions appropriate for the evolution of biological life, as we know it. Based
on these results we may now better estimate the abundance of life in our stellar
neighborhood [Wandel 2011; 2013].
There are two approaches to the search for life outside of the Solar system: (i) looking
for biotic signatures (biomarkers) in the spectra of Earth-like extra solar planets, and
(ii) searching for intelligent electromagnetic signals (SETI). The success probability
of both methods depends critically on the distance to the nearest candidates.
The first method requires spectral analyses of extra solar planets, looking for water
vapor and gases produced by biotic systems, like oxygen (photosynthesis) or methane.
Spectroscopy of exoplanets is marginally possible with present technology, and even
with planned future projects it may be feasible only for relatively nearby exoplanets.
In addition to the technological challenge, spectral methods could miss many potential
life forms; as alien life may be very different from life on Earth, we could fail to
recognize it by spectral analyses.
The second approach circumvents these limitations by looking not for the physical
signs of biotic life, but rather for technological, radio (or other electromagnetic
radiation) broadcasting civilizations. Also this strategy, however, has drawbacks:
complex life and in particular intelligent life is presumably much scarcer than simple,
mono-cellular life, and hence the distances to the nearest broadcasting civilizations
may be very large, possibly beyond the detection range of present, and perhaps even
future radio telescopes.
In order to assess the feasibility of detecting biotic planets and intelligent
extraterrestrial signals it is essential to estimate the distances to the eventual targets.
This work goes in this direction by applying the recent results from the Kepler
mission. In order to estimate the abundance of biotic life I derive useful expressions
and figures for the distance to biotic exoplanets and to putative civilizations. It is
suggested that the probability for the evolution of biotic life may be estimated by
future spectral observations of exoplanet biomarkers. Similarly it is argued that future
planned radio telescopes may constrain the abundance of radio loud civilizations.
How far is the closest biotic planet?
How common are worlds harboring life? The recent findings of Kepler indicate that
Earth-sized planets may be found around almost every star. However, assuming that
life may develop only on Earth-like planets orbiting Sun-like stars (an assumption
likely to be too conservative, as alien life may develop in environments very different
from Earth's biosphere), the number of candidates may be reduced to about 10% of all
stars.
As is well known, the Drake equation (eq. 5 below) estimates the number civilizations
in the Milky Way (also referred to as "the Galaxy"). By analogy, the number of biotic
planets in the Galaxy, Nb, may be assessed by a "biotic Drake equation"

Nb = R* Fs Fp Fe nhz Fb Lb. (1)
The first five terms are astronomical factors and the last two may be called "biotic
parameters". The astronomical factors include the rate of star birth in the Galaxy, R*,
the fraction of stars suitable for evolution of life, Fs, and three "planetary" factors: the
fraction of stars that have planets, Fp, the fraction of Earth-sized planets, Fe, and the
number of such planets within the Habitable Zone, nhz. These five "astronomical
factors" can be combined into a single parameter Rb, the rate at which stars suitable
for the evolution of biotic life are formed in the Galaxy,
Rb = R* Fs Fp Fe nhz. (2)
The average star birth rate in the Galaxy is R* ~ 10 yr-1 [e.g. Carroll and Ostile, 2007].
If evolution of life is assumed to be limited to stars similar to our Sun, then Fs ~ 0.1.
However, this assumption is probably a too restrictive hypothesis. The Kepler data
show that Earth size planets are frequent within the Habitable Zone of lower Main
Sequence small stars [e.g. Dresing and Charbonneau, 2013], which are the majority of
all stars. If life can evolve on planets of red dwarfs [Guinan and Engle, 2013, Scalo, et
al., 2007] then Fs ~ 1 (since 75% of all stars are red dwarfs).
Recent exoplanet findings, in particularly those by the Kepler mission, suggest that
probably most stars have planetary systems, hence Fp ~ 1. Analyses of the Kepler
results shows that 7-15% of the Sun-like stars have an Earth-sized planet within their
habitable zone [Petigura et al., 2014], which gives Fe nhz ~ 0.1. If biotic life is not
restricted to Earth-like planets and to the Habitable Zone (e.g. as in the case of
Jupiter's moon Europa) then Fe nhz may be even bigger, up to order unity. Combining
all these factors gives for the product of the astronomical parameters in equation (1) a
probable range of 0.1 < Rb < 10 yr-1.
The "biotic parameters" in eq. (1) are F b, the probability of the appearance of biotic
life within a few billion years on a planet with suitable conditions, and Lb, the average
longevity of biotic life in units of Gyr (109 years). Equations (1) and (2) give
Nb ~ 1011 (Rb/R*) Fb (Lb/10), (3a)
Similarly, the space density of biotic planets, nb, may be written as
nb ~ n* (Rb/R*) Fb (Lb/10), (3b)
where n* ~ 0.01 ly-3 is the average space density of stars in the Galaxy. Considering
the history of life on Earth, Lb is likely to be at least a few billion years, so for stars
similar to the Sun (or smaller) Lb ~10 (1010 yr). Substituting the values of Lb and R*
equations (3a,b) become
Nb ~ 1010 Rb Fb, (4a)
nb ~ 0.001 Rb Fb ly-3. (4b)
Since the average distance between biotic worlds is db ~ nb-1/3, eq. (4b) gives
db ~ 10 (Rb Fb) -1/3 ly. (4c)

Eq. (4c) gives the probable distance to our nearest biotic neighbor, plotted in Fig. 1, as
a function of the biotic factor Fb.
Figure 1. The probable distance to our nearest biotic neighbor, db vs. the biotic factor
Fb, for two values of the parameter Rb. For the break in the upper curve see the
discussion following eq. (7a).
Estimating the Biotic Parameter
Given the recent progress in understanding the demographics of planets, in particular
Earth-like planets (the "astronomical factor"), the biotic parameter, namely the
probability of the evolution of biotic life, remains the major missing factor for
estimating the distance to our neighbor biotic planets.
Simple life has appeared on Earth 3.5-3.8 Gyr ago - less than 1 Gyr after Earth’s
formation and merely ~0.1 Gyr after the establishment of appropriate environmental
conditions (the end of the heavy bombardment), a time very short compared to the
ages of Earth and the stars. If Earth is a typical case (the mediocrity principle), it is
plausible that Fb is close to unity. On the other hand, as the origin of life on Earth is
very poorly understood, some experts in that area assign an extremely low probability
to a similar scenario happening elsewhere (the "Rare Earth Hypothesis"; Benner et al.
2002). According to this approach Fb may be extremely small.
Bayesian analysis demonstrates that as long as Earth remains the only known planet
with biotic life, any value could be assigned to Fb [Turner, 2012]. Hence the
abundance of extraterrestrial biotic life remains an open question, depending on the
(yet unknown) probability for biotic life to evolve on planets with suitable conditions
within a given cosmic time. However, a breakthrough in this area may be reached in
the near future, if spectral characteristics such as oxygen and other biomarker gases
are detected in the atmospheres of Earth-like exoplanets, e.g. by studying eclipses1
[Rauer et al. 2011; Palle et al. 2011; Loeb and Maoz 2013] or by advanced space
telescopes, such as the James Webb Space Telescope2 (JWST), the Darwin mission3
1
http://sci.esa.int/sre-fa/47037-exoplanet-spectroscopy-mission-esm (oct 2014)/
2
http://www.jwst.nasa.gov (oct 2014)/
3
http://.esa.int/Our−Actiities/Space−Science/Darin−oerie oct 2014)/
1
2
3
4
-6 -5 -4 -3 -2 -1 0
log db (ly)
log Fb

and the Terrestrial Planet Finder4. If a few planets with bone fide biosignatures are
found, the biotic parameter Fb could be assigned an approximate value.
Quantitatively, suppose that out of a sample of Nc appropriate candidates (Earth-like
planets within the Habitable Zone of a star aged at least a few Gyr), biosignatures are
detected in the spectra of Nbs planets. Straightforward probability argumentation
would imply that the likelihood of biotic life evolution is of the order of Fb~Nbs /Nc.
This value should be modified to account for eventual selection effects and sampling
corrections. On the other hand, if out of the above sample of Nc candidate planets no
one shows a definite biosignature, this null result would impose an upper limit
Fb<1/Nc. If and when the number of planets with biosignatures grows, a probability
distribution function may be constructed, depending on planet lifetime, size, parent
star type etc.
Assuming Fb is in the range of 0.001 < Rb Fb < 1, eq. (4a) gives that the number of
biotic planets in the Milky Way is between millions and billions, and the
corresponding distance to the nearest biotic world (given by eq. (4c)) is between 10
and 100 light years.
The distance to putative civilizations
In this section we extend the above analyses to putative civilizations and apply it to
the Search for Extra Terrestrial Intelligence (SETI). The number of civilizations in the
Milky Way (Nc) may be expressed by the Drake equation,
Nc = R* Fs Fp Fe nhz Fb Fc Lc . (5)
Similarly to eq. (1), the eight variables on the right hand side may be divided into two
groups: the first five are astronomical factors and the last three - one biotic (Fb) and
two "civilization" factors. The latter two are related to the development of intelligent
life: the intelligence-communicative factor Fc, defined as the probability that one or
more of the species on a planet harboring biological life will eventually develop a
civilization using radio communication, and Lc, the broadcasting longevity (in years)
of such a civilization.
Expressions analogous to eqs. (4a,b), for the number of communicative civilizations
(Nc) and their abundance (space density, nc) are easily derived by replacing Lb in eqs.
(3a,b) with Fc Lc,
Nc ~ 1000 Rb Fb Fc Lc3 (6a)
and
nc ~ 10-10 Rb Fb Fc Lc3 ly-3. (6b)
where Lc3=Lc/(1000 years). The normalization Lc3 is just for convenience and does not
presume any specific value to the longevity of radio-communicative civilizations (this
will be discussed later).
Even if communicative civilizations thrive in the Milky Way, we may be unable to
detect their radio signals, unless the typical distance between them is within our
detection range. As the parameter Rb is relatively well estimated, and Fb may be
estimated in the near future, e.g. by finding biosignatures as discussed above, the
4
http://science.nasa.gov/missions/tpf (oct 2014)/

major uncertainty in eqs. (6a,b) remains in the two unknown "civilization
parameters", the probability for the evolution of civilizations using radio
communication, Fc, and their longevity (the duration of their "radio loud" phase) Lc.
By analogy to eq. (4c) the average distance between communicative civilizations can
be derived from eq. (6b),
dc ~ 2000 (Rb Fb Fc Lc3) -1/3 ly for dc<1000 ly (7a)
Eq. (7a) assumes that the average distance between neighbor civilizations is smaller
than the smallest dimension of the system. Since the Galaxy has a shape of a thin disk,
this assumption is valid only when the distance dc is smaller than the scale height of
the stellar distribution in the Galaxy (the thickness of the disk), which is ~1000 ly (in
other words, as long as the product Rb Fb Fc Lc3 > 10). Otherwise (if Rb Fb Fc Lc3 <
10), we must take into account the flat geometry of the Galaxy. In that case we may
calculate the average distance by assuming that Nc civilizations are uniformly
distributed on the area of the Glactic disk (a circle with a diameter of dG~100,000
light years ). Equating this to the area of Nc circles each having a radius dc gives π dc2
Nc ~ π dG2 and the average distance between neighbor civilizations is dc ~ 105 Nc-1/2
ly. Substituting Nc from eq. (6a) gives for this case
dc ~ 3000 ( Rb Fb Fc Lc3 ) -1/2 ly for dc > 1000 ly (7b)
Figure 2. The average distance between neighbor civilizations (d) vs. the average
longevity of a communicative civilization Lc, for several values of the product RF =
Rb Fb Fc. On the vertical right axis are marked the relevant detection ranges of
leakage and beamed radio signals by the Arecibo and SKA telescopes (see text).
0
1
2
3
4
5
0 2 4 6 8
log d (ly)
Log Lc (years)
Beamed
Arecibo
Beamed SKA
Leakage SKA
Leakage
Arecibo

Fig. 2 shows the average distance between neighbor civilizations (eqs. 7a,b) vs. the
average longevity of a communicative civilization Lc, for several values of the product
RF = Rb Fb Fc.
Unlike the biotic factor, the civilization parameters Fc and Lc cannot be inferred even
intuitively from the evolution of life on Earth. As the evolution of complex life on
Earth took about ~ 4 billion years, the probability for the evolution of complex and
intelligent life during a few billion years could be anywhere between unity
(corresponding to Earth being a typical case) and very small (if the appearance of
complex life and intelligence is an extremely rare event [e.g. Cuntz et al. 2012] or
typically requires a much longer time. Also Lc, the average longevity of a
communicative civilization, cannot be inducted from its short history on Earth and
could be anywhere between a few hundred years and billions of years.
Communicative civilizations may disappear within a relatively short time after
developing radio technology because of self destruction (wars or ecological disasters)
or else become less detectable due to the development of radio-quiet communication
channels. On the other hand, civilizations may survive such "childhood diseases" by
spreading to other planets and last much longer. Obviously the weighted average of
the longevity would be increased by older, long lasting (and broadcasting)
civilizations.
The SETI success probability
There are two scenarios for detecting radio signals from extraterrestrial civilizations:
(1) finding a purposeful, directed broadcast attempt, including an interstellar
automatic radio beacon or (2) civilizations may be detected through no special efforts
of their own. The latter hypothesis, often called eavesdropping, is concerned with the
extent to which a civilization can be unknowingly detected through the by-products of
its daily activities, e.g. the leakage of its own radio communication to space. The
range for detecting such radio signals depends on the receiver sensitivity and on the
transmitting power, as well as on the level of the background noise and on whether
the signal is directed or isotropic. Beamed transmissions directed at a specific target
would be much stronger and thus detectable from longer distances than the semi-
isotropic broadcasting, typical for radio stations, looked after by eavesdropping. Future
radio observatories such as EVLA (Expanded Very Large Array), LOFAR (Low
Frequency Array) and Square Kilometer Array (SKA) may be able to detect low-
frequency radio broadcast leakage from a civilization with a radio power similar to
ours out to a distance of a few hundred of light years [Loeb and Zaldarriaga, 2007].
SKA would be able to detect an airport tower radar from 30 light years5. Beamed
transmissions could be detected over much larger distances. For example, a targeted
search by the Arecibo telescope could detect alien signals sent by a similar device
(i.e., with a similar power, ~1013 Watt/m2/radian2) and aimed at Earth from distances
of a few thousands of light years. Noteworthy, the sensitivity of all-sky surveys is
much lower and the above detection ranges need to be decreased by a factor of 10 --
100. Eqs. (7a,b) imply that even with rather "optimistic" values of the other
parameters (Rb Fb Fc ~ 1), unless Lc is longer than a million years, the average
distance between neighbor civilizations is thousands of light years, far beyond the
range of eavesdropping even by future telescopes such as SKA.
5
https://www.skatelescope.org/key-documents (oct. 2014)/

Transmissions beamed at Earth, either unintentionally, like an aviation radar or
communication satellite, or intentionally like the Arecibo message of 19746, may be
detected from considerably larger distances. For example, a beamed transmission at
the broadcasting power similar to that of the Arecibo radar can be detected by the
Arecibo radio telescope at a range of ~ 3000 light years, and by future telescopes such
as SKA the detection range may increase to ~30,000 light years, virtually across the
Milky Way. These ranges are shown on the right vertical axis in fig. 2. Note however
that the effective broadcasting time of beamed signals may be significantly shorter
than the total communicative longevity, as discussed below.
The expressions for the average distance between civilizations derived above can be
used to estimate the success chances of SETI by calculating the probability that a
broadcasting civilization happens to lie within the detection range of present and
future radio telescopes. Let us first consider eavesdropping (looking for leakage
signals). Using the sensitivity of future radio telescopes such as SKA, the
eavesdropping detection range is of the order of 100 light years. Equation (7a) shows
that a neighbor civilization is likely to exist within this distance if the "Drake product"
Fb Fc Lc is of the order of a million years or more. For smaller values of the Drake
product we may define the likelihood p(d), that a civilization happens to exist at a
distance d < dc, that is, closer to Earth than the average distance between neighboring
civilizations. A straightforward geometric approach (fractional volume) gives
p(d) ~ ( d / dc )3. (8)
Fig. 3 shows the likelihood p(d<100), that a broadcasting civilization happens to exist
within a distance of 100 ly from Earth, as a function of the average longevity of
communicative civilizations, for several values of the Drake product.
6
http://www.seti.org/seti-institute/project/details/arecibo-message (nov. 2014)
-12
-10
-8
-6
-4
-2
0
0 2 4 6 8
p(d<100 ly)
log Lc (years)

Figure 3. The probability of a civilization to exist within a distance of 100 light years
from Earth, vs. the average longevity of a communicative civilization, Lc, for several
values of the product RF = Rb Fb Fc.
Combining eqs. (8) and (7a,b) gives the probability to detect leakage signals in terms
of the Drake parameters (assuming a detection range of 100 ly, appropriate for
planned radio arrays such as SKA):
p (d <100 ly) ~ 10-4 Rb Fb Fc Lc3 dc < 1000 ly, (9a)
p (d <100 ly) ~ 3 10-5 ( Rb Fb Fc Lc3 ) 3/2 dc > 1000 ly. (9b)
As in eq. (7a), the condition on dc in eq. (9a) is equivalent to a condition on the
product Rb Fb Fc Lc3 > 10, and in eq. (9b) Rb Fb Fc Lc3 < 10. For example, if we
assume that communicative civilizations are common (Rb Fb Fc ~ 1), and if they
typically transmit for ten thousand years (Lc3 ~ 10), the probability that a civilization
is presently broadcasting within ~ 100 ly from Earth is 0.001.
The probability of detecting beamed signals
As discussed above, assuming the broadcasting power of putative civilizations is
comparable to ours, eavesdropping on leakage signals has a quite limited range; the
Arecibo telescope could detect leakage signals from civilizations broadcasting at the
power of Earth at a distance of only a few light years, and future telescopes such as
SKA up to ~100 ly. On the other hand, beamed transmissions may be detected from
considerably larger distances. For example, a beamed transmission comparable to that
of the Arecibo radar may be detected by the Arecibo dish at a range of ~ 3000 ly, and
by future telescopes such as SKA up to ~30,000 ly. Apparently, these increased
detection ranges should give a significantly higher detection probability. On the other
hand, beamed signals may not be continuously aimed in our direction, contrary to
leakage signals. This effect is likely to reduce the effective broadcasting duration. It
may be described by introducing a "beaming parameter" b, the fraction of the
broadcasting lifetime of a civilization during which it is actually sending signals
beamed in our direction. This beaming may happen either unintentionally, as
communication with satellites, spacecrafts, or planets in their own solar system, or
deliberately as interstellar messages [e.g. Zetkov 2006]. In other words, bLc is the
integrated duration of beamed broadcasting in the direction of Earth.
For Rb Fb Fc b Lc3 < 10 (see eq. 9b) the probability to find a civilization within the
detection range of beamed signals by Arecibo end SKA, respectively, is
p (d< 3000 ly) ~ 1 ( Rb Fb F c b Lc3 )3/2 Arecibo, (10a)
and
p (d<30,000 ly) ~ 1000 ( Rb Fb Fc b Lc3 )3/2 SKA. (10b)
For example, assuming that communicative civilizations are common, that is Rb Fb Fc
~ 1, and that on average signals are beamed at Earth during an integrated time of bLc
~ 10 years, equations (10a,b) give a detection probability p ~10-3 by Arecibo and p~1
by SKA. If actually Rb Fb F c b Lc3 <10 it is not surprising that SETI has not yet
detected an alien signal (the "Great Silence"), and it may remain silent even with the

increased sensitivity of future telescope arrays. If, on the other hand, Rb Fb F c b Lc3
>10, then applying eq. (9a) to beamed signals gives
p(d< 3000 ly) ~ 10-4 Rb Fb Fc b Lc3 Arecibo,
and
p(d<30,000 ly) ~ 1 SKA,
implying that SKA might be able to detect signals beamed at Earth by putative
civilizations.
Estimating the Civilization Parameters
Similarly to the biotic factor, also the civilization parameters Fc and Lc are presently
unknown. If SKA and advanced future radio arrays fail to detect intelligent
extraterrestrial signals, eqs. (9a,b) and (10b) may be used to place an upper limit on
the products Fc Lc and Fc bLc, respectively. On the other hand, if an extraterrestrial
signal from another civilization is detected, the present ignorance in the civilization
parameters may be removed, or at least significantly constrained. If by then also
biomarkers of exoplanets are detected, so that Fb can be estimated to some extent, the
product Fc Lc could be assigned an approximate value; suppose that out of a sample of
Nbs suitable civilization candidates (that is, Earth-like planets aged at least a few Gyr
with a biosignature) intelligent signals are detected from Nis ones; here, in analogy to
the section on the biotic parameter above, Nbs is the number of planets with biotic
signature, and Nis is the number of planets from which intelligent signals are detected.
A similar argument as in the case of the biotic factor would count for the
"communicative factor", or the likelihood of a communicative civilization to evolve
on a biotic planet, multiplied by the average broadcasting longevity, leading to a value
of the order of
Fc Lc ~ 10 Gyr Nis / Nbs,
where 10 Gyr is the age of the Galaxy. As in the case of the biotic fator, this
expression needs to be modified by eventual selection effects and sampling
corrections, as well as by putative contributions to Nis from non biotic planets such as
automated beacons.
Summary
The recent results of the Kepler mission significantly reduce the uncertainty in the
astronomical parameters of the Drake equation. I derive expressions for the space
density of biotic worlds as a function of the (yet unknown) probability for the
evolution of biotic life and the uncertainty in the astronomical parameters. Similar
expressions are derived for the distance to putative communicative civilizations,
depending on two additional unknown factors in the Drake equation, the probability
of evolution from simple biotic life to a communicative civilization and its longevity.
Additionally, the probability to detect radio signals from other civilizations with
present and future radio telescopes is estimated in terms of these factors. The
extended analyses, updated by the Kepler results, presented in this paper suggests that
our nearest biotic neighbor exoplanets may be as close as 10 light years. Even with a
less optimistic estimate of the biotic probability, for example that biotic life evolves
on one in a thousand suitable planets, our biotic neighbor planets may be expected

within 100 light years. On the other hand, the distance to the nearest putative
civilizations, even for optimistic values of the Drake parameters, is estimated to be
thousands of light years.
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