Investigating Galaxy-Filament Alignments in Hydrodynamic Simulations Using Density Ridges

Mon. Not. R. Astron. Soc. 000,1–11 (2015) Printed 19 August 2015 (MN LATEX style ﬁle v2.2)

Investigating Galaxy-Filament Alignments in Hydrodynamic Simulations using Density Ridges

Yen-Chi Chen,1,3? Shirley Ho,2,3 Ananth Tenneti,2,3 Rachel Mandelbaum,2,3 Rupert Croft,2,3 Tiziana DiMatteo,2,3 Peter E. Freeman,1,3 Christopher R. Genovese,1,3 Larry Wasserman1,3 1Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 2Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 3McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA

19 August 2015

ABSTRACT

In this paper, we study the filamentary structures and the galaxy alignment along filaments at redshift z = 0.06 in the MassiveBlack-II simulation, a state-of-the-art, high-resolution hydrodynamical cosmological simulation which includes stellar and AGN feedback in a volume of (100 Mpc/h)3. The filaments are constructed using the subspace constrained mean shift (SCMS; Ozertem & Erdogmus(2011) and Chen et al. (2015a)). First, we show that reconstructed filaments using galaxies and reconstructed filaments using dark matter particles are similar to each other; over 50% of the points on the galaxy filaments have a corresponding point on the dark matter filaments within distance 0.13 Mpc/h (and vice versa) and this distance is even smaller at high-density regions. Second, we observe the alignment of the major principal axis of a galaxy with respect to the orientation of its nearest filament and detect a 2.5 Mpc/h critical radius for filament’s influence on the alignment when the subhalo mass of this galaxy is 9 12 between 10 M /h and 10 M /h. Moreover, we find the alignment signal to increase significantly with the subhalo mass. Third, when a galaxy is close to filaments (less than 0.25 Mpc/h), the galaxy alignment toward the nearest galaxy group depends on the galaxy subhalo mass. Finally, we find that galaxies close to filaments or groups tend to be rounder than those away from filaments or groups. Key words: (cosmology:) large-scale structure of Universe, hydrodynamics

1 INTRODUCTION structure growth of the Universe without assumptions on the relationship between the luminous and dark matter; see e.g Weak gravitational lensing by large-scale structure of the Hoekstra et al.(2002); Van Waerbeke et al.(2005); Jarvis Universe, commonly known as cosmic shear, is a promis- et al.(2006); Schrabback et al.(2010); Lin et al.(2012); Hey- ing technique to constrain cosmological parameters. It is mans et al.(2012); Jee et al.(2013); Huff et al.(2014). If arXiv:1508.04149v1 [astro-ph.CO] 17 Aug 2015 among the key science cases of various ongoing and upcom- systematics can be sufficiently controlled for future missions, ing surveys, such as the Kilo-Degree Survey (KiDS1), Hyper cosmic shear has the potential to be the most constraining Suprime Cam (HSC2), Dark Energy Survey (DES3), Large cosmological probe, thus understanding and controlling sys- Synoptic Survey Telescope (LSST4), Euclid5 and the Wide- tematics in the weak lensing measurements needs to improve Field Infrared Survey Telescope (WFIRST6). Theoretically, significantly over the next few years for its potential to come it provides valuable information on both the geometry and to fruition with large data volumes in these upcoming surveys. ? E-mail: [email protected] 1 Cosmic shear is typically measured through two-point http://kids.strw.leidenuniv.nl/ correlations of observed galaxy ellipticities. In the weak 2 http://www.naoj.org/Projects/HSC/ 3 http://www.darkenergysurvey.org/ lensing regime, the observed ellipticity of a galaxy is the 4 http://www.lsst.org/lsst/ sum of its intrinsic ellipticity t and gravitational shear 5 http://sci.esa.int/euclid/ γ : obs t + γ. When the intrinsic shapes of galaxies are ≈ 6 http://wfirst.gsfc.nasa.gov/ spatially correlated, these intrinsic alignment (IA) correla-

c 2015 RAS

2 Yen-Chi Chen et al. tions can contaminate the gravitational shear signal and lead as a tool to understand the relationship of galaxy alignments to biased measurements if not properly removed or modeled. with the large-scale density field. Since early work establishing its potential effects (Croft & We start with a brief introduction about density ridges, Metzler 2000; Heavens et al. 2000; Catelan et al. 2001; Crit- the model for filaments we are using, in 2 and describe § tenden et al. 2001), IA has been examined through observa- the MassiveBlack-II Simulation we applied in 3. Then we § tions (e.g., Hirata et al. 2007; Joachimi et al. 2011; Blazek describe our main results in 4 and our conclusions in 5. § § et al. 2012; Singh & Mandelbaum 2014), analytic modeling, and simulations (e.g., Schneider et al. 2012; Tenneti et al. 2014, 2015). See Troxel & Ishak(2014); Joachimi et al. 2 DENSITY RIDGES AS FILAMENTS (2015), and references therein, for recent reviews. To create a fully predictive model of IA would require We detect filaments through SCMS introduced in Ozertem & the understanding of the complex processes involved in the Erdogmus(2011); Chen et al.(2015a). SCMS is a gradient- formation and evolution of galaxies and their dark matter based method that detects filaments as “galaxy density halos, as well as how these processes couple to large-scale ridges”. environment. The shapes of elliptical, pressure-supported Essentially, filaments from SCMS are defined as follows. 3 Given galaxies located at X1, ,Xn R , the smoothed galaxies are often assumed to align with the surrounding ··· ∈ dark matter halos, which are themselves aligned with the density field (also known as the kernel density estimator) is stretching axis of the large-scale tidal field (Catelan et al. n 1 X x Xi 2001; Hirata & Seljak 2004, 2010). This tidal alignment p(x) = K | − | , (1) nb3 b model leads to shape alignments that scale linearly with fluc- i=1 tuations in the tidal field, and it is thus sometimes referred to where K is a Gaussian and b is the smoothing bandwidth as “inear alignment”, although nonlinear contributions may that controls the amount of smoothing on each particle. In still be included (Bridle & King 2007; Blazek et al. 2011, this paper, we apply b = 1 Mpc/h. Note that the density field 2015). As for spiral galaxies, where angular momentum is p does not incorporate any boundary condition at the edge likely the primary factor in determining galaxy orientation, of the simulation box. Let g(x) = p(x),H(x) = p(x) ∇ ∇∇ IA modeling is typically based on tidal torquing theory, lead- be the gradient and Hessian matrix of p(x). Ridges of p(x) ing to a quadratic dependence on tidal field fluctuations (Pen are the collection of points et al. 2000; Catelan et al. 2001; Hui & Zhang 2002; Lee & F = x : vj (x) g(x) = 0, λ2(x) < 0, j = 2, 3 , (2) Pen 2008), although on sufficiently large scales, the contri- { · } bution linear in the tidal field may become dominant. where vj (x), λj (x) are the j-th eigenvector/value for H(x). Filaments in the cosmic web play a key role in the See Figure1 for an example about density ridges. More prop- large- scale tidal field since they are related to the gra- erties of ridges of a function can be found in Eberly(1996); dient and the Hessian matrix of the matter density field Ozertem & Erdogmus(2011); Genovese et al.(2014); Chen (Hahn et al. 2007a,b; Sousbie et al. 2008; Forero-Romero et al.(2014, 2015c). et al. 2009; Aragón-Calvo et al. 2010; Cautun et al. 2013). Intuitively, at a point on the ridge, the gradient is the As a result, it is expected that filaments would affect the same as v1(x), the eigenvector corresponds to the largest shapes and alignments of their nearby galaxies. There is ev- eigenvalue, and the density curves downward sharply in di- idence for anti-alignment between the galaxy spin orienta- rections orthogonal to the gradient. When p is smooth and tion of disk galaxies and the direction of nearby filaments the eigengap (Libeskind et al. 2013; Tempel et al. 2013; Tempel & Libe- β(x) = λ1(x) λ2(x) (3) skind 2013; Aragon-Calvo & Yang 2014; Dubois et al. 2014; − Welker et al. 2014; Laigle et al. 2015; Zhang et al. 2015), is positive, the ridges have the properties of filaments (Chen and an alignment between galaxy shape and the orientation et al. 2015c). That is, F decomposes into a set of smooth of the nearest filament (Altay et al. 2006; Zhang et al. 2009; curve-like structures with high-density. Since the ridges are Tempel & Libeskind 2013; Zhang et al. 2013). Other evi- smooth, for any point x F , the orientation of ridges at x, dence also indicates that direction of a galaxy pair (Tempel ∈ denoted as µRidge(x), is well-defined. & Tamm 2015) and the alignment of satellite galaxies toward their host galaxies (Tempel et al. 2015) are dependent on their nearby filaments. The effect of filaments on intrinsic 3 MASSIVEBLACK-II SIMULATION galaxy shapes is worth studying since filaments are expected to trace the tidal fields directly and yet the current theoret- In this work, we detect filaments in the MassiveBlack-II ical model for IA only includes halos but does not explicitly (MBII) hydrodynamic simulation (Khandai et al. 2015), and include filaments; see e.g. Schneider & Bridle(2010). study the alignments of the shapes of stellar matter compo- One can, in principle, test and constrain IA models nents in galaxies with the filaments. MB-II is a state-of-the- and marginalize over free parameters in specific models; this art, high-resolution cosmological hydrodynamic simulation process could be improved in the quasilinear and nonlinear performed in a cubic periodic box of size 100 Mpc/h on a regime via the tighter priors on model parameters that we side. The simulations have been performed with the code could obtain with a 3D filament map of the universe which p-gadget, which is a hybrid version of the parallel code overlaps with sources in the weak lensing fields. In this pa- gadget2 (Springel et al. 2005) that has been modified and per, we apply the subspace constrained mean shift (SCMS) upgraded to run on Petaflop-scale supercomputers. MBII in- filament finder to the source density in a cosmological hy- cludes the physics of multiphase interstellar medium (ISM) drodynamic simulation to test whether we can use filaments model with star formation (Springel & Hernquist 2003),

c 2015 RAS, MNRAS 000,1–11

Galaxy-Filament Alignment 3

ΠF

Group Center dF

dC µC µF

Filament

Figure 2. Example of µC , µF , dC , dF . The big red dot denotes a galaxy group, the blue curve is the filament, and the small black points are galaxies. For a given point (galaxy), the brown arrow is µC and the purple arrow is µF . The length of the dotted brown line is dC and of the dashed purple line is dF . Note that the Figure 1. Illustration of density ridges (blue curves) in a den- projected point onto the filament is the pink point. sity field. Each black dot is a subhalo and the big red dots are galaxy groups. The color from white-green-yellow-orange denotes the density induced by smoothing the subhalos. Note that this 2-D figure is for illustration; our analysis is applied to 3-D data. obtained from the eigen-decomposition of the reduced inertia tensor. We consider all the star particles belonging to the subhalo in the calculation of the inertia tensor. The eigenvectors of the inertia tensor are denoted as µ , µ , and µ with black hole accretion and associated feedback processes (Di 1 2 3 the corresponding eigenvalues being λ , λ , and λ , where Matteo et al. 2008, 2012) in addition to gravity and hydro- a b c λ > λ > λ . The lengths of the principal axes of the ellip- dynamics. This simulation has been run from z = 159 to a b c 3 soid (a, b, c), which are represented by these eigenvectors, are z = 0.06 using Npart = 2 1792 dark matter and gas par- × given by square roots of the eigenvalues (√λa, √λb, √λc). ticles with a gravitational smoothing length, = 1.85kpc/h We can now define the intermediate-to-major axis ratio (q) in comoving units. The mass of each dark matter particle is 7 and the minor-to-major axis ratio (s) as mDM = 1.1 10 M /h and the initial mass of a gas parti- × 6 cle is mgas = 2.2 10 M /h. The cosmological parameters b c × q = , s = (4) in the simulation chosen according to WMAP7 (Komatsu a a et al. 2011) are as follows: amplitude of matter fluctuations Note that an iterative procedure is adopted in calculat- σ = 0.816, spectral index n = 0.96, mass density param- 8 s ing the shapes such that the axis ratios converge. For ad- eter Ω = 0.275, cosmological constant density parameter m ditional details regarding the iterative method, see Tenneti Ω = 0.725, baryon density parameter Ω = 0.046, and Λ b et al.(2015). Hubble parameter h = 0.702. For each galaxy, we have two intrinsic quantities: the To generate halo catalogs, the friend-of-friends (FOF) number of star particles n and the total mass of this subhalo finder algorithm (Davis et al. 1985) is used with a link- halo M (subhalo mass). Throughout this paper, we use only ing length of 0.2 times the mean interparticle separation. subhalo mass. The subfind code (Springel et al. 2001) is used on the halo catalogs to generate subhalo catalogs. Here, subhalos are defined as locally overdense, self-bound particle groups which consist of at least 20 gravitationally bound particles. How- 3.2 Large-Scale Structure ever, to ensure that the measured shape of a galaxy is reli- able, we restrict our galaxy sample to those subhalos with In our analysis, we define galaxy groups as those subhalos with subhalo mass > 1013M /h. This gives 315 galaxy at least 500 star particles. This is based on the convergence groups, which corresponds to a comoving number density tests in Tenneti et al.(2014). 4 3 3.15 10− (h/Mpc) . Let C and F denote the collection of × all groups (of galaxies) and filaments. Given any galaxy located at x (x is the 3D position in the box), let ΠC (x) C 3.1 Shapes of galaxies ∈ and ΠF (x) F be the ‘projected’ point onto the nearest ∈ In this paper, we use the shapes of the stellar components group/filament. Namely, ΠC (x) (or ΠF (x) respectively) is of galaxies in MBII which are calculated in Tenneti et al. the point in C (or F ) whose distance to x is smallest among (2015) to quantify intrinsic alignments of galaxies. Here, we all points in C (or F ). In general, this projection is unique give a brief description of the method adopted to calculate (although some regions may have non-unique projection, the these shapes. The shapes of galaxies are modeled as ellip- probability that a galaxy falls within these regions is 0). We soids in three dimensions by the eigenvalues and eigenvectors then define the associated direction to the nearest group and c 2015 RAS, MNRAS 000,1–11

4 Yen-Chi Chen et al.

Notation Deﬁnition Type Remark

n Number of star particles Integer > 500 M Halo mass Scalar dC Distance to the nearest galaxy group Scalar dF Distance to the nearest ﬁlament Scalar µC Direction to the nearest galaxy group Vector µF Orientation of the nearest ﬁlament Vector q First and second principal axis ratio Scalar [0, 1] ∈ s First and third principal axis ratio Scalar [0, 1] ∈ µ1 First principal axis Vector µ2 Second principal axis Vector µ3 Third principal axis Vector

Table 1. Table of quantities associated with a galaxy. to the nearest ﬁlament as Difference of filaments using galaxies versus DM

ΠC (x) x 25% 50% 75% 90% µC (x) = − (5) ΠC (x) x 50000 | − | µF (x) = µRidge(ΠF (x)). (6)

Note that µC is the direction toward the nearest galaxy 40000 group while µF is the direction of the nearest filaments. We also define the projection distances dC (x) = ΠC (x) x | − | and dF (x) = ΠF (x) x . Namely, for a galaxy at position x, 30000 | − | µC (x) is the direction from this galaxy to the nearest galaxy group. And µF (x) is the orientation of the nearby filament. Frequency

Figure2 illustrates all the above quantities in a 2-D picture. 20000 10000 4 RESULTS

4.1 Agreement of Filaments from Galaxies versus 0 Dark Matter Particles 0.0 0.1 0.2 0.3 0.4 0.5 Difference (Mpc/h) To establish the promise of recovering filaments tracing dark matter particles using only galaxies, we first study the sim- Figure 3. Agreement of filaments detected using galaxies ver- ilarity for filaments obtained by using galaxies only versus sus using dark matter particles. We apply our filament finder to using dark matter particles. The dark matter particles are both galaxies and dark matter particles and then compare the dif- from a random subsample with size 400, 000, which is ap- ference between the two corresponding filament catalogues. This proximately the same order as the number of subhalos we picture shows the distribution of difference in filament position. have ( 500, 000). In Figure3, we show the difference be- The four color bars denote the quantile values of 25%, 50%, 75% ∼ and 90%. The difference for filaments recovered from galaxies and tween the two filament catalogues. Since both catalogues dark matter particles is small. contain points on the filaments, the difference is computed using projected distance between points from two catalogues (Chen et al. 2015b). To be more specific, let D and G be F F the collection of points on the filaments from dark matter filaments differ at a distance less than 0.13 Mpc/h and about particles and from galaxies. Then for each point in D, we 90% of them differ at the distance less than 0.5 Mpc/h. F find its nearest distance to any member of G. This gives We also study the agreement for the two catalogues at F a distance value (also known as projected distance) to each different densities. For each point on the filaments, we assign point in D. Similarly, for every point in G, we can find a density value to them by using the distance to the 1000-th F F the corresponding projected distance to D so that we will nearest dark matter particles (Figure4). The 1000 is cho- F assign a distance value to each element of G. The distri- sen arbitrarily; we have tried other values and the result F bution of all the distance values in D and G provides remains similar. The inverse of this distance is an effective F F the information about similarity between these two filament density (at overdense regions, this distance is small while at catalogues. If they are similar, this distribution will be con- void region, this distance is large). We then rank points on centrated around 0. On the other hand, if the two catalogues filaments according to their densities and plot the distribu- are different, this distribution will spread out. Note that we tion of difference under different density ranking categories. have tried a random sample with size 800, 000 and the result The high-density filaments are those whose density ranking remains similar. is among the top 10% (red) and top 25% (orange). The low According to Figure3, we see that the two catalogues density filaments are those whose density ranking is in the are similar to each other; more than 50% of the points on bottom 25% (green) and bottom 10% (blue). The result is

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Galaxy-Filament Alignment 5

Density: dark matter particles

10 All galaxies Density: top 10% ● Density: top 25% Density: bottom 25% 8 ● Density: bottom 10% ●

● 6

●

● ● ● 4 ● ● ●

● ● ● ● ● ●

Probability Distribution ● 2 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0

0.0 0.1 0.2 0.3 0.4 0.5 Difference (Mpc/h)

Figure 4. Agreement of filaments detected using galaxies versus using dark matter particles under different environmental densities. We rank points on filaments according to the densities of dark matter particles (using densities from galaxies yields a similar result). Then we plot distributions of filament differences under different density regimes. Filaments at high-density regions are colored by red and orange (density within the top 10% and 25%) whereas low density filaments are colored by green and blue (density in the bottom 25% and 10%). The black curve denotes the distribution using all galaxies (which is the distribution of Figure3, note that we use the different bin size). We see a clear pattern that the two filament catalogues are similar at high-density regions and get less similar when the density decreases.

given in Figure4. We observe that the distribution of differ- compared to two galaxies with random orientations. The ence for both catalogue is small, and the difference is even trend is reversed for the minor principal axis (with KS-test 17 smaller for filaments reside in high-density regions. The rea- p-value 1 10− ). Thus, we conclude that the major (first) × son why the difference is density-dependent is because galax- principal axis for a galaxy tend to align along filaments while ies are a biased tracer for the matter density field so that the minor axis tends to misalign to the filaments. galaxies trace the large-scale structure structures better at To study how the subhalo mass of a galaxy affects the high-density regions. Note that the result remains similar alignment signal, we further partition galaxies by their mass when we replace dark matter density by galaxy density. into three mass-groups To conclude, Figure3 and Figure4 show that the filaments from galaxies and the filaments from dark matter 109M /h < M < 1010M /h, particles are similar and this similarity is stronger for high- 1010M /h < M < 1011M /h, (7) density regions. For the following analysis on the galaxy 11 12 alignment, we use the filaments from galaxies. 10 M /h < M < 10 M /h

and plot the average alignment signal µj µF within each h| · |i mass bin. Note that the above three mass-groups contain 4.2 Principal Axes Alignment to Filaments 88% of all subhalos we have (about 11% of the subhalos have We first examine the correlation between principal axes and subhalo mass M < 109M /h and 0.6% have subhalo mass 12 µF , the orientation of the nearest filament of a galaxy. Note M > 10 M /h). The result is given in the first two panels that since both µj and µj are describing the same axis, we in Figure6. The left (first) panel shows a clear patten that − take the absolute value of inner product between µj and µF . the average alignment signal for major axis increases as the We compute the alignment signal µj µF for galaxies subhalo mass increases (this slope has a 4σ significance) and | · | close to filaments (dF < 1 Mpc/h) but not close to groups the effect of misalignment for minor axis is also augmented (dC > 2 Mpc/h). Note that µj µF 1 means that the j-th for massive galaxies. Altay et al.(2006); Zhang et al.(2009); | · | ≈ principal axis align along µF while µj µF 0 indicates Tempel & Libeskind(2013); Zhang et al.(2013) also report | · | ≈ that they are misaligned. In Figure5, we show the excess a similar mass dependency on the alignment signal. probability compared to the distribution of inner product The middle (second) panel of Figure6 shows the same between two random unit axes. We find that the alignment analysis as the left panel but at a different distance range signal for first principal axis (blue curve) is very significant to filaments. We now focus on galaxies whose distance to 28 (with KS-test p-value being 4 10− ). By comparing the filaments is within 1 Mpc/h < dF < 2 Mpc/h. That is, the × blue curve in both the left and right side of Figure5, we middle panel shows the alignment signal for galaxies that see that the distribution of the alignment is concentrated are mildly close to filaments (but not too close). Our result at values 1. This means we have more aligned galaxies shows that, unlike galaxies being very close to filaments (left ≈ c 2015 RAS, MNRAS 000,1–11

6 Yen-Chi Chen et al. Galaxy-Filament Alignment 7

dF < 1Mpc/h, dC > 2Mpc/h 1Mpc/h < dF < 2Mpc/h, dC > 2Mpc/h Alignment of the First Principal Axis 0.80

−4 − −4 Slope: (2.4 ± 0.6) × 10 Slope: (0.3 ± 1.7) × 10 0.78 1.3σ − 2σ − 11.4 2.8σ 0.1 − − σ 4.2σ − 0.3σ σ ● − ● − ● − ●

|> − |> − − − 4.6σ −● −

− |>

F F − − −● − 0.5 0.7

0.76 σ − − F − σ µ − µ − − − − ● − − ● − µ − − − ⋅ − − ⋅ ⋅

Figure 6. Alignment signals µj µF versus subhalo mass and dF ,thedistancetofilaments.Notethatweremovegalaxiesthatare Figure 6. Alignment signals |hµj · µF i| versus subhalo mass and dF , the distance to filaments. Note that we remove galaxies that are close to groups (i.e. all galaxies|h satisfy· i|dC > 2Mpc/h). Left: We show how alignment signals change as a function of subhalo mass at close to groups (i.e. all galaxies satisfy dC > 2 Mpc/h). Left: We show how alignment signals change as a function of subhalo mass at dF < 1Mpc/h.Theslopeof µ1 µF versus dF is indicated in the panel. We observe a significant (4)lineare↵ect from subhalo d < 1 Mpc/h. The slope of |hµ1 · µ i| versus d is indicated in the panel. We observe a significant (4σ) linear effect from subhalo massF on the alignment of first|h principal· F i| axis alongF the nearby filament orientation. Middle: The same analysis as left panel but with mass on the alignment of first principal axis along the nearby filament orientation. Middle: The same analysis as left panel but with di↵erent range for distance to filaments (1 Mpc/h < dF < 2Mpc/h). Compared with left panel, we still see an alignment signal but different range for distance to filaments (1 Mpc/h < dF < 2 Mpc/h). Compared with left panel, we still see an alignment signal but the mass-dependency disappears. Right: The alignment signal for the first principal axis, µ1 µF ,asafunctionofdF .Notethatwe the mass-dependency disappears. Right: The alignment signal for the first principal axis, h|µ1 · µF |i, as a function of dF . Note that we display the significance on top of the alignment value for each mass bin. The alignment signalh| is· significant|i when dF < 2.5Mpc/h (left sidedisplay of the the orange significance line). on top of the alignment value for each mass bin. The alignment signal is significant when dF < 2.5 Mpc/h (left side of the orange line).

Alignment of the First Principal Axis Alignment of the First Principal Axis tance to filaments is small (less than 2.5 Mpc/h), the align- d < 1Mpc/h, d > 2Mpc/hq < 0.83 s < 0.68 F C q > 0.83 ment signals > 0.68 is significant (> 2σ). However, when the dis- Random tance is aboveRandom 2.5 Mpc/h, we do not observe any significant First (µ ) 1 − alignment signal. This result− is consistent with the left and

|> (µ ) |> − − Second − 2 − − − − F − F 1.4 − − µ − Third (µ ) µ middle− panels of− Figure6 since the two panels both satisfy ⋅ − 3 ⋅ − − 1 Random 1 dF < 2.5 Mpc/h. µ µ

<| <| Finally, we focus on the alignment signal for ﬁrst prin-

1.2 − −● ● − −● cipal axis and study how the shape (q and s) influences the ● − − − ● − − −● − signal. We partition galaxies according to their q and s. The ● − ● ● δ − −● − − ● − − ● ● ● ● − ● − − − −● − − − − −● cut on q is 0.83 and the cut on s is 0.68; both cuts are chosen 1.0 − − ● ● − − − −● 1+ − − − − −● ● − − − 0.70 0.72 0.74 0.76 0.78 0.80 0.70 0.72 0.74 0.76 0.78 0.80 ● − ● − ● − −● − ● − − by the median value for all galaxies. The result is given in − − −9.0 9.5 10.0 10.5− 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 − ● − log(11850M/M ) Figure7. Thelog( leftM/M panel) shows the alignment signal for the − − 6405 8384 −● 2118 3279 ⊙ ⊙ 0.8 1142 4548 17647 major axis under the cut on q. We find that the two groups Figure− 7. The459 correlation between shapes and the alignment signal. Notedo not that have we focussignificant on the difference alignment (significance signal of first is principal only 0.42 axis.σ). We study72 how a galaxy’s shape is correlated with µ1 µ .Wesplitthegalaxiesintogroupsaccordingtotheirshapes,measuredby |h · F i| The right panel shows the same analysis under the cut on the q0.6 and s.Theseparationcutsonq and s are chosen by the medians of.q Weand sees for a significant galaxies with differencedF < 1Mpc (3.36/hσ)and ford theC > two2Mpc groups/h . Left: We separate galaxies into two groups by q:moreellipticalgalaxies(ofq< galaxies.0.83, orange) Namely, and an more elongated spherical galaxy galaxies (with (q> smaller0.83, red).s) There is no significant di↵erence between these two groups (0.42). Right: We separate galaxies into two groups by s:moreelliptical 0.2 0.4 0.6 0.8 tends to align more along nearby filaments compared to a galaxies (s<0.68, green) andµ ⋅ moreµ spherical galaxies (s>0.68, blue). In this case, we observe a significant di↵erence between the two <| j F|> spherical one. This is not an effect due to measurement error groups (3.36). An elliptical galaxy seems to align more along the filaments compared with a spherical one. since in the simulations, all the galaxies have > 500 particles and the shapes and orientations are well-measured even in Figure 5. Distribution of alignment signals µj µF . Note that |h · i| the sample that are closer to round. we only consider galaxies away from groups (dC > 2 Mpc/h) q after adjusting the e↵ect from subhalo mass. The first expect to see that galaxies close to groups and filaments are hbuti close to filaments (dF < 1 Mpc/h). We observe a significant caseincrease can for beµ found1 µ at the1. This top showsright andthat bottomthe major left principal panel on average rounder than those that are far away. And if this |h · F i| ≈ ofaxis Figure tend to10. align Wealong observe the a orientation decreasing of pattern the nearby as dF filament.or dC e4.3↵ect isPrincipal stronger for Axes groups Alignment (perhaps to due Groups to a stronger tidal increases.The δ in the In Y-axisother words, is the excess for galaxies probability close compared to filaments to the or field), then we should see a higher q for galaxies that are We also study how filaments influence the galaxy alignment groups,distribution we expect of random their angle.q to The be higher error bars (more are rounded calculated galax- from closer to groups. toward the nearest galaxy groups. We focus on the inner ies).the bootstrap. In both panels, The number the subhalo below shows mass the within sample each size bin for does each Note that in the upper left panel (1010.0M /h < M < product between the major (first) principal axis and the di- notbin. change too much so that this e↵ect cannot be explained 1010.6M /h), we find a decreasing trend for the average sub- rection to the nearest galaxy groups. Namely, we test how by the mass di↵erence. The second case is on the di↵erence halo mass when the distance to large-scale structure is in- the alignment signal µ1 µC is different for galaxies within between groups and filaments. In every panel of Figure 10, | · | panel), the alignment signal is not mass-dependent (only creasing.a filament Moreover, versus outside at the filaments. same distance, To classify galaxies a galaxy close toas we find that, for galaxies at the same distance to either fil- 0.2σ). groupsbeing inside tend a to filament be lower or mass out of compared filaments, with we call those a galaxy close aments or groups, q is always higher for galaxies close to to filaments. Namely, one will find more low-mass galaxies On the right panelh i of Figure6, we plot the average align- in filaments if their distance to filament dF is less than a groups. (with subhalo mass less than 1010.6M /h) at strong tidal ment signal for the first principal axis at different distance distance threshold τ. Otherwise, we say this galaxy is out binsAn to show explanation how the to distance the above affects cases the is duealignment to the signal. di↵er- forceof filaments regions.. Note We do that not we find only a similar consider patten galaxies in other that are mass at enceNote in that the here ratio we of only elliptical focus galaxies.on galaxy If with elliptical subhalo galaxies mass range,least 1. so00 thisMpc/h phenomenaaway from occurs the nearest only for group light to galaxies. make sure A arebetween more [10 likely9M to/h, be1012 in/nearM /h]. groups As expected, and filaments when the and dis- if possiblethis galaxy reason is not is in that, this group.in a region with strong tidal ef- they are usually rounder than disk galaxies, then we would fect, matter concentrates around the large-scale structures c 2015 RAS, MNRAS 000,1–11 MNRAS 000, 1–10 (2015) Galaxy-Filament Alignment 7

dF < 1Mpc/h, dC > 2Mpc/h 1Mpc/h < dF < 2Mpc/h, dC > 2Mpc/h Alignment of the First Principal Axis 0.80

−4 − −4 Slope: (2.4 ± 0.6) × 10 Slope: (0.3 ± 1.7) × 10 0.78 1.3σ − 2σ − 11.4 2.8σ 0.1 − − σ 4.2σ − 0.3σ σ ● − ● − ● − ●

|> − |> − − − 4.6σ −● −

− |>

F F − − −● − 0.5 0.7

0.76 σ − − F − σ µ − µ − − − − ● − − ● − µ − − − ⋅ − − ⋅ ⋅

j − j − − ● − − 1 µ µ − ● − − µ − <| − <| − <| − − − − − 0.74 − − − First (µ1) First (µ1) Second (µ2) Second (µ2) 0.72 Third (µ3) Third (µ3) Random Random 0.70 0.72 0.74 0.76 0.78 0.80 0.70 0.72 0.74 0.76 0.78 0.80 9.0 9.5 10.0 10.5 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 0.70 0 1 2 3 4 5 log(M/M ) log(M/M ) Distance to Filament (Mpc/h) ⊙ ⊙ Figure 6. Alignment signals µ µ versus subhalo mass and d ,thedistancetofilaments.Notethatweremovegalaxiesthatare |h j · F i| F close to groups (i.e. all galaxies satisfy dC > 2Mpc/h). Left: We show how alignment signals change as a function of subhalo mass at d < 1Mpc/h.Theslopeof µ1 µ versus d is indicated in the panel. We observe a significant (4)lineare↵ect from subhalo F |h · F i| F mass on the alignment of first principal axis along the nearby filament orientation. Middle: The same analysis as left panel but with di↵erent range for distance to filaments (1 Mpc/h < dF < 2Mpc/h). Compared with left panel, we still see an alignment signal but the mass-dependency disappears. Right: The alignment signal for the first principal axis, µ1 µ ,asafunctionofd .Notethatwe h| · F |i F display the significance on top of the alignment value for each mass bin. The alignment signal is significant when dF < 2.5Mpc/h (left side of the orange line). Galaxy-Filament Alignment 7

Alignment of the First Principal Axis Alignment of the First Principal Axis q < 0.83 s < 0.68 q > 0.83 s > 0.68 Random Random − − |> − − − |> − − − F − F − µ − µ − − ⋅ − ⋅ − − 1 1 µ µ <| <| 0.70 0.72 0.74 0.76 0.78 0.80 0.70 0.72 0.74 0.76 0.78 0.80 9.0 9.5 10.0 10.5 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 log(M/M ) log(M/M ) ⊙ ⊙

FigureFigure 7. 7.TheThe correlation correlation between between shapes shapes and and the the alignment alignment signal. signal. Note Note that that we we focus focus on on the the alignment alignment signal signal of of first first principal principal axis. axis. We study how a galaxy’s shape is correlated with µ1 µ .Wesplitthegalaxiesintogroupsaccordingtotheirshapes,measuredby We study how a galaxy’s shape is correlated with|h µ1· µFFi| . We split the galaxies into groups according to their shapes, measured by the q and s.Theseparationcutsonq and s are chosen|h by· thei| median of q and s for galaxies with d < 1Mpc/h and d > 2Mpc/h . the q and s. The separation cuts on q and s are chosen by the median of q and s for galaxies with FdF < 1 Mpc/h and CdC > 2 Mpc/h . Left:Left:WeWe separate separate galaxies galaxies into into two two groups groups by byq:moreellipticalgalaxies(q: more elliptical galaxiesq< (q <0.083,.83, orange) orange) and and more more spherical spherical galaxies galaxies (q> (q >0.083,.83, red). red). ThereThere is is no no significant significant di difference↵erence between between these these two two groups groups (0 (0.42.42σ).).Right:Right:WeWe separate separate galaxies galaxies into into two two groups groups by bys:moreellipticals: more elliptical galaxiesgalaxies (s< (s <0.068,.68, green) green) and and more more spherical spherical galaxies galaxies (s> (s >0.068,.68, blue). blue). In In this this case, case, we we observe observe a a significant significant di difference↵erence between between the the two two groupsgroups (3 (3.36.36σ).). An An elliptical elliptical galaxy galaxy seems seems to to align align more more along along the the filaments filaments compared compared with with a a spherical spherical one. one. 8 Yen-Chi Chen et al.

q after adjustingGalaxy alignment the e ↵toect the nearest from galaxy subhalo group mass.Galaxy The alignment first to theexpect nearest galaxy to see group that galaxiesGalaxy alignment close to the groups nearest andgalaxy filaments group are h i case can be foundIn atfilament the (dF top < 0.25 right Mpc) and bottom left panelIn filament (dF < on0.5 Mpc) average rounder than thoseIn filament that (dF < are 1 Mpc) far away. And if this Out of filament (dF > 0.25 Mpc) Out of filament (dF > 0.5 Mpc) Out of filament (dF > 1 Mpc) of Figure 10. We observeRandom a decreasing pattern as dF orRandomdC e↵ect is stronger for groupsRandom (perhaps due to a stronger tidal increases. In other words, for galaxies close3 to filaments or field), then we3 should see a higher q for galaxies3 that are Slope: (2.4 ± 1) × 10− Slope: (1.9 ± 0.7) × 10− Slope: (1.8 ± 0.6) × 10− groups, we expect their q to be higher (more rounded galax- closer to groups.

|> − |> |> 10.0− C C − C ies). In both panels, the subhalo− mass− within each bin− does − Note that in the upper− left panel− (10 −M /h < M < µ − µ − µ − − − − − − − ⋅ − − ⋅ − 10.6 ⋅ − not change1 too much so that this e↵ect cannot be1 explained− 10 M /h), we ﬁnd1 a decreasing− trend for the average sub- µ − µ µ −

by the mass<| di↵erence. The second case is on the<| di↵erence halo mass when the<| distance to large-scale structure is in- between groups and filaments. In every panel of Figure 10, creasing. Moreover, at the same distance, galaxies close to −3 −3 −3 we find that, for galaxiesSlope: at the(1.4 ± same0.7) × distance10 to either fil- Slope:groups (1.7 ± 1) tend× 10 to be lower massSlope: compared (2.3 ± 1.7) with× 10 those close aments or groups, q is always higher for galaxies close to to filaments. Namely, one will find more low-mass galaxies h i 10.6 groups. 0.70 0.72 0.74 0.76 0.78 0.80 0.70 0.72 0.74 0.76 0.78 0.80 (with subhalo mass0.70 less 0.72 0.74 than 0.76 0.78 10 0.80 M /h) at strong tidal 9.0 9.5 10.0 10.5 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 An explanation to the above cases is due to the di↵er- force regions. We do not find a similar patten in other mass log(M/M ) log(M/M ) log(M/M ) ence in the ratio of elliptical galaxies.⊙ If elliptical galaxies range,⊙ so this phenomena occurs only⊙ for light galaxies. A

areFigure more 8. likelyThe eto↵ect be for in/near filaments groups on µ and1 µC filaments,thegalaxyalignmentalong‘thedirectiontowardthenearestgroup’.Wefocusonthe and if possible reason is that, in a region with strong tidal ef- Figure 8. The effect for filaments on |h µ1 · µCi| , the galaxy alignment along ‘the direction toward the nearest group’. We focus on the theygalaxies arewith usuallydC rounder> 1Mpc/h thanto makedisk galaxies, sure|h they· theni| are not we inside would a group.fect, We matter then partition concentrates galaxies around into two the types: large-scale in filaments structures and out galaxies with dC > 1 Mpc/h to make sure they are not inside a group. We then partition galaxies into two types: in filaments and out filamentsfilaments by by imposing imposing a a threshold threshold ⌧τ onon the the distance distance to to filaments filaments (see (see 4.34.3 forfor more more details). details). Left:Left: ⌧τ =0= 0..2525 Mpc Mpc/h/h.Namely,agalaxy. Namely, a galaxy §§ MNRASwhosewhose distance distance000, 1–10 to to(2015) filaments filaments is is less less than than 0 0..2525 Mpc Mpc/h/h willwill be be considered considered withinwithin filaments filaments.Otherwisethisgalaxyisclassifiedas. Otherwise this galaxy is classified as outout of of filaments. Middle: ⌧ =0.50 Mpc/h. Right: ⌧ =1.00 Mpc/h.Theredcolordenotes µ1 µC for galaxies that are inside a filament filaments. Middle: τ = 0.50 Mpc/h. Right: τ = 1.00 Mpc/h. The red color denotes µ1 µ for galaxies that are inside a filament ||hh ·· Cii|| andand the the blue blue color color is is the the same same but but for for galaxies galaxies out out of of filaments. filaments. Note Note that that we we also also attach attach the the significance significance for for the the slope slope using using the the linear linear regression.regression.

dC < 5 Mpc/h dF < 5 Mpc/h, dC > 2 Mpc/h The result is given in Figure8.− We− consider three dif- 4.4 Shape Analysis − − ferent distance thresholds: 0.25 Mpc− /h−(left), 0.50 Mpc/h −−− − − −− − − Now−− we study−− the correlation between the shape of galaxies (middle), and 1 Mpc/h (right). In− every panel, we observe − − −− − and their proximity to galaxy groups and filaments. In par- − −− −−−− − − that, for galaxies in filaments (red curves),− the alignment−−−−− − sig-− − −−− −−− ticular,− − we focus−− on q −for−− each− galaxy since it measures the nal significantly depends (the significance− − ranges from 2.4 −− − −−−− −− − ∼ ratio− to− the length of first and−− second principal axis and is 3.0σ) on the subhalo mass for the− galaxy. On− the other hand, − − a useful summary− statistic for the ellipticity. the alignments signal for galaxies outside− filaments (blue − − Axis Ratio Axis Ratio We partition galaxies according to their subhalo mass curves) are significant only when we set τ −= 0.25 Mpc/h − into four groups: but this dependency disappears for other cases.− Moreover, − −− −− 10−.0 10.6 when we increase the threshold τ, the slope (the− linear− −− effect− −− 10 − M /h−− <−− M < 10 M /h, −− −− −− −− −− 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 − from mass on galaxy alignments toward groups) for galaxies 1010.6M− /h < M− < 1011.0M /h, within filaments decreases but the9 slope 10 for galaxies 11 12 out of 13 9 10 11 12 13 (8) log(M/M ) log(10M11/.M0M) /h < M < 1011.4M /h, filaments increases. This suggests that the majority⊙ of the ⊙ 11.4 12.0 Figuremass-dependency 9. Impact from is from subhalo galaxies mass with on thedF shapes< 0.25 of Mpc a galaxy./h. Left: the result for galaxies10 M close/h < to M groups < 10 (d M< 5Mpc/h. /h). Right: C the result for galaxies close to filaments but not close to groups (dF 2Mpc/h). is The different two distance from ranges equation will ( be7) used in Figure 10.Inbothcases,weobserveastrongimpactonbothq, s from subhalo mass.

~~c 2015 RAS, MNRAS 000,1–11~~

so that there will be many newly formed galaxies. These compared to most observations. More analysis needs to be young galaxies are generally light, which decreases the aver- done in future for real observations. age mass. (ii) We find that galaxies align along with their nearby filaments and this alignment is stronger for massive galaxies when the galaxy is close to filaments (dF < 1 Mpc/h). This corroborates the past literature (Altay et al. 2006; Zhang 5CONCLUSION et al. 2009; Tempel & Libeskind 2013; Zhang et al. 2013). Moreover, we discover that the alignment signal has a sphere In this paper, we study the correlation between galaxy ori- of influence of 2.5 Mpc/h in radius. Namely, the principal entation and filaments by applying the density ridge model axes of a galaxy whose distance to the nearest filaments is to the smoothed particle hydrodynamic simulation. A short less than 2.5 Mpc/h would be influenced by the nearby fila- summary for what we have found is as follows: ments. This critical radius has not been previously reported (i) We demonstrate that filaments constructed using density in the literature. ridges from galaxy density field are similar to filaments con- (iii) We also observe an interesting pattern: the galaxy align- structed from dark matter density field. This analysis, along ment toward the nearest galaxy group is mass-dependent with the fact that density ridges are statistically consistent when this galaxy is near a filament within 0.25 Mpc/h.For in both theory (Chen et al. 2015c) and simulation (Chen galaxies close to a filament, massive galaxies tend to align et al. 2015a), suggests that we might be able to reconstruct along the direction toward the nearest group. For galaxies filaments of dark matter field by using only galaxies. How- away from filaments, subhalo mass has little impact on the ever, this simulation goes down to quite low subhalo mass alignment toward a group.

~~MNRAS 000, 1–10 (2015) 8 Yen-Chi Chen et al.~~

Galaxy alignment to the nearest galaxy group Galaxy alignment to the nearest galaxy group Galaxy alignment to the nearest galaxy group In filament (dF < 0.25 Mpc) In filament (dF < 0.5 Mpc) In filament (dF < 1 Mpc) Out of filament (dF > 0.25 Mpc) Out of filament (dF > 0.5 Mpc) Out of filament (dF > 1 Mpc) Random Random Random Slope: (2.4 ± 1) × 10−3 Slope: (1.9 ± 0.7) × 10−3 Slope: (1.8 ± 0.6) × 10−3

~~|> − |> |> − C C − C − − − − − − − µ − − − µ − − µ − − ⋅ − − ⋅ − ⋅ − 1 1 − 1 − µ − µ µ − <| <| <|~~

Slope: (1.4 ± 0.7) × 10−3 Slope: (1.7 ± 1) × 10−3 Slope: (2.3 ± 1.7) × 10−3 0.70 0.72 0.74 0.76 0.78 0.80 0.70 0.72 0.74 0.76 0.78 0.80 0.70 0.72 0.74 0.76 0.78 0.80 9.0 9.5 10.0 10.5 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 log(M/M ) log(M/M ) log(M/M ) ⊙ ⊙ ⊙

Figure 8. The e↵ect for filaments on µ1 µ ,thegalaxyalignmentalong‘thedirectiontowardthenearestgroup’.Wefocusonthe |h · C i| galaxies with dC > 1Mpc/h to make sure they are not inside a group. We then partition galaxies into two types: in filaments and out filaments by imposing a threshold ⌧ on the distance to filaments (see 4.3 for more details). Left: ⌧ =0.25 Mpc/h.Namely,agalaxy § whose distance to filaments is less than 0.25 Mpc/h will be considered within filaments.Otherwisethisgalaxyisclassifiedasout of filaments. Middle: ⌧ =0.50 Mpc/h. Right: ⌧ =1.00 Mpc/h.Theredcolordenotes µ1 µ for galaxies that are inside a filament |h · C i| and the blue color is the same but for galaxies out of filaments. Note that we also attach the significance for the slope using the linear regression. 8 Yen-Chi Chen et al.

dC < 5 Mpc/h dF < 5 Mpc/h, dC > 2 Mpc/h −− − − −− − −−− − − − −− − − −− − −− − − − − −−− − − −−−−−−−− − − − − −−− − − − −−− −−− − −−−− −− − − − − −− − − − − − − − − Axis Ratio Axis Ratio − − − − −− −− − −− −−− −− − −−−− −− −− −− −− −− 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 − − 9 10 11 12 13 9 10 11 12 13 log(M/M ) log(M/M ) ⊙ ⊙ Figure 9. Impact from subhalo mass on the shapes of a galaxy. Left: the result for galaxies close to groups (d < 5Mpc/h). Right: Figure 9. Impact from subhalo mass on the shapes of a galaxy. Left: the result for galaxies close to groups (dCC < 5 Mpc/h). Right: the result for galaxies close to ﬁlaments but not close to groups (d < 5Mpc/h and d > 2Mpc/h). The two distance ranges will be the result for galaxies close to ﬁlaments but not close to groups (dFF < 5 Mpc/h and dCC > 2 Mpc/h). The two distance ranges will be usedused in in Figure Figure 1010.Inbothcases,weobserveastrongimpactonboth. In both cases, we observe a strong impact on both q,q, s s fromfrom subhalo subhalo mass. mass.

sobecause that therehere we will separate be many galaxies newly by formed subhalo galaxies. mass to control These comparedgroups tend to mostto be observations. lower mass compared More analysis with needs those to close be youngthe effect galaxies from are subhalo generally mass light, on whichq. Therefore, decreases we the need aver- a doneto filaments. in future Namely, for real oneobservations. will find more low-mass galaxies agefine mass. mass bin to reduce the mass-dependency on q. Figure9 (ii)(withWe find subhalo that massgalaxies less align than along 1010.6 withM /h their) at nearbystrong tidal fila-

shows how q and s change as the subhalo mass changes. mentsforce regions. and this We alignment do not find is astronger similar pattenfor massive in other galaxies mass h i h i This pattern corroborates what is observed in Tenneti et al. whenrange, the so galaxy this phenomena is close to occurs filaments only (dF for< light1 Mpc galaxies./h). This A (2014). Note that Schneider et al.(2012) observed a similar corroboratespossible reason the is past that, literature in a region (Altay with et al. strong2006 tidal; Zhang ef- 5CONCLUSIONresult using dark matter halos and dark matter halo shapes. etfect, al. matter2009; Tempel concentrates & Libeskind around2013 the; large-scaleZhang et structuresal. 2013). Figure 10 displays how q changes as dF or dC changes. Moreover,so that there we discover will be that many the newly alignment formed signal galaxies. has a sphere These h i InWe this stack paper, galaxies we study around the filaments correlation (and between groups) galaxy and then ori- ofyoung influence galaxies of 2are.5 Mpcgenerally/h in light, radius. which Namely, decreases the principal the aver- entationpartition and galaxies filaments according by applying to their the distance density ridgeto filaments model axesage mass. of a galaxy whose distance to the nearest filaments is to(and the groups) smoothed into particle 10 bins hydrodynamic with a bin width simulation. of 0.5 Mpc A/h short(so less than 2.5 Mpc/h would be influenced by the nearby fila- summarywe only consider for what distance we have to found filaments/groups is as follows: less than 5 ments. This critical radius has not been previously reported (i)MpcWe/h demonstrate). For galaxies that stacking filaments around constructed filaments, using we havedensity an in5 the CONCLUSION literature. ridgesadditional from constraint galaxy densitydC > field2 Mpc are/h similarto eliminate to filaments the effect con- (iii) We also observe an interesting pattern: the galaxy align- In this paper, we study the correlation between galaxy ori- structedfrom galaxy from groups. dark matter For each density bin, field. we also This show analysis, the average along ment toward the nearest galaxy group is mass-dependent entation and filaments by applying the density ridge model withsubhalo the mass. fact that density ridges are statistically consistent when this galaxy is near a filament within 0.25 Mpc/h.For to the smoothed particle hydrodynamic simulation. A short in bothOverall, theory we ( findChen two et cases al. 2015c that) lead and to simulation a change ( inChen the galaxies close to a filament, massive galaxies tend to align q after adjusting the effect from subhalo mass. The first summary for what we have found is as follows: eth i al. 2015a), suggests that we might be able to reconstruct along the direction toward the nearest group. For galaxies filamentscase can beof dark found matter at the field top by right using and only bottom galaxies. left How-panel (i)away We demonstratefrom filaments, that subhalo filaments mass constructed has little impact using density on the ever,of Figure this simulation10. We observe goes a down decreasing to quite pattern low subhalo as dF or massdC alignmentridges from toward galaxy a density group. field are similar to filaments con- increases. In other words, for galaxies close to filaments or structed from dark matter density field. This analysis, along groups, we expect their q to be higher (more rounded galax- with the fact that density ridges areMNRAS statistically000, 1– consistent10 (2015) ies). In both panels, the subhalo mass within each bin does in both theory (Chen et al. 2015c) and simulation (Chen not change too much so that this effect cannot be explained et al. 2015a), suggests that we might be able to reconstruct by the mass difference. The second case is on the difference filaments of dark matter field by using only galaxies. How- between groups and filaments. In every panel of Figure 10, ever, this simulation goes down to quite low subhalo mass we find that, for galaxies at the same distance to either fil- compared to most observations. More analysis needs to be aments or groups, q is always higher for galaxies close to h i done in future for real observations. groups. (ii) We find that galaxies align along with their nearby fila- An explanation to the above cases is due to the differ- ments and this alignment is stronger for massive galaxies ence in the ratio of elliptical galaxies. If elliptical galaxies when the galaxy is close to filaments (dF < 1 Mpc/h). This are more likely to be in/near groups and filaments and if corroborates the past literature (Altay et al. 2006; Zhang they are usually rounder than disk galaxies, then we would et al. 2009; Tempel & Libeskind 2013; Zhang et al. 2013). expect to see that galaxies close to groups and filaments are Moreover, we discover that the alignment signal has a sphere on average rounder than those that are far away. And if this of influence of 2.5 Mpc/h in radius. Namely, the principal effect is stronger for groups (perhaps due to a stronger tidal axes of a galaxy whose distance to the nearest filaments is field), then we should see a higher q for galaxies that are less than 2.5 Mpc/h would be influenced by the nearby fila- closer to groups. ments. This critical radius has not been previously reported Note that in the upper left panel (1010.0M /h < M < in the literature.

~~1010.6M /h), we ﬁnd a decreasing trend for the average sub- (iii) We also observe an interesting pattern: the galaxy align-~~

halo mass when the distance to large-scale structure is in- ment toward the nearest galaxy group is mass-dependent creasing. Moreover, at the same distance, galaxies close to when this galaxy is near a ﬁlament within 0.25 Mpc/h. For

~~c 2015 RAS, MNRAS 000,1–11~~

Galaxy-Filament Alignment 9 Galaxy-Filament Alignment 9 10 < log(M/M ) < 10.6 10.6 < log(M/M ) < 11 ⊙ ⊙ 1.95 2.24 2.11 2.35 2.41 2.5 2.5 2.53 2.51 2.6 − − − − − − − − − 6.05 6.14 − − − − − − − − − 6.21 6.24 − − − − 6.26 6.21 2.71 − − − − − − − 6.26 6.28 6.24 6.3 2.4 2.91 2.96 − − − − − 3.02 3.13 3.08 − − − − − − − − −3.22 − − − − − − 3.19 −3.12 6.32 − − − − − − 6.34 6.26 − − − 6.33 6.27 −6.39 − −6.33 −6.33 6.41 −6.31

<= more elongated, Stacking on centers of galaxy groups <= more elongated, Stacking on centers of galaxy groups Stacking on Filaments, away from clusters by 2 Mpc/h Stacking on Filaments, away from clusters by 2 Mpc/h Averaging over all distance bins Averaging over all distance bins 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 012345 012345 Distance (Mpc/h) Distance (Mpc/h) 11 < log(M/M ) < 11.4 11.4 < log(M/M ) < 12 ⊙ ⊙

~~15.54~~

− 15.09 15.48 15.09 45.97 47.37 15.4 48.08 − 15.76 15.26 47.22− 49.17− − − − 15.51 − 47.02− 49.14 48.09 − − − 15.7 15.14 − − − − −48.07 − − − − − − − − − 48.52 − − − − − − − − − − − − − − − − − − − − − − − − 15.59 − − − 15.4 − − − − − 45.78 15.06 14.92− − − − 49.31 45.2 44.52 −43.48− 15.03 − − − − − − 14.62 − 14.57 14.31 − 45.41 44.58− 15.09− 42.27 − 15.35 − 39.31 44.48

Figure 10. Influence from groups and filaments on the shape of galaxies. We display how q changes as the distance to filaments (blue) Figure 10. Influence from groups and filaments on the shape of galaxies. We display howh qi changes as the distance to filaments (blue) and groups (brown) changes. Note that we partition galaxies according to their subhalo massh i to adjust the mass-dependency on q .The and groups (brown) changes. Note that we partition galaxies according to their subhalo mass to adjust the mass-dependency onh qi . The number near q at each bin is the average subhalo mass within that bin. h i number nearh qi at each bin is the average subhalo mass within that bin. h i

(iv) Finally, we find that the ellipticity of a galaxy is correlated ment and weak lensing to be improved if one incorporates galaxies close to a filament, massive galaxies tend to align and the tidal field is often explicitly or implicitly used to with its distance to groups and filaments when the subhalo the e↵ect from filaments. This might be a way to extend the along the direction toward the nearest group. For galaxies define a filament (Hahn et al. 2007a,b; Forero-Romero et al. mass is between 1010.6M and 1011.4M . A galaxy that is current linear or non-linear alignment model (Bridle & King away from filaments, subhalo mass has little impact on the 2009; Cautun et al. 2013). Therefore, the principal axes and close to either a group or a filament tends to be less elliptical 2007; Blazek et al. 2011, 2015) since the alignment along alignment toward a group. the shape of a galaxy are expected to be correlated with its (more rounded). filaments can be viewed as a new type of non-linear e↵ect. (iv) Finally, we find that the ellipticity of a galaxy is correlated nearby filament. Based on the galaxy-filament interaction we withThe its distance galaxy-filament to groups alignment and filaments observed when in the this subhalo paper have found, we expect the future survey on intrinsic align- canmass be is explained between 10 by10 the.6M intrinsicand 10 alignment11.4M . A model galaxy and that the is ment and weak lensing to be improved if one incorporates

relationshipclose to either between a group tidal or a filament field and tends filaments. to be less The elliptical intrin- the effect from filaments. This might be a way to extend the sic(more alignment rounded). model links the galaxy principal axes to the current linear or non-linear alignment model (Bridle & King ACKNOWLEDGMENTS tidal field (Catelan et al. 2001; Hirata & Seljak 2004, 2010) 2007; Blazek et al. 2011, 2015) since the alignment along and theThe tidal galaxy-filament field is often alignment explicitly observed or implicitly in this used paper to Thisfilaments work can is supported be viewed in as part a new by the type Department of non-linear of Energy effect. definecan be a explained filament (Hahn by the et intrinsic al. 2007a alignment,b; Forero-Romero model and et the al. under grant DESC0011114; YC is supported by DOE; SH is 2009relationship; Cautun between et al. 2013 tidal). Therefore, field and the filaments. principal The axes intrin- and supported in part by DOE-ASC, NASA and NSF; AT was thesic shapealignment of a modelgalaxy links are expected the galaxy to be principal correlated axes with to the its supported for the duration of this work by NASA ROSES 12- nearbytidal field filament. (Catelan Based et al.on the2001 galaxy-filament; Hirata & Seljak interaction 2004, 2010 we) EUCLID12-0004. RM was supported in part by NSF under have found, we expect the future survey on intrinsic align- Grant. No. AST-1313169 and NASA ROSES 12-EUCLID12- c 2015 RAS, MNRAS 000,1–11 MNRAS 000, 1–10 (2015) 10 Yen-Chi Chen et al.

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~~c 2015 RAS, MNRAS 000,1–11~~

~~Galaxy-Filament Alignment 11~~

~~This paper has been typeset from a TEX/ LATEX ﬁle prepared by the author.~~

~~c 2015 RAS, MNRAS 000,1–11~~