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Cosmology with 300,000
standard sirens
C.Cutler & D.Holz, PRD 80, 104009 (2009)
Big Bang Observer (BBO)
and DECIGO:
4 very sensitive
mini-LISAs
BBO Noise Curve
NS/NS
gw 1015
10 5

for a 3-yr observation w/
BBO’s angular resolution
 ~ (500s)(2  0.3Hz)/SNR ~ 1 arc sec

--consistent with earlier results by Cornish&Crowder(2005)
BBO’s distance error (from noise)
D/D ~ 1/SNR ~ 0.01

Actually, BBO’s distance error
is dominated by Weak Lensing
WLD
 0.044 z
D
Holz&Linder (2005)
Number of Galaxies in Error Cylinder
Hubble Ultra Deep Field: dN

2
1,000/arc
min
d
Cosmological Parameter Extraction
What goes in: Assume have measured
250,000 NS-NS binaries out to z=3, with perfectly
determined redshifts, z. Fit for
5 parameters:
H 0 , m , X , w 0 , w a
wher
e
w(z)  p/  &
Following standard convention, also assume forecasted
2
Planck prior: constrains m h to ~1%, plus a constraint
on DA of Hubble scale at decoupling.
2.5e5 NSs up to z=3  H0 to 0.1%
For CDM  H0 to 0.025%



2.5e5 NSs up to z=3  w0 to ~0.01
 wa to ~0.1


With more accurate analysis of lensing effects, and including priors
from next-generation ground-base DE projects (Stage III):
20,000
--- Hirata, Holz & Cutler (2010)
Of course, BBO is far in the future ,
and by the time it flies, DE FoM of
20,000 may be no big deal.
On the other hand, this method of measuring
D(z) is highly independent of others, and
potentially has far better systematics.
Caveat re a Selection Effect
Hirata pointed out: the probability of correctly identifying
the host galaxy has a small but non-negligible dependence
on its magnification: higher  means higher SNR, so a smaller error
box and a brighter galaxy. If not accounted for, would lead to
systematic bias in DL (z).
Possible ways of “correcting” for this effect:
1) Use thegamma-ray
burst sources to calibrate it out. I.e.,

using those same ~1000 galaxies to create a new synthetic data set,
giving the “calibration” binaries random orientations and
coalescence times. Analyze the data 2 different ways: with and
without the benefit of the exact sky location. The difference is an
estimate of the systematic bias.
2) Include this effect in a proper Bayesian analysis. Would need
to include more parameters, especially a parametrized model of
the NS-NS merger rate as a function of z, galaxy type, etc.
Other Astrophysics from BBO/Decigo (1)
1. Early Warning System for ALL short/hard
gamma-ray bursts (assuming they are due to mergers)
 BBO will predict time and location of ALL NS-NS and BHNS mergers, months in advance. Because of beaming,
probably only a small fraction, will lead to observable gammaray bursts.
 We will learn which kinds of mergers (components,
masses, orientations) lead to observable bursts, and which
do not. In particular, BBO will tell us binary’s orientation, so
we can study beaming.
 Can still look for afterglows, even when there are no
observed gamma rays (so-called “orphan afterglows”).
Other Astrophysics from BBO/Decigo (2)
2. Detect mergers of Intermediate Mass BHs to z>20
Estimated rate ~30/yr, with ~20/yr at z > 10, based on
merger-tree simulations by Volonteri, assuming MBHs do grow
from stellar BH remnants. (By comparison, for same model,
Einstein Telescope would detect ~2/yr, almost all at z<8.)
Summary:
When we eventually build a deci-Hz space-based GW mission
approaching the target sensitivities of BBO or Decigo, then
Catalogue of Inspiraling Compact
Binaries will be a Goldmine
Offer cosmological measurements with very high
accuracy , and potentially far better systematics.
Plus: A complete catalogue of all NS and BH
binary mergers in the universe. an All-sky
gamma-ray burst monitor, high-z IMBHs, weak
lensing, strong lensing, …..
extras
BBO/Decigo as WL mission
1Gpci  i

E.g., BBO’s measurement of lensing convergence
power spectrum would be more accurate than the
most ambitious other proposed WL missions.
Other Astrophysics
from BBO/Decigo
 Early Warning System for ALL short/hard
gamma-ray bursts.
 Detect mergers of Intermediate Mass BHs to z>20
(estimated rate: ~30/yr, with ~20/yr at z > 10).
 Strong Lensing: expect hundreds of “multiplyimaged” (in GWs) binaries, with time-delays of order
a year, and measured to <0.1 sec. Can probe
structure of lensing galaxies/clusters.
BBO: Pie in the Sky?
One idea: 6-satellite BBO/Decigo +ET
Example of possible plan:
Step 1. One mini-LISA +ET : rates, gamma
ray bursts, high-z IMBHs
Step 2. Two mini-LISAs + ET: high –
precision cosmology
Step 3. Full BBO: Inflationary GW
background.
Caveat re Calibration
BBO interferometry in BBO Mission Concept Study
(Phinney et al., 2003) is very “LISA-like”: no applied forces
along sensitive direction.
Later it was realized that this design would greatly
oversaturate current UV photodiodes. Harry et al.(2006)
proposed a more “LIGO-like” design,with forces on the test
mass to keep photodiode operating near dark fringe. But
this spoils calibration accuracy unless the force is measured
very accurately. DECIGO is in same situation.
We have spoken with several instrumentalists, and are
optimistic that this is a solvable problem; e.g.,
1) Widen beam onto array of ~1000 photodiodes
2) Use interferometry to measure applied force

BBO/Decigo as WL mission
i

7
     ~ 10

i 
i
2
2
Comparable to most ambitious/optimistic other WL
experiments, such as JDEM or LSST, which measure WL
shear thru correlations in galaxy shape distortions.
We estimate that BH-BH binaries likely contribute about
as much to  2 as NS-NS binaries. Though we assume the
BH-BH merger rate is ~1/20 the NS-NS rate, each
2
i
 is ~25 times larger.


 i 
Recent work: more careful analysis of WL error.
WLD
 0.044 z
D
for single source
Cutler&Holz(2009) estimated that for N sources at same z:

WLD
 (0.044 z) /N1/ 2
D
for N sources
That’s correct if you take an average, but because the
distribution of magnifications is quite skew, the average is not
the best estimator. The maximum likelihood estimator gives:
WLD
 (0.030 z) /N1/ 2
D
for N>4 sources
see Hirata,Holz&Cutler(2010); Shang&Haiman(2010)
Decigo Roadmap
2007 08
09
10
11
12
13
Mission
R&D
Fabrication
14
15
16
17
18
19
R&D
Fabrication
DECIGO Pathfinder
(DPF)
20
21
22
23
24
25
R&D
Fabrication
Pre-DECIGO
DECIGO
Objectives
Scope
Test of key technologies
Observation run of GW
Detection of GW w/
minimum spec.
Test FP cavity
between S/C
Full GW astronomy
1 S/C
1 arm
3 S/C
1 interferometer
3 S/C,
3 interferometer
3 or 4 units
from Kawamura
26
Decigo: Pre-conceptual design
Differential FP interferometer
Arm length: 1000 km
Mirror diameter: 1 m
Laser wavelength：0.532 m
Finesse: 10
Laser power: 10 W
Mirror mass: 100 kg
S/C: drag free
3 interferometers
Arm cavity
Arm cavity
Laser
Photodetector
Drag-free S/C
from Kawamura
Mirror
Optical Follow-ups
Recall that BBO gives DL and a small error box on
sky. Optical astronomers must still provide 300,000
redshifts. Is this realistic?
• By the time BBO
 flies, the LSST could have determined
photometric redshifts (accurate to 2-3%) for a large fraction
of galaxies over 1/3 of the sky.
•There are several proposed wide-field spectroscopic surveys.
E.g., BigBOSS would meaure ~5 million spectroscopic
redshifts per year (~4,000 at a time) for galaxies in the range
0.2 < z < 3.5, over an area of 14,000 sq. degrees.
(WFMOS instrument on Subaru telescope would have been
Comparable to BigBoss, but their funding was just cut.)
Nominal BBO parameters (used in paper)
,
• ,
Laser power = 300 x LISA,
arm length = 0.01 x LISA,
mirror D ~ 10 x LISA,
S1/acc2 = 0.01 x LISA
Binaries as standard GW sirens
(using quadrupole approximation for simplicity)
I ij   M A rAi rAj
A

D
1
d2
hij  PTT 2 Iij (t  D)
D
dt
h(t) ~ D1  r 22 ~ D1
M1 M 2 2 / 3
x F(angles)
f
1/ 3

M
df 96 8 / 3 M1 M 2 11/ 3
 
f
+ higher order terms
1/ 3
dt 5
M
Summary:
If we can build a deci-Hz space-based GW mission
approaching the target sensitivities of BBO or Decigo, and
with excellent calibration accuracy (at ~ 104 level), then
inspiraling Compact Binaries will be
 Goldmine
a Cosmology
Offer cosmological measurements, with far better accuracy
than with any other proposed methods, and potentially far
better systematics (modulo those 2 caveats).
Plus: great WL mission, gamma-ray burst monitor,
high-z IMBHs, strong lensing, …..
Copyright 2010. All rights reserved.
Summary:
If we can build a deci-Hz space-based GW mission
approaching the target sensitivities of BBO or Decigo, and
with excellent calibration accuracy (at ~ 104 level), then
inspiraling Compact Binaries will be
 Goldmine
a Cosmology
Offer cosmological measurements with very hight accuracy ,
and potentially far better systematics.
Plus: All-sky gamma-ray burst monitor, high-z
IMBHs, weak lensing, strong lensing, …..
Copyright 2010. All rights reserved.