Estimating the Contribution of Dynamical Ejecta
in the Kilonova Associated with
GW170817
LIGO Scienti
fi
c Collaboration and Virgo Collaboration
(
See the end matter for the full list of authors.
)
Received 2017 October 11; revised 2017 October 14; accepted 2017 October 15; published 2017 December 1
Abstract
The source of the gravitational-wave
(
GW
)
signal GW170817, very likely a binary neutron star merger, was also
observed electromagnetically, providing the
fi
rst multi-messenger observations of this type. The two-week-long
electromagnetic
(
EM
)
counterpart had a signature indicative of an
r
-process-induced optical transient known as a
kilonova. This Letter examines how the mass of the dynamical ejecta can be estimated without a direct
electromagnetic observation of the kilonova, using GW measurements and a phenomenological model calibrated to
numerical simulations of mergers with dynamical ejecta. Speci
fi
cally, we apply the model to the binary masses
inferred from the GW measurements, and use the resulting mass of the dynamical ejecta to estimate its contribution
(
without the effects of wind ejecta
)
to the corresponding kilonova light curves from various models. The
distributions of dynamical ejecta mass range between
=-
--
MM
10
10
ej
32
for various equations of state,
assuming that the neutron stars are rotating slowly. In addition, we use our estimates of the dynamical ejecta mass
and the neutron star merger rates inferred from GW170817 to constrain the contribution of events like this to the
r
-process element abundance in the Galaxy when ejecta mass from post-merger winds is neglected. We
fi
nd that if
10% of the matter dynamically ejected from binary neutron star
(
BNS
)
mergers is converted to
r
-process
elements, GW170817-like BNS mergers could fully account for the amount of
r
-process material observed in the
Milky Way.
Key words:
gravitational waves
–
methods: data analysis
–
stars: neutron
1. Introduction
On 2017 August 17, 12:41:04 UTC, the Laser Interferometer
Gravitational-wave Observatory
(
LIGO
)
/
Virgo gravitational-
wave
(
GW
)
observatory network, composed of LIGO Hanford
Observatory, LIGO Livingston Observatory, and Virgo, recorded
GWs consistent with a binary neutron star
(
BNS
)
inspiral and
merger
(
Abbott et al.
2017c
)
. This signal was subsequently
named GW170817.
In addition to the GW signature, the merger of a BNS system
is expected to have multiple electromagnetic
(
EM
)
signatures
over different timescales
(
Nakar
2007
; Metzger & Berger
2012
)
. The LIGO
/
Virgo sky localization of GW170817
(
Abbott et al.
2017c
)
spurred an intensive multi-messenger
campaign covering the whole EM spectrum to search for
counterparts
(
see Abbott et al.
2017d
for an extended list
)
.
Within hours, broadband observations
—
backed by archival
data investigation
—
revealed an optical transient
(
Arcavi et al.
2017
; Coulter et al.
2017
; Lipunov et al.
2017
; Pian et al.
2017
;
Soares-Santos et al.
2017
; Tanvir et al.
2017
; Valenti et al.
2017
)
, a type of transient called a kilonova
(
Li &
Paczynski
1998
; Metzger
2017
)
originating from neutron-rich
matter unbound from the system
(
e.g., Evans et al.
2017
;
McCully et al.
2017
; Smartt et al.
2017
; Troja et al.
2017
)
.
Broadly, two types of ejecta are expected to contribute to
kilonovae: dynamical ejecta produced at the time of the merger
(
Rosswog et al.
1999
; Metzger et al.
2010
; Roberts et al.
2011
;
Barnes & Kasen
2013
; Bauswein et al.
2013
; Hotokezaka
et al.
2013
; Rosswog
2013
; Tanaka & Hotokezaka
2013
;
Bovard et al.
2017
; Dietrich & Ujevic
2017
; Dietrich
et al.
2017b
; Radice et al.
2016
; Sekiguchi et al.
2016
)
, and
post-merger winds produced by the remnant system, for
example from an accretion disk around a black hole or massive
neutron star
(
Dessart et al.
2009
; Perego et al.
2014
; Fernández
et al.
2015
; Kasen et al.
2015
; Kiuchi et al.
2015
; Martin et al.
2015
; Foucart et al.
2016
; Ciol
fi
et al.
2017
; Fujibayashi et al.
2017
; Shibata et al.
2017
; Siegel & Metzger
2017
)
.
Both EM and GW measurements rely on models to connect
the underlying properties and composition of the ejecta to their
respective observations. The process of interpreting ejecta
based on EM observations is described in Alexander et al.
(
2017
)
, Arcavi et al.
(
2017
)
, Chornock et al.
(
2017
)
, Covino
et al.
(
2017
)
, Cowperthwaite et al.
(
2017
)
, Diaz et al.
(
2017
)
,
Drout et al.
(
2017
)
, Evans et al.
(
2017
)
, Kasen et al.
(
2017
)
, McCully et al.
(
2017
)
, Nicholl et al.
(
2017
)
, Pian
et al.
(
2017
)
, Smartt et al.
(
2017
)
, Tanaka et al.
(
2017
)
, Troja
et al.
(
2017
)
, and Abbott et al.
(
2017d
)
. We use phenomen-
ological calculations that estimate the dynamical ejecta mass
from the pre-coalescence binary properties, which GW
observations can constrain. This mass is a critical ingredient
needed to predict the contribution of dynamical ejecta to the
EM light curve associated with this kilonova transient. Going
forward, this procedure would also assist in the interpretation of
future follow-up observations where a dim counterpart was
detected, or none at all.
This Letter shows how dynamical ejecta masses obtained
from GW parameter estimates of GW170817 via phenomen-
ological
fi
ts to numerical models for the mass and velocity of
dynamically ejected matter in BNS systems
(
Dietrich & Ujevic
2017
, hereafter DU17
)
can predict kilonova light curves.
The Astrophysical Journal Letters,
850:L39
(
13pp
)
, 2017 December 1
https:
//
doi.org
/
10.3847
/
2041-8213
/
aa9478
© 2017. The American Astronomical Society.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 3.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
1
Similar numerical work has produced
fi
tting formulae in the
case of neutron-star black-hole
(
NSBH
)
binaries
(
Kawaguchi
et al.
2016
)
. While the GW detection of GW170817 cannot
rule out the presence of a black-hole companion, the BNS
interpretation is favored
(
Abbott et al.
2017c
)
. Consequently,
we do not include the NSBH scenario in this work, and only
employ the
fi
tting formulas for ejecta mass and velocity from
BNS simulations
(
DU17
)
. The GW170817 analysis extracted
the BNS source parameters using Bayesian inference
(
Abbott
et al.
2017c
)
, and those results are used here to estimate the
mass of the dynamical ejecta. This approach accounts for the
dependence of the amount of ejected matter on the size and
stiffness
(
Kawaguchi et al.
2016
)
of the components of the
binary, characterized by the equation of state
(
EOS
)
and its
in
fl
uence on the mass
–
radius relationship
(
Lattimer &
Prakash
2001
; Özel & Freire
2016
)
.
Bayesian inference with a GW signal model applied to the
strain data provides a posterior distribution of component
masses
(
m
i
)
and dimensionless spins
(
c
º
∣∣(
)
S
cGm
i
i
i
2
, where
S
is the angular momentum of the neutron star
(
NS
))
consistent
with the observations
(
Veitch et al.
2015
)
. Assuming NS spins
are small
(
χ
0.05, hereafter
“
low-spin
”
)
, we obtain distribu-
tions of ejecta between 10
−
3
and 10
−
2
M
e
. Allowing for larger
NS spins
(
χ
0.89, hereafter
“
high-spin
”
)
pushes some ejecta
values higher, of the order of 10
−
1
M
e
at its highest. In this
Letter, we focus on dynamical sources, so it is important to
recall that this analysis may not account for a signi
fi
cant
fraction of the ejecta mass; winds could produce comparable or
even more ejecta than from dynamical sources. Using the GW-
derived dynamical ejecta estimates, the derived light curves
vary signi
fi
cantly between the adopted models, in both color
evolution and time and magnitude of peak emission; in extreme
cases, they can reach beyond 15th magnitude in optical bands.
Like supernovae
(
Terasawa et al.
2001
)
, neutron star mergers
are believed to contribute to the abundance of heavy elements
(
Lattimer & Schramm
1974
)
through r-process nucleosynthesis
(
Burbidge
1954
)
. Using our GW estimates of dynamical ejecta
masses and the merger rates inferred from the BNS discovery
(
-
+
1540
1220
3200
Gpc
−
3
yr
−
1
; Abbott et al.
2017c
)
, we estimate
a present-day
r
-process density of
–
10 10
1.7
3.2
M
e
Mpc
−
3
contributed by BNS mergers. Under the assumption that all
BNS mergers produce the same amount of dynamical ejecta
that we infer for GW170817, this estimate is consistent with the
Galactic values and suggests that the associated nucleosynth-
esis is one of the primary contributors to
r
-process abundances.
2. Predicted Dynamical Ejecta Mass
In general, the amount of ejecta from binary mergers
depends on the masses and EOS of the two components, their
rotation, and, most importantly for post-merger winds, the
neutrino
/
radiation hydrodynamics and the magnetic
fi
elds, e.g.,
Hotokezaka et al.
(
2013
)
, Martin et al.
(
2015
)
, Dietrich et al.
(
2017b
)
, Radice et al.
(
2016
)
, Sekiguchi et al.
(
2016
)
, and
Siegel & Metzger
(
2017
)
. Based on detailed numerical studies
of merging, irrotational binaries, the phenomenological
fi
ts
devised by
DU17
relate the dynamical ejecta mass
M
ej
to the
gravitational mass of the component stars
(
m
)
, their baryonic
mass
(
m
b
)
, and their radii
R
(
or equivalently compactnesses
=
C
Gm Rc
2
)
. Contributions due to winds were not included
in the simulations used by
DU17
, and thus are not part of the
fi
ts for
M
ej
, even though they may lead to comparable ejecta
masses.
Because the EOS in neutron stars is poorly constrained, two
approaches are taken to describe the bulk properties of the
binary components. In the
fi
rst approach, we assume an EOS
and infer
m
b
and
C
from the binary
’
s measured gravitational
masses using a zero-temperature non-rotating model
(
computed
using the Oppenheimer
–
Volkoff equations, Oppenheimer &
Volkoff
1939
)
. Different EOSs will predict different radii and
baryonic masses for the same gravitational masses and, as such,
will affect the amount of ejecta and the predicted light curve of
the kilonova. The EOS of cold, dense, degenerate matter is
poorly constrained
(
see Oertel et al.
2017
for a recent review
)
,
so we evaluate a representative selection of the EOS considered
in Özel & Freire
(
2016
)
. The tidal deformabilities allowed by
GW170817
(
Abbott et al.
2017c
)
do disfavor stiffer EOSs;
however, many remain compatible with our measurements.
Due to observational constraints, we restrict ourselves to EOSs
that have a maximum mass above 1.97
M
e
(
Demorest
et al.
2010
; Antoniadis et al.
2013
)
. Speci
fi
cally, we consider
EOS calculations from Glendenning
(
1985
, GNH3
)
, Müther
et al.
(
1987
; MPA1
)
, Wiringa et al.
(
1988
; WFF1-2
)
, Engvik
et al.
(
1996
; ENG
)
, Müller & Serot
(
1996
; MS1, MS1b
)
,
Akmal et al.
(
1998
; APR3-4
)
, Douchin & Haensel
(
2001
; SLy
)
,
and Lackey et al.
(
2006
;H4
)
.
In the second case, we take an approach that does not assume
a speci
fi
c EOS to compare against our EOS-speci
fi
c results.
The internal structure of the NSs in a binary is encoded in the
gravitational waveform through the
(
dimensionless
)
tidal
deformabilities
(
denoted
Λ
)
of the NSs
(
Flanagan & Hinderer
2008
; Damour et al.
2012
; Del Pozzo et al.
2013
; Wade
et al.
2014
)
. One can infer
m
b
and
C
from the binary
’
s
measured gravitational masses and tidal deformabilities by
applying
fi
ts from Coughlin et al.
(
2017
)
and Yagi & Yunes
(
2017
)
, which give
m
b
(
m
,
C
)
and
C
(
Λ
)
, respectively. While
some error is incurred using these additional
fi
ts, it is small
compared to the estimated uncertainty of the
fi
ts for the
dynamical ejecta properties and the intrinsic uncertainty in
current numerical relativity simulations. Speci
fi
cally, for the
EOS considered by Yagi & Yunes
(
2017
)
, the error in the tidal
deformability-compactness relation is
<
10% for the nuclear
EOS, while for the baryonic mass
fi
t, the maximum error found
by Coughlin et al.
(
2017
)
is
<
3%. When applying these
fi
ts, we
also exclude cases with component masses above 3
M
e
,a
standard upper bound on NS masses
(
Kalogera & Baym
1996
)
,
and restrict the compactness to be below the Buchdahl bound
(
Buchdahl
1959
)
of 4
/
9
;
0.44, which similarly only affects a
few cases.
2.1. Sources of Uncertainties in Ejecta Mass Estimation
Many caveats must be considered when assessing the
uncertainty in estimates of
M
ej
. The amount of ejecta from
mergers also depends on various microphysics, such as the
particular treatment of thermal effects, neutrino transport, and
magnetic
fi
elds
(
Dessart et al.
2009
; Bauswein et al.
2013
;
Perego et al.
2014
; Radice et al.
2016
; Sekiguchi et al.
2016
;
Bovard et al.
2017
; Ciol
fi
et al.
2017
)
, which lead to
uncertainties about the ejecta
’
s structure, angular distribution,
and composition
(
Kasen et al.
2013
; Tanaka & Hotokezaka
2013
; Barnes et al.
2016
)
. These parameters are not included in
the
M
ej
fi
ts in
DU17
. Additionally, the
DU17
fi
ts ignore the
effects of spin on dynamical ejecta, which can change the
amount of ejecta
(
Kastaun & Galeazzi
2015
; Dietrich et al.
2017a
; Kastaun et al.
2017
)
. In particular, aligned spin can
2
The Astrophysical Journal Letters,
850:L39
(
13pp
)
, 2017 December 1
Abbott et al.