Pulsar timing arrays can test models of massive black hole formation and growth - Vikram Ravi With Stuart Wyithe and the PPTA team
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Pulsar timing arrays can test models
of massive black hole formation and
growth
Vikram
Ravi
With
Stuart
Wyithe
and
the
PPTA
team
Conclusions
1. Pulsar
=ming
arrays
are
expected
to
be
sensi=ve
to
gravita=onal
waves
from
binary
super-‐massive
black
holes
(SMBHs)
– A
global
signal
and
individual
sources
are
both
poten=ally
detectable
2. Self-‐consistent
modeling
of
the
binary
SMBH
popula=on
can
result
in
interes=ng
constraints
on
SMBH
forma=on
and
growth
Simulated
data
with
es=ma=on
noise
5-‐year
PPTA
datasets
for
best
pulsars
and
GWs
at
predicted
amplitude
Timing
residual
(ns)
MJD
MJD
Gravita=onal
wave
grab-‐bag
Time
Time
Wide
binary
STRAIN:
Coalescing
stellar
supermassive
ΔD black
holes
binaries,
irregular
h= Parkes
Pulsar
neutron
stars,
core-‐
D Timing
Array
collapse
supernovae
D
Laser
Supermassive
black
hole–related
coalescences,
wide
stellar
binaries
4
GW
signal
from
binary
SMBHs
∞
Present-‐day
SED
in
GWs
from
a
N(z) dE GW
popula=on
of
sources
(Phinney
2001):
ΩGW ( f ) = ∫ 2
ρ c c (1+ z)
f
df
dz
0
dh 2 ⎛ d 3 N mergers ⎞ ⎛ dt ⎞
The
(one-‐sided)
GW
strain
power
spectrum:
df
= ∫ dM ∫ C dz ⎜ ⎟ ⎜ ⎟ h 2 (MC , f )
€ ⎝ dMC dzdt ⎠ ⎝ df ⎠
SMBH
merger
rate
(per
GW
frequency-‐evolu=on
Mean
squared
unit
redshiT,
mass)
of
circular
binaries
strain
amplitude
€
h 2 ∝ MC10 / 3 ( f (1+ z)) 2 / 3 Dcom −2
MC=109
M
Mean
strain
amplitude
Time
to
merger
(yr)
MC=109
M
MC=108
M
Separa=on
(pc)
€
MC=108
M
MC=109
M
MC=108
M
Frequency
(Hz)
Frequency
(Hz)
Frequency
(Hz)
Millisecond
pulsar
=ming
arrays
Measure
pulse
arrival
=mes
from
20
millisecond
pulsars
for
many
years,
to
look
for
the
effects
of
GWs
Three
projects:
the
Fold
a
number
of
END
pulses,
and
compare
PPTA,
the
European
PTA,
NANOGrav
(North
to
template
at
America)
expected
=me
from
known
ephemeris
Flux
density
Residual
START
Start
=me
recorded
by
Pulse
phase
maser
clock.
The
effect
of
GWs
on
=ming
measurements
GWs
affect
the
measured
pulsar
rota=on
frequencies
like
a
Strain
at
Earth
Strain
at
pulsar
Doppler
shiT:
Δυ (t) 1
= cos(2φ )(h(t) − h(t − R /c)) z
υ 2
Gravita=onal
Δυ (t') t
wave
The
induced
residuals
are
given
by:
R(t) = ∫ 0 dt'
υ
The
induced
€ residuals
will
be
correlated
for
different
pulsars:
y
x
t=0
test
€ par=cles
Expected
correla=on
between
pulsars
for
isotropic
Pulsar
vector
R
posi=on
in
x-‐y
plane,
at
Correla=on
GW
background
angle
Φ
Estabrook
&
Wahlquist
(1975)
Sazhin
(1978),
Detweiler
(1979)
Hellings
&
Downs
(1983)
Angular
separa=on
(0
-‐
π)
Modeling
PTA
=ming
residuals
Auto-‐covariances
Cross-‐covariances
• Determinis=c
components,
• Earth
=me-‐standard
encoded
by
the
pulsar
=ming
errors
model
parameters.
• Solar
system
• Stochas=c
components:
ephemerides
errors
– measurement
noise
(not
• Instrumental
effects
correctable)
– ISM
varia=ons
(correctable)
Residual
power
spectral
density
– intrinsic
=ming
noise
(poten=ally
par=ally
correctable)
Frequency
Modeling
PTA
=ming
residuals
Auto-‐covariances
Cross-‐covariances
• Determinis=c
components,
• Earth
=me-‐standard
encoded
by
the
pulsar
=ming
errors
model
parameters.
• Solar
system
• Stochas=c
components:
ephemerides
errors
– measurement
noise
(not
• Instrumental
effects
correctable)
– ISM
varia=ons
(correctable)
Residual
power
spectral
density
– intrinsic
=ming
noise
(poten=ally
par=ally
correctable)
Frequency
Sta=s=cs
of
the
expected
GW
signal
Ravi
et
al.
(2012)
RealisaDon
of
an
GW
strain
isotropic,
We
use
a
hierarchical
galaxy
formaDon
model
(stochasDc
Guo
et
al.
G
2011),
W
coupled
with
the
Millennium
&
Millennium-‐II
sbackground
imulaDons,
to
model
the
binary
SMBH
populaDon
A
more
realisDc
signal
GW
strain
model,
accounDng
for
binary
SMBH
populaDon
characterisDcs
10
10
Sta=s=cs
of
the
expected
GW
signal
Ravi
et
al.
(2012)
RealisaDon
of
an
GW
strain
isotropic,
stochasDc
GW
background
A
more
realisDc
signal
GW
strain
model,
accounDng
for
binary
SMBH
populaDon
characterisDcs
11
11
Regions within which individual binaries with
SUMMARY:
the
expected
GW
signal
from
binary
SMBHs
looks
somewhat
like
a
stochasDc,
isotropic
background
with
the
possibility
of
a
few
detectable
sources,
parDcularly
at
higher
GW
frequencies.
Key
scien=fic
ques=ons:
1. SMBH
forma=on:
when,
how
and
under
what
condi/ons
did
SMBHs
form?
90%
2. SMBH
growth:
what
is
the
mass
assembly
history
of
SMBHs?
3. SMBH
binary
physics:
50%
what
are
the
effects
of
binary
environments
(stars,
gas)
on
SMBH-‐SMBH
coalescence
/mescales?
How
eccentric
are
bound
SMBH
binaries?
We
are
addressing
these
ques=ons
by
matching
GW
signal
models
to
PPTA
data
SUMMARY:
the
expected
GW
signal
from
binary
SMBHs
looks
somewhat
like
a
stochasDc,
isotropic
background
with
the
possibility
of
a
few
detectable
sources,
parDcularly
at
higher
GW
frequencies.
Key
scien=fic
ques=ons:
1. SMBH
forma=on:
when,
how
and
under
what
condi/ons
did
SMBHs
form?
90%
2. SMBH
growth:
what
is
the
mass
assembly
history
of
SMBHs?
3. SMBH
binary
physics:
50%
what
are
the
effects
of
binary
environments
(stars,
gas)
on
SMBH-‐SMBH
coalescence
/mescales?
How
eccentric
are
bound
SMBH
binaries?
We
are
addressing
these
ques=ons
by
matching
GW
signal
models
to
PPTA
data
A
self-‐consistent
predic=on
for
ΩGW
• We
use
the
latest
MPA
semi-‐analy=c
galaxy
forma=on
model
(Guo
et
al.
2011)
– Assump=ons:
circular
binaries,
SMBHs
in
every
halo,
growth
through
cold
gas
accre=on
following
all
mergers
– This
predic=on
for
ΩGW
is
based
on
self-‐consistent
modeling
• We
re-‐tune
the
model
to
match
the
current
compila=on
of
(dynamically-‐obtained)
SMBH
and
bulge
masses.
– McConnell
&
Ma
(2012)
find
that
the
mean
ra=o
MBH/Mbulge
has
increased
by
a
factor
of
1.8
since
Haring
&
Rix
(2004)
– We
don’t
quite
use
the
McConnell
&
Ma
(2012)
sample.
Instead,
we
use
the
most
accurate
SMBH/bulge
mass
es=mates
in
each
case
• The
treatment
of
satellite
stripping
=mescales
is
conserva=ve
(i.e.,
wrt
McWilliams
et
al.)
ΩGW
=
energy
density
in
GWs,
per
log
f,
as
frac=on
of
closure
density
95%
confidence
upper
limits
Posterior
PDF
of
the
GW
energy
density
from
the
model
If
all
binaries
had
ini=al
eccentrici=es
as
given,
the
GW
energy
density
would
be
amenuated
to
the
leT
of
the
domed
lines
Simulated
data
with
es=ma=on
noise
5-‐year
PPTA
datasets
for
best
pulsars
and
GWs
at
predicted
amplitude
Timing
residual
(ns)
MJD
MJD
Conclusions
1. Pulsar
=ming
arrays
are
expected
to
be
sensi=ve
to
gravita=onal
waves
from
binary
super-‐massive
black
holes
(SMBHs)
– A
global
signal
and
individual
sources
are
both
poten=ally
detectable
2. Self-‐consistent
modeling
of
the
binary
SMBH
popula=on
can
result
in
interes=ng
constraints
on
SMBH
forma=on
and
growth
Where
does
the
GW
power
come
from?
We
use
a
hierarchical
galaxy
formaDon
model
(Guo
et
al.
2011),
coupled
with
the
Millennium
&
Millennium-‐II
simulaDons,
to
model
the
binary
SMBH
populaDon
19
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