Cosmicflows-3: Two Distance–Velocity Calculators - IOPscience (2024)

Galaxy velocities deviate from Hubble-Lemaître expansion. Deviations can be considerable, as evidenced by the motion of the Local Group of 631km s⁻¹ with respect to the rest frame of the cosmic microwave background (CMB; Fixsen et al. 1996). There are numerous instances, particularly nearby, when it is useful to have a better approximation between observed velocities and physical distances than provided by the simple assumption of uniform cosmic expansion.

The NASA/IPAC Extragalactic Database (NED) has provided estimates of galaxy distances given observed velocities based on a model by Mould et al. (2000). In alternatives, deviations are induced by up to three mass concentrations, associated with the Virgo Cluster, the Great Attractor, and the Shapley Concentration. The parameters of this model are the positions of the mass centers, the velocities induced at our location by each, and the assumption that the masses have spherically symmetric geometry with density gradients ρ(x) ∝ r⁻², where r is the distance from a mass center.

This model has a direct lineage from models by Faber & Burstein (1988), Han & Mould (1990), and Han (1992). The latter of these, although it does not entertain the Shapley Concentration, considers added details, the most important being the local velocity anomaly (Faber & Burstein 1988; Tully 1988). These early studies surmised that this feature is related to the proximity of the Local Void (see also Lahav et al. 1988), a proposal that has now been robustly confirmed (Rizzi et al. 2017; Anand et al. 2019; Tully et al. 2019). Already, then, the Han (1992) model and variants capture the major features affecting the local velocity field, although another player to have emerged is the vast underdensity at the CMB dipole anti-apex, the Dipole Repeller (Hoffman et al. 2017), and the Perseus−Pisces filament (Haynes & Giovanelli 1988) significantly inhibits the flow in the CMB dipole direction.

Many other contributions could be entertained (Coma, Horologium–Reticulum, Hercules, etc.). It should be clear that any parametric model with a moderate number of parameters will only crudely approximate the peculiar velocity field. Also, for a model to be useful to the community, it should be relatively painless and efficient for a user to acquire the desired information for a random target. The facility to be described is based on a velocity field responding to the full complexity of structure on scales of 1–200 Mpc. Two models are offered. One restricted to 38 Mpc is based on a fully nonlinear analysis. The other extending to 200 Mpc is derived from an analysis in the linear dynamical regime. Both are publicly accessible at the interactive platform to be described.

Details of the two underlying models will be discussed in the next section, but the user interface functions are the same for both. The facility can be accessed at the Extragalactic Distance Database (EDD).⁶

A user can enter the celestial coordinates of a target with a choice of coordinate systems. Examples are shown in Figures 1 and 2. Observational data from the Cosmicflows-3 compendium of distances (Tully et al. 2016) can be displayed in a cone chosen by the user centered on the target. A blue locus plots the averaged expectation velocity along the line of sight as a function of distance.⁷ Cursor control can access specific distance and velocity values along the locus. Hovering over a datum gives name, velocity, and distance specifics for that item. Zoom and translation functions are activated by side-panel toggles.

The red dashed, straight line in every plot shows the relationship between velocity and distance with uniform expansion if the Hubble Constant is 75 km s⁻¹ Mpc⁻¹. This line is for illustrative purposes only! Velocities and distances are determined completely independently of each other in the Cosmicflows-3 compilation. The models make no assumption about the value of H₀.

The distance−velocity tool does not directly give peculiar velocities, V_pec. The tool gives expectation distances, d, at observed velocities, V_obs (or expectation observed velocities at specified distances). To a reasonable approximation, .⁸ It has been demonstrated (Tully et al. 2016) that Cosmicflows-3 distances and velocities are compatible with H₀=75 km s⁻¹ Mpc⁻¹, with zero-point uncertainty at the level of 3%. Users interested in peculiar velocities can contemplate applying alternative values of H₀ at their risk. Note that altering the zero-point associated with Cosmicflows distances alters the H₀ value that would be most consistent, but the products H₀d would be unchanged. Hence, the relationship between V_obs and V_pec given in the formula above is independent of the zero-point calibration.

The reference velocities are different for the two models. In the case of the local nonlinear model, velocities are with respect to the Galactic center. With the large-scale linear model, velocities are with respect to the Local Group. Justifications for these choices will be given in the section discussing the models. In any event, it must be noted that there are variants of both these reference frames in the literature. The definition of the Galactic Standard of Rest (gsr) depends on the distance of the Galactic center and the amplitude of Galactic rotation at the Sun, as well as a small solar deviation. There are alternative choices (de Vaucouleurs et al. 1991; Eisenhauer et al. 2005; Reid et al. 2009). Our model is based on the solution by van der Marel et al. (2012). As a measure of the uncertainties inherent in the translation to the Galactic rest frame, differences between the four cited alternatives are 12±5 km s⁻¹.

Similarly, there are alternative versions of the Local Group rest frame (Yahil et al. 1977; Karachentsev & Makarov 1996; Courteau & van den Bergh 1999). We prefer a variant we call the Local Sheet (ls) reference frame (Tully et al. 2008). The three former (Local Group) solutions are derived from the properties of galaxies within 1 Mpc. The ls solution is derived from the properties of galaxies outside 1 Mpc yet within 5 Mpc. See Tully et al. (2008) for the argument that this solution is the most stable. Uncertainties between the alternative Local Group frames are at the level of 19±10 km s⁻¹.

The linear model extends to velocities of 15,000km s⁻¹ and cosmological corrections reach ∼4%. The corrected velocity V_ls^c is related to the observed velocity V_ls by

where

when Ω_m=0.27 and Ω_Λ=0.73 and (Wright 2006).

In the top panel of Figure 2 velocities are observed values (averaged over group members) but in this representation there is a slight curvature of the Hubble relation manifested in the departure of the red dashed curve from the faint gray straight line. Velocities in the bottom panel are increased by the cosmological correction so the red dashed Hubble line is straightened. In detail the correction depends on the choices of the cosmological matter and energy density parameters Ω_m and Ω_Λ, but differences in the correction between reasonable values of these parameters are negligible within the velocity range being considered. f(z=0.05) decreases by 0.1% if Ω_m increases and Ω_Λ decreases by 0.03.

Hover with the cursor over a datum element of the linear model to obtain input distance and velocity information. The element may be an individual galaxy or a group and is identified by the parameter PGC1, the Principal Galaxies Catalog identification (de Vaucouleurs et al. 1991) of the brightest member. The Nest parameter identifies the membership of elements in the Two Micron All Sky Survey (2MASS) group catalog of Tully (2015a).

For convenience, formulae are given here for conversions between heliocentric velocities, V_h, and the reference frames used in the distance−velocity tools where the angles are Galactic longitude and latitude (l, b).

gsr:

ls:

Between gsr and ls:

Two calculators are offered: one limited to distances less than 38 Mpc (V_obs∼2850 km s⁻¹) based on a fully nonlinear dynamical model and the other extending to 200 Mpc (15,000 km s⁻¹) at lower resolution and based on a linear model.

3.1.Nonlinear Model Limited to 38 Mpc

3.2.Linear Model Extending to 200 Mpc

As an example of the service that the distance−velocity calculator provides, consider an effort to determine the Hubble Constant from a measurement of the distance to the gravitational wave event GW170817 that occurred in the galaxy NGC4993 (Abbott et al. 2017). By happenstance, the distance, d∼40 Mpc, is at the extremity of coverage provided by the nonlinear model (although that model is embedded within the 100 Mpc scale tidal field deduced from a linear analysis of Cosmicflows-2). It comfortably lies within the domain of coverage of the new linear model.

What is the appropriate velocity to accompany the distance measurement for an estimate of the Hubble Constant? It is important to understand the environment of the target on a range of scales. Most immediately, does the target lie in a group? In the case of NGC4993, yes, this galaxy lies in a group with the dominant member NGC4970. The group is identified as HDC751 (Crook et al. 2007), 2M++1294 (Lavaux & Hudson 2011), Nest100214 (Tully 2015a), and PGC145466 (Kourkchi & Tully 2017). In the latter catalog, there are 22 galaxies linked with the group, with km s⁻¹. In alternate reference frames of interest, km s⁻¹, km s⁻¹, and km s⁻¹.

On a larger scale, this PGC145466=NGC4970 group lies roughly along the line of sight toward the Great Attractor (Dressler et al. 1987), 18° (∼13 Mpc) removed from the dominant Centaurus Cluster (d=40.5±1.6 Mpc, V_ls=3285 km s⁻¹). There is a clear infall pattern in the line of sight toward the Centaurus Cluster, with objects to the immediate foreground falling away from us toward the cluster and objects behind manifesting backside infall toward us. This effect extends in a weakened fashion to the NGC4993 line of sight. At a distance of around 40 Mpc, there is ambiguity whether the NGC4970 group with NGC4993 is frontside falling away or backside falling forward with respect to the overdensity around the Centaurus Cluster. Figure 3 is extracted from the distance–velocity calculator in the NGC4993 direction, with the nonlinear solution superimposed on the linear solution. There is close agreement between the two at distances less than 30 Mpc. At greater distances the nonlinear model runs about 100km s⁻¹ below the linear model but the nonlinear model is poorly constrained at its edge of application. Considering the linear model, within 10 Mpc foreground of ∼40 Mpc observed velocities are running about 100km s⁻¹ below the H₀=75 fiducial line while by 50 Mpc the observed velocities drop to about 300km s⁻¹ below the fiducial line. The consequence is an ambiguity due to this Centaurus Cluster overdenity infall pattern. The amplitude of the wave is 200km s⁻¹ in the linear regime (and greater if nonlinear effects would be taken into account).

It is most common to derive estimates of the Hubble Constant in the reference frame of the CMB. However nearby galaxies are participating in a coherent flow, a coherence that extends to include the NGC4970 group with NGC4993 as a member. A correction for the flow is required if working in the CMB frame that is closely equivalent to working without a correction in the ls (Local Group) frame. This comment is a cautionary reminder of the jeopardy of evaluating the Hubble Constant locally. Should we live in a large scale under- or over density, it would be necessary to make measurements beyond this feature to be comfortable in the CMB frame.

Finally, it is to be appreciated that the distances in this distance−velocity calculator are based on a specific zero-point calibration that may or may not pass the test of time. The H₀=75 km s⁻¹ Mpc⁻¹ fiducial line is consistent with the current Cosmicflows-3 data compilation. A user of the distance−velocity calculator may have a distance that is implicitly based on a different zero-point scale. However, as discussed in Section 2, peculiar velocities are decoupled from the Hubble Constant. A user can consider the distance−velocity calculator distance scale to be elastic, with the fiducial Hubble line flexing accordingly, but the peculiar velocity amplitudes with respect to the fiducial line will be unchanged at a given observed velocity.

In review of the case for NGC4993, as a best effort at accounting for deviations from cosmic expansion, an estimate can be made of the value of the Hubble Constant, taking V_obs=2783 km s⁻¹, the value for the NGC4970 group, and V_pec somewhere between −100 and −300 depending on the user's preferred distance and whether that places the target foreground or background to the Centaurus Cluster overdensity.

Cosmicflows is a continuously evolving program. It is anticipated that the distance−velocity calculators will be updated at intervals. The resolution can be improved with greater computational effort. In combination, the quasi-linear methodology of Hoffman et al. (2018) can be exploited. There is the intention of extending the numerical action orbit reconstruction model of Shaya et al. (2017) to 100 Mpc. Cosmicflows-4 is on the horizon, with constraints to be provided by ∼30,000 distances.

The latest models will be made available at the EDD.¹¹