A Search for Earth’s Nearest Twin
Kyriam Anne Maletta
9484561
BSc Physics with Astrophysics
School of Physics and Astronomy
The University of Manchester
Third Year Dissertation
March 2017
Abstract
The Sun and the Earth were used as models to determine the habitability criteria of an
exoplanetary system. This was followed by a brief analysis of the most common exoplanet detection
methods, in particular transit photometry, the radial velocity method, gravitational microlensing and
astrometry. It was concluded that the astrometric method is the most appropriate for detecting nearby
Earth-sized exoplanets in the near future. A spectroscopic analysis of the atmosphere and composition
of an Earth analogue was provided, highlighting the elements that could indicate the presence of life.
The astrometric method and the planetary analysis were incorporated in a survey, whose purpose is to
detect possible Earth twins. The survey operates within a radius of 20 pc from the Sun, aiming to target
a minimum of 11 stars and a maximum of 50 stars for a duration of 5 years.
,A Search for Earth’s Nearest Twin Kyriam Anne Maletta
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1. Introduction
Until the 16th century, the Earth was thought to be unique. That was the time when the
geocentric view of the Solar System was officially accepted by most scientists and philosophers, leading
them to believe that the Earth was special. This idea was then challenged by individuals such as
Nicolaus Copernicus, Galileo Galilei and Giordano Bruno, who supported the idea of a heliocentric view
of the Solar System. In his work “De l’Infinito, Universo e Mondi”, Bruno went as far as to state that:
“there are countless suns and countless earths all rotating around their suns in exactly the same way as the
seven planets of our system… The countless worlds in the universe are no worse and no less inhabited than
our Earth”. [1] This leads us to the modern view of the Universe, in which the Sun is simply one of many
stars in one of many galaxies, and to the so-called Principle of Mediocrity, which states that there is
nothing special about the Solar System or the planet Earth.
During the past two decades, enormous progress has been made in detecting planets orbiting
around other stars. As of today, 3593[2] exoplanets have been discovered and confirmed. A total of 49 of
these planets have the potential of being habitable, 18 of which are Earth-sized. [3]
This dissertation will begin by establishing the criteria a planet would need to fulfil in order to
be considered potentially habitable. It will describe some of the detection methods currently in use for
exoplanets, namely the transit method, the radial velocity method and gravitational microlensing, with
particular emphasis on the astrometric method. A survey will be drafted, in which astrometry will be
used to detect potentially habitable planets around potential host stars. The survey will also include the
methods to analyse the atmosphere and the composition of a planet, in order to verify its habitability.
2. Criteria for Planetary Habitability
There are many factors to consider when establishing the habitability of a planet. The main
criteria discussed in this section have been selected using the Earth and the Sun as models, as they form
the only known system to support life. For the purpose of this dissertation, only carbon-based life will
be considered.
2.1 The Characteristics of the Star
The following characteristics of the host star are modelled according to the Sun, and therefore
the star should be similar to the Sun in size, age and composition. The effective temperature (Teff),
luminosity (L), and lifetime (τ) of a star may be roughly deduced from the mass. Upper and lower limits
on the mass of the potential host star can be placed. [4] The host star should not exceed 1.5 M⊙, as it
would not live on the main sequence for long enough to allow a planet to develop life. A star with mass
less than 0.5 M⊙, on the contrary, is likely to be extremely close to the planet, enough to be tidally
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locked before life has the chance to form. The assumption that the star should be a main sequence star
is based on the fact that it has to be stable for most of its lifetime. Instabilities such as frequent high
energy activity would hinder the formation of life on orbiting planets. A range of luminosities, L, can be
deduced from the mass-luminosity relation. For main sequence stars of mass M between 0.5 M⊙ and 2
M⊙, this relation is as follows:
∝ . (1)
According to equation 1, the stellar luminosities can range between ~ 0.06 L⊙ - 5.06 L⊙. If the star is
considered as a blackbody with effective temperature Teff, its luminosity is proportional to the fourth
power of the temperature multiplied by its surface area. Consequently,
∝ , (2)
so the effective (or surface) temperature range is ~ 3000 K – 9000 K. The main sequence lifetimes, τ,
can be estimated from the mass-lifetime relation:
.
∝ , (3)
which implies a range of lifetimes between ~ 3.6 - 56 billion years.
These calculations provide a great deal of information about the host star. In particular, these
values of mass, luminosity and effective temperature correspond to three spectral classes: F, G and K. [5]
Specifically, stars with luminosity class V (main sequence stars) from spectral classes F2 to K9 can be
taken into account. Therefore, it is these types of stars that are more likely to host a habitable planet.
The lower limit on the lifetime indicates that the star should spend a minimum of 3.6 billion years on
the main sequence, which is enough time for life to begin to develop.
2.2 The Habitable Zone
Astrobiologists agree that the basic requirement for the formation of carbon-based life on a
planet is the presence of liquid water. The habitable zone is the range of orbits around a host star within
which a planet in possession of an atmosphere could sustain liquid water. [6] This area is sometimes
referred to as the Goldilocks zone, as the distance between the star and the planet is such that the
conditions are “just right” for water to remain in its liquid state.
The limits of the habitable zone depend on the luminosity of the host star. The luminosity
increases with time as the star ages, so the boundaries of the habitable zone also change, moving
further away. The continuously habitable zone (CHZ) takes into account this evolution. The habitable
zone boundaries can be estimated from the inverse square law relationship between flux and distance,
d, given below:
∗
= , (4)
4 ∗
where ∗ is the stellar luminosity and ∗ is the stellar flux.
3
