Gravita'onal waves andElectromagne'c signals
from Neutron Star binary mergers

Z
Kyohei Kawaguchi

ICRR, The University of Tokyo
Collaborator: Kenta Kiuchi, Masaru Shibata (AEI/Kyoto U.),
Koutarou Kyutoku (Kyoto U.), Yuichiro Sekiguchi (Toho U.),
Masaomi Tanaka (Tohoku U.), Keisuke Taniguchi (U. Ryukyus)

2019.09.04 @Kyoto University

IntroducOon

Compact Binary•

A compact binary: A binary system composed ofcompact objects, such as a black hole (BH),a neutron star (NS), (and/or a white dwarf)

Black hole•A region of the space-Dme whereanything, including lights, can notescape for its strong gravity.
The surface of the region is called
the Event horizon.

•

Black hole can have only three physicalparameters;
The mass,
spin angular momentum,
and charge.
For astronomical situaDons, the charge
is consider to be neutralized.
ref) U. Kraus (2014)

Neutron star•

A neutron star is an extremely densestar formed as the result of thecollapse of a massive star.

•

Most of them are observed as pulsars,
which are rapidly rotaDng, highly
magneDzed neutron stars,
emiNng a strong beams.

•

1-2Msun, typically ~1.4 Msun, ~10 kmref) http://essayweb.net/

NS equaDon of state (EoS)•

The NS radius / maximum NS mass
is sensiDve to the equaDon of state(EoS) of NS, which is sDll notcomprehended yet.
Precise measurement of the
NS radius / maximum NS mass
provides us the informaDon of the
NS EoS.

P

<∞

AP3

lity AP4
a
s
au

C

2.0

1.

PAL1

2.

MS2

J1614-2230

SQM1

1.5

MS0

MPA1

ENG

SQM3
FSU
J1903+0327

Mass (M()

•

GR

2.5

Re

4.

GM3

PAL6

J1909-3744

3.

MS1

5.

GS1

Double neutron stars sysystems

6.

1.0

7.
8.
9.

n

0.5

tio
Rota

10

0.0

7

8

9

10

11
12
Radius (km)

13

14

15

Figure 3 | Neutron starref)mass–radius
diagram. et.
Theal.
plot
shows non-rotating
P. Demorest(2010)
27
mass versus physical radius for several typical EOSs : blue, nucleons; pink,nucleons plus exotic matter; green, strange quark matter. The horizontal bands
show the observational constraint from our J1614-2230 mass measurement of(1.97 6 0.04)M[, similar measurements for two other millisecond pulsars8,28
and the range of observed masses for double neutron star binaries2. Any EOS

11

12

13

14

Gravitational waves (GWs)•

Gravitational waves are the ripplesof curvature that propagate at the
speed of light, and their existence
is predicted by general relativity.

•

The binary system composed ofcompact objects, such as NS-NS,
BH-NS and BH-BH binary, arethe eﬃcient sources ofgravitational waves.

http://www.amnh.org/

2<latexit sha1_base64="rtAUIdb6TTs5vThMPG+8Wspo8m0=">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</latexit>gµ⌫ = ⌘µ⌫ + hµ⌫ + O(h )✓<latexit sha1_base64="dGB+rBI4MNVIURT+ALZc0ochJJ0=">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</latexit>

2

@
@t2

◆

r2 hµ⌫ = 0

Compact binary mergers•

Compact binaries eﬃciently emit gravitaDonal waves shrinking theirorbital separaDon, and the objects eventually merge→ compact binary mergers•

GravitaDonal waveform from a binary merger contains
rich physical informaDon of the source(masses, spins, distance, inclinaDon, etc…)

Ref: K. Hotokezaka et al. 2013

GravitaDonal waves froma compact binary merger (leading order)
Kepler’s law:total massm = m1 + m2
m1 m2⌘=
(m1 + m2 )2
⌘m2
E=
a
r
<latexit sha1_base64="89nJIWmea7wYN5qZRJ9OMm2msTc=">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</latexit>

m1 a<latexit sha1_base64="2vLWcUWBcVpl4x0w4nsLbUnstAI=">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</latexit><latexit sha1_base64="NWR6Beo3+PsT9yVuoZs23w/bwxA=">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</latexit>

m2:symmetric mass raOo<latexit sha1_base64="UieViuDOybGxMZpHKJzUilKwZIQ=">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</latexit><latexit sha1_base64="PevQCx9QoTGgog84hKZUioeM4GA=">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</latexit>:total energy<latexit sha1_base64="VcqgPK3GmFqz4ZnD5pJ92+VKTAw=">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</latexit>

⌦
1
f=
=
2⇡
2⇡

Quadrupole formula2⇡ 2/3 M5/3 2/3
|h| ⇡
fGW
D
<latexit sha1_base64="hi30XJgcdfV18FiCCQA95xRb9cA=">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</latexit>“Chirp signal”<latexit sha1_base64="145aodHbTSWsGX+9aNWpMcstewY=">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</latexit>

ĖGW =<latexit sha1_base64="NysfKF/p/9WiMwkS1MjEHPK1Kgg=">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</latexit>ma3:orbital frequency

32⌘ ⇣ m ⌘5:energy loss via GW emission
5a<latexit sha1_base64="HzpagrbyciAMnMqKeN7mIaQSRtM=">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</latexit>

dfGW
96 8/5
11/3=⇡ Mchirp fGW
dt
5fGW = 2f

:GW frequency<latexit sha1_base64="nd63f4+XpmwWhil9RIGGrWK0ZwE=">AAACcXichVHLSsNAFD2Nr1pfVTeKm9BSEYQyrYIiCEUXuqyttULVksRJDeZFkhZq6Q/4AwquWhARP8ONP+DCTxCXFdy48DYNiIp6h5k5c+aeO2dmZFvXXI+xp5DQ1z8wOBQejoyMjo1PRCen9lyr6ii8oFi65ezLkst1zeQFT/N0vm87XDJknRfl083ufrHGHVezzF2vbvNDQ6qYmqopkkfUkVpuHDiGuFVsrqdFtRyNsyTzQ/wJUgGII4isFb3BAY5hQUEVBjhMeIR1SHCplZACg03cIRrEOYQ0f5+jiQhpq5TFKUMi9pTGCq1KAWvSulvT9dUKnaJTd0gpIsEe2S3rsAd2x57Z+6+1Gn6Nrpc6zXJPy+3yxPlM/u1flUGzh5NP1Z+ePahY9b1q5N32me4tlJ6+dnbRya/lEo151mYv5L/Fntg93cCsvSrXOzx3hQh9QOr7c/8Ee+lkaimZ3lmOZzaCrwhjDjEs0HuvIINtZFGgcx1cooV2qCPMCqIQ66UKoUAzjS8hLH4AZhSOsQ==</latexit>

Mchirp = m⌘ 3/5 : chirp mass<latexit sha1_base64="eDx9D0TkoqzGYRBL215MA8iJ9LE=">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</latexit>

D<latexit sha1_base64="8eSQWchmR3f/b2eGJyudXC45MVg=">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</latexit>: luminosity distancePostNewtonian expansion
PostNewtonian expansion:
2m⌘
A(x) =
x A0 + A0.5 x0.5 + A1 x + A1.5 x1.5 + A2 x2 + · · ·DissecerP<latexit sha1_base64="pz42fhMP/T/Vf363kSmBYqJsR64=">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</latexit>

h = Aei GW<latexit sha1_base64="Sl6UBNMJeIjAtg53jFX8gHw2xwA=">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</latexit><latexit sha1_base64="iFVePBYPqFiLLzUms9/Kv4Lb37k=">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</latexit>

dx
64⌘ 5
=
x 1 + a1 x + a1.5 x1.5 + a2 x2 + · · ·dt
5

PostNewtonian
ecerp latibro eht fo yticolev ralugn
a ehT・ Parameter:

x := (⇡mfGW )eht fo yticolev ralugna eht naht edutingam※Note that amplitude factors dependon the inclinaOon angle• 0PN: chirp mass:

2/3<latexit sha1_base64="5ukixomBiY+4WocZTssLm3heWig=">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</latexit>

HB S + L = J⇡<latexit sha1_base64="cMsnQR7VcGoytkse1+/apUcdl20=">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</latexit>

L

Mchirp = m⌘ 3/5

•

m1 m2
⌘=
(m1 + m2 )2

1PN: symmetric mass:<latexit sha1_base64="UieViuDOybGxMZpHKJzUilKwZIQ=">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</latexit>•

1.5PN: spin:<latexit sha1_base64="fVR9MSsa4Fz+JYE+qjLyPkpA5HI=">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</latexit>

2
A+
=
(1
+
cos
i)
0
revresbo eht morf devresbo mrofev•aw5PN:
ehT →'dal deformability:
2 eht ot ralimis eb yam enalp
eb nA
ac⇥
h
c
i
h
w
e
n
o
=
2cos
i
0
)HB-HB : smrofevaw emarF gnissecerP (<latexit sha1_base64="FWulxzX58UppbD1pedQvSwFyJJQ=">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</latexit>a<latexit sha1_base64="eDx9D0TkoqzGYRBL215MA8iJ9LE=">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</latexit>i<latexit sha1_base64="LWgpgDGJgn/e3mAJXpUjY/+8Tz8=">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</latexit>

⇣m⌘

Si
i =
m2i

⇤i
<latexit sha1_base64="uekPFmUHqTAVUXkURxXaMsZml5Q=">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</latexit>

DetecDng gravitaDonal waves•

GravitaDonal waves are detected by measuring
the change of the distance by laser interferometerhTTij (t)

PolarizaOons of GW

h+<latexit sha1_base64="hXEQAJs+7hVVw7SkxlhGRP/mNtU=">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</latexit>h⇥<latexit sha1_base64="ok4d0xfnrZetjr4FEO0S99frdIM=">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</latexit><latexit sha1_base64="J4n/X09JFKEZqCGiggfPUqpwX98=">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</latexit>

PENDIXA.
ANALYTICAL
MODELSOFCOMPACT
BINARYMERGERSAPPENDIXA.
ANALYTICAL
MODELSOFCOMPACT
BINARY
MERGE
plus modecross modeon as,
nditionas,Transverse-Tracelessgauge:0 0
1 1
y
0 0 0 0 00 0
B
C
B
C
0
h
h
0
0
h
h
0
+
⇥
TT TT
i(!t i(!tkz z) kz z)
+
⇥
B= B
Ce C
hµ⌫ h(z,
t)
=
. .
(z,
t)
e
µ⌫
@ 0@ h0⇥ h⇥h+ h0+ A0 A
0 0 0 0 00 0
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(A.6)
(A

d2 X i
1 TT jdalledthe theplusplus
mode
and andthe thecrosscrossmode,
are⇡thepolarization
mode
mode,
respectively,
which
are
the
polarizaḧX
Forrespectively,
face-onwaves: which
ij
2
dt
2
es.
waves.
<latexit sha1_base64="OQJWoVyY6ZrAbjaQy9dUFrdV/yE=">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</latexit>•GravitaDonal wave detectors
advanced LIGO

Hanford

Livingston
hcps://www.ligo.caltech.edu/

advanced Virgo

GW sources for ground-based GW detectors
Compact binary mergers• Core collapse Super Novae

KAGRA

•

•

RotaDng Neutron stars•

Primordial GW (InﬂaDon)•

Cosmic Strings

hcp://www.virgo-gw.eu/

hcp://gwcenter.icrr.u-tokyo.ac.jp/

GravitaDonal wave events
PHYSICAL REVIEW LETTERS

PRL 116, 061102 (2016)•

Compact binary mergers are among
the main targets of ground-based
gravitaDonal-wave detectors,
such as LIGO, Virgo, and KAGRA•

Since 14th of September 2015,
many GW events have been detected•

Binary BH (BBH; BH-BH)••

properties of space-time in the strong-field, high-velocity
regime and confirm predictions of general relativity for the
nonlinear dynamics of highly disturbed black holes.
II. OBSERVATIONOn September 14, 2015 at 09:50:45 UTC, the LIGO
Hanford, WA, and Livingston, LA, observatories detected

the coincident signal GW150914 shown in Fig. 1. Th
detection was made by low-latency searches forgravitational-wave transients [41] and was reported
three minutes of data acquisition [43]. Subsematched-filter analyses that use relativistic models
pact binary waveforms [44] recovered GW150914
most significant event from each detector for the otions reported here. Occurring within the 10-ms

・GW150914 (The ﬁrst GW event)

Ref: B.P.Abbot et al. 2016

GW150914, GW151012,
GW151226, GW170104,
GW170608, GW170809,
GW170814, GW170817,
GW170818, GW170823

Binary NS (BNS; NS-NS)
GW170817

week en
12 FEBRUA

BH-BH
NS Binary
BH-NS

FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series arwith a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and ba
filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L
þ0.5
GW150914 arrived first at L1 and 6.9−0.4
ms later at H1; for a visual comparison, the H1 data are also shown, shifted in tim
amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected odetector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent w
recovered from GW150914 [37,38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90%
regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template wa

BNS (NS-NS)

13

Parameter esDmaDon(intuiDve picture)

Ref: GravitaOonal Wave Open Science Center (hcps://www.youtube.com/watch?v=ﬁQtwPn6kfw)•

Physical informaDon is extracted from the signalby the comparison with theoreDcal waveform templates

Then one can write Equation (51) as
L(t)= F+ (✓, ,L

Parameter esDmaDon)h+ (t) + F⇥ (✓, ,)h⇥ (t),where F+ and F⇥ are the antenna pattern functions for the two polarizations defined osky-plane basis by
F+ ⌘ d : e + , F ⇥ ⌘ d : e ⇥ .
Using the geometry in the right-hand panel of Figure 3, one can show that

Detector sensi'vity

1
1 + cos2 ✓ cos 2 cos 2
cos ✓ sin 2 sin 2 ,21F⇥ =1 + cos2 ✓ cos 2 sin 2 + cos ✓ sin 2 cos 2 .
2
F+ =Ref: B.P.Abbot et al. 2017<latexit sha1_base64="gWGIKfUVOJIynEI5RLpY5QPxckQ=">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</latexit>

Sn1/2 (f )Ref: Sathyaprakash& Schutz 2009

posterior

Figure 3: The relative orientation of the sky and detector frames (left panel) and the e↵ect of a roby the angle in the sky frame (left panel).

These are the antenna-pattern response functions of the interferometer to the two polarizof the wave as defined in the sky plane [359]. If one wants the antenna pattern referred t

prior

signalwaveform template

Living Reviews in Relativity
http://www.livingreviews.org/lrr-2009-2~ d)~ / p(✓)~
p(✓|<latexit sha1_base64="CYvlT7sMVSESOToamX61zcG7QWA=">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</latexit>

Ydet✓~ = (m1 , m2 ,<latexit sha1_base64="PXzD+/X5IwSTXZT8LjIBSEI4OuY=">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</latexit>

likelihood~ ✓)~ L (d|~ ✓)~ = exp
Ldet (d|det1,<latexit sha1_base64="2DQue++HBCMtiitZ7XBqZvhaxms=">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</latexit>

2 , ⇤1 , ⇤2 , · · ·

"

#
Z 1 ˜
~ 2
|d(f ) h̃(f ; ✓)|2df
Sn,det (f )0:intrinsic parameters, dL , ✓, , , i · · · ) :extrinsic parametersdetector noise spectrum

NS binary mergers
NS Binary
BH-NS

NS-NS

General picture
InspiralMerger107yr~~10-100ms

Post-Merger

NS-NS

BH-NS

G
EOS
ν
B

PN

1s~

Full GR, dynamical

Full GR, staOonary

zero temperatureﬁnite temperatureν cooling & heaOng
MHD

ρ

T

B

General picture
InspiralMerger107yr~~10-100ms

Post-Merger

NS-NS

BH-NS

G
EOS
ν
B

PN

1s~

Full GR, dynamical

Full GR, staOonary

zero temperatureﬁnite temperatureν cooling & heaOng
MHD

ρ

T

B

Inspiral phase:
Tidal deformaDon•

GravitaDonal waveform from a binary
merger contains
rich physical informaDon of the source(masses, spins, distance, inclinaDon, etc…)•

In parDcular, if the binary contains a NS,
the informaDon of the internal structureof the NS can be extracted•

During the inspiral, a NS is deformed by
the Ddal force of the companion object.
DeformaDon of a NS (s) accelerates theorbital shrinking, and modiﬁes
gravitaDonal waveforms
19

Tidal deformation

Tidal
GW (t)
Modification in the GW phase

Eﬀect of Ddal deformaDon•

Radius & Tidal deformability
15H>125H>H>HB>BRef) Kiuchi et al. 2017

(a)

(b)

Tidal deformability

FIG. 3. (a) The mass-radius relation for the matched causal EOS with ϵmatch = ϵnuc and for candidate neutron-star equationsof state that display the range of uncertainty in stiﬀness.
(b) Tidal deformability versus mass for stars based on the same EOSs. The top solid curve, displaying the tidal deformabilityof stars based on the matched causal EOS, is an upper limit set by causality on tidal deformability. Stars based on softer EOSs
have smaller tidal deformabilities.
10 000
SLy

MPA1

H4

MS1

Matched Causal

8000

Λ

6000

4000

2000

0
1.0

1.2

1.4

1.6
M

(

1.8

2.0

⊙)

FIG. 4. The dimensionless tidal deformability Λ is plotted against mass for several EOSs. For any given mass, the MatchedRef) Oeveren & Friedman 2017
Causal EOS places an upper limit on the value of Λ.

✓ 2
◆5
c
c RNS
⇤ sponding= G to a smaller orbital⇠ (and gravitational wave)
GMNS star with highGM
NSdeformability
frequency. A neutron
tidal<latexit sha1_base64="WMkxFZNFyfHKVG9dtfYLPPbHpdY=">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</latexit>

✓

2

◆5

therefore has fewer cylces during
which to accumulate（dimensionless）tidal
deformability
phase relative to a point-particle. As a result, the eﬀectof MNS on |∆Φ(fcutoﬀ )| is complicated, and depends on
EOS and the parameters of the binary.
Nevertheless, stiﬀer EOSs result in larger values of|∆Φ| for given neutron star masses or mass ratios. As
can be seen in Fig. 5, |∆Φ(fcutoﬀ )| decreases with massQ =E =Quadrupole moment@@
tidal field

ijthe other hand,ij |∆Φ(fi jratio for all EOSs. On
cutoﬀ )| hascomplicated behavior with respect to neutron star mass
for all EOSs when the spin of the companion black holeis zero (Fig. 6). In addition, one can see in Fig. 5 andFig. 6 that |∆Φ(fcutoﬀ )| increases with the stiﬀness of
the EOS, and is largest for our EOS, but only by a few
radians at most. Here, based on our estimate of ∆Φ, theconstraint set by causality is remarkably strong, stronger
than the already stringent constraint on Λ: ∆Φmax (M )<latexit sha1_base64="aJenXKMDU2QbNsOYCQJKLK6bQ0U=">AAACJnicbVDLSgMxFM3UV62vUZdugkVwY5kRQTeFogguW7AP6AzDnTRt02YeJBmhDPM1bvwVNy4qIu78FNMHYlsPBA7n3JPkHj/mTCrL+jJya+sbm1v57cLO7t7+gXl41JBRIgitk4hHouWDpJyFtK6Y4rQVCwqBz2nTH95N/OYTFZJF4aMaxdQNoBeyLiOgtOSZ5ZqXskFWvnC4DnUgdQhwfJ8tqk4MQjHgHvtlA6faZ55ZtErWFHiV2HNSRHNUPXPsdCKSBDRUhIOUbduKlZtO7iScZgUnkTQGMoQebWsaQkClm07XzPCZVjq4Gwl9QoWn6t9ECoGUo8DXkwGovlz2JuJ/XjtR3Rs3ZWGcKBqS2UPdhGMV4UlnuMMEJYqPNAEimP4rJn0QQJRutqBLsJdXXiWNy5JtlezaVbFyO68jj07QKTpHNrpGFfSAqqiOCHpGr2iM3o0X4834MD5nozljnjlGCzC+fwCx/KaJ</latexit>•

From the observed waveforms, the %dal deformability of a NS can be extracted•

The Ddal deformability reﬂects the internal structure of a NS, and its measurement
can be used to constrain the NS equa'on of state (EOS)21

GW templates for NS binaries•

Physical informaDon is extracted from observed gravitaDonalwaves by the comparison
with theoreDcal
templates
Parameter estimation
methods—To
measure the source
for templates
GW170817, weparameter es→ an accurateparameters
waveform
areperformed
crucial for
timation on the Advanced LIGO-Virgo data available atthe LIGO Open Science Center [7, 8]. Our analysis wasparameter es'ma'on

performed with the PyCBC Inference software [9, 10] andthe parallel-tempered emcee sampler [11, 12] for sampling• The waveforms including the 'dal eﬀects are analyDcallyover the parameter space using Markov Chain Monte Carlo(MCMC) techniques[13].
derived by post-Newtonian(PN)
calculaDon
The LOSC data files
include a post-processing noise(and by the EﬀecDve-One-Body
formalism)
subtraction performed by the LIGO-Virgo Collaboration[8, 14]. The LOSC documentation states that these data
been truncatedremove tapering effects due to the• Newtonianhave(Flanagan
et al.to2008)
cleaning process [8], however the LOSC data shows evi• 1 PN (Vines
et al.
2011) after GPS time 1187008900 in the LIGO
dence
of tapering
Hanfordet
detector.
To avoid any contamination of our re• 2.5 PN (Damour
al. 2012)
sults we do not use any data after GPS time 1187008891.
• Self force informed(Bernuzzi
al. 2015,
2018)theThe power resum.
spectral density(PSD)etused
to construct
was calculated
Welch’smethodwith• Dynamicallikelihood
Dde (Hinderer
et al. using
2016,
Lackeyet al.[15]2018)
16 second Hann-windowed segments (overlapped by 8 s)
taken from GPS time 1187007048 to 1187008680. The
PSD estimate
is truncated
8 s last
lengthpartin theoftime• Tidal eﬀects become
signiﬁcant
intothethedomainusing the method described in Ref. [16]. The gravitationalinspiral. However,theusedmodel
on isPN
calcula'on
wave datain thebased
likelihood
takenfrom the interval
1187008691justto 1187008891. merger.
would not be accurate
before theRef. [17] found that choice of the low-frequency cutoff can have an effect on the measurement of the neutronstar tidal deformability and used a different power spectral density estimation technique to that used in our analysis [18]. We investigated the effect of changing our esti-ref) De et al. 2018

2

FIG. 3. Measurability [19] of the chirp mass M, SNR ⇢ and bi˜ in the frequency range 10 Hz - 2000 Hz.
nary deformability ⇤Each detector’s parameter measurability is scaled to the maximum frequency to show the relative accumulation of measure-

PredicOon by numerical simulaOons is important for modeling the Odal correcOon(at least needed to be checked)

Numerical RelaDvity SimulaDon•

Numerical-rela'vity (NR) simula'onis the unique method to predict
dynamics and gravitaDonal waves in
the merger phase—a regime where
the non-linear eﬀect of hydrodynamics
should be taken into account in theframework of general relaDvity.

Einstein’s equaOon
Euler equaOon
8⇡Gµµ⌫rµ (⇢u ) = 0 rµ T = 0
Gµ⌫ = 4 Tµ⌫c
EquaOon of state (EOS)(+MHD, viscosity, neutrino, etc., )P = P (⇢), P (⇢, T, Ye ), · · ·

-0.1

-0.1

of
term in ⇤, p
400
600
800
1000
0
200 exponent
400
600the nonlinear
800
1000⇡ 2/3f [Hz]even if it is also set to be a fitt
f [Hz]
by employing several hybr
the tidal part 15H125-125of the gravitational-wave phase computed
15H135-135
15H121-151 determined15H116-158
Hybrid125H135-135
125H125-125
125H116-158
fitting parameters,a and p, are
7 determfrom the hybrid
waveforms, tidal (= Hybrid 125H121-151
pp ,H135-135
H125-125
H121-151
H116-158
ing
where Hybrid isthe phase of the hybrid waveforms),
for
HB135-135
HB125-125
HB121-151
HB116-158
B135-135
B125-125normalized by the 2.5 PN0.1order
B121-151
B116-158
0.1 the equal-mass binaries
Z

0

200

NS-NS waveform model

fmax

TT /e↵

Mismatchem^Hybrid
tidal -^tidal^Hybrid
tidal -^tidal [rad][rad]Hybrid(equal-mass) tidal-part phase given by2 [12]em
I 00 =
tidal (f )tidal (f )• Based on FIG.
4. The di↵erence
between the tidal-part
phase
of
the
FIG.
5.
The
di↵erence
betweenthetidal-part
phase
of
the
our latest
numerical-relaOvity
waveforms,
✓
◆
fmin
0.05
0.05
hybrid waveforms and the2.5PN
tidal-part3 phase39
model describedhybridwaveforms
andthetidal-partphase model described
5/2
=
⇤
x
a waveform
model
for
NS-NS
mergersisderivedtidal
in Eq. (2.15) for the equal-masscases, where
the phases
in Eq. (2.21) for the unequal-mass cases. Here, the phases
32
2
are aligned for 10 Hz0  f 
 1000 Hz employing Eqs. (2.12)
are aligned for 010 Hz  f  1000 Hz employing Eqs. (2.12)
where t0 and 0 are parameters that
3115
28024205
4283 5/2
and (2.13).
and(2.13).
3/2 et al.
2• A NS-NS GW
model is also derived
inDietrich⇥ 1+x ⇡x +
x⇡x,
degrees of freedom for choosing the ti
1248
3302208
1092-0.05
gins. Thus, we minimize I 00 for the f2017 , 2019 based on -0.05
diﬀerent NR waveforms and(2.14)
˜ tasfitting
is performe
respectively.
Werefer top,⇤
the binary
tidal
deformais
as
large
as
0.08
rad
for
f
⇡
1000
Hz.
However,itis
0 , and
0 . TheTidalEOB waveforms -0.1
-0.1
and1000 Hz.
bility. For realistic
cases,
thefmax
tidal=contributions
to thesmaller than the phase error in the numerical-relativity
2/3
where
x
=
(⇡m
f
)
is
a
dimensionlessPN
parame0
0
200
400
600
800
1000
0
200
400
600
800
1000 of 15H
gravitational-wave phase areby the contribuwaveforms associated with the finite-di↵erencing [29].
Wedominateduse the hybrid
waveformter, and= ⇤f 1[Hz]=⇤2 for the equal-masscases. ˜ We
• Though their and our models
are ⇤derived
independently,
f [Hz]
tions from the ⇤terms [19].
Assumingthat parameters
the contribu-because
miningthefitting
15H135-135
15H125-125
15H121-151
15H116-158
notethat the tidal-partphase of the hybrid waveforms
˜125H121-151
tions from the ⇤terms tribution
and those of
fromthemosthigher-order⇤ issignificant for
two models give almost consistent
125H135-135 results 125H125-125
125H116-158
in
Fig.
2
is
aligned
with
the
2.5
PN
order
tidal-part
2. Unequal-mass
H135-135 cases
H125-125
H121-151
H116-158
terms are always sub-dominant
in the startidalpart of employed
thenary neutronmodelsinphasegiven by Eq. (2.14)
for 10 Hz  phase,f  50we
Hzextend
employHB135-135
HB125-125
HB121-151
HB116-158
the formulaof Eq. (2.15) by replacing
we obtain
B135-135
B125-125
B121-151
B116-158
Eqs.
(2.12) and(2.13).
We offind thatthetidal-part˜
Next, we extendingthe
tidal-part
phase
model
3/32 to 3/128⌘ [38] and ⇤ to ⇤ as
phase
of
the
hybridwaveforms
deviatessignificantly from
(2.15) FIG.
to unequal-masscases.
Considering
the depen di↵erence
a =of12.55,
4. Kiuchi,
The di↵erence
betweenthe tidal-part phase of the
FIG. 5. Thethe⇣ between the⌘tidal-part phase
Ref: KKEq.
et
al.
2018,
K.
KK
et
al.
2019
3
39
the
2.5
PN
order
tidal-part
phase
in
the
high-frequency
dence on thesymmetric
mass
ratio,
the
1
PN
order
tidal
2/3
p
5/2
˜
˜
hybrid waveforms and the tidal-part phase model described tidal
hybridwaveforms
andthetidal-part
phase
model
described=⇤ 1 + a⇤ xx
p = 4.240.
Comparison
withfDietrich+17
range,
&
500
Hz (x
0.075
),128⌘and thecorrection intoEq.
the(2.15)
phase
written
in &
terms
offor
them
0 = 2.7 M
forcanthebe
equal-masscases,
wherethephasesin Eq.
(2.21)
for2 the unequal-mass cases. Here, the phases
for 10 Hz  depends
f  1000 Hz
employingEqs.
(2.12)
are aligned
 f28024205
 1000 Hz employing
Eqs. (2.12)
deviation
non-linearlyon ⇤(notethequantities
symmetricare
andanti-symmetriccontributionsof neutronfaligned
3115 for 10 Hz
4283phase
min = 10 Hz, fmax = 1000 Hz,
3/2
2
Figure4showstheand (2.13).
⇥ ⇤).
1and
+ (2.13).
xindi⇡x +x⇡x5/2 di↵erence,
m1 =shownmas
1.35
star tidal deformation
in M
Fig.
This
2 =[19]sun 2 are already normalized by
1248
3302208
1092
part of the hybrid waveforms and th✓ cates◆ that the non-linear contribution of ⇤ is appreciably(2.21)
339 ˜model of Eq. (2.15) for theequal-masHybrid
1PN
5/2Original
0.001000˜
presentinforthehigh-frequency
range.
=⇤x
respectively.
We
refer
to
⇤
as
the
binarytidal
deformais
as
large
as
0.08
rad
for
f
⇡
1000
Hz.
However,
it
is
tidal
tidal
phasesareareusedalignedfor10
Hz  f  1
128⌘
2
where
the
valuesinEq.
(2.17)
foraandp.
bility.
Forrealistic
cases,
thetidal
contributions
to
the
In
Fig.
3,
we
plot
the
relativedeviationofthesmaller
than
the
phase
error
in
the
numerical-relativity
"
! #
Eqs.
(2.12)
and(2.13).
AlthoughtheRef:Dietrich
et
al.
2017,
201
˜the hybrid waveforms
5 shows
the phase
betweenthecontribuhybridpgravitational-wave
phasedi↵erence
are dominatedby thewaveforms
associatedthe offinite-di↵erencing[29]. Figure
tidal-part
phase
from
the
2.5
3115
6595 with⇤
0.0tions from the ⇤areHzdeterminedby described
employing⇥ 1+
1 4⌘
x , (2.18)
fmrg
1000
terms
[19].
Assuming
that
the contribuwaveforms
and the˜tidal-part
phase
model
in only th
˜
0.000100
1248 7098⇤
of 15H125-125
asthe
a two
reference,
˜ terms
tions fromtheunequal-mass⇤
and thosehigher-order
Eq. (2.21)
for thecases.fromHere,phases we find
2. Unequal-mass cases
phasemodel,
termsaligned
are always
the
tidal
part of Eq.
the (2.15)
are 0.1
again
for sub-dominant
10theHz tidal-part f in1000
Hz employing
˜˜where ⇤ and ⇤ are definedbyphase,
we2.5
extendformulaEq.fitting(2.15)parametersbyforreplacingthan
0.05oftheradexcept15H135-135.
2 Strictly speaking, this formula is not complete
Eqs. up(2.12)
and(2.13).
Althoughto thePN the˜
0.000010
7.5PN
we orderextendthe tidal-part phase model areof 0.2
3/32
to 3/128⌘
⇤ to
⇤ as
⇥
cates
that
there
is onlya small di↵edetermined
only[38]
by andemployingthehybridwaveform
8 Next,togravitational2because the 2 PN order tidal correction
7PN
˜⇤ = Eq. (2.15)
1 + 7⌘
31⌘(⇤+⇤)
to unequal-masscases.
Consideringthedepen1
2
radiation reaction is neglected. We overlook
such correctionin (2.17),of 15H125-125,
that⌘ thedetermined
phase errorfrom di↵waveform
6PN Eq.
⇣we find models
13
3
39
dence
on
the
symmetric
mass
ratio,
the
1
PN
order
tidal
i
2/3
p
5/2
NRTidal˜ 1rad˜forAppendix
p
this work because it is expected to be sub-dominant[12].
0.3 tidal= than ⇡forms
⇤
+(see
a⇤
x
xunequal-massis always
smaller
0.07
theseD). The phase er
2
Kawaguchi
128⌘2
correction to the phase can be written in terms of the

0.000001

and

1

0

4⌘ 1 + 9⌘

11⌘

(⇤1

⇤2 )

(2.19)

cases.

symmetricof neutron200
400 600and
800anti-symmetric1000 1200 1400 contributions
1600 1800
24
star tidal deformation as [19]R

NRTidalv2
3115⇥ 1 +0.05 x
1248

28024205

4283

5/2
0.10
⇡x3/2 + 0.15
x20.20⇡x0.25,33022081092!
ˆGeneral picture
InspiralMerger107yr~~10-100ms

Post-Merger

NS-NS

BH-NS

G
EOS
ν
B

PN

1s~

Full GR, dynamical

Full GR, staOonary

zero temperatureﬁnite temperatureν cooling & heaOng
MHD

ρ

T

B

Mass ejecDon (NS-NS)
Ref: Y. Sekiguchi et al. 2015

Tidal torque driven

Shock heaOng driven

A fracOon of NS material would be ejected from the system during the merger.

(e.g. Hotokezaka et al. 2013; Bauswein et al. 2013; Sekiguchi et al. 2016; Radice et al. 2016; Dietrich et al. 2017; Bovard et al. 2017)

Remnant NS & torus
1051

1.8e+

1050

1.6e+

1049

1.4e+

1048

Poloidal Toroidal

1047∆x = 12.5 m

1045

10

∆ x = 12.5 m∆ x = 70 m
∆ x = 110 m←KH instability

6.0e+
0

5

10

15

< α >12< α >13

10-2

20

25

30

t - tmerger [ms]

10

10-2

∆ x = 12.5 m∆ x = 70 m
∆ x = 110 m

FIG. 4. Magnetic-field energy (left), rotational
the runs. The solid and dashed curves in the lef

10-3

-4

15

20

merger [ms]

25

10
Ref:
K.
Kiuchiet5al. 2015,
2017
30
10
15

20

t - tmerger [ms]

25

30

10-3

8.0e+

∆x = 110 m-1∆ x = 12.5 m∆ x = 70 m
∆ x = 110 m

1.2e+

1.0e+

17

∆x = 70 m

1046

-1

Erot [erg]EB [erg]

Turbulence in the contact surface→ampliﬁcaOon of magneOc ﬁeld
→The remnant NS and accre'on torus would be highly magne'zed.

5

10

15

20

t - tmerger [ms]25

30

Tidal disrupDon of NS (BH-NS)•

If the Odal force of the BH exceeds the self-gravityof the NS, the NS is 'dally disrupted.

•

The NS should be Odally disrupted outside the
ISCO of the BH to form a ejecta or remnant torus,otherwise enOre NS material would be swallowedby the BH.

•

Whether Odal disrupOon occurs or not
depend on the binary parameters.

mBH /mNS<latexit sha1_base64="N0vnTgqeDtKzn1WVc5VPLBtiuMI=">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</latexit>

SBH<latexit sha1_base64="8qjtGuXNCrbYFOPETKLeUbn0Zmw=">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</latexit>

RNS<latexit sha1_base64="6diUWgqP0lolWXX4sOPUqTl4OPU=">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</latexit>ref) Kyutoku et al. 2010, 2011

General picture
InspiralMerger107yr~~10-100ms

Post-Merger

NS-NS

BH-NS

G
EOS
ν
B

PN

1s~

Full GR, dynamical

Full GR, staOonary

zero temperatureﬁnite temperatureν cooling & heaOng
MHD

ρ

T

B

Post-merger mass ejecDon
Viscous GRRHD simulaOon for merger remnant(Ref: S. Fujibayashi et al. 2018)Material ejecOon from the remnant torus would occur
driven by ampliﬁed magneOc ﬁelds or eﬀecOve viscous heaOng due to magneOc turbulence(see also e.g. Siegel et al. 2018, Fernandez et al.2018 for GRMHD simulaOons)

such
that
the initialmaximum
strengthsuch that the after
initialtidal
maximummagnetic-fieldstrength
is magnetic-field
gravitational-wave
amplitudemaxim
gravitational-wave
becomes
maximal.byTheejectabecomes
disruption[8,25].
The amplitude
massisaccretionis enhanced
turbulencelike
motion15
15
10
G. Even
if thiswe start
ais simulation
withtothis
ad
hoc
are
definedtobefluid
elements
that
reside10 G. Even if The
we initialstart amagnetic-field
simulation
withad hocareindefinedbefluidelements
that
resideoutsidethe
BH
configuration
given
terms
that is generated by these magnetohydrodynamics (MHD)olocalized
magnetic
field, the andresultingsurroundand−1
where uttorqueis the exerted
lower time
localized seed ofmagnetic
field,
the resulting
torus
surroundhave utorus−1
where uas
the havelower
time
componentofthe vector
potential
asseed[45]t<gravitational
as byuthebyt< instabilities
tiswell
BH comes
in afourturbulencelike
state
the
four
velocity.
Thiscriterionmeans
ing the remnant BH comes toing
bethe
in aremnant
turbulencelike
stateto be thevelocity.
This criterion means
fluid
the nonaxisymmetricstructurethatof the accretion
torus [seeyxglobal2 are eventually.
amagnetic
field
isnaturally
formedelements
aregravitationallyunbounded.
and a global magnetic
field−isyand
naturally
formedeventually.
elements
gravitationallyunbounded.
The
primary
Aj ¼ ð−ðy
Þδ
þ
ðx
−
x
Þδ
ÞA
maxðP
−
P
;
0Þ
;
Fig. 1(c) and visualization in Ref. [50]].
NS j
NS j
b
c
Figure 2 plots the ejecta mass, torus mass, mass acwhere xNS and yNS denote the coordinate center of the NS,
cretion rate onto the BH, and ratio of the magnetic-field
P is the pressure, Pc ¼ Pðρ ¼ 0.04ρ max Þ, and j ¼ x; y, andenergy, EB , to internal energy, Eint , as functions of time. We
z. ρ max is the maximum rest-mass density and we set Ab
define the merger time tmrg to be the time at which thesuch that the initial maximum magnetic-field strength isgravitational-wave amplitude becomes maximal. The ejecta
1015 G. Even if we start a simulation with this ad hoc
are defined to be fluid elements that reside outside the BH
localized seed magnetic field, the resulting torus surroundand have ut< −1 where utis the lower time component ofing the remnant BH comes to be in a turbulencelike state
the four velocity. This criterion means that the fluid
and a global magnetic field is naturally formed eventually.
elements are gravitationally unbounded. The primary

RelaDvisDc jets•

Ref: K. Kiuchi et al. 2015

RelaDvisDc jets could be launchedfrom the BH accreDon torus system
FIG.
online).
Snapshotsof thetherest-mass
densitylines
profilethe magnetic-fieldlines
just after tidal disr
1 (color online). Snapshotsof 1the(color
rest-massdensity
profile withmagnetic-field(a) with
just after
tidal disruption,(b)(a)
at anformed aner the mergerFIG.
early
phase
of
accretion
torus,
and
(c)
in
the
final
phase.
The
isosurfaces
for
10
,
10
,
and
10
g=cm
early phase of accretion torus, and (c) in the final phase. The isosurfaces for 10 , 10 , and 10 g=cm are denoted by yellow, green, andare denoted by ye
11

10

9

3

11

10

9

3

Thebymagnetic-fieldlinesInarethe white
curves. In thepanel,
isosurfacesregion.
are drawn for the threeblue. The magnetic-field lines areblue.
shown
the white curves.
theshown
middlebypanel,
the isosurfaces
aremiddle
drawn forthe thethree-quarter•

global structure of the magneDc
ﬁelds would play an important role

064034-2

064034-2

evolution of NS merger disks
7
Ref:GRMHD
R. Fernandez
et al. 2018

0.2

Ye

0.3

0

0.1

-0.5

064034-2

0
10

0.5

5

0

[s 1 ]

contribuDon from neutrino
Ruiz, Lang,pairPaschalidis & Shapiro
annihilaDon seems to be subdominantz [107 cm]•2

z [107 cm]

FIG. 1 (color online). Snapshots 1of the rest-mass density profile with the magnetic-field lines (a) just after tidal disruption, (b) at an
0.5
early phase of accretion torus, and0.5(c) in the final phase. The isosurfaces for 1011, 1010 , and 109 g=cm3 are denoted by yellow, green, and0.4
blue. The magnetic-field lines are shown by the white curves. In the middle panel, the isosurfaces are drawn for the three-quarter region.

0
5

-0.5

10
5.0 mst

10 ms

t = 66 mst

230 ms

10

1

-0.5

1030
0.5

Fig. 1.— Snapshots of the rest-mass density, normalized to its initial maximum value ⇢

1029
1028

0

1027
1026

-0.5

= 5.9 ⇥ 1014 (1.625 M /M

)2 g cm

3 (log1025

B2p /8p [erg cm 3 ]0

kT [MeV]0.5
z [107 cm]

Ref: M. Ruiz et al. 2016t

Ruiz, Lang, Paschalidis & Shapiroz [107 cm]

2

Post-merger waveforms (NS-NS)•

Post-merger waveforms would containrich physical informaDon,such as the evolu'on of the merger remnant andinforma'on of high density part of NS EoS•

Challenging for both detecDon andwaveform modeling•Complicated physical eﬀects, such as MHD, thermal
eﬀect, and ν radiaDon, should be taken into accountin the numerical simulaDons

GW spectra
1
Post merger

f A Deff /m0

Detector sensi'vity

0.1

0.01

15H135-135
125H135-135
H135-135
15H125-125
125H125-125
H125-125500

Ref: B.P.Abbot et al. 2017

700

1000
1500 2000
f [Hz]

3000

Ref: K. Kiuchi et al. 2017 , KK et al. 2018

FIG. 1. The comparison of Fourier spectra of gravitational

Post-merger waveforms (BH-NS)ref) Kyutoku et al. 2015

The merger~post merger part of the BHNS
waveform could be diﬀerent if the NS is'dally disrupted→The high frequency part (>1kHz) of GW is
important(see also e.g. Shibata et al. 2009, Lackey et al. 2014,
Pannarale et al. 2015)aligned-spin
0.15
5e-22
4e-22
3e-22
2e-22
1e-22
0
-1e-22-2e-22-3e-22-4e-22APR4-5e-22
MS1
10

0.1
0.05
0
-0.05
-0.1
-0.15
15

20
tret[ms]

25

30

GW comparison between diﬀerent
binary components (Q=1)
No tidal disruption

Tidal disruption

33

Ref: Foucart et al. 2018

Dh/M0

•

Waveforms in the inspiral phase would have almost
the same behavior as BNS or BBH.
→it is important to dis'nguish it from BNS or BBH
h[100Mpc]•

ElectromagneDc Counterparts
to NS binary mergers•

Various transient EM counterparts areproposed for NS binary mergers•

for example,•

short-hard gamma-ray-burst•

Axerglow•

cocoon emission•

kilonovae/macronovae•

radio ﬂare, etc.

•

Host galaxy idenOﬁcaOon, remnant
properOes, environment•

Possible synthesis site of r-process nuclei
Ref: B. Metzger and E. Berger 2012

short-hard gamma-ray burst•

L~1051erg/s, Δt=0.01-1000 s•

launched by highly relaOvisOc jet (Γ~100-1000)•

Long-sox GRB: ≥ 2s
deaths of massive stars•

Short-hard GRB: ≤ 2s
neutron star binary merger?
E. Nakar / Physics Reports 442 (2007) 166 – 236
E. Nakar / Physics Reports 442 (2007) 166 – 236

sGRB light curve
10

x 104

5
GRB 910718
T90 = 0.25 s

DuraOon distribuOon of GRBs

x 104

171

120 GRB 941228
T90 = 62 s
100
4

8

N

counts/sec

80
6

3

60
40

4
2

20
0

2

10−2

10−1

100

101
T90 [sec]

102

103

1
0
0.25
0.5
0
0.25
0.5
Fig. 1. The bimodal
duration
distribution
of
GRBs.
The
observations(2041 bursts in the current BATSE catalog) are marked by the thick stairs.
t(sec)t(sec)ref) Nakar 2007

Kilonova/Macronova•

A Kilonova/macronova is a electromagneOc (EM)emission which expected to be associate witha NS binary merger.

•

Ejected material is neutron-rich→heavy radioacOve nuclei would be synthesizedin the ejecta by the so-called
r-process nucleosynthesis→EM emission in opOcal and infrared wavelengths
could occur by radioacOve decays of heavy elements: kilonova/macronova
Li & Paczyński 1998, Kulkarni 2005,
Metzger et al. 2010 …

Ref: K. Hotokezaka et al. 201336

R-process nucleosynthesis
Credit) Sho FujibayashiZβdecayN captureN⌧Ncap ⌧ ⌧ dec<latexit sha1_base64="Rs9wf7gaMtiaGEU5pLuIublymYI=">AAACD3icbVDLSgNBEJz1bXxFPXoZDKKnsCuCehO9eJIIrglkQ+iddJLB2QczvUJY8gle/BUvHlS8evXm3zh5gJpY0FBUddPdFaZKGnLdL2dmdm5+YXFpubCyura+UdzcujVJpgX6IlGJroVgUMkYfZKksJZqhChUWA3vLgZ+9R61kUl8Q70UGxF0YtmWAshKzeI+DwiyZh7oiF8JSPuBUj9KECIBb6HoN4slt+wOwaeJNyYlNkalWfwMWonIIoxJKDCm7rkpNXLQJIXCfiHIDKYg7qCDdUtjiNA08uFDfb5nlRZvJ9pWTHyo/p7IITKmF4W2MwLqmklvIP7n1TNqnzRyGacZYSxGi9qZ4pTwQTq8JTUKUj1LQGhpb+WiCxoE2QwLNgRv8uVp4h+WT8ve9VHp7HycxhLbYbvsgHnsmJ2xS1ZhPhPsgT2xF/bqPDrPzpvzPmqdccYz2+wPnI9vDUeczw==</latexit>

−3

10

2

0

2.6 × 10
2.6 × 1032.9
−1
−1
1.1 × 10
1.1 × 1022.3
−3
−3
5.5 × 10
5.5 × 105.60
3.410000
× 10−7 15000
3.4 × 10−7
20000 5.36 25000
0.0 Wavelength (Å)
0.0
3.30
0.0
0.0
0.96

Absolute

10

0.15
0.20
0.25
0.30
5000
0.35
0.40

Pl

E

−2

10−2

Ejecta opacity
-12

−3

10

-13

0

5000

-11

10000

15000

20000

25000

Temperature (K)Absolute magnitude
Absolute magnitude

Mass fraction

Absolute magnitude
Absolute magnitudeaPlanck mean opacity (cm2 g−1)

Expansion opacity (cm2 g−1)

Mass fractionref) Tanaka et al. 2018,2019
Figure 8. Same as Figure
but for s-shell
M.3 Tanaka
et al.elements.
-10
0
5
10
15
20
Note—
Mass fraction of lanthanide elelected to systematicallystudy
the opacitiesofelements
Lanthanide-poor
case
Days
after
the
mergerdpsments.
f
Table 1. Planck mean opacity for elementwith diﬀerent-17
open shells: Ba is an open s-shell gelement,
Se b Mass
Ru fraction
Te Ba Nd of Er0= 0.30-0.40-17lanthanide
andactinide10
mixtureSe and Te are openYep-shellelements, Ru is an griopen dYe
=
0.30
Ye
=
0.25
Ye
=
0.10-0.40
Y=
0.20-0.30
elements.
d
p
s d
p
s f
shell delement,p-16ands fNde and Er are open f-shell elements.
zr
a
b
c
0
c
-16
Ji
Ye
X(La) 10Planck
X(La+Ac)κ
Averagemean opacity
for
We
focus
on
neutralatom
andsinglyanddoublyz ionized
-1
Y
=
H
0.40
0.35
0.30
0.25
0.20
0.15
0.10
−13
−3 e
10
2 g−1
-15
T = 5, 000 − 10, 000 K (ρ = 1 × 10
cm
KJ
cm g
ions because these ionization states are most common
in
H
-15
-1
and t = 1 day
after
the
merger).
K
kilonova at t >1 day after the merger (Kasen et al. 2013;
−2
∼
d
0.10
7.1
×−1
1010
1.7 × elements
10−1 d with
27.0 Z ≥ 93,
-14
-2
1.1
×
10
excluding
10
Tanaka & Hotokezaka2013).
-14
0.15
2.6 × no10−1
2.6 data
× 10−1
32.9
for whichatomicare available.
-2
In Figure 1,-13these elements are shown with three dif10
0.20 1.1 × 10−1 1.1 × 10−1
22.3
ferent abundance
patterns in the ejecta of NS merg-13
10-3
0.25 5.5 × 10−3-3 5.5 × 10−3
5.60
ers. While relativistic
simulations of NS mergers predict
10
-12
−7
−7
wide ranges of-12Ye between 0.05 and 0.45, the detailed
0.30 3.4 × 10
3.4 × 10
5.36
-4
Ye distributions
depend on the NS masses and their ra10
0.35 0.0 Lanthanides
0.0
3.30
-11
10-4
tios as well as-11the adopted nuclear equations of state
For0.40the easein analytical
0.0 of applications
0.0
0.96 models, we(Sekiguchi et -10
al. 2015, 2016). In this paper, we assume
average valuesofthePlanckmean
opacities
in
Table
-5
a
10-5 give Note—
10 fraction of lanthanide elea flat mass distribution
between
Ye10= 0.10 and
0.40 as
5
15
20
Mass
-100
40
50
60
70
8040
90 50 100
30 that
60 representative70
80 of 0dynamical
90
100
1.30However,itisemphasized
theaverage
opacities
5 ejecta.
10
15
20
Days
after
the
mergerAs shown in Figure
ments.
Lanthanide-rich
caseAtomicnumberDays after the merger
Atomicnumberb
are derived
only
at
T
=
5,
000
−
10,
000
K
and
there
is
1 (orange line),-17 the dynamical ejecta consist of a wide
Mass fraction of lanthanide and actinideg-17
Y
Figure1. a strong
Element
abundances independence
the ejecta ofatNS
range
of r-processelements
34) totemperature
T mergers< 5, 000atK. Furelements.
e = 0.20-0.30from the first (Z =
103
103
gr
Ye = 0.10-0.20
t = 1 day after theabundances for
Ye = 0.10
Y=
0.10
c merger. The orange line showsirethird (Z = 78)
the post-merger-16 abundance peaks. For
thermore,Average
the expansion
also
dependPlanck opacities
mean
opacityfor on the
Yederived= 0.15
Ye = 0.15
zi
dynamical ejecta (Wanajo et al. 2014), which isby averag-16−13−3
ejecta,weconsidersingleYmodels0.25(green)
and
Y1
=
0.20
Yeof
= 0.20Jze2nucleosynthesis
2
T
=
5,
000
−
10,
000
K
(ρ
=
×
10
g
cm
e
density
(and
thus,
the
positionintheejecta)aswell
ing theresults
of
Y
=
0.10
−
0.40
assuming
a
flat
e
10
10
HJ
Ye = 0.25
Y
=
0.25
e
0.30 (blue) fora case-15simplicity. The former represents
Ye distribution.
The
blue
and
green
lines
nucleosynthesis
andt =after
1 day
after
theshow
merger).
K
H
Ythe
Ye = 0.30
as thetime
themerger.
Therefore,
we need fulle = 0.30-15d−1K
results from trajectories
of
Y
=
0.25
and
0.30,
respectively,
which
Ye = 0.35
Ye = 0.35
thatcontains the second (Z = 52) abundance
peak and a
1.1 ×
10 e excluding
elements
with Z≥ 93,
1numerical
calculations
quantitatively
connect
Ye = 0.40
represent
abundance
patterns of tohigh-Yejecta. obser101 the10
e = 0.40
e Ypost-merger
small amount-14
of Lanthanides. The latter is a Lanthanidefor which
notheatomicdata areBlack points
connected
withline abundanceshow
the available.
solar
abundance-14
vational
properties
with
distributions.
free model without
elements of Z > 50. For all the modratios ofr-processelements(Simmereretal.
2004).
0100
10els, the nucleosynthesis
abundances of each Ye are taken-13-13
4.2. Light curves
from Wanajo et al. (2014).
inantlybyneutrino
heating(Wanajo
&
Janka
2012;
−1
For the atomic
structure calculations, we use two dif-12
10
10−1
In
this
section,
we
apply
our
new
opacitydata
to-12
Perego et al. 2014; Fujibayashi et al. 2017) and nuclear
ferent codes, HULLAC (Bar-Shalom et al. 2001) andradiative
transfer
simulationsofkilonovae.
We
use
recombination(Fernández&
Metzger2013).
These(Jönsson
et al. 2013). The HULLAC code,-11
For the ease of applications in analytical models, weGRASP2K
e
10−2
10−2
-11
components
are as a wholedenotedas “post-merger”
a Monte-Carloradiative
transfercode developed bywhich
employsaparametricpotential
method,
is
used
give
averagevaluesof the Planckejecta
mean opacities
in Tableejecta inthispaper.
The post-merger
canconsistTanaka&Hotokezaka(2013);
Tanakaetal.
(2014)
andto−3 provide atomic
data for many elements while the
-10
−3
-100
10
10
1.
However,itisemphasizedthattheaverage
opacities
5
10
15
20
of less 0neutronrichmaterial
thanindynamical
GRASP2K
code,0 which
ab-initio
calcu510 20000
15 25000
20
further5000updated
by Kawaguchi
et al. (2018)
10000
15000
20000
25000 to in0
5000
10000 enables
15000 moreDays after the merger
ejecta (Justet al. only
2015;atMartin2015;
et al.
are derived
T = 5, et000al.
− 10,
000Wu
K and
there islations based on theTemperatureDays
multiconfiguration
Dirac-HartreeWavelength (Å)(K) after the merger
clude special-relativistic
eﬀects. We adopt a simple-17
2016; Lippuner
etal. 2017); neutrino
absorption
as000
well
a strong
temperaturedependence
at
T
<
5,
K.
FurFock (MCDHF) method, is used to provide benchmarkgone-dimensionalejectabymodelwitha power-law
denYe = 0.10-0.20
FigureMulti-color
light
curves in
optical(griz)
as a9.hightemperaturecausedviscousheatingmakes
FigureTop:
Abundance
distributionfordiﬀerentY(Wanajoet al. 2014).
left:
Expansion
opacityasrcalculaa function
calculations
forBottom
a10.
few
elements.
Such
benchmarkethermore,theexpansiononthe−3 opacities also dependisity structureρ ∝ rrich fromv = 0.05c
to vYe = 0.2c
-16 (JHK) filters for the models with high Ye (Ye =ejected material
lessor Planckelectronfraction
areandimportantbecausesystematic
improvementofof wavelengthfor each
Ye .neutron
Bottomright:
mean
opacityasationsfunctionof NIR
temperaturefor eachYe .
zdensity
(and
thus,
the
positionintheejecta)aswell
et peral. 2010;
Metzger2017),If which
gives an av0.30
−
0.40,
top),
intermediate
Y
(Y
=
0.20
−
J 0.30, middle),(number (Metzgerof protons
nucleon)higher.
the ejectaeethe accuracies is not always obtained with the HULLAC
H
the time
afterof themerger.
Therefore,
wefromfull-15 Ye (Ye = 0.10 − 0.20, bottom) compared
and lowwith theare freeasfrom
Lanthanide
elements,
theemissionerage
velocity⟨v⟩=
0.1c. The
total
mass
isneedset tobecode especiallywhen little data are available Kin NIST
ture.post-merger
Sincenumericalthepotentials
ofd-shell
mixtureobservedof r-processcurves
elements
are almost always
higher bycalculations
to quantitatively
connectof
GW170817/AT2017gfo(compiledejectacan⊙ .bebrighterandbluer,elements
which
canobser-Atomic
Mejionization= 0.03M
Spectra light
Database(ASD,
Kramida et al. 2015).
2−1
Villaretbe called“blue properties
kilonova”(Metzger& Fernández
2014;
vational
with
distributions.
are generally
higherthan thoseofabundancef -shellelements,
thethan κ =0.1-14− al.
0.52017).
cm g even for high Ye , except for
10

[p]
Y =
[p] + [n]<latexit sha1_base64="SaVd2X1sVUpAeLMgS2c0qtc2OlM=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARBKEkIuhGKLpxWcE+JA1hMr1ph04mYWYilBA3/oobF4q49S/c+TdOHwutHriXwzn3MnNPmHKmtON8WaWFxaXllfJqZW19Y3PL3t5pqSSTFJo04YnshEQBZwKammkOnVQCiUMO7XB4Nfbb9yAVS8StHqXgx6QvWMQo0UYK7D18F8BFN5KE5l7qF+N27Am/COyqU3MmwH+JOyNVNEMjsD+7vYRmMQhNOVHKc51U+zmRmlEORaWbKUgJHZI+eIYKEoPy88kFBT40Sg9HiTQlNJ6oPzdyEis1ikMzGRM9UPPeWPzP8zIdnfs5E2mmQdDpQ1HGsU7wOA7cYxKo5iNDCJXM/BXTATFpaBNaxYTgzp/8l7ROaq5Tc29Oq/XLWRxltI8O0BFy0Rmqo2vUQE1E0QN6Qi/o1Xq0nq036306WrJmO7voF6yPbwh+lp4=</latexit>

gnitudeThe ejecta opacity varies signiﬁcantly (0.1—10 cm^2/g) depending onwhether lanthanide elements are synthesized or not, which reﬂects the electron fracOon, Ye, of ejecta.
(Kasen et al. 2013, Barnes et al. 2013, Tanaka et al. 2013)

NS-NS

Post-merger Ejecta

Dynamical Ejecta

Mtot . Mmax,spin⇠ 0.1 M<latexit sha1_base64="dJHhiMlA+b1JbQ4dArNeY5ikTQ8=">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</latexit><latexit sha1_base64="AUm3G4LiIIWfTYzJmz2iIAFijLc=">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</latexit><latexit sha1_base64="F87NGFCAsdqNSTKKdQwPZAfIdeI=">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</latexit>

Long-surviving
remnant

tlife<latexit sha1_base64="xHhet1VMCiw5eYe7qBlOTQLfqsg=">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</latexit>Md1s

tlife & 1 s<latexit sha1_base64="JAGdOv4G+x5tmHEzzOgnrtkPAYQ=">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</latexit>

Lanthanide-free⇠ 0.001M<latexit sha1_base64="+LLZ34nV1VBmiD7o7DCM/dpt3FY=">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</latexit>

MtorusMtot . Mthr
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BH-NS with Tidal disrupOon ⇠ 0.001 0.1M
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without Tidal disrupOon. 0.001 M<latexit sha1_base64="XvXdiXC3llJ4kY7DvL4K20KH6GA=">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</latexit>. 0.001 M<latexit sha1_base64="XvXdiXC3llJ4kY7DvL4K20KH6GA=">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</latexit>

Kilonova lightcurves could show large diversity reﬂecOng the variety
in the binary parameters or the binary composiOon

Lanthanide-rich

Mtot & Mthr
Prompt Collapse

tlife ⌧ 1 s

The ﬁrst NS-NS merger event:
GW170817

PRL 119, 161101 (2017)

•

•
•
•

GW170817

PHYSICAL REVIEW LETTERS

week ending
20 OCTOBER 2017∼100ofs (calculated
On 17thAugust starting
2017,from 24 Hz) in the detectors’
sensitive band, the inspiral signal ended at 12∶41:04.4 UTC.
LIGO and
Virgoa reported
In addition,
γ-ray burst was observed 1.7 s after the
coalescence
time [39–45].
The combinationof data fromfromthe ﬁrst
detecDonof gravitaDonal
waves
the LIGO and Virgo detectors allowed a precise sky
2a binary
NS localization(BNS; NS+NS
binary)positionto an areaof 28 degmerger. This measurement enabled an electromagnetic follow-up campaign that
identified a counterpart near the galaxy NGC 4993, conSNR=32.4
sistent with the localization and distance inferred fromgravitational-wave data [46–50].
From the gravitational-wave signal, the best measured
Distance~40 Mpc
combinationof the masses is the chirp mass [51]M ¼ 1.188þ0.004−0.002 M ⊙ . From the union of 90% credibleintervals obtainedusingdifferent
waveform models (see2week ending
Sky PRL
localizaDon:
28
deg
P
H
Y
S
I
C
A
L
R
E
V
I
E
W
L
E
T
T
E
R
S
20 OCTOBER 2017
119,(2017)
Sec.
IV161101for details),
the total mass of the system is between
2.73 and 3.29 M⊙ . The individual masses are in the broad
5°
range30°of 0.86 to 2.26 M⊙ , due to correlations
between theirmay be neutron stars or black holes. At early times, for low
uncertainties. This suggests a BNS as the source of theorbital and gravitational-wave frequencies, the chirplike
gravitational-wave signal, as the total masses of knowntime evolution of the frequency is determined primarily byNmasses m1 and
BNS systems are between 2.57 and 2.88 M⊙ with compo-a specific combination of the component
m2 , the chirp mass M ¼ ðm1 m2 Þ3=5 ðm1 þ m2 Þ−1=5 . As thenents between 1.17 and ∼1.6 M ⊙ [52]. Neutron
stars
in
E
orbit shrinks and the gravitational-wave frequency grows
0° general have precisely measured masses as large as 2.01 #12h
0.04 M⊙15h[53], whereas
stellar-mass black holes found inrapidly, the gravitational-wave phase is increasingly influenced by relativistic effects related to the mass ratio
binaries in our galaxy have
9h masses substantially greater18h
q ¼ m2 =m1 , where m1 ≥ m2 , as well as spin-orbit andthan the components of GW170817 [54–56].
spin-spin couplings [98].
-30° Gravitational-wave observations-30° alone are able to meaThe details of the objects’ internal structure become
sure the masses of the two objects and set a lower limit onimportant as the orbital separation approaches the size of25
50 here75 do nottheir compactness, but the results0 presented
Mpc stars such asthe bodies. For neutron stars, the tidal field of the
exclude objects more compact than neutroncompanion induces a mass-quadrupole moment [99,100]
FIG. 1. Time-frequency representations[65] of data 2017containing
quark stars, black holes, or more exotic objects [57–61].
Ref:TheLIGO/Virgothecoalescence[101].
ratiooftheFIG. 3. Sky location reconstructed for GW170817 by a rapid 41and accelerates
the gravitational-wave event GW170817, observed by the LIGOThe detection of GRB 170817A and subsequent electro-

GW170817:Constraints onbinary parameters
7•

Tidal deformability

Binary parameters were constrained
Dghtly as ever was (SNR~32),
˜ goes to zero in the limit ⇤˜ ! 0. To
the posterior for ⇤,and'dal deformability
avoid thethe misinterpretationthat there isis indeed
no evidence for˜ = 0, we reweight the posterior for ⇤˜ by dividing by the⇤measured(constrained)
in
this
event
˜ In pracprior used, e↵ectively imposing a flat prior in ⇤.

Ref: LIGO/Virgo 2017,2018

3000
PhenomPNRT
PhenomDNRTSEOBNRT
TaylorF2

2500

12

2000
M

2

S1
tice, this is done by dividing a histogram of the posteriorMS
1b⇥ prior. The resulting histogram
⇤
16
1500
by
a
histogram
of
the
is
4
˜=
⇤
(1 + 12q)⇤+ (12density+ q)qesti⇤2
1 kernel5then resampledandsmoothed
withLess Compact
13(1 + q)
H4mation. We have verified the validity of the reweighting
1000
More Compact
procedure by comparing the results to runs where we fix
MPA1
˜ This di↵ers from the⇤2 = 0 and use a flat prior in ⇤.
SL
Massesof thebinarycomponents
500
yFIG. 9.only
Inferredspinparameters
using the PhenomPNRT
AP
reweighting
procedurein thesmall,
next-to-leadingR4
as in Fig. 8, but in the low-spin case where the dimenorder tidal e↵ect. model
sionless component spin magnitudes < 0.05. The posterior
inclination After reweighting there is still some support at ⇤˜ = components
0.
0probability densities for the dimensionless spin
-in-volume
0
200
400
600
800
1000
1200
1400
1600
and
for
are
plottedatthereference
gravitational
wave
frep
For
the
high-spinprior,
we
can
only
place
a
90%
upper
ance prior1
1.40
quency of f = 100 Hz.
nclose thelimit on
0.0035the tidal parameter, shownin Fig. 11 and listed
TaylorF2
h analyses
PhenomDNRT
FIG. 10. PDFs for the tidal deformability parameters ⇤1 andmodel, this 90% up1.35 II and IV. For the TaylorF2
location ofin Tables
PhenomPNRT
0.0030⇤2 using the high-spin (top) and low-spin (bottom) priors.
normalizedper limit can be directly compared
SEOBNRT to the value reportednd the verThe blue shading is the PDF for the precessing waveform
0.0025in [3].1.30
We note, however, that due to a bookkeeping error
als.
PhenomPNRT. The 50% (dashed) and 90% (solid) credibleby the small uncertainty in chirp mass. The lengths ofthe valuein [3]
shouldhave beenby800
of in mass regions are shown for the four waveform models. The seven
1.25 reported
these
bands
are determined
the instead
uncertainty
0.0020black curves are the tidal parameters for the seven represen700.
Our
improved
value
of
730
is
⇠
10%
less
than
this
ratio.
They
have
most
of
their
support
near
the
⇤
=
⇤
53+15
deg
1
2
11
tative EOS models using the masses estimated with the Phe1.20
r both thecorrectedline withcorresponding
to the
equal
mass
case,
and
end
at
the
0.0015value. As
the ⇤1 –⇤posterior
(Fig.
10),
2
nomPNRT model, ending at the ⇤1 = ⇤2 boundary.
surementsthe three models 90%
lower
limit
for
the
mass
ratio.
The
predicted
valueswith the NRTidal prescription predict
1.15
uminosityof the tidal parameters for the EOSs MS1, MS1b, and H4 0.0010
thatareconsistent
withcredible
each otherandnclination90% upper limits lie
˜ = ⇤1 = ⇤2 when m1 = m2 :M
welloutsideofthe90%
regionfor both theand is defined such that ⇤
chirp
1.10
s reportedless than
the TaylorF2
by ⇠priors,
10%.andFor
low- mod- 0.0005
low-spinresults
and high-spin
for theall waveform
ents [108]16 (m1 + 12m2 )m41 ⇤1 + (m2 + 12m1 )m42 ⇤2
spinprior,
we
can
now
place
a
two-sided
90%
highest
els.
This
can
be
compared
to
Fig.
5
of
[3]
where
H4
was
˜
1.05
09, 110] to
⇤=
. (5)
1.4
1.5
1.6
1.7
1.8 with the
5
˜ 90%
still
marginallyconsistentcredible
region. 0.0000 0
13
(m
+
m
)
1
2
posterior density(HPD)
credibleinterval
on
⇤
that
does
200
400
600
800
1000 1200 1400 1600
m1 (M )42˜
˜ = 0. This 90% HPD interval is the smallest
not contain ⇤<latexit sha1_base64="x846jOhmCMWlQsZ+Kjw5IIEqVXk=">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</latexit>

PDF

m2 (M )

<latexit sha1_base64="B/+8ZdSln360m8bM1yXYEhJ8xzU=">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</latexit><latexit sha1_base64="qD/pLocRAXh1OmQpxb8zc2C16Rg=">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</latexit>

MS1

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H4

MPA1

APR4
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WFF1

1
FF

W

⌘

GW170817: Constraints onbinary parameters

6
Ref: LIGO/Virgo
2018

Binary inclination ✓JN
Binary inclination ✓JN using EM distance constraint [104]Detector frame chirp mass Mdet
Chirp mass M
Primary mass m1
Secondary mass m2
Total mass m
Mass ratio qE↵ective spin e↵
Primary dimensionless spin 1
Secondary dimensionless spin 2
˜ with flat priorTidal deformability ⇤•Low-spin prior (  0.05)

146+2527 deg151+1511 deg1.1975+0.0001
0.0001 M+0.0011.186 0.001 M(1.36, 1.60) M(1.16, 1.36) M
2.73+0.04
0.01 M(0.73, 1.00)
0.00+0.02
0.01(0.00, 0.04)(0.00, 0.04)+420
300+500
190 (symmetric)/ 300 230 (HPD)

High-spin prior (  0.89)
152+2127 deg153+1511 deg1.1976+0.0004
0.0002 M+0.0011.186 0.001 M(1.36, 1.89) M(1.00, 1.36) M
2.77+0.22
0.05 M(0.53, 1.00)
0.02+0.08
0.02(0.00, 0.50)(0.00, 0.61)(0, 630)

Mass
raOo-spin
degeneracy
TABLE II. Properties for GW170817 inferred using the PhenomPNRT waveform model. All
properties
are source
properties+z
det
except for the detector frame chirp mass M= M(1 + z). Errors quoted as x y represent the median, 5% lower limit,
and< 0.89< 0.05 by
95% upper limit. Errors quoted as (x, y) are one-sided 90% lower or upper limits, and are used when one side is boundeda prior. For the masses, m1 is bounded from below and m2 is bounded from above by the equal mass line. The mass ratio
˜ we quote results using a constant (flat) prior
˜ In the high-spin case we
1.0 in ⇤.
is bounded by q  1. For the tidal parameter ⇤,˜ while in3/5
quote a 90% upper limit for ⇤,the low-spin case we report both the symmetric 90% credible interval and the 90%
highest posterior density (HPD)
chirpinterval, which is the smallest interval that contains 90% of0.9the probability.

Chirp mass gives rigid lower limit to the total massm=M⌘

2.72 M<latexit sha1_base64="MlMYNiuS4aoTnoVQIpuGXUHQLHw=">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</latexit>

sion e↵ects would be measurable,
and hence increases the
0.7
lower bound on the luminosity distance. Meanwhile, the0.6upper bound on the luminosity
distance is achieved with
face-o↵ binary inclinations, and is nearly the same foror
0.5 cases.
both high-spin and low-spin
This same weak constraint
on precession leads to a
0.4
1.4
tighter constraint on the inclination angle in the highcase
when using the0.3precessing signal model Phedepends only weakly on the mass raOo for ﬁxed spin
chirp
mass
0.02 0.00 0.02 0.04 0.06 0.08 0.10
nomPNRT, ✓JN = 152+21
27 deg, as comparedeffto the low-

Tidal deformability:

˜ < 800 (90%)
⇤

q

•

0.8

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0.12

9

GW170817:
ElectromagneDc Counterparts
The Astrophysical Journal Letters, 848:L12 (59pp), 2017 October 20•

ElectromagneDc (EM) counterparts
to GW170817 were observed simultaneously
over the enDre wavelength range(from radio to gamma wavelengths)•

The follow-up observaDon of
the electromagneDc counterparts
allowed us to idenDfy the host galaxy(NGC4993: ~40 Mpc)

Ref: P. S. Cowperthwaite 2017

Figure 1. Localization of the gravitational-wave, gamma-ray, and optical signals. The left panel shows an orthographic projection of the 90% credible reg
LIGO (190 deg2; light green), the initial LIGO-Virgo localization (31 deg2; dark green), IPN triangulation from the time delay between Fermi and INTEG
blue), and Fermi-GBM (dark blue). The inset shows the location of the apparent host galaxy NGC 4993 in the Swope optical discovery image at 10.9 hmerger (top right) and the DLT40 pre-discovery image from 20.5 days prior to merger (bottom right). The reticle marks the position of the transient in bo

ical
Opt

In the mid-1960s, gamma-ray bursts (GRBs) were discoveredby subsequent sGRB discoveries (see the compilat
42 erg/s Data: Villar +, 1711.11576r~10ﬁrstby the Vela satellites, and their cosmic origin wasestablishedanalysis by Fong et al. 2015 and also Troja et al. 2016).
star binary mergers arei also expected, however, toby Klebesadel et al. (1973).-16
GRBs are classiﬁed as long or short,isotropic electromagneticz signals, which include (i) earlybased on their duration and spectral hardness(Dezalay et al. 1992;
emission, aJso-called kilonova/macronova (Kouveliotou et al. 1993). Uncovering the progenitors of GRBs
Inandfrainfraredrkilonova;
Lihas been one of the key challenges
inhigh-energy
astrophysics
H 1998; Kulkarni 2005; Rosswoed & Paczyński
-15
Metzger et al. 2010; Roberts
et al. 2011; Barnes & Kase
ever since(Lee & Ramirez-Ruiz 2007). It has long been
K
Kasen
et
al.
2013;
Tanaka&Hotokezaka 2013; Grossm
suggested that short GRBs might be related to neutron
star
Ne
2014;
Barnesetal.
2016;
Tanaka2016; Metzger 2017
mergers (Goodman 1986; Paczynski 1986; Eichler et al. 1989;
ar-14
Narayan et al. 1992).
In radioactive decay of rapid neutron-capture process (rIn 2005, the ﬁeld of short gamma-ray burst (sGRB) studies fr nuclei(Lattimer & Schramm 1974, 1976) synthes
adynamicalreand accretion-disk-wind ejecta during theexperienced a breakthrough (for reviews see Nakar 2007; Berger
andd(ii)
2014) with the identiﬁcation-13of the ﬁrst host galaxies of sGRBs
 delayed radio emission from the interaction of theejecta with the ambient medium (Nakar & Piran 2011; Pi
and multi-wavelength observation (from X-ray to optical and2013; Hotokezaka & Piran 2015; Hotokezaka et al. 201
radio) of their afterglows (Berger et al. 2005; Fox et al. 2005;
late-time infrared excess associated with GRB 13060
Gehrels et al. 2005; Hjorth et al. 2005b; Villasenor et al. 2005).
-12
interpreted as the signature of r-process nucleosynthesis
These observations provided
strong hints that sGRBs might be
et al. 2013b; Tanvir et al. 2013), and more candidat
associated with mergers of neutron stars with other neutron stars
identiﬁed later (for a compilation see Jin et al. 2016).
or with black holes. These hints included: (i) their association with0 (Barthelmy
2
4 al. 2005;6
8Here, we10
14effort958 that led to the ﬁreport on12
the global
both elliptical and star-forming galaxies
etdetection of gravitational and electromagnetic radiation
Prochaska44
et al. 2006; Berger et al. 2007; Ofek et al. 2007; Troja
t
(day)
after
mergersinglesource. An ∼ 100 s long gravitational-wave
et al. 2008; D’Avanzo et al. 2009; Fong et al. 2013), due to a very

Observed lightcurves and spectra provided
the physical implicaDon to
the merger ~ post-merger dynamics of the system(property of merger remnant,r-process nucleosynthesis,
existence of relaDvisDc jets,…)

Optical-IR EM counterparts of GW170817

Absolute AB Maginitude•

Ab

Ref: V. A. Villar 2017

•

GW170817:
Kilonova/macronova with mulDple components

What is the origin of blue/red

Data: Summarized in Villar et al. 2017
D=40 Mpc
4.0

relative flux F¸ (plus offset)

AB absolute magnitude

-15
-14
-13

-11

a

3.5

-16

-12

g
light r-process component
Infrared heavyr r-process component
composite~10 days zi t = 1.5 dayJH
K t = 2.5 day

OpOcal
~1day

3.0

2.5

2.0

t = 4.5 day

1.5

1.0
t = 7.5 day
0.5

10

0.5

1.0

1.5

2.0

2.5

3.0

g (0.40-0.55 ¹m)
r (0.55-0.70 ¹m)
i (0.70-0.85 ¹m)
j (1.10-1.35 ¹m)
h (1.50-1.80 ¹m)
k (2.00-2.30 ¹m)

10

10
0.0

1

b

broadband luminosity, ¸F¸ (1041 ergs s¡1 )-17ref) Masaomi’s slideBlue (lanthanide-free)

Red (lanthanide-rich)

0

-1

0

wavelength (microns)

2

4

6

8

10

days since merger

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
tFigure[day]5 | A unified kilonova model explaining the optical/infrared counterpart of12

14

Ref: D. Kasen et al. 2017

GW170817. The model is the superposition of the emission from two spatially distinct
components: a ‘blue’ kilonova (light r-process ejecta with M = 0.025M , v = 0.3c
A Kilonova/macronova ejecta
modelwith mulOple components well interprets the opOcal-Infrared observaOonand X = 10 ) plus a ‘red’ kilonova (heavy r-process ejecta with M = 0.04M ,(see e.g., Kasliwal et al. 2017,
Cowperthwaite et al. 2017, Kasen et al. 2017, Villar et al. 2017)v = 0.15c, and X = 10 ). a, Optical–infrared spectral time series, where the black line
!

lan

k

•

k

"4

!

lan

"1.5

is the sum of the light r-process (blue line) and heavy r-process (red line) contributions.
early-blue component(~1day) from lanthanide-free ejecta (~0.01 M_sun, opacity ~0.1-1 cm^2/g)b, Composite broadband light curves. The light r-process component produces the rapidly+ long-lasOng red component(~10days)fromlanthanide-richejectaevolving optical emission
while the heavy
r-processcomponent produces theextended (~0.04 M_sun, opacity ~10 cm^2/g)
infrared emission. The composite model predicts a distinctive colour evolution, spectral※radia'on transfer eﬀect
among the mul'ple ejecta components would change the ejecta mass es'ma'on
continuum shape and infrared spectral peaks, all of which resemble the properties of
AT 2017gfo.

45

Gamma ray burst?

Ref: LIGO/Virgo/Fermi/INTEGRAL 2017
10

θjet
≤5o

Frequency (Hz)Event rate (counts/s)

Event rate (counts/s)

Event rate (counts/s)

tart

2500

ger
Bs
Mer
GR
Lightcurve from Fermi /GBM (10θobs
14o–28o

50 keV)

2250
2000
1750
1500

n ≈ 10-4 – 5x10-3 cm-3

1250

E ≈ 1049 – 1050 erg

1750 Lightcurve from Fermi /GBM (50300 keV)

1500
1250
1000
750
Lightcurve from INTEGRAL/SPI-ACS
120000 (> 100 keV)
117500Radio observaOon (VLBI)

115000

Mooley et al. 2018

112500400 Gravitational-wave time-frequency map
300

230 days

200

75 days

100
50

10

8

6

4
2
0
Time from merger (s)

2

4

6

Figure 2. The joint, multimessenger detection of GW170817 and GRB 170817A. Top: The summed GBM lightcurve forsodium iodide (NaI) detectors 1, 2, and 5 for GRB 170817A between 10 and 50 keV, matching the 100 ms time bins of SPI-ACS
data. The background estimate from Goldstein et al. (2016) is overlaid in red. Second: The same as the top panel but in the
50–300 keV energy range. Third: The SPI-ACS lightcurve with the energy range starting approximately at 100 keV and witha high energy limit of least 80 MeV. Bottom: The time-frequency map of GW170817 was obtained by coherently combining
LIGO-Hanford and LIGO-Livingston data. All times here are referenced to the GW170817 trigger time T0GW .

•Gamma ray signal was detected 1.7s aner the GW trigger…however, not typical short hard GRB?

•

Superluminal moDon of the radio counterpart→ existence of a relaDvisDc jetdistances, hence we conservatively use here D = 26 Mp
the lower bound of the 90% credible interval on lumino
ity distance derived from the GW signal (Abbott et a
2017a). If we conservatively assume that the peakof t
3
GW signal and the first photons were emitted simult
The measurement of the GW polarization is cruneously, attributing the entire (+1.74 ± 0.05) s lag
cial for inferring the binary inclination. This infaster travel by the GW signal, this time di↵erence prclination, ◆, is defined as the angle between thevides an upper bound on v. To obtain a lower bounline of sight vector from the source to the detecon v, one can assume that the two signals were emitt
tor
and
the
orbitalangularmomentum
vectorof
The ﬁrst opportunity ofat times di↵ering by more than (+1.74 ± 0.05) s with t
the binary system. For electromagnetic (EM) phefasterEM signal making up some of the di↵erence. A
nomenaitistypicallynotpossibletotellwhetheramul'-messenger astronomy
a conservative bound relative to the few second delasystem is orbiting clockwise or counter-clockwisewith the combinaDon
GW andface-on
EM orobservaDon
discussed in Section 2.1, we assume the SGRB sign(or, equivalently,
face-off), and sources
was emitted 10 s after the GW signal. The resultin
are therefore usually characterized by a viewing
angle: min (◆, 180◆). By contrast, GW meaconstraint on the fractional speed di↵erence is

MulD-messenger Astronomy•

Ref: LIGO/Virgo 2017

surements can identify the sense of the rotation,
v
15
16
3
⇥
10


+7
⇥
10
.
(
and thus ◆ ranges from 0 (counter-clockwise) toFigure 1. GW170817 measurementof H0 . Marginalv
EM
180 deg (clockwise). Previous GW detections byized posterior density for H0 (blue curve). Constraints
The intergalactic
mediumdispersion
has negligible
im
LIGO had large uncertainties in luminosity disat 1- and 2 from
Planck (Planck
Collaboration
et al.
v = photon
vGW
vEMare2016)
SHoES (Riess
et al. speed,
2016)
shown
pact onthe andgamma-ray
with
an in
expecttance and inclination (Abbott et al. 2016a) because
green anddelay
orange.many
The maximum
value small
the two LIGO detectors that were involved arepropagation
orders ofa posteriori
magnitudeand minimal
68.3%
credible interval from this PDF
isRef:
LIGO/Virgo/Fermi/INTEGRAL
2017
nearly co-aligned, preventing
a precise2DavidpolarizaRadice, Liang
Dai: Multimessenger
ParameterthanourerrorsonvEstimation
GW .1 of GW170817+12.0
1
H0 = 70.0 8.0 km s Mpc . The 68.3% (1 ) andtion measurement. In thepresent
case,
thankstomuch
than
10 intervalss are proposed
Mdet = (1 + z) (M1 M2 )3/5 /(M1 + M2 )1/5Lags
is the detector95.4%(2 longer) minimal
credibleare indicatedinbyaltern0
Virgo as an additionalframe
detector,thecosineofthechirp mass, q = M2 /M1  1 is the binary mass
Fit
tive models(e.g.,
Ciolfi& Siegel 2015; Rezzolla & K
dashedanddottedlines.
ratio, e↵ = (M1 1z + M2 2z )/(M1 + M2 ) anda =inclination can be constrained
at 68.3% (1 ) con( 1zspin com- and emission
2z )/2 are the parameters describing
1mar2015),of photons before the merg
ponentsalignedwiththebinaryorbitalangularmomenfidence to the range [ 1.00, 0.81] corresponding
ofpossible
a random(Tsangchance association
betweenthe optitum, and tc,1 and tc,2 are the arrival times
at Livingston
is alsoet al. 2012).
Hence,
certain e
to inclination angles between[144,respectively.
180] deg.
and at Hanford,
NotThisaiming to measure the2
cal counterpart
and NGC
4993
to di↵erence
be 0.004% (seesource’s orientation and its sky position,
we independently
otic
scenarios
can extend
this
time
window
implies that the plane ofthebinaryorbit
isalmost,maximize the likelihood at each detector with respect
tothe
Methods
sectionfor
details).
In
whatfollows
a constant towaveourphaseline
and anamplitude
normalization,
BHB of magnitude
LS220
( 100
s, 1000 s), yieldinga 2 orders
broa
3
but not quite, perpendicular
of
sight
DD2
and we assume that tc,1 and tc,2 can be independently
adwe assume
thatthe optical counterpart
isSFHoassoci1justed.
This whichapproximation
greatly simplifies
eningtheofparamthe allowed
velocity range on either side. Wh
to the source (◆ ⇡ 180
deg),
is consistent
ated
with
GW170817,
and that this source resides
eter estimation by reducing the number of parameters.
with the observation ofacoincident
GRB
(LVC,
the
emission
times
of
the
two messengers are inherent
Since GW170817 has a high matched filtering signal-to0
in
NGC
4993.
ratio (SNR), this simplification does not bias the
GBM, & INTEGRALnoise2017
in prep.;values
Goldsteinetmodel butdependent,
conservative
assumptions yield dr
maximum-likelihoodof the parameters
Toonlycompute1 H
0 we need to estimate the backleads toSavchenko
percent-level increase
their uncertainties [51].
al. 2017, ApJL, submitted;
et al.of2017,
matic
improvements
overexisting
indirect(Kosteleck
0
250
500
750 at 1000
1250
1500
groundflow
velocitythepositionofAssuming GW and EM data to be
independent,
we Hubble
˜
canreport
write theinferences
joint GW
andEM
likelihoodastheproduct
ApJL, submitted). We
on
cos
◆
47
direct(Cornishet2018al. 2017)
co
NGC 2017)
4993. Inand
theRef:traditional
electromagnetic
calof the separate likelihoods, namely & Russell
Radice& DaiFig. 1. Remnant
disk mass
as a functionof the tidal
deformabecause our prior for it is flat, so the posterior is

Host galaxy + GW luminosity distance→ Hubble parameter•

Time delay of Gamma ray observaDon:→ GW propagaDon speed•

Tidal deformability + EM Constraint→ Tighter limit on the NS property(e.g. Radice & Dai 2018, Kiuchi et al. 2019)log(Mdisk /M )<latexit sha1_base64="2V5Q0UxgalilCVaroka4NJJOYes=">AAACg3ichVHLSgMxFD2Or1pfVTeCIMWiCGJJa0ERBPGBboRWrRWslJkx1qHzYiYd0NKdK3/AhSsFEXWpf+DGH3DhJ4hLBTcuvJ0OiIp6Q5KTk3tuThLF1jVXMPbYIDU2Nbe0htrC7R2dXd2Rnt4N1yo7Ks+qlm45m4rscl0zeVZoQuebtsNlQ9F5TinN1/ZzHndczTLXxb7Ntw25aGq7mioLogqRwfwC14Uc9Wa8QiXvGNGlXHU8gIsr1UIkxuLMj+hPkAhADEGkrcgF8tiBBRVlGOAwIQjrkOFS20ICDDZx26gQ5xDS/H2OKsKkLVMWpwyZ2BKNRVptBaxJ61pN11erdIpO3SFlFMPsgV2yF3bPrtkTe/+1VsWvUfOyT7NS13K70H3Uv/b2r8qgWWDvU/WnZ4FdTPleNfJu+0ztFmpd7x0cv6xNrw5XRtgZeyb/p+yR3dENTO9VPc/w1ROE6QMS35/7J9hIxhMT8WQmFZudC74ihAEMYZTeexKzWEYaWTr3EFe4wa3ULI1JSSlVT5UaAk0fvoQ08wHSrJSe</latexit>log(Mdisk /M )•

GW170817:Further constraints on
Λ/Radius/Maximum mass•

Analysis of GW data with further assumpDons•

Lower limit on the NS Ddal deformability / radius
based on EM observaDon•

Upper limit on the maximum mass
based on EM observaDon

Analysis of GW data with further
assumpDons

4

directly in an EOS parameter space. We sample unifavored over “stiff” EOSs such as H4 or MS1, which preformly in all EOS parameters within the following ranges:
dict larger values of the tidal deformability parameter andlie outside the 90% credible region.
0 2 [0.2, 2], 1 2 [ 1.6, 1.7], 2 2 [ 0.6, 0.6], and3 2 [ 0.02, 0.02] and additionally impose that the adiRef: LIGO/Virgo 2018abatic index (p) 2 [0.6, 4.5]. This choice of prior
M
2000
S1
rangesLess Compact• Tighter constraints
onfor the EOS parameters was chosen such that ourMparametrization encompasses a wide range of candidate
S1b
the NS Ddal deformability
andradiusEOSs [110]. Then for each sample, the four EOS paMore Compact
rameters and the masses are mapped to a (⇤1 , ⇤2 ) pair
+390
1500
are obtained by considering
through the Tolman-Oppenheimer-Volkoff (TOV) equa1.4
120
tions describing the equilibrium configuration of a spherical star [119]. The two tidal deformabilities are then used
• the same NS toEoS
for thetwo
objects
1000
computewaveform
template.
Sampling directly in the EOS parameter space allows for(c.f. twin stars)
certain prior constraints to be conveniently incorporated in
the analysis. In our analysis, we impose the following cri500
teria on all EOS and mass samples: (i) causality, the speed• current lowerof limit
themustNSbe maximum
masssound infor
the NS
less than the speedof light (plusto allow: forimperfect parameterization)
up to the cen(Mmax > 1.9710%Msun
Antoniadis
et al. 2013)
0tral pressure of the heaviest star supported by the EOS; (ii)
4
0
250
500
750
1000
1250 6
internal consistency, the EOS must support the proposed1
masses of each
1 component; and (iii) observational consis1 ˜
˜ 90%
Massasprior⇤R̂ (km)B⇤
tency, the EOS must have a maximum mass at least
high
FIG. 1. Marginalized
posterior for the tidal deformabilities of theas previously observed NS masses, specificallyUniform
1.97 M .
222+420
10.7+2.1± 0.2 369 < 485
138
two binary components
of1.6
GW170817. The green shading shows
Another condition the EOS must obey is that ofDouble
thermody+453+2.1
neutron the
starposterior
245
10.9using
0.2⇤a (⇤
125
< 521
3.00
3.0
0 151
obtainedthe
1.6 ±s , q) EOS-insensitive renamic stability; the EOS mustbemonotonicallyincreasing
+448
t
it
i+2.1
Galactic neutronlation
star to233±
0.2for612
516 while theimposecommonEOS
the two<bodies,
144 a 10.8
il m
il m 1.6(d✏/dp > 0). This condition
is
built
into
the
parametrizallgreen, blue, and orange
lines denote 50% (dashed) and 90%
ah need to explicitly impose it.
ahtion [110],dd2.5+420so2.5we do cnothhcredible clevels
for the posteriors obtained using EOSTABLE I. Results(solid)
from parameteruu estimation analyses using threeB
B138
insensitive
without a maximum
different mass priorchoicesrelations,with thea parameterizedcommon EOSEOS
constraint,
requirement,
independent
EOSs(takenfrom [52]), reand applying the masscausalminimum andconstraint
to ⇤(m)
. We
show
2.0
2.0
RESULTS
spectively.
grey
shadingintervals
corresponds
to the unphysical re˜The
90% credible intervals
for ⇤
, 90%
credibleand systemgion
⇤
<
⇤
while
the
seven
black
scatterregions give theatic errors for R̂, Bayes2 factors1 B comparing our common EOS
tidal parameters predicted by characteristic ˜EOS models for thisWe begin 1.5
by demonstrating the improvementtointhe
theunconstrained
mearesults,
1.5 and the 90% upper limits on ⇤.
event [113, 115, 121–125].
surement of the tidal deformability parameters due to imposing a common but unknown EOS for the two
tronNSs.
star, Inand Galactic
neutron star component mass priWe next
1.0 the marginalized joint posterior PDF for
1.0 explore what inferences we can make about theFig. 1 we showors, respectively.
We findthat, Wein comparison
thespectral
un- EOS pastructureof NSs.
do this usingtothe
the individual tidal deformabilities. We show results fromconstrained
the common
EOSaboveassumption
signif- with the rerameterization
described
in combination
our analysis using the ⇤a (⇤s , q) relation in green
and the analysis,
0.5
icantly reduces
the medianvalue and 90%
confidence
upNSs14
up 0to at least1
parametrized0.5EOS without
a10
maximum12mass constraint
8
14
0 in
1quirement that8 the EOS
10 must support12
˜
perwhereboundby about
and 19%,respectively,
forthe heaviest
M , a28%
conservative
based onblue. These
are Decomparedresults
theof ⇤1.97
Ref:
et al.to 2018
R (km)from [52],Restimate
(km)

⇤

= 190

it

lim

BH

H4

SLy
MPA1

APR4

m (M )

H4

SLy
MPA1

APR4

WFF1

m (M )<latexit sha1_base64="PB/Ejl8HzSbkvpZu4xUCunt3at8=">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</latexit>

WFF1

˜ = 222
⇤

draft

BH

lim

it

2

<latexit sha1_base64="4RRCsTaHWppjXvD6xBMc5EL/dh4=">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</latexit>

4

Lower limit on
the NS Ddal deformability / radius
Bauswein et al.

The lower bound of Mthres given by the measured total
mass of GW170817 is shown as dark blue band. The
radius Rmax of the nonrotating maximum-mass NS isthus constrained to be larger than 9.26+0.17
0.03 km.
Instead of using Eq. (1) it may be more realistic toassume that the remnant was stable for at least 10 milliseconds to yield the observed ejecta properties (high• component) (Margalit & Metzger 2017;
masses, blue
Nicholl et al. 2017; Cowperthwaite et al. 2017). In thiscase our numerical simulations suggest that Mthres
Mtot 0.1 M . This strengthens the radius constraints
to R1.6 10.68+0.15
9.60+0.14
0.04 km and Rmax
0.03 km.
Figure 2 shows these radius constraints overlaid on
mass-radius relations of di↵erent EoSs available in the•literature. Our new radius constraints for R1.6 and Rmax
derived from GW170817 exclude EoS models describing
very soft nuclear matter. For the three EoSs excluded by
our “realistic” constraint in Fig. 2, e.g. the softest EoS
in Hebeler et al. (2013), we crosschecked that numerical simulations with the binary masses of GW170817 do
6indeed resultin a prompt collapse.

(Eqs. (2) or (3)) derived from simulations, and (3) aclearly defined working hypothesis (delayed/no collapseof the merger remnant). All assumptions can be further substantiated and refined by more advanced models
2 and future observations,David Radice,
Liang bars
Dai: Multimessenger
Parameter Estimation of GW170817
and error
can be robustly
Ref: Radice & Dai 2018
quantified.
1/5
Mdet(1 + z) measurement:(M1 M2 )3/5 /(M1 +M2 )total
is thedetector(1)= MassThe
binarymass can 0
frame chirp mass, q = M2 /M1  1 is the binary massFit
be measured
with
good
accuracy
and
the
error
bars
are
ratio,
=
(M
+
M
)/(M
+
M
)
and
=
e↵
1 1z
2 2z
1
2
a
with
Wedescribing
fully propagate
the error 1( givenare confidence.
the parametersspin com1z
2z )/2highponentsalignedwith the using
binary theorbitalangularpriormomenthroughour analysis
low-spinresults oftum, and tc,1 and tc,2 are the arrival times at Livingston
Abbott et al. (2017). If GW170817 was an asymmetricand at Hanford, respectively. Not aiming to measure themergerorientationas tentatively
bywethehigh ejecta mass, 2
source’sand itssuggested
sky position,
independently
maximizelikelihood
detectorwithto bandthe truethe
Mtotlies at attheeachupper
boundofrespect
the errora andconstant
wave phaseand an amplitude
normalization,
BHB
LS220
our radiusconstraints
become stronger.
3
DD2
SFHo
and we assume that tc,1 and tc,2 can be independently ad(2) Accuracy of empirical relations for Mthres : The 1
justed. This approximation greatly simplifies the paramempirical
relations(Eqs. the(2) numberand (3))inferred frometer
estimation
by reducingof areparameters.
Since
GW170817 hassimulations
a high matchedfiltering signal-tohydrodynamical(Bauswein
et al. 2013a, 0
1
noise
ratio
(SNR),
thissimplification
does
not
bias
the scat2016) and carry a systematic error and an intrinsic
maximum-likelihood values of the parameters but only1
ter (stemmingfromthe sample
ofuncertainties
candidate EoSs,
leads
to percent-level
increaseof their[51]. which
250
500by AT750 2017gfo
1000
1250
1500
doRevisiting
not perfectly
fulfillanalyticfit).tidal
Mthresdeformability
has been 0
lower
bound
on
derived5
Assuming
GWthe
and
EMthe
data
to be independent,we˜
canwrite the joint
GW and EM
likelihood
as theof
product
numericallydetermined
witha precision±0.05 M .
ofDeviations
the separatebetween
likelihoods,
namelybounce, equalno bounce,
unequalFig. 1.no
Remnant
disk mass as a functionof thetidal deformaTable 3 fits and numerical data are on aver⇥of the Remnant,⇤ M , and M
˜
Dependence of age
the Fateonshort-lived,
equal
short-lived,
unequal2dyn
P than{dGW ,0.03
dEM }|✓
P[d1.38Pdisk[dEM|✓],thM (1)less
M =andat |✓]
most
0.075. Webility
do parameter ⇤. The data points show the results from ourq<
GW
R1.6 < 10.68 km
simulations,whileequal
the dashed line long-lived,shows theunequal
fit in the form of
long-lived,
˜not include
thisuncertainty
in
our
error
analysis
because
q
⇤
type
M
[M
]
M
[M
]
th
dyn
disk
Eq.
(3).
The
gray
shadedregioninthelowerpanel shows the
where
d
and
d
denote
the
GW
and
EM
data,
reGW
EM
3.0
0.774 242
long
0.013
GW170817
uncertainty
we
use
in
Eq.
(4).
We
find
that
disk formation
the 1.8
numericallydetermined
M0.26
of
all
testedmicrospectively.
thres
1.7 short
0.011
0.045
600
is
suppressed
in
the
case
of
promptBH
formation.
We1.6
computethe first
factor with0.036
the relative
binning
physicalcandidate
EoSs
smallerthan theshort 7.6 ⇥10 3is significantly
2.5 excluded
MPA1
method
[52,
53].
We
use
the
noise-subtracted
LIGO
data
3
0.1
1.5
short
⇥thres10 (Mmax0.033
maximumof the6.5M) sequence
for the radius
1
500 1.8
releaseof GW170817
andinclude 3frequencies
in the range
0.774 272
long
0.011
0.26
is much smaller than current statistical errors [24]. This
given
the
. 0.26
Recallthatthemaxima
[23,
1000]
Hz.
Therespective
exclusion
higherfrequency
GW
data
1.7by
long
0.013 ofEoS
choice is also consistent with the use of data from our
2.0
1.6
long (Mmax
0.014
0.27
˜givenof400the) sequencesarebymaximally
resultsinM
a thresslightly
broaderposterior
of
⇤
whose
supportsimulations not accounting for the possibility of first or3
1.5 short
9.8 ⇥ 10 larger
0.042
SLy
Radice and Dai (2018)
also
extends
to somewhat
values,as discussed
in der phase transitions in dense(unrealistically)
sti↵
EoSs
only
constrainedbycausality.
matter. Finally, we exclude
excluded˜
detail
in
Ref.
[53].
It
is
important,however,toremark
that
Note.
—
We
specifythemodelsbyq(=0.774)
and
⇤
to
be
˜
1.5
⇤
>
5000
which
is
unreasonablewith any plausible EOS.
300
APR4
We
thus remain
conservativeby determining minimum
0.01
compared withthose
in touch
Table when1.
thetwo shown
NSs first
the GW frequency is between
Current models of the EM signal are not yet suffiNSkHz
radii
theIt maxima
thewhether
sequences
1.0
and through1.5 kHz [54].
is thus notof
clear
or notdefinedcientlyadvanced to follow the same procedure as for the
200causality.
WFF1
1.0
chance of ejecting
0.05M ,9models,
but also
thearemass
asymmebycurrent
waveform
which
typically
constructed GW data. However, extant light curve models indicate
˜ < models,by addingcorrections
to point
particle
try of q = 0.774
does tidal
not save
any model
with⇤377. are that 0.02 0.05 M of material with a broad distribution
LB
100
reliable
past
1
kHz,
e.g.,
Ref.
[55].
Consequently,
On the other hand, if the maximum mass is as large as to be in electron fraction and asymptotic velocity of ⇠0.1 c is
0.5
1 Simulations
0.001
conservative,
we restrict
our analysis
to theof the neededfor determining
Mthresand part
corresponding
fits to explain the observations [17,19–21,23]. Because
2.1M , manymodelsproducelong-lived
remnants.
AcGW
signalbelow
frequency
of
1
kHz,
which
is
theoretically
employaconformallyflat
spatialmetricwithaGWbackreac0of their properties, these ejecta are thought to originatetually,asymmetric binaries considered here are
8
10
12
14
16 all thewellunderstood.
We useetthe
phenomenological
waveformtion
scheme(Oechslinal.
2007;
Bausweinetal.
2013a),
which
1.0
1.2
1.4
1.6
from winds launched from the remnant accretion disk afcapable of explaining the luminosity of AT 2017gfo. The
model
IMRPhenomD
NRTidalimplemented
in LALSuite.
resultsinaslightly
decelerated
inspiral(compared
to
fully
relaq
200 250300 [56].
350 Long
400 term
450simulations
500 550of post600
R [km]
termerger,e.g., Ref.
˜ of models that can eject 0.05M is 242.
lowest value of⇤We
follow
Ref. [2] andfor thecom- merger
tivistic
calculations)thuschoiceleads ofto priors.
a slightBoth
overestimationof disks indicate that these winds can~ entrain 10 40 %binary tidal deformability Λ
Figure 2 suggests
that,
if
M
is willlarger
2.1M, in Mponenthave
flat
priorsinquantify
thethan
range
[0.5,
7.7]
. of
MthresbyCorner⇠ 0.05
Mmax
. We
this
e↵ect
futurework
Figure4.masses
plot
for
the
constraining
themassrathe total disk mass [22, 57–74]. Consequently, we canFigure 2. Mass-radiusrelationsofdi↵erent
EoSs
with
˜ Coughlin
˜ vectorstioq, boundandtidal
deformability
assuming
aal.
chirp
mass
The
two
dimensionless
spin⇤
their
moduliandemphasizethata smalloverestimation
impliesourradiusthe loweron⇤derivedbyAT
2017gfomayofthatuniRef: Bauswein et al. 2017thenRef:ethave2018
Figure3. Disk mass
vs. theconservatively
estimatethatbinary
a disktidalof atdeformability.
least 0.04 M The
Ref:
etofal.
very conservative (red area) and “realistic” (cyan area)
conM=
1.188M
and
based
on
the
ejectaestimated
obtained
arefoundconservative.
formlydistributed
in [0,
have isotropic orienta-errorbars denote the typical relative
cconstraints
become looser
than
that
in 0.89]
this andstudy.
errorKiuchi
of a factor
two2019andlog(Mdisk /M )Constraints from the fact that
EM counterparts are observed<latexit sha1_base64="S5+jr15l03leoLch5r1+zFo0U94=">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</latexit>log(Mdisk /M )Lower limit on the NS Ddal deformability/ radius based on the predicDon ofnumerical relaDvity simulaDons

˜ & 400⇤<latexit sha1_base64="jvVaxAt2ibsLAiJTio385PoTp14=">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</latexit>

WFF1
˜ > 197<latexit sha1_base64="p8M7WGapyBkmlHVuU5DTVhxR/Po=">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</latexit>

Mdisk [Msun]

˜

SLy APR4

M [M ]MPA1

˜ > 197⇤˜⇤<latexit sha1_base64="o5uKkoEeAUxn3FToEYXAQdtJ+o0=">AAACgnichVG7SgNBFD2urxhfURtBhGBQxCLMRkGRFKKNRQpfUcFI2N1MdHBf7E4CuqSy8wcsrBREgp1+go0/YOEniKWCjYU3mwVRUe8wM2fO3HPnzIzumsKXjD22KK1t7R2dsa54d09vX39iYHDTdyqewfOGYzretq753BQ2z0shTb7telyzdJNv6QdLjf2tKvd84dgb8tDlu5a2Z4uyMDRJVDExGhSkMEs8WciRqKTVikHBs5K5xVo2M5MpJlIszcJI/gRqBFKIYsVJXKGAEhwYqMAChw1J2IQGn9oOVDC4xO0iIM4jJMJ9jhripK1QFqcMjdgDGvdotROxNq0bNf1QbdApJnWPlEmMswdWZy/snl2zJ/b+a60grNHwckiz3tRyt9h/Mrz+9q/Kolli/1P1p2eJMuZCr4K8uyHTuIXR1FePTl/W59fGgwl2wZ7J/zl7ZHd0A7v6alyu8rUzxOkD1O/P/RNsZtLqdDqzOpNaWIy+IoYRjGGS3nsWC1jGCvJ07jHquMGt0qZMKaoy3UxVWiLNEL6Ekv0AjCqUBQ==</latexit>< 242

Upper limit on
the NS maximum mass
6•

Upper limit on the NS maximum mass fromthe fact that the remnant NS is likely to be
temporarily survived and collapsed eventually to a BH

Ref: Margalit & Metzger Here2017
we

BNS merg
with the Gcome placemaxmass. The
pared to thtighter contion of sim
HMNS for•ilar observ
GW170817
the short G
2010; Fong•and promp
On the2.17M (9straining•causality, a(e.g. Lasky
2015; Gao
max,rotmaxof Mmax hradius me2016) and
MTOV [M ]area).
NS radius
2.14
2.16
2.18
2.20
2.22
Note the interesting
general
trend
shown
by
the
maximum
Fig. 4.— Constraints on properties of the NS EOS — radius of(Nicholl0.9
et0.945
1.3M NS, forR1.3 ,M
andmaximalnon-rotating
gravitational mass,
mass in Fig. 3: the aestimatesgrow
systematically
more,
the
TOV
g
Mmax
— based on joint GW-EM observations of GW170817. Dif0.94
0of GW1708
2.825
with
increasingly
massivebinarysystemsas andwithdecreasferent EOS
are represented
points,the colorof which corre2.220
a low M0.9
masponds to theof thegivenlight
EOS towith
observational
ing ejected masses0.935(comparetoconsistency
the shading
from
dark
max
laboration
constraints. The similarly colored diagonal curves represent
poly2.800
2ofn,mergingblue). Hence, future
detections
binarytropicEOSs of index
while the grey
shadedsystems
regions to the bot0.93
0by the fut
tom
right
are
ruled
out
by
the
requirementofcausality(seetext).
with masses smaller
than that1 of GW 5170817 will help set
with a lowe
2.200
Clearly, a low NS maximal mass is preferred due to constraints
0.925
0.9
2.775
detectioneven tighter constraints
maximum
mass
MTOV . grey curve shows
rulingonouttheSMNS
formation.
The background
2.180
3
6
the cumulative probability distributionfunction that the maxievolving 0K
0.92
g4 than a given value 10
mum
mass
M
is
less
(see
text),
from
which
max
tion of a l
5.
CONCLUSIONS
7
g
2.160
2.750
we find Mmax
. 2.17M at 90% confidence.
The bottom panel
0.915
9masses 0.9
meshowsmassesof observed
Galactic 8NSs, fromwhich
a lower limitWe
have
combinedtherecentGW
observations
ofmergg
GW170817
withbeing
on Mmax can be placed (vertical dashed line).
0.91
0
2.725
well-fit bying systems of binary neutron stars via the event GW 17081712
Koranda et al. 1997) which is conservative
since R1.3
0.905
0.9
deviation
11 masswith a quasi-universal
relationlarger
betweenthe radiusmaximum
2.140
isgenerally
than
the
of
a
maximummassthat the H
2.700
2.120
g
2
0.9
of
nonrotatingstellarmodelsM
andthemaximum
mass
NS,
R
.
A
tighter
estimate
of
R
3.1GM
/c
TOV
max
1.3
max
a commonMmax . 2.16 M
2
2.1shownrotation
2.2 shaded
2.5
is therefore
also(lightThe backthat can be supported
through
uniform
to2.3
setregion).
new 2.4
andmerger.
2.675
ground
grey
curve
shows
the
cumulative
probability
disA simpl
tighter constraints on MTOV .
Mmax
mass)
0.000
0.005
0.010
0.015
0.020
0.025
tribution function that
the(solar
maximummass Mmax is lesstained fro
Our estimate follows
simpleandis
Mej [M ]than a agiven
value.line
Thisofwasarguments
calculated bymarginalizing
Mg + 0.07
Ref: Rezzolla et al. 2018
Ref: Shibata et al. 2019

. 2.17 M

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Presence of EM counterparts

No observaDon of magnetor-like acDvity
GRB associaDon

M<latexit sha1_base64="/C0UE0tUTmbBdbjA3yCG87j7y9A=">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</latexit>⇡ 1.2MM

f0 / fMS

Mg [M ]

<latexit sha1_base64="WUGMUIcFzL77/mdyjI5ya2xEtes=">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</latexit><latexit sha1_base64="zmT9cwdjzU19zRnhchV38yBhIE0=">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</latexit>. 2.3 Mf0 / fMS

4O3 observaOon

Third observing run (O3)
Ref: hcps://www.ligo.org/scienOsts/GWEMalerts.php•

The third observing run has been started from this April.

O3 detecDon candidates
hcps://gracedb.ligo.org/superevents/public/O3/•

BH-BH: 20 (21) candidates••

NS-NS: 1 (4) candidates••

S190828l, S190828j, S190728q, S190727h,
S190720a, S190707q, S190706ai, S190701ah,
S190630ag, S190602aq, S190521r, S190521g,
S190519bj, S190517h, S190513bm,
S190512at, S190503bf, S190421ar, S190412m,
S190408an(, S190426c)

S190425z (, S190718y, S190510g, S190426c)

BH-NS: 1 (3) candidates•

S190814bv (, S190901ap, S190426c)

BH-NS candidate: S190814bv•

DetecDon candidates of BH-NS merger has
been reported at Aug. 14, 2019 21:10:39 UTC•

False alarm rate~1 per/ 1025 yrs.

•

D~267±52 Mpc. (GW170817: ~40 Mpc)•

Sky localizaDon: 23 deg2 (90%)

2019/8/14

2019/8/15

Mass gap: one of objects is 3 Msun < M < 5 Msun
NSBH: one of objects is M< 3 Msun and the another is M > 5 Msun

S190814bv: EM follow up
4

Gomez et al.

Gomez et al.

Figure 3. Our Magellan search limits compared to several potential optical emission light curve models. The black arrows

igure 1. Localization region of S190814bv overlaid with the locations of galaxies observed in our Magellan search on 2019and lines represent the 90% range for the limiting absolute magnitudes in each night, using the relevant distance of eachugust 16 (red) and 17 (blue). These represent all galaxies present in the GLADE catalog within the 50% localization volume,targeted galaxy. Also shown are the model light curves for the kilonova associated with GW170817 (blue; Villar et al. 2017b),⇤
a lanthanide-rich kilonova with an ejecta mass of 0.01 M (red), and afterglows based on the median short GRB properties
rresponding to about 50% of all galaxies in this region down to a luminosity of 0.15 L , and about 75% of the integrated(Fong et al. 2015) for on-axis (purple) and o↵-axis (15 ; grey) viewing angles. The right-hand-side ordinate shows the relevant
alaxy luminosity within the region.
apparent magnitudes for the mean distance of S190814bv (267 Mpc) to provide an indication of the rough depth required toGomez et al. 2019 (arXiv:1908.08913)• No electromagneDc
counterpart has been observed
itially considered the first possible NS-BH merger, its
currently publicly available, and assumptions about thedetect the various models.

robability of being such an event is only 13% and its
lse alarm rate (FAR) is only 1 in 1.6 years (with aorresponding 14% probability that it is terrestrial in
rigin).
On 2019 August 14 at 21:10:39 UTC (=58709.88240
MJD), ALV detected a GW candidate event, desigated S190814bv, with an incredibly low FAR of 1 in
56 ⇥ 1025 yr, a luminosity distance of 267 ± 52 Mpc,
nd a 90% (50%) confidence localization region of 23 (5)eg2 (LIGO Scientific Collaboration & Virgo Collaboation 2019a,b); see Figure 1 for the localization map.

model with a nominal ejecta mass of 0.01 M and a highopacity, which has a peak brightness of Mi ⇡ 13 mag
neutron star equation of state.
(i ⇡ 23.5 25 mag at the distance range of S190814bv)
Here we report our optical follow-up of S190814bv uson a timescale of about 1 2 days (Figure 3). Such amodel is beyond the reach of our observations.
ing the Magellan Baade 6.5 m telescope to target galaxFinally, it is possible that an NS-BH merger canies within the localization volume. In §2 we present ourlaunch a relativistic jet as in short GRBs (Berger 2014;
Magellan observations. In §3 we compare the results
Paschalidis et al. 2015). The currently-available GW
information does not provide any insight on the incliof our search to the kilonova emission of GW170817,
nation angle of the binary, so here we compare to bothto theoretical kilonova models, and to on- and o↵-axis
on- and o↵-axis models using the median properties ofshort GRB afterglows (Fong et al. 2015) in the BOXFIT
afterglow models. We summarize and draw initial consoftware package (van Eerten & MacFadyen 2011). We
clusions in §4.
find that an on-axis afterglow can be ruled out by ourobservations, while a model with an o↵-axis viewing an-

gle of & 15 will be dimmer than about 24 mag, beyond
the limits of our search.
We therefore conclude that for the region covered byour search we can generally rule out an optical counterpart similar to or brighter than GW170817, as wellas an on-axis jet typical of cosmological short GRBs.
However, we cannot rule out potential scenarios suchas low-mass and lanthanide-rich kilonova, or an o↵-axisjet. We note again that current parameter estimation
indicates no matter outside of the remnant’s horizon so
it is possible that S190814bv did not produce any EM
radiation.

•~200 galaxies in 50% conﬁdent volume (1.8x104 Mpc3)•

OpDcal counterparts similar to /brighter than GW170817 are not likely
2. GALAXY-TARGETED FOLLOW-UP WITH

4. DISCUSSION AND CONCLUSIONSWe presented Magellan follow-up observations of the
NS-BH merger candidate S190814bv. Our search tar-

S190814bv: ImplicaDon
Mass measurement for O2 events:

50
q
40

13

1/2

m2 (M )

1/4

30

1/8

20
10
0
0

Ref) LIGO and Virgo 2018
GW170817
GW170608

GW151226
GW151012

2040
m1 (M )GW170104
GW170814

GW170809
GW170818

60

80

GW150914
GW170823

GW170729• FIG.
S190814bv
could
ﬁrst
event
does
not
support
4. Parameter estimation
summarybe
plots theI. Posterior
probability
densitieswhichof the masses,
spins, and
SNR ofthe GW events. q~1
For thetwo-dimensional distributions, the contours show 90% credible regions. Left panel: Source frame component masses m1 and m2 . We use theconvention that m1 m2 , which produces the sharp cut in the two-dimensional distribution. Lines of constant mass ratio q = m2 /m1 are shownKAGRA joining O3
Ref: hcps://www.ligo.org/scienOsts/GWEMalerts.php•

KAGRA is planning to join O3 at the end of this year

Importance of KAGRA•

KAGRA joining to the detector
network will contributes tothe improvement of sky localizaDon•

Enables to test the polarizaDon
modes of GW beyond GR(e.g., H. Takeda et al. 2018)

Improvement in sky localizaOon for BNS
GW S KY L OCALIZATION(assuming HL~K~I)
HLV

7

HKLV

HIKLV

SNR

0

0.05

0.4

0

0.05

0.4

0

0.05

0.4

12

74

80

80

30

34

34

12

13

12

14

43

56

58

21

21

22

9.3

8.1

9.0

16

37

35

45

15

13

15

6.1

5.8

5.9

20

22

24

24

8.0

7.8

8.3

3.1

3.8

3.9

lization region values for BNS runs in square degrees. Each set of three columns corresponds to a network configuration
C. Pankow
al. event
2018with a distance adjust such thatC. M.
spin magnitude (below network). Each row corresponds
to the etsame
the Will
SNR2014

Summary•

AnalyDcal/numerical studies for compact binary mergers have beenenable us to achieve comprehensive understanding of observaDons.

•

GW170817 achieved the measurement of the NS Ddal deformability
and conﬁrmed that GW observaDon has a great impact on NS physics.

•

The simultaneous observaDon of EM counterparts to GW170817
marked up the beginning of mulD-messenger astronomy era.

•More and more GW events with more precise measurements ofphysical parameters would be achieved in the future.

•

Further theoreDcal invesDgaDon is needed to maximize the scienDﬁcreturns from the GW/EM events.

Appendix

independent calibration errors [87], and obtained consistent
results.

GW150914’s source corresponds to a stellar-mass BBH
with individual source-frame masses msource¼ 36þ−45 M ⊙1and msource¼ 29þ−44 M⊙ , as shown in Table I and Fig. 1.
2
The two BHs are nearly equal mass. We bound the mass
ratio to the range 0.66 ≤ q ≤ 1 with 90% probability. For
comparison, the highest observed neutron star mass is
2.01 & 0.04M ⊙ [91], and the conservative upper-limit forFirst GW event: GW150914
III. RESULTS

The results of the analysis using binary coalescencewaveforms are posterior PDFs for the parameters describing the GW signal and the model evidence. A summary isprovided in Table I. For the model evidence, we quote(the logarithm of) the Bayes factor Bs=n week
¼ Z=Z
ending n, which
PHYSICAL REVIEW LETTERS
12 FEBRUARY 2016
PRL 116, 061102 (2016)is the evidence for a coherent signal hypothesis divided
properties of space-time in the strong-field, high-velocity
coincident signal
GW150914
in Fig.
1. The initialby that forthe(Gaussian)noise[5]. shown
At theorder, thePleading
detection was made by low-latency searches
forMgenericregime and confirm predictions of general relativity for the
M 1=2
Bayes factor
and the optimal
SNR¼was½ reportedarek hhk jhgravitational-wave
transients[41] ρ
andwithinnonlinear dynamics of highly disturbed black holes.
k i%2minutesacquisition [43]. Subsequently,
related by threeln Bs=n≈ ρof=2data[88].
matched-filter analyses that use relativistic models of comII. OBSERVATION
Before pact
discussing
parameter
estimatesin asdetail,webinary waveforms[44] recovered
GW150914
theOn September 14, 2015 at 09:50:45 UTC, consider
the LIGO how
most significant
event fromiseachdetector for
observathe inference
affectedbythethechoice oftions reported here. Occurring within the 10-ms intersite
Hanford, WA, and Livingston, LA, observatories detected
the compact-binary waveform model. From Table I, we seethat the posterior estimates for each parameter are broadly
consistent across the two models, despite the fact thatthey are based on different analytical approaches and thatthey include different aspects of BBH spin dynamics. The
models’ logarithms of the Bayes factors, 288.7 & 0.2 and
290.3 & 0.1, are also comparable for both models: the data
do not allow us to conclusively prefer one model over theother [89]. Therefore, we use both for the Overall column
in Table I. We combine the posterior samples of both
distributions with equal weight, in effect marginalizing
over our choice of waveform model. These averaged results
give our best estimate for the parameters describing
GW150914.
In Table I, we also indicate how sensitive our results areto our choice of waveform. For each parameter, we givesystematic errors on the boundaries of the 90% credibleintervals due to the uncertainty in the waveform models
considered in the analysis; the quoted values are the 90%
range of a normal distribution estimated from the varianceof results from the different models. (If Xwere an edge of a⌘<latexit sha1_base64="B/+8ZdSln360m8bM1yXYEhJ8xzU=">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</latexit>

Mchirp<latexit sha1_base64="qD/pLocRAXh1OmQpxb8zc2C16Rg=">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</latexit>

FIG. 1. Posterior PDFs for the source-frame component masses
msourceand msource. We use the convention that msource≤ msource,
1221which produces the sharp cut in the two-dimensional distribution.
In the one-dimensional marginalized distributions we show theOverall (solid black), IMRPhenom (blue), and EOBNR (red)
PDFs; the dashed vertical lines mark the 90% credible interval
for the Overall PDF. The two-dimensional plot shows thecontours of the 50% and 90% credible regions plotted over acolor-coded PDF.

241102-6
FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, rightcolumn panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filteredwith a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-rejectfilters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain.
þ0.5
GW150914 arrived first at L1 and 6.9−0.4
ms later at H1; for a visual comparison, the H1 data are also shown, shifted in time by thisamount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto eachdetector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with thoserecovered from GW150914 [37,38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90% credible
regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template waveforms[39]. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linear combination ofsine-Gaussian wavelets [40,41]. These reconstructions have a 94% overlap, as shown in [39]. Third row: Residuals after subtracting thefiltered numerical relativity waveform from the filtered detector time series. Bottom row:A time-frequency representation [42] of thestrain data, showing the signal frequency increasing over time.

GW170817: upper limit to Λ

terior. Given its extensive previous
use LALInference for our main r
RapidPE for
exploratory studies, l
Ref: LIGO/Virgo
2017,2018
parisons to future work. For the t
1.0
the 90% highest posterior density cr
is (0, 560) for SEOBNRv4T and (100.9
sumS. We note that the lower bou
˜ = 0 is not the result of railinof ⇤0.8bound. The posterior value is the sa
the upper limits of the 90% credible
0.7
Recently, De et al. performed anof the GW data to measure the tid
0.6
Their results are broadly consistent
here, but are made under the assu
merging NSs have the same EOS. T
0.5
two NSs have identical radii and tha
bility of the individual stars are rel
0.4mate relation ⇤1 = q 6 ⇤2 , whereas w
rameters to vary independently. Fu
0.3
0200 400 600 800 1000 1200 1400 1600
the TaylorF2 waveform model and˜components 1z and 2z to be uni(similar to our low-spin prior on th
˜FIG. 12. PDFs for the tidal parameter ⇤ and mass ratio q
Their results for their least restricti
using the PhenomPNRT model for the high-spin (blue) andthey allow m1 and m2 to vary unifo
low-spin (orange) priors. Unlike Fig. 11, the posterior is notmost directly comparable to our res
˜
reweighted by the prior, so the support that is seen at ⇤ = 0
90% symmetric credible interval ofis due to smoothing from the KDE. The 50% (dashed) and
I of [138]). This can be compared toq< 0.89< 0.05˜⇤Mchirp relaDon<latexit sha1_base64="cv4iwg3J6d0W/zh9DPXb1j9qo3E=">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</latexit>

m1=m2 for the equal-mass case [Msun]

1.15

1.2 1.25 1.3

1.35 1.4

1.45 1.5 1.55

1.6

15H
125H
H
HB
B

1.5x10-5~cmM [Msun]

1000

-5

2x10

1x10-55x10-6
Ref: KK et al. 2018

q=0.7-1
100

0
400

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Mc [Msun]
0.002

FIG. 8. Binary tidal deformability as a function of the chirp

0.0018••

GW170817:
Kilonova/macronova with mulDple components

What is the origin of blue/red

Data: Summarized in Villar et al. 2017
D=40 Mpc
4.0

relative flux F¸ (plus offset)

AB absolute magnitude

-15
-14
-13

-11

a

3.5

-16

-12

g
light r-process component
Infrared heavyr r-process component
composite~10 days zi t = 1.5 dayJH
K t = 2.5 day

OpOcal
~1day

3.0

2.5

2.0

t = 4.5 day

1.5

1.0
t = 7.5 day
0.5

10

0.5

1.0

1.5

2.0

2.5

3.0

g (0.40-0.55 ¹m)
r (0.55-0.70 ¹m)
i (0.70-0.85 ¹m)
j (1.10-1.35 ¹m)
h (1.50-1.80 ¹m)
k (2.00-2.30 ¹m)

10

10
0.0

1

b

broadband luminosity, ¸F¸ (1041 ergs s¡1 )-17ref) Masaomi’s slideBlue (lanthanide-free)

Red (lanthanide-rich)

0

-1

0

wavelength (microns)

2

4

6

8

10

12

14

days since merger

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
tFigure[day]5 | A unified kilonova model explaining the optical/infrared counterpart ofRef: D. Kasen et al. 2017

GW170817. The model is the superposition of the emission from two spatially distinct

ElectromagneOc (EM) counterparts
to GW170817 were observed simultaneously
ejecta components: a ‘blue’ kilonova (light r-process ejecta with M = 0.025M , v = 0.3c
over the enOre wavelength(fromradio(heavy
to r-process
gamma
and X range= 10 ) plusa ‘red’ kilonova
ejectawavelengths)with M = 0.04M ,
!

lan

k

"4

!

"1.5

= 0.15c, and X = 10 ). a, Optical–infrared spectral time series, where the black line
A Kilonova/macronova vmodelwith mulOple components well interprets the opOcal-Infrared observaOonis the sum of the light r-process (blue line) and heavy r-process (red line) contributions.
(see e.g., Kasliwal et al. 2017,
Cowperthwaite et al. 2017, Kasen et al. 2017, Villar et al. 2017)b, Composite broadband light curves. The light r-process component produces the rapidly
k

•

lan

evolving optical emission while the heavy r-process component produces the extended
early-blue component(~1day) from lanthanide-free ejecta (~0.01 M_sun, opacity ~0.1-1 cm^2/g)
infrared emission. The composite model predicts a distinctive colour evolution, spectral+ long-lasOng red component(~10days)fromlanthanide-richejectacontinuum shape andinfrared spectral
peaks, allof which resemble the propertiesof (~0.04 M_sun, opacity ~10 cm^2/g)
AT 2017gfo.

65

ProperDes of kilonovae / macronovaeref) Li & Paczyński 1998

Order EsOmaOon<latexit sha1_base64="PVbd6pqU4NRIq26Dbj5/l7OLM6A=">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</latexit>

tpeak ⇡ 3.3 days✓
◆1/2 ⇣
✓
◆1/2
⌘
1/2
M
v

⇥
0.03M
0.2c
1 cm2 /g

Lpeak ⇡ 2.0 ⇥ 1041 ergs/s✓◆✓◆1/2 ⇣✓◆ 1/2
f
Mv ⌘1/2

⇥
10 6
0.03M
0.2c
1 cm2 /g<latexit sha1_base64="EllYR/E4apuz2tXjhy/kGJS2IM8=">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</latexit>

Meje :ejecta mass
veje :expanding velocity:opacityf : energy conversion rate
<latexit sha1_base64="K37+hlJ1NDdlUjKH83ENbdcQLNs=">AAACCnicbVDLSsNAFJ3UV62vqEs3g0VwUUoigo9V0Y3LCsYWmlIm05t26GQSZiZCCN278VfcuFBx6xe482+ctllo64GBwzn3cOeeIOFMacf5tkpLyyura+X1ysbm1vaOvbt3r+JUUvBozGPZDogCzgR4mmkO7UQCiQIOrWB0PfFbDyAVi8WdzhLoRmQgWMgo0Ubq2YfhpV/LfRlhECAHmV+jsSgCfk0SDeOeXXXqzhR4kbgFqaICzZ795fdjmkYgNOVEqY7rJLqbE6kZ5TCu+KmChNARGUDHUEEiUN18essYHxmlj8NYmic0nqq/EzmJlMqiwExGRA/VvDcR//M6qQ7PuzkTSapB0NmiMOVYx3hSDO4zCVTzzBBCJTN/xXRIJKHatFExJbjzJy8S76R+UXdvT6uNq6KNMjpAh+gYuegMNdANaiIPUfSIntErerOerBfr3fqYjZasIrOP/sD6/AFgeZra</latexit>

Tpeak ⇡ 3.1 ⇥ 103 K✓◆1/4 ✓◆ 1/8 ⇣
✓
◆ 3/8
⌘
1/8
f
M
v

⇥
10 6
0.03M
0.2c
1 cm2 /g<latexit sha1_base64="yeCy6UGlSOnSX30jNK0+hKAqiLQ=">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</latexit>•

The emission is expected to be bright in the op'cal and infrared wavelength.

•

The mass, velocity, morphology, and the composi'on(electron frac'on) of the ejecta characterize
the lightcurve of the kilonova/macronova.
66

R-process nucleosynthesis
Credit) Sho FujibayashiZβdecayN captureN⌧Ncap ⌧ ⌧ dec<latexit sha1_base64="Rs9wf7gaMtiaGEU5pLuIublymYI=">AAACD3icbVDLSgNBEJz1bXxFPXoZDKKnsCuCehO9eJIIrglkQ+iddJLB2QczvUJY8gle/BUvHlS8evXm3zh5gJpY0FBUddPdFaZKGnLdL2dmdm5+YXFpubCyura+UdzcujVJpgX6IlGJroVgUMkYfZKksJZqhChUWA3vLgZ+9R61kUl8Q70UGxF0YtmWAshKzeI+DwiyZh7oiF8JSPuBUj9KECIBb6HoN4slt+wOwaeJNyYlNkalWfwMWonIIoxJKDCm7rkpNXLQJIXCfiHIDKYg7qCDdUtjiNA08uFDfb5nlRZvJ9pWTHyo/p7IITKmF4W2MwLqmklvIP7n1TNqnzRyGacZYSxGi9qZ4pTwQTq8JTUKUj1LQGhpb+WiCxoE2QwLNgRv8uVp4h+WT8ve9VHp7HycxhLbYbvsgHnsmJ2xS1ZhPhPsgT2xF/bqPDrPzpvzPmqdccYz2+wPnI9vDUeczw==</latexit>

Ejecta opacity

2

[p]
Ye =
[p] + [n]<latexit sha1_base64="SaVd2X1sVUpAeLMgS2c0qtc2OlM=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARBKEkIuhGKLpxWcE+JA1hMr1ph04mYWYilBA3/oobF4q49S/c+TdOHwutHriXwzn3MnNPmHKmtON8WaWFxaXllfJqZW19Y3PL3t5pqSSTFJo04YnshEQBZwKammkOnVQCiUMO7XB4Nfbb9yAVS8StHqXgx6QvWMQo0UYK7D18F8BFN5KE5l7qF+N27Am/COyqU3MmwH+JOyNVNEMjsD+7vYRmMQhNOVHKc51U+zmRmlEORaWbKUgJHZI+eIYKEoPy88kFBT40Sg9HiTQlNJ6oPzdyEis1ikMzGRM9UPPeWPzP8zIdnfs5E2mmQdDpQ1HGsU7wOA7cYxKo5iNDCJXM/BXTATFpaBNaxYTgzp/8l7ROaq5Tc29Oq/XLWRxltI8O0BFy0Rmqo2vUQE1E0QN6Qi/o1Xq0nq036306WrJmO7voF6yPbwh+lp4=</latexit>

Opacity (cm2 g−1)

Mass fractionref) Tanaka study
et al. 2018lected to systematicallythe opacities of elements
3
d
p
s
f
10with diﬀerent open shells: Ba is an open s-shell element
Se
Ru
Te Ba NdEr0
Ye = 0.10−0.40
10
Se and Te are open p-shellelements, Ru is an open dYe = 0.25
Ye = 0.30
Ye = 0.25
Ye = 0.10-0.40
shellelement, and Nd and
Ye = Er
0.30are open f-shell elements
2
10We focus on neutral atom and singly and doubly ionized-1
10
ions because these ionization states are most common inkilonova
at t >
1 day after the merger (Kasen et al. 2013
1
∼
10
10-2
Tanaka & Hotokezaka 2013).
In Figure 1, these elements are shown with three dif0
ferentabundance patterns in the ejecta of NS merg-3
1010
ers. While relativistic simulations of NS mergers predict
wide ranges of Ye between 0.05 and 0.45, the detailed
Ye distributions depend on the NS masses and their ra10−1
10-4
tios as well as the adopted nuclear equations of state
Lanthanides(Sekiguchi et al. 2015, 2016). In this paper, we assume-5−2
10
10 a flat mass distribution between Ye = 0.10 and 0.40 as
30
40
50
60
70
80
90
100
0
5000 of dynamical
10000
15000 As20000
representativeejecta.
shown in25000
FigureAtomic number
1 (orange line), the Wavelength
dynamical(Å)
ejecta consist of a wide
Figure 1. Element abundances in the ejecta of NS mergers at
range of r-process elements from the first (Z = 34) toFigure5. Line expansion opacities for mixture of elements= 1 day after the merger. The orange line shows abundances for
third(Zmergers= 78) abundance
the line
post-merger
the ejecta of NS(see Figure peaks.
1). TheFor
orangerepresen
dynamical ejecta (Wanajo et al. 2014), which is derived by averagejecta,
weconsidersingleYmodelsof
0.25(green)andeng the nucleosynthesis resultsof Ye =opacity
0.10 − 0.40
assuminga theflat opacity
The ejecta
variessigniﬁcantly(0.1—10
on is calculated within the cm^2/g)
dynamicaldepending
ejecta, whicht
0.30(blue)
forsimplicity.
The
formerrepresentsacase
Ye distribution. The blue and green lines show the nucleosynthesis
abundance
patternof Yethe= 0.10− 0.40.
The blueandgreen linwhetherlanthanide
are synthesized
or
not,
which
reﬂects
electron
fracOon,Ye,ofejecta.
esultsfrom trajectories
of Yeelements= 0.25 and 0.30,
respectively, whichthat
contains
thesecond(Z=
52)
abundance
peak
represent the opacities in the high-Ye post-merger ejecta,and
whia
epresent the abundance patternsof high-Y
post-merger
ejecta. et al.small
eal.
amountLanthanides.
The latter
Lanthanide(Kasenet2013,
Barnes2013,
Tanakaet al. 2013)
are calculatedwiththeofabundance
patterns
of Yeis=a 0.25
and 0.3
Black points connected with the line show the solar abundance−13−
free model without elements of Z > 50. For all the mod-

Mass EjecDon Mechanisms•

In the last decades, many eﬀorts have been made to study
the mass ejecOon process and evoluOon of the merger
remnant performing numerical-relaOvity simulaOons•

Dynamical mass ejec'on
mass ejecOon driven by Odal interacOon
orshock heaOng during the collision(e.g., Hotokezaka et al. 2013; Bauswein et al. 2013;
Sekiguchi et al. 2016; Radice et al. 2016; Dietrich et al.
2017; Bovard et al. 2017)•

Post-merger mass ejec'on
mass ejecOon from the merger remnant driven by
eﬀecOve viscosity and/or neutrino heaOng(e.g., Dessart et al. 2009; Metzger & Fernández 2014;
Perego et al. 2014; Just et al. 2015; Shibata et al. 2017;
Lippuner et al. 2017; Fujibayashi et al. 2018, Siegel et al.
2018, Fernandez et al.2018)

Dynamical mass ejecOon@merger

Post-merger mass ejecOon@axer merger

The Astrophysical Journal Letters, 789:L39 (6pp), 2014 July 10

Dynamical ejecta
Dynamical ejecta mass

1

Ref: Hotokezaka et al. 2013

NS-NS models
10

APR4
SLy
ALF2
H4
MS1

Mej/10-2Msun

10

Mej/10-2Msun

Ref: S. Wanajo et al. 2014
Y. Sekiguchi et al. 2015

The Astrophysical Journal Letters, 778:L16 (5pp), 2013 November 20

0.1

1

0.1

0.01 Figure 2. Color-coded distributions for density, temperature, Ye , and S/kB (from0.01
left to right)
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.13
(negative sides of top panels) planes at the end of simulation.
(A color version of this figure
available
Mtotis/2R
1.35 in the online journal.)

Ye distribuOon

Ref: Wanajo et al. 2014

mass fraction

Figure 2. Ejecta masses as a function of the compactness of the neutron star, which is defined by GMtot /2
theE0
respectively. Left panel:models. Each point shows the ejecta mass for the equal mass forcases.
10NS–NS
valuesthe various Q. Right panel: BH–NS
wit
x-y models. The filled and open symbols correspond to the models
x-z
shaded region in each panel shows the ejecta masses allowed in order to reproduce the observed Goriely
near-infr
y-z
0.02 ! Mej /M⊙ ! 0.1 for-1 the NS–NS and BH–NS models, respectively. The lower and upper bounds
10respectively.
(A color version of this figure is available in the online journal.)

The
namic
t
10
plane. A
thelight
Yecurve=0
as a hypermassive neutron star with a lifetime of !10 ms isForsim
the ejecta usin
formed after the merger.
More massive NS–NS mergers result
10-3
the Modom
frequency
in hypermassive neutron stars with a lifetime of "10 ms or in
Each 20nu
Hotokezaka
black holes. For such a case, the ejecta mass decreases withture
dec
-4 of the shorter duration of mass ejection.
and elemental
increasing Mtot because
10
by Ye a0.0 disruption
0.1 of 0.2
0.3star results
0.4 in 0.5 in the ultraviol
BH–NS ejecta. Tidal
a neutron
neutronYby taking into
anisotropic mass ejection for a BH–NS merger(Kyutoku et al.
e
The
Letter,weinclu2013). As a result, theejectaisconcentratednear
thebinary0neutron10 in Figure 1, and it is shaped like a disksolarabundanc
orbital
plane
as
shown
rates, w
x-y
-3
-2
sun
x-z
of the radiation
or crescent.
CLIB7
y-z
(e.g. Hotokezaka et al. 2013; Bauswein et al. 2013; Sekiguchi et al. 2016;
Dietrichal. 2017;
Bovard2017)wise,(2thTheRadiceamountetof al.
ejectafor the
BH–NSetmodels
is smaller
for et al.Hotokezaka-12016;10
et al. 2
The heating
more compact neutron star models with fixed values of χ and Q
elements1990)
is oneaas shown in Figure 2. This is because tidal disruption occurs inmasses-2
simulations.
Asa less significant manner.
This dependence of the BH–NS ejecta
10ertiesrate computeda

Dynamical ejecta of mass <~10 —10 M-2

is typically formed, depending on the NS masses and EOS.
s fraction

Ye parOally becomes large due to shock heaOng and neutrino irradiaOon(cf. NS Ye~<0.1) Yet, substanOal amount of ejecta remains
to be Ye<0.25 and lanthanide is synthesizedon the compactness of neutron stars is opposite to the case ofPost-merger ejecta
0S.Fujibayashi, K.Kiuchi,
10-1 N.Nishimura, Y.Sekiguchi, and M.Shibata

.
-2. M
M
[10
Mej
/
sun]
b,ej Mb,MNS

Viscous GRRHD simulaOon for merger remnant(Ref: S. Fujibayashi et al. 2018).
Mb,ej [Msun s-1]

16

10-2
10-3

Ejected mass

10-4

4
102
1031

(a)

(e)

0
10-3

60

Ek,ej [1050erg]

p + ν e → n + e+

−
n
+
ν
→
p
+
e
Neutrino/Viscosity-driven
Ejectevis=0.04
vis=0.02
vis=0.01
vis=0.00

1020
10-1
1
10-2

(d)

0.5

5 Figure 13.

Figure 13. Same as Figure 12 but at t
1.5
2 component
2.5 toward 3the pola
viscosity-driven(b)[s]t = 1 s. toward
component
equatorial
direction
Same as Figure 12Timebut
atFor ↵visthe= 0.02(top panels),the1viscosity-driven component toward the polar direction, while for ↵vis = 0.04 (bottom

4 component toward the equatorial direction.

10-4

Mass per bin [M sun]

0.2

Mass per bin [M sun]Vej [c]Figure 8. Time evolution of the baryon mass(panel (a)),
kinetic
Ye distribuOonof ejecta
3energy (panel (b)), and average velocity -2(panel (c)) of the ejecta,
10
2mass ejectionrate(panel
(d)),
and
ratio
of Ṁb,ej to Ṁb,MNS (panel
10-21
 vis=0.02(e)). For all the panels, di↵erent colors of thecurves indicate the vis=0.04
0results for di↵erent models DD2-135135-0.00-H,
DD2-135135-0.0110-30.3(c)H, DD2-135135-0.02-H,
DD2-135135-0.04-H.
10-3
10-4

.
Mb,MNS.
Mb,ej [Msun s-1]

which0.1is shown in the panel (b) of-5Fig. 8. Here, we assumed0 that10-5the internal energy 10of the ejecta would be
totally-1 transformed into the kinetic0 energy
during(d) the 10
0.1
0 0.1 0.2 0.3 0.4 0.5
101000.2 0.3 0.4 0.5
10Ye
subsequent expansion.
Unlike the massrate
Yes [kB ] accretion-2
and 10theneutrino
emission
rate
shown
in
Sec.
3.3,ofofFigurethe15
14. panels),
Massthehistogramof theejectapanels
as a isfunctionof mainly
Ye
Figure 13. Same as Figure 12 but at t = 1 s. For ↵vis Figure= 0.02 (topejecta shownin thesecomposedtheFigure14.
Masshistogramthe ejeviscosity-driven component toward the polarmass
direction,and
while
for
↵
=
0.04
(bottom
panels),itiscomposedprimarilyoftheviscosity-driven
numberand(right) at t of
= 1.3s.(left)
The
distributionsof the at
elecvis s/kB energy
and s/kt = 1.3 s.inThe fod
kinetic
theejectamonotonically-3 (left)B (right)
10component
towardtheequatorial
direction.
colo
tron fraction (leftpanel)
andthe specificentropy(rightpanel)
are the ferent
tron fraction(left panel)andspecifice~10-2—10-1 Msun is ejected from the remnant torus,
ontheeﬀecOveviscousparameter
creasedepending
with
↵
for
t
.
0.2
s.
regions.
T
plotted.
The
red
and
green
curvesdenotetheresultsforthemodelsvis
plotted.
The
red
and
green
curvesdenotetelements
respectively.
10-4 DD2-135135-0.04-H and DD2-135135-0.02-H,
DD2-135135-0.04-H
and DD2-135135-0.02The panel(c) showstheetevolution
thepaverageveloc- (and the lifeOme of the remnant NS. (see also e.g. Siegel
et al. 2018,
Fernandez
al.2018
for of
GRMHD
simulaOons)2
ity of10
theejecta,which
is definedirradiaOon
by Vej = 2Ek,ej /Mb,ej .
post-merger ejecta would typically haveYe>0.25due
to neutrino
For the101 early viscosity-driven ejecta, which is ejected for
if remnant neutron star is suﬃciently long-lived(t>~1sec.).→ lanthanide-poor ejecta
t . 0.2
100 s, the average velocity is in the range 0.15–0.2 c,

z

3448

there
never enoughmaterialin thelesspolar
regions
to achievefortheisaverage
is obtained
for timesthanthe HMNS
lifetidesiredtemperature,and hence quantities
the averageareis computed
not computedthe(butaveragedthermodynamic
using
After collapse
to a BH, the polar region is evacuated, so the radwholeevolution).
forThethe average is
obtainedfor times
less material
than the HMNS
lifetielectronfractionof theis a monoto(but averaged
quantities
computedusing
functionof thethermodynamic
HMNS lifetime.
This is aaredirectconsequence
wholeevolution).
thehigherlevel of neutrino irradiation introduced by the HMN
electronmaterial
is a time
monotoa thermalin
A The
roughaverage
estimateofthe fractionchange ofinofejectaYthee overYe
distribuOon
function of the HMNS lifetime. This is a direct consequence
the higher level of neutrino irradiation introduced by the HMN
A rough estimate of the change
in Ye over a thermal time inequatorial

Remnant NS LifeDme

B. D. Metzger and R. Fernández

Downloaded from http://mnras.oxfordjourn

Figure 4. Mass histograms of material
with positive velocity, evaluate
polar◦
is restricted to latitudes within 60 of the mid-plane (top) and within
entropy (b,f), expansion time (c,g), and maximum mass number of r-p
and Z̄ = 36. Different curves correspond to models with different HM(A ! ALa = 139).

Figure 4. Mass histograms of material with positive velocity, evaluate
is restricted to latitudes within 60◦ of the mid-plane (top) and within
entropy (b,f), expansion time (c,g), and maximum mass number of r-p(stableFigure
HMNS,
2. top)Snapshots
and t000A3
in the(prompt
evolution
BH,of bottom).
models tInfA3p15
The nine contiguous(stable HMNS,
panelstop)
onand
the t000A3
left and Z̄
(prompt
BH, bottom).
The
nine contiguous
panelson thelMetzger& of
Fernández
al. 2014=4.36.
Different
curvescorrespond
toetmodelswithdifferent
HM
FigureRef:
Masshistograms
material withpositive
velocity,
evaluateg (e,f) atshow
timedensity
0.03 s,(a,b),
corresponding
neutrino heating
approximately(c,d), andto viscous
10 orbitsheating
at the initial(e,f) atdensity
time 0.03
peak.
s, corresponding
The two (A10 orbits
density
The t! Aapproximately
La = 139).
of thethe initial
mid-plane(top)peak.
and within
is restricted
to latitudestowithin
60◦ at• panels
3 s (800
orbitsonat the right
initial(g,h)
density
showpeak).
the electron
The white
fraction
contours
at timeshow
2.3thes (800gain orbits
surface,at theinsideinitialwhich
densitypeak).
white contours
the gain surface,insideentropy(b,f),The
expansion
time (c,g),show
and maximum
mass number
ofwhr-p
ir absorption
emission
by of
nuclei.
neutrinos
Modelsandsuppress
antineutrinos
neutrino
dominatesand viscousover theirsourceabsorption
terms below
by nuclei.
a density
Modelsof andsuppress
and viscous
sourceterms below
a densityZ̄ = 36. neutrino
Different curves
correspondto modelswith differentHM−3
g cmd andion of 10
panels(FM13)
f).
for numerical reasons (as in the polar region of panels d and f).
(A ! ALa = 139).

Life Ome of the remnant NS has a large impact on the Ye distribuOon of the post merger ejecta(See also Lippuner et al. 2017)

••

GW170817:
Kilonova/macronova with mulDple components

What is the origin of blue/red

Data: Summarized in Villar et al. 2017
D=40 Mpc
4.0

relative flux F¸ (plus offset)

AB absolute magnitude

-15
-14
-13

-11

a

3.5

-16

-12

g
light r-process component
Infrared heavyr r-process component
composite~10 days zi t = 1.5 dayJH
K t = 2.5 day

OpOcal
~1day

3.0

2.5

2.0

t = 4.5 day

1.5

1.0
t = 7.5 day
0.5

10

0.5

1.0

1.5

2.0

2.5

3.0

g (0.40-0.55 ¹m)
r (0.55-0.70 ¹m)
i (0.70-0.85 ¹m)
j (1.10-1.35 ¹m)
h (1.50-1.80 ¹m)
k (2.00-2.30 ¹m)

10

10
0.0

1

b

broadband luminosity, ¸F¸ (1041 ergs s¡1 )-17ref) Masaomi’s slideBlue (lanthanide-free)

Red (lanthanide-rich)

0

-1

0

wavelength (microns)

2

4

6

8

10

12

14

days since merger

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
tFigure[day]5 | A unified kilonova model explaining the optical/infrared counterpart ofRef: D. Kasen et al. 2017

GW170817. The model is the superposition of the emission from two spatially distinct

ElectromagneOc (EM) counterparts
to GW170817 were observed simultaneously
ejecta components: a ‘blue’ kilonova (light r-process ejecta with M = 0.025M , v = 0.3c
over the enOre wavelength(fromradio(heavy
to r-process
gamma
and X range= 10 ) plusa ‘red’ kilonova
ejectawavelengths)with M = 0.04M ,
!

lan

k

"4

!

"1.5

= 0.15c, and X = 10 ). a, Optical–infrared spectral time series, where the black line
A Kilonova/macronova vmodelwith mulOple components well interprets the opOcal-Infrared observaOonis the sum of the light r-process (blue line) and heavy r-process (red line) contributions.
(see e.g., Kasliwal et al. 2017,
Cowperthwaite et al. 2017, Kasen et al. 2017, Villar et al. 2017)b, Composite broadband light curves. The light r-process component produces the rapidly
k

•

lan

evolving optical emission while the heavy r-process component produces the extended
early-blue component(~1day) from lanthanide-free ejecta (~0.01 M_sun, opacity ~0.1-1 cm^2/g)
infrared emission. The composite model predicts a distinctive colour evolution, spectral+ long-lasOng red component(~10days)fromlanthanide-richejectacontinuum shape andinfrared spectral
peaks, allof which resemble the propertiesof (~0.04 M_sun, opacity ~10 cm^2/g)
AT 2017gfo.

73

The Astrophysical Journal Letters, 789:L39 (6pp), 2014 July 10

Dynamical ejecta
Dynamical ejecta mass

1

Ref: Hotokezaka et al. 2013

NS-NS models
10

APR4
SLy
ALF2
H4
MS1

Mej/10-2Msun

10

Mej/10-2Msun

Ref: S. Wanajo et al. 2014
Y. Sekiguchi et al. 2015

The Astrophysical Journal Letters, 778:L16 (5pp), 2013 November 20

0.1

1

0.1

0.01 Figure 2. Color-coded distributions for density, temperature, Ye , and S/kB (from0.01
left to right)
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.13
(negative sides of top panels) planes at the end of simulation.
(A color version of this figure
available
Mtotis/2R
1.35 in the online journal.)

Ye distribuOon

Ref: Wanajo et al. 2014

mass fraction

Figure 2. Ejecta masses as a function of the compactness of the neutron star, which is defined by GMtot /2
theE0
respectively. Left panel:models. Each point shows the ejecta mass for the equal mass forcases.
10NS–NS
valuesthe various Q. Right panel: BH–NS
wit
x-y models. The filled and open symbols correspond to the models
x-z
shaded region in each panel shows the ejecta masses allowed in order to reproduce the observed Goriely
near-infr
y-z
0.02 ! Mej /M⊙ ! 0.1 for-1 the NS–NS and BH–NS models, respectively. The lower and upper bounds
10respectively.
(A color version of this figure is available in the online journal.)

The
namic
t
10
plane. A
thelight
Yecurve=0
as a hypermassive neutron star with a lifetime of !10 ms isForsim
the ejecta usin
formed after the merger.
More massive NS–NS mergers result
10-3
the Modom
frequency
in hypermassive neutron stars with a lifetime of "10 ms or in
Each 20nu
Hotokezaka
black holes. For such a case, the ejecta mass decreases withture
dec
-4 of the shorter duration of mass ejection.
and elemental
increasing Mtot because
10
by Ye a0.0 disruption
0.1 of 0.2
0.3star results
0.4 in 0.5 in the ultraviol
BH–NS ejecta. Tidal
a neutron
neutronYby taking into
anisotropic mass ejection for a BH–NS merger(Kyutoku et al.
e
The
Letter,weinclu2013). As a result, theejectaisconcentratednear
thebinary0neutron10 in Figure 1, and it is shaped like a disksolarabundanc
orbital
plane
as
shown
rates, w
x-y
-3
-2
sun
x-z
of the radiation
or crescent.
CLIB7
y-z
(e.g. Hotokezaka et al. 2013; Bauswein et al. 2013; Sekiguchi et al. 2016;
Dietrichal. 2017;
Bovard2017)wise,(2thTheRadiceamountetof al.
ejectafor the
BH–NSetmodels
is smaller
for et al.Hotokezaka-12016;10
et al. 2
The heating
more compact neutron star models with fixed values of χ and Q
elements1990)
is oneaas shown in Figure 2. This is because tidal disruption occurs inmasses-2
simulations.
Asa less significant manner.
This dependence of the BH–NS ejecta
10ertiesrate computeda

Dynamical ejecta of mass <~10 —10 M-2

is typically formed, depending on the NS masses and EOS.
s fraction

Ye parOally becomes large due to shock heaOng and neutrino irradiaOon(cf. NS Ye~<0.1) Yet, substanOal amount of ejecta remains
to be Ye<0.25 and lanthanide is synthesizedon the compactness of neutron stars is opposite to the case of

EvoluDon of Remnant NS &torus: EﬀecDve viscosity
1051

1.8e+

1050

1.6e+

1049

1.4e+

1048

Poloidal Toroidal

1047∆x = 12.5 m

1045

10

∆ x = 12.5 m∆ x = 70 m
∆ x = 110 m←KH instability

6.0e+
0

5

10

15

< α >12< α >13

10-2

20

25

30

t - tmerger [ms]

10

10-2

∆ x = 12.5 m∆ x = 70 m
∆ x = 110 m

FIG. 4. Magnetic-field energy (left), rotational
the runs. The solid and dashed curves in the lef

10-3

-4

15

20

merger [ms]

25

10
Ref:
K.
Kiuchiet5al. 2015,
2017
30
10
15

20

t - tmerger [ms]

25

30

10-3

8.0e+

∆x = 110 m-1∆ x = 12.5 m∆ x = 70 m
∆ x = 110 m

1.2e+

1.0e+

17

∆x = 70 m

1046

-1

Erot [erg]EB [erg]

Turbulence in the contact surface→ampliﬁcaDon of magneDc ﬁeld
→eﬀecDve viscosity would play a role

5

10

15

20

t - tmerger [ms]2530RelaDvisDc jets

Black hole-Neutron star
(BH-NS) merger•

Ref: Kyutoku et al. 2018

If the NS is 'dally disrupted
substanOal amount of material would remain/ejectedaxer the merger

For BHNS merger, lanthanide fracOon of the ejecta
would be higher in the absent of shock heaOng
and neutrino irradiaOon(e.g. Just et al. 2015, Foucart et al. 2017,Kyutoku et al. 2018)

5

Ref: Foucart et al. 2018

FIG. 9. Rest-mass density (top), temperature (middle), and electron fraction (bottom) profi
3 ms after the onset of merger, when the mass and electron fraction of the ejecta approximate
scale compared to Figs. 1, 2 and 3. Black (top) and white (middle an• Kilonova emission wouldNote
alsothebe di↵erent
diﬀerentspatial
due tounbound component identified by the conditions ut < 1 (shown only for ⇢ 106.5 g cm 3 to
diﬀerence in the ejecta morphology
andfromcomposiOon
indistinguishable
hut < 1 on panels presented here [11]. The velocity vector v i ⌘ ui /ut
density profiles. We also show isodensity contours for ⇢ = 107 (yellow-dotted), 109 (orange-d
blue-solid)
the temperature and electron-fraction profiles.
• Whether NS is Odally disrupted
or on
not,

and the remnant disk/ejecta mass depends
strongly on the binary parameters.
D.

Convergence

We check the convergence77of our results by simulating

14 shows various quantities
cussed so far) and low-reso
servatively assuming first-or

NS-NS candidate: S190425z

BH-BH Candidates:
S190828l, S190828j