# Leveraging gravitational-wave memory to distinguish neutron star-black hole
binaries from black hole binaries

Shubhanshu Tiwari  Physik-Institut, Universität Zürich, Winterthurerstrasse
190, 8057 Zürich, Switzerland  Michael Ebersold  Physik-Institut, Universität
Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland  Eleanor Z. Hamilton
Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich,
Switzerland

###### Abstract

In the observation of gravitational waves (GWs) from a compact binary
coalescence where the mass of one of the companions is less than
$5~{}M_{\odot}$ the nature of the object is ambiguous until the measurements
of tidal effects give evidence for the presence of a neutron star (NS) or a
low mass black hole (BH). The relevance of tidal effects in a neutron star-
black hole (NSBH) binary system depends crucially upon the mass and the spin
of the companion BH. These effects become important predominantly when the
binary system is of comparable mass and/or has large aligned spins. Depending
upon the masses and spins the NS can even get tidally disrupted before the
innermost stable circular orbit (ISCO) is reached. The gravitational-wave
signatures of various tidal effects are encoded in the phasing of the signal
and in the case of tidal disruption an abrupt cutoff of the signal amplitude
occurs. In this work we show that tidal effects can also be captured by the
nonlinear memory of the GW signal. Although small in amplitude, nonlinear
memory is present at low frequency in contrast to the oscillatory GW signal.
We introduce nonlinear memory in the NSBH and binary black hole (BBH) waveform
models and show how the addition of memory aids in distinguishing NSBH systems
from BBH systems for a larger part of the parameter space. We discuss the
recently detected events of interest by LIGO-Virgo and provide the future
prospects for the third generation detectors where nonlinear memory can play a
crucial role in inferring the nature of the coalescence as BBH or NSBH from
its GW signal alone.

###### pacs:

04.30.-w, 04.30.Tv

##  I Introduction

Neutron star-black hole binary systems are an extremely rich and versatile
resource for gravitational wave astronomy. The recent detection of two NSBH
binaries from their gravitational wave signal by the LIGO–Virgo detector
network Aasi  _et al._ (2015); Acernese  _et al._ (2015) has provided evidence
for their existence in our universe Abbott  _et al._ (2021a). However, most of
the confidence in the nature of these binaries comes from the measurement of
the masses of the lighter companions, which are well within the mass range of
known NS Antoniadis  _et al._ (2016); Abbott  _et al._ (2017a, 2020a); Alsing
_et al._ (2018). Conclusive evidence for a companion being a NS through GW
observation can only come from the measurement of tidal effects Binnington and
Poisson (2009); Damour and Nagar (2009); Chatziioannou  _et al._ (2018); Le
Tiec and Casals (2021); Charalambous  _et al._ (2021). Unambiguous detection
of a population of NSBH systems will have unique and complementary
consequences for a wide range of topics such as astrophysics Broekgaarden  _et
al._ (2021) and cosmology Vitale and Chen (2018). It should also be noted that
the detection of a BBH system where at least one of the companions has a mass
similar to that of a NS ($\lesssim 3~{}M_{\odot}$) will also have strong
consequences and a clear hint toward new physics Abbott  _et al._ (2019).

The GWs from NSBH systems exhibit unique differences when compared to either
binary neutron star (BNS) or BBH systems. First, the tidal effects in the case
of NSBH are not as pronounced compared to BNS systems as only one companion
can evince tidal effects. This leads to an increase in difficulty measuring
tidal effects. Second, NSBH systems can go to very high mass ratios
$m_{\mathrm{BH}}/m_{\mathrm{NS}}$ as the BH mass is not bounded, unlike BNS
systems. With high mass ratio the tidal effects in NSBH systems become
uninformative as the NS will plunge into the BH before having any substantial
effect on the waveform Matas  _et al._ (2020). For systems where the BH is
only slowly spinning and has a substantially larger mass than the NS, the GW
signal resembles a BBH system with same masses Foucart  _et al._ (2013a). This
was the case for GW190814 Abbott  _et al._ (2020b). In this event a
$23.2^{+1.1}_{-1.0}~{}M_{\odot}$ BH coalesced with a
$2.59^{+0.08}_{-0.09}~{}M_{\odot}$ compact object, whose nature is unknown. It
could be either the heaviest NS or the lightest BH observed in a compact
binary system. Lastly, for NSBH systems where the companions are of similar
masses or the BH has high positive spin, finite size effects cause a dephasing
of the waveform relative to a BBH with same masses and spins while tidal
forces on the NS affect the amplitude of the waveform Flanagan and Hinderer
(2008); Vines and Flanagan (2013). Depending on its equation of state, the NS
can be entirely torn apart in a tidal disruption event Kyutoku  _et al._
(2010, 2011); Foucart  _et al._ (2013b). Such an event can be accompanied by
the formation of a torus remnant around the BH Foucart (2012); Lovelace  _et
al._ (2013) and a kilonova Metzger (2017); Tanaka (2016), if the tidal
disruption happens before the innermost stable circular orbit (ISCO). Then
also the GW signal is highly affected, the amplitude of the merger is heavily
suppressed and the ringdown part is missing completely Pannarale  _et al._
(2015); Kawaguchi  _et al._ (2017). As the tidal disruption event can only
happen for NSBH systems it would be a smoking gun evidence for a NSBH binary.
However, it should be noted that the disruption frequency will be in the
frequency range of a few kHz where the detectors’ sensitivity is not optimal
Matas  _et al._ (2020); Buikema  _et al._ (2020). The scenario of tidal
disruption is not only the best case for the unambiguous identification of
NSBH system but also can lead to potential electromagnetic counterparts
Metzger (2017); Foucart  _et al._ (2017); Barbieri  _et al._ (2020); Foucart
(2020); Fragione (2021). In this work we motivate the use of gravitational-
wave memory as a complementary resource for identifying the tidal disruption
scenario which will help in distinguishing NSBH from BBH mergers.

The gravitational memory effect predicts a persistent physical change to
spacetime induced by the passage of transient gravitational radiation.
Therefore, the proper distance between the locations of freely falling
observers differ before and after a GW passes through. There are two kind of
memory effects: the first is a linear memory effect associated typically with
components or matter being unbound, e.g. binaries on hyperbolic orbits
Zel’dovich and Polnarev (1974); Braginsky and Thorne (1987); Turner and Will
(1978). The second kind, the nonlinear memory effect is directly related to
the nonlinearity of general relativity Christodoulou (1991); Thorne (1992);
Blanchet and Damour (1992). Here we concentrate on the type of nonlinear
memory known as Christodoulou memory or displacement memory, which is the most
prominent kind of memory present in GWs from bound compact binary systems,
hence we will refer to it from here on as just memory. This additional
nonoscillatory component to a GW signal can be understood as being sourced by
the traveling GWs themselves. The GW memory effect also has close connections
to the symmetry group of asymptotically flat spacetimes, the Bondi-Metzner-
Sachs (BMS) group Bondi  _et al._ (1962); Sachs (1962a, b), and its
corresponding conserved quantities (see, e.g., Ref. Strominger (2017) for more
details). Several studies have been performed on the prospect of detecting
memory with LIGO, LISA or other future GW detectors Favata (2010); Lasky  _et
al._ (2016); Johnson  _et al._ (2019); Islo  _et al._ (2019); Boersma  _et
al._ (2020); Hübner  _et al._ (2020, 2021).

The memory component of GWs from compact binary coalescences (CBCs) slowly
accumulates during the inspiral and significantly jumps during the merger
phase of the evolution when spacetime curvature is highest. This adds a late-
time low frequency component to the waveforms of CBC systems. This occurs at
the point in the signal where the frequencies go beyond the sensitive range of
current generation ground-based detectors. This low frequency component has
been used to look for sources that emit GWs at very high frequencies McNeill
_et al._ (2017), for example very light BBH mergers Ebersold and Tiwari
(2020), thus providing a creative way to widen the parameter space of GW
searches. In this context, the utility of memory for detection and
interpretation of sources can become significant when the purely oscillatory
part of the signal extends to such high frequencies that the detectors become
less sensitive. Tidal disruption of neutron stars in NSBH systems is likely to
happen at a few kHz and therefore beyond the sensitive spot of the detectors
Pannarale  _et al._ (2015); Buikema  _et al._ (2020). We show that in this
case the memory can provide crucial information about the nature of the
system.

The rest of the paper is organized as follows: In Sec. II we describe the
waveform model we use, which includes memory for the case of NSBH and BBH
coalescences. We then discuss the parameter space where memory can be utilized
to identify the tidal disruption event in Sec. III. In Sec. IV we quantify the
amount to which memory can contribute toward the distinguishability of NSBH
and BBH mergers. We discuss the current events of interest in Sec. V and
finally give our conclusions in Sec. VI.

##  II Memory of neutron star-black hole systems

Current state-of-the-art waveforms used in GW data analysis do not contain
memory. However, the contribution from the memory effect to the gravitational
waveform can be computed from any waveform in the time-domain Favata (2009a);
Talbot  _et al._ (2018); Ebersold  _et al._ (2019); Ebersold and Tiwari
(2020). It is convenient to decompose the GW polarizations into modes $h_{\ell
m}$ via

$\displaystyle
h_{+}(t)-\mathrm{i}h_{\times}(t)=\sum_{\ell=2}^{\infty}\sum_{m=-\ell}^{\ell}h_{\ell
m}(t)\,{}_{-2}Y_{\ell m}(\iota,\Phi)\,,$ (1)

where the basis ${}_{-2}Y_{\ell m}(\iota,\Phi)$ is formed by the spin-weighted
spherical harmonics with spin weight -2. The angles $\iota$ and $\Phi$ denote
inclination and a reference phase of the source (typically the phase at
coalescence for compact binaries). For nonprecessing binaries the memory
contribution can be assumed to be linearly polarized and only appears in the
plus polarization. Additionally, considering only the dominant oscillatory
waveform mode $h_{22}$, the general formula for the memory Ebersold and Tiwari
(2020) simplifies to:

$\displaystyle
h_{+}^{\textnormal{mem}}(T_{R})=\frac{R}{7c}\sqrt{\frac{5}{6\pi}}\int^{T_{R}}_{-\infty}dt\,|\dot{h}_{22}(t)|^{2}\,{}_{-2}Y_{20}(\iota,\Phi)\,,$
(2)

where the integral from past infinity is taken from the start of the
oscillatory waveform to retarded time $T_{R}$. The overdot represents the time
derivative and $R$ is the distance to the source. Neglecting contributions
from higher order oscillatory modes typically leads to underestimating the
memory amplitude by up to $10\%$. Higher order memory modes for the case of
nonprecessing binaries are negligible Talbot  _et al._ (2018).

The waveform model we use for the oscillatory waveform from aligned-spin NSBH
systems is called SEOBNRv4_ROM_NRTidalv2_NSBH Matas  _et al._ (2020). It is a
frequency-domain model based on the BBH model SEOBNRv4 Bohé  _et al._ (2017)
relying on the effective-one-body (EOB) framework Buonanno and Damour (1999);
Dietrich  _et al._ (2017). Tidal effects on the phase are incorporated from
Ref. Dietrich  _et al._ (2019) and the amplitude is corrected to account for
tidal disruption inspired by Ref. Pannarale  _et al._ (2015) as well as
numerical relativity (NR) simulations of NSBH coalescences Matas  _et al._
(2020). The model takes five parameters, the respective masses and
dimensionless aligned spins of the BH and the NS, $M_{\mathrm{BH}}$,
$M_{\mathrm{NS}}$, $\chi_{\mathrm{BH}}$ and $\chi_{\mathrm{NS}}$, and the
dimensionless tidal deformability parameter of the NS defined as

$\displaystyle\Lambda_{\mathrm{NS}}=\frac{2}{3}k_{2}\frac{R_{\mathrm{NS}}^{5}}{M_{\mathrm{NS}}^{5}}\,,$
(3)

where $k_{2}$ is the Love number and $R_{\mathrm{NS}}$ is its radius
Chatziioannou (2020). Henceforth, we assume both spins to be zero and only
comment on the impact of nonzero spins later on. If $\Lambda_{\mathrm{NS}}=0$,
the model reduces to a BBH waveform model. Since the memory contribution is
computed in the time-domain, we call the NSBH waveform model in the time-
domain via the LIGO Algorithmic Library (LAL) Suite LIGO Scientific
Collaboration (2021). Fig. 1 shows the oscillatory waveform above 500 Hz for a
binary system with component masses 2.5 and 1.5 $M_{\odot}$. The primary
objects is a BH and for the secondary object we consider two cases: first we
consider an NS with $\Lambda_{\mathrm{NS}}=200$ and second a BH. One can
clearly distinguish the typical inspiral-merger-ringdown signal in the BBH
case, whereas the merger-ringdown part is heavily suppressed in the NSBH case
due to tidal disruption. Knowing the oscillatory waveform we can compute the
dominant memory contribution according to Eq. 2, which is also shown for both
cases in Fig. 1. The jump in the memory is considerably higher in the BBH
case.

Fig. 1: The oscillatory GW amplitude tapered at 500 Hz of an NSBH and a
corresponding BBH coalescence at a distance of 100 Mpc and at an inclination
angle of $\iota=90^{\circ}$. We also show the memory contribution of the two
systems.

Fig. 2: The GW amplitude of the memory contribution from a NSBH system at 100
Mpc. Shown is the last part of the inspiral, from a frequency of 200 Hz until
the merger. $\Lambda=0$ corresponds to a BBH system. The inset shows the same
GW signals but with a low-frequency cutoff at 10 Hz.

Figure 2 shows the amplitude of the memory contribution for different values
of $\Lambda_{\mathrm{NS}}$. The memory accumulated in the inspiral and merger
is largest for a BBH and gets substantially smaller with increasing values of
$\Lambda_{\mathrm{NS}}$. Here the memory is computed from the point where the
inspiral frequency passes 200 Hz. The contribution from earlier times is
neglected since its effect on the memory amplitude is insignificant. A GW
detector is only sensitive above a certain frequency and will therefore not
see the eventual offset in the strain, but rather the rise in memory since
that also contains nonzero frequencies. By applying a low-frequency cutoff
with a high-pass filter we see how the memory is observed in the detector. We
choose the cutoff frequency to be 10 Hz since that is the lower end of
advanced LIGO’s design sensitivity aLi  (zero detuned high power configuration
of the detectors). The resulting signal is a burst at the time of the merger,
as shown in the inset of Fig. 2 for a NSBH system with different values of the
NS tidal deformability.

As a cross check for our memory calculation according to Eq. 2 we apply the
method developed in Ref. Mitman  _et al._ (2021) directly to NR waveforms of
NSBH mergers by the SXS collaboration Foucart  _et al._ (2019). Although it
was stated earlier that extracting memory from NR simulations is possible
Pollney and Reisswig (2011), it is dependent on the extraction method and
usually just neglected. Only recently it was computed directly from numerical
relativity Mitman  _et al._ (2020) and shown how it can be added to waveforms
in the SXS catalog of NR waveforms Boyle  _et al._ (2019); Mitman  _et al._
(2021). Essentially by exploiting the BMS balance laws, the GW strain can be
corrected to include the displacement memory. For the available nonspinning
simulations SXS:BHNS:0001, SXS:BHNS:0002, SXS:BHNS:0004 and SXS:BHNS:0006 Duez
_et al._ (2019); Kidder  _et al._ (2019a, b); Buonanno  _et al._ (2019), which
were also used to tune the model SEOBNRv4_ROM_NRTidalv2_NSBH Matas  _et al._
(2020), we find no major discrepancies in the memory amplitude with both
approaches. Although, a systematic comparison would go beyond the scope of
this paper.

The amplitude of the memory as compared to the oscillatory part of the
gravitational wave signal is much smaller, typically about an order of
magnitude. For fixed total mass, the memory amplitude is maximal in equal mass
systems and decreases with more unequal masses. Moreover, it has a distinct
dependence on the inclination angle of Talbot  _et al._ (2018)

$\displaystyle
h_{+}^{\textnormal{mem}}\sim\sin^{2}\iota\left(17+\cos^{2}\iota\right)\,,$ (4)

thus it is maximal for edge-on systems and vanishes for face-on systems.
However, it has a completely different frequency content than the oscillatory
inspiral-merger-ringdown signal. It is basically just a burst saturating
toward the lower frequencies at the time of the merger.

##  III Nonlinear memory as an identifier of tidal disruption event

Identifying the nature of the compact objects in a CBC from their GW signal
alone where one of the companions is low mass $<5~{}M_{\odot}$ is a
challenging task. For example, we have seen the detection of the events
GW190814 Abbott  _et al._ (2020c), GW190425 Abbott  _et al._ (2020a), GW200105
and GW200115 Abbott  _et al._ (2021a), where at least one of the components
was low mass and without an electromagnetic (EM) counterpart, the nature of
the lighter companion was not well established. The prima facie reason for
this challenge can be largely attributed to the fact that we rely on the
measurement of tidal deformation parameters different from null. Measuring
tidal deformation parameters is difficult as these effects are small and often
become more prominent at higher frequencies where the detectors’ sensitivities
are not optimal Matas  _et al._ (2020); Hinderer  _et al._ (2010); Lackey  _et
al._ (2014). Inclusion of memory provides a complementary way to infer the
nature of the less massive compact object.

In this section we start by summarizing the different morphologies of NSBH
binaries following Refs. Pannarale  _et al._ (2015); Matas  _et al._ (2020)
and discuss how the memory relates with each of these cases. Then we briefly
discuss the impact of linear memory generation and the influence of an aligned
BH spin on the memory and a potential tidal disruption event. Later we present
the case for when memory is most useful for identifying the nature of compact
objects in a low-mass CBC signal when EM counterparts are not detected.

###  III.1 Memory signal for various cases of tidal disruptions

In an NSBH inspiral due to gravitational wave emission, the BH exerts tidal
forces on the NS. If the NS approaches sufficiently close to the BH that the
tidal forces overcome the self gravity of the NS, it can lose mass in a
process called mass shedding. This can lead to the tidal disruption of the NS,
where it is completely torn apart due to the strong gravitational field of the
BH. Depending on whether the mass shedding begins before the innermost-stable
circular orbit (ISCO), after which the NS plunges into the BH and finally
merges, the characteristic imprint on the emitted GW signal will be different.
The fate of the NS depends mainly on its equation of state (and therefore the
tidal deformability), the mass ratio and the spin of the BH. NSBH coalescences
can be roughly classified in three categories Pannarale  _et al._ (2015);
Matas  _et al._ (2020):

  * (i)

Nondisruptive mergers: The NS crosses the ISCO before mass shedding occurs and
it plunges as a whole into the BH. The waveform looks similar to a BBH but
with a slightly suppressed amplitude in the merger and ringdown.

  * (ii)

Mildly disruptive mergers: Although the NS undergoes mass shedding prior to
crossing the ISCO, it is not completely torn apart. In the GW signal the
merger and ringdown phase is suppressed but still present.

  * (iii)

Disruptive mergers: In this case the NS gets tidally disrupted before reaching
the ISCO and a remnant torus of matter forms. The GW signal lacks a clear
merger and ringdown part, instead the amplitude tapers off.

The amplitude of the memory signal is largely correlated with the oscillatory
waveform as can be seen in Fig. 3. The nature of the coalescence determines
the morphology of the oscillatory waveform and therefore also affects the
memory amplitude. For the first case of nondisruptive mergers, where the
oscillatory waveform is BBH-like, the memory is more pronounced. This is
because most of the memory is generated when the gravitational field is the
strongest and therefore, like the oscillatory signal, the memory signal looks
almost as in the case of a BBH with the same masses. For the other two cases
where tidal disruption occurs, the lack of the merger-ringdown part of the
signal means there is less overall contribution to the generation of memory,
causing it to be much weaker. It should be noted that although the amplitude
of the memory signal corresponds to the peak amplitude of the oscillatory
signal the frequency spectra of the memory signal is completely different.
When the CBC system consists of two low mass companions the oscillatory
waveform can peak at frequencies beyond the sensitivities of the detectors but
the memory signal will always appear at the low frequency cutoff of the
detector. The correlation of the memory with the nature of the NSBH is shown
in Fig. 3, where we plot the root-sum-squared amplitude $h_{rss}$ of the
memory waveform for a fixed NS mass of $1.5~{}M_{\odot}$ and with varying
tidal deformability parameter $\Lambda_{\mathrm{NS}}$ and mass of the BH
$M_{\mathrm{BH}}$. The different regimes can be clearly distinguished, the
borders between disruptive/mildly disruptive and mildly
disruptive/nondisruptive are indicated with red and yellow lines respectively.

Fig. 3: The $h_{rss}$ of the memory amplitude for edge-on NSBH binaries is
plotted as a function of the NS tidal deformability and the mass of the BH.
The red (yellow) curve corresponds to the light- (dark-) gray region of the
top right plot in Fig. 2 of Ref. Matas  _et al._ (2020). The region below the
yellow curve contains nondisruptive mergers, in between the curves there are
mildly disruptive mergers without a torus remnant and above the red curve we
find disruptive mergers with a torus remnant. The mass of the NS is fixed to
$1.5~{}M_{\odot}$ and the luminosity distance is 100 Mpc.

In the case of disruptive mergers, a substantial amount of matter can be
ejected. A fraction of this matter can become unbound at relativistic
velocities, which in turn can lead to the production of linear memory with an
amplitude proportional to the amount of dynamically ejected mass. Assuming the
most extreme configuration favorable to the production of linear memory, which
is that all ejecta is moving away from the remnant as a point mass of
$0.1~{}M_{\odot}$ and velocity of $0.3~{}c$ Foucart  _et al._ (2013b); Kyutoku
_et al._ (2015), the amplitude of the linear memory computed following Ref.
Favata (2009a) can be of a similar order of magnitude as the nonlinear memory.
Even in this case the build-up time of the linear memory is much slower than,
and not comparable to, the jump of the nonlinear memory close to merger, thus
it will be mostly discarded by the low-frequency cutoff. In a realistic
scenario, the contribution to linear memory will only occur from the asymmetry
in the distribution of ejecta, which would render the mass contributing to the
production of linear memory much smaller. Another mechanism known to cause
linear memory is the recoil or kick that the remnant receives due to
anisotropic radiation of gravitational radiation, though its amplitude is
generally at least two orders of magnitude smaller than the nonlinear memory
as shown in Ref. Favata (2009b).

Considering a spin component of the BH that is aligned with the orbital
angular momentum of the binary, tidal disruption occurs for a wider region in
the parameter space as can be seen in Fig. 2 of Ref. Matas  _et al._ (2020).
In contrast for anti-aligned-spins tidal disruption is less favored. The
reason is that aligned-spin systems tend to stall out the coalescence whereas
antialigned systems are less stable and hence they plunge faster into each
other Campanelli  _et al._ (2006). We recall that memory has a similar
dependence on the spin, due to the longer coalescence time for aligned-spin
systems, more memory amplitude is accumulated Talbot  _et al._ (2018);
Ebersold and Tiwari (2020).

###  III.2 Complementing the oscillatory signal with memory

The tidal deformability does not considerably affect the oscillatory waveform
below $\sim 500$ Hz Pannarale  _et al._ (2011); Hotokezaka  _et al._ (2016) in
a typical NSBH inspiral. Beyond this rough threshold a higher value of the
tidal deformability leads to a faster inspiral and depending on the mass ratio
of the system the NS could get tidally disrupted. Typical frequencies where
tidal disruption can occur are in the kHz-range. This frequency is due to the
fact that canonically the maximum mass of the NS will be less than
$3~{}M_{\odot}$ Rhoades and Ruffini (1974); Abbott  _et al._ (2018a);
Cromartie  _et al._ (2020); Fonseca  _et al._ (2021); Nathanail  _et al._
(2021) while the BH mass is likely to be above this limit. Since tidal
disruption is favored for more equal mass systems we assume
$M_{\mathrm{BH}}\sim\mathrm{a\;few}\;M_{\odot}$. Since tidal disruption is a
late stage inspiral phenomenon, the low total mass of the system means the
frequency at which it occurs will be high. However, at higher frequencies the
sensitivity of current generation detectors starts to fall off. We note that
there are proposals for GW detectors which will be sensitive at high
frequencies like Ackley  _et al._ (2020) for which the oscillatory signal
might be fully in band during the late inspiral and merger. As mentioned
previously, the memory signal will occur at low frequencies and thus can
provide additional information. Depending on whether the NS was tidally
disrupted, swallowed by the BH as a whole or the system is actually a BBH, the
burst of memory in the low frequencies is significantly different.

The dependence of the memory signal on the orientation or inclination angle of
the binary is out of phase with the dependence of the oscillatory signal; the
memory is maximal for an edge-on system while the oscillatory signal peaks
when the system is face-on. This feature of the memory signal becomes very
useful when we have events with low mass companions and with similar masses
(mass ratio closer to 1) without any EM counterpart detection. If the event is
accompanied by EM radiation the nature of the coalescence can be deduced
independently from the GW signal. An NSBH merger is expected to be accompanied
by a short gamma ray burst (GRB) if the NS gets tidally disrupted outside the
BH’s horizon Berger (2014). This is due to the fact that more mass is ejected
during the tidal disruption of a NS as compared to the case when the NS is not
tidally disrupted Foucart  _et al._ (2015). This can lead to a jet formation
which is expected to be oriented perpendicular to the plane of the binary’s
orbit. Thus a GRB would most likely be observed if the NSBH is face-on
Gompertz  _et al._ (2020). In that case the help of memory is minimal and the
nature of the binary could be established by the presence/absence of a GRB. In
contrast if the system is edge-on only the GW signal can be observed and
memory will be maximum. So the maximum contribution from memory happens when
the event is expected not to have any other means to infer the nature of the
coalescence apart from its GW signal. It should be noted that in addition to
the short GRBs, NSBH mergers can also power kilonovae, a bright short lived
quasi thermal emission mostly in infrared and optical wavelengths Metzger  _et
al._ (2010); Coulter  _et al._ (2017) and delayed afterglow mostly in x-ray
and radio energies Hallinan  _et al._ (2017); Troja  _et al._ (2017). These EM
counterparts can be visible for off-axis mergers and can probe the nature of
the compact objects even if the orbital plane is face-off and the GRB jet is
not facing the observer. However, the detection of kilonovae and afterglow is
challenging without a precise sky direction information of the source which is
at best of the order of a few square degrees from GW detectors Abbott  _et
al._ (2018b). In the case when the GRB is off-axis, memory plays a crucial
role in identifying if the system can be a potential candidate to follow up
potential kilonovae and afterglow by flagging the event as tidally disrupted
NSBH or not.

##  IV Prospects for identifying tidal disruption events using nonlinear
memory

In this section we present the parameter space where memory aids in
distinguishing a NSBH binary merger undergoing tidal disruption from a BBH
merger and quantify the degree to which memory can be useful. To do so we work
with a metric which is widely used to measure how much two waveforms differ
known as the match. To compute the match between different waveform templates
we define the overlap or inner product between two templates $h$ and $g$ as
Sathyaprakash and Dhurandhar (1991); Finn and Chernoff (1993)

$\displaystyle\langle h|g\rangle:=4\mathrm{Re}\int
df\frac{\bar{h}(f)g(f)}{S_{n}(f)}\,.$ (5)

$S_{n}(f)$ denotes the power spectral density (PSD) of the detector noise. The
match $\mathcal{M}$ is then computed by maximizing the overlap over
coalescence time $t_{c}$ and phase of the templates $\phi_{c}$ Damour  _et
al._ (1998),

$\displaystyle\mathcal{M}(h,g)=\max_{t_{c},\phi_{c}}\left[\frac{\langle
h|g\rangle}{\sqrt{\langle h|h\rangle\langle g|g\rangle}}\right]\,.$ (6)

We compute the match between different NSBH and BBH waveform templates and
investigate how the addition of memory affects the match. The waveforms used
here are the ones described in Sec. II.

The resulting matches are presented in Fig. 4 for a range of simulated
detector noise PSDs, namely advanced LIGO at design sensitivity aLi , Einstein
Telescope (ET) Maggiore  _et al._ (2020) and Cosmic Explorer (CE) Abbott  _et
al._ (2017b). The mass of the NS is always fixed to $1.5~{}M_{\odot}$ and we
vary the mass of the BH $M_{\mathrm{BH}}$ and the tidal deformability
$\Lambda_{\mathrm{NS}}$ of the NS. For the BBH template the tidal
deformability is of course always zero, so in the limit of
$\Lambda_{\mathrm{NS}}\rightarrow 0$ we should always find a match of 1. The
oscillatory templates start at 500 Hz where the effect of tidal deformation
starts to have a major impact and a high-pass filter is applied to the memory
waveforms in order to cut frequencies below 10 Hz. All waveforms are generated
at an inclination angle of $90^{\circ}$ (edge-on orientation) where the effect
of memory is maximized and also it is the case where the addition of memory
will be the most beneficial, as discussed in Sec. III.2. The plots on the left
hand side show the match between only the oscillatory waveform templates. We
can clearly see that the match falls for larger values $\Lambda_{\mathrm{NS}}$
and for more equal mass systems. This is expected as in this parameter space
the systems can get tidally disrupted and therefore lack the final merger-
ringdown part of the waveform compared to a corresponding BBH waveform.
Otherwise the more unequal the masses of the two objects get and the smaller
$\Lambda_{\mathrm{NS}}$, the waveform becomes more BBH-like and therefore the
match remains high and it is harder to distinguish the systems.

The plots on the right of Fig. 4 show the matches but with the addition of
memory to both the waveform templates. We find that lines of constant match
are generally shifted toward the bottom right compared to the plots on the
left. This is as anticipated, since systems that are tidally disrupted have
much less memory amplitude compared to a corresponding BBH system. Moreover,
we see that adding memory especially improves the distinguishability for small
values of $\Lambda_{\mathrm{NS}}$ in almost equal mass binaries. Measured
values of $\Lambda_{\mathrm{NS}}$ from the observation of GW170817 Abbott  _et
al._ (2017a), which had a mass ratio of less than 1.5, show support for
$\Lambda_{\mathrm{NS}}$ around 300 and $\Lambda_{\mathrm{NS}}\lesssim 600$ for
even the broadest prior Abbott  _et al._ (2018a), this is the region of
$\Lambda_{\mathrm{NS}}$ where memory contributes the most for increasing the
distinguishability. This is due to the fact that if one companion is a NS,
these systems are likely to be disrupted, producing a dip in memory, whereas
if both are BHs the memory amplitude benefits from the equal masses and peaks.
As displayed in Fig. 4 the improvement in mismatch for advanced LIGO is only
small, but still noticeable and in a quite interesting part of the parameter
space. The mismatch will become more pronounced in future detectors since
these will be not only more sensitive overall, but also are expected to be
especially more sensitive toward lower frequencies.

Fig. 4: The plots on the left hand side show the match of the GW signal
between the oscillatory waveform in the latest stages of the inspiral above
500 Hz and the merger/plunge from a NSBH and a corresponding BBH for different
mass ratios and tidal deformabilities, these results are consistent with
results obtained in Pannarale  _et al._ (2011). The plots on the right hand
side show the same but including the memory contribution. The mass of the
secondary object is fixed to $1.5~{}M_{\odot}$. We display the match for
different PSDs of current and future detectors, starting with advanced LIGO
aLi  on top, the Einstein Telescope Maggiore  _et al._ (2020) in the middle
and Cosmic Explorer Abbott  _et al._ (2017b) at the bottom. The oscillatory
waveform is only taken into account above a frequency of 500 Hz as only there
the waveforms start to differ according to Ref. Hotokezaka  _et al._ (2016);
Pannarale  _et al._ (2011). A yellow line marks a match of 0.97, where
waveform templates can be distinguished to 90% confidence if the event has an
SNR of 10.

Following Ref. Baird  _et al._ (2013) one can associate the calculated matches
with confidence regions of distinguishability of the two waveform templates.
These computations are done under the assumptions of Gaussian and stationary
noise using the Fisher Matrix formalism which is valid only for the case of
high signal-to-noise ratio events Vallisneri (2008). We also note that this
criteria is necessary but not a sufficient condition as shown in Ref. Pürrer
and Haster (2020). Although the results presented here are robust, a full
parameter estimation study can vary the confidence intervals where the memory
contribution occurs. Since we have three parameters that define the templates,
namely total mass, mass ratio and tidal deformability of the NS, a match of
0.97 corresponds to a 90% confidence region at a signal-to-noise ratio (SNR)
of 10. In Fig. 4 a yellow line indicates the contour of 0.97 match, below
which the BBH and NSBH templates can be distinguished well if the part of the
signal above 500 Hz has SNR of $\geq 10$. From the figure we note that the
cosmic explorer performs better than the Einstein Telescope, this can be
attributed to the better sensitivity of Cosmic Explorer in the midfrequency
region of $10-100$ Hz.

##  V Interpretation of the detected events

In this section we narrow down the discussion to four detected events which
are of interest to us, namely GW190814, GW200105, GW200115 and GW190425. As
discussed in Sec. III, for all of these binary coalescences at least one of
their progenitors has a mass in the range where it can be a NS ($\lesssim
3M_{\odot}$). However, since no EM counterpart was detected or tidal
deformation measured, an ambiguity as to the nature of the compact object
remains.

GW190814 had companions with masses $23.2^{+1.1}_{-1.0}~{}M_{\odot}$ and
$2.59^{+0.08}_{-0.09}~{}M_{\odot}$ in the 90% credible intervals. The nature
of the lighter companion is therefore particularly ambiguous. As discussed in
Sec. II, the amplitude of the memory signal decays with higher mass ratios.
Additionally, the high total mass causes the merger to happen slower (occur at
lower frequencies) and likewise the memory build-up which therefore almost has
no amplitude for frequencies above 10 Hz. Thus memory cannot contribute in
gaining supplementary information about such events.

GW200105 and GW200115 were identified as NSBH mergers based on the mass
estimate of the lighter companion in the binary as
$\\{1.9^{+0.3}_{-0.2}~{}M_{\odot},\,1.5^{+0.7}_{-0.3}~{}M_{\odot}\\}$
respectively. The masses of the heavier companions were estimated as
$\\{8.9^{+1.2}_{-1.5}~{}M_{\odot},\,5.7^{+1.8}_{-2.1}~{}M_{\odot}\\}$
respectively. The spin magnitude of the heavier companion for GW200105 was
estimated to be below 0.23 at the 90% credible level and for GW200115 the spin
had support for the negative spin projection with respect to the orbital
angular momentum plane at 88% probability Abbott  _et al._ (2021a). As
expected, given the high mass ratio, the tidal deformation and spin of the
secondary object were difficult to measure and could not confirm the presence
of a NS. Tidal disruption for these events was deemed to be unlikely, due to
the high mass ratio and low positive aligned spin components Abbott  _et al._
(2021a); Zhu  _et al._ (2021). The inclusion of memory for these events is not
particularly helpful here. As can be seen from Fig. 4, for mass ratios greater
than 3 the contribution of memory is negligible for the LIGO detectors at its
design sensitivity. However, it should be noted that for the future generation
of GW detectors, especially Cosmic Explorer, memory will be a necessary
feature for distinguishing such events with high confidence as NSBH or BBH
binaries.

GW190425 was observed by LIGO Livingston detector and was identified as a
compact binary coalescence event with a total mass of
$3.4^{+0.3}_{-0.1}~{}M_{\odot}$. This is the event of primary interest for
this work: it is considerably more massive than any other BNS system known, of
the 19 Galactic BNSs the most massive has a total mass of $2.89~{}M_{\odot}$
Farrow  _et al._ (2019); Agazie  _et al._ (2021). Nonetheless, the individual
components are below the highest precise NS mass measurement of
$2.14~{}M_{\odot}$ Cromartie  _et al._ (2020). Still an ambiguity in
determining the nature of the components remains, since no matter effects were
visible in the GW signal nor was an associated electromagnetic observation
reported Coughlin  _et al._ (2019); Boersma  _et al._ (2021).

We performed a follow-up search for nonlinear memory on the event GW190425. We
employed the transient search and reconstruction algorithm coherent WaveBursts
(cWB) Klimenko  _et al._ (2016) which is sensitive to the memory signal
Ebersold and Tiwari (2020). We utilize the publicly available data of 4096
seconds duration from the LIGO Livingston detector LIGO Scientific
Collaboration and Virgo Collaboration (2019); Abbott  _et al._ (2021b) where
the glitches were modeled and removed using the BayesWave algorithm Abbott
_et al._ (2019); Cornish and Littenberg (2015). We excise the oscillatory
maximum likelihood waveform from the data and conduct a follow-up analysis for
the detection of memory. We choose a 40 second time window after the frequency
of the oscillatory waveform goes beyond 512 Hz (we refer to this as the on-
source time). The rest of the data (of about 4000 seconds in duration) is
considered for the estimation of the background (we refer to this as the off-
source time). Furthermore, we tune our search to look only for the triggers
with central frequency below 200 Hz, this is motivated by the fact that the
nonlinear memory signal does not contribute above 150 Hz as shown in Ref.
Ebersold and Tiwari (2020).

In our analysis we find the loudest trigger in the on-source time to have a
false-alarm Rate of about 100 per second with off-source time of 4000 seconds,
this corresponds to a p-value of $0.39$ which is statistically insignificant.
Here we cannot claim that the event GW190425 is either a NSBH or BBH due to
the nondetection of memory, since we do not expect to be able to detect memory
with the sensitivity of the detector at the time of this event. We only expect
to detect memory with p-value $\leq 0.05$ if the progenitor of GW190425 was a
BBH and the merger should be at a distance of around 2 Mpc, so orders of
magnitude closer to us than what it actually was. It should be noted that the
sensitivity to our algorithm in this case is especially deteriorated as this
event was a single detector event and the false-alarms are more difficult to
remove.

##  VI Conclusion

In this work we have provided yet another nonfungible property of memory; to
distinguish tidally disrupted events of NSBH systems from the BBH systems.
Even though the memory signal is much weaker compared to the oscillatory
signal it contributes in the part of the parameter space where, for the
oscillatory signal, distinguishing tidally disrupted NSBH events from BBH
systems is most difficult (equal masses and relatively small tidal
deformability parameter). Memory also aids the most for edge-on systems, where
a potential EM counterpart is less likely to be observed.

We have also quantified the effect of adding memory to waveform models for
current and future generation of detectors in terms of (mis-)match and
provided evidence that memory contributes in enlarging the parameter space for
the distinguishablity of the tidally disrupted NSBH systems from BBH systems.
We discuss the consequences of adding memory for the recently detected events
in particular GW190425, where we found that for current sensitivity of
detectors the use of memory to determine the nature of the lighter object is
inconclusive.

The present work motivates the future development of models with the inclusion
of memory, as this provides several advantages not limited to only NSBH
systems. For example since memory signal has a very different dependence on
the orientation of the binary than the oscillatory signal, it can potentially
contribute to better measurement of the inclination angle especially for equal
mass systems.

##  VII Acknowledgments

The authors are grateful to Francesco Pannarale for his meticulous reading and
comments on the early version of the draft. We thank Maria Haney, Giovanni A.
Prodi and David Nichols for insightful discussions and comments. S. T. and M.
E. are supported by the Swiss National Science Foundation (SNSF) grant No.
200020-182047. E. Z. H is supported by SNSF grant No. IZCOZ0-189876.
This research has made use of data, software and/or web tools obtained from
the Gravitational Wave Open Science Center (https://www.gw-openscience.org/ ),
a service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo
Collaboration. LIGO Laboratory and Advanced LIGO are funded by the United
States National Science Foundation (NSF) as well as the Science and Technology
Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS),
and the State of Niedersachsen/Germany for support of the construction of
Advanced LIGO and construction and operation of the GEO600 detector.
Additional support for Advanced LIGO was provided by the Australian Research
Council. Virgo is funded, through the European Gravitational Observatory
(EGO), by the French Centre National de Recherche Scientifique (CNRS), the
Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef,
with contributions by institutions from Belgium, Germany, Greece, Hungary,
Ireland, Japan, Monaco, Poland, Portugal, Spain. The authors are grateful for
computational resources provided by the LIGO Laboratory and supported by
National Science Foundation Grants PHY-0757058 and PHY-0823459. We also
acknowledge the provision of computational resources from the Physik-Institut
of the University of Zurich.

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# A Visually Classified Spectroscopic Object Catalog for SDSS-IV MaNGA

Joshua L. Steffen  Department of Physics & Astronomy, University of Iowa, Iowa
City, IA 52242  Hai Fu  Department of Physics & Astronomy, University of Iowa,
Iowa City, IA 52242

###### Abstract

We provide a catalog of visually classified objects in the MaNGA integral
field spectroscopic survey. The MaNGA survey is designed to target a single
galaxy with each of its integral field units (IFUs); however, many of these
fields will host ancillary objects. We identify these discrete objects by
cleaning up SDSS photometric objects in MaNGA’s fields-of-view. We then use
the spectra from MaNGA’s data-cubes to spectrally classify the identified
objects. The catalog contains the positions and classifications of 1385 stars,
11,439 galaxies, and 107 broad-line AGN (BLAGN) from the 10,130 unique MaNGA
fields. We also provide spectroscopically derived parameters for the galaxies
including; stellar masses, gas and stellar kinematics, and emission-line
fluxes and equivalent widths. This catalog effectively expands the size of the
MaNGA catalog by $\sim$50%, increasing the utility of the MaNGA project.

##  1 Introduction

MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) is a massive
integral field spectroscopic survey of nearby galaxies. The project feeds 17
IFUs (optical fiber bundles; Law et al. (2015)) into two dual-channel BOSS
spectrographs (Drory et al., 2015) on SDSS’s 2.5 meter telescope. The survey
targets nearby galaxies within a redshift range of 0.01 $<$ $z$ $<$ 0.15 and a
luminosity range of -17.7 $<$ $\mathcal{M}_{\rm i}$ $<$ -24.0, where
$\mathcal{M}_{\rm i}$ is the rest frame i-band absolute magnitudes from
elliptical Petrosian apertures. MaNGA’s final data release (DR17; Abdurro’uf
et al. (2021)) contains 10,130 unique observations.

Each IFU observation is designed to cover a single galaxy out to 1.5 $R_{\rm
eff}$ and 2.5 $R_{\rm eff}$ (where $R_{\rm eff}$ is the half light radius).
The extended spatial coverage was intended to be used to study galaxy
properties across the spatial dimensions, but the it also allows many
ancillary objects to fall into MaNGA’s fields-of-view. Here, we provide the
first catalog that identifies and classifies all spectroscopic objects within
MaNGA’s 2392 arcmin2 footprint.

##  2 Methods

Figure 1: A example of our identification and classification pipeline for a
single MaNGA field (Plate-IFU: 12512-12702). The top row shows SDSS
pseudocolor images for the MaNGA field. The image on the left shows the 40′′
field with SDSS’s photoObj catalog overlaid in blue circles and SDSS’s
spectroscopic catalog overlaid in red squares. The white hexagon represents
MaNGA’s field-of-view. The image in the middle shows the same field but with
the cleaned catalog in green circles. The numbers above the green circles are
object IDs. The right image shows the same object with a wider field (160′′
across). The bottom three rows show the spectra for each object. The black
spectra represents the extracted spectra from MaNGA’s data-cubes, the red
spectra is SPFIT’s best-fit model spectra, and the blue spectra are the best-
fit emission lines. In the top left corner of each spectra plot shows the
object ID and our spectral classification.

The construction of our MaNGA object catalog consists of two main stages. We
first identify objects in MaNGA’s fields-of-view by cross-matching the survey
with previous catalogs. Next, we use the spectra provided in MaNGA’s data-
cubes to spectroscopically classify the objects. Along with the spectral
classification, we can use the best-fit spectral models to extract observed
and derived properties of these objects.

Properly deblending discrete objects in crowded fields is a challenge. Some
algorithms under-deblend imaging data such that it misses sources in crowded
fields. Other algorithms over-deblend fields such that several objects are
assigned to a single extended object. MaNGA’s targeting catalog, the NASA
Sloan Atlas111NSA v1_0_1; http://www.nsatlas.org (NSA), frequently combines
objects in crowded fields while SDSS’s photometric catalog,
photoObj222https://www.sdss.org/dr17/imaging/catalogs/, frequently places
extra sources over galaxies with clumpy light distributions. Instead of
attempting to create our own deblending algorithm, we decide to remove false
sources from the photoObj catalog in the MaNGA fields.

We visualize the MaNGA fields by overlaying the photoObj catalogs over SDSS
pseudocolor images. We then remove these false sources by visual inspection.
There are also some objects that are absent in the photoObj catalog; we add
the positions of these objects into our catalog. We also corrected a few cases
in which the given positions are off when compared to the light distribution.
We show an example of the object identification process in the top row of
Figure 1.

SDSS’s photoObj table separates stars from galaxies based on photometry. With
MaNGA, we can perform a more rigorous classification scheme using the spectra
from the survey’s data-cubes. We extract the spectra for every identified
object with a 1′′ radius circular aperture. We then fit the spectra with the
spectral fitting algorithm, spfit333https://github.com/fuhaiastro/spfit (Fu et
al., 2018).

spfit is designed to simultaneously fit the stellar continuum and emission
lines following the Penalized Pixel-Fitting method (Cappellari & Emsellem
(2004); Cappellari (2017)) using the simple stellar population models from
MIUSCAT (Vazdekis et al., 2012). We use the redshift of the MaNGA target, from
the NSA catalog, as the initial guess for the redshift for all objects in a
given MaNGA field. spfit allows doppler shifts to the model templates, but it
will fail to model objects with substantially different redshifts ($\Delta
v\geq$ 2000 km s-1).

We visually classify the identified objects by comparing the observed spectrum
with the best-fit model. Since spfit has a redshift tolerance of $\Delta
v\geq$ 2000 km s-1, we first sort objects in two redshift based categories;
z_corr and z_off. Objects with the z_corr designation have redshifts that are
comparable to the MaNGA target while objects with the z_off designation have a
redshift that is notably different from the MaNGA target. Within the z_corr
designation, objects are classified as galaxies or BLAGN. Within the z_off
designation, objects are classified as galaxies, BLAGN, or stars. Stars,
galaxies, and BLAGN can be distinguished based on their distinct spectral
features. Finally, objects whose signal-to-noise is to low to discern any
spectral features are classified as “low signal” and objects with missing
spectra (from being near the edge of an IFU) or defective spectra are
classified as “defective.” spfit is designed to model galaxy spectra near the
input redshift, so projected galaxies, BLAGN, and foreground stars will not be
properly modeled by the fitting algorithm. We show an example of the extracted
and modeled spectra in Figure 1. Object #0 and Object #2 have galaxy type
spectra while object #1 has the spectra of a foreground star.

##  3 Results

By visually cleaning the SDSS photoObj catalog, we identify 15,592 objects
(including MaNGA targets) within the 10,130 unique MaNGA fields. We then use
MaNGA’s spectra to visually classify each object and find 11,439 galaxies (of
which 10,988 are z_corr and 451 are z_off), 1385 stars, 107 BLAGN (of which 84
are z_corr and 23 are z_off), 2367 low signal observations, and 294 defective
spectra.

Our spectral fitting code, spfit, computes a number of derived properties from
the modeled galaxy spectra. spfit provides emission line fluxes, equivalent
widths, and gas kinematics calculated from the fitted emission lines and
stellar kinematics and stellar masses from the stellar continuum. Because the
properties are derived from spectra extracted from a 1′′ radius circular
aperture centered on each object, they are only for the centers of the
galaxies. We provide the positions, classifications, and derived parameters in
the tables on our Github (https://github.com/jlsteffen/MaNGAObj). Since spfit
is designed to model galaxy spectra, the non-galaxy objects will have null
values for the derived parameters.

##  4 Applications

Previous versions of this catalog have already been used for studying
kinematic galaxy pairs in MaNGA (Fu et al., 2018; Steffen et al., 2021,
Steffen et al. 2022, in preparation), but this catalog has many other
potential applications. For instance, it may be used to study stars or BLAGN
with MaNGA’s spectroscopy, to study galaxy clusters, or to mask ancillary
objects out of the MaNGA fields.

We acknowledge support from the National Science Foundation grants,
AST-1614326 and AST-2103251. Sloan

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