Cosmicflows-3: Two Distance $-$ Velocity Calculators

Key words: large scale structure of universe — galaxies: distances and redshifts Draft version December 17, 2019 Typeset using LATEX preprint2 style in AASTeX62

Cosmicﬂows-3: Two Distance−Velocity Calculators Ehsan Kourkchi,1 Hel´ ene` M. Courtois,2 Romain Graziani,2 Yehuda Hoffman,3 Daniel Pomarede,` 4 Edward J. Shaya,5 and R. Brent Tully,1 1Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA 2University of Lyon, UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon 69622, France 3Racah Institute of Physics, Hebrew University, Jerusalem, 91904 Israel 4Institut de Recherche sur les Lois Fondamentales de l’Univers, CEA, Universite’ Paris-Saclay, 91191 Gif-sur-Yvette, France 5University of Maryland, Astronomy Department, College Park, MD 20743, USA

ABSTRACT Tools are provided at the Extragalactic Distance Database website that provide rela- tionships between the distances and velocities of galaxies based on smoothed versions of the velocity fields derived by the Cosmicflows program. 1. INTRODUCTION This model has a direct lineage from mod- Galaxy velocities deviate from Hubble-Lemaˆıtre els by Faber & Burstein(1988), Han & Mould expansion. Deviations can be considerable, as (1990), and Han(1992). The latter of these, al- evidenced by the motion of the Local Group though it does not entertain the Shapley Con- of 631 km s−1 with respect to the rest frame of centration, considers added details, the most the cosmic microwave background (Fixsen et al. important being the Local Velocity Anomaly 1996). There are numerous instances, particu- (Tully 1988; Faber & Burstein 1988). These larly nearby, when it is useful to have a better early studies surmised that this feature is re- approximation between observed velocities and lated to the proximity of the Local Void (see physical distances than provided by the simple also Lahav et al.(1988)), a proposal that has assumption of uniform cosmic expansion. now been robustly confirmed (Rizzi et al. 2017; The NASA/IPAC Extragalactic Database Tully et al. 2019; Anand et al. 2019). Al- (NED) has provided estimates of galaxy dis- ready, then, the Han(1992) model and vari- tances given observed velocities based on a ants capture the major features affecting the model by Mould et al.(2000). In alternatives, local velocity field, although another player to arXiv:1912.07214v1 [astro-ph.CO] 16 Dec 2019 deviations are induced by up to three mass con- have emerged is the vast underdensity at the centrations, associated with the Virgo Cluster, cosmic microwave background dipole anti-apex; the Great Attractor, and the Shapley Concen- the Dipole Repeller (Hoffman et al. 2017) and tration. The parameters of this model are the the Perseus−Pisces filament (Haynes & Gio- positions of the mass centers, the velocities in- vanelli 1988) significantly inhibits the flow in duced at our location by each, and the assump- the CMB dipole direction. tion that the masses have spherically symmet- Many other contributions could be enter- ric geometry with density gradients ρ(x) ∝ r−2 tained (Coma, Horologium-Reticulum, Her- where r is the distance from a mass center. cules, ...). It should be clear that any paramet- 2 ric model with a moderate number of parame- The red dashed straight line in every plot ters will only crudely approximate the peculiar shows the relationship between velocity and velocity field. Also, for a model to be useful to distance with uniform expansion if the Hub- the community, it should be relatively painless ble Constant is 75 km s−1 Mpc−1. This line and efficient for a user to acquire desired infor- is for illustrative purposes only! Velocities mation for a random target. The facility to be and distances are determined completely in- described is based on a velocity field respond- dependently of each other in the Cosmicflows-3 ing to the full complexity of structure on scales compilation. The models make no assumption

1 − 200 Mpc. Two models are offered. One re- about the value of H0. stricted to 38 Mpc is based on a fully non-linear The distance−velocity tool does not directly analysis. The other extending to 200 Mpc is de- give peculiar velocities, Vpec. The tool gives ex- rived from an analysis in the linear dynamical pectation distances, d, at observed velocities, regime. Both are publicly accessible at the in- Vobs (or expectation observed velocities at spec- teractive platform to be described. ified distances). To a reasonable approxima- 4 tion, Vobs = H0d + Vpec. It has been demon- strated (Tully et al. 2016) that Cosmicflows- 2. DISTANCE−VELOCITY USERS 3 distances and velocities are compatible with −1 −1 MANUAL H0 = 75 km s Mpc , with zero-point uncer- tainty at the level of 3%. Users interested in pe- Details of the two underlying models will be culiar velocities can contemplate applying alter- discussed in the next section, but the user in- native values of H at their risk. Note that alter- terface functions are the same for both. The 0 ing the zero point associated with Cosmicflows facility can be accessed at the Extragalactic Dis- distances alters the H value that would be most tance Database (EDD).12 0 consistent but the products H d would be un- A user can enter the celestial coordinates of 0 changed. Hence, the relationship between V a target with a choice of coordinate systems. obs and V given in the formula above is indepen- Examples are shown in Figures1 and2. Ob- pec dent of the zero point calibration. servational data from the Cosmicflows-3 com- The reference velocities are different for the pendium of distances (Tully et al. 2016) can be two models. In the case of the local non-linear displayed in a cone chosen by the user centered model, velocities are with respect to the Galac- on the target. A blue locus plots the averaged tic center. With the large scale linear model, expectation velocity along the line of sight as a velocities are with respect to the Local Group. function of distance.3 Cursor control can access Justifications for these choices will be given in specific distance and velocity values along the the section discussing the models. In any event, locus. Hovering over a datum gives name, veloc- it must be noted that there are variants of both ity, and distance specifics for that item. Zoom these reference frames in the literature. The def- and translation functions are activated by side- inition of the Galactic Standard of Rest (gsr) de- panel toggles. pends on the distance of the Galactic center and the amplitude of Galactic rotation at the Sun, 1 http://edd.ifa.hawaii.edu 2 Pre-publication, access to the linear model calculator is at http://edd.ifa.hawaii.edu/CF3calculator 4 Davis & Scrimgeour(2014) discuss the more rigorous 3 All distances in this tool are luminosity distances, formulation Vpec = (f(z)Vobs − H0d)/(1 + H0d/c) where dL, related through redshift, z, to comoving distances, f(z) is given by Eq. 2. Differences from the approximate −1 dm by the equation dL = dm(1 + z). formula grow with z to ∼ 30 km s by z = 0.05. 3

Figure 1. Velocities as a function of distance in the direction of the Virgo Cluster plotted with the non- −1 linear numerical action calculator. The Virgo Cluster lies at 16.0 Mpc with Vgsr = 1096 km s . The blue curve from the model is noisy because the number of local constraints is small at each step in the averaging but the characteristic triple-value curve (3 distances sharing the same observed velocity) associated with −1 −1 infall around a massive cluster is clear. The red dashed line assumes H0 = 75 km s Mpc . Data constraining the model are shown as large red circles if distance uncertainties are 5% or less (brown extra large circles for Virgo and Fornax clusters), and as small green circles if uncertainties are over 5% but not more than 15%. Data with larger uncertainties are represented by black plus signs but do not constrain the model. as well as a small solar deviation. There are tions are derived from the properties of galax- alternative choices (de Vaucouleurs et al. 1991; ies within 1 Mpc. The Local Sheet solution Eisenhauer et al. 2005; Reid et al. 2009). Our is derived from the properties of galaxies out- model is based on the solution by van der Marel side 1 Mpc yet within 5 Mpc. See Tully et al. et al.(2012). As a measure of the uncertainties (2008) for the argument that this solution is the inherent in the translation to the Galactic rest most stable. Uncertainties between the alter- frame, diﬀerences between the four cited alternative Local Group frames are at the level of natives are 12 ± 5 km s−1. 19 ± 10 km s−1. Similarly, there are alternative versions of The linear model extends to velocities of the Local Group rest frame (Yahil et al. 1977; 15,000 km s−1 and cosmological corrections c Karachentsev & Makarov 1996; Courteau & van reach ∼ 4%. The corrected velocity Vls is re- den Bergh 1999). We prefer a variant we call the lated to the observed velocity Vls by: Local Sheet (ls) reference frame (Tully et al. 2008). The three former (Local Group) solu- c Vls = f(z)Vls (1) 4

Figure 2. Velocities as a function of distance plotted with the linear calculator. Cosmological corrections become noticeable in this extended domain; the two panels give alternate representations (see text). The blue curve is derived from interpolation of velocities on a grid of distances with intervals of 6.25 Mpc, where the value at each point is averaged over the 8 nearest grid points weighted by the inverse square of separation. In the top panel, velocities are the observed values in the Local Sheet frame and the red dashed locus of constant H0 has curvature away from the grey dotted straight line. In the bottom panel, velocities are adjusted for the cosmological eﬀect and the red dashed Hubble line is straight. In the two panels of 14 this ﬁgure, the data are coded by the mass of entities: large brown circles if mass greater than 10 M , 13 14 13 smaller red circles if mass is between 10 and 10 M , and black plus signs if mass is below 10 M . The coordinates are chosen to be the same is in Fig.1. Major clusters in the cone in this direction are the Virgo Cluster at 16 Mpc and Abell 1367 at 88 Mpc. 5 where Between Galactic standard of rest and Local 2 2 Sheet: f(z) = 1+1/2(1−q0)z−1/6(2−q0 −3q0)z (2)

Vls = Vgsr − 37 cos l cos b + 66 sin l cos b − 15 sin b q0 = 1/2(Ωm − 2ΩΛ) = −0.595 (3) (6) when Ω = 0.27 and Ω = 0.73 and z = V /c m Λ ls 3. MODELS (Wright 2006). In the top panel of Figure2 velocities are ob- Two calculators are offered; one limited to dis- −1 served values (averaged over group members) tances less than 38 Mpc (Vobs ∼ 2850 km s ) but in this representation there is a slight cur- based on a fully non-linear dynamical model and −1 vature of the Hubble relation manifested in the the other extending to 200 Mpc (15,000 km s ) departure of the red dashed curve from the faint at lower resolution and based on a linear model. grey straight line. Velocities in the bottom 3.1. Non-linear Model Limited to 38 Mpc panel are increased by the cosmological correction so the red dashed Hubble line is straight- This calculator presents a smoothed version ened. In detail the correction depends on the of the current day (z = 0) velocity field derived choices of the cosmological matter and energy from the numerical action orbit reconstruction of Shaya et al.(2017). In brief summary, orbits density parameters Ωm and ΩΛ but differences in the correction between reasonable values of are followed for 1382 tracers (either groups or these parameters are negligible within the ve- individual galaxies) that collectively dominate locity range being considered. f(z = 0.05) the mass content associated with luminosity within 38 Mpc ' 2850 km s−1. The tracers are decreases by 0.1% if Ωm increases and ΩΛ decreases by 0.03. either (or both) important mass constituents or Hover with the cursor over a datum element have very accurately known distances (15% or of the linear model to obtain input distance and better uncertainties in the Cosmicflow-3 com- velocity information. The element may be an pendium). Physically consistent orbits are fol- individual galaxy or a group and is identified lowed from z = 4 to z = 0. The orbit re- by the parameter PGC1, the Principal Galax- construction is embedded in a tidal field at ies Catalog identification (Paturel et al. 1996) distances greater than 38 Mpc based an the of the brightest member. The Nest parame- Cosmicflows-2 velocity model of Tully et al. ter identifies the membership of elements in the (2014). 2MASS group catalog of Tully(2015a). There can be no hope of untangling the com- For convenience, formulae are given here plexity of orbits after shell crossing, so orbits for conversions between heliocentric veloci- describe the centers of mass of the ensemble of a group today. The initial distribution at z = 4 ties, Vh, and the reference frames used in the distance−velocity tools where the angles are of our sample is well dispersed, but by today Galactic longitude and latitude (l, b). the entities have become concentrated in the Galactic standard of rest: current observed structure. For practical rea- sons, the density of tracers is highest nearby. Vgsr = Vh+11.1 cos l cos b+251 sin l cos b+7.25 sin b Consequently, the model is most robust within (4) ∼ 15 Mpc and is poorly sampled in the voids. Local Sheet: The orbits of our Galaxy and Andromeda

Vls = Vh − 26 cos l cos b + 317 sin l cos b − 8 sin b (M31) are followed separately in the numeri- (5) cal action model of Shaya et al.(2017). These 6 galaxies are each the central host of distinct estimates and a 2MASS group catalog (Tully collapsed halos. We (Tully 2015b; Kourkchi & 2015a). A group is assigned the weighted aver- Tully 2017) equate groups with collapsed halos; age distance of the available measures and the the term ”Local Group” is a misnomer. The averaged velocity of all known members. As a Galactic Standard of Rest is the natural coor- consequence, although distances to individual dinate system for studies of the orbital history galaxies can have large uncertainties, there are of the Milky Way. a multitude of groups that are relatively well The model distance−velocity curve (blue) is constrained. The dynamically dominant groups derived from interpolation of the model veloc- with distance measures are identified by larger ities on a grid of distances with grid intervals symbols in the displays of the linear model in 0.2 Mpc at the origin increasing to 1 Mpc in- plots analogous to Figure2. 6 tervals at 38 Mpc, the outer limit of the model. The present Graziani et al.(2019) model The value at a grid point is averaged over the is constructed on a relatively coarse grid at four nearest mass points weighted by the inverse 6.25 Mpc spacings. There remains an issue square of separation. Pause the cursor over the of limited observations at latitudes within 15◦ blue curve for distance and velocity information of the plane of our Galaxy. Nearby, within at a chosen location. Pause the cursor over in- ∼ 8, 000 km s−1, our filtered reconstruction dividual entries for information on data points. is relatively successful across this zone. How- ever, at greater distances the gap of the zone 3.2. Linear Model Extending to 200 Mpc of obscuration becomes too large for a good This second calculator is based on the three- reconstruction. dimensional velocity and density fields of The Local Sheet (or alternative Local Group) Graziani et al.(2019). The likelihood model reference frame is preferred in this model be- seeks consistency between velocities and the cause of the cancellation of the Milky Way and matter distribution in the linear regime of a M31 motions toward each other. Averaged ve- direct relationship between the gradient of the locities are appropriate in the linear regime. velocity field and densities. The procedure is Nearby galaxies have modest dispersions in the an extension of that by Lavaux(2016). Care Local Sheet frame (Karachentsev et al. 2002). is taken to negate Malmquist bias (Strauss & All nearby galaxies share similar large peculiar Willick 1995) and the asymmetry in velocity motions in the frame of the cosmic microwave errors in translations to distance from the loga- background. rithmic modulus. Multiple constrained realiza- tions are averaged following Hoffman & Ribak 4. PRACTICAL EXAMPLE (1991). As an example of the service that the Dis- Cosmicflows-3 provides distance and velocity tance −Velocity calculator provides, consider an measures. The 17,647 individual galaxy en- effort to determine the Hubble Constant from tries are collected into 11,501 entities through a measurement of the distance to the gravita- grouping, with two or more galaxies with dis- tional wave event GW170817 that occurred in 5 tance estimates in 1704 groupings. Linkages the galaxy NGC 4993 (Abbott et al. 2017). By are established between galaxies with distance 6 Beyond 10,000 km s−1∼ 130 Mpc the group mass 5 The exact numbers of individual and grouped en- assignments from Tully(2015a) become unreliable be- tities change as minor corrections are made. See cause correction factors for missing components become http://edd.ifa.hawaii.edu for updated catalogs. very large. 7 happenstance, the distance, d ∼ 40 Mpc, is ment between the two at distances less than at the extremity of coverage provided by the 30 Mpc. At greater distances the non-linear non-linear model (although that model is em- model runs about 100 km s−1 below the linear bedded within the 100 Mpc scale tidal field de- model but the non-linear model is poorly con- duced from a linear analysis of Cosmicflows-2). strained at its edge of application. Considering It comfortably lies within the domain of cover- the linear model, within 10 Mpc foreground of age of the new linear model. ∼ 40 Mpc observed velocities are running about −1 What is the appropriate velocity to accom- 100 km s below the H0 = 75 fiducial line while pany the distance measurement for an estimate by 50 Mpc the observed velocities drop to about of the Hubble Constant? It is important to 300 km s−1 below the fiducial line. The conse- understand the environment of the target on a quence is an ambiguity due to this Centaurus range of scales. Most immediately, does the tar- Cluster overdenity infall pattern. The ampli- get lie in a group? In the case of NGC 4993, yes, tude of the wave is 200 km s−1 in the linear this galaxy lies in a group with the dominant regime (and greater if non-linear effects would member NGC 4970. The group is identified be taken into account). as HDC 751 (Crook et al. 2007), 2M++ 1294 It is most common to derive estimates of the (Lavaux & Hudson 2011), Nest 100214 (Tully Hubble Constant in the reference frame of the 2015a), and PGC1 45466 (Kourkchi & Tully cosmic microwave background. However nearby 2017). In the latter catalog, there are 22 galax- galaxies are participating in a coherent flow, a ies linked with the group, with < Vhelio >= coherence that extends to include the NGC 4970 2995 ± 25 km s−1. In alternate reference frames group with NGC 4993 as a member. A cor- −1 of interest, < Vgsr >= 2851 km s , < Vls >= rection for the flow is required if working in −1 −1 2783 km s , and < Vcmb >= 3308 km s . the cosmic microwave background frame that On a larger scale, this PGC1 45466 = is closely equivalent to working without a cor- NGC 4970 group lies roughly along the line of rection in the Local Sheet (Local Group) frame. sight toward the Great Attractor (Dressler et al. This comment is a cautionary reminder of the 1987), 18◦ (∼ 13 Mpc) removed from the dom- jeopardy of evaluating the Hubble Constant lo- inant Centaurus Cluster (d = 40.5 ± 1.6 Mpc, cally. Should we live in a large scale under- −1 Vls = 3285 km s ). There is a clear infall pat- or over-density, it would be necessary to make tern in the line of sight toward the Centaurus measurements beyond this feature to be com- Cluster, with objects to the immediate fore- fortable in the cosmic microwave background ground falling away from us toward the cluster frame. and object behind manifesting backside infall Finally, It is to be appreciated that the dis- toward us. This effect extends in a weakened tances in this DV calculator are based on fashion to the NGC 4993 line of sight. At a a specific zero-point calibration that may or distance of around 40 Mpc, there is ambiguity may not pass the test of time. The H0 = whether the NGC 4970 group with NGC 4993 75 km s−1 Mpc−1 fiducial line is consistent with is front-side falling away or back-side falling the current Cosmicflows-3 data compilation. A forward with respect to the overdensity around user of the DV calculator may have a distance the Centaurus Cluster. Figure3 is extracted that is implicitly based on a different zero-point from the DV Calculator in the NGC 4993 direc- scale. However, as discussed in Section 2, pe- tion, with the non-linear solution superimposed culiar velocities are decoupled from the Hubble on the linear solution. There is close agree- Constant. A user can consider the DV calcula- 8

Figure 3. A zoomed extraction from the Distance-Velocity calculator in the direction of the galaxy NGC 4993. The result from the non-linear calculator terminating at 38 Mpc is overlaid as a black curve on the result from the linear calculator. Departures from the Hubble expectation with the linear model are ∼ −100 km s−1 nearward of ∼ 42 Mpc, increasing in amplitude to ∼ −300 km s−1 longward of that point. tor distance scale to be elastic, with the fiducial ploited. There is the intention of extending the Hubble line flexing accordingly, but the peculiar numerical action orbit reconstruction model of velocity amplitudes with respect to the fiducial Shaya et al.(2017) to 100 Mpc. Cosmicflows-4 line will be unchanged at a given observed ve- is on the horizon, with constraints to be pro- locity. vided by ∼ 30, 000 distances. In review of the case for NGC 4993, as a best The latest models will be made available at effort at accounting for deviations from cosmic the Extragalactic Distance Database.7 expansion, an estimate can be made of the value of the Hubble Constant, H = (V − V )/d 0 obs pec Acknowledgements taking V = 2783 km s−1, the value for the obs Many people have contributed directly or indi- NGC 4970 group, and V somewhere between pec rectly to this substantial undertaking. Special −100 and −300 depending on the user’s pre- thanks to Gagandeep Anand, Igor Karachent- ferred distance and whether that places the tar- sev, Dmitry Makarov, Lidia Makarova, Don get foreground or background to the Centaurus Neill, Luca Rizzi, Mark Seibert, Kartik Sheth, Cluster overdensity. and Po-Feng Wu. This catalog could hardly 5. FUTURE AUGMENTATIONS have been assembled without the resources of Cosmicflows is a continuously evolving pro- NED, the NASA/IPAC Extragalactic Database, gram. It is anticipated that the Distance−Velocity and the Lyon extragalactic database HyperLeda. calculators will be updated at intervals. The Financial support for the Cosmicflows program resolution can be improved with greater compu- has been provided by the US National Sci- tational effort. In combination, the quasi-linear methodology of Hoffman et al.(2018) can be ex- 7 http://edd.ifa.hawaii.edu 9 ence Foundation award AST09-08846, an award support has been provided by the Lyon Insti- from the Jet Propulsion Lab for observations tute of Origins under grant ANR-10-LABX-66 with Spitzer Space Telescope, and NASA award and the CNRS under PICS-06233 and the Israel NNX12AE70G for analysis of data from the Science Foundation grant ISF 1358/18. Wide-field Infrared Survey Explorer. Additional

REFERENCES Abbott, B. P., Abbott, R., Abbott, T. D., et al. Hoffman, Y., Carlesi, E., Pomarède,D., et al. 2017, Nature, 551, 85, doi: 10.1038/nature24471 2018, Nature Astronomy, 2, 680, Anand, G. S., Tully, R. B., Rizzi, L., Shaya, E. J., doi: 10.1038/s41550-018-0502-4 & Karachentsev, I. D. 2019, ApJ, 880, 52, Karachentsev, I. D., & Makarov, D. A. 1996, AJ, doi: 10.3847/1538-4357/ab24e5 111, 794, doi: 10.1086/117825 Courteau, S., & van den Bergh, S. 1999, AJ, 118, Karachentsev, I. D., Sharina, M. E., Makarov, 337, doi: 10.1086/300942 D. I., et al. 2002, A&A, 389, 812, Crook, A. C., Huchra, J. P., Martimbeau, N., doi: 10.1051/0004-6361:20020649 et al. 2007, ApJ, 655, 790, doi: 10.1086/510201 Kourkchi, E., & Tully, R. B. 2017, ApJ, 843, 16, Davis, T. M., & Scrimgeour, M. I. 2014, MNRAS, doi: 10.3847/1538-4357/aa76db 442, 1117, doi: 10.1093/mnras/stu920 Lahav, O., Lynden-Bell, D., & Rowan-Robinson, de Vaucouleurs, G., de Vaucouleurs, A., Corwin, M. 1988, MNRAS, 234, 677, Jr., H. G., et al. 1991, Third Reference doi: 10.1093/mnras/234.3.677 Catalogue of Bright Galaxies (Volume 1-3, XII, Lavaux, G. 2016, MNRAS, 457, 172, 2069 pp. 7 figs.. Springer-Verlag Berlin doi: 10.1093/mnras/stv2915 Heidelberg New York) Lavaux, G., & Hudson, M. J. 2011, MNRAS, 416, Dressler, A., Faber, S. M., Burstein, D., et al. 2840, doi: 10.1111/j.1365-2966.2011.19233.x 1987, ApJL, 313, L37, doi: 10.1086/184827 Mould, J. R., Huchra, J. P., Freedman, W. L., Eisenhauer, F., Genzel, R., Alexander, T., et al. et al. 2000, ApJ, 529, 786, doi: 10.1086/308304 2005, ApJ, 628, 246, doi: 10.1086/430667 Paturel, G., Bottinelli, L., di Nella, H., et al. 1996, Faber, S. M., & Burstein, D. 1988, Motions of Principal Galaxy Catalogue. Second edition: galaxies in the neighborhood of the local group PGC CD-ROM. (Large-Scale Motions in the Universe: A Vatican study Week), 115–167 Reid, M. J., Menten, K. M., Zheng, X. W., et al. Fixsen, D. J., Cheng, E. S., Gales, J. M., et al. 2009, ApJ, 700, 137, 1996, ApJ, 473, 576, doi: 10.1086/178173 doi: 10.1088/0004-637X/700/1/137 Graziani, R., Courtois, H. M., Lavaux, G., et al. Rizzi, L., Tully, R. B., Shaya, E. J., Kourkchi, E., 2019, MNRAS, 130, doi: 10.1093/mnras/stz078 & Karachentsev, I. D. 2017, ApJ, 835, 78, Han, M. 1992, ApJ, 395, 75, doi: 10.1086/171631 doi: 10.3847/1538-4357/835/1/78 Han, M., & Mould, J. 1990, ApJ, 360, 448, Shaya, E. J., Tully, R. B., Hoffman, Y., & doi: 10.1086/169135 Pomarède,D. 2017, ApJ, 850, 207, Haynes, M. P., & Giovanelli, R. 1988, Large-scale doi: 10.3847/1538-4357/aa9525 structure in the local universe - The Strauss, M. A., & Willick, J. A. 1995, PhR, 261, Pisces-Perseus supercluster, ed. V. C. Rubin & 271, doi: 10.1016/0370-1573(95)00013-7 G. V. Coyne, 31–70 Tully, R. B. 1988, Nature, 334, 209, Hoffman, Y., Pomarède,D., Tully, R. B., & doi: 10.1038/334209a0 Courtois, H. M. 2017, Nature Astronomy, 1, —. 2015a, AJ, 149, 171, 0036, doi: 10.1038/s41550-016-0036 doi: 10.1088/0004-6256/149/5/171 Hoffman, Y., & Ribak, E. 1991, ApJL, 380, L5, —. 2015b, AJ, 149, 54, doi: 10.1086/186160 doi: 10.1088/0004-6256/149/2/54 10

Tully, R. B., Courtois, H., Hoffman, Y., & van der Marel, R. P., Fardal, M., Besla, G., et al. Pomarède,D. 2014, Nature, 513, 71, 2012, ApJ, 753, 8, doi: 10.1038/nature13674 doi: 10.1088/0004-637X/753/1/8 Tully, R. B., Courtois, H. M., & Sorce, J. G. 2016, AJ, 152, 50, doi: 10.3847/0004-6256/152/2/50 Wright, E. L. 2006, PASP, 118, 1711, Tully, R. B., Pomarède,D., Graziani, R., et al. doi: 10.1086/510102 2019, ApJ, 880, 24, Yahil, A., Tammann, G. A., & Sandage, A. 1977, doi: 10.3847/1538-4357/ab2597 ApJ, 217, 903 Tully, R. B., Shaya, E. J., Karachentsev, I. D., et al. 2008, ApJ, 676, 184, doi: 10.1086/527428