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The Unusual Milky Way-Local Sheet System: Implications for Spin Strength and Alignment

The Milky Way and the Local Sheet form a peculiar galaxy system in terms of the unusually low velocity dispersion in our neighbourhood and the seemingly high mass of the Milky Way for such an environment. Using the TNG300 simulation we searched for Milky Way analogues (MWA) located in cosmological walls with velocity dispersion in their local Hubble flow similar to the one observed around our galaxy. We find that MWAs in Local-Sheet analogues are rare, with one per (160-200 Mpc)^3 volume. We find that a Sheet-like cold environment preserves, amplifies, or simplifies environmental effects on the angular momentum of galaxies. In such sheets, there are particularly strong alignments between the sheet and galaxy spins; also, these galaxies have low spin parameters. These both may relate to a lack of mergers since wall formation. We hope our results will bring awareness of the atypical nature of the Milky Way-Local Sheet system. Wrongly extrapolating local observations without a full consideration of the effect of our cosmic environment can lead to a Copernican bias in understanding the formation and evolution of the Milky Way and the nearby Universe.


INTRODUCTION
The Milky Way (MW) is an SBb/c galaxy with an estimated mass between 8.3 × 10 11 M and 2 × 10 12 M (Karukes et al. 2020). It is located near the center of a flat sheet of galaxies extending up to 4 Mpc along along the supergalactic plane (Kroupa, Theis & Boily 2005;Metz, Kroupa & Jerjen 2007;Pawlowski, Kroupa & Jerjen 2013) with a density close to the mean density of the Universe (Klypin et al. 2015) and delineated by a ring of luminous galaxies, the "Council of Giants" (McCall 2014). The "Local Sheet" in which our galaxy is located belongs to a class of cosmic structures known as cosmic walls. It is bounded to the supergalactic north and south by the Local Void and the Southern Void respectively (Tully et al. 2008). There are no galaxies in the line of sight between the our galaxy and the center of both north and southern voids. The Milky Way is sitting at the edge of a cosmic cliff.
An increasing body of evidence points to the Milky Way and its immediate cosmic environment as somewhat uncommon occurrences in the Universe. The velocity dispersion measured for galaxies located within 3 Mpc from our own galaxy is σv ∼ 25 − 40 km s −1 (Karachentsev et al. 2002(Karachentsev et al. , 2003, one order of magnitude lower than predictions (Peebles 1980; Governato et al. 1997) and observed pairwise velocity dispersions (Landy 2002;Zehavi et al. 2002;Scoccimarro 2004). The "coldness" of the local Hubble flow seems to be a global property of the Local Sheet as indicated by observations around the nearby Centaurus A / M83 system, showing a dispersion of σv ∼ 32 km s −1 (Karachentsev et al. 2007). The coldness of the local Hubble flow can be explained as the result of the characteristic geometry and dynamics of cosmic walls (Aragon-Calvo, Silk & Szalay 2011). The central regions of walls are less dense than their surrounding denser "ring" of filaments, producing a local expansion on top of the global Hubble flow which damps peculiar velocities.
The halo mass function in walls also indicates the peculiarity of Milky Way Analogue (MWA) galaxies as it is roughly one order of magnitude lower than the global mass function in the MW mass range (Aragón-Calvo (2007); Ganeshaiah Veena et al. (2018), see also Neuzil, Mansfield & Kravtsov (2020)). The rarity of MWA galaxies is evident, arXiv:2208.03338v1 [astro-ph.GA] 5 Aug 2022 The dots correspond to background galaxies inside the search radius, the solid line indicates the best fit to the model given in sec. 2.1. The peculiar velocity dispersion is indicated by the dashed lines. The vertical dotted line marks the radius of zero velocity. We also show the unperturbed Hubble expansion v = Hr as the dashed gray line. The mass and fitting parameters are shown in the figure. Gray dots correspond to real galaxies presented in Karachentsev et al. (2003).
albeit not explicitly addressed, in studies of MWA in which constraints on halo mass, local density and geometry are included and also in constrained realizations of the Local Group. In both cases a large volume or a large number of realizations are needed in order to find MWA candidates (see for instance Garrison-Kimmel et al. (2014) and Fattahi et al. (2016)).
Walls are dynamically young structures, being the result of the gravitational collapse along one axis (Zel'dovich 1970). In the tidal torque theory (Hoyle 1949;Peebles 1969;White 1984), the tidal field governs spin. In a collapsing wall environment, this tidal field squashes protohaloes into a plane. Any aspherical lumps on the protohalo will get caught in the tidal field, imparting torque to the halo, with its spin tending to end up perpendicular to the axis of collapse (see also Neyrinck et al. 2020). This alignment between galaxy spin axes and their parent wall planes is small but statistically significant in dark matter computer simulations (Aragón-Calvo et al. 2007b;Hahn et al. 2007). Locally, the alignment of edge-on spiral galaxies (including our own) perpendicular to the Local Sheet is so strong that it can be seen by eye. As shown in Navarro, Abadi & Steinmetz (2004), gas/stars can retain their primordial orientation better than dark matter, due to the latter being more affected by mergers. The strength of the alignment signal in our neighborhood may be the result of disk galaxies keeping their original spin alignment and a quiet mass growth and low velocity dispersion in the relatively low density of the Local Sheet. On the other hand, mergers are a well known mechanism for angular momentum acquisition (Vitvitska et al. 2002). In the case of galaxy interactions within walls, mergers would tend to induce a spin aligned with the normal of the wall, not with the plane, as prescribed by the TTT.

N-BODY SIMULATION AND LSS ANALYSIS
The analysis presented here is based on Illustris TNG300 (Nelson et al. 2018), a cosmological hydrodynamical simulation of galaxy formation enclosed in a box of 205h −1 Mpc of side containing dark matter and gas particles with masses of 5.9 × 10 7 and 1.1 × 10 7 h −1 M respectively. The cosmological parameters used are given by Planck results (Planck Collaboration et al. 2016). While TNG300 has a relatively low mass resolution it has the large volume needed to sample rare cold Local Sheet environments as we will see in the following sections.
We defined two set of haloes: background haloes used to sample the velocity field and Milky Way Analogues. The background halo sample consisted of subfind haloes in the mass range 1×10 9 <M< 5×10 12 M and Vmax > 20 km s −1 . MWAs were defined as central haloes with Vmax > 20 km s −1 in the mass range 10 12 < M < 2 × 10 12 M . We extracted mass accretion histories for the MWA sample and identified merger events as increases in 30% of the total mass of the halo between snapthots. The MWA sample was classified into spiral and ellipticals using a custom convolutional neural network feed with synthetic images created from the stellar component of the halos observed in the r, g, i SDSS filters (Aragon-Calvo, in preparation, see for instance Rodriguez-Gomez et al. (2019)). For every MWA halo we computed the spin parameter following the definition of Bullock et al. (2001) where J is the angular momentum, M200 and R200 are the virial mass and radius respectively and V200 the circular velocity.
The density field used for cosmic web analysis was computed by running a resimulation of TNG300 sampled on a regular grid with 512 3 particles. The initial conditions were sharp-k-smoothed in order to target structures larger than 4 h −1 Mpc as described in Aragon-Calvo et al. (2010) and evolved to z = 0 using the GADGET-2 N-body code (Springel et al. 2005). From the final snapshot we labeled wall regions using the Hessian-based MMF method (Aragón-Calvo et al. 2007a; Aragon-Calvo & Yang 2014).

Measuring the Hubble flow
The Hubble flow around MWAs was measured by first selecting background haloes inside a shell of 1 < r < 4 Mpc centered in the target MWA galaxy. This distance range was chosen to roughly follow the range used in real measurements in the local Universe (Karachentsev et al. 2009) although extending to a larger radius in order to increase the number of available galaxies. Only MWAs with more than 10 neighbours were included in the analysis. We computed velocity dispersions σv from the model-subtracted radial velocities centered on the MWA using the model (Peirani & de Freitas Pacheco 2008): v(r) = H0r − H0R0(R0/r) 1/2 , where r is the distance from the MWA and H0 and R0 are the fitted Hubble constant and radius of the zero-velocity surface respectively (see Fig. 1). Figure 2 shows the distribution of σv and Hubble flow excess (H0-H) measured from the MWA sample. The distribution of both σv and H0-H have a roughly log-normal character. The peak of the velocity dispersion is surprisingly low, around σv ∼ 50km s −1 . However our MWA sample is restricted to relatively massive galaxies and does not include galaxies in pairs, groups or clusters which can have a much higher σv. The tail of the distribution, being ∼log-normal, extends to much higher values in σv and the mean of the distribution is 178 km s −1 . The peak in the Hubble excess distribution is located at H0-H ∼ 10 km s −1 . The tail of the distribution extends into the negative hundreds (not shown in Fig. 2 for clarity). The median value of H0-H is -2.2 km s −1 , close to the global expansion. The reported range in the velocity dispersion 25 < σv < 40 corresponds to 3σ − 1σ events for H0-H=0. Interestingly, from Fig. 2 we should expect to measure a Hubble flow excess around our galaxy of ∼ H + (10 − 15) km s −1 Mpc −1 . Figure 3 shows the effect of cosmic environment, defined in terms of geometry (walls) and σv, on the halo mass function (see also Aragón-Calvo (2007); Ganeshaiah Veena et al. (2018)). The mass function decreases in height and slope with decreasing Hubble velocity dispersion. The effect of environment is even stronger when we consider only haloes in walls. At low masses the mass function in all environments is a scaled version of the global mass function. The slope in the mass function begins to decrease with increasing mass around 10 12 M . The "knee" of the curve associated with a characteristic mass in cold environments is more than one order of magnitude lower than the "knee" of the global population. The slope in the mass function in cold wall environments is significantly steeper than the global population, the effect being even more pronounced after the characteristic mass range. The Milky Way is right at the border of the knee in the mass function in walls in the two regimes of σv considered here. The probability of drawing a MWA in cold wall environments from the general population P (> M ) = (N (> M )env/N (> M )global lies somewhere between 0.2% and 0.001% for the ranges in mass and σv considered here. This is equivalent to finding one MWA in a box of side ∼ 160 and ∼ 200 Mpc respectively. If we take the lowest estimate of σv ∼ 25 km s −1 Milky Way analogues in cold Local Sheet environments can be considered extremely rare events.

Spin parameter
Before addressing environmental effects, we study the spin parameter distribution of galaxies separated only by their morphology. Figure 4 (a) shows that spirals have in general a higher λ compared to ellipticals with the peaks in their λ distribution, P (z), at λ ∼ 0.03 and λ ∼ 0.015 respectively (see also Du et al. (2021); Rodriguez-Gomez et al. (2022)). Note that we use a strict definition of morphology, rejecting galaxies with < 90% probability of being a spiral/elliptical given by the neural network. Both spirals and ellipticals with 3 or more major-merger events since z = 1 have a higher spin parameter, supporting the idea of angular momentum acquisition via mergers (Vitvitska et al. 2002).
The effect of environment on λ is shown in Fig. 4 (b). Both spirals and ellipticals in walls have lower λ in cold environments. The peak in P (λ) increases with σv and the trend saturates for values higher than σv ∼ 100 km s −1 . In all cases spirals have a higher λ compared to ellipticals in their respective environment. Importantly, P (λ) for galaxies in cold and hot environments not only differ in the position of their peaks but also in their character. The P (λ) of galaxies in cold walls has a more narrow peak centered at a lower λ value and has a lower high-λ tail indicating a systematic lack of high-λ galaxies in this environment. This effect is more pronounced in the case of spirals.

Spin alignment
Finally, we show the alignment of galaxy spins with walls they inhabit. Figure 6 (right panel) shows that the alignment signal increases with decreasing σv and increasing halo mass. The alignment signal of haloes with mass < 2×10 12 is weak, consistent with previous findings (Aragón-Calvo et al. 2007b;Hahn et al. 2007) and showing a weak dependence with environment. In comparison, haloes above this mass present a significant alignment signal and dependence with environment. The star/disk component of galaxies is more strongly aligned than the dark matter component. Regarding cosmic environment, galaxies in cold environments are more strongly aligned than galaxies in hot environments. The strength in the alignment of the stellar component of galaxies in cold walls, similar to our Local Sheet, is very close to the observed value reported in Navarro, Abadi & Steinmetz (2004). Interestingly, the Milky Way has a somewhat high λ for its environment (see arrow in Fig. 6 center panel). We note that the high λ galaxies are also the strongest aligned. However the sample size is too small to draw a firm conclusion and report here. We will study this in a future work.

CONCLUSIONS AND DISCUSSION
In this work we present evidence that the Milky Way, a common galaxy by mass with respect to the global population, is an outlier when we consider the environment in which it is located. Improving on previous works, we describe the Local Sheet environment in terms not only of its geometry, but also its dynamics. We find that a Local Sheet and Milky Way environment, consisting of an unusually massive galaxy in a cold wall, is rare, occurring only once in a 160-200 Mpc box. We note that given the uncertainties on the mass of our galaxy, the measured σv and the general size and shape of the Local Sheet, our results should only be taken as an approximate indication of the rarity of such systems. Adding conditions to a situation will always eventually give a vanishingly small probability so we adopt somewhat conservative constraints and define the MW-Local Sheet system in terms of only three parameters: LSS geometry, LSS dynamics and halo mass. Our results apply only to Milky Way analogues, if we consider the more massive Milky Way -Andromeda system, with a combined mass of ∼ 3 − 4 × 10 12 M , such event is even rarer, so we do not analyze the joint situation of two large galaxies in a cold wall. But note that after the two galaxies merge, the situation will be the same as we analyze here, except with a larger combined mass. A cold wall with a galaxy of this larger mass would be extremely rare; a much larger box than the TNG300 volume we analyze would be necessary to obtain an example.
We show that both spiral and elliptical galaxies located in cosmological walls with low σv have a lower spin parameter, characterized by a narrower peak in the distribution located at lower λ and a lack of high-λ galaxies. This could indicate a lack of mergers in the quiet wall environments (Hellwing et al. 2021) (see also Fig. 4) emphasized by the low σv. At the same time, we found a strong alignment signal between the spin of spiral galaxies (selected using a neural network) and the plane of their host wall. The value of the alignment strength is close to the observed value around our galaxy. To our knowledge this is the strongest spin alignment Figure 6. Spin alignment of spiral galaxies in walls. We include galaxies with 95% probability of being spiral. The alignment cos θ corresponds to the angle between the spin vector of the galaxy/halo and the plane of its host wall. We compute the alignment for the stars and dark matter components and cold and hot environments. The gray area indicates the dispersion inside each bin for the spin alignment of the star component of galaxies in cold environments. The other cases have similar dispersion. in walls reported in N -body simulations. This is significant since we observe an unusually strong spin alignment of spiral galaxies around our galaxy, yet no previous study to date has been able to reproduce it.
Our results highlight the importance of carefully characterizing the environment around our galaxy. The effect of the geometry and coldness of Local Sheet environment on angular momentum processes may help us better understand current problems in galaxy formation such as the co-rotating plane of satellites around M31 (Ibata et al. 2013), the missing satellite problem (Klypin et al. 1999) among others.

DATA AVAILABILITY
The data underlying this article were accessed from the Illustris TNG datababse (https://www.tng-project.org). The derived data generated in this research will be shared on reasonable request to the corresponding author.