Download Numerical Evolu4on of Soliton Stars

Numerical
Evolu.on
of
Soliton
Stars
Dr.
Jayashree
Balakrishna
(HSSU
Saint
Louis,
Missouri)
Collaborators:
M.
Bondarescu
(Ole
Miss.
),
R.
Bondarescu
(Penn.
State),
G.
Daues
(N.C.S.A),
F.S.
Guzman
(Mexico),
E.
Seidel
(LSU,
NSF)
Overview
•  What
is
Dark
MaPer?
•  Possible
Dark
MaPer
Candidates.
•  What
are
soliton
stars
°
role
in
dark
maPer
cosmology:
halos,
compact
objects.
°
forma.on
of
soliton
stars.
°proper.es
of
compact
soliton
stars.
In
spherical
Symmetry.
In
Full
3D
GR‐
gravita.onal
radia.on.
Dark
MaPer
Dark
maPer:
maPer
whose
presence
is
inferred
by
its
gravita.onal
effects
even
though
it
cannot
actually
be
seen.
Dark
MaPer:
Galac.c
Rota.on
Curves
Direct
Proof
of
Dark
MaPer
Hubble
Expansion:
Relevance
of
scalar
fields
in
cosmology
•  Redshi[
in
light
(distant
galaxies)
propor.onal
to
distance.
•  Expansion
of
the
universe:
co‐moving
distance
between
points
(difference
in
their
coordinates)
remains
constant
but
physical
distance
between
•  points
increases.
Dark
MaPer
and
Dark
Energy
•  Hubble
Telescope
observa.ons
1998
of
distant
supernovae
showed
that
the
expansion
of
the
universe
was
accelera.ng
rather
than
slowing
down.
•  Postulated
dark
energy
(non
zero
cosmological
constant
working
like
a
repulsive
force).
•  Present
es.mates
are
about
70%
of
the
energy
density
is
provided
by
this
dark
energy.
Only
about
5%
of
the
density
is
luminous
maPer
leaving
about
25%
being
dark
maPer.
Nature
of
Dark
MaPer
•  Primordial
Nucleosynthesis:
Current
es.mates
of
light
element
abundances
fit
predic.ons
of
BBN
to
a
high
degree.
This
is
an
es.mate
of
baryon
(protons+neutrons)
abundances.
•  These
es.mates
show
that
dark
maPer
is
essen.ally
non‐baryonic.
Axions
as
Dark
MaPer
Why
they
are
preferred?
i)
They
are
non‐baryonic
ii)
They
are
predicted
by
par.cle
physics
as
a
solu.on
to
the
lack
of
CP
viola.on
in
strong
interac.ons.
iii)
They
are
light
and
behave
as
cold‐dark
maPer
and
can
explain
galaxy
forma.on
and
large
scale
structure.
Axion
Mass
Range
−6
•  Lower
bound
10 eV / c
≈
to
keep
the
density
cri.cal
density
−3
•  Upper
bound
10 eV / c
€
to
prevent
excessive
energy
loss
in
stars
and
€
supernovae.
2
M Pl
€
The
mass
of
a
compact
star
~
where
m
is
m
the
mass
of
the
par.cle
it
is
made
of
€
Detec.on?
10 −22 eV
•  Extremely
light
scalar
par.cles
(
)
could
in
principle
form
dark
maPer
halos.
•  Heavier
par.cles
can
form
compact
objects.
€
•  Can
there
be
stars
made
of
scalar
par.cles
that
have
signatures
that
could
be
detected?
Gravita.onal
Radia.on
What
is
an
axion‐star?
•  Axions
are
scalar
par.cles
that
can
be
described
by
real
fields.
These
par.cles
could
clump
together
by
a
Jeans
instability
mechanism
to
form
stars
called
soliton
stars.
•  There
are
also
scalar
par.cles
that
can
be
described
by
complex
scalar
fields
(also
possible
dark
maPer
candidates)
that
could
form
stars
by
the
same
mechanism.
Such
hypothe.cal
stars
are
called
boson‐
stars.
•  These
stars
held
together
by
a
balance
between
the
aPrac.ve
force
of
gravity
and
the
dissipa.ve
nature
of
the
uncertainity
principle
(field).
Boson
and
Soliton
Stars:
Equa.ons,
Configura.ons
and
Evolu.ons.
•  Spherically
Symmetric
Boson
Stars:
E.
Seidel,
and
W.‐M
Suen,
Phys.
Rev.
D.
42,
1990.
(seidel‐
suen
Boson)
•  Soliton
Stars:
Ground
State
and
Forma.on:
E.
Seidel
and
W.‐M.
Suen,
Phys.
Rev.
Le=.,
66,
1659
(1991).
(seidel‐suen
Soliton)
•  Soliton
Stars
Ground
State:
M.
Alcubierre,
R.
Becerril,
F.
S.
Guzman
Class.Quant.Grav.
20,
2883,
(2003).
(Alcubierre
et
al)
•  Boson
Stars:
Spherically
Symmetric
and
3D
evoluSons:
J.
Balakrishna,
PhD
thesis
Washington
University
1999.
•  Boson
Stars
on
a
3D
Grid:
F.
S.
Guzman,
Phys.
Rev.
D.
73,
021501(R)
(2006)
Recent
Work
•  Evolu.on
of
3D
Boson
Stars
with
Waveform
Extrac.on:
J.
Balakrishna:
R.
Bondarescu,
G.
Daues,
F.
S.
Guzm
´an
and
E.
Seidel
Class.
Quant.
Grav.
23,
2631
(2006).
(J.B.
et
al
boson)
•  Numerical
Simula.ons
of
Oscilla.ng
SolitonStars:
Excited
States
in
Spherical
Symmetry
and
Ground
State
Evolu.ons
in
3D:
J.
Balakrishna,
R.
Bondarescu,
G.
Daues,
M.
Bondarescu
Phys.
Rev.
D.
77,
024028,
2008.
(J.B.
et
al.
soliton)
The
equa.ons
•  Coupled
Einstein‐Klein
Gordon
system:
Ac.on:
Metric
(spherical
symmetry+
polar
slicing):
Solu.ons
•  Boson
Stars
(complex
field)
‐
.me
dependent
field,
.me
independent
metric
with
energy
density
being
.me
independent.
•  Soliton
Stars
(real
field)‐
no
equilibrium
configura.on.
Fields
and
metrics
have
.me
dependence.
Asympto.cally
Flat:
φ (r =∝) = 0 => φ1,3,.. (r =∝) = 0.
€
A0 (∝) = 1, A2,4,.. = 0.
C2 j = eigenvalue
€
Soliton
Star
Profile
(Alcubierre
et.
Al)
Boson
Star
Profile
(Seidel‐Suen
Boson)
Mass
Profile:
Boson
Star
Ground
State
S‐Branch
Boson
Star
Evolu.on
(Seidel‐Suen
boson
unpert.
M=0.33,
phi(0)=0.1))
Star
Radius:
Perturbed
Stable
Star
Mass
Loss
Mass
Profile:
Ground
State
Soliton
Star
Soliton
Stars
•  Expected
to
be
unstable
(No
equilibrium
configura.ons).
•  Truncated
solu.on
as
a
small
perturba.on:
S‐branch
Soliton
Star:
M=.5726,
phi1(0)=0.2828,
jmax=3
(Alcubierre
et
al)
Mass
loss
<
0.003%
of
the
original
mass
by
t=5000.
Excited
States
(j.b
et
al.):
Oscillatons
•  Role
of
Excited
States
in
Cosmology:
could
be
intermediate
states
in
the
forma.on
process
of
these
stars.
•  Are
they
stable?
Mass
Profile:
First
Excited
State
S‐branch
Excited
State
star
collapsing
to
a
black
hole
In
the
polar
slicing
condi.on
we
use
the
radial
metric
rises
sharply
as
an
apparent
horizon
forms
signaling
the
onset
of
black
hole
forma.on.
Phi(0)=0.2828,
dr=‐0.1
perturba.on
is
due
to
discre.za.on
of
the
grid.
S‐
branch
star
going
to
the
ground
state:
Ini.al
configura.on
Mass
Profile
Evolu.on
of
S‐branch
n=1
star
going
to
ground
state.
Metric
at
the
end
of
the
run
compared
to
the
metric
of
a
ground
state
star
close
to
the
one
it
sePles
down
to.
2
M
=
.44M
•  The
mass
of
the
star
at
the
end
of
the
run
is
Pl /m
The
profile
shown
in
comparison
has
a
mass
of
M = .43M Pl2 /m
€
€
Decay
Times
If
an
excited
state
S‐branch
star
can
lose
enough
mass
it
goes
to
the
ground
state
otherwise
it
collapses
to
a
black
hole.
A
comparison
of
.me
scale
of
collapse
of
n=1
S‐branch
stars
with
the
same
numbers
of
grid
points
(~
187)
covering
the
star
is
shown.
Cascading
Stars:
5
node
star
5
node
star:
Density
profile
with
intermediate
4
node
state
FULL
3D
EVOLUTIONS
•  3D
evolu.ons
take
longer
(more
equa.ons):
resolu.on,
convergence
issues.
•  instabili.es
and
assymetries
d/dx
d/dy
versus
d/dy
d/dx
•  Gauge
issues‐
how
to
step
through
space.me
(more
degrees
of
freedom).
•  SO
WHY?
More
realis.c
Cactus
Code:
www.cactuscode.org
deveoped
by
AEI
LSU
•  It
is
a
modular
code.
The
modules
are
called
thorns.
(We
changed
the
ini.al
data
and
added
gauge
condi.on.
We
also
had
an
ini.al
value
solver
for
the
Boson
Star.)
•  It
uses
a
BSSN
formalism
for
the
evolu.on
equa.ons
with
and
without
maPer.
•  Special
credit
to
F.
Siddhartha
Guzman
for
his
scalar
field
evolver.
Boson
Stars
versus
Soliton
Stars
•  Challenges
for
Soliton
Star.
Gravita.onal
Waves
have
a
high
damping
rate
allowing
full
extrac.on
on
a
short
.me
scale
(compared
to
Neutron
Stars).
*S.
Yoshida,
Y.
Eriguchi,
T.
Futamase,
Phys.
Rev.
D.
50,
6235
(1994).
Gravita.onal
Waveform
Gravita.onal
Wave:
Newman‐Penrose
Scalar
Soliton
Star
3D
(J.B.
et
al.
PRD
2008)
Code
Test
Newman‐Penrose
scalar:
Metric
Y20
perturba.on
of
stable
soliton
star.
Zerilli
Func.on
Stable
Star
Energy
Output
Conclusion
•  We
have
seen
that,
in
principle,
scalar
par.cles
can
form
stable
stars.
•  They
have
ground
states
and
excited
states.
The
excited
states
although
inherently
unstable
can
cascade
to
a
stable
ground
state
configura.on
losing
mass
via
emission
of
scalar
radia.on.
•  Excited
states
can
be
intermediate
states
during
the
forma.on
of
these
stars.
•  They
have
gravita.onal
wave
signatures
that
damp
on
a
short
.me
scale.
Cri.cal
Density
•  The
smooth
universe
has
a
‘geometry’
ini.ally
parallel
free
trajectories
2
.


Flat:
stay
parallel,
2
2
8ΠGρ kc
Λc
2 a
− 2 +
Closed:
converge,
H =   =
a
3
3
a
 
Open:
diverge.
2
ρcr
€
€
3H
=
8πG
How
do
we
know
there
is
dark
maPer
•  Theore.cal:
The
cri.cal
density
is
needed
for
infla.on
and
its
predic.ons
to
work.
Luminous
maPer
is
5%
of
this.
There
must
be
non‐
luminous
stuff.
If
70
%
is
dark
energy
then
25%
must
be
dark
maPer.
•  Rota.on
curves
of
stars
shows
the
speeds
do
not
match
what
they
would
be
if
the
observed
mass
was
all
there
was.
Friedmann‐Robertson
Walker
Metric.
2
2
2
2
ds = a(t) ds3 − dt
a(t)
=
scale
factor.
2
.
 
2
2
a
8ΠG
ρ
kc
Λc
H2 =  =
− 2 +
a
3
3
a
 
from
oo
component
of
Einstein’s
equa.on
..
2
a
4ΠG
3p
Λc
2
H+ H = = −
(ρ + 2 ) +
a
3
3
c
.
€
Λ = Cosm.const.
2
k / a = curvature
G = grav.const.
from
trace
of
Einstein
Field
Eqns.
(perfect
fluid
\MaPer
dominated:
w=0
=>
Radia.on
dominated
w=1/3
=>
2
p = wρc => a(t) = a0 t
€
2
3(w+1)
a(t) ∝ t 2 / 3
1/ 2
a(t) ∝ t