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-Lema^ıtre 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 alter- native 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.