# MIGHTEE-Hi: The relation between the Hi gas in galaxies and the cosmic web

Madalina N. Tudorache,1 M. J. Jarvis,1,2 I. Heywood,1,3,4 A. A. Ponomareva,1
N. Maddox,5 B. S. Frank,4,6,7 N. J. Adams,8 R. A. A. Bowler,8 I. H.
Whittam,1,2 M. Baes,9 H. Pan,2,1 S. H. A. Rajohnson,7 F. Sinigaglia,10,11 K.
Spekkens12
1Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford
OX1 3RH, UK
2Department of Physics and Astronomy, University of the Western Cape, Robert
Sobukwe Road, 7535 Bellville, Cape Town, South Africa
3Department of Physics and Electronics, Rhodes University, PO Box 94,
Makhanda, 6140, South Africa
4South African Radio Astronomy Observatory, 2 Fir Street, Black River Park,
Observatory, Cape Town 7925, South Africa
5University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität,
Scheinerstr. 1, 81679 Munich, Germany
6The Inter-University Institute for Data Intensive Astronomy (IDIA),
Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch,
7701, South Africa
7Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch
7701, South Africa
8Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy,
School of Natural Sciences, The University of Manchester, Manchester,
M13 9PL, UK
9Sterrenkundig Observatorium, Department of Physics and Astronomy,
Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium
10Department of Physics and Astronomy, Università degli Studi di Padova,
Vicolo dell’Osservatorio 3, I-35122, Padova, Italy
11INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5,
I-35122, Padova, Italy
12Department of Physics and Space Science, Royal Military College of Canada,
PO Box 17000, Station Forces, Kingston, Ontario, K7K 7B4, Canada E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We study the 3D axis of rotation (3D spin) of 77 Hi galaxies from the MIGHTEE-
Hi Early Science observations, and its relation to the filaments of the cosmic
web. For this Hi-selected sample, the alignment between the spin axis and the
closest filament ($\lvert\cos\psi\rvert$) is higher for galaxies closer to the
filaments, with $\langle\lvert\cos\psi\rvert\rangle=0.66\pm 0.04$ for galaxies
$<5$ Mpc from their closest filament compared to
$\langle\lvert\cos\psi\rvert\rangle=0.37\pm 0.08$ for galaxies at $5<d<10$
Mpc. We find that galaxies with a low Hi-to-stellar mass ratio
($\log_{10}(M_{\rm HI}/M_{\star})<0.11$) are more aligned with their closest
filaments, with $\langle\lvert\cos\psi\rvert\rangle=0.58\pm 0.04$; whilst
galaxies with ($\log_{10}(M_{\rm HI}/M_{\star})>0.11$) tend to be mis-aligned,
with $\langle\lvert\cos\psi\rvert\rangle=0.44\pm 0.04$. We find tentative
evidence that the spin axis of Hi-selected galaxies tend to be aligned with
associated filaments ($d<10$ Mpc), but this depends on the gas fractions.
Galaxies that have accumulated more stellar mass compared to their gas mass
tend towards stronger alignment. Our results suggest that those galaxies that
have accrued high gas fraction with respect to their stellar mass may have had
their spin axis alignment with the filament disrupted by a recent gas-rich
merger, whereas the spin vector for those galaxies in which the neutral gas
has not been strongly replenished through a recent merger tend to orientate
towards alignment with the filament. We also investigate the spin transition
between galaxies with a high Hi content and a low Hi content at a threshold of
$M_{\mathrm{H{\sc{I}}}}\approx 10^{9.5}M_{\odot}$ found in simulations,
however we find no evidence for such a transition with the current data.

###### keywords:

galaxies: kinematics and dynamics – galaxies: evolution – galaxies: formation
– cosmology: large-scale structure of Universe

††pubyear: 2021††pagerange: MIGHTEE-Hi: The relation between the Hi gas in
galaxies and the cosmic web–MIGHTEE-Hi: The relation between the Hi gas in
galaxies and the cosmic web

##  1 Introduction

On the largest scales, the Universe contains a network-like distribution of
galaxies, gas and dark matter - the cosmic web (Bond et al., 1996). This
cosmic web, formed of clusters, walls, voids and filaments, was predicted by
Zel’dovich’s model of the evolution of the non-linear growth of primordial
density perturbations (Zel’dovich, 1970). Early evidence of its existence was
presented in Davis et al. (1982) and de Lapparent et al. (1986), who found a
web-like distribution of galaxies. The efforts to trace this elusive web have
continued since, as more and more galaxy surveys such as the Sloan Digital Sky
Survey (SDSS, York et al. 2000), the 2dF Galaxy Redshift Survey (2dFGRS,
Colless et al. 2001) or the 2MASS Redshift Survey (2MRS, Huchra et al. 2012)
were conducted. As well as using galaxy catalogues, N-body simulations showed
that cold dark matter (CDM) could be responsible for the formation of the
voids, walls and filaments (e.g. Springel et al., 2005).

Tracing the cosmic web is vital for understanding the environment of the
galaxies. Several galaxy properties, such as stellar mass, colour, star
formation rate (SFR) and specific star formation rate (sSFR) have been shown
to be sensitive to the external conditions. Using the SDSS, Kuutma et al.
(2017) showed that for a fixed environment density level, there was a higher
elliptical-to-spiral ratio towards the filament spines and a decrease in SFR,
however this occurs without an increase in mass. Laigle et al. (2017) showed
that for the COSMOS catalogue, massive galaxies were closer to filaments, and
for fixed stellar mass, red galaxies were closer to the spine of the filament.
Furthermore, studies such as Kleiner et al. (2017) and Crone Odekon et al.
(2018) have investigated the link between the neutral hydrogen (Hi) content in
galaxies and the large-scale structures, with different results regarding the
correlation between position of the galaxy and its Hi content, and how it is
fuelled by the filaments.

A key property of galaxies is their angular momentum, which could improve our
understanding of their morphology and its dependence on the environment.
Strong evidence of the alignment of the angular momentum vector of the
galaxies and their associated filament is yet to be found. Since the first
study on this topic in a hydrodynamical simulation by Hahn et al. (2010), who
reported that massive disk galaxies were aligned with the filaments, several
other hydrodynamical simulation studies carried out do not agree with this
result. The most significant prediction in the current literature is that low-
mass galaxies tend to be rotationally aligned with their closest filaments,
whilst high-mass galaxies have a tendency towards mis-alignment. This arises
from the theoretical considerations of the tidal torque theory (Peebles, 1969;
White, 1984), which relates the spin angular momentum of a proto-galaxy to its
tidal interactions with the surrounding matter. Simulations such as those by
Aragón-Calvo et al. (2007), Dubois et al. (2014a); Codis et al. (2015) and
Kraljic et al. (2020) confirm this result, whilst Ganeshaiah Veena et al.
(2018) also predict alignment between the angular momentum vector of the dark
matter haloes and the filaments of the cosmic web. Whilst the simulations
mentioned above find hints of a spin transition from alignment to mis-
alignment - for example, Kraljic et al. (2020) find a spin transition for a
stellar mass of $\sim 10^{10}M_{\odot}$, other simulations such as Ganeshaiah
Veena et al. (2018) find no such transition and report a preference for
overall mis-alignment at all masses.

Observational evidence for a spin-alignment at a certain stellar mass is
lacking. Krolewski et al. (2019) reports no spin alignment using the Mapping
Nearby Galaxies at Apache Point Observatory (MaNGA; Bundy et al., 2015)
integral-field survey, whilst Welker et al. (2020) finds a spin transition
within a stellar-mass interval of $10^{10.4}M_{\odot}-10^{10.9}M_{\odot}$
using the Sydney-AAO (Australian Astronomical Observatory) Multi-object survey
(SAMI, Croom et al. 2012).

Concentrating on the Hi gas, Kraljic et al. (2020) find a possible spin
transition threshold in Hi mass at $M_{\mathrm{H{\sc{I}}}}=10^{9.5}M_{\odot}$
using the SIMBA (Davé et al., 2019a) simulation. Blue Bird et al. (2020),
using the COSMOS Hi Large Extragalactic Survey (CHILES, Fernández et al.
2016), find that the spins of their galaxies in their HI-selected sample tend
to be aligned with the cosmic web. However, their study does not find any
significant mass transition between the aligned and the mis-aligned spin. In
addition to a mass dependence, the type of the galaxy has also been shown to
relate to the filaments. Kraljic et al. (2021) using the MaNGA integral-field
survey find that the spins of late-type galaxies (LTGs) are preferentially
aligned to their closest filament, whilst S0 type galaxies have a preferential
perpendicular alignment to their closest filament. The result regarding the
elliptical/S0 galaxies has been previously identified in studies such as
Tempel et al. (2013) using SDSS and Pahwa et al. (2016) using the 2MASS
Redshift Survey. Scd types have also been shown to have a preferential
parallel alignment, whilst Sab galaxies have been shown to have a preferential
perpendicular alignment (Hirv, A. et al., 2017). There are, however, studies
which find no particular preference for alignment for spiral galaxies (Pahwa
et al., 2016; Krolewski et al., 2019), or they find a perpendicular preference
for alignment for these galaxies (Lee & Erdogdu, 2007).

As is clear, the overall picture of the relationship between the galaxy spin
vector and the direction of the filaments in which it may reside is confusing,
with many results from both simulations and observations disagreeing to
different degrees. Thus, further work is necessary to elucidate the link
between these properties of galaxies and the large scale structure.

For this study, we use a Hi galaxy sample provided by the MeerKAT
International GigaHertz Tiered Extragalactic Exploration (MIGHTEE, Jarvis et
al. 2016) Early Science release to compute the 3D spin vector of the galaxies,
using optically-selected galaxies from the COSMOS and XMM-LSS fields, to find
the filaments of the cosmic web. The sample we use is the largest Hi sample to
date used to conduct a study like this, which enables us to make stronger
statistical statements than in Blue Bird et al. (2020). This allows us to
compute the angular momentum using position angles and inclinations from the
Hi moments, which was not possible in studies such as Kleiner et al. (2017) or
Crone Odekon et al. (2018), since they used single-dish surveys with large
numbers of detections, but without the power to sufficiently resolve
kinematics for many of the sources. The structure of this paper is organised
as follows. Section 2 introduces the MIGHTEE Survey, as well as the methods
employed to compute the cosmic web and the spin of the Hi galaxies. Section 3
discusses the results obtained. The summary and conclusions are presented in
Section 4.

##  2 Methodology

Table 1: Short summary of the MIGHTEE-HI Early Science data products used in this paper. Area covered |  $\sim 1$ deg2 COSMOS field
---|---
$\sim 3$ deg2 XMM-LSS field
Frequency range |  $1320-1410$ MHz
Redshift range |  $0.02-0.09$
Channel width |  $209$ kHz
Median $\mathrm{H}_{\mathrm{I}}$ channel rms noise |  $85$ $\mu$Jy beam-1
$N_{\mathrm{HI}}$ sensitivity ($3\sigma$) |  $1.6\times 10^{20}$ cm-2 (per channel)
Synthesised beam |  $14.5"x11"$ COSMOS field
$12"x10"$ XMM-LSS field
Hi mass lower limit |  $\sim 10^{6.7}M_{\odot}(z=0.02)$
$\sim 10^{8.5}M_{\odot}(z=0.09)$

###  2.1 The MIGHTEE survey

Figure 1: The filament distribution projected in 2D obtained by running
DisPerSE with mirror boundary conditions for the COSMOS catalogue in a
redshift interval $0.02<z<0.09$. Left: Angular distance in right ascension
versus angular distance in declination. Top right: Radial comoving distance
versus angular distance in declination. Bottom right: Radial comoving distance
versus angular distance in right ascension of the filament distribution
overlaid on top of the galaxies in the optical sample. The red stars represent
the Hi galaxies detected by MIGHTEE. The colour bar represents the radial
comoving distance in Mpc.

The MIGHTEE survey is one of the eight Large Survey Projects (LSPs) which are
being undertaken by MeerKAT (Jonas, 2009). MeerKAT consists of an array of 64
offset-Gregorian dishes, where each dish consists of a main reflector with a
diameter of $13.5$ m and a sub-reflector with a diameter of $3.8$ m. MeerKAT’s
three band receivers, UHF–band ($580<\nu<1015$ MHz), L–band ($900<\nu<1670$
MHz) and S–band ($1750<\nu<3500$ MHz) all collect data in spectral mode. The
MIGHTEE survey has three major components: radio continuum (Heywood et al.,
2021), polarisation and spectral line. For this work we use the spectral line
information in the L–band with $4096$ channels with a channel width of $209$
kHz, which corresponds to $44$ km s-1 at $z=0$.

MIGHTEE-Hi (Maddox et al., 2021) is the Hi emission part of the MIGHTEE
survey. Its initial data products, as part of the Early Science release, were
obtained using the ProcessMeerKAT calibration pipeline (Frank et. al in
prep.). This pipeline is a paralellised CASA111http://casa.nrao.edu-based
(McMullin et al., 2007) pipeline whose calibration routines and strategies are
standard (i.e. flagging, delay, bandpass, and complex gain calibration). It
performs spectral-line imaging using CASA’s TCLEAN task. The continuum
subtraction was done in two domains. Visibility domain subtraction was
perfomed using the standard CASA routines UVSUB and UVCONTSUB. This process
was followed by an image plane based continuum subtraction using per-pixel
median filtering, which was applied to the resulting data cubes to reduce the
impact of the direction-dependent artefacts. An in-depth description of the
procedures employed for data reduction and data quality assessment will be
presented in Frank et al. (in prep.). The summary of the data used in this
paper is shown in Table 1.

There are $\sim 270$ galaxies in the full Early Science Hi catalogue. In this
paper we use a reduced sample of $77$ galaxies taken from Ponomareva et al.
(2021), with the number being lower than the full Early Science catalogue due
to two factors. The first is that we could not obtain accurate kinematically
measured inclination and position angles for 183 galaxies due to insufficient
signal-to-noise (our kinematic modelling (Ponomareva et al., 2021) requires
$>3.5\sigma$ per resolution element) and/or not being sufficiently spatially
or spectrally resolved in the MIGHTEE data cube (our kinematic modelling
requires at least three resolution elements, both spatially and spectrally;
beam and channel width are shown in Table 1). The second factor is that the
redshift range we chose ($0.02<z<0.09$) means we remove a further $10$
galaxies from the sample. We adopt this cut due to the small number of
spectroscopic redshifts for galaxies within the COSMOS and XMM-LSS fields at
$z<0.02$, which do not provide enough information to identify the filamentary
structures.

###  2.2 The Cosmic Web

Several computational techniques have been developed for the detection of
large-scale structures (see Libeskind et al. (2017) for a full review of all
available algorithms). The Discrete Persistent Structure Extractor (DisPerSE,
Sousbie 2011) is a topological algorithm based on discrete Morse theory
(Milnor, 1963) that computes the skeleton of the cosmic web using Delaunay
Tessellation Field Estimator (DTFE; Schaap & van de Weygaert, 2000). This is
achieved by using the DTFE on a distribution of particles or a distribution of
galaxies resulting in a density field. As the filaments are string-like
structures connecting the galaxy clusters and bordering the voids, the DTFE
can easily detect the variations in the field due to the structures. DisPerSE
has been used to compute the filaments in studies such as Galárraga-Espinosa
et al. (2020) for the Illustris-TNG simulation (Nelson et al., 2019), in
Laigle et al. (2017) for the Horizon-AGN simulation (Dubois et al., 2014b) and
in Kraljic et al. (2020) for the SIMBA simulation (Davé et al., 2019b).
DisPerSe has also been used to compute filaments from observations such as the
CHILES survey by Luber et al. (2019), the Galaxy And Mass Assembly survey
(GAMA, Driver et al. 2009) by Kraljic et al. (2017) and SDSS by Winkel et al.
(2021).

In this paper we use DisPerSE to determine the skeleton of the cosmic web
based on the distribution of galaxies from the COSMOS and XMM-LSS fields.
These are two of the most widely studied extragalactic fields accessible from
the southern hemisphere and have been the subject of a large number of multi-
wavelength surveys over the past decade. In this paper we use the imaging data
described in Adams et al. (2021), which includes optical and near-infrared
imaging from the HyperSuprimeCam Strategic Survey Programme DR1 (HSC; Aihara
et al., 2018) and near-infrared imaging is sourced from the UltraVISTA survey
in the COSMOS field (McCracken et al., 2012) and the VISTA Deep Extragalactic
Observations (VIDEO; Jarvis et al., 2013) Survey in the XMM-LSS field.
Spectroscopic redshifts from a variety of surveys have been compiled by the
HSC team222https://hsc-release.mtk.nao.ac.jp/doc/index.php/dr1_specz/ and we
use these in this paper. These spectroscopic data provide the accurate
redshifts for the filament finding and the imaging data provide the spectral
baseline to derive stellar mass estimates of the galaxies within our sample.

We use all spectroscopic redshifts over the redshift range $0.02<z<0.09$, from
a range of surveys and summarised in Adams et al. (2021). Within this range,
we have 500 spectroscopic redshifts in the COSMOS field, and 2197
spectroscopic redshifts in the XMM-LSS field. We note that the heterogeneous
nature of the spectroscopic redshifts across these fields may results in
biases in some relations. For this reason, we restrict our analysis to those
relations that should be largely invariant to the heterogeneous nature of the
spectroscopic redshifts, i.e. those concerning the alignment of the galaxies’
spin axis with the direction of the filaments.

To find the filaments, the critical points of the density field are
identified: we obtain maxima, minima and saddle points. The filaments
themselves are computed by connecting a maximum point to a saddle point. As an
algorithm, DisPerSE can also return the walls, voids and clusters if needed.
The distribution of the filaments is dependent on two important parameters:
the boundary conditions (BCs) and the significance level. DisPerSE can be used
with four boundary conditions, which deal with the edges of the distribution:
periodic, mirror, void and smooth. The periodic boundary conditions consist of
normal periodic conditions. The mirror boundary conditions are implemented by
generating galaxies which mirror the ones on the edges, whilst the smooth
boundary conditions are implemented by generating galaxies based on an
interpolated density field. The void boundary conditions, which do not add any
boundary galaxies at the edges, fail to provide a coherent filament network -
so it was discarded in our work.

The other parameter, the significance level, deals with the level at which a
structure is picked up as a filament or not. The significance level is
described by a threshold in a persistance diagram - which can be drawn as the
absolute value of the ratio between two critical points in a pair and the
value at the lowest critical point of the two (the background density). The
choice of threshold heavily influences the detected filaments, since a low
threshold will pick out structures that might not be filaments, whilst a high
threshold might smooth out real structures.

Following Luber et al. (2019), we split our sample into slices of equal
redshifts $\Delta z=0.01$ from $z=0.02$ to $z=0.09$. We choose a threshold of
$3.5\sigma$, motivated by the comparisons in Sousbie (2011) and use the mirror
boundary conditions to aid comparison with previous work (e.g. Blue Bird et
al., 2020). Figure 1 shows an example for the filament network converted into
3D Cartesian coordinates for mirror boundary conditions along with the
galaxies used to compute it. The choice of the significance level ensures that
our filaments are robust and that the big structures are picked up without
washing out some of the relevant finer structures.

Figure 2: Normalised histogram of both the Hi galaxies (red solid line) and
the optical galaxies (black dashed line) from the COSMOS and XMM-LSS fields in
the redshift range of $0.02<$ z $<0.09$ as a function of distance from the
cosmic web obtained using mirror boundary conditions on DisPerSE.

(a)

(b)

Figure 3: Schematic of a galaxy and its closest filament in (RA, Dec, z)
coordinates. (left) Illustration of the position angle (PA), the inclination
($i$), the unit spin vector ($\hat{L}$) and the direction of rotation for a
galaxy. (right) Illustration of a galaxy and its unit spin vector next to its
closest filament vector along with the angle $\psi$ between them.

###  2.3 Distance to the closest filament

To calculate the distance from a galaxy to the spine of the closest filament,
we used the skeleton generated by DisPerSE - which consists of a network of
points which can be used to construct small segments to assemble the filament
network. The midpoint of each segment was then cross-matched with our Hi
galaxy sample in each redshift slice. This provides the physical separation -
for which we use the 3D position of the filament point - between each galaxy
and its closest filament. This method does not provide the true exact distance
to the filament, as it would require computing the right angle between the
point and the segment. However, the size of filament segments are on average
$\sim 1$ Mpc. In the extreme case of the galaxy lying within 1 Mpc of the
filament this would result in an uncertainty of the order unity, however the
fractional uncertainty obviously decreases for a galaxy that resides at a
greater distance to the filament: for a galaxy 5 Mpc from the filament, the
uncertainty on the distance is $\sim 1$ per cent due to this assumption, i.e.
a negligible source of uncertainty given the uncertainty around the filament
distribution itself. Figure 2 shows the histogram of the distances from the Hi
galaxies in our sample and the nearest filament (red), as well as the galaxies
with spectroscopic redshifts from the optical catalogue used to compute the
large-scale structures and their closest filament (black). As can be seen, the
galaxies are all $\lesssim 50$ Mpc from the nearest filaments (and $\lesssim
40$ Mpc for the Hi galaxies). When measuring the 3D distance, we did not take
into account redshift distortion effects as we considered it a
$2^{\mathrm{nd}}$ order effect.

###  2.4 Spin of the galaxy

Following the treatment in Lee & Erdogdu (2007), which uses a thin-disk
approximation, the spin unit vector of a galaxy can be characterised in local
spherical coordinates as:

$\displaystyle\hat{L}_{r}$ $\displaystyle=\cos i$ (1)
$\displaystyle\hat{L}_{\theta}$ $\displaystyle=\sin i\sin\mathrm{PA}$ (2)
$\displaystyle\hat{L}_{\phi}$ $\displaystyle=\sin i\cos\mathrm{PA}$ (3)

where PA is the position angle and $i$ is the inclination angle of the galaxy.
The values for both the PAs and the $i$’s were measured using 3D kinematic
modelling, as presented in Ponomareva et al. (2021). The inclination angle is
defined as $i=0$ if face-on and $i=\pi/2$ if edge-on, whilst the PA is
measured from the north counterclockwise to the receding side of a galaxy.

The unit spin vector is converted into Cartesian coordinates, with the
spherical vector related to the Cartesian vector by:

$\left[\begin{array}[]{c}\hat{L}_{x}\\\ \hat{L}_{y}\\\
\hat{L}_{z}\end{array}\right]=\left[\begin{array}[]{ccc}\sin\alpha\cos\beta&\cos\alpha\cos\beta&-\sin\beta\\\
\sin\alpha\sin\beta&\cos\alpha\sin\beta&\cos\beta\\\
\cos\alpha&-\sin\alpha&0\end{array}\right]\left[\begin{array}[]{c}\hat{L}_{r}\\\
\hat{L}_{\theta}\\\ \hat{L}_{\phi}\end{array}\right],$ (4)

where $\alpha=\pi/2-\mathrm{DEC}$ and $\beta=\mathrm{RA}$, with DEC and RA
corresponding to declination and right ascension, respectively. Figure 3(a)
illustrates the unit spin vector along with the angles used for its
calculation and the direction of rotation for the galaxy. There is a sign
ambiguity which arises in $\hat{L}_{r}$, which has been shown in Trujillo et
al. (2006). Following past work (Lee & Erdogdu, 2007; Kraljic et al., 2021),
we choose to take the positive sign in $\hat{L}_{r}$. Kraljic et al. (2021)
has shown that if the sign of $\hat{L}_{r}$ is flipped in Equation 4, the
overall effect of a galaxy being either aligned or mis-aligned does not change
due to the symmetry.

###  2.5 Angle between galaxy and filament

To calculate the angle between the spin galaxy vector and the filament, we
crossmatch the galaxy with the closest filament, which is defined by a
starting point $f_{1}(\mathrm{RA}_{1},\mathrm{Dec}_{1},z_{1})$ and an end
point $f_{2}(\mathrm{RA}_{2},\mathrm{Dec}_{2},z_{2})$, where $z$ is the
redshift centred on the midpoint of the filament segment. These points are all
generated using the skeleton from DisPerSE. To calculate the spherical
components of the filament vector we then write:

$\displaystyle f_{\mathrm{RA}}$
$\displaystyle=f_{2}(\mathrm{RA}_{2})-f_{1}(\mathrm{RA}_{1}),$ (5)
$\displaystyle f_{\mathrm{Dec}}$
$\displaystyle=f_{2}(\mathrm{Dec}_{2})-f_{1}(\mathrm{Dec}_{1}),$ (6)
$\displaystyle f_{z}$ $\displaystyle=f_{2}(z_{2})-f_{1}(z_{1}).$ (7)

The filament vector is then converted into Cartesian coordinates in order to
compute the dot product between the spin vector of the galaxy $\mathbf{L}$ and
the filament vector $\mathbf{f}$. To find the cosine of the angle between the
galaxy spin vector and the filament vector $\psi$, we divide the dot product
by the modulus of the filament vector, as the spin vector is already
normalised to 1:

$\cos\psi=\frac{f_{x}\cdot\hat{L}_{x}+f_{y}\cdot\hat{L}_{y}+f_{z}\cdot\hat{L}_{z}}{|\mathbf{f}|},$
(8)

where $f_{x}$, $f_{y}$, $f_{z}$ are the Cartesian components of the filament
vector $\mathbf{f}$ and $\hat{L}_{x}$, $\hat{L}_{y}$, $\hat{L}_{z}$ are
defined as before. Figure 3(b) shows a schematic of the two vectors and
$\psi$. To analyse the orientation of the galaxy spin relative to the spine of
the filament we take the absolute value of the cosine, which gives us the
acute value of the angle $\psi$ independent of the direction of the normalised
filament vector $\hat{f}$. Following the convention in Kraljic et al. (2020),
for $\lvert\cos\psi\rvert<0.5$ the two are considered mis-aligned, whilst for
$\lvert\cos\psi\rvert>0.5$ they are considered aligned.

##  3 Results

###  3.1 Spin alignment as a function of distance-to-filament

As can be seen in Figure 2, all of the Hi-selected galaxies in our sample lie
within $40$ Mpc of their associated closest filament - with the majority of
the sample within 10 Mpc ($36$ Hi-selected galaxies). For our Hi-selected
galaxy sample, $50$% of the galaxies are within $10.6$ Mpc, whilst $50$% of
the optical galaxies used to compute the cosmic web are within $11.6$ Mpc.
Using the method described in Section 2.5, we calculated the spin axis for the
77 galaxies in our sample and the cosine of the angle between the spin axis of
each galaxy and its closest filament. The results can be seen in Table 2 and
Figure 4, where we separate our sample into different distance ranges. We use
these distance ranges as bins for which we calculate the means and the
medians, to highlight the overall trend. Whilst the errors on the means
(medians) are computed using the standard errors, it is more difficult to
calculate the errors on the individual $\langle\lvert\cos\psi\rvert\rangle$
values. This is due to the nature of the filament-finding algorithm which does
not provide any information on the uncertainty in the length or direction of
the filaments. Hence, in order to be able to provide an estimate of the
uncertainty for $\cos\psi$, we determined the filament distribution by
randomly omitting 5 per cent of the optical galaxies and computing a new
network 100 times. We then used the new network to find the closest filament
to the galaxy and to recalculate $\cos(\psi)$. Therefore, for each galaxy, we
had 101 values for the cos-angle, which allows us to determine the standard
deviation on each $\cos(\psi)$ value. These are shown in Figure 4. We truncate
the error bars where the formal uncertainty gives a value above
$\lvert\cos\psi\rvert=1$ and below $\lvert\cos\psi\rvert=0$. Clearly the
result is noisier where we lack large numbers at the larger distances to the
filaments, however there is a clear result for alignment for the galaxies
within $5$ Mpc of their closest filament.

We use the Mann-Whitney U test (Mann & Whitney, 1947) on the distributions
with different distance ranges to compare their medians, shown in Table 3. We
find significant evidence for alignment between the spin axis of the Hi-
selected galaxies and their closest identified filaments. For example, for the
galaxies within $5$ Mpc of their closest filament we find
$\langle\lvert\cos\psi\rvert\rangle=0.66\pm 0.04$, whereas those galaxies that
lie $>5$ Mpc away from their nearest filament give a mean alignment of
$\langle\lvert\cos\psi\rvert\rangle=0.44\pm 0.04$, with a Mann-Whitney test
giving a $p-$value of $5\times 10^{-4}$, providing strong evidence that the
two distributions are significantly different. The trend continues for the
distributions of the galaxies within $10$ Mpc of their closest filament and
away from $10$ Mpc of their nearest filament, with a Mann-Whitney $p-$value of
$3.1\cdot 10^{-2}$. The only distribution without a statistically significant
$p-$value is for the galaxies within $20$ Mpc of their closest filaments and
those beyond $20$ Mpc. This is likely due to the low number of galaxies which
are beyond $20$ Mpc from their closest filament.

This is in agreement with the results obtained by Blue Bird et al. (2020), who
used only 10 galaxies (which were within 10 Mpc of their closest filament) and
also found that galaxy spins tend to be aligned with the filaments of the
cosmic web.

Figure 4: $\lvert\cos\psi\rvert$ for the galaxy sample as a function of distance to the closest filament computed with mirror boundary conditions. The black horizontal dotted line represents the spin value 0.5, whilst the vertical dotted lines mark the 5 Mpc, 10 Mpc and 20 Mpc distance cuts respectively. The blue and black stars represent the medians and the means of each bin, respectively. Uncertainties on the individual values of $\cos\psi$ are determined using the method outlined in Section 3.1. Table 2: The mean of the cosine of the angle between the Hi spin of the galaxy and its closest filament $\cos{\psi}$ and the p-values for the Kolmogorov-Smirnov test for different distance ranges.  Distance Cut | ${\langle\lvert\mathbf{cos\psi}\rvert\rangle}$ | $\mathbf{p_{KS}}$
---|---|---
$0$ Mpc $<d<5$ Mpc | $0.66\pm 0.04$ | $5\cdot 10^{-2}$
$5$ Mpc $<d<10$ Mpc | $0.37\pm 0.08$ | $9\cdot 10^{-2}$
$10$ Mpc $<d<20$ Mpc | $0.40\pm 0.06$ | $4\cdot 10^{-3}$
$d>20$ Mpc | $0.50\pm 0.06$ | $10^{-9}$
full range | $0.51\pm 0.03$ | $10^{-19}$

To verify our result, we shuffled the PAs and the $i$’s in the sample. With
this shuffled galaxy sample, we cross-matched it with the filamentary
structures and then recalculated the cosine of the angles. We repeated this
process 2000 times and used a Kolmogorov-Smirnov test (Noether, 1978) to
determine whether our measured alignments are consistent with the null-
hypothesis of a randomly oriented spin vector for our galaxy sample, which we
show in Table 2. The $p-$values for the whole sample for the KS test is
$10^{-19}$. Thus we can strongly reject the null hypothesis of the spin axis
of galaxies being randomly oriented with respect to the orientation of the
filaments.

Table 3: A comparison between the $\cos{\psi}$ distributions for different distance cuts using the p-values for the Mann-Whitney U test. Distribution 1 | Distribution 2 | $\mathbf{p_{MW}}$
---|---|---
$d<5$ Mpc |  $d>5$ Mpc | $10^{-4}$
$d<5$ Mpc |  $5$ Mpc $<d<10$ Mpc | $2\cdot 10^{-3}$
$d<10$ Mpc |  $d>10$ Mpc | $3.1\cdot 10^{-2}$
$d<10$ Mpc |  $10$ Mpc $<d<20$ Mpc | $1.7\cdot 10^{-2}$
$d<20$ Mpc |  $d>20$ Mpc | $4.3\cdot 10^{-1}$

There are not many studies investigating the link between the distance of the
galaxy from the filament and $\lvert\cos\psi\rvert$. Krolewski et al. (2019)
do not find any connection between the distance to the filament and the spin
of galaxies using the MaNGA integral-field survey. However, the distance cuts
they use are much smaller than the ones used in this paper: $0.3$ Mpc, $1.0$
Mpc and $1.8$ Mpc. We can explore larger ranges in our study due to MeerKAT’s
field of view. The mean of $\lvert\cos\psi\rvert$ for all their cuts is in the
range $\langle\lvert\cos\psi\rvert\rangle=0.62$ to
$\langle\lvert\cos\psi\rvert\rangle=0.67$, which is in accordance with our
results, since for the closest galaxies to the filaments, the alignment is
stronger. A key difference in methodology is that they use 2D angles, which
could cause a confusion between filaments and walls, leading to the walls
dominating the effect (Welker et al., 2020).

###  3.2 Spin alignment as a function of Hi Mass

A better understanding of the Hi content of a galaxy is vital in understanding
galaxy evolution. As Hi extends to larger radii than stars in galaxies, it is
more easily perturbed during tidal interactions and hence, more sensitive to
external influences (Yun et al., 1994).

We investigate how $\lvert\cos\psi\rvert$ depends on the Hi-mass of the
galaxies. In Figure 5333We choose not to show the uncertainties on each value
of $\cos\psi$ in the remaining figures for clarity, but note that Figure 4
does show these estimated uncertainties., the relationship between
$\lvert\cos\psi\rvert$ as a function of Hi mass is shown. The black vertical
dotted line marks the $10^{9.78}M_{\odot}$ value, which represents the median
of $M_{\mathrm{H{\sc{I}}}}$ for our sample. This value is close to
$10^{9.5}M_{\odot}$, at which the spin transition was observed in the
simulation performed by Kraljic et al. (2020), which overall agrees with our
findings, as the lower left corner of Figure 5 is less populated compared to
the other regions.

However, we find $\langle\lvert\cos\psi\rvert\rangle=0.52\pm 0.04$ for
galaxies with $\log_{10}(M_{\rm HI}/M_{\odot})<9.78$, which is consistent with
that of the full sample, where $\langle\lvert\cos\psi\rvert\rangle=0.51\pm
0.03$. For the sample with a $\log_{10}(M_{\rm HI}/M_{\odot})>9.78$, we find
$\langle\lvert\cos\psi\rvert\rangle=0.50\pm 0.04$, with the Mann-Whitney U
test p-value of 0.4. Therefore, we find no statistical difference in the spin
alignment of galaxies with Hi mass less than or greater than the median value
of $10^{9.78}$ M⊙.

Therefore, similar to the study by Blue Bird et al. (2020), we find no
evidence for a spin transition at an Hi mass of $\sim 10^{9.5}$ M⊙.
Additionally, we performed a correlation test between Hi mass and
$\lvert\cos\psi\rvert$ to verify the relationship between the parameters.
Using Kendall’s Tau (Kendall, 1938) and Spearman Rank correlation (Glasser &
Winter, 1961), we find no evidence for a correlation: a $\tau$ of $-0.06$ with
an associated p-value of $0.5$ and a Spearman Rank coefficient of $-0.08$ with
an associated p-value of $0.5$.

Figure 5: $\lvert\cos\psi\rvert$ for the galaxy sample as a function of Hi
mass computed with mirror boundary conditions. The vertical black dashed line
represents the median of the Hi mass for our sample. The 77 galaxies were
firstly split in 8 bins of $\lvert\cos\psi\rvert$, then they were split in 8
bins of Hi mass. The black triangles represent the median of the Hi mass for
each bin of $\lvert\cos\psi\rvert$ whilst the blue triangles represent the
medians of $\lvert\cos\psi\rvert$ for each bin of $M_{\mathrm{H\sc I}}$.

###  3.3 Spin alignment as a function of other factors

In addition to distance-to-filament and Hi mass, we investigate other key
properties relating galaxies to their environment: the HI-to-stellar mass
ratio and the baryon fraction. We used the ancillary data extracted by the
MIGHTEE-HI team for the $ugrizYJHK_{s}$ photometry as detailed in Maddox et
al. (2021). The Spectral Energy Distribution (SED) fitting code LePhare
(Arnouts et al., 1999; Ilbert et al., 2006) was then used to derive the
stellar mass. The uncertainty in stellar mass for each galaxy that we adopt is
$\sim 0.1$ dex (Adams et al., 2021).

Figure 6: $\lvert\cos\psi\rvert$ for the galaxy sample as a function of log
HI-to-stellar mass ratio computed with mirror boundary conditions. The 77
galaxies were firstly split in 8 bins of $\lvert\cos\psi\rvert$, then they
were split in 8 bins of $M_{\mathrm{H{\sc I}}}/M_{\star}$. The black triangles
represent the medians of log HI-to-stellar mass ratio for each bin whilst the
blue triangles represent the medians of $\lvert\cos\psi\rvert$ for each bin.
The width of the bins is denoted by the width (height) of the error bars for
the blue (black) points.

####  3.3.1 Hi – stellar mass ratio

The stellar mass of a galaxy is linked to both the environment and the
intrinsic properties of the galaxy - for example, galaxies with a higher
stellar mass tend to be in dense environments (e.g. Vulcani et al., 2011).

To determine if there is a difference in the behaviour in the alignment of the
spin axis of a galaxy to its nearest filament, we split our sample according
to its Hi-to-stellar mass ratio at the median of the sample ($\log_{10}(M_{\rm
HI}/M_{\star})=0.11$). For $\log_{10}(M_{\rm HI}/M_{\star})<0.11$, we find
$\langle\lvert\cos\psi\rvert\rangle=0.58\pm 0.04$, which is significantly
higher than that for the sample with $\log_{10}({M_{\rm HI}/M_{\star}})>0.11$,
$\langle\lvert\cos\psi\rvert\rangle=0.44\pm 0.05$ with a Mann-Whitney U test
p-value of $0.012$. Figure 6 shows the behaviour of the $\lvert\cos\psi\rvert$
as a function of $\log_{10}({M_{\rm HI}/M_{\star}})$ \- where we see a dearth
of galaxies for $\log_{10}({M_{\rm HI}/M_{\star}})<-0.5$. Thus, we find
evidence for the spin changing from aligned to mis-aligned for the galaxies
below and above the median of the HI-to-stellar mass ratio $\log_{10}({M_{\rm
HI}/M_{\star}})=0.11$, respectively. Furthermore, the KS test ($p=7.5\cdot
10^{-3}$) suggests that for $\log_{10}({M_{\rm HI}/M_{\star}})<0.11$, the
distribution of $\lvert\cos\psi\rvert$ is not consistent with being drawn from
an underlying random galaxy spin alignment distribution.

Both the Kendall Tau and Spearman Rank tests also suggest a weak correlation
between the Hi-to-stellar mass ratio and the $\lvert\cos\psi\rvert$: a $\tau$
of $-0.209$ with an associated p-value of $0.007$ and a Spearman Rank
coefficient of $-0.311$ with an associated p-value of $0.006$.

Figure 7: $\lvert\cos\psi\rvert$ as a function of the log of the baryon mass
fraction $f_{b}=M_{\mathrm{baryon}}/M_{\mathrm{dyn}}$. The vertical black
dashed line represents the median $f_{b}$ for our sample. The 77 galaxies were
firstly split in 8 bins of $\lvert\cos\psi\rvert$, then they were split in 8
bins of $f_{b}$. The black triangles represent the medians of the baryon mass
fraction for each bin whilst the blue triangles represent the medians of
$\lvert\cos\psi\rvert$ for each bin. The width of the bins is denoted by the
width (height) of the error bars for the black (blue) points.

####  3.3.2 Baryonic mass versus dynamical mass

Finally, we explore the effect of the dark matter, through the dynamical mass
and the baryon mass fraction. We calculate the dynamical mass $M_{\rm dyn}$
as:

$M_{\rm dyn}=\frac{R}{G}V_{\mathrm{rot}}^{2},$ (9)

where $V_{\mathrm{rot}}$ is the rotational velocity of the galaxy and $R$ is
the radius at which the rotational velocity is measured from the resolved Hi
rotation curves, which tend to extend much further than the stellar disk into
the dark matter halo (see Ponomareva et al., 2021, for details). We then
define the baryon mass fraction as $f_{b}=M_{\mathrm{baryon}}/M_{\rm dyn}$,
where $M_{\mathrm{baryon}}=1.4\cdot M_{\mathrm{H{\sc{I}}}}+M_{\star}$. The
factor of 1.4 is included to account for the primordial abundance of metals
and helium (Arnett, 1999), however it does not include the molecular gas
component.

Following the same method as above, we split the galaxy sample at the median
of the baryon mass fraction, $\log_{10}(f_{b})=-0.6$. Here, the average value
of $\lvert\cos\psi\rvert$ tends to be marginally mis-aligned for galaxies with
a lower baryon mass fraction: $\langle\lvert\cos\psi\rvert\rangle=0.47\pm
0.05$, whilst for the higher baryon mass fraction, it tends towards alignment:
$\langle\lvert\cos\psi\rvert\rangle=0.55\pm 0.04$. Figure 7 shows
$\lvert\cos\psi\rvert$ as a function of the baryon mass fraction - it can be
seen that for the lower baryon mass fraction there is a spread in $\cos\psi$,
whilst for the highest baryon mass fraction ($\log_{10}(f_{b})>-0.2$), the
galaxies all tend to be aligned. This implies that galaxies with high stellar
and/or Hi mass tend to retain their alignment with the filament, whilst the
galaxies with a higher dark matter fraction are less likely to be aligned with
the filaments. However, we find no evidence for a correlation using both the
Kendall’s Tau $\tau=0.07$ and the Spearman Rank coefficient ($0.11$), with
associated p-values of $0.38$ and $0.36$, respectively. Similarly to the
$M_{\mathrm{H{\sc{I}}}}/M_{\star}$ , we notice a spin transition at the median
value of the baryon mass fraction $\log_{10}(f_{b})=-0.6$, from
$\langle\lvert\cos\psi\rvert\rangle=0.47\pm 0.05$ to
$\langle\lvert\cos\psi\rvert\rangle=0.55\pm 0.04$, although the Mann-Whitney U
p-value of $0.132$ shows that this is not significant given the current
sample. Therefore, galaxies with a lower dark matter content are more likely
to be aligned, but for the rest of the galaxies the alignment is consistent
with being random. This will require more data and future analysis to see if
any trend exists.

Table 4: The mean of the cosine of the angle between the Hi spin of the galaxy and its closest filament $\cos{\psi}$ and comparison parameters: Hi Mass $M_{\mathrm{H{\sc{I}}}}$, Hi-to-stellar mass ratio $M_{\mathrm{H{\sc{I}}}}/M_{\star}$ and baryon mass fraction $f_{b}$. Parameter | Cut | ${\langle\lvert\mathbf{cos\psi}\rvert\rangle}$ | $\mathbf{p_{MW}}$
---|---|---|---
$\log_{10}\Big{(}\frac{M_{\mathrm{H{\sc{I}}}}}{M_{\odot}}\Big{)}$ | $<9.78$ | $0.52\pm 0.04$ | $0.40$
$>9.78$ | $0.50\pm 0.05$
$\log_{10}\Big{(}\frac{M_{\mathrm{H{\sc{I}}}}}{M_{\star}}\Big{)}$ | $<0.11$ | $0.58\pm 0.04$ | $0.01$
$>0.11$ | $0.44\pm 0.05$
$\log_{10}(f_{b})$ | $<-0.598$ | $0.47\pm 0.05$ | $0.13$
$>-0.598$ | $0.55\pm 0.04$
Figure 8: $\lvert\cos\psi\rvert$ as a function of distance as presented in
Figure 2, with the Hi-stellar mass ratio
$\log_{10}(M_{\mathrm{H{\sc{I}}}}/M_{\star})$ overlaid as a colourmap.

###  3.4 Discussion

Taken together, our results suggest that the stellar mass of a galaxy has a
strong influence on the spin of the galaxy in relation to the filaments. In
Figure 8 we show the $M_{\rm HI}/M_{\star}$ ratio as a function of the
distance from the nearest filament. It shows that those galaxies with the
lowest $M_{\rm HI}/M_{\star}$ ratio, and therefore the highest stellar mass,
given that our sample is selected on Hi mass, tend to be aligned. The stellar
mass being an important influence on the spin would be consistent with several
simulations (Dubois et al., 2014a; Kraljic et al., 2020), where they find a
transition at a stellar mass of $M_{\star}\sim 10^{10}$ M⊙, from aligned to
mis-aligned. Furthermore, Welker et al. (2020) found a similar spin transition
between lower mass and higher mass galaxies using the SAMI survey around
$10^{10.4}M_{\odot}-10^{10.9}M_{\odot}$. To understand whether there is a
bias, such that galaxies with higher stellar mass tend to be found in denser
environments and closer to the filaments, we checked their position with
respect to their closest filament. As can be seen in Figure 9, the stellar
mass of the galaxies is randomly distributed, therefore we find no evidence
that this could be the reason for our results on the spin-alignment between
galaxies and their closest filaments. Due to the fact that our sample is Hi
selected, comparisons with other studies using stellar mass would be biased
and uninformative for our study.

Figure 9: The stellar mass for the galaxy sample as a function of distance to
the closest filament computed with mirror boundary conditions.

We also investigate whether the dark matter content affects the relation
between the spin-axis of the galaxy and the orientation of its nearest
filament by determining the baryonic mass fraction. We find that for the
highest baryonic mass fractions that the galaxies tend to align with the
nearest filament. However, we find no evidence of a trend of alignment with
baryonic mass fraction. Both of these reinforce the evidence from the $M_{\rm
HI}/M_{\star}$ ratio, that the stellar mass is a key factor in determining
whether a galaxy is aligned with its nearest filament or not.

We also note that some of the trends that we do find could also be linked with
the morphology of the galaxies - as the baryon mass fraction varies depending
whether a galaxy is elliptical or spiral. As mentioned before, Kraljic et al.
(2021) found a dependence of the shape of the galaxy and its alignment with
the filament - S0 type galaxies are more likely to be mis-aligned. Other
environmental factors, such as the gas inflows around the filaments or galaxy
mergers in the filament regions could also influence the alignment of the spin
of the galaxies. Welker et al. (2014) have shown that galaxies that have
undergone fewer mergers are more likely to be aligned with the filaments,
whilst galaxies that have undergone mergers along the filaments are more
likely to have their spins swung to mis-alignment - especially for major
mergers. Given that it is more likely for the more massive galaxies to have
undergone a merger in the past, the fact that in our Hi-selected sample it is
those galaxies with a relatively larger stellar mass which tend to be more
aligned, appears to be at odds with this finding from simulations. However, it
is difficult to interpret our results in this context due to the fact that our
sample is Hi-selected and dominated by relatively low-stellar mass objects and
contains very few objects with masses above the mass where the spin transition
appears in observations and simulations (Welker et al., 2020). However, we
also expect gas-rich mergers to increase the amount of neutral gas in galaxies
(Ellison et al., 2018) and this may provide an explanation of our results,
where we see that those galaxies which are misaligned do have higher Hi mass
fractions compared to their stellar mass. Such a merger history may also be
apparent in the stellar populations of the galaxies and thus a fruitful future
line of enquiry would be to investigate whether the aligned and misaligned
populations exhibit different star formation histories, ongoing enhanced star
formation or morphological evidence of a merger event happening.

It is difficult to explore this with the current sample due to the limited
number of objects, as we do not have the number statistics, or the filament
constraints. However, it will be possible as the MIGHTEE survey expands to the
full 20 deg2 area, substantially increasing the sample size we would have to
work with. For the $5$ deg2 in the COSMOS $+$ XMM-LSS Early Science data,
which is not to full depth and was taken with a coarser channel width than
will be done for the rest of the survey, we have about $50$ detections per
square degree. For the full MIGHTEE survey, we expect around $\sim 1000$
detections at $z<0.1$ (Maddox et al., 2021), as such we will be able to
investigate sub-samples of the galaxies in relation to their filaments,
binning with respect to morphology, age and also the actual spin and angular
momentum of the galaxies within the sample.

Table 5: The coefficients and p-values for the two correlation tests, Kendall’s Tau and Spearman Rank, for each parameter against the $\lvert\cos\psi\rvert$. Parameter | Kendall’s Tau | Spearman Rank
---|---|---
$\tau$ | p-value | coefficient | p-value
Distance | $-0.144$ | $0.065$ | $-0.205$ | $0.074$
$M_{\mathrm{H{\sc{I}}}}$ | $-0.058$ | $0.452$ | $-0.083$ | $0.472$
$M_{\mathrm{H{\sc{I}}}}/M_{\star}$ | $-0.209$ | $0.007$ | $-0.311$ | $0.006$
$f_{b}$ | $0.069$ | $0.377$ | $0.107$ | $0.355$

##  4 Conclusions

In this work, we present a study of the 3D spins of 77 Hi galaxies identified
with the MIGHTEE-HI survey, and their link to the filaments of the cosmic web.
The large-scale filaments are computed using DisPerSE and optical galaxies
from the COSMOS and XMM-LSS fields. We took into consideration several
parameters that might affect the alignment between the galaxies and the
filaments and found that:

  * •

distance-to-filament: galaxies closer ($<5$ Mpc) to the spine of the filament
tend to be aligned with their nearest filament.

  * •

Hi content of galaxy: no spin transition was found using the Hi mass of the
galaxy for mirror boundary conditions for
$\log_{10}(M_{\mathrm{H{\sc{I}}}}/M_{\odot})<9.78$.

  * •

Hi-to-stellar mass ratio of galaxy: we find a preference for alignment for the
galaxies with a lower Hi-to-stellar mass ratio and overall throughout the
sample, as well as a spin transition.

  * •

baryon mass fraction of galaxy: we find those galaxies with the highest baryon
mass fraction to exhibit alignment with their nearest filament. However, we
find no trend across the range of baryonic mass fraction probed.

Overall, we find the compelling evidence that the neutral gas fraction
relative to the stellar mass of a galaxy is clearly related to the alignment
of the galaxy spin vector and the nearest filament. Furthermore, galaxies show
greater evidence for alignment the closer they are to the filament, suggesting
that there is an interplay between the galaxy spin axis and the filament. We
suggest that this is due to those galaxies which have undergone a recent gas-
rich merger have their spin-orientation disrupted with respect to the
filament, whereas those galaxies which have not undergone a recent merger tend
to retain their alignment and their evolution is dictated by secular
processes. Such a scenario could be investigated further by measuring the
star-formation histories of the galaxies as a function of their spin alignment
with the filaments. Given that the number statistics in this study are
limited, it would benefit from additional data. However, it underlines the
potential of the MIGHTEE Large Survey Program, as well as the MeerKAT
telescope. With more data expected in the coming years , the sample size of Hi
galaxies will increase significantly and enable a big step forward in
understanding how galaxies are powered by fuel drawn from the cosmic web.
Whilst a study with respect to redshift will be difficult with MIGHTEE alone,
combining information from MIGHTEE with the deeper and narrower Looking At the
Distant Universe with the MeerKAT Array (LADUMA; Blyth et al., 2016) may
provide the necessary redshift baseline. However, the need to at least
marginally resolve galaxies for the kinematic modelling would limit the sample
to the largest or most Hi-rich galaxies, given MeerKAT’s synthesised beam.

## Acknowledgements

We thank the anonymous referee for their useful comments and feedback. We
thank Thijs van der Hulst for insightful comments. MNT, MJJ and IW acknowledge
support from the Oxford Hintze Centre for Astrophysical Surveys which is
funded through generous support from the Hintze Family Charitable Foundation.
IH, MJJ and AAP acknowledge support from the UK Science and Technology
Facilities Council [ST/N000919/1]. IH acknowledges support from the South
African Radio Astronomy Observatory which is a facility of the National
Research Foundation (NRF), an agency of the Department of Science and
Innovation. NM acknowledges support of the LMU Faculty of Physics. The MeerKAT
telescope is operated by the South African Radio Astronomy Observatory, which
is a facility of the National Research Foundation, an agency of the Department
of Science and Innovation. We acknowledge use of the Inter-University
Institute for Data Intensive Astronomy (IDIA) data intensive research cloud
for data processing. IDIA is a South African university partnership involving
the University of Cape Town, the University of Pretoria and the University of
the Western Cape. The authors acknowledge the Centre for High Performance
Computing (CHPC), South Africa, for providing computational resources to this
research project. This work is based on data products from observations made
with ESO Telescopes at the La Silla Paranal Observatory under ESO programme ID
179.A-2005 (Ultra-VISTA) and ID 179.A- 2006(VIDEO) and on data products
produced by CALET and the Cambridge Astronomy Survey Unit on behalf of the
Ultra-VISTA and VIDEO consortia. Based on observations obtained with
MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-France-
Hawaii Telescope (CFHT) which is operated by the National Research Council
(NRC) of Canada, the Institut National des Science de l’Univers of the Centre
National de la Recherche Scientifique (CNRS) of France, and the University of
Hawaii. This work is based in part on data products produced at Terapix
available at the Canadian Astronomy Data Centre as part of the Canada-France-
Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. The
Hyper Suprime-Cam (HSC) collaboration includes the astronomical communities of
Japan and Taiwan, and Princeton University. The HSC instrumentation and soft-
ware were developed by the National Astronomical Observatory of Japan (NAOJ),
the Kavli Institute for the Physics and Mathematics of the Universe (Kavli
IPMU), the University of Tokyo, the High Energy Accelerator Research
Organization (KEK), the Academia Sinica Institute for Astronomy and
Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was
contributed by the FIRST program from Japanese Cabinet Office, the Ministry of
Education, Culture, Sports, Science and Technology (MEXT), the Japan Society
for the Promotion of Science (JSPS), Japan Science and Technology Agency
(JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and
Princeton University.

This research made use of Astropy,444http://www.astropy.org a community-
developed core Python package for Astronomy (Astropy Collaboration et al.,
2013, 2018).

## Data Availability

The MIGHTEE-HI spectral cubes will be released as part of the first data
release of the MIGHTEE survey, which will include cubelets of the sources
discussed in this paper. The derived quantities from the multi-wavelength
ancillary data was released with the final data release of the VIDEO survey
mid 2021. Alternative products are already available from the Herschel
Extragalactic Legacy Project (HELP; Shirley et al., 2021) and also soon from
the Deep Extragalactic VIsible Legacy Survey (DEVILS; Davies et al., 2021).

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