Living with Neighbors. III. The Origin of the Spin-Orbit Alignment of Galaxy Pairs: A Neighbor versus the Large-scale Structure
aa r X i v : . [ a s t r o - ph . GA ] F e b D RAFT VERSION F EBRUARY
4, 2021Typeset using L A TEX twocolumn style in AASTeX63
Living with Neighbors. III. The Origin of the Spin–Orbit Alignment of Galaxy Pairs:A Neighbor Versus the Large-scale Structure J UN -S UNG M OON ,
1, 2 S UNG -H O A N
1, 2 A ND S UK -J IN Y OON
1, 21
Department of Astronomy, Yonsei University, Seoul, 03722, Republic of Korea Center for Galaxy Evolution Research, Yonsei University, Seoul, 03722, Republic of Korea (Accepted for publication in ApJ)
ABSTRACTRecent observations revealed a coherence between the spin vector of a galaxy and the orbital motion of itsneighbors. We refer to the phenomenon as “the spin–orbit alignment (SOA)” and explore its physical originvia the IllustrisTNG simulation. This is the first study to utilize a cosmological hydrodynamic simulation toinvestigate the SOA of galaxy pairs. In particular, we identify paired galaxies at z = 0 having the nearestneighbor with mass ratios from 1/10 to 10 and calculate the spin–orbit angle for each pair. Our results are asfollows. (a) There exists a clear preference for prograde orientations (i.e., SOA) for galaxy pairs, qualitativelyconsistent with observations. (b) The SOA is significant for both baryonic and dark matter spins, being thestrongest for gas and the weakest for dark matter. (c) The SOA is stronger for less massive targets and fortargets having closer neighbors. (d) The SOA strengthens for galaxies in low-density regions, and the signal isdominated by central–satellite pairs in low-mass halos. (e) There is an explicit dependence of the SOA on theduration of interaction with its current neighbor. Taken together, we propose that the SOA witnessed at z = 0 has been developed mainly by interactions with a neighbor for an extended period of time, rather than tidaltorque from the ambient large-scale structure. Keywords:
Galaxy interactions (600), Galaxy pairs (610), Galaxy encounters (592), Galaxy kinematics (602), Hy-drodynamical simulations (767) INTRODUCTIONThe anisotropy of galaxy orientations has been a matter ofinterest for many decades. Early researchers had already sus-pected that galaxies have a preferred orientation in the sky(Reynolds 1922; Brown 1938, 1939; Wyatt & Brown 1955).With the advent of sky surveys, more evidence was discov-ered to support such an idea. Brown (1964) reported a system-atic alignment of position angles of spiral galaxies in a clus-ter environment. Hawley & Peebles (1975) provided proof thatgalaxies in the Coma cluster are preferentially aligned towardthe cluster center. Until now, many subsequent observations re-vealed that there are multiple types of galaxy alignments ona variety of scales (see a review by Joachimi et al. 2015, andreferences therein). For instance, previous studies found thatthe spatial distribution of satellites in a galaxy group is elon-gated along both the major axis of the central galaxy (e.g.,Sastry 1968; Carter & Metcalfe 1980; Binggeli 1982; Brainerd2005; Yang et al. 2006; Faltenbacher et al. 2007) and the direc-tion of the neighboring groups (e.g., Binggeli 1982; West 1989;Plionis 1994; Wang et al. 2009; Paz et al. 2011). The orienta-tion (or spin) of galaxies appears to be aligned in a specific di-rection within a group (e.g., Thompson 1976; Pereira & Kuhn2005; Agustsson & Brainerd 2006; Faltenbacher et al. 2007;Huang et al. 2018) and even within the Local Superclus-
Corresponding author: Suk-Jin [email protected] ter (e.g., MacGillivray et al. 1982; Flin & Godlowski 1986;Kashikawa & Okamura 1992; Godlowski 1993; Hu et al.2006).It is now broadly accepted that an anisotropy of the uni-verse naturally arises within the framework of the standardcosmology. Small density fluctuations in the primordial uni-verse evolve and collapse under gravity into dark matter (DM)halos, which grow hierarchically via repeated mergers and ac-cretions (e.g., White & Rees 1978). The hierarchical growth ofhalos takes place along preferential directions. Massive halosare fed with material via anisotropic flow from voids to sheets,to filaments, and then to nodes, constituting the large-scalestructure (LSS) commonly referred to as the cosmic web (e.g.,Cautun et al. 2014). Furthermore, a tidal field generated by thesurrounding LSS acts on the DM halos and galaxies to stretchtheir shape and induce their spin (Peebles 1969; Doroshkevich1970; White 1984; see also Sch¨afer 2009 for a review). Thusthe observed alignments between shape, kinematics, and distri-bution of galaxies are, so to speak, inevitable outcomes stem-ming from the geometry of the LSS (e.g., Catelan et al. 2001;Crittenden et al. 2001; Lee & Pen 2001; Porciani et al. 2002;Codis et al. 2015a; Lee 2019).The alignment between the halo and the LSS is one of themost intensively studied subjects. Theoretical studies based onnumerical simulations arrived at a conclusion that there is amass-dependent alignment between the halo spin and the LSS,suggesting that the spin vector of the less (more) massive halosprefers to be parallel (perpendicular) to the filamentary struc-ture (Arag´on-Calvo et al. 2007; Hahn et al. 2007; Codis et al. M OON , A N & Y OON N -body sim-ulation, L’Huillier et al. (2017) investigated various kinds ofalignments within interacting halos and stated that spin vectorsof neighboring pairs are aligned with their orbital angular mo-mentum vectors. An et al. (2021) analyzed DM halo pairs withoverlapping virial radii and detected a signal of the SOA, whichis stronger for gravitationally bound (i.e., merging) pairs. Bothstudies confirmed the SOA of halo pairs based on DM-onlysimulations, but so far there has been no attempt to use numer-ical simulations to examine the SOA on the scale of a galaxypair.The SOA can be understood in the context of the effectsof both LSS and neighbors. As already addressed, previousstudies have found the alignment between the galaxy spinand the LSS (e.g., Tempel & Libeskind 2013; Tempel et al.2013; Dubois et al. 2014), which is attributed to the large-scaletidal field (e.g., Sch¨afer 2009) and the preferential accretionof material (e.g., Libeskind et al. 2014; Kang & Wang 2015).With the proximity of two galaxies in a pair, a common lo-cal tidal field determines their angular momenta in the earlyuniverse. The anisotropic accretion along the cosmic web nat-urally leads to the SOA because the galaxy spin is influencedby the orbital angular momentum of the accreted matter. Onthe other hand, a well-known example of the effect of interac-tions on the galaxy orientation is given by satellites in mas-sive groups. Due to the tidal effect of the central halo, themajor axis of the satellite is eventually aligned to the direc-tion of the halo center (Usami & Fujimoto 1997; Pereira et al.2008; Rong et al. 2015), which is called the radial align-ment of satellites and has been investigated in many studiesthrough both observations (Thompson 1976; Pereira & Kuhn2005; Agustsson & Brainerd 2006; Faltenbacher et al. 2007;Huang et al. 2018; Rong et al. 2019) and theoretical models(Ciotti & Dutta 1994; Usami & Fujimoto 1997; Kuhlen et al.2007; Pereira et al. 2008; Rong et al. 2015; Tenneti et al. 2015;Knebe et al. 2020). Similarly, Welker et al. (2018) showed, us-ing a cosmological simulation, that the alignment between thespin of a central galaxy and the orbits of its satellites is devel-oped in the inner region of the halo by gravitational torquesfrom the central, while the dynamics of satellites in the outerregion is more governed by the geometry of the LSS.In this series of papers, we have highlighted the impact ofinteracting neighboring galaxies (or halos) on galaxy evolu-tion by means of both observations and theoretical models.Moon et al. (2019, Paper I) investigated the impact of galaxyinteractions on star formation based on the Sloan Digital SkySurvey and showed that the star formation activity is enhancedor reduced depending on neighbors’ hydrodynamic properties.An et al. (2019, Paper II), using a set of cosmological N -bodysimulations, found that the dominance of flyby interactionsover mergers increases at lower redshifts, for less massive ha-los, and in denser environments. In the present paper, we ex-plore the SOA of galaxy pairs using a state-of-the-art cosmo-logical hydrodynamic simulation from the IllustrisTNG project(Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018;Pillepich et al. 2018a; Springel et al. 2018). This is the first RIGIN OF S PIN –O RBIT A LIGNMENT OF G ALAXY P AIRS METHODS2.1.
The IllustrisTNG Simulation
For the present study, we use the public data releaseof the IllustrisTNG project (Nelson et al. 2019). The Il-lustrisTNG project is a suite of cosmological magnetohy-drodynamical simulations performed with the moving-meshcode
AREPO (Springel 2010). The simulation assumes a Λ CDM cosmology with Ω m = 0 . , Ω Λ = 0 . , Ω b = 0 . , h = 0 . , σ = 0 . , and n s =0 . (Planck Collaboration et al. 2016). A set of physi-cal models describing galaxy formation and evolution isemployed in the simulation suite, including primordial andmetal-line radiative cooling, star formation, chemical enrich-ment, stellar feedback-driven outflow, supermassive black holegrowth, and active galactic nucleus feedback (for details, seeWeinberger et al. 2017; Pillepich et al. 2018b). The model rea-sonably well reproduces the fundamental properties and scal-ing relations of observed galaxy populations (Marinacci et al.2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et al.2018a; Springel et al. 2018).We use the TNG100 run (see for details Nelson et al. 2019),which has a box with a side length of 75 h − Mpc. The data re-lease contains three realizations of the same volume at differentresolution levels (TNG100-1, -2, and -3) and their dark matter-only counterparts (-Dark). The main results presented here arebased on the highest-resolution run (TNG100-1), which in-cludes 1820 DM particles and an equal number of initial gascells, and the corresponding mass resolution is 7.5 × M ⊙ and 1.4 × M ⊙ for dark matter and baryonic components,respectively. The gravitational softening length for collision-less particles is 1.0 h − kpc in comoving units and is furtherlimited to 0.5 h − kpc in physical units below z = 1 . The soft-ening of gas cells is adaptively scaled to be proportional to thecell radius. The simulation starts from z = 127 and outputs100 snapshots from z = 20 to z = 0 with a maximum timespacing of ∼
200 Myr.The data provided in each snapshot includes the halo cata-log and the merger tree. Dark matter halos are identified bythe friends-of-friends (FoF) algorithm with a linking length of0.2 times the mean interparticle separation. Subhalos, locallyoverdense and self-bound substructures within the FoF halos,are detected by using the
SUBFIND code (Springel et al. 2001;Dolag et al. 2009). Each subhalo with nonzero stellar mass cor-responds to a single galaxy, making each FoF halo equivalent to a group or a cluster of galaxies. We refer to the most mas-sive subhalo in each FoF halo as a central and to other subhalosas satellites. The merger tree enables a subhalo at any epochto be connected to its progenitors or descendants at differ-ent snapshots. The
SubLink code (Rodriguez-Gomez et al.2015) generates the merger tree used in this study.2.2.
Sample Selection
We start by defining a sample of paired galaxies from theTNG100. To avoid selecting spurious objects, we only considersubhalos with the stellar mass M ∗ > h − M ⊙ at z = 0 ,which typically contains at least 100 star particles. The sampleis also restricted to subhalos that are identified as of a cos-mological origin in the SubhaloFlag field of the subhalocatalog (Nelson et al. 2019), excluding non-cosmological ob-jects such as overdense clumps embedded within galaxies. Bydefinition, a subhalo is flagged as a cosmological one if it isformed either (i) as a central, (ii) outside the virial radius of itshost halo, or (iii) with the dark matter fraction higher than 0.8.We consider these luminous, cosmological subhalos as galax-ies throughout the paper.The nearest neighboring galaxy is identified for all targetgalaxies with M ∗ > h − M ⊙ at z = 0 . The nearest neigh-bor should have a stellar mass larger than at least one-tenth ofthe target’s mass to ensure a strong influence exerted on the tar-get galaxy. Once the identification is made, we limit our anal-ysis to pairs of galaxies with the stellar mass ratio between thetarget and neighbor, | µ ∗ | = | log( M ∗ , nei /M ∗ , target ) | < . , be-cause our interest is in paired galaxies of comparable mass, notsatellites around a giant galaxy. When a target galaxy and itsnearest neighbor are both members of the same FoF halo, thetarget is regarded as paired with the neighbor and used in ouranalysis. In total, the sample contains 7607 target galaxies at z = 0 . We note that not all the targets are in isolated binary sys-tems; only 3494 galaxies out of the 7607 are mutually pairedwith each other. Note also that we do not consider whether thenearest neighbor is a central or a satellite during the sampleselection process, and thus our sample includes both central–satellite and satellite–satellite pairs; 2681 and 4926 galaxiesbelong to each group, respectively.2.3. Remarks on Paired Galaxies
Our sample selection is on the basis of the subhalo proper-ties identified by the halo finder, but the ability of halo find-ers is known to be incomplete for interacting systems (e.g.,Muldrew et al. 2011; Knebe et al. 2013; Behroozi et al. 2015).Specifically, the
SUBFIND algorithm, which is used in thisstudy, assigns particles unbound to any substructure in an FoFhalo to the background halo (see Springel et al. 2001). Thiscauses loosely bound particles in the outskirt of the smallerof the two interacting galaxies (i.e., identified as a satellite)are assigned to the larger (i.e., a central). Hence, the mem-bership of particles to subhalos is severely affected by thepresence of a companion, and the spurious mass loss occur-ring in satellites increases the mass ratio of galaxy pairs asthe two galaxies approach each other (Behroozi et al. 2015;Rodriguez-Gomez et al. 2015; Patton et al. 2020). Fortunately,as shown in Behroozi et al. (2015), the position of a subhalo,defined as the location of the particle with the lowest gravita-tional potential, is relatively robust as long as the halo finderdetects the subhalo. The stellar mass, however, is very vulner-able to numerical mass loss. M OON , A N & Y OON
Figure 1.
Examples of paired galaxies in TNG100. The selected six pairs are equal-mass (1/3 < µ ∗ <
3) central–satellite pairs where the centralshows the largest difference in stellar mass from the original catalog. Star particles assigned in centrals and satellites are colored red and blue,respectively. In each panel, the original stellar half-mass radius is shown as a gray dashed circle, and the updated radius as a black circle.
We update the stellar mass, M ∗ , of each paired galaxy as thevalue at the snapshot where the less massive of the two galaxiesin a pair reaches its maximum stellar mass ( t max ), as suggestedin Rodriguez-Gomez et al. (2015). We then calculate the stel-lar half-mass radius, r h , which is defined as the radius of asphere containing half of the stellar mass. The calculation of r h is based on the stellar mass at t max and the distribution of starparticles at z = 0 without using the particle membership in-formation obtained by the halo finder. Here, unlike the originaldefinition of t max , we define the time when a galaxy is pairedwith its current neighbor ( t nei ) and limit the search of t max tosnapshots (i) after t nei and (ii) within the past 2 Gyr. Theseconditions are applied to prevent too early t max for galaxiesthat gradually lose mass regardless of interactions with theircurrent neighbors. In practice, we determine t nei by findingthe earliest snapshot where the nearest neighbor at z = 0 re-mains the same without any change, paying special attention tothe following two cases. First, for galaxies with broken mergertrees, which are mostly ones deprived of DM, we repair thetrees by filling in the missing progenitors with subhalos hav- For the same reason, Patton et al. (2020) defined t max as the time when agalaxy reaches its maximum stellar mass within the past 0.5 Gyr. We insteaduse t nei as a constraint to take into account the difference in interaction timefor each pair, but ∼
90 % of targets have t max within the past 0.5 Gyr. Ad-ditionally, we impose an upper limit of 2 Gyr in lookback time to minimizethe effect of physical stripping, which affects only ∼ ing the largest number of star particles in common. Second,some galaxies always have the same nearest neighbor sincetheir stellar masses reach 10 h − M ⊙ , below which we can-not correctly identify the neighbor at a given mass resolution.For these galaxies, the earliest snapshot where the neighboris identified (i.e., the time when the stellar mass exceeds 10 h − M ⊙ ) is used as (the lower limit of) t nei .Figure 1 demonstrates several examples of close galaxy pairsin TNG100. The six pairs are selected among central–satellitepairs that have a large difference between the stellar mass at t max and at z = 0 . Star particles in centrals and satellites areshown in red and blue, respectively, according to the member-ship information determined by the halo finder at z = 0 . It isclear that, for these pairs, the halo finder assigns stars in theouter part of the satellites as members of the centrals. Conse-quently, this makes the updated r h of centrals smaller and thatof satellites larger than the catalog values, as seen by compar-ing the solid and dashed circles. We compare the updated massand size with those stored in the halo catalog in Figure 2. Panel(a) shows the ratio of the new to the original stellar masses withrespect to the separation to the nearest neighbor, γ nei , definedas γ nei = d nei r h , target + r h , nei , (1)where d nei is the 3D distance to the nearest neighbor, and r h , target and r h , nei are the stellar half-mass radii of the targetand the nearest neighbor, respectively. For centrals (red), the RIGIN OF S PIN –O RBIT A LIGNMENT OF G ALAXY P AIRS γ nei ≡ d nei / (r h, target + r h, nei ) M * ( n e w ) / M * ( o l d ) centralsatellite (a) γ nei ≡ d nei / (r h, target + r h, nei ) | μ * | ( n e w ) | μ * | ( o l d ) (b) γ nei ≡ d nei / (r h, target + r h, nei ) r h ( n e w ) / r h ( o l d ) (c) Figure 2.
Comparison between the updated and the catalog values of (a) the stellar mass, (b) the stellar mass ratio, and (c) the stellar half-massradius with respect to the separation to the nearest neighbor for centrals (red circle) and satellites (blue triangle) in the paired galaxy sample. Theinsets show the mean changes in the subhalo properties at a small separation. updated stellar mass decreases below the catalog value as theneighbor approaches. On the contrary, the updated stellar massof satellites (blue) increases as the separation decreases. Thediscrepancy in the stellar mass starts to appear at γ nei ∼ butbecomes significant at γ nei < , for both centrals and satel-lites (see the inset). The decrease in the centrals’ mass and theincrease in the satellites’ mass result in the smaller mass ra-tio, as presented in panel (b). Similarly, the change in the totalstellar mass is followed by the change in the stellar half-massradius in panel (c). We stress again that, although there may besome real effect of interactions, the mass transfer between thecentral and satellite is primarily numerical and not physical inmost cases, as discussed previously.2.4. Spin–Orbit Angle
To quantify the strength of the SOA, we first calculate thespin vector of a target and the orbital angular momentum vec-tor of its neighbor. The spin vector, S , denotes an angular mo-mentum vector within the stellar half-mass radius, that is, S = X i m i ( r i × v i ) only if r i < r h , (2)where m i is the mass of the i th star particle, and r i and v i are the position and velocity with respect to the galaxy cen-ter, respectively. As shown in Figure 1, many paired galaxiesare more or less overlapped with each other, making it diffi-cult to separate the two galaxies. For this reason, we choose touse only the spin at the central region within r h determined inSection 2.3. We measure the spin vector ( S ) separately for eachparticle type (gas, star, and DM) with the same size of aperture,considering the misalignment between them (e.g., Chisari et al.2017; Duckworth et al. 2020; Khim et al. 2020). The orbitalangular momentum vector, L , is calculated by taking the crossproduct of the position vector ( d nei ) and the velocity vector( v nei ) of the nearest neighbor in the reference frame of the tar-get, namely L = d nei × v nei . (3)In all the calculations, the position of each galaxy center is de-fined as the location of the particle at the lowest potential, andthe velocity is the mass-weighted mean velocity of all particleswithin r h .The spatial resolution of TNG100 ( ∼ z = 0 ) is not satisfactory to resolve the inner struc-ture of galaxies. Nevertheless, about 98 % of galaxies in our Figure 3.
Definition of the spin–orbit angle θ SL , which is the anglebetween the spin vector of the target S and the orbital angular mo-mentum vector of the neighbor L . sample have r h larger than the softening length for star par-ticles, and about 60 % of the galaxies have r h exceeding 2.8times the softening length where the force is exactly Newto-nian. We need only the spin direction within r h for our analy-sis, and therefore we do not expect the resolution changes theoverall results. To obtain a more reliable measurement of thespin vector, we require a minimum of 100 elements for eachparticle type within r h . Note that we also exclude 173 severelyoverlapped pairs with γ nei < from the sample to preventcontamination from particles belonging to the neighbor. Thecriteria leave 4226, 7287, and 7434 galaxies with an availablespin vector for gas, DM, and stars, respectively.We define the spin–orbit angle θ SL as the angle between thespin vector ( S ) and the orbital angular momentum vector ( L )in a pair (see Figure 3). Note that the angle, θ SL , is measuredfrom S to L in the counterclockwise direction when viewedfrom the positive z-side, within the range from 0 ◦ (aligned) to ± ◦ (anti-aligned). We refer to the case where cos θ SL > | θ SL | < ◦ ) as ‘prograde’ and the case where cos θ SL < | θ SL | > ◦ ) as ‘retrograde,’ respectively. The probabilitydistribution function (PDF) of the spin–orbit angle is expressedas n (cos θ SL ) = N (cos θ SL ) h N rand (cos θ SL ) i , (4)where N (cos θ SL ) is the number of pairs in each bin, and h N rand (cos θ SL ) i is the expected number of pairs from therandom isotropic sample with the same size. Therefore, n (cos θ SL ) is close to unity in a uniform distribution, and,if paired galaxies have a preference for a spin–orbit angle M OON , A N & Y OON −1.0 −0.5 0.0 0.5 1.0 cos θ SL n ( c o s θ S L ) All Sa plef prog = 56.27%p KS < 0.0001p K < 0.0001 Ma%chedf prog = 56.32%p KS < 0.0001p K < 0.0001 (a) Gas −1.0 −0.5 0.0 0.5 1.0 cos θ SL All Sa plef prog = 53.62%p KS < 0.0001p K < 0.0001 Ma%chedf prog = 55.24%p KS < 0.0001p K < 0.0001 (b) S%ar −1.0 −0.5 0.0 0.5 1.0 cos θ SL All Sa plef prog = 52.94%p KS < 0.0001p K < 0.0001 Ma%chedf prog = 53.88%p KS < 0.0001p K < 0.0001 (c) DM Figure 4.
PDF of the spin–orbit angle of paired galaxies in TNG100 for (a) gas, (b) stars, and (c) DM. Black lines show the PDFs for galaxiesthat have at least 100 corresponding cells or particles within r h . The shaded region shows the standard deviation estimated from 1000 randomlygenerated isotropic samples with the same size as the original sample. Gray lines show the PDFs for galaxies with at least 100 cells or particlesavailable for all the three components of galaxies within r h . The two lines are almost identical in panel (a). The p -values of the KS test ( p KS ) andthe Kuiper’s test ( p K ) and the prograde fraction ( f prog ) are given on each panel. All p -values less than 10 − are denoted as < of θ SL , n (cos θ SL ) would be greater than 1. We compute thestandard deviation of PDFs, σ rand (cos θ SL ), over 1000 ran-dom isotropic samples and, following Yang et al. (2006), use σ rand (cos θ SL ) / h N rand (cos θ SL ) i to evaluate the significanceof the alignment. RESULTS3.1.
Spin–Orbit Alignment
Figure 4 shows the PDF of the spin–orbit angle, n (cos θ SL ),for paired galaxies in TNG100. Black lines in panels (a), (b),and (c) represent the results obtained for gas, stars, and DM, re-spectively. It is obvious that the paired galaxies prefer progradeorientations to retrograde ones; n (cos θ SL ) is greater than 1 forcos θ SL & θ SL .
0. The preference ofprograde orientation is common in all panels. The maximumsignificance compared to the random isotropic sample is 9.8 σ ,6.5 σ , and 4.9 σ at cos θ SL ∼ SciPy module (Virtanen et al. 2020) to quantify the statisticaldifference of the PDF of the spin–orbit angle from the uniformdistribution. The p -values of the hypothesis that the samples inpanels (a)–(c) are drawn from the random orientation are allless than 10 − ( p KS < While the widely used KStest strongly suggests that the spin–orbit orientation is not ran-dom, the sensitivity of the KS test is not uniform across theentire distribution (i.e., most sensitive near the median), andhence it may not be adequate for directional data (e.g., anglesand vectors). Therefore, we additionally test the isotropy us-ing the Kuiper’s test (see Stephens 1965; Paltani 2004) in the astropy module (Astropy Collaboration et al. 2018), whichis similar to the KS test but rotation-invariant. The probabil-ity that the distribution of θ SL is drawn from isotropic S and L (against a sinusoidal PDF of n ( θ SL ) ∼ | sin( θ SL ) | ) is found to bevery low ( p K < f prog , as a simple metric to quantify the We denote the p -values less than 10 − as ‘ < p -values to as many decimalplaces as possible, due to their high sample-to-sample variability (see, e.g.,Boos & Stefanski 2011; Lazzeroni et al. 2014). prevalence of prograde orientations, such that f prog = N (cos θ SL > N total , (5)where N (cos θ SL >
0) is the number of galaxies on progradeorbits and N total is the total number of galaxies, and the ex-pected value of f prog for the isotropic orientation is 50 %. Theprograde alignment for the gas spin vector is the strongest, andthe strength decreases in the order of gas, stars, and DM; f prog is 56.3 ± ± ± r h . Gas-poor galaxies usuallycontain a small number of gas cells, making the sample size ofpanel (a) smaller than the others. We repeat the analysis usinggalaxies commonly included in all three panels to remove theselection effect and display the result as gray lines in Figure 4.For this ‘matched’ sample, the result does not change signifi-cantly. There is a clear signal of prograde alignment, and thestrongest alignment is obtained for gas, followed by stars, andthe weakest is for DM. The only notable difference is that theprograde fraction for stars and DM become slightly higher thanthat for the whole sample; f prog = σ = p f (1 − f ) /N ∼ r h , and the galaxy pairs should have γ nei > —that is, the distance between the two galaxies shouldbe greater than six times of the mean r h of the two, while,on average, more than 90 % of their stellar mass is enclosedwithin × r h (see also Pillepich et al. 2018a). Furthermore, RIGIN OF S PIN –O RBIT A LIGNMENT OF G ALAXY P AIRS n ( c o s θ S L ) f rog = 62.37% p KS < 0.0001p K < 0.0001 nei % 20 f rog = 55.08% p KS < 0.0001p K < 0.0001
20 < γ nei % 40 f rog = 51.84% p KS = 2.03e-2p K = 7.28e-3 γ nei > 40 G a s n ( c o s θ S L ) f rog = 56.99% p KS < 0.0001p K < 0.0001 f rog = 52.19% p KS = 1.05e-3p K = 2.58e-3 f rog = 52.17% p KS = 2.55e-2p K = 2.23e-3 S t a r −1 0 1 cos θ SL n ( c o s θ S L ) f rog = 55.60% p KS < 0.0001p K < 0.0001 −1 0 1 cos θ SL f rog = 52.65% p KS = 7.15e-3p K = 2.44e-2 −1 0 1 cos θ SL f rog = 51.02% p KS = 4.45e-2p K = 9.42e-2 D M Figure 5.
PDF of the spin–orbit angle of paired galaxies in subsamples split by separation. From left to right, the separation to the neighbor γ nei increases. The spin–orbit angle of each galaxy is calculated separately for gas (top), stars (middle), and DM (bottom). The format is the same as inFigure 4. we expect that the problem should be most prominent for DM,which is more spatially extended than the other components,but the alignment for the DM appears to be the weakest in Fig-ure 4. Therefore, we conclude that at least the SOA for stars isreliable, although one must keep in mind that the alignment formore extended components like gas and DM can be artificiallyexaggerated.Figure 5 shows the PDF of the spin–orbit angle as a func-tion of the separation to the nearest neighbor ( γ nei ). The sam-ple is split into four subsamples by separation to the neighbor.The figure clearly shows that the alignment signal becomesweaker as the separation increases. There is a significant ex-cess in the fraction of prograde orientations for paired galaxies with γ nei < , and the p -values from the KS and the Kuiper’stests for this subsample are extremely small ( p < . ) forall the components of gas, stars, and DM. The prograde frac-tion decreases with increasing separation, and the p -values alsoincrease. This indicates that a strong signal of the SOA re-quires the presence of close neighbors. In Figure 6, we plot theprograde fraction as a function of the separation to the near-est neighbor. First of all, the prograde fraction is larger than50 % even at a relatively large separation ( γ nei ∼ ), whichsuggests that paired galaxies generally prefer prograde orienta-tions rather than random ones. As already seen in Figure 5, theprograde fraction decreases as the separation increases. Whilethe spin direction of galaxies with γ nei > are almost ran- M OON , A N & Y OON γ nei ≡ d nei / (r h, target + r h, nei ) f p r o g ( % ) (a) Gas γ nei d nei / (r h, target + r h, nei )(b) Star γ nei d nei / (r h, target + r h, nei )(c) DM Figure 6.
Prograde fraction of the spin–orbit angle calculated for (a) gas, (b) stars, and (c) DM as a function of the separation to the nearest neighbor.Error bars represent the standard error of the percentage. domly distributed with respect to the orbit, the prograde frac-tion sharply increases at γ nei < and reaches to 68.6 ± ± ± < γ nei < (the leftmost bin) for gas, stars, and DM, respectively.The SOA that we find here is in line with previous stud-ies (L’Huillier et al. 2017; Lee et al. 2019a). For instance,L’Huillier et al. (2017) discovered the SOA for paired galax-ies within the virial radius of the neighboring halo (on ascale of hundreds of kiloparsecs), using an N -body simulation.Lee et al. (2019a) observationally found the kinematic coher-ence within a distance of 1 Mpc. Back in Figures 5 and 6, thealignment signal extends out to γ nei ∼ , which correspondsto d nei ∼ kpc on average with a large spread, and hence thescale of the alignment seen in this study is roughly comparableto that of previous results. Going a step further, we make use ofa cosmological hydrodynamic simulation to study the SOA ofgalaxy pairs for the first time. The result from the IllustrisTNGshows that a strong prograde alignment is established even ifbaryonic processes are taken into account.3.2. Mass and Environment Dependence
In order to deepen our understanding of the SOA, we explorethe factors that influence the strength of the alignment signal.Galaxy mass and environment are key factors that play a rolein galaxy evolution, each representing the internal and externalaspects of galaxy characteristics. We thus begin by examiningthe dependence of the SOA on mass and environment. As forthe mass, we simply use the stellar mass of the target, M ∗ ,defined by the method described in Section 2.3. As for the en-vironment, we calculate the number density of galaxies, whichis defined as Σ k = 3 k π ( d k / Mpc) , (6)where d k is the distance to the k th nearest neighbor from thetarget. To calculate the density, we consider only luminous sub-halos of the cosmological origin (see Section 2.2). We take thegeometric mean of Σ and Σ as a representative estimate ofthe local density Σ .Figure 7 shows the PDF of the stellar spin–orbit angle fornine subsamples split by the stellar mass and the local density.We present only the result for stars, which is the most robust,but similar trends are also seen for gas and DM. We find thatthe significance of alignment increases as both the stellar mass and the local density decrease. Low-mass target galaxies inlow-density environments (shown in the top left panel) exhibitthe strongest alignment signal ( p KS < p K < f prog = ± f prog = ± f prog = ± γ nei < ; shown as gray lines).Figure 8 presents the prograde fraction as functions of thestellar mass and the local density. As shown in the top panels,the dependence on the stellar mass is marginal. The progradefraction for stars (solid lines) increases with decreasing thestellar mass only when the galaxies reside in low-density en-vironments (log Σ ≤ Σ >
1) does not depend on the stellar mass. On the otherhand, the dependence on the local density in the bottom pan-els is more pronounced. Paired galaxies in low-density regionsgenerally show a higher prograde fraction than those in high-density regions. This trend is valid for all components (gas,stars, and DM) of low- and intermediate-mass target galax-ies ( M ∗ ≤ M ⊙ ). To summarize, the SOA signal becomesmore robust as both the stellar mass and the local density de-crease, and the local density seems to be a more critical factorthan the stellar mass. Lee et al. (2019a) observed that faint orblue target galaxies have a stronger alignment than bright or redones. The trend we find is consistent with theirs, given the factthat low-density regions are largely populated by blue galax-ies (e.g., Bamford et al. 2009), although they did not directlyinspect the local environment.Figure 9 shows the prograde fraction as a function of the stel-lar mass ratio between the target and the nearest neighbor. Wedo not find any significant effect of the stellar mass ratio, butthere is a slight increase in the prograde fraction for pairs withlarge | µ ∗ | compared to those with small | µ ∗ | . Gray lines showthe case for target galaxies with 10 . < M ∗ /M ⊙ < to get RIGIN OF S PIN –O RBIT A LIGNMENT OF G ALAXY P AIRS n ( c o s θ S L ) All Sample p KS < 0.0001p K < 0.0001f prog = 62.19% γ nei < 20 p KS < 0.0001p K < 0.0001f p%og = 68.56% * /M ⊙ ⊙ ≤ ⊙9.5 A ⊙Samp e p KS = 1.26e-3p K = 1.54e-3f prog ⊙=⊙57.64% γ nei < 20 p KS < 0.0001p K < 0.0001f p%og = 64.68% * /M ⊙ ≤ 10 A Samp e p KS = 1.07e-3p K < 0.0001f p%og = 57.06% γ nei < 20 p KS = 1.16e-3p K = 6.58e-3f p%og = 63.07%
10 < og M * /M ⊙ ≤ 12 o g Σ ≤ n ( c o s θ S L ) All Sample p KS = 1.48e-2p K = 6.15e-3f prog = 55.61% γ nei < 20 p KS = 1.45e-3p K = 7.08e-4f prog = 69.74% All Sample p KS = 5.00e-1p K = 3.67e-1f prog = 50.56% γ nei < 20 p KS = 4.12e-2p K = 6.41e-2f prog = 60.00% All Sample p KS = 4.38e-2p K = 6.25e-3f prog = 51.96% γ nei < 20 p KS = 3.01e-2p K = 2.57e-2f prog = 57.45% < l o g Σ ≤ −1 0 1 cos θ SL, * n ( c o s θ S L ) All Sample p KS = 4.46e-2p K = 1.09e-1f prog = 51.37% γ nei < 20 p KS = 2.34e-1p K = 2.56e-1f prog = 46.95% −1 0 1 cos θ SL, *
A Samp e p KS = 6.10e-1p K = 8.22e-1f prog = 50.44% γ nei < 20 p KS = 3.87e-1p K = 4.68e-1f prog = 52.65% −1 0 1 cos θ SL, *
A Samp e p KS = 1.97e-2p K = 2.49e-2f prog = 53.34% γ nei < 20 p KS = 2.09e-1p K = 2.64e-1f prog = 53.75% l o g Σ > Figure 7.
PDF of the stellar spin–orbit angle of paired galaxies in subsamples split by the stellar mass and the local density. The stellar mass M ∗ increases from left to right columns, and the local density Σ increases from top to bottom rows. Black lines and dark gray shades are for the wholesample, and gray lines and light gray shades are for paired galaxies with γ nei <
20. The format is the same as in Figure 4. rid of the effect of stellar mass, but the result is barely differ-ent from the whole sample. The dependence of the alignmenton the mass ratio is generally insignificant within the range of / < µ ∗ < , and all results of this paper are qualitativelyunchanged if we restrict our analysis only to equal-mass pairs(e.g., / < µ ∗ < ).3.3. Impact of Halo-scale Environments
The presence of the SOA governed by environment raisesadditional questions: Does the halo-scale environment play aparticular role in the formation of the SOA? Does it matter ifa galaxy is a central or a satellite in a halo? Is the halo-scaleenvironment more important than the large-scale one? We tryto answer such questions in this subsection. Figure 10 shows the PDF of the stellar spin–orbit angle for subsamples splitby whether the target and neighbor are a central or a satel-lite. Since the target and neighbor in each pair share the sameFoF halo by definition (see Section 2.2), there are three pos-sible target–neighbor combinations: central–satellite, satellite–central, and satellite–satellite pairs. We can see that there is aclear difference between the subsamples. The central–satellitepairs in panel (a) exhibit a clear signal of SOA; the p -values ofboth the KS and Kuiper’s tests are < ± p -values of both tests are < ± M OON , A N & Y OON log M * /M ⊙ f p r o g ( ⊙ ) log Σ 0 log M * /M ⊙ log M * /M ⊙ GasStarDM log Σ > 1 −1 0 1 2 3 log Σ (Mpc −3 ) f p r o g ( % ) ≲ /M ⊙ −1 0 1 2 3 log Σ (Mpc −3 ) ≲ /M ⊙ −1 0 1 2 3 log Σ (Mpc −3 )
10 ⊙ log M ≲ /M ⊙ Figure 8.
Top: prograde fraction of the spin–orbit angle as a function of the stellar mass within fixed ranges of the local density. The spin–orbitangle of each galaxy is calculated separately for gas (solid lines), stars (dashed lines), and DM (dotted lines). For each line, the three bins containan equal number of galaxies. Error bars represent the standard error of the percentage. Bottom: the same as the upper panels, but as a function ofthe local density within fixed ranges of the stellar mass. −1.0 −0.5 0.0 0.5 1.0 μ * ≡ log(M *, nei / M *, arge ) f p r o g ( % ) (a) Gas −1.0 −0.5 0.0 0.5 1.0 μ * ≡ log(M *, nei / M *, arge ) (b) S ar −1.0 −0.5 0.0 0.5 1.0 μ * ≡ log(M *, nei / M *, arge ) (c) DM All Sample9.5 < log M * /M ⊙ < 10.0 Figure 9.
Prograde fraction of the spin–orbit angle calculated for (a) gas, (b) stars, and (c) DM as a function of the stellar mass ratio of the neighborto the target. Black lines are for the whole sample, and gray lines are for target galaxies with 10 . < M ∗ /M ⊙ < . Error bars represent thestandard error of the percentage. the satellite–satellite pairs in panel (c) do not show a significantlevel of SOA; p KS is only 0.024, p K is 0.009, and the progradefraction is 51.4 ± γ nei < (shown as gray lines). While the pro-grade fraction for the central–satellite and the satellite–central RIGIN OF S PIN –O RBIT A LIGNMENT OF G ALAXY P AIRS −1.0 −0.5 0.0 0.5 1.0 cos θ SL, * n ( c o s θ S L ) All Sa ple p KS < 0.0001p K < 0.0001f prog = 57.80% γ nei < 20 p KS < 0.0001p K < 0.0001f prog = 64.02% (a) Central−Satellite −1.0 −0.5 0.0 0.5 1.0 co% θ SL, *
All Sa ple p KS < 0.0001p K < 0.0001f prog = 57.95% γ nei < 20 p KS < 0.0001p K < 0.0001f prog = 61.31% (b) Satellite−Central −1.0 −0.5 0.0 0.5 1.0 co% θ SL, *
All Sa ple p KS = 2.40e-2p K = 9.17e-3f prog = 51.41% γ nei < 20 p KS = 5.79e-1p K = 3.94e-1f prog = 51.36% (c) Satellite−Satellite Figure 10.
PDF of the stellar spin–orbit angle of (a) central–satellite pairs (central targets with a satellite neighbor), (b) satellite–central pairs(satellite targets with a central neighbor), and (c) satellite–satellite pairs (satellite targets with a satellite neighbor). Black lines are for the wholesample, and gray lines are for paired galaxies with γ nei <
20. The format is the same as in Figure 4. −1 0 1 2 3 log Σ (Mpc −3 ) f p r o g ( % ) Gas −1 0 1 2 3 log Σ (Mpc −3 ) Star −1 0 1 2 3 log Σ (Mpc −3 ) Cen-SatSat-CenSat-Sat DM
11 12 13 14 log M /M f p r o g ( ⊙ ) Gas
11 12 13 14 log M /M Star
11 12 13 14 log M /M DM Figure 11.
Top: prograde fraction of the spin–orbit angle as a function of the local density for central–satellite pairs (solid lines), satellite–centralpairs (dashed lines), and satellite–satellite pairs (dotted lines). The spin–orbit angle of each galaxy is calculated separately for gas (left), stars(middle), and DM (right). For each line, the three bins contain an equal number of galaxies. Error bars represent the standard error of the percentage.Bottom: the same as the top panels, but as a function of the halo mass (the mass enclosed in a sphere with a mean density of 200 times the criticaldensity). pairs increases with decreasing the separation as already shownin Figure 6, the satellite–satellite pairs alone show no signal of alignment ( p KS = p K = f prog = ± γ nei < ).2 M OON , A N & Y OON
It is obvious that the SOA is developed by interactions be-tween a central and its satellites. This reminds us of the so-called radial alignment in galaxy groups. It is known thatthe major axes of satellites in a massive group tend to bealigned toward the direction of the central galaxy, which isdue to the tidal torque induced by the DM halo embeddingthe satellites (e.g., Pereira & Kuhn 2005; Pereira et al. 2008;Rong et al. 2015). Given the radial alignment, it is possible toexpect that the spin of the satellites is (perpendicularly) alignedwith the direction to the central because the tidal torque alsochanges the angular momentum perpendicular to the orbitalplane (Usami & Fujimoto 1997). However, the main differencebetween the radial alignment and the SOA is that the latter ismore prevalent in low-density regions (see Figures 7 and 8),while the former is explained by the assumption of a massivegroup which is abundant in dense environments.In Figure 11, we investigate the correlation between theSOA and the inter- and intra-halo-scale environments. The toppanels show the prograde fraction as a function of the localdensity for central–satellite pairs (solid lines), satellite–centralpairs (dashed lines), and satellite–satellite pairs (dotted lines).Interestingly, there is a strong connection between the cen-tral/satellite type and the local density. The satellite–satellitepairs are in environments distinct from the others in that themajority of them reside in dense regions. This seems reason-able because the number ratio of satellites to centrals is high indense regions such as clusters or groups, and massive centralsin such regions are also difficult to meet the mass ratio criterion(i.e., | µ ∗ | < . ) with much less massive satellites. Therefore,the absence of the SOA for the satellite–satellite pairs in Fig-ures 10 and 11 is essentially identical to the weak alignment inhigh-density regions shown in Figures 7 and 8. Nevertheless,central–satellite (and satellite–central) pairs show a higher pro-grade fraction than satellite–satellite pairs at fixed local den-sity (e.g., 0.5 < log Σ < M c ), definedas the total mass enclosed within a sphere with a mean densityequal to 200 times the critical density. The prograde fractiondecreases as the halo mass increases. As expected, the ma-jority of satellite–satellite pairs are located in massive halos,and the difference in the mean halo mass between the satellite–satellite and central–satellite pairs is more dramatic than that inthe local density. A significant SOA is evident only for galaxiesin less massive halos, and hence mostly central–satellite (andsatellite–central) pairs.In this paper, we do not attempt to disentangle further the rel-ative importance among the local density, the halo mass, andthe central/satellite type due to their strong degeneracy. Themessage from Figure 11, however, is quite clear; the SOA isbetter developed in simpler systems where only a few galax-ies are involved. We may infer from this that the SOA iscreated by long-lasting interactions. Galaxy pairs in massivegroups (mostly satellite–satellite pairs) are often unbound toeach other and influenced by a third neighbor (Moreno et al.2013), and therefore they are predominantly in flyby interac-tions (An et al. 2019). In contrast, pairs in low-density regions and less massive halos are likely to interact with a single neigh-bor for an extended period of time. DISCUSSIONOur analysis shows that the spin direction of each galaxy in apair is in alignment with the orbital angular momentum vectorof the pair system. The alignment is stronger as the separationto the neighbor decreases (Section 3.1). The signal increasesweakly as the target’s stellar mass decreases (Section 3.2). Thestrength of the alignment is closely related to the environmentwhere the galaxy pairs reside, showing a significant signal atlow-density regions (Section 3.2) and for interactions betweencentrals and satellites in low-mass halos (Section 3.3).The spin direction of galaxies is often associated with thegeometry of the LSS. One can anticipate that the anisotropicnature of the LSS helps to generate the SOA in galaxy pairs.However, the general trend of the SOA is not fully consistentwith this picture. For instance, the spin–LSS alignment ap-pears stronger for massive galaxies located in filaments (e.g.,Codis et al. 2018; Ganeshaiah Veena et al. 2019; Kraljic et al.2020), while the SOA is stronger for less massive galaxies insparser environments. For galaxy pairs in filaments, the orbitalplane’s normal vectors tend to be perpendicular to the filamentaxis (Tempel & Tamm 2015; Mesa et al. 2018), which seemsto conflict with the finding that less massive galaxies, show-ing a stronger signal of the SOA, prefer spin vectors parallel tothe filaments (e.g., Wang et al. 2018; Welker et al. 2018, 2020).Besides, the preferred direction of satellite accretion along thecosmic flow is expected to be more pronounced in massive ha-los (Libeskind et al. 2014; Kang & Wang 2015; Tempel et al.2015), but the SOA is more significant in less massive halos.The properties of the SOA indicate that the formation of thealignment is related to long-term interactions between pairedgalaxies rather than set by the underlying LSS. Figure 12shows the correlation between the prograde fraction and thetime when a galaxy is paired with its current neighbor ( t nei ;see the definition in Section 2.3). An earlier t nei means thatthe galaxy interacts with its current neighbor for a more ex-tended period without the interference of a third neighbor. Thefigure shows a strong correlation between the prograde frac-tion and the duration of the interaction. Galaxy pairs interact-ing for a longer time generally show a higher prograde frac-tion compared to recently formed pairs for gas, stars, and DMin common. While the study on the effect of interactions onthe galaxy spin mainly focused on its strength but not thedirection (e.g., Cervantes-Sodi et al. 2010; Choi et al. 2018;Lee et al. 2018), some recent studies hinted that the interac-tions could develop the dynamical alignment of galaxy pairs(e.g., Lee et al. 2019a, 2020). In particular, Lee et al. (2020)observed that paired galaxies with an SOA-like coherence alsoexhibit similarity in colors and claimed that this is evidenceof recent interactions between the two galaxies in alignment.The results in this paper are compatible with this interactionscenario. The interaction can easily influence low-mass galax-ies with low angular momenta (see Figures 7 and 8). A moresignificant SOA is developed for pairs with an earlier t nei (seeFigure 12), which on average have a closer neighbor (see Fig-ures 5 and 6) and reside in less massive halos at lower-densityregions (see Figure 11).The spin and shape of a satellite are known to be regulatedby the tidal torque induced by the massive central halo (a.k. a., the radial alignment of satellites) and has been investi- RIGIN OF S PIN –O RBIT A LIGNMENT OF G ALAXY P AIRS Time since t nei (Gyr) f p r o g ( % ) (a) Gas Time since t nei (Gyr) (b) Star
Time since t nei (Gyr) (c) DM
Figure 12.
Prograde fraction of the spin–orbit angle calculated for (a) gas, (b) stars, and (c) DM as a function of t nei (see the definition in Section2.3)—that is, the time span of the interaction after the current nearest neighbor remains the same without change. Error bars represent the standarderror of the percentage. gated in many previous studies (e.g., Usami & Fujimoto 1997;Pereira & Kuhn 2005; Pereira et al. 2008; Rong et al. 2015).Our results are in line with these studies, especially in the sensethat the alignment is created between centrals and satellites(see Figure 10), but the main difference is that the SOA sig-nal is dominated by low-mass halos (see Figure 11). While thedifference is likely because we restrict our sample to pairs ofcomparable mass, a question remains whether the tidal torqueof the comparable-mass neighbor is sufficient to change thespin of the target. Moreover, it is counterintuitive that there isno clear trend of the SOA with the mass ratio (see Figure 9).Some theoretical studies predict that the radial alignment canbe generated in low-mass halos less massive than the MilkyWay–sized ones (e.g., Pereira et al. 2008; Knebe et al. 2020),but more detailed studies are needed.In addition to the tidal effect, direct collisions between gasin contact pairs may facilitate the formation of the SOA. Forexample, hydrodynamic forces such as ram-pressure can causean abrupt change in the spin of the gas component during closeencounters (e.g., Capelo & Dotti 2017). In this scenario, thealignment is first established for the gas, and then stars borntherein inherit the angular momentum from the gas, while theDM is only weakly associated with the others through gravita-tional forces. This can explain the reason why the SOA signaldecreases in the order of gas, stars, and DM (see Figure 4). Theram-pressure is usually more violent in retrograde interactions(Barnes 2002; Blumenthal & Barnes 2018), and the selectiveremoval of retrograde systems could be partially responsiblefor the high prograde fraction.The observation of the SOA is rather challenging becausethe dynamics of both galaxies in pairs should be determined.There are very few observations to be compared to our simu-lation results. Lee et al. (2019a) observed the SOA-like coher-ence up to a distance of 800 kpc, which is similar to the spa-tial scale we found. Their findings are compatible with manyof our results (e.g., the trend with mass and color) but not all(e.g., the trend with mass ratio). However, a direct quantita-tive comparison is difficult due to the difference in the sampleselection and methodology. Specifically, Lee et al. (2019a) se-lected multiple neighbors for each target and inspected the av-eraged (projected) radial velocity. Although it would be possi-ble to generate a mock observation for a better comparison, it is not trivial and beyond the scope of this paper. Several observa-tional studies have focused on the orbital motion of small satel-lites within a group, rather than galaxy pairs, generally show-ing no clear preference (Zaritsky et al. 1997; Herbert-Fort et al.2008; Hwang & Park 2010). This is understandable since ourresults also do not show strong evidence for the SOA in mas-sive halos. Obviously, more observations are required to con-firm the predictions of this paper. We expect that ongoing IFUsurveys would be useful to perform more observational testsin the near future, considering that these surveys contain anumber of galaxy pairs with kinematic data available (e.g.,Barrera-Ballesteros et al. 2015; Feng et al. 2020).We leave a more in-depth investigation of the mechanismsbehind the SOA to future work. In this study, using a cosmo-logical hydrodynamic simulation, we investigated the SOA ofgalaxy pairs only at z = 0 and provided significant evidencefor the SOA. Also, we studied its dependence on the mass andenvironment and concluded that the current result favors theinteraction origin. However, this analysis alone is not conclu-sive as to the origin of the alignment. To further understandthe origin of the SOA, a detailed investigation of the formationand evolution of the SOA over cosmic time is required. Specif-ically, this includes the key question of the timing of the SOAformation. For instance, we may expect this: if the SOA is cre-ated by the primordial tidal torquing, the alignment occurs inthe very early universe; if the SOA is developed by the pref-erential accretion, it is established before the galaxy is pairedwith its current neighbor; if the SOA is related to the tidal forcefrom the neighbor, it is tied to the orbital phase of the system;or if the SOA is produced by the contact encounter, it formsonly after the close passage. We plan to clarify this issue andfurther constrain the underlying physical mechanism for thealignment in forthcoming papers. CONCLUSIONWe have analyzed the alignment between the spin vector ofa target and the orbital angular momentum vector of its nearestneighbor, which we refer to as the spin–orbit alignment (SOA).We used a cosmological hydrodynamic simulation of the Il-lustrisTNG project (Section 2.1) and identified paired galaxieswith comparable-mass neighbors at z = 0 (Section 2.2). Ourfinal sample consists of 7434 target galaxies with the updated4 M OON , A N & Y OON mass and size, which are corrected for the artificial mass lossof satellites (Section 2.3). We calculated the angle between thespin and the orbital angular momentum vectors (the spin–orbitangle; θ SL ) of the pairs separately for each component (i.e.,gas, star, and DM; Section 2.4). We have found a significantpreference for prograde orientations ( | θ SL | < ◦ ) for galaxypairs at z = 0 . We investigated the dependence of the SOA ongalaxy properties, including mass and environment (Section 3).Our results are summarized as follows:1. Galaxy pairs at z = 0 statistically prefer prograde orien-tations ( | θ SL | < ◦ ). The significance over the isotropicsample at cos θ SL ∼ σ for gas, 6.5 σ for stars, and4.9 σ for DM. The alignment is the strongest for gas andthe weakest for DM (Section 3.1).2. The strength of the SOA increases with decreasing sep-aration from the nearest neighbor. The number fractionof pairs in prograde orientation is as high as 70 % forgas spins and 60 % for stars and DM at the separation of γ nei < . The SOA signal extends out to γ nei ∼ ,which is roughly 600 kpc on physical scale (Section 3.1).3. Galaxy pairs in lower-density environments show ahigher prograde fraction, which holds true for low- andintermediate-mass target galaxies ( M ∗ ≤ M ⊙ ). Theprograde fraction slightly increases for low-mass galax-ies, but the dependence on the stellar mass is less pro- nounced compared to the dependence on the local den-sity. The spin–orbit angle does not show a clear trendwith the mass ratio of interacting pairs (Section 3.2).4. The SOA is created only between centrals and satel-lites. A clear signal is detected in both central–satelliteand satellite–central pairs. The central/satellite type isclosely linked to the local density and the halo mass.Galaxy pairs with a strong SOA are mostly located inlow-density regions and low-mass halos (Section 3.3).5. The prograde fraction increases with the interaction du-ration with the current neighbor ( t nei ). The SOA can becreated either by the effect of galaxy–galaxy interactionsor by the anisotropic nature of the LSS. The current ev-idence favors the scenario where the SOA is developedby interactions with a neighbor for an extended periodwithout the interference of a third neighbor, rather thanthe influence of the underlying LSS (Section 4).ACKNOWLEDGMENTSThis work is supported by the Mid-career ResearcherProgram (No. 2019R1A2C3006242) and the SRC Pro-gram (the Center for Galaxy Evolution Research; No.2017R1A5A1070354) through the National Research Founda-tion of Korea.REFERENCES Agustsson, I., & Brainerd, T. 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