# An Enigmatic 380 kpc Long Linear Collimated Galactic Tail

Dennis Zaritsky${}^{1,\href https://orcid.org/0000-0002-5177-727X}$ Jacob P.
Crossett${}^{2,\href https://orcid.org/0000-0002-9810-1664}$, Yara L.
Jaffé${}^{2,\href https://orcid.org/0000-0003-2150-1130}$, Richard
Donnerstein${}^{1,\href https://orcid.org/ 0000-0001-7618-8212}$, Ananthan
Karunakaran${}^{3,\href https://orcid.org/0000-0001-8855-3635}$, Donghyeon J.
Khim${}^{1,\href https://orcid.org/0000-0002-7013-4392}$, Ana C.C.
Lourenço${}^{2,4,\href https://orcid.org/0000-0002-4393-7798}$, Kristine
Spekkens${}^{5,6,\href https://orcid.org/0000-0002-0956-7949}$, Ming
Sun${}^{7,\href https://orcid.org/0000-0001-5880-0703}$, Benedetta
Vulcani${}^{8,\href https://orcid.org/0000-0003-0980-1499}$
1 Steward Observatory, University of Arizona, Tucson, AZ, 85721, USA
2 Instituto de Física y Astronomía, Universidad de Valparaíso, Avda. Gran
Bretaña 1111, Casilla 5030, Valparaíso, Chile
3 Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía,
18008 Granada, Spain
4 European Southern Observatory (ESO), Alonso de Cordova 3107, Santiago, Chile
5 Department of Physics and Space Science, Royal Military College of Canada
P.O. Box 17000, Station Forces Kingston, ON, K7K 7B4, Canada
6 Department of Physics, Engineering Physics and Astronomy, Queen’s
University, Kingston, ON, K7L 3N6, Canada
7 Department of Physics and Astronomy, University of Alabama in Huntsville,
301 Sparkman Dr NW, Huntsville, AL 35899, USA
8 INAF- Osservatorio astronomico di Padova, Vicolo Osservatorio 5, I-35122
Padova, Italy
E-mail<EMAIL_ADDRESS>
###### Abstract

We present an intriguing, serendipitously-detected system consisting of an
S0/a galaxy, which we refer to as the “Kite", and a highly-collimated tail of
gas and stars that extends over 380 kpc and contains pockets of star
formation. In its length, narrowness, and linearity the Kite’s tail is an
extreme example relative to known tails. The Kite (PGC 1000273) has a
companion galaxy, Mrk 0926 (PGC 070409), which together comprise a binary
galaxy system in which both galaxies host active galactic nuclei. Despite this
systems being previously searched for signs of tidal interactions, the tail
had not been discovered prior to our identification as part of the validation
process of the SMUDGes survey for low surface brightness galaxies. We confirm
the kinematic association between various H$\alpha$ knots along the tail, a
small galaxy, and the Kite galaxy using optical spectroscopy obtained with the
Magellan telescope and measure a velocity gradient along the tail. The Kite
shares characteristics common to those formed via ram pressure stripping
(“jellyfish" galaxies) and formed via tidal interactions. However, both
scenarios face significant challenges that we discuss, leaving open the
question of how such an extreme tail formed. We propose that the tail resulted
from a three-body interaction from which the lowest-mass galaxy was ejected at
high velocity.

###### keywords:

galaxies: kinematics and dynamics galaxies: structure galaxies: formation
galaxies: dwarf

††pubyear: 2023††pagerange: An Enigmatic 380 kpc Long Linear Collimated
Galactic Tail–An Enigmatic 380 kpc Long Linear Collimated Galactic Tail

##  1 Introduction

Galactic tails, or more broadly galactic detritus, may be a signature of a
process or event acting to transform galaxies. As such, their discovery and
characterisation help us unravel how galaxies evolve. The classic example of
such an analysis is that of galactic tidal features (Toomre & Toomre, 1972;
Toomre, 1977), which triggered a revolution in our understanding of the role
of interactions and mergers of galaxies (cf., Schweizer, 1986; Barnes &
Hernquist, 1992a). Mergers and accretion are now central to the accepted
hierarchical formation paradigm (e.g., Davis et al., 1985) and individual
systems at various stages along a merger sequence have been identified
(Hibbard & van Gorkom, 1996).

Gravity is not the only force that can extract matter from a galaxy. For
example, galaxies moving through environments with a sufficiently high ambient
density (such as the intracluster medium of massive clusters) can lose gas due
to ram pressure stripping (Gunn & Gott, 1972). Among the most convincing
examples of ram-pressure stripping at play are HI observations of cluster
galaxies displaying gaseous tails and undisturbed stellar disks (Haynes et
al., 1984; Cayatte et al., 1990; Chung et al., 2009; Jaffé et al., 2015) and
the "jellyfish" galaxies seen in clusters (Kenney & Koopmann, 1999; Smith et
al., 2010; Ebeling et al., 2014; Fumagalli et al., 2014; Poggianti et al.,
2016, 2017; McPartland et al., 2016; Jaffé et al., 2018) and groups (Vulcani
et al., 2021a; Kolcu et al., 2022). It is expected that such hydrodynamic
interactions, as well as other environmental effects, are responsible for the
increased fraction of quenched galaxies in dense environments (e.g. Dressler
et al., 1987; Peng et al., 2010).

Extreme examples of galactic detritus garner attention because they challenge
our quantitative understanding of these phenomena. For example, the recent
discovery of a 250 kpc-long HI tail in the outskirts of the galaxy cluster
Abell 1367 has proven difficult to explain in any scenario (Scott et al.,
2022). Sometimes, a particular example elicits bold new suggestions, such as
that invoking a runaway supermassive black hole (van Dokkum et al., 2023).

We report the discovery of an extraordinary tail with a variety of interesting
features. First, with a projected of 380 kpc (7 arcmin), it is the longest
optical tail of which we are aware. This length is $>$ 6 times that of the
longest jellyfish tails seen in H$\alpha$ (e.g., D100 and JO206, Yagi et al.,
2016; Poggianti et al., 2017) and longer than most traced by HI emission
(e.g., J0206 and FGC 1287; Ramatsoku et al., 2019; Scott et al., 2022), with
the exception of a $\sim 500$ kpc long, amorphous feature tailing a Virgo
cluster galaxy pair (Koopmann et al., 2008). The only even longer galactic
structures are some radio-detected, head-tail systems that can reach lengths
$>$ 600 kpc (Vallee & Roger, 1987) but which are clearly associated with
relativistic electron jets interacting with the intracluster medium. Second,
it is one sided, emanating along the disk plane of its apparent host galaxy.
Third, it is highly collimated, with a length to width ratio of $\sim$ 40\.
Fourth, it is exceedingly close to linear in projection. Fifth, it originates
from an S0/a galaxy, which we would expect to be gas-poor, yet the tail is
sufficiently gas-rich to support star formation along its length. Sixth, it
lies in a low-density galactic environment with no cluster or group nearby,
but is in a close binary galaxy system where both galaxies have active
galactic nuclei.

Figure 1: The Kite galaxy and its companion, Mrk 0926. Features along the tail
are labelled a-j as shown. The candidate disrupted galaxy, Kite A, is also
labelled. Image obtained from the Legacy Survey public archive and is in the
$g$-band. Bar at bottom right shows the length of 1 arcmin or the equivalent
physical length at the distance of the Kite, 54 kpc.

Aside from inspiring questions regarding their origin and the impact of such
phenomenon on galactic evolution, tails and other galactic detritus are used
to address a range of unrelated topics, including the nature of the dark
matter potential (Dubinski et al., 1999; Springel & White, 1999), the
formation of dark matter-free, tidal dwarf galaxies (Mirabel et al., 1992; Duc
& Mirabel, 1994; Barnes & Hernquist, 1992b; Hunsberger et al., 1996; Elmegreen
et al., 1993), the nature of star formation in an environment different than
that typically found within galaxies (de Grijs et al., 2003; Knierman et al.,
2003; Boquien et al., 2009; Giunchi et al., 2023), and the character of the
circumgalactic and intergalactic environment (Sun et al., 2007; Tonnesen &
Bryan, 2010a; Fossati et al., 2016; Vulcani et al., 2019; Sun et al., 2021).
It stands to reason that extreme cases provide novel constraints for all of
these topics to exploit.

The discovery and initial characterisation of the galaxy that we have named
the “Kite" on the basis of its morphology are described in §2. Because of the
possibility of chance superpositions of features enhancing the tail’s
appearance, length, or coherence, and to search for signs of current star
formation, we obtained optical spectroscopy along the tail. The spectroscopic
observations and results are presented in §3. We present a brief discussion of
various aspects of this system in §4, highlighting areas that place the
strongest constraints on possible formation scenarios and where subsequent
investigation is warranted. We adopt a standard $\Lambda$CDM cosmology (flat,
$\Omega_{m}=0.282$, H${}_{0}=69.7$ km s-1 Mpc-1; Hinshaw et al., 2013) when
needed.

##  2 Discovery and Characterisation

We serendipitously discovered the Kite during a search for low surface
brightness (LSB) galaxies in the Legacy Survey (Dey et al., 2019) images
(Systematically Measuring Ultra-Diffuse Galaxies (SMUDGes); Zaritsky et al.,
2019, 2021, 2022, 2023). The list of candidate LSB galaxies returned by the
search algorithm is contaminated by a number of artificial and physical
sources that are not the intended targets. Briefly, SMUDGes processes the
images by removing or replacing high surface brightness sources, filtering the
residual images for angularly-large sources, proceeding through a variety of
selection steps to winnow the number of LSB detections, and ultimately
producing a list of high-confidence ultra-diffuse galaxy (UDG) candidates. The
final step in the vetting process includes a visual examination of the
candidate list. One of those objects is the subject of this study.

Upon visual inspection, we identified the candidate located at
$(\alpha,\delta)=(346.2203^{\circ},-8.8093^{\circ})$, which is object i in
Figure 1, to be near the end of a linear sequence of low surface brightness
features leading back to PGC 1000273 $(346.183294^{\circ},-8.703178^{\circ})$,
an edge-on S0/a galaxy (Nair & Abraham, 2010) with $cz=13813\pm 25$ km s-1 in
the CMB frame and M${}_{i}=-21.41$ AB mag (recessional velocity and magnitude
from NED111The NASA/IPAC Extragalactic Database (NED) is funded by the
National Aeronautics and Space Administration and operated by the California
Institute of Technology.) that we have named the “Kite" galaxy given its
single-sided tail morphology (Figure 1). It has a companion galaxy, projected
only 57 kpc away at a comparable redshift $(z=0.0470)$, that is a QSO (Mrk
0926, or alternately PGC 070409). This pair had attracted previous attention
because the Kite galaxy also shows signs of nuclear activity (identified
spectroscopically as “composite" by Liu et al., 2011, in a study of binary
active galaxies), although neither Liu et al. (2011) nor a subsequent study
(Weston et al., 2017) identified clear signs of an interaction between the
galaxies.

The tail structure comprises both well-defined knots of emission and diffuse
emission strewn nearly linearly out to a projected separation from the Kite of
7 arcmin (420.0 arcsec from feature j in Figure 1 to the center of the Kite
galaxy). This separation corresponds to 380 kpc at the galaxy’s adopted
distance (187 Mpc) . The width of the tail is more difficult to constrain
precisely although it is comparable to the width of the Kite galaxy itself,
which is $\sim$ 10 arcsec. This suggests a length-to-width ratio for the tail
of $\sim$ 40\. The position angles on the sky between the Kite galaxy and the
various letter-labelled features along the tail are presented in Table 1 and
illustrate the near-linearity of the tail. Features b and c are somewhat less
consistent with a linear distribution, but the dispersion in position angle
even including these two is only 2.5∘ (it is 0.6∘ without those two features).
Finally, a small galaxy, Kite A, is also projected onto the tail.

Some of the features identified in Figure 1 also have NUV emission (1771 -
2831 Å) that is detectable in the GALEX (Martin et al., 2005) Medium Imaging
Survey (Bianchi et al., 2014) images (see Table 1). We illustrate this finding
of knots near the end of the tail in Figure 2. A check mark in the NUV column
of Table 1 indicates that we visually identified emission in the GALEX image
corresponding to the location of the optically-identified associated feature.
NUV emission typically indicates the presence of relatively young ($\lesssim$
few 100 Myr) stellar populations (e.g. Bianchi, 2011). The presence of such
young stars helps differentiate these knots from other features in the image
and aids in confirming that there are no similar LSB structures beyond feature
j of the tail, on either side of what we have defined to be the tail, or on
the opposite side of the Kite galaxy.

Figure 2: Optical and NUV features toward the end of the Kite tail. Left panel
shows a zoom-in view using the $g$-band image from Figure 1 with features
labelled. Right panel shows the same area drawn from a GALEX NUV image from
the Medium Imaging Survey.

The local environment of the Kite and Mrk 0926 is not one conducive to ram
pressure stripping. The Kite and Mrk 0926 form a triplet system with the
galaxy SDSS J230439.88-083712.6 (Yang et al., 2007). This third galaxy is 2.3
magnitudes fainter than the Kite galaxy and $\sim 300$ kpc away, with no
visible signs of debris or interaction with the main pair. Given its distance,
morphology, and lower mass, this galaxy is unlikely to be related to this
feature. Additionally, there are no other known clusters or groups around this
system within 3 Mpc and 4000 km s-1 (Yang et al., 2007; Szabo et al., 2011;
Wen et al., 2012). In fact, there are only three additional galaxies listed in
SDSS DR7 within 1 Mpc of the Kite galaxy. With such a low local density, it
unlikely that there is a sufficiently dense medium to produce the observed
tail via ram pressure stripping.

##  3 Spectroscopic Follow-Up

###  3.1 Tail Features

We observed most of the features labelled in Figure 1 using the Baade Magellan
telescope and the IMACS spectrograph (Dressler et al., 2011) with the f/4
camera on the nights of 25 and 26 September 2022 in the long slit mode. We
selected the 1200 line grating, for a spectral dispersion of 0.2Å pix-1 (we
then binned 2$\times 2$ pixels) and a wavelength coverage of 6000 to 7600Å,
although here we focus solely on the spectral region around H$\alpha$. We
generally obtained three 15 min exposures, although in two slit positions we
were limited to a single 15 minute exposure by observing conditions, which
were generally variable. We reduced the data in a standard manner, extracted
1-D spectra, visually examined the spectra for emission and absorption lines,
and measured the observed wavelength of the lines using a Gaussian line
fitter. We present heliocentric measurements of $cz$ in Table 1 and use
spectra with multiple emission lines to estimate that the internal recessional
velocity uncertainty is 14 km s-1. The comparison with the SDSS velocity for
the Kite galaxy itself suggests a possible systematic error as large as $\sim
190$ km s-1, but perhaps the SDSS value includes the emission line velocity we
measure, which is much closer to the SDSS value. Regardless, when comparing
our measured kinematics along the tail, the internal uncertainties are the
ones of interest.

In all cases where we are able to measure a redshift for the targeted feature,
that redshift measurement is consistent with the feature being at the distance
of the Kite galaxy. We typically find H$\alpha$ emission in the spectrum of
each targeted feature, especially if we have the full 45 minutes of exposure
time. However, because we employed offset pointing based on broad band optical
images, a lack of H$\alpha$ emission for any target (denoted by the cross in
Table 1) does not necessarily imply a lack of H$\alpha$ flux in that feature.
In two features (a and e), we find measurable [N II] and [S II] in addition to
H$\alpha$. These are weaker than H$\alpha$ and we do not incorporate them into
the redshift measurement. In no other target than the Kite galaxy itself and
Kite A do we detect enough continuum to attempt an absorption line
measurement. With the exception of feature b, the measured recessional
velocities show a gradual, consistent decline from the velocity of the Kite
galaxy toward the tip of the tail with a total amplitude of slightly over 150
km s-1. The velocity gradient demonstrates that the tail is unlikely to be
oriented exactly on the plane of the sky. Hence, it is likely longer than 380
kpc.

In Figure 3 we highlight the kinematic behaviour of the tail near its origin
(Feature a). We find that the ionised gas is kinematically offset from the
stars in the galaxy, as traced by the stellar absorption features, even at
small radii. The emission is also clearly asymmetric relative to the Kite even
at this level of spatial resolution, with no convincing signature of a hidden
second tail with different velocity.

###  3.2 Kite A

Our spectrum of Kite A shows an asymmetric broad absorption line corresponding
to H$\alpha$ in the observed frame of the Kite. Because of the asymmetry our
determination of the line centroid is uncertain at the level of $\sim$ 100 km
s-1. As such we can confidently place Kite A in the Kite environment, but
cannot with similar confidence place it in the tail. Nevertheless, it is
likely that Kite A is in the tail given its precise projection on the tail and
reasonably close redshift. Our best estimate of the redshift (Table 1) places
it along the sequence of velocities for the other features. We speculate that
the asymmetric absorption line arises because Kite A is rotating and the slit
did not evenly sample both sides of the galaxy.

Table 1: Spectroscopic Follow-up Results

Feature | $\alpha$ | $\delta$ | PAa | NUV | H$\alpha$ | $cz^{b}$
---|---|---|---|---|---|---
| (∘J2000) | (∘J2000) | $(^{\circ})$ |  |  | (km s${}^{-1})$
Kitec | 346.1833 |  $-$8.7032 | … | $\times$ | $\times$ | 13991
ad | 346.1871 |  $-$8.7157 | 163.3 | $\times$ | ✓ | 14158
b | 346.1885 |  $-$8.7307 | 169.4 | ✓ | ✓ | 14328
c | 346.1954 |  $-$8.7510 | 166.0 | ✓ | … | …
Kite A | 346.2062 |  $-$8.7709 | 162.0 | ✓ | $\times$ |  $\sim$ 14160
d | 346.2075 |  $-$8.7753 | 161.6 | ✓ | ✓ | 14109
ee | 346.2116 |  $-$8.7860 | 161.3 | ✓ | ✓ | 14058
f | 346.2151 |  $-$8.7982 | 161.7 | ✓ | $\times$ | …
g | 346.2160 |  $-$8.8009 | 161.7 | ✓ | … | …
h | 346.2166 |  $-$8.8055 | 162.2 | ✓ | ✓ | 13989
i | 346.2201 |  $-$8.8090 | 161.0 | ✓ | $\times$ | …
j | 346.2196 |  $-$8.8142 | 162.1 | ✓ | … | …

a PA is measured on the sky, N to E with the Kite galaxy at the origin. No PA
measurement is presented for the Kite because of isophote twisting.

b Heliocentric corrected recessional velocity. The uncertainty is estimated to
be 14 km s-1, except for the Kite A measurement due to uncertainties in the
slit position.

c SDSS $cz$ = 14180 km s-1.

d [N II] also detected.

e [N II] and [S II] also detected.

Figure 3: Emission and absorption features for the Kite and the nearby Feature
a from Figure 1). The bottom panel shows a Gaussian smoothed zoom in on the
Kite 2D spectrum. Spectral direction along the x axis and spatial along the y
axis. Absorption and emission features labelled. The absorption affects the
continuum symmetrically, while the emission is only present below the
continuum spectrum. The H$\alpha$ emission is offset to larger $\lambda$
relative to the absorption. The shift corresponds to 160 km s-1. The H$\alpha$
emission extends 12 arcsec below the continuum, which corresponds to 11 kpc.
The upper panel shows extracted 1D spectra centred on the continuum (dotted
line) and for the region below the continuum where H$\alpha$ emission is
visible (solid line). We have normalised the continua of the two spectra to
simplify comparison. H$\alpha$ absorption is seen in both, although deeper in
the continuum spectrum, while H$\alpha$ and [N II] emission are clear in the
off-continuum spectrum. Flux is in arbitrary linear units.

##  4 Discussion

A natural initial interpretation of the Kite, given its one-sided, linear tail
is that it is the result of ram pressure stripping (RPS). There is at least
one likely RPS feature that is nearly as long (250 kpc; Scott et al., 2022)
although those authors question that feature’s RPS origin. Another RPS tail
(D100; Yagi et al., 2007) is only 60 kpc long but shares many morphological
similarities with the Kite, and yet a third is both long and appears in an
edge-on galaxy (GMP 2640; Smith et al., 2010; Grishin et al., 2021). D100 has
a length-to-width ratio of 30, is linear, and has star formation along its
length (Cramer et al., 2019), although it is more of a polar than a planar
feature relative to its host galaxy. Yagi et al. (2016) struggled to explain
the origin of D100, invoking possible confinement by the ambient intracluster
medium to maintain the high degree of collimation. Subsequent work (Jáchym et
al., 2017; Cramer et al., 2019) advanced the RPS interpretation and invoked an
array of possible mechanisms to maintain the tail’s narrowness (e.g., Tonnesen
& Bryan, 2010b; Roediger & Brüggen, 2008). However, unlike D100 or GMP 2640,
the Kite is not in a dense environment. Hydrodynamic interactions in lower
density environments also occur but show much more subtle features than that
of the Kite (Vulcani et al., 2021b). We conclude that something other than RPS
is responsible for the Kite’s tail. What does this mean for the inferred
origin of the Kite galaxy with its long narrow tail, and possibly for similar
systems like D100 that are attributed to RPS but face difficulties when
modelled in detail?

If we abandon the RPS interpretation for the Kite, then the next most natural
interpretation is that of tidal forces. The tail material could then come
either from the Kite galaxy itself, as tidal material presumably drawn out by
a close passage with Mrk 0926 or a third galaxy (presumably Kite A), or from a
tidally shredded low mass satellite, whose remaining core may be Kite A.
Because tidal tails tend to follow the elliptical nature of the original
orbit, the projected linear nature of the tail suggests that in either
scenario we are viewing the system at a particularly fortuitous orientation
where the interaction happened on a plane perpendicular to the plane of the
sky. This requirement may be somewhat more plausible in the Kite-Mrk 0926
interaction scenario because we at least know that we viewing the Kite galaxy
itself nearly edge-on.

The scenario where the tail is the result of the near destruction of a
satellite galaxy presents an avenue for solving the difficulty in finding
sufficient gas in an S0/a galaxy to form a star-forming tail and the lack of
obvious morphological disturbance in either the Kite galaxy or Mrk 0926.
However, it faces challenges of its own. First, it requires the additional
condition that the satellite orbit lies in (nearly) the same plane as the
Kite’s disk. Second, distributing material from roughly $r=0$ to at least 380
kpc requires a large impulse difference, $\Delta E$, among the dwarf galaxy
constituents that then implies a nearly direct collision with the Kite and a
gravitational potential for the Kite that is sufficiently centrally
concentrated that small differences in impact parameter translate to large
$\Delta E$. Even so, much of the material ejected with the largest velocities
(that currently at the tip of the tail) must be gaseous to power the ongoing
star formation and would need to find its way through the disk plane of the
galaxy. A candidate for the surviving core of this galaxy is Kite A, located
near Feature d at $(346.2061^{\circ},-8.7710^{\circ})$.

Accepting geometrical coincidences, both scenarios face additional hurdles. A
close interaction between the Kite and Mrk 0926, which would be required to
generate a long tidal tail, would also tend to form a bridge between the
galaxies and disturb the morphology of the interacting galaxies (Toomre, 1977;
Barnes & Hernquist, 1992a), neither of which is observed. Additionally, the
interaction typically generates a second long tail from the other galaxy, but
none is observed to emanate from Mrk 0926. The news is not all negative for
this scenario, as giant tidal tails are often found to have star formation
near their ends (Mirabel et al., 1991, 1992).

Regardless of what forces created the tail, there are some general puzzles
that the tail poses. Consider that an age for the tail, $t$, can be estimated
by dividing the length of the tail by the transverse velocity at which the tip
of tail receded from the Kite galaxy, $v_{t}$. By doing so we estimate
$t=371/v_{t}$ Gyr, where $v_{t}$ is in units of km s-1. We do not know
$v_{t}$, but for typical values of galaxy internal velocities or pairwise
velocity differences (Davis & Peebles, 1983) this implies lifetimes of one to
several Gyr. A measurement of the star formation history of the tail would be
one test of this age estimate, but we cannot do this for the emission line
regions with our current data.

Given Kite A’s plausible association with the tail, we attempt to use its
spectral energy distribution (SED) to place constraints on the most recent
star formation, which we might plausibly connect to the age of the tail. We
measure aperture magnitudes, where the circular aperture is defined to include
the W1 flux and is 10.5 arcsec in radius. Our measurements for the FUV, NUV,
$g$, $r$, $z$, W1, and W2 AB magnitudes are 21.7, 21.3, 18.9, 18.1, 17.5,
17.6, and 17.9, respectively. A value of FUV-NUV = 0.4 mag indicates the
presence of a young ($\lesssim$ 300 Myr) stellar population and is nearly a
dust-free indicator (EFUV-NUV = 0.11 EB-V; Bianchi, 2011). We aimed for a more
robust determination using PROSPECTOR (Johnson et al., 2021) to fit stellar
population models to the SED, but found that the uncertainties in age, once a
range of plausible star formation histories is allowed, is too large to
provide a meaningful constraint on our hypothesis.

Adopting an age for the tail of $\gtrsim$ 1 Gyr leads to several apparent
problems. First, star formation, as inferred from the H$\alpha$ detections, is
occurring at various locations along the tail and must be producing at least
some high mass stars to produce the necessary ionising radiation. Note that
H$\alpha$ flux alone in a tail is not sufficient to indicate star formation
(Boselli et al., 2016). However, in our case the knot morphology and the
ubiquitous NUV flux, indicative of young stars, suggests that here the
H$\alpha$ is indeed related to ongoing star formation. This star formation
rate must either be maintained over the $\gtrsim$ Gyr lifetime, or something
must have triggered star formation at nearly 400 kpc from the galaxy in the
last few million years. This may not be a insurmountable challenge because, as
we mentioned before, such star formation is often observed in giant tidal
tails (Mirabel et al., 1991, 1992) and clumping of matter along the tails is
reproduced in simulations (Barnes & Hernquist, 1992b; Elmegreen et al., 1993).
Similarly, star formation is often observed in jellyfish galaxies (Vulcani et
al., 2018; Poggianti et al., 2019).

Second, the dispersion in position angles among the identified features within
the Kite tail, excluding features b and c which appear slightly offset from
the low surface brightness continuous tail, is $0.6^{\circ}$. At 380 kpc this
offset corresponds to 4 kpc. For a $\gtrsim$Gyr lifetime this offset implies
that velocities perpendicular to the tail but on the plane of the sky can not
differ by more than $\sim$4 km s-1, which is smaller than the typical velocity
dispersion in galaxies with substantial gas reservoirs. This suggests either
that there is a mechanism acting to actively maintain the collimation, as
invoked by Yagi et al. (2016) and Jáchym et al. (2017) for D100, or the tail
is much younger than we estimate, which in turn implies that the transverse
velocity is much larger than the typical internal velocities in galaxies. The
latter might lead one to consider more exotic models such as that of a runaway
massive black hole (van Dokkum et al., 2023), although we note that the black
hole model would face its own challenges here. Consider that any
circumgalactic gas parcels that it may have influenced to form stars would
have a velocity consistent with the halo velocity dispersion ($\sim 100$ km
s-1) rather than with the internal velocity dispersion of a putative satellite
galaxy. Such a large velocity would cause the star formation clumps to drift
away from the tail axis at a rate of 125 kpc/Gyr. For us to find the clumps
within $\sim$10 kpc of the tail axis along the entire tail requires that all
of these clumps formed within the last $\sim$ 100 Myr, which in turn implies a
black hole speed of nearly 4000 km s-1 if it is to reach a distance of 380
kpc. As large as this value seems, it is not beyond the realm of possibility
(Campanelli et al., 2007; Healy & Lousto, 2022), although statistically
unlikely (Schnittman & Buonanno, 2007).

Finally, the linearity of the feature is also a challenge considering the
likely asymmetric nature of the gravitational potential at large radii.
Torques on the matter in the tail would seem likely to produce a bend in the
tail over a Gyr timescale even if the original geometry allowed for projection
to create the illusion of linearity. Again, a much shorter tail lifetime would
alleviate such concerns.

###  4.1 Our Proposal

Given the various reasons to favour a short lifetime for the tail and the
presence of Kite A in the tail, we propose a gravitational origin for the tail
arising from the ejection of Kite A from the Kite-Mrk 0926 system. A
hyperbolic orbit, where Kite A has a velocity significantly larger than the
escape speed, not only addresses issues related to the lifetime of the feature
but relaxes the orientation constraints because Kite A and its associated
detritus would be travelling on near linear trajectories in 3-D. There is
still the coincidental alignment of the orbital plane with the Kite’s disk
plane but perhaps that is advantageous in realising an interaction among the
three galaxies that allows Kite A to be ejected. For a time since pericenter
passage of 300 Myr, consistent with the youngest stellar population in Kite A,
Kite A would need to have a mean transverse velocity of 460 km s-1 to reach
its current projected position, which is almost certainly larger than the
escape speed at its current position. The tidal material would both lead and
trail Kite A, resulting in a nearly linear feature with Kite A in the middle.
Finally, a close interaction, which is needed to provide a sufficient kick to
Kite A, might also be responsible for fuelling the central black holes in the
Kite and Mrk 0926 (Liu et al., 2011; Weston et al., 2017).

###  4.2 Other Contexts

We close the discussion by commenting on the implication of the existence of a
system such as the Kite on other interesting systems. We identified this
system initially because Feature i was flagged as a potential UDG. In any of
the formation scenarios envisioned, clumps along the tail are expected to be
dark matter free. If such clumps are able to remain gravitationally bound and
survive they will contribute to a dark matter free galaxy population (Bennet
et al., 2018; van Dokkum et al., 2018). In fact, van Dokkum et al. (2022) note
that their two dark matter free galaxies are part of a large linear sequence
of galaxies. A potential difference between those two galaxies and the
features within the Kite tail is that the former host globular clusters. We do
not yet know if any of the Kite features host globular clusters.

A second interesting class of system is that of the diffuse star-forming
isolated stellar systems found in the Virgo cluster (Jones et al., 2022), but
which might also exist elsewhere. Those authors note that these are at least
140 kpc from any nearby potential parent and are young. They have relatively
high metallicities, suggesting their gas comes from more massive galaxies,
which they interpret to mean a likely RPS origin. However, if the origin of
the gas is as proposed here, from a galaxy like Kite A, then one would expect
to measure a relatively high metallicity.

##  5 Summary

We present the discovery of an extraordinary tail emanating from what we have
dubbed the Kite galaxy. The tail is unusual in its physical length (a
projected length of 380 kpc), its collimation (it has a length to width ratio
of 40), and its linearity (all of the detected knots along the tail scatter in
position angle by less than 3∘). It is oriented parallel to the disk of the
Kite galaxy. The Kite galaxy and its nearby companion, Mrk 0926, are both
active galaxies, with Mrk 0926 being by far the more active.

We present results from spectroscopy at various points along the tail. There
is recent and ongoing star formation along the tail, as evidenced by NUV and
H$\alpha$ flux. The velocities show a moderate velocity gradient along the
tail and demonstrate that the various knots are physically associated with the
tail. We identify a galaxy, Kite A, along the tail that has a velocity that is
consistent with it lying in the tail. This galaxy has UV emission that
indicates the presence of young stars but does not show evidence for ongoing
star formation.

The two most commonly invoked origin scenarios for tail features, ram pressure
or tidal stripping, face significant challenges that we discuss. Of the two,
we have a preference for a tidal origin, but acknowledge the difficulties in
making such a model work. Some of the difficulties are mitigated if the age of
the tail is quite short, but this supposition leads to more exotic formation
models. We propose that a three-body encounter between the Kite, Mrk 0926, and
Kite A resulted in the rapid ejection of Kite A. The resulting hyperbolic
orbit explains the linearity of the debris field and the tail’s narrowness.
Detailed simulations are necessary to assess the viability of this proposal.
We briefly describe how such events may also help explain other puzzling
observations. The Kite system is a record-breaking, enigmatic source that
presents a variety of interesting problems to resolve.

## acknowledgments

DZ acknowledges financial support from AST-2006785 and thanks both the
Astronomy Department at Columbia University for their gracious welcome during
his sabbatical and Greg Bryan for discussions about this object. JPC
acknowledges financial support from ANID through FONDECYT Postdoctorado
Project 3210709. YLJ acknowledges financial support from ANID BASAL project
No. FB210003. MS acknowledges support from the NASA grant 80NSSC22K0353, and
the USRA award 9_0221, under NASA contract NNA17BF53C. BV acknowledges support
from the INAF Mini Grant 2022 “Tracing filaments through cosmic time” (PI
Vulcani). ACCL thanks for the financial support of the National Agency for
Research and Development (ANID) / Scholarship Program / DOCTORADO BECAS
CHILE/2019-21190049. KS acknowledges support from the Natural Sciences and
Engineering and Research Council of Canada. This research has made use of the
NASA/IPAC Extragalactic Database, which is funded by the National Aeronautics
and Space Administration and operated by the California Institute of
Technology. This paper includes data gathered with the 6.5 meter Magellan
Telescopes located at Las Campanas Observatory, Chile. .

## Data Availability

The optical imaging presented here is publicly available through the Legacy
Survey (https://datalab.noirlab.edu/ls/dataAccess.php) while the NUV data is
available through the Mikulski Archive for Space Telescopes (MAST;
https://science.nasa.gov/astrophysics/astrophysics-data-centers/multimission-
archive-at-stsci-mast). We present the results from Magellan spectroscopy in
Table 1 and the 2-D spectra will be shared upon reasonable request to the
corresponding author.

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# A Simple Feature Method for Prosody Rhythm Comparison

###### Abstract

Of all components of Prosody, Rhythm has been regarded as the hardest to
address, as it is utterly linked to Pitch and Intensity. Nevertheless, Rhythm
is a very good indicator of a speaker’s fluency in a foreign language or even
of some diseases. Canonical ways to measure Rhythm, such as $\Delta C$ or
$\%V$, involve a cumbersome process of segment alignment, often leading to
modest and questionable results. Perceptively, however, rhythm does not sound
as difficult, as humans can grasp it even when the text is not fully
intelligible. In this work, we develop an empirical and unsupervised method of
rhythm assessment, which does not rely on the content. We have created a
fixed-length representation of each utterance, Peak Embedding (PE), which
codifies the proportional distance between peaks of the chosen Low-Level
Descriptors. Clustering pairs of small sentence-like units, we have attained
averages of 0.444 for Silhouette Coefficient using PE with Loudness, and 0.979
for Global Separability Index with a combination of PE with Pitch and
Loudness. Clustering same-structure words, we have attained averages of 0.196
for Silhouette Coefficient and 0.864 for Global Separability Index for PE with
Loudness.

Index Terms: prosody, rhythm embeddings, rhythm comparison, prosody assessment

##  1 Introduction

The word Rhythm comes from a Greek word which means regular movement, as the
pace of a poem or the metrics of a verse. Prosody-wise, Rhythm is the cadence
and alternation of stressed and unstressed syllables. The components of
prosody – Pitch, Loudness, Rhythm – are often referred to as if they were
independent and disentagleable. That is true for Pitch and Loudness, which are
the perceptual qualities of physical quantities of the sound – F0 and
intensity, respectively – which can have well-defined values in the spectrum.
Rhythm, however, is not a physical quantity that is measurable on a frame-
basis. Instead, it is a measure of how the other two behave in time.

The concept of Rhythm is often erroneously taken as a synonym of speech rate
[1, 2]. Whereas Rhythm is about the proportion of the distances between
stressed syllables, speech rate is about how fast a speaker utters a sentence-
like unit (SLU). Consider, for example, the sentence ”Please call Stella” from
the VCTK corpus111More on this corpus later on.. The distance between the
first and the second stressed syllables and the distance between the second
and the third stressed syllables approximately keep their proportion across
different speakers. However, the length of this utterance ranges from 0.9
seconds (for fast speakers) to 1.71 seconds (for slow speakers). Considering
these extreme cases, we can say that the Rhythm is the same, but the speech
rate is very different.

Most of the features that have been used to describe Rhythm do not encompass
how the stresses are distributed along the utterances, but consist of average
metrics instead. In this work, we look for a feature that allows to compare
prosody while encompassing Rhythm information, and that allows for a direct
and simple comparison of two SLUs. This is mostly attainable if all SLUs are
represented by feature vectors of the same length. In a previous work [3], we
explored the use of prosody transfer embeddings for prosody comparison. Here,
we propose to extract a vector of fixed-length enconding which represents the
maxima of prosodic features in their position in the segment. To this we call
Peak Embedding (PE). We take 10 SLUs which are phonetically rich and
rhythmically contrastive, utterred by many speakers, and evaluate their
clustering. Assuming that SLUs with the same text share Rhythm, Intonation and
Energy to a large degree, we hypothesise that these features are as good to
discriminate prosody as they are able to generate good clustering metrics.
Based on the same principles, we take 5 words with two different rhythmic
structures, and evaluate the extent to which these two rhythmic classes are
clustered.

##  2 Related Work

To account for the rhythmic distinction between stressed-timed and syllable-
timed languages, and clarify how Rhythm might be extracted from the speech
signal, Ramus [4] proposed three different features, each taking one value per
utterance: (1) the proportion of vocalic intervals within the sentence (%V),
(2) the standard deviation of the duration of vocalic intervals within each
sentence ($\Delta V$), as well as (3) the standard deviation of the duration
of consonantal intervals within each sentence ($\Delta$C). Other metrics have
also been proposed, such as PVI [5], based on the sum of the differences
between pairs of consecutive intervals, or YARD [2], a metric similar to PVI
in which z-transformed syllable durations are used for calculation, rather
than raw intervals.

In a large review of Rhythm metrics, Arvaniti [6] concluded that in spite of
their abundant use, most of these metrics are largely affected by
methodological choices like the type of speech (spontaneous/read), or the
syllable complexity of the texts. As Wagner [2] states, Ramus’ Rhythm measures
“provide a working discrimination of rhythmic classes based on syllable
complexity, but they miss a representation of the sequential nature of
Rhythm”. Furthermore, this class of metrics requires a considerable overhead
of segment alignment and processing.

Other methods rely on the Envelope Modulation Spectrum, proposed by Tilsen
[7], which uses spectral analysis of the amplitude envelope of vocalic energy.
Studies on intelligibility for different diseases or health impairments have
used this method later on [8, 9, 10].

In the speech conversion realm, [11] developed a system to convert the Pitch,
Content, Rhythm or Timber from a source sentence into the same component of a
target utterance. This was achieved by using a triple information bottleneck
on a system with an encoder for each component (except timber). MOS results
showed that not only the conversion of Rhythm was less successful than the
conversion of Content and Pitch, but also that when Rhythm was paired with
another component the results were worse than with the other component alone.
This points towards the difficulty in actually separating Rhythm from the
other components. More recently, [12] developed another system of speech style
conversion, this time focusing on Rhythm. Interestingly, the MOS were better
than in [11] and Rhythm was not assessed separately from the other components.

##  3 Methodology

The methodology we follow consists of analysing data corresponding to
different sentence-like units (SLU) with Peak Embeddings based on two
different features: Pitch and Loudness. As a baseline, we used temporal
functionals. We take as a premise that (1) two SLUs with the same content and
context, and uttered by native speakers are very similar prosody-wise; (2) a
feature is as good to encode prosody as it is able to lead to well-separated
clusters of contrastive utterances. At second step, we inspect the clustering
behaviour of words, assuming that words with the same stressed syllable
distribution and intonation have similar rhythmic patters. We analyse this by
using specific metrics to assess clustering. We also inspect the t-SNE
projections [13]222t-SNE is a method that permits visualization of data in a
two-dimensional space. of the utterances.

###  3.1 Features

####  3.1.1 Baseline Functionals

The Geneva Minimalistic Acoustic Parameter Set (eGeMAPS) [14] is a set of
functionals computed on top of LLDs, specifically chosen to provide a common
ground for research in various areas of automatic voice analysis, namely
paralinguistics. For a baseline, we used the six temporal features of eGeMAPS:
rate of loudness peaks, mean length and standard deviation of continuously
voiced regions, mean length and standard deviation of unvoiced regions, number
of continuous voiced regions per second (pseudo-syllable rate). Each of these
features corresponds to one global value per SLU, which means that, in
practice, it is not possible to reflect the local properties of the utterance,
on which Rhythm heavily relies. Having these features as a baseline shall help
us better understand the contribution of the Peak Embeddings we are proposing
here. Also, these features resemble the features of [4], described in Section
2, thus providing us with an interesting reference.

####  3.1.2 Peak Embeddings

The Peak Embeddings (PE) we propose are extracted as follows: (1) Take a low-
level descriptor of a speech segment; (2) Normalise; (3) Smooth with moving
average; (4) Divide into 10 equal-sized chunks; (5) Do max-pooling of each
chunk. As a result, these embeddings have a fixed dimension, which allows them
to store information about the proportional regions where peaks occur, thus
also encompassing durational aspects. We have extracted PE for Pitch and
Loudness, as these are the components of Prosody with direct acoustic
correlates. By using these embeddings we are incorporating the temporal
dimension of Pitch and Loudness. For Pitch and Loudness, we used the LLDs of
eGeMAPS. We have also combined the PE of Pitch with the PE of Loudness, both
by concatenation (;) and sum (+).

###  3.2 Clustering Metrics

####  3.2.1 Silhouette Coefficient

The Silhouette Coefficient [15] measures how the samples in a data set are
similar to the ones of its own class when compared to samples in other
classes. It ranges from -1 to 1, where negative values mean assignments to the
wrong cluster, 0 indicates cluster overlap, and 1 indicates the best
separation possible. For each sample x, the Silhouette Score is

$S=\frac{b(x)-a(x)}{max(a(x),b(x))}\,,$ (1)

where $a(x)$ is the mean intra-cluster distance and $b(x)$ is mean nearest-
cluster distance. The Silhouette Coefficient is the mean Silhouette Score of
all samples.

####  3.2.2 Geometrical Separability Index

Thornton Index (TH) [16], also known as Geometrical Separability Index (GSI),
corresponds to the fraction of a set of points that have the same
classification labels as their first neighbour. It can be described as

$GSI=\frac{1}{n}\Sigma^{n}_{i=1}f(x_{i},x^{\prime}_{i})\,,$ (2)

where $x^{\prime}_{i}$ is the nearest neighbour of $x_{i}$, $n$ is the number
of points, $f$ is a function that is 1 if $x_{i}$ and $x^{\prime}_{i}$ belong
to the same class and zero otherwise. Therefore, GSI will tend to 1 if
opposite labels exist in well-separated groups [17].

##  4 Experiments

###  4.1 Corpora

####  4.1.1 VCTK Data Set

We have used the CSTR VCTK Corpus [18]. It comprises 110 English speakers of
different varieties of English, with approximately 400 utterances per speaker.
These correspond to a phonetically-rich paragraph, which is common to all
speakers, and a newspaper text which is different for all speakers. We
considered only the sentences of the phonetically rich paragraph. For more
size homogeneity, we cropped the original sentences into the resulting SLU in
Table 1.

Table 1: Sentence-Like Units. $\sim$ means that a part of the original utterance was omitted on that place. ID | Text
---|---
001 | Please call Stella.
002 |  Ask her to bring these things $\sim$
003 |  Six spoons of fresh snow peas $\sim$
004 |  $\sim$ a big toy frog for the kids.
005 |  She can scoop these things into three red bags $\sim$
006 |  $\sim$ they act like a prism and form a rainbow.
007 |  The rainbow is a division of white light $\sim$
008 |  These take the shape of a long round arch $\sim$
009 |  $\sim$ a boiling pot of gold at one end.
010 | People look but no one ever finds it.

####  4.1.2 Intonation Data Set

We used a small intonation data set, comprising 20 original stimuli recorded
by a native female speaker of Standard European Portuguese and reproductions
of it by 17 different speakers. The 20 original stimuli correspond to the
possible combinations of five words: Banana, Bolo, Gelado, Leite, and
Ovo333The translation of these words in English is, respectively, Banana,
Cake, Ice Cream, Milk, and Egg. with four different intonations: Declarative,
Interrogative, Pleasure, and Displeasure. Each utterance corresponds to one
word uttered with one particular intonation. In total, there are 340 imitation
utterances, of which 320 are labelled as good, which are the ones we used.

###  4.2 Experimental Set Up

####  4.2.1 Sentence-Like Units

We computed the clustering metrics of all 45 ($C_{10,2}=45$) possible pairs of
SLUs, for all features we are considering. To better understand the utility of
each feature, we computed the average value of each cluster metric for each
feature and all pairs (Table 2).

####  4.2.2 Isolated Words

We computed the clustering metrics of all 4 intonation types, for all features
we are considering. We compared the Rhythm of different words by assuming that
words with a similar syllabic structure have similar Rhythm. Given five words
with stress on the penultimate syllable (paroxytone), we split them into two
classes: words with 3 syllables (“banana”, “gelado”) and words with 2
syllables (“bolo”,“leite”, “ovo”). We are comparing within each intonation
type, as we expect that the same word can have different rhythms for different
intonations. Average results for each intonation type are on the right-most
columns of (Table 2).

###  4.3 Results

The average Clustering Metrics are in Table 2. The best clustered SLU pairs
with different Peak Embeddings are in Table 3. The t-SNE projections of the
pairs of SLUs with the best clustering results for different PEs are in Figure
1. The t-SNE projection of the intonation type with the best clustering
results for words of different Rhythm is in Figure 2.

Table 2: Clustering Metrics: average for the 45 pairs of SLU; average for the 4 intonation types. | SLU | Word
---|---|---
|  SC $\uparrow$ |  GSI $\uparrow$ |  SC $\uparrow$ |  GSI $\uparrow$
Baseline Funcs. | 0.147 | 0.730 | 0.112 | 0.796
Pitch | 0.371 | 0.951 | 0.040 | 0.744
Loudness | 0.444 | 0.958 | 0.196 | 0.864
Pitch; Loudness | 0.394 | 0.979 | 0.137 | 0.841
Pitch+Loudness | 0.400 | 0.955 | 0.127 | 0.795
Table 3: SLUs with best(+) and worst(-) clustering metrics for each feature type. (Good results are easier to attain when SLUs are prosodically more different.) | Pitch | Loudness
---|---|---
+ | (4,10) | (3,9) | (8,9) | (3,6) | (3,9) | (5,10)
| (5,9) | (6,10) | (5,10) | (6,10) | (4,10) | (5,9)
- | (5,6) | (7,9) | (2,8) | (2,7) | (1,5) | (3,8)
| (5,8) | (3,8) | (9,10) | (1,7) | (1,9) | (7,9)
| P;L | P+L
+ | (4,6) | (6,8) | (6,10) | (8,9) | (3,8) | (1,9)
| (5,10) | (5,9) | (3,9) | (4,10) | (3,6) | (5,9)
- | (1,9) | (7,9) | (1,7) | (5,6) | (3,8) | (1,9)
| (5,8) | (1,2) | (2,8) | (1,6) | (7,9) | (1,5)

(a)

(b)

(c)

(d)

Figure 1: t-SNE projections of the pairs of SLUs which attained the best
clustering results for Peak Embeddings on based on Pitch (P), Loudness(L),
Pitch;Loudness (P;L) and Pitch+Loudness (P+L). Values on top of the plots
correspond to SC and GSI, respectively). Figure 2: t-SNE projection for words
of different syllable structure, with intonation Displeasure, Peak Embeddings
of Loudness.

##  5 Discussion

On the left-most columns (SLU) of Table 2 we see that Peak Embeddings based on
Loudness achieve the best clustering results of all for SC, and the second
best for GSI. This indicates that a temporal representation of Loudness can
account for most of the prosodic differences between SLUs. Cluster compactness
(measured by the SC) does not improve when we combine Pitch to Loudness.
Global Separability improves when we concatenate Loudness and Pitch; it does
not improve when we add them. This means that Loudness and Pitch provide
different types of informativeness and that their peaks do not necessarily
coincide. On the right-most columns (Word) of Table 2 we see that Peak
Embeddings based on Loudness achieve the best clustering results of all for
both metrics. For single words, the information of Loudness in time is what
better accounts for a word’s rhythm. We see in the example of Figure 2 that,
although with little compactness, words with two syllables tend to be
separated from words of three syllables. However, the most relevant result in
Table 2 is that in all cases Peak Embeddings attain better results than the
Baseline Results, which means that Rhythm comparison based on functionals is
clearly suboptimal. Percentages of consonants and vowels do not give us much
information on the rhythm of a specific sentence, as it does not have
information on the places where stresses (peaks) happen.

Looking at SLUs with the best and worst separation, in Table 3, some sentence
pairs are noteworthy. For all features, pairs (7,9) and (1,9), are amongst the
pairs with worst separability. As these sentences are not particularly similar
in terms of prosody, we argue this may be due to prosody caracteristics that
are more difficult to encode or even high speaker variability. (5,9) is
amongst the best for all the considered features; (3,9), (5,10), (4,10),
(6,10) are amongst the best for three of the features. They share the fact
that in each pair none of the sentences is trimmed at the same end: either
they are trimmed on opposite ends or one is trimmed and the other is not.
(8,9) is only at the top six for Pitch and P+L, possibly because Pitch is what
better accounts for the different intonations of the SLUs (rising vs falling).

In any case, we ought to say that the results we have for separability are
fairly high, as we saw in Table 2. The difference between most pairs’
clustering is more about the compactness of the cluster than it is about the
separability of the set. This means that these results should be taken with
some caution, as the metrics for the SLU pairs are very close and the
threshold we are imposing (six best SLUs) can make us ignore relevant pairs.

##  6 Conclusion

In this work, we have assessed a method for representing maxima of prosody
Low-Level Descriptors in time, Peak Embeddings. We have explored how they can
account for the rhythmic properties of variable-length speech segments, by
assessing how different pairs of SLUs and words were clustered. For SLUs, we
reached an average GSI of 0.979 when concatenating the Peak Embeddings of
Pitch and Loudness, and an average of 0.444 SC for Peak Embeddings of Loudness
only, against an SC of 0.147 and a GSI of 0.730 for the temporal features of
eGeMAPS, which we took as baseline. For words, we reached an average GSI of
0.864 and 0.196 SC with for Peak Embeddings of Loudness, against an SC of
0.112 and a GSI of 0.796 for baseline features. This strengthens our
conviction that a description of Rhythm – or Prosody, in general – without
local sensitivity is doomed to be poorly informative, and that a temporal
representation of prosodic features is very relevant. As future work, we would
like to investigate how robust this method is across languages and utterance
types.

##  7 Acknowledgements

This work was supported by national funds through Fundação para a Ciência e a
Tecnologia (FCT), with reference UIDB/50021/2020 and PhD grant
SFRH/BD/139473/2018.

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