Distance determination beyond
the nearest galaxies (?)
Masamune Oguri (University of Tokyo)

2016/5/24 Astronomical Distance Determination@Beijing

Gravitational wave standard sirens
Masamune Oguri (University of Tokyo)

2016/5/24 Astronomical Distance Determination@BeijingFebruary 11, 2016

Saul Loeb/Getty Images

nonlinear dynamics of highly disturbed black holes.
II. OBSERVATION

gravitational-wave transients [41] and was reported within
three minutes of data acquisition [43]. Subsequently,
Abbottal. (2016)matched-filter analyses that use
relativisticetmodelsof compact binary waveforms [44] recovered GW150914 as themost significant event from each detector for the observations reported here. Occurring within the 10-ms intersite

Gravitational waves detected!

On September 14, 2015 at 09:50:45 UTC, the LIGO
Hanford, WA, and Livingston, LA, observatories detectedweek ending
12 FEBRUARY 2016

REVIEW LETTERS

GW150914
FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, rightat 09:50:45 UTC.
For visualization,
all time series are filteredof column panels) detectors. Times are shown relative to September 14, 2015 GWs
fromamerger
a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-reject
ed, withfilters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain.
ect GW150914 arrived first at L1 and 6.9 ms later at H1; for a visual comparison,of the~30
BHs!
H1 dataMsun
are also shown,shifted in time by thisto-þ0.5−0.4

nal amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto each

GW150914 was “super-luminous”
54• 3 M⨀ ~ 5×10 erg converted to the GW energy• this was emitted within ~0.1 sec
56 erg/s,thus
thepeakluminosity
was~10•which was much more luminous than SNe/GRBs

Gravitational wave standard sirens• we can infer masses of inspiraling compact binaries
from the waveform• observed strain amplitude is inversely proportional
to the luminosity distance to the source• we can measure the luminosity distance directly,
incld. absolute distance scale H0 (Schutz 1986)
louderless loudVIEW LETTERS

week ending
12 FEBRUARY 2016

Inspiralh/5/3Mz

DL (z)f

2/3

5/3 11/3
˙f / Mz f→ chirp mass Mz
and distance DL

Merger/Ringdown→ final BH mass,spin,
andanalytic
numerical analytic
distance
DL(post-Newtonian) relativity (QNM)

Abbott et al. (2016)

Standard siren at work
luminosity distance

GW150914
observed waveformfitted to GR predictedwaveforms→ luminosity distanceDL = 410+160−180 Mpcbinary inclination→ inferred redshift
assuming standard
cosmological model+0.03
z = 0.09−0.04

FIG. 2. Posterior PDFs for the source luminosity distance DL andFIG. 3. PDFs for the source-frame mass andnant BH produced by the coalescence of theCosmology with gravitational waves• inspiraling compact binaries (BH-BH, NS-NS, BH-NS)
are excellent standard sirens that allow us tomeasure absolute distances to the sources
with gravitational waves• if we get redshifts to the sources from otherobservations (electromagnetic counterparts)
we can directly constrain the distance-redshift
relation at cosmological distances→ useful constraints on H0, Ωm, w, ...
(Holz & Hughes 2005; Dalal et al. 2006; Cutler & Holz 2009;
Nissanke et al. 2010; ...)

Precision cosmology with GWs
even a small−3 number−1
10
Gpc
yearof well-measured GWs
with EM counterpartsfor z can constrain
cosmology
information on theabsolute distance scale
H0 is very precious

un
be

be

am

Dalal, Holz, et al.

amed

ed

! errorh errorunbebe

am

amed

ed

Gravitational lensing as noise
yartlighsourceobslens (dark matter+baryon)• deflection of light ray due to gravitational lensingchanges apparent brightness of observed images→ effectively changes the luminosity distanceDobs = D̄µ1/2h⇡ D̄ 1~ z)(✓,iGravitational lensing as noise• lensing is the most important source of errors
in cosmology with GW standard sirens(also for high-z SNeIa, time delay cosmography, ...)• effect is larger at higher-z• can be averaged out, butbeware that lensing effectis quite non-Gaussian

Takahashi, Oguri, et al. (2011)

Gravitational wave detectors• second generation (~2018)2
3[~10 −10 BH-BHs]

Advanced LIGO,VIRGO, KAGRA, ...

•56
third generation (~2025?) [~10 −10 BH-BHs]

Einstein Telescope, LIGO Cosmic Explorer, ...
(~10 km underground)• space (~2035?)

LISA, DECIGO, ...

Pros and cons
Pros
• clean physics, can easily/robustly predict signals
from the first principle (assuming GR)•−1
can reach high-z relatively easily (h ∝ DL )Cons
• GWs are hard to detect!

• need to identify electromagnetic counterpartsfor redshifts − how easy/secure??

Localizing GWs• it is essential to identify electromagnetic (EM)counterparts for measuring redshifts(necessary for cosmology)• several challenges− angular resolution of GW observations isnot great− not clear how bright EM counterparts are− for BH-BH mergers we usually don’t expect
EM counterparts

Abbott et al. (2016)

Location of GW150914 on the sky

gure 2.
Comparison of different GW sky maps, showing the 90% credible level contours for each algorithm. This is an
rthographic projection centered on the centroid of the LIB localization. The inset shows the distribution of the polar angle ✓HLquivalently, the arrival time difference tHL ).

• expected directionof GW150914 is
not well-constrained,
2with area ~600 deg• more GW detectors
will improve theaccuracy

Abbott et al. (2016)

Expected localization accuracy
3 detectors
2→ ~100 deg

Figure 8: Schematic network sensitivity and localization accuracy for face-on binary
systems with advanced-detector networks. The ellipses show 90% confidence localizatio
timing triangulation alone, and the red crosses show regions of the sky where the s
2 for a BNS sy
confidently detected. The top two plots show the localization expectedthe LIGO Hanford (H)–LIGO Livingston (L)–Virgo (V) network (HLV) in the 2016 –2017 – 2018 run (right). The bottom two plots show the localization expected for a BNS
by the HLV network in the 2019+ run (left) and by the four-detector network (HILV
LIGO sites – in Hanford, Livingston and India (I) – and Virgo operating in 2022+ w
final design sensitivity (right). The inclusion of a fourth site in India provides good l

4-5 detectors→ ~10 degDo we really need EM counterpartsfor cosmology with GW standard sirens?

Oguri Phys. Rev. D93(2016)083511

Cross-correlation approach• in the future we will have a bunch of burst GW
events, possibly without EM counterparts• idea: constrain distance-redshift relation withcross-correlation of GW sources (known DL)
and galaxies (known z)• no need of follow-up observations for individual
GW events!

Cross-correlation approach• cross-correlation ofspatial distributions

GWsgalaxies~w(✓) = h GW (✓~0 ) gal (✓~0 + ✓)i• when Dobs>D(zgal)

cross-correlation issmall

Dobs

D(zgal)w(θ)θ

Cross-correlation approach• cross-correlation of
GWs

galaxies

spatial distributions~w(✓) = h GW (✓~0 ) gal (✓~0 + ✓)i• when Dobs≈D(zgal)

cross-correlation is
large

Dobs

D(zgal)w(θ)θ

Cross-correlation approachgalaxies• cross-correlation of
spatial distributions

GWs~w(✓) = h GW (✓~0 ) gal (✓~0 + ✓)i• when Dobs<D(zgal)

cross-correlation issmall

Dobs

D(zgal)w(θ)θ

Apparent clustering due to lensing• weak lensing changes
observed distanceDobs=const

h1/2
D=D̄µ⇡ D̄ 1
D=constobs~ z)(✓,• since lensing effecti

is position-dependent
it induces additional
clustering patternon the skyχχ ranges between diﬀerent redshift bins, and bg
0 there is no overlap
med thatof redshift
at spectroscopic
there is no overlapof redshift ranges between diﬀerent redshift bins, and bg is thehegalaxies.
overlap of redshift ranges between diﬀerent redshiftbins,Phys.
and Rev.
bg is D93(2016)083511
the bias
Oguri
troscopicgalaxies.
der the cross-correlation between the GW sources and the spectroscopic galaxies. Fromies.
e cross-correlation between the GW sources and the spectroscopic galaxies. From Eq. (8)e cross-correlation
powerspectrum
ionbetween the GW
sourcesand theasspectroscopic galaxies. From Eq. (8), we
correlation power spectrum as
wer spectrum as
wi gj
si gj
ti gj
C(ℓ)
=C(ℓ)
+C(ℓ)
wi gj
si gj
ti gj
(ℓ)t=C (ℓ) + C (ℓ)
wi gj
si gCji gj
C(ℓ) = C (ℓ)!+ C (ℓ)
(18)
"#∞"
#1/2!
H(z)
ℓ+∞gsgsij
physicalspatial"H(z)#! ∞ si gj C (ℓ) =ℓ+1/2(z)bbP;
zGWgms dz Wgi (z)WH(z)W0 i (z)Wj (z) ℓ j2+ 1/2
C (ℓ)s = g dz
bGWχb2g Pm;z χdz Wi (z)Wj 0(z) 2 bGW bg Pm χ=;z(19)χcorrelation
χ0"#! ∞ χ! z′")#1/2 ′!
! ztℓ+H(zg "′tj gj! ∞′′κ′1/2 ′;z(ℓ)(z ; )z) # ′2 ℓbg+Pm
g dz
z =tj gj Ct dz Wi (z)′′′ Wjκ (z′ )W H(z′1/2H(zbg′ Pχm;z χ(ℓ)t =dz
g0 i (z)′ W′κ dz′ Wj (z ))W (z ; ℓz)+0′2′
4 χ ;z(20)dz Wi (z) 0 dz Wj (z )W 0(z ; z) ′2 bg Pm
χ′χ C tj gj . The
duetoweaklensingsi gj clustering
0ar power spectrumfor Pm (k; z) inχapparent
bothCandpower
spectrum
C si gj com
si gj
tj gj
si gj
er spectrum for Pm (k;z) in both
Cand C. The power
spectrum C
comes fromsgtgsgijjjijz distributions.
.P(8)
and
physicalof spectrum
spatialOn theother hand,Cz) represents
in bothC the andC correlation. Thepower
C On
comesfromthetj gjm (k;d represents
the physicalcorrelationof spatial
distributions.
theotherhand,C,w
tj gj on luminosity dista
termofEq.
(8),isthecorrelation
of
the
weak
lensingeﬀect
esecondphysicalcorrelationofspatialdistributions.
On
the
other
hand,
C, whichdistances ofterm of Eq. (8), is the correlation of the weak lensing eﬀect on luminosity
ectroscopic
galaxies.
Since
matterfluctuations
along
the line-of-sightcontributes
tolenw8), isgalaxies.
the correlation
ofthe allweaklensingeﬀect
on theluminosity
distances
of GW
opic
Since allmatterfluctuations
alongline-of-sightcontributes
toweak1.1
negligible
cross-correlations
betweenluminosity
andredshift
bins
which
are
wellseparateince
allmatter
fluctuations
along
theline-of-sightcontributes
toweak
lensing,le cross-correlations between luminosity and redshift bins which are well separated with
tions between luminosity and redshift bins which are well separated with each

Cross-correlation signals

0.9

zg+0.05
zg-0.05

Oguri Phys. Rev. D93(2016)083511

Forecast• GWs from third-generation
exp. + galaxies from Euclid(0.3<z<1.5)• lmax comes from accuracyof GW localizations
fiducial: lmax = 100 (→ ~1deg)
optimistic: lmax = 300• tight constraints on H0 andw possible with the crosscorrelation approach(without any follow-up!)

Summary• gravitational waves from mergers of compact
binaries are a promising, totally new absolute
distance indicator at cosmological scale• recent observation of GW150914 suggested
its enormous potential• usually identifications of EM counterparts areneed to get redshifts and constrain distanceredshift relation• a cross-correlation approach is proposed whichenables GW cosmology without follow-up