NATURE OF BINARY BLACKHOLES PROBED BY
CROSS-CORRELATION OF GW AND GALAXIESAtsushi J. Nishizawa (Nagoya IAR)
Atsushi Nishizawa (Nagoya KMI), Sachiko Kuroyanagi (Nagoya IAR)
Observational Cosmology Workshop in Hirosaki, Oct. 23-25, 2017

THE FIRST DETECTION OF GRAVITATIONAL WAVE
▸ First detection of GW with LIGO inSep. 2015
▸ Four GW events so far detected▸ Let’s forget about the fourth event(NS-NS binary)▸ Two BHs rotating each othermerged▸ What strikes people in addition tothe first GW detection was …

Abbott+ 2016, PRL 116, 6

SURPRISINGLY MASSIVE BLACK HOLES EVER DETECTED!!
▸ The most massive stellar BH ever detected!
▸ Need to form super massive progenitor

Zsun/50

Zsun/5Zsun

T.Yoshida+ 2014

http://www.ligo.org/

OPTICAL / X-RAY / RADIO FOLLOWUP OBSERVATIONS▸ EM counterpart -> redshift -> cosmology thru dL(z)relation (standard siren)▸ identifying host galaxy -> BH formation▸ no detection so far due to large positional uncertainty▸ few candidates (sGRB, Kilo-nova, but for NS binary)▸ immediate follow-up required (hours, days)▸ more observations (HSC, DECam, PS1, …) but none ofthem claims detection.
▸ ToO observation in HSC, a week behind theGW151226 but variable object HSC160107-T035 fits
none of the known transient templates.
M. Yoshida+ 2016

http://www.ligo.org/

CROSS-CORRELATION OF GW AND GALAXY
density map for galaxy type I▸ no need to identify individual counterpart▸ can also be applied well after the GW event

density map for galaxy type II

density map for galaxy type III▸ may give a hint to the origin of massive BHs
in galaxy▸ using real galaxy data, we can naturally take
into account the clustering of particular typeof galaxies▸ Originally proposed by Namikawa+ 2014
probabilistic distribution map of GWs

CROSS-CORRELATION FORMULAEwcrossP(⇥) = h GW (✓ 0 ) gal (✓ 0 + ✓)i/ZXi,jexp|✓ j |=⇥

1(21✓ i )Covi (GW error region

✓i )

Td2

▸ Cross-correlation of GW is subject
to positional uncertainties▸ Here we consider 2D angularcorrelation function but it can easily
be extended to 3D CCF.

✓i⇥galaxy

69✓j▸ Integration for all the pairs would
be highly time consuming▸ Replace integral with MC integral

CROSS-CORRELATION FORMULAEw

crossP(⇥) = h GW (✓ 0 ) gal (✓ 0 + ✓)i

/ZX
i,j

exp|

✓ j |=⇥

1(21✓ i )Covi (GW sources.
.

d2▸ Cross-correlation of GW is subject
to positional uncertainties▸ Here we consider 2D angularcorrelation function but it can easily
be extended to 3D CCF.

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✓i )

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galaxy69✓j▸ Integration for all the pairs would
be highly time consuming▸ Replace integral with MC integral

DATA (GALAXY) = REAL SDSS GALAXIES▸ SDSS DR7 photo-z sample

SDSS DR7 galaxy sky-distribution (color : JK patch)▸ subsample by photo-z (red/bluegalaxies are classified based on the best
fit SEDs)▸ each sub-sample further classified
based on SF activity (starburst, passive,green, AGN, …)▸ JK subsample by Healpix (Nside=16) forerror estimation
RED sample(>RS-1.2σ)

BLUE sample(<RS-3.5σ)
Dobos+ 2012

redshift distribution for different class of galaxy (Dobos+ 2012)

DATA (GW) = MOCK SIMULATED SOURCES▸ At the position of selected galaxy (wmass weighted), put GW source

Probabilistic sampling of GW sources▸ randomly assign BH binary properties(M1>5Msun, M1+M2<100Msun)▸ observed orientation is also random
assuming 3 detectors▸ generate random 100 points aroundtrue position of GW (Gaussian dist.)
3sigma (radial)oo3sigma (2D ellipsoid)comoving number density

positional error distribution

ANGULAR CORR. FUNC. - EFFECT OF POSITIONAL UNCERTAINTY ▸ wo positional error, the angular power
spectrum is well fitted by power-law
0.7(w / ✓)▸ positional error suppress the power on
small scales ( ✓ < 1 )▸ errorbar includes sample variance andshot-noise from 30 JK-resampling.

ANGULAR CORR. FUNC. - COMPARISON BTWN RED AND BLUE GALAXIES ▸ Let’s assume GWs are associated with RED galaxies and we find ~1,400 GW sources▸ Cross-correlation with RED galaxies clearly has significant signal than that with BLUE
BLUE-GW cross correlation

Not detected

RED-GW cross correlation

DetectedCAN WE DISTINGUISH THE RED/BLUE GALAXY ASSOCIATION?
2null =X ✓ w(✓i )ii0◆2Significance of detecting the clustering▸ Now, lets consider the case where GWs areassociated with RED/BLUE galaxies.
▸ number of GWs required to distinguish theassociated galaxy population.
▸ Delta chi^2 gives us how the detection ofclustering is significant compared to theother.
▸ 100 GWs are not sufficient but a few 100 /1000 GWs are enoughPREL

if GWs are associatedto only RED galaxies

IMINARY

SUMMARY▸ Gravitational wave has been detected and more is expected in near future.
▸ The detected GWs are emitted by the binary of anomalously massive stellar blackholes.
▸ Given that those massive blackholes are only able to be populated in some particular types ofgalaxies, GWs and galaxies might be spatially correlated.
▸ We estimate the cross-correlation between GW-galaxy for mock GW data based on the SDSSgalaxies considering the uncertainty on the positional determination of GW.
▸ If the GW are populated in RED galaxies, we expect a significant correlation signal with RED
galaxies once the number of GWs reaches to a few 100 but no-signal with BLUE galaxies.
▸ Caveat : the significance of association will depend on the model (GW sources are associated withwhat types of galaxies actually), i.e. if GWs are associated with the population of weakly clustered
galaxies, the significance will decrease.
▸ Future : We will see the significance when GWs are associated with the different types of galaxies,
or finer classes of population, like AGN, SBG, etc…, and what happens after KAGURA?