# SETI: The Drake Equation

In the [link:diploma-10|previous lecture], we looked at two of
the upcoming missions aimed at searching for extrasolar life:
NASA's *Kepler* and ESA's *Darwin*. In this lecture and
the subsequent lectures, we examine the more-speculative side of
the search for life: the search for extraterrestrial intelligence
(SETI). This lecture focuses on the Drake Equation, a useful tool
in this endeavour.

## Background

So far, we have considered extrasolar life to be **passive**:
it is something which sits there, waiting for us to discover it
through our **own endeavours**. However, suppose that some
extrasolar life is sentient, intelligent, and technologically
advanced. Then, this life may be making attempts to **signal**
its presence, and to contact other lifeforms in the Milky Way
galaxy.

In fact, this signaling might not be deliberate. The case of
Earth itself can be used as an example. Beginning with the first
**radio transmission** by **Marconi**, in 1897, a sphere of
artificial electromagnetic radiation has been expanding outwards
from the Earth at the speed of light. This sphere now has a
radius of over 100 light years; if detected by an
**extraterrestrial intelligence**, it could be used to deduce
the existence of intelligent life in our Solar System.

## The Drake Equation : Introduction

Before we go about deciding how to **detect** the signals of an
extraterrestrial civilization, we must first establish **how
many** of these civilizations we expect to exist in our galaxy,
whose presence we might be able to detect. To assist in this
task, **Frank Drake** developed a now-famous equation, which
estimates the number of communicating (deliberate or otherwise)
extraterrestrial civilizations which exist in the Galaxy at any
one point in time.

The Drake Equation may be written as the **product** of a
number of terms:

N = R_{*} f_{p} n_{e} f_{l}
f_{i} f_{c} L'''

Here, the terms have the following meanings:

**N**- The number of civilizations in Galaxy whose
electromagnetic emissions are detectable.

**R**_{*}- The rate of formation of stars suitable for the development of
intelligent life, in stars per year.

**f**_{p}- The fraction of those stars with planetary systems.
**n**_{e}- The number of planets, per solar system, with an environment
suitable for life.

**f**_{l}- The fraction of suitable planets on which life actually
appears.

**f**_{i}- The fraction of life bearing planets on which intelligent life
emerges.

**f**_{c}- The fraction of civilizations that develop a technology that
releases detectable signs of their existence into space.

**L**- The length of time such civilizations release detectable signals
into space, in years.

A couple of important points concerning the Drake Equation should
be made. Firstly, the **symbols** used in the equation are not
universal; different people use different sets of symbols,
although their **general meaning** remains the same. Secondly,
the Drake Equation is not the only possible equation which can be
used to estimate **N**; alternative formulas could be
developed. However, the Drake Equation remains the **most
popular** tool to estimate our chances of detecting
extraterrestrial intelligence.

In the following sections, we will look at how we might estimate each term in the Drake Equation.

## The Drake Equation : R_{*}

Estimation of **R _{*}** relies on our knowledge of

**star formation**. Although this area is still the subject of much work, we have a pretty complete knowledge of the rate at which stars form. In the case of

**solar-type stars**, which are not too hot and not too cold to harbour a solar system suitable for life to develop, the rate of star formation comes out at about

**1 per year**.

The Orion Nebula, a region of star formation

## The Drake Equation : f_{p}

As discussed in Lecture 1, the planets in our own
Solar System formed as a natural consequence of the **birth**
of the Sun. Based on the fact that planets are regularly being
found around other stars, many astronomers believe that the
formation of planets around single solar-type stars is
**inevitable**. Therefore, a good estimate for
**f _{p}** is

**1**.

The formation of a solar system

## The Drake Equation : n_{e}

When it comes to estimating **n _{e}**, and the
remaining terms in the Drake Equation, our knowledge is much less
certain than it was for

**R**and

_{*}**f**. To date, no

_{p}**terrestrial**extrasolar planets have been detected. However, this is primarily due to the limitations of our own detection technology; the situation can be expected to change with the launch of the

*Kepler*mission in 2006 (see [link:diploma-1|Lecture 1]). Until then, if we take our own Solar System as

**representative**of all extrasolar systems, then we might estimate

**n**as

_{e}**0.25**, reflecting the fact that out of our four terrestrial planets, only one (the Earth) is situated within the

**habitable zone**.

Planet Earth, the only habitable planet of our Solar System

## The Drake Equation : f_{l}

To estimate **f _{l}** we can rely on our knowledge of
how life developed on Earth (see [link:diploma-4|Lecture
4]). With the discovery of all the different types of

**extremophile**which are found on Earth (see [link:diploma-6|Lecture 6]), it appears life can develop in pretty

**hostile environments**, so long as the essential conditions are fulfilled:

**liquid water**,

**organic compounds**and a

**source of energy**. Therefore, we can estimate

**f**as

_{l}**1**, indicating that we expect life to develop on

**all**terrestrial planets situated within a habitable zone.

## The Drake Equation : f_{i}

Estimation of **f _{i}** is difficult. Anthropologists
still argue about the reasons why one particular branch of the

**ape family**went down an

**evolutionary pathway**which led to the ultimate development of

**modern-day humanity**, the only-known example of intelligent, sentient lifeforms. It is still not clear whether this development is inevitable or merely a product of chance. However, given that there are

**other**terrestrial species (such as dolphins and chimpanzees) which could develop into

**sentient beings**in the future, some scientists conclude that if life develops, then intelligent life will also develop. Therefore, we can estimate

**f**as

_{i}**1**.

Early human life on Earth

## The Drake Equation : f_{c}

If sentient lifeforms develop, it seems inevitable that they will
progress toward a technological level where they **broadcasts
signals** of its existence out into the Galaxy. However, we
should recognize that there is a **sociological factor**
involved here. Do the lifeforms **deliberately** broadcast
signals indicating their presence? Or does this process occur
**inadvertently**, as is the case with Earth? Or do the
lifeforms take deliberate measures to **hide** their existence,
by shielding their electromagnetic transmissions?

Marconi, the first person on Earth to transmit radio signals

These questions are very difficult to answer: if we do not know
what these lifeforms look like, how can we possibly guess at how
they might **think**? With the absence of any knowledge
whatsoever in this area, we can only make estimations based on
our knowledge of ourselves: humanity as a species has broadcast
its existence both inadvertently and deliberately. On this basis,
we can estimate **f _{c}** as

**1**.

## The Drake Equation : L

As with **f _{c}**, estimation of

**L**requires us to make conjectures about the sociological factors at work in an extraterrestrial civilization. In the case of the Earth, the

**population**has grown

**exponentially**over the past two centuries; but so has the chance that we might

**destroy**ourselves through man-made catastrophes. Present-day threats to humanity include

**nuclear war**(e.g., the situation with Iraq and North Korea),

**disease**(e.g., HIV/AIDS and the new flu-like epidemic spreading from the Far East), and

**environmental disaster**(e.g., global warming).

The mushroom cloud produced by the detonation of a hydrogen bomb

With all of these threats to our existence, it is not certain
whether humanity will **survive** to the turn of the next
century. If we take a pessimistic view that we will **destroy
ourselves** by then, then the amount of time our technological
civilization will have existed will be a mere **two
centuries**: from the start of the industrial revolution until
somewhere in the 21st century. On this basis, we can estimate
**L** as **200 years**.

## The Drake Equation : Putting it all together

Based on the above estimates of each term in the Drake Equation,
the **expected number** **N** of civilizations in the Galaxy
which are currently producing electromagnetic signals is
**50**. Taking the radius of the galactic disk as 15
kiloparsecs, and assuming that stars are spread evenly throughout
this disk, then on average we can expect to find one
**communicating civilization** in each **14 square
kiloparsecs** of the disk (i.e., in each 120 by 120 parsec
region).

Therefore, the **nearest** communicating civilization can be
expected to be around **120 parsecs away**. One of the topics
we will address in the next lecture is how we are addressing the
technological challenge of **detecting** and/or
**communicating** with such a neighbour civilization. Before
then, however, we must address some of the **limitations** of
the Drake Equation.

## The Drake Equation : Limitations

The biggest problem with the Drake Equation should be
self-evident: we were forced to make a number of **estimates**
in calculating a final value for **N**. For the terms appearing
in the equation, our ability to estimate values can be summarized
thus:

**R**is well-known_{*}**f**is reasonably well-known_{p}**n**is uncertain_{e}**f**is highly uncertain_{l}**f**is extremely uncertain_{i}**f**is extremely uncertain_{c}**L**is extremely uncertain

In fact, every time the Drake Equation is used to estimate
**N**, a different value is found! Some scientists find a
**large** value for **N**, others conclude that **N** is 1,
indicating that we are **alone** in the Galaxy. *The
Universe* finds a value of 10, five times smaller than the value
found in this lecture.

A secondary problem with the Drake Equation lies in its own
**incompleteness**: there may be a number of important factors
which have been **omitted**, such as the probability that life
develops in solar systems situated within dense **molecular
clouds**, where no electromagnetic signals can escape.