1. 1
Detailed
Numerical
Modeling
of
Multi-­‐
Planet
Systems
Our
scientific
understanding
of
the
Universe
through
astronomical
measurements
has
been
improving
enormously
over
the
last
few
decades,
but
there
is
still
so
much
to
learn.
One
of
the
topics
at
the
forefront
of
astrophysical
research
is
exoplanets,
planets
that
orbit
stars
or
stellar
remnants
outside
of
our
own
solar
system.
Since
the
discovery
of
the
first
exoplanet
in
1995,
51-­‐Pegasi,
the
field
has
been
growing
rapidly.
Today,
more
than
1,800
new
exoplanets
have
been
confirmed
through
a
variety
of
observational
techniques
and
over
4,000
additional
candidate
planets
are
awaiting
confirmation
[6].
The
Kepler
spacecraft,
launched
by
NASA
in
2009,
is
responsible
for
a
large
majority
of
these
discoveries,
and
more
importantly,
for
most
of
the
nearly
500
multi-­‐planet
systems
that
have
been
discovered.
These
Kepler
multi-­‐planet
systems
are
one
of
the
many
surprises
that
have
been
brought
to
light
from
our
interest
in
exoplanets
[1].
Many
Kepler
multi-­‐planet
systems
contain
planets
with
very
tight
orbits.
Some
of
these
systems
contain
“Hot
Jupiters”
Jupiter
sized
planets
with
orbital
periods
less
than
Mercury’s
(e.g.,
[2,3,4,5]).
Kepler
multi-­‐planet
systems
with
close
planets
that
have
masses
ranging
from
Earth-­‐like
to
Jupiter-­‐like
and
orbits
of
only
a
few
days
challenge
the
existing
theories
of
planetary
creation
and
evolution.
Because
many
of
these
planets
are
on
tight
orbits,
orbiting
very
close
to
the
central
star,
tides
are
expected
to
play
a
key
role
in
the
formation,
evolution,
and
survival
of
Kepler
multi-­‐planet
systems.
Tides
are
a
secondary
effect
of
the
gravitational
forces
between
objects.
They
arise
because
one
side
of
an
object
feels
stronger
gravitational
attraction
than
the
other.
In
the
simple
case
of
a
two-­‐object
system,
tides
affect
the
spin
of
the
components
and
–
more
importantly
–
the
orbital
separation,
in
an
attempt
to
drive
the
system
into
an
equilibrium
state
where
the
spin
frequency
of
each
object
is
equal
to
the
orbital
frequency.
NASA
has
archived
all
the
recorded
data
regarding
exoplanets
for
public
use[6].
This
archive
contains
a
wealth
of
information
about
each
system’s
orbital
period,
planetary
radius
and
mass,
as
well
as
other
statistics
regarding
the
system’s
characteristics.
To
start
with,
my
research
would
focus
on
specific
Kepler
multi-­‐
planet
systems
with
two
close
planets
that
have
tight
orbits,
as
this
is
the
simplest
case
in
terms
of
Kepler
multi-­‐planet
systems.
My
goal
is
to
look
at
the
observed
properties
of
these
systems
and
understand
how
tides
affect
their
formation,
evolution,
and
long-­‐term
survival.
I
will
accomplish
my
goal
by
extracting
pertinent
data
from
the
relevant
Kepler
systems
to
create
state
of
the
art
numerical
models.
These
numerical
models
will
include
the
most
up
to
date
understanding
of
tidal
dissipation
and
its
uncertainties
[7].
The
computational
tools
needed
to
construct
these
models
have
already
been
developed
in
the
theoretical
astrophysics
group
at
NU
(part
of
CIERA,
the
Center
for

2. 2
Interdisciplinary
Exploration
and
Research
in
Astrophysics).
By
comparing
my
numerical
model
with
the
observations,
I
will
attempt
to
explain
trends
in
the
data,
potentially
shedding
light
on
how
tides
affect
the
secular
evolution
of
two-­‐planet
systems.
This
work
will
also
potentially
reveal
new
trends
in
the
properties
of
the
systems.
From
there
I
will
attempt
to
generalize
my
findings
in
relation
to
more
complex
systems
with
more
exoplanets
involved,
as
well
as
to
apply
my
results
to
the
confirmed
exoplanets
that
arise
from
the
large
pool
of
candidate
planets,
which
is
updated
continuously.
This
research
is
important
to
the
field
of
astrophysics
for
many
reasons.
First
off,
the
Kepler
mission
gave
astrophysicists
a
wealth
of
information
on
exoplanets.
The
number
of
exoplanets
discovered
by
Kepler
is
massive
compared
to
the
conventional
methods
in
place
before
Kepler.
This
research
will
help
maximize
the
benefits
of
the
Kepler
mission,
which
produced
so
much
raw
data
that
can
be
looked
through
and
played
with.
Secondly,
the
Kepler
mission
created
a
multitude
of
other
projects
related
to
the
discovery
of
exoplanets.
These
projects
will
be
compiling
similar
data
to
what
Kepler
produced,
so
knowing
what
to
do
with
this
type
of
data
will
be
imperative
to
maximize
future
results
from
these
other
projects.
Additionally
this
kind
of
theoretical
work
can
provide
important
constraints
on
the
physical
mechanisms
entering
the
evolution
of
planetary
systems.
Specifically,
it
will
allow
us
to
learn
about
tidal
theories,
which
are
yet
not
well
constrained,
and
we
can
become
more
precise
with
our
models
for
the
future.
I
will
be
taking
many
steps
to
prepare
for
this
research
project.
I
am
enrolled
in
ASTRO
330-­‐ISP
Astrophysics
for
Spring
2015
in
order
to
better
familiarize
myself
with
the
necessary
background
information
regarding
astrophysics.
I
will
also
be
taking
a
fifth
credit
of
independent
study,
ASTRO
399,
with
Professor
Frederic
Rasio,
who
will
be
my
sponsor
for
this
project.
Professor
Rasio
and
I
have
already
talked
about
using
this
independent
study
credit
to
better
educate
me
on
the
intricacies
regarding
exoplanets
and
the
Kepler
multi-­‐planet
systems
I
will
be
focusing
on.
I
have
also
taken
the
entire
PHYS
330
Classical
Mechanics
sequence,
which
covers
planetary
motion
and
the
evolution
of
planetary
orbits,
amongst
other
topics
in
classical
mechanics.
I
have
completed
courses
in
Python
and
am
a
proficient
coder.
This
is
helpful
in
the
data
analysis
aspect
of
the
project,
which
will
most
likely
involve
the
use
of
Python
in
order
to
extract
the
information
from
the
NASA
archive
that
is
relevant
to
my
project.
With
the
completion
of
ASTRO
330
in
the
spring,
the
help
of
Professor
Rasio,
and
my
knowledge
of
Python,
I
will
have
all
of
the
necessary
preparation
I
need
in
order
to
accurately
assess
the
data
and
attempt
to
understand
how
tides
effects
the
formation,
evolution,
and
survival
of
Kepler
multi-­‐planet
systems.
I
would
like
to
continue
research
on
exoplanets
after
this
project
and
delve
deeper
into
the
intricacies
of
how
these
Kepler
multi-­‐planet
systems
form
in
order
to
see
what
they
can
tell
us
about
the
formation
of
solar
systems
as
a
whole.

3. 3
Reference
List:
1.
Howard,
A.
W.
et
al.
Nature
http://dx.doi.org/10.1038/nature12767
(2013)
2.
Valsecchi,
Francesca;
Rasio,
Frederic
A
et
al.
2014,
The
Astrophysical
Journal,
Volume
786
Issue
2,
pg
102
3.
Valsecchi,
Francesca;
Rasio,
Frederic
A
et
al.
2014,
The
Astrophysical
Journal
Letters,
Volume
787
Issue
1,
pg
L9
4.
Valsecchi,
Francesca;
Rasio,
Frederic
A
et
al.
2014,
The
Astrophysical
Journal
Letters,
Volume
793
Issue
1,
pg
L3
5.
Li,
Shu-­‐Lin
et
al.
2010,
Nature,
Volume
463
Issue
7284,
pg
104-­‐106
6.
NASA
Exoplanet
Archive,
http://exoplanetarchive.ipac.caltech.edu
7.
Hut,
P.
et
al.
1982,
Astronomy
and
Astrophysics,
vol.
110
no.
1,
pg
37-­‐42