2MTF - VII. 2MASS Tully-Fisher survey final data release: distances for 2,062 nearby spiral galaxies

TL;DR

This paper presents the final data release of the 2MASS Tully-Fisher survey, providing distance and velocity measurements for over 2,000 nearby spiral galaxies, and confirms consistency with cosmological models.

Contribution

The paper delivers the complete 2MTF dataset with updated HI data, improved distance estimates, and bulk flow measurements consistent with the Lambda-CDM model.

Findings

Distances agree with Cosmicflows-3 data

Bulk flow amplitudes are consistent with Lambda-CDM

Mean distance uncertainties are around 22%

Abstract

We present the final distance measurements for the 2MASS Tully-Fisher (2MTF) survey. The final 2MTF catalogue contains 2,062 nearby spiral galaxies in the CMB frame velocity range of 600 km s$^{-1}$ $< cz < 10,000$ km s$^{-1}$ with a mean velocity of 4,805 km s$^{-1}$. The main update in this release is the replacement of some archival HI data with newer ALFALFA data. Using the 2MTF template relation, we calculate the distances and peculiar velocities of all 2MTF galaxies. The mean uncertainties of the linear distance measurements are around 22\% in all three infrared bands. 2MTF measurements agree well with the distances from the Cosmicflows-3 compilation, which contains 1,117 common galaxies, including 28 with SNIa distance measurements. Using distances estimated from the `3-bands combined' 2MTF sample and a $\chi^2$ minimization method, we find best-fit bulk flow amplitudes of $308 \pm 26$ km s$^{-1}$, $318 \pm 29$ km s$^{-1}$, and $286 \pm 25$ km s$^{-1}$ at depths of $R_I = $ 20, 30 and 40 $h^{-1}{\rm Mpc}$, respectively, which is consistent with the $\Lambda$CDM model and with previous 2MTF results with different estimation techniques and a preliminary catalogue.

Tables

Table 1. Table 1: Photometric and corrected H i width data for 2MTF galaxies.

2MASX-ID	RA	DEC	$c{z}_{2MRS}$	$m_K$	$m_H$	$m_J$	${ϵ}_{m_K}$	${ϵ}_{m_H}$	${ϵ}_{m_J}$	$W_c$	${ϵ}_{W_c}$
	[deg] (J2000)	[deg] (J2000)	[km s-1]	[mag]	[mag]	[mag]	[mag]	[mag]	[mag]	[km s-1]	[km s-1]
00005604+2020165	$0.23345$	$20.33799$	$6804$	$11.124$	$11.616$	$12.339$	$0.061$	$0.062$	$0.046$	$406$	$5.1$
00005891+2854421	$0.24550$	$28.91172$	$6899$	$10.818$	$11.085$	$11.515$	$0.059$	$0.048$	$0.029$	$440$	$11.8$
00010478+0432261	$0.26987$	$4.54060$	$9151$	$11.029$	$11.274$	$11.919$	$0.047$	$0.036$	$0.026$	$476$	$23.0$
00011976+3431326	$0.33238$	$34.52571$	$5032$	$10.405$	$10.704$	$11.384$	$0.037$	$0.028$	$0.023$	$439$	$5.9$
00013830+2329011	$0.40968$	$23.48363$	$4371$	$9.330$	$9.591$	$10.327$	$0.024$	$0.021$	$0.019$	$544$	$8.0$
00014193+2329452	$0.42471$	$23.49588$	$4336$	$9.930$	$10.154$	$11.056$	$0.025$	$0.021$	$0.019$	$635$	$10.6$
00024636+1853106	$0.69321$	$18.88622$	$7882$	$10.776$	$10.935$	$11.652$	$0.042$	$0.032$	$0.027$	$518$	$11.2$
00035889+2045084	$0.99545$	$20.75235$	$2309$	$8.400$	$8.700$	$9.438$	$0.008$	$0.007$	$0.006$	$384$	$6.0$
00041299+1047258	$1.05410$	$10.79052$	$7887$	$10.678$	$10.943$	$11.652$	$0.045$	$0.036$	$0.029$	$412$	$12.2$
00051672-1628368	$1.31967$	$-16.47691$	$7412$	$10.135$	$10.448$	$11.174$	$0.028$	$0.026$	$0.020$	$528$	$12.1$
00055236+2232083	$1.46812$	$22.53567$	$6644$	$11.221$	$11.520$	$12.320$	$0.045$	$0.039$	$0.037$	$273$	$6.5$
00064016+2609164	$1.66731$	$26.15452$	$7556$	$10.965$	$11.338$	$11.938$	$0.045$	$0.044$	$0.034$	$393$	$14.7$
00071951+3236334	$1.83139$	$32.60925$	$5076$	$9.865$	$10.136$	$10.914$	$0.026$	$0.022$	$0.019$	$461$	$4.8$
00080679+0943037	$2.02831$	$9.71773$	$6423$	$10.523$	$10.826$	$11.450$	$0.049$	$0.041$	$0.033$	$408$	$9.2$
00084772+3326000	$2.19883$	$33.43332$	$4808$	$9.731$	$9.974$	$10.639$	$0.027$	$0.024$	$0.020$	$457$	$5.5$
00090421+1055081	$2.26760$	$10.91890$	$6674$	$10.605$	$10.974$	$11.870$	$0.043$	$0.035$	$0.033$	$464$	$4.6$
00092866+4721208	$2.36937$	$47.35583$	$5153$	$11.218$	$11.562$	$12.181$	$0.066$	$0.062$	$0.045$	$308$	$11.8$
00093281+4808068	$2.38672$	$48.13519$	$5388$	$11.018$	$11.229$	$11.965$	$0.046$	$0.039$	$0.032$	$384$	$11.2$
00102637+2859164	$2.60990$	$28.98794$	$7850$	$11.171$	$11.552$	$12.460$	$0.046$	$0.041$	$0.039$	$432$	$8.2$
00103277+2859464	$2.63654$	$28.99624$	$7033$	$10.409$	$10.648$	$11.435$	$0.033$	$0.024$	$0.024$	$428$	$24.3$
00111259-3334428	$2.80248$	$-33.57855$	$7853$	$10.295$	$10.601$	$11.187$	$0.044$	$0.034$	$0.021$	$503$	$41.9$
00121573+2219187	$3.06553$	$22.32180$	$7629$	$10.584$	$10.896$	$11.571$	$0.034$	$0.024$	$0.023$	$514$	$9.3$
00143187-0044156	$3.63279$	$-0.73760$	$3946$	$11.028$	$11.312$	$11.984$	$0.069$	$0.056$	$0.046$	$310$	$7.1$
00144010+1834551	$3.66711$	$18.58203$	$5392$	$9.479$	$9.843$	$10.654$	$0.024$	$0.016$	$0.015$	$554$	$5.5$
00155127+1605232	$3.96365$	$16.08977$	$4213$	$10.509$	$10.813$	$11.550$	$0.040$	$0.028$	$0.022$	$298$	$6.6$
00164417+0704337	$4.18407$	$7.07609$	$3966$	$9.750$	$10.099$	$10.873$	$0.022$	$0.016$	$0.016$	$387$	$4.8$
00165087-0516060	$4.21202$	$-5.26830$	$3968$	$10.510$	$10.800$	$11.449$	$0.055$	$0.044$	$0.033$	$268$	$21.0$
00180131-5905008	$4.50560$	$-59.08359$	$8924$	$11.072$	$11.464$	$12.346$	$0.053$	$0.041$	$0.039$	$443$	$22.5$
00181053+1817323	$4.54393$	$18.29227$	$5521$	$11.219$	$11.439$	$12.253$	$0.058$	$0.031$	$0.034$	$349$	$5.1$
00183335-0616195	$4.63899$	$-6.27206$	$6520$	$11.116$	$11.436$	$12.205$	$0.044$	$0.037$	$0.033$	$277$	$12.0$
Table 1 is available in its entirety online. A portion is shown here for guidance regarding its form and content.

Table 2. Table 2:  Distances and peculiar velocities for 2,062 2MTF galaxies.

2MASX ID	$c{z}_{CMB}$	$\log \frac{d_z}{d_{\mathrm{TF},K}}$	$\log \frac{d_z}{d_{\mathrm{TF},H}}$	$\log \frac{d_z}{d_{\mathrm{TF},J}}$	$V_{pec,K}$	$V_{pec,H}$	$V_{pec,J}$	$V_{WF15,K}$	$V_{WF15,H}$	$V_{WF15,J}$	Flag
- -	[km s-1]	[- -]	[- -]	[- -]	[km s-1]						[- -]
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
00005604+2020165	$6439$	$-0.127\pm 0.078$	$-0.156\pm 0.075$	$-0.160\pm 0.080$	$-2165\pm 389$	$-2756\pm 476$	$-2843\pm 524$	$-1889\pm 1152$	$-2316\pm 1110$	$-2377\pm 1185$	–
00005891+2854421	$6546$	$-0.071\pm 0.092$	$-0.057\pm 0.088$	$-0.023\pm 0.093$	$-1145\pm 243$	$-907\pm 184$	$-340\pm 73$	$-1066\pm 1388$	$-859\pm 1334$	$-342\pm 1406$	–
00010478+0432261	$8717$	$-0.061\pm 0.091$	$-0.042\pm 0.087$	$-0.041\pm 0.092$	$-1265\pm 265$	$-838\pm 170$	$-823\pm 174$	$-1226\pm 1827$	$-845\pm 1756$	$-831\pm 1851$	–
00011976+3431326	$4694$	$-0.092\pm 0.083$	$-0.081\pm 0.079$	$-0.081\pm 0.085$	$-1106\pm 211$	$-964\pm 175$	$-956\pm 187$	$-995\pm 896$	$-879\pm 857$	$-873\pm 922$	–
00013830+2329011	$3982$	$-0.218\pm 0.075$	$-0.200\pm 0.070$	$-0.212\pm 0.077$	$-2582\pm 452$	$-2318\pm 374$	$-2491\pm 442$	$-1996\pm 692$	$-1833\pm 641$	$-1941\pm 705$	–
00014193+2329452	$4018$	$-0.385\pm 0.069$	$-0.352\pm 0.062$	$-0.382\pm 0.069$	$-5768\pm 916$	$-5053\pm 721$	$-5717\pm 908$	$-3559\pm 636$	$-3254\pm 575$	$-3538\pm 638$	–
00024636+1853106	$7516$	$-0.069\pm 0.084$	$-0.027\pm 0.078$	$-0.035\pm 0.084$	$-1252\pm 242$	$-451\pm 81$	$-605\pm 117$	$-1187\pm 1449$	$-467\pm 1352$	$-611\pm 1454$	–
00035889+2045084	$1946$	$0.027\pm 0.087$	$0.038\pm 0.085$	$0.035\pm 0.091$	$120\pm 24$	$164\pm 32$	$152\pm 32$	$123\pm 391$	$170\pm 380$	$158\pm 407$	–
00041299+1047258	$7601$	$0.073\pm 0.097$	$0.083\pm 0.093$	$0.078\pm 0.098$	$1192\pm 266$	$1341\pm 287$	$1271\pm 287$	$1271\pm 1696$	$1449\pm 1633$	$1365\pm 1720$	–
00051672-1628368	$7086$	$-0.111\pm 0.076$	$-0.102\pm 0.070$	$-0.116\pm 0.077$	$-2037\pm 357$	$-1864\pm 305$	$-2149\pm 381$	$-1806\pm 1243$	$-1671\pm 1150$	$-1893\pm 1263$	–
00055236+2232083	$6237$	$0.208\pm 0.117$	$0.203\pm 0.118$	$0.181\pm 0.120$	$2369\pm 638$	$2330\pm 633$	$2128\pm 588$	$2983\pm 1675$	$2920\pm 1696$	$2605\pm 1728$	–
00064016+2609164	$7203$	$0.023\pm 0.092$	$0.016\pm 0.090$	$0.030\pm 0.095$	$389\pm 83$	$274\pm 57$	$488\pm 107$	$386\pm 1534$	$265\pm 1489$	$491\pm 1571$	–
00071951+3236334	$4608$	$-0.083\pm 0.076$	$-0.064\pm 0.072$	$-0.076\pm 0.079$	$-1041\pm 182$	$-792\pm 131$	$-942\pm 171$	$-885\pm 810$	$-677\pm 760$	$-804\pm 835$	–
00080679+0943037	$6043$	$0.057\pm 0.100$	$0.057\pm 0.098$	$0.063\pm 0.102$	$749\pm 172$	$749\pm 169$	$824\pm 193$	$786\pm 1384$	$788\pm 1362$	$872\pm 1418$	–
00084772+3326000	$4608$	$-0.052\pm 0.077$	$-0.029\pm 0.074$	$-0.026\pm 0.080$	$-648\pm 115$	$-369\pm 63$	$-340\pm 63$	$-554\pm 821$	$-302\pm 782$	$-275\pm 847$	–
00090421+1055081	$6310$	$-0.057\pm 0.077$	$-0.058\pm 0.072$	$-0.082\pm 0.079$	$-871\pm 154$	$-891\pm 148$	$-1297\pm 236$	$-828\pm 1122$	$-846\pm 1053$	$-1191\pm 1142$	–
00092866+4721208	$4884$	$0.003\pm 0.107$	$-0.004\pm 0.108$	$0.002\pm 0.111$	$50\pm 12$	$-35\pm 9$	$40\pm 10$	$36\pm 1206$	$-48\pm 1211$	$27\pm 1245$	–
00093281+4808068	$4976$	$-0.163\pm 0.103$	$-0.137\pm 0.100$	$-0.155\pm 0.105$	$-2241\pm 532$	$-1828\pm 421$	$-2111\pm 510$	$-1866\pm 1179$	$-1573\pm 1149$	$-1776\pm 1205$	–
00102637+2859164	$7507$	$-0.097\pm 0.076$	$-0.099\pm 0.073$	$-0.133\pm 0.079$	$-1843\pm 322$	$-1893\pm 318$	$-2662\pm 484$	$-1668\pm 1322$	$-1710\pm 1257$	$-2299\pm 1362$	–
00103277+2859464	$6677$	$-0.014\pm 0.103$	$0.003\pm 0.100$	$-0.018\pm 0.104$	$-199\pm 47$	$63\pm 14$	$-267\pm 64$	$-218\pm 1579$	$42\pm 1539$	$-284\pm 1600$	–
00111259-3334428	$7586$	$-0.042\pm 0.107$	$-0.038\pm 0.104$	$-0.019\pm 0.107$	$-763\pm 188$	$-683\pm 164$	$-329\pm 81$	$-737\pm 1873$	$-666\pm 1811$	$-334\pm 1876$	–
00121573+2219187	$7258$	$-0.063\pm 0.078$	$-0.055\pm 0.072$	$-0.056\pm 0.079$	$-1121\pm 201$	$-962\pm 159$	$-993\pm 181$	$-1051\pm 1302$	$-912\pm 1207$	$-939\pm 1322$	–
00143187-0044156	$3589$	$-0.097\pm 0.109$	$-0.101\pm 0.109$	$-0.106\pm 0.112$	$-893\pm 224$	$-935\pm 235$	$-987\pm 254$	$-798\pm 897$	$-832\pm 902$	$-873\pm 926$	–
00144010+1834551	$5037$	$-0.056\pm 0.065$	$-0.051\pm 0.057$	$-0.058\pm 0.066$	$-703\pm 105$	$-638\pm 84$	$-726\pm 110$	$-646\pm 753$	$-589\pm 662$	$-667\pm 768$	–
00155127+1605232	$3838$	$0.108\pm 0.101$	$0.112\pm 0.102$	$0.106\pm 0.105$	$830\pm 193$	$857\pm 201$	$816\pm 197$	$954\pm 895$	$989\pm 901$	$936\pm 927$	–
00164417+0704337	$3598$	$0.019\pm 0.084$	$0.021\pm 0.082$	$0.016\pm 0.087$	$133\pm 26$	$154\pm 29$	$108\pm 22$	$155\pm 698$	$177\pm 678$	$130\pm 719$	–
00165087-0516060	$3597$	$0.159\pm 0.132$	$0.159\pm 0.134$	$0.161\pm 0.135$	$1088\pm 328$	$1088\pm 336$	$1099\pm 342$	$1316\pm 1089$	$1315\pm 1112$	$1332\pm 1120$	–
00180131-5905008	$8707$	$-0.011\pm 0.090$	$-0.021\pm 0.086$	$-0.050\pm 0.091$	$-185\pm 38$	$-401\pm 79$	$-1022\pm 214$	$-219\pm 1804$	$-427\pm 1730$	$-1002\pm 1828$	–
00181053+1817323	$5150$	$-0.094\pm 0.089$	$-0.063\pm 0.088$	$-0.080\pm 0.092$	$-1224\pm 251$	$-790\pm 160$	$-1020\pm 218$	$-1110\pm 1057$	$-747\pm 1049$	$-943\pm 1097$	–
00183335-0616195	$6064$	$0.119\pm 0.121$	$0.116\pm 0.122$	$0.099\pm 0.124$	$1457\pm 406$	$1427\pm 401$	$1235\pm 353$	$1663\pm 1684$	$1624\pm 1705$	$1378\pm 1736$	–
Table 2 is available in its entirety online. A portion is shown here for guidance regarding form and content.

Table 3. Table 3: Bulk flow amplitudes measured in the 2MTF sample.

	Hong et al. (2014)	this work
	[km s-1]	[km s-1]
$R_I=20h^{-1}\mathrm{Mpc}$	$310.9\pm 33.9$	$307.8\pm 25.9$
$R_I=30h^{-1}\mathrm{Mpc}$	$280.8\pm 25.0$	$317.6\pm 29.4$
$R_I=40h^{-1}\mathrm{Mpc}$	$292.3\pm 27.8$	$286.1\pm 25.5$

Equations

$$v_{pec}=cz-H_{0}r,$$

$$M_K-5\log h=-22.188-10.74(\log W-2.5),$$

$$M_H-5\log h=-21.951-10.65(\log W-2.5),$$

$$M_J-5\log h=-21.370-10.61(\log W-2.5),$$

$$\log \left(\frac{d_z}{d_{\mathrm{TF}}^{\ast }}\right)=\frac{-\Delta M}{5},$$

$$M_{obs}-5\log h=m_{obs}+k_X-A_X-I_X-T_X-5\log v_{CMB}-15,$$

$$V_{WF15}=cz\ln \left(cz/H_{0}r\right)=cz\ln (d_z/d_{\mathrm{TF}}),$$

$${\chi }^2=\sum _{i=1}^N\frac{{\left[\log (d_{z,i}/d_{\mathrm{model},i})-\log (d_{z,i}/d_{\mathrm{TF},i})\right]}^2\cdot w_i^r{w}_i^d}{{\sigma }_i^2\cdot {\sum }_{i=1}^N(w_i^r{w}_i^d)},$$

$$v_{\mathrm{rms}}^2=\frac{H_0^2{f}^2}{2{\pi }^2}\int W^2(kR)P(k)\text{d}k,$$

Full text

††pagerange: 2MTF - VII. 2MASS Tully-Fisher survey final data release: distances for 2,062 nearby spiral galaxies–2MTF - VII. 2MASS Tully-Fisher survey final data release: distances for 2,062 nearby spiral galaxies

1 Introduction

The matter distribution in the Universe appears to be homogeneous and isotropic on large scales (a.k.a. the cosmological principle). However, on relatively small scales, structures such as clusters, filaments, walls and voids dominate the matter distribution (Geller & Huchra, 1989; Gott et al., 2005). Studies of cosmological structures or lack thereof provide tight constraints on the cosmological model (Bernardeau et al., 2002; Jones et al., 2009; Scrimgeour et al., 2012; Lombriser et al., 2012; Alpaslan et al., 2014). Useful information on the matter distribution field can be obtained from galaxy redshift surveys, gravitational lensing studies and X-ray and Sunyaev-Zel’dovich cluster searches (e.g. Eisenstein et al., 2005; Hong et al., 2016; Bautista et al., 2017; Van Waerbeke et al., 2013; Planck Collaboration et al., 2014a; Salvati et al., 2018, and references therein). The peculiar motions of galaxies induced by inhomogeneous matter distribution are also useful probes for tracing structures. These are typically measured using redshift-independent distances (Springob et al., 2007; Masters et al., 2008; Campbell et al., 2014; Tully et al., 2016), proper motions (Brunthaler et al., 2005) or the kinetic Sunyaez-Zel’dovich effect (Kashlinsky et al., 2011). Moreover, such measurements trace both the visible and the dark matter distributions (Hong et al., 2014; Scrimgeour et al., 2016; Springob et al., 2016; Qin et al., 2018).

The line-of-sight peculiar velocity is the non-Hubble component of a galaxy’s motion, which can be estimated in the nearby Universe by

[TABLE]

where $H_{0}$ is the Hubble constant, $z$ is the redshift of the galaxy and $r$ is the redshift independent distance. In the context of this paper the Tully-Fisher (TF) relation (Tully & Fisher, 1977), which combines measurements of galaxy luminosity and rotational velocity, provides a good tool to accurately measure redshift independent distances for large numbers of spiral galaxies. However, many other distance-determination techniques exist, including supernova type Ia (Phillips, 1993), Fundamental Plane (Dressler et al., 1987) and surface brightness fluctuations (Tonry & Schneider, 1988).

The SFI++ catalog (Springob et al., 2007) is the largest TF sample to date, and includes peculiar velocity information for 4,861 spirals. Because of the effect of extinction in its input catalogues, SFI++ contains a large gap close to the Galactic plane ($|b|<15^{\circ}$). It therefore misses significant parts of massive nearby structures such as the Hydra-Centaurus, Norma and Vela superclusters and the Great Attractor (Kraan-Korteweg & Lahav, 2000; Kraan-Korteweg et al., 2017), whilst introducing possible biases in cosmological parameters derived from peculiar velocity fields measured in a non-spherical region (Andersen et al., 2016).

The 2MASS Tully-Fisher Survey (2MTF, Masters et al., 2008; Hong et al., 2013; Masters et al., 2014) uses the infrared magnitudes in the $J$, $H$ and $K$ bands from the 2MASS Redshift survey (2MRS, Huchra et al., 2012) in order to reduce the extinction effect due to the Galactic plane, leaving only a small Zone of Avoidance at Galactic latitudes of $|b|\leq 5^{\circ}$. Combined with high-quality 21-cm Hi spectral data, the final 2MTF sample provides 2,062 peculiar velocity measurements for nearby spirals. In this paper, we present the final 2MTF sample and describe the 2MTF data collection and reduction process in Section 2. The final catalog is presented in Section 3. Comparisons between 2MTF distances and Cosmicflows-3 measurements are made in Section 4. Finally, we update our previous calculations of the bulk flow amplitude for the 2MTF sample in Section 5.

2 Observational data and methodology

The 2MTF survey is a Tully-Fisher survey of nearby spiral galaxies, producing high-quality redshift independent distance and peculiar velocity measurements. The observational methods and data reduction are described in detail by Hong et al. (2014), which we briefly summarise below.

2.1 Photometric data

All target galaxies in 2MTF are selected from the 2MRS catalog with the following criteria: total $K$-band magnitude $K<11.25$ mag, velocity $cz<10,000$ km s*-1*, and 2MASS co-added axis ratio $b/a<0.5$. About 6,600 2MRS galaxies meet the selection criteria and became our 2MTF target galaxies. Because the TF template relations vary with the type of spiral galaxy (Masters et al., 2008), we also adopt the morphological type code $T$ to calibrate the galaxies to the correct template relations. The co-added axis ratio used above formally differs from the $I$-band axis ratio used by Masters et al. (2008) when building the TF template relation. This may introduce small differences in the final measurements, but with no significant bias (Hong et al., 2014). We follow Masters et al. (2008) in making galaxy internal dust extinction and $k$-corrections.

2.2 H i spectra widths

High-quality galaxy rotation widths as measured from Hi spectra are a key part of accurate TF measurements. The 2MTF Hi spectral data derive from our own new observations using the GBT and Parkes telescopes, new observations provided by the ALFALFA survey, and high signal-to-noise ratio archival data.

2.2.1 GBT and Parkes observations

The 2MTF project observed 1,193 target galaxies in the sky area of $\delta>-40^{\circ}$ using the Green Bank Telescope using a position-switching mode (Masters et al., 2014). 727 galaxies were detected in Hi, and 383 of them are of a quality that allows them to be included into the final 2MTF catalogue. All the ‘well-detected’ galaxies have signal-to-noise ratio S/N $\geq 10$, and show normal Hi profiles consistent with non-interacting, non-confused spiral galaxies. In addition, all galaxies meet further data quality selection criteria as described in Section 2.2.4. The smoothed GBT velocity resolution is 5.15 km s*-1*.

For $\delta\leq-40^{\circ}$, the Parkes radio telescope was employed to conduct Hi observations, also in position-switching mode, but one in which the target galaxy was always observed by one of seven central beams of the Parkes multibeam receiver (Hong et al., 2014). From the 305 target galaxies, we obtained 110 high signal-to-noise ratio Hi spectra which were included into the final 2MTF sample. The Parkes Hi spectra provide a velocity resolution of $3.3$ km s*-1* after Hanning smoothing.

All Hi spectra obtained by GBT and Parkes telescope were measured using the IDL routine awv_fit.pro. This routine measures Hi line widths using several methods. The WF50 width is adopted as our preferred width for this study.

2.2.2 ALFALFA data

Duplication of observations in the northern hemisphere was avoided by leaving the 7000 deg2 covered in the ALFALFA survey (Giovanelli et al., 2005). Overall, ALFALFA contains $\sim 31,500$ extragalactic Hi sources with redshift out to $z<0.06$ (Haynes et al., 2018). We extracted 545 high-quality spectra and Hi widths for galaxies which passed the 2MTF selection criteria from the complete ALFALFA catalog. For consistency with the GBT and Parkes analysis, we used the WF50 width measurements.

2.2.3 Archival data

Besides our own observations and the ALFALFA data, we also used Hi widths from archival sources where the data was high quality. The largest archival data source we adopted was the Cornell Hi digital archive (Springob et al., 2005) of Hi observations of 9,000 galaxies ($cz<28,000$ km s*-1*), obtained from single-dish telescopes. According to the Hi line quality, Springob et al. (2005) marked the Hi lines with codes G (Good), F (Fair), S (Single peak) and P (Poor). Only G (Good) and F (Fair) galaxies were accepted into the 2MTF catalog. A total of 711 Hi widths from the Cornell Hi digital archive were included.

Hi width measurements from other sources were also included (Theureau et al., 1998, 2005, 2007; Mathewson et al., 1992; Paturel et al., 2003). We collected raw Hi widths from these catalogs and corrected for observational effects following the same procedure as for our own observations (for more details, see Hong et al., 2013).

2.2.4 Data Selection

To improve the distance measurement accuracy, further data quality limits were adopted. Galaxies with $cz<600$ km s*-1* (CMB frame), Hi spectra with S/N ratio $<5$, or relative Hi error $\epsilon_{\mathrm{w}}/w_{\mathrm{HI}}>10\%$ were omitted. When one galaxy was observed with more than one telescope, we preferred the newer data, i.e., our own observations and ALFALFA data have higher priority than the archival data.

2MASX J00383973+1724113 has a reported 2MASS axis ratio of $b/a$ = 0.36, which doesn’t represent the outer blue disk present in the galaxy. We give this galaxy a flag of ‘W’ in final data table, for optional exclusion.

2.3 Tully-Fisher distances

For calculating the Tully-Fisher distances and peculiar velocities for 2MTF galaxies, we use the TF template relations developed by Masters et al. (2008):

[TABLE]

where $M_{K}$, $M_{H}$, and $M_{J}$ are the absolute magnitudes and $W$ is the corrected Hi linewidth. The TF template relation depends on the galaxy morphology in all bands; the above relations refer to galaxies of type Sc.

As described in Hong et al. (2014), the uncertainties of TF peculiar velocities are log-normal. So the preferred way to quote distances for 2MTF is the logarithmic quantity $\log(d_{z}/d_{\mathrm{TF}})$,

[TABLE]

where $d_{z}$ is the redshift distance of the galaxy in the CMB frame, $d^{*}_{\mathrm{TF}}$ is the galaxy’s redshift-independent distance from the TF relation before Malmquist bias correction (which will be corrected in the final step of the calculation), and $\Delta M=M_{obs}-M(W)$ is the difference between the absolute magnitude calculated using a redshift distance and the absolute magnitude predicted by the TF template relations of Equation 2. The corrected absolute magnitude $M_{obs}$ contains the terms for $K$-correction ($k_{X}$), extinction correction due to the Galaxy ($A_{X}$), internal extinction correction of the galaxy itself ($I_{X}$) and the morphological type correction $T_{X}$ which arises from the different slopes and zero points of the TF relation between different types of galaxies, we adopt the same equation as Masters et al. (2008) of

[TABLE]

where $X$ represents $K,H$ or $J$, $v_{CMB}$ is the recession velocity of the galaxy in the CMB frame. We make all corrections following Masters et al. (2008).

The error in this logarithmic quantity includes four components: intrinsic error, inclination error, Hi width error and NIR magnitude error (see Section 3.2 and Appendix A of Hong et al., 2014, for more details), where we adopt an intrinsic error inversely proportional to the HI width to represent the fact that the scatter of the TF relation decreases with the Hi width (Giovanelli et al., 1997; Masters et al., 2006). The error in redshift is considered negligible because of its much higher accuracy. The final error in the logarithmic quantity is the sum in quadrature of all components in logarithmic units. To improve measurement accuracy, we used the galaxy group information presented by Crook et al. (2007) to assign the same redshift distance $d_{z}$ to all galaxies in the same group, whilst $\log(d_{z}/d_{\mathrm{TF}})$ was calculated separately.

The final step of data reduction is the Malmquist bias correction. There are two types of Malmquist bias. Homogeneous Malmquist bias which arises from distance-dependent selection effects. This bias affects all galaxies regardless of their position. Inhomogeneous Malmquist bias is caused by the variation of density along the line of sight. As described by Strauss & Willick (1995), this bias is smaller in redshift space than distance space because of much smaller measurement errors. Thus we corrected for homogeneous Malmquist bias only, and considered the inhomogeneous bias to be negligible. We divided the sample into two parts north and south of declination $\delta=-40^{\circ}$, which reflects the fact that the completeness is different in these two sky regions. Corrections were made using the procedure of Hong et al. (2014), which in turn follows the procedure of Springob et al. (2014).

3 Catalog presentation

We present the photometric data from 2MRS catalog and corrected Hi widths for the 2,062 2MTF galaxies in Table 1. The definition of the columns of the table is as follows:

Column (1). — The 2MASS XSC ID name.

Column (2) and (3). — Right ascension (RA) and declination (DEC) in the J2000.0 epoch from the 2MASS XSC.

Column (4). — The barycentric redshift $cz_{\rm 2MRS}$ from the 2MRS (km s*-1*).

Column (5 - 7). — The NIR magnitudes in the $K$, $H$ and $J$ bands from the 2MASS XSC, respectively.

Column (8 - 10). — The errors of the NIR magnitudes in $K$, $H$ and $J$ bands from the 2MASS XSC.

Column (11). — The corrected Hi width (km s*-1*).

Column (12). — The error of corrected Hi width (km s*-1*).

Table 2 contains the logarithmic distance quantity measured by 2MTF, together with linear peculiar velocities defined by Eq. (1), the latter is provided for convenience. We also include the peculiar velocities generated from the estimator introduced by Watkins & Feldman (2015):

[TABLE]

where $z$ is the redshift of the galaxy and $r$ is the redshift-independent distance (the Tully-Fisher distance in this paper). We adopt a low redshift approximation of the accurate WF15 estimator (Eq. 7 of Watkins & Feldman 2015) here, since the redshift of 2MTF galaxies is much smaller than unity. All measurements are made in the CMB reference frame, so we convert the recession velocities of galaxies to this frame using a solar motion of $v=384$ km s*-1* towards to $(l,b)=(263.99^{\circ},48.26^{\circ})$ (Planck Collaboration et al., 2014b). Table 2 is organized as follows:

Column (1). — The 2MASS XSC ID name.

Column (2). — The CMB frame redshift $cz_{\rm CMB}$ (km s*-1*).

Column (3 - 5). — The logarithmic quantities and errors measured by $K$, $H$ and $J$ band magnitude, respectively.

Column (6 - 8). — The peculiar velocities and errors measured by $K$, $H$ and $J$ band magnitude, respectively (km s*-1*).

Column (9 - 11). — The peculiar velocities and errors calculated by WF15 estimator in $K$, $H$ and $J$ band magnitude, respectively (km s*-1*).

Column (12). — Data quality warning flag, a flag ‘W’ reminds one to use the measurement of the galaxy carefully.

Fig. 1 and Fig. 2 show the sky coverage and redshift distribution, respectively, of the final 2MTF catalogue which contains 2,062 galaxies with good data quality. As shown in Fig. 1, the 2MTF catalog provides a fairly uniform distribution across the sky with a narrow gap near the Galactic plane ($|b|\leq 5^{\circ}$). In the southern sky $\delta<-40^{\circ}$, the target density is lower because we have only Parkes observations in this area. Galaxies in the final 2MTF catalogue cover a CMB velocity range of 600 km s*-1*$<cz<10,000$ km s*-1* with a mean velocity of $cz=4,805$ km s*-1*.

Fig. 3 shows the relative errors of the linear TF distances measured in the three 2MASS bands. The mean relative errors are 22%, 22% and 23% in the $K$, $H$ and $J$ bands respectively.

4 Comparison with Cosmicflows-3

We compare the 2MTF redshift-independent distances with the distances listed in the Cosmicflows-3 catalogue (Tully et al., 2016). The Cosmicflows-3 catalogue includes around 17,700 distances, measured by various authors and various methods, mainly Tully-Fisher and Fundamental Plane.

Cross-matching 2MTF with Cosmicflows-3 by sky position and redshift, we found 1,117 common galaxies within a velocity difference $|cz|\leq 150$ km s*-1*. A comparison of the distance moduli of the 2MTF and Cosmicflows-3 measurements reveals only a few outliers far from the line of distance equality. On the whole, there is excellent agreement as shown in Fig. 4. With a 3$\sigma$ outlier clip, the mean difference between Cosmicflows-3 and 2MTF measurements are $0.03\pm 0.01$ mag, $0.06\pm 0.01$ mag and $0.06\pm 0.01$ mag in the $K$, $H$ and $J$ bands respectively. The corresponding scatter is 0.35, 0.34 and 0.33 mag, respectively. For linear distances, We find the Cosmicflows-3 measurements are 1.4%, 2.8% and 2.8% larger than 2MTF distances in three bands respectively. These results are consistent with those reported by Qin et al. (2019).

Cosmicflows-3 also contains a compilation of 391 supernova type Ia (SNIa) distances for redshifts $z\leq 0.1$, with the distance modulus provided being the average of multiple measurements, where available. Modern SNIa distances can be highly accurate (e.g. Jha et al., 2007; Amanullah et al., 2010), and thus allow a more stringent test of 2MTF data quality. A cross-match between 2MTF and Cosmicflows-3 SNIa distances finds 28 galaxies which have hosted SNIa events. We present the comparison of the distance moduli in Fig. 5. Again, no significant systematic bias in 2MTF distance measurements is found, with the mean difference between 2MTF and Cosmicflows-3 measurements being $0.12\pm 0.08$ mag with a standard deviation of 0.40 mag. However, the outlier in this plot is 2MASS 09220265+5058353 which hosted SN 1999b. According to the NASA/IPAC Extragalactic Database (NED), the distance moduli measured using SN 1999b vary from 30.20 to 31.16 mag, compared with our larger $K$-band 2MTF measurement of $32.22\pm 0.43$ mag. Neglecting this outlier, the mean difference between 2MTF and Cosmicflows-3 SNIa measurements is only $0.08\pm 0.06$ mag with a standard deviation of 0.32 mag. In linear distance space, we find the Cosmicflows-3 SNIa measurements are 3.7% smaller than 2MTF distances in mean, the opposite trend of the whole Cosmicflows-3 sample. However, the difference is not significant.

5 Bulk flow in the full 2MTF sample

Bulk flow is measured from the dipole of the peculiar velocity field, and represents the averaged peculiar motion of the galaxies in the survey volume with respect to the CMB. In standard theory, it is believed to arise from acceleration induced by mass distributions within and beyond the sample volume, and therefore provides a useful probe of the mass distribution in the local Universe. It is also a powerful tool to test different cosmological models (e.g. Hudson et al., 2004; Ma & Scott, 2013; Ma & Pan, 2014; Hong et al., 2014; Scrimgeour et al., 2016; Qin et al., 2018, and references therein). The high-accuracy distance estimates, the well-defined selection function, and the uniform sky coverage of 2MTF makes this survey easier to use for bulk flow measurements.

Using the preliminary 2MTF sample, Hong et al. (2014) measured the bulk flow at the depths of 20$~{}h^{-1}{\rm Mpc}$, 30$~{}h^{-1}{\rm Mpc}$ and 40$~{}h^{-1}{\rm Mpc}$, and found the amplitude to be within the range of the $\Lambda$CDM model. Qin et al. (2018) combined the 2MTF catalog with the 6dFGSv survey, making an accurate bulk flow measurement at the scale of 40$~{}h^{-1}{\rm Mpc}$, and again showed consistency with the $\Lambda$CDM model.

In this paper, we measured the bulk flow of the final 2MTF sample using the $\chi^{2}$ minimization method of Hong et al. (2014):

[TABLE]

where $d_{\mathrm{model},i}$ is the model-predicted distance of the $i$’th galaxy, $\sigma_{i}$ is the error of $i$’th galaxy’s logarithmic distance ratio $\log(d_{z}/d_{TF})$, $w^{r}_{i}$ is the weight to make the sample’s weighted redshift distribution match a Gaussian function at a number of depths (here we choose $R_{I}=$ 20, 30 and 40$~{}h^{-1}{\rm Mpc}$), $w^{d}_{i}$ is the weight to correct for the effect of the slightly different number density in the northern and southern sky areas (see Section 4.1 of Hong et al., 2014, for more details). Instead of using the peculiar velocity data from individual bands, we combine the data from all $K$, $H$ and $J$ bands into a ‘3-bands combined sample’ for greatest accuracy. In the combined sample, every galaxy is used three times with different peculiar velocities measured from three different bands, with each peculiar velocity counted separately during the minimization procedure. As the errors in our TF distances are log-normal, this fit process works in log space instead of linear space. The fitting method is less sophisticated than the $\eta$MLE technique of Qin et al. (2018) which can, in principle, model generic non-normal error distributions. But, since the major errors in 2MTF are the multiplicative distance errors, the current technique is more than adequate. Moreover, it allows a more straightforward comparison with our previous results. The errors of the bulk flow velocities were estimated using the jackknife method with 50 sub-samples, randomly selected by removing 2% of the 2MTF sample each time.

The theoretical prediction of the bulk flow amplitude varies with the depth of the galaxy sample (Ma & Pan, 2014), so our theoretical curve was calculated using a Gaussian window function $W(kR)=\exp(-k^{2}R^{2})/2$ and a matter power spectrum $P(k)$ generated by the CAMB package (Lewis et al., 2000):

[TABLE]

where $k$ is the wavenumber, $H_{0}$ is the Hubble constant and $f=\Omega_{\mathrm{m}}^{0.55}$ is the linear growth rate (Li et al., 2012; Hong et al., 2014). For the calculation of the theoretical curves, we adopt the cosmological parameters reported by Planck Collaboration et al. (2016) with $\Omega_{m}=0.308$, $\Omega_{b}=0.0484$, $n_{s}=0.9677$ and $\rm{H}_{0}=67.81~{}\rm{km}~{}\rm{s}^{-1}~{}\rm{Mpc}^{-1}$.

The best-fit bulk flow velocities for the three different depths are presented in the Table 3 together with the results measured by Hong et al. (2014) using the preliminary 2MTF sample. We also plot the bulk flow velocity amplitudes in Fig. 6, where the solid line is the $\Lambda$CDM prediction and the dashed lines indicate the $\pm 1\sigma$ points of the theoretical line (i.e. $\pm 34$ per cent). The best-fit bulk flows agree with our previous measurements but have smaller uncertainties, mainly because the new sample has a larger size and the updated ALFALFA data has higher accuracy than the previous archival data. Again, our results are consistent with the $\Lambda$CDM model prediction at 68% confidence level, which supports the correctness of the $\Lambda$CDM model in the local Universe.

6 Summary

2MTF is an all-sky survey which provides accurate Tully-Fisher distances for galaxies in the local Universe with a well-defined selection function. Due to the use of near-infrared photometry, the survey has more uniform sky coverage than similar previous surveys. The Zone of Avoidance around the Galactic plane is only $|b|\leq 5^{\circ}$.

Together with good quality Hi data from new observations, the ALFALFA survey and high signal-to-noise ratio archival data, 2MTF provides high-accuracy distance measurements for 2,062 nearby spiral galaxies. The mean relative error in the final 2MTF sample is 22%. We compare our measurements with the published distances in Cosmicflows-3, which represents the largest compendium of nearby galaxy distances. We find no substantial systematic difference between 2MTF and Cosmicflows-3 distances. Higher accuracy SNe Ia distances were also compared for 28 cross-matched objects. Again, no substantial systematic difference was found.

The best-fit bulk flow velocity amplitudes are $V=308\pm 26$ km s*-1*, $V=318\pm 29$ km s*-1*, and $V=286\pm 25$ km s*-1*at depths of $R_{I}=$ 20, 30 and 40$~{}h^{-1}{\rm Mpc}$ respectively, consistent with our previous measurements using the preliminary 2MTF sample but with higher accuracy. The fit results agree with the $\Lambda$CDM prediction at the 68% confidence level.

Acknowledgments

The authors wish to acknowledge the contributions of John Huchra (1948 - 2010) to this work. The 2MTF survey was initiated while KLM was a post-doc working with John at Harvard, and its design owes much to his advice and insight. This work was partially supported by NSF grant AST- 0406906 to PI John Huchra.

Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020, and the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. TH was supported by the National Natural Science Foundation of China (Grant No. 11473034, U1731127), the Key Research Program of the Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SLH021), the strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB23010200), and the Open Project Program of the Key Laboratory of FAST, NAOC, Chinese Academy of Sciences.