Off the baryonic Tully-Fisher relation: a population of baryon-dominated ultra-diffuse galaxies
Pavel E. Mancera Piña, Filippo Fraternali, Elizabeth A. K. Adams, Antonino Marasco, Tom Oosterloo, Kyle A. Oman, Lukas Leisman, Enrico M. di Teodoro, Lorenzo Posti, Michael Battipaglia, John M. Cannon, Lexi Gault, Martha P. Haynes, Steven Janowiecki, Elizabeth McAllan, Hannah J. Pagel, Kameron Reiter, Katherine L. Rhode, John J. Salzer, Nicholas J. Smith
DDraft version September 10, 2019
Typeset using L A TEX twocolumn style in AASTeX62
Off the baryonic Tully-Fisher relation: a population of baryon-dominatedultra-diffuse galaxies
Pavel E. Mancera Pi˜na ,
1, 2
Filippo Fraternali , Elizabeth A. K. Adams ,
2, 1
Antonino Marasco ,
1, 2
Tom Oosterloo ,
2, 1
Kyle A. Oman , Lukas Leisman , Enrico M. di Teodoro , Lorenzo Posti , Michael Battipaglia , John M. Cannon , Lexi Gault , Martha P. Haynes , Steven Janowiecki , Elizabeth McAllan , Hannah J. Pagel , Kameron Reiter , Katherine L. Rhode , John J. Salzer , and Nicholas J. Smith — Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD, Groningen, The Netherlands ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7900 AA Dwingeloo, The Netherlands Department of Physics and Astronomy, Valparaiso University, 1610 Campus Drive East, Valparaiso, IN 46383, USA Research School of Astronomy and Astrophysics - The Australian National University, Canberra, ACT, 2611, Australia Universit´e de Strasbourg, CNRS UMR 7550, Observatoire astronomique de Strasbourg, 11 rue de l’Universit´e, 67000 Strasbourg, France Department of Physics & Astronomy, Macalester College, 1600 Grand Avenue, Saint Paul, MN 55105, USA Cornell Center for Astrophysics and Planetary Science, Space Sciences Building, Cornell University, Ithaca, NY 14853, USA University of Texas, Hobby-Eberly Telescope, McDonald Observatory, TX 79734, USA Department of Astronomy, Indiana University, 727 East Third Street, Bloomington, IN 47405, USA
ABSTRACTWe study the gas kinematics traced by the 21-cm emission of a sample of six H i –rich low surfacebrightness galaxies classified as ultra-diffuse galaxies (UDGs). Using the 3D kinematic modelling code Barolo we derive robust circular velocities, revealing a startling feature: H i –rich UDGs are clearoutliers from the baryonic Tully-Fisher relation, with circular velocities much lower than galaxieswith similar baryonic mass. Notably, the baryon fraction of our UDG sample is consistent with thecosmological value: these UDGs are compatible with having no “missing baryons” within their virialradii. Moreover, the gravitational potential provided by the baryons is sufficient to account for theamplitude of the rotation curve out to the outermost measured point, contrary to other galaxies withsimilar circular velocities. We speculate that any formation scenario for these objects will require veryinefficient feedback and a broad diversity in their inner dark matter content. Keywords: galaxies: dwarf — galaxies: formation — galaxies: evolution — galaxies: kinematics anddynamics — dark matter INTRODUCTIONThe baryonic Tully-Fisher relation (BTFR; McGaughet al. 2000, 2005) is a tight sequence in the bary-onic mass–circular velocity plane followed by galaxiesof different types (e.g. den Heijer et al. 2015; Lelliet al. 2016a; Ponomareva et al. 2017). It has beenof paramount importance and widely used for calibrat-ing distances to extragalactic objects and to constrain,for example, semi-analytical and numerical models of
Corresponding author: Pavel E. Mancera Pi˜[email protected] galaxy formation and evolution (e.g. Governato et al.2007; Dutton 2012; McGaugh 2012; Sales et al. 2017,and references therein).Among the galaxies populating the BTFR, low surfacebrightness (LSB) galaxies are of particular interest, andhave been used to investigate the mass distribution andstellar feedback processes at dwarf galaxy scales (e.g.Zwaan et al. 1995; de Blok 1997; Dalcanton et al. 1997;Di Cintio et al. 2019).Ultra-diffuse galaxies (UDGs; van Dokkum et al.2015) are an especially notable subset of the LSB galaxypopulation due to their extremely low surface bright-ness values while having effective radii comparable toL (cid:63) galaxies. While these galaxies have been known for a r X i v : . [ a s t r o - ph . GA ] S e p Pavel E. Mancera Pi˜na et al. decades (e.g. Sandage & Binggeli 1984; Impey et al.1988), their recent detection in large numbers in differ-ent galaxy clusters, groups, and even in isolated envi-ronments (e.g. Rom´an & Trujillo 2017; Leisman et al.2017; Mancera Pi˜na et al. 2019), has sparked a renewedinterest in them.Many UDGs in isolation are H i –rich, opening the pos-sibility of investigating their gas kinematics. The mostsystematic study of H i in UDGs has been carried outby Leisman et al. (2017), who studied 115 sources fromthe Arecibo Legacy Fast Arecibo L-band Feed Array( ALFALFA ) catalogue (Giovanelli et al. 2005), as well asa small subsample of three sources with interferomet-ric H i data, that meet the optical criteria of having R e ≥ (cid:104) µ ( r, R e ) (cid:105) ≥
24 mag arcsec − , ac-cording to Sloan Digital Sky Survey photometry. Theauthors reported that such galaxies are H i –rich for theirstellar masses and have low star formation efficiencies,similar to other gas-dominated dwarfs (e.g. Geha et al.2006). Perhaps most intriguing, Leisman et al. (2017)reported that the velocity widths ( W ) of the globalH i profiles of their UDGs were significantly narrowerthan in other ALFALFA galaxies with similar H i masses.However, without resolved H i imaging of a significantsample, this result could be attributed to a very stronginclination selection effect for their sample, or system-atics when deriving W .Taking all of the above as a starting point, in thiswork we undertake 3D–kinematical modeling of resolvedH i synthesis data to study the gas kinematics of sixH i –rich UDGs. The rest of this Letter is organized asfollows: in Section 2 we introduce our sample of galaxieswith their main properties and we describe our strategyfor deriving their kinematics. We present our resultsand discussion in Section 3, to then conclude in Section4. Throughout this work we adopt a ΛCDM cosmologywith Ωm = 0.3, Ω Λ = 0.7 and H = 70 km s − Mpc − . SAMPLE AND KINEMATICSOur sample consists of six galaxies identified as H i –bearing UDGs by Leisman et al. (2017). They haveM HI ∼ M (cid:12) and are relatively isolated, by requir-ing that any neighbor with measured redshift within ±
500 km s − should be at least at 350 kpc away inprojection. Moreover, they have R e > H i –rich UDGs represent ∼
6% of all galaxies with M HI ∼ . M (cid:12) , with a cosmic abundance similar to cluster UDGs (Jones etal. 2018; Mancera Pi˜na et al. 2018). from the Westerbork Synthesis Radio Telescope (pro-gram R13B/001; PI Adams) and the rest from the KarlG. Jansky Very Large Array (programs 14B-243 and17A-210; PI Leisman). The observations and data re-duction procedure are described in Leisman et al. (2017)and more details will be given in Gault et al. (in prep.).Three more galaxies for which we have data are excludedfrom this analysis. AGC 238764 seems to have orderedrotation of about 20 km s − , but our data-cube missessignificant flux with respect to the ALFALFA detection.AGC 749251 shows hints of a velocity gradient but it isbarely resolved and we are not able to constrain its in-clination better than i (cid:46) ◦ . AGC 748738 shows signsof a gradient in velocity but the data are very noisy. Wedecide not to consider these three galaxies to keep a re-liable sample for the kinematic fitting, but more detailson these sources will be given in Gault et al. (in prep.).We estimate the baryonic mass of our UDGs asM bar = 1.33 M HI + M (cid:63) , with M HI given by:M HI M (cid:12) = 2 . × (cid:18) dMpc (cid:19) (cid:18) F HI Jy km s − (cid:19) (1)where we assume (Hubble flow) distances as listed inLeisman et al. (2017), and fluxes derived from the totalH i –maps using the task flux from gipsy (Vogelaar &Terlouw 2001).Stellar masses are obtained from the mass-to-lightratio–color relation of Herrmann et al. (2016) for an ab-solute magnitude in the g band and a ( g − r ) color.In order to derive such measurements we perform aper-ture photometry following the procedure described inMarasco et al. (2019) on deep optical data, obtainedwith the One Degree Imager of the WIYN 3.5-m tele-scope at the Kitt Peak National Observatory (Leismanet al. 2017; Gault et al. in prep.).We find a mean M HI / M (cid:63) ≈
15, confirming that thebaryonic budget is mainly set by the H i content, whichwe can robustly measure. Table 1 gives the name, dis-tance, inclination, baryonic mass, gas-to-stellar massratio, circular velocity, central surface brightness andcolor of our galaxies. Figure 1 shows the stellar image,0 th -moment map, major-axis position-velocity (PV) di-agram, and observed velocity field for a representativecase, AGC 248945. Figure 2 shows the PV diagrams forthe rest of our sample.Rotation velocities are derived with the software Barolo (Di Teodoro & Fraternali 2015), which fitstilted-ring disc models to the H i data-cubes (e.g. Iorio Version 1.4, http://editeodoro.github.io/Bbarolo/ ff the btfr: a population of baryon-dominated udg s Table 1.
Name, distance, inclination, baryonic mass, gas-to-stellar mass ratio, circular velocity, central surfacebrightness and color of our sample.Name Distance Inclination log(M bar / M (cid:12) ) M gas / M (cid:63) V circ µ (g , g − r (Mpc) (deg) (km s − ) (mag arcsec − ) (mag)AGC 114905 76 33 9.21 ± +4 . − . +6 − ± ± ± +11 . − . +6 − ± ± ± +12 . − . +5 − ± ± ± +1 . − . +3 − ± ± ± +9 . − . +4 − ± ± ± +2 . − . +6 − ± ± Note —Distances, taken from Leisman et al. (2017), have an uncertainty of ± ± ◦ . The central surface brightness is obtained from an exponential fit to the g − band surfacebrightness profile. RA (J2000) D E C ( J )
20 0 20
Offset [arcsec] V L O S [ k m / s ] AGC 248945
RA (J2000) D E C ( J ) k m s − Figure 1.
A representative galaxy from our sample, AGC 248945.
Left : H i contours on top of the r − band image; the contoursare at 0.88, 1.76 and 3.52 × H i atoms per cm , the outermost contour corresponds to S/N ≈
3. The blue ellipse shows theinclination the galaxy would need to be in the BTFR (see the text for details).
Middle : PV-diagram along the kinematic majoraxis; black and red contours correspond to data and Barolo best-fit model, respectively; the yellow points show the recoveredrotation velocities.
Right : Observed velocity field, at the same scale as the left panel. The grey line shows the kinematic majoraxis and the grey ellipse the beam. et al. 2017; Bacchini et al. 2018). This approach is par-ticularly suited to deal with our low spatial resolutiondata (2 − Barolowill be given in Mancera Pi˜na et al. (in prep.), here webriefly summarize our methodology.We give the position angle and inclination to Barolo.For the former we choose the angle that maximizes theamplitude of the PV slice along the major axis. Theinclination of each galaxy is derived by minimizing the residuals between its observed 0 th -moment map andthe 0 th -moment map of models of the same galaxyprojected at different inclinations between 10 ◦ − ◦ .We have tested this method blindly, without a prioriknowledge of the position angle, inclination nor rota-tion velocity, on a sample of 32 H i –rich dwarfs drawnfrom the apostle cosmological hydrodynamical simu-lations (Fattahi et al. 2016; Sawala et al. 2016), fromwhich mock data-cubes have been produced at reso-lution and S/N matching our observations, using the Pavel E. Mancera Pi˜na et al. -40 -20 0 20 40
Offset [arcsec] -30-1501530
AGC 749290
20 0 20
Offset [arcsec] -30-1501530 V L O S [ k m / s ] AGC 114905
20 0 20
Offset [arcsec]
AGC 219533
25 0 25
Offset [arcsec]
AGC 122966
50 0 50
Offset [arcsec]
AGC 334315
Figure 2.
PV slices along the major axes of our galaxies. Contours and points as in Figure 1, where AGC 248945 is shown.The narrowness of the PV diagrams suggests low gas velocity dispersions, as confirmed by Barolo. martini software (Oman et al. 2019). We find that wecan consistently recover the position angle within ± ◦ and the inclination within ± ◦ as long as i (cid:38) ◦ , withno systematic trends. These small uncertainties in po-sition angle and inclination have no significant impacton the recovered rotation velocities.We run Barolo with fixed inclination and positionangle, and the rotation velocity and velocity dispersionas free parameters, for our fiducial inclination i , as wellas for i +5 ◦ and i − ◦ . We find rotation velocities (V rot )suggesting flat rotation curves for all our sample. Forcalculating V rot , we use the mean velocity of the rings,as found with our fiducial inclination. The associateduncertainties come from the 16 th and 84 th percentilesof the velocity distribution obtained when consideringthe uncertainty in our inclination. To convert from V rot to circular velocity (V circ ), we correct for pressure sup-ported motions using Barolo as well (cf. Iorio et al.2017). As suggested by the narrowness of the PV dia-grams (Fig. 1 and 2), we find low velocity dispersions(Mancera Pi˜na et al. in prep.), giving rise to very smallasymmetric drift corrections ( (cid:46) − ). RESULTS AND DISCUSSIONIn Figure 3 we present the circular velocity–baryonicmass plane for our H i –rich UDGs, compared with galax-ies from the SPARC (Lelli et al. 2016b), SHIELD (Mc-Nichols et al. 2016) and LITTLE THINGS (Iorio et al.2017) samples. Clearly, all the UDGs studied here liesignificantly above the BTFR.Our galaxies rotate about 3 times lower than galaxieswith comparable M bar and effective radius (but highersurface brightness). Alternatively, they have about 10–100 times the M bar of galaxies with similar V circ (butsmaller effective radius and higher surface brightness,on average). These low velocities are consistent with the Version 1.0.2, http://github.com/kyleaoman/martini observations by Leisman et al. (2017) and Janowiecki etal. (2019) of H i –rich UDGs having narrower W thangalaxies of similar H i mass.Before discussing the implications of this result we ad-dress its robustness. The baryonic masses here derivedcannot be substantially overestimated: H i line fluxescan be measured with good accuracy (and we find fluxesin agreement with those derived from ALFALFA data byLeisman et al. 2017), and the distances to the galaxies inour sample ( (cid:104) d (cid:105) ∼
90 Mpc) are large enough to be wellrepresented by Hubble flow models, so the estimationof their H i mass is reliable. The H i –rich nature of ourgalaxies also implies that the stellar mass and its sys-tematics play a rather minor role: even M (cid:63) = 0 wouldnot move the galaxies significantly in Figure 3.A severe underestimation of the rotation velocities isalso unlikely. First, the H i emission of the galaxies ex-tends out to radii ≈ i ≈ ◦ − ◦ ) for all of them, whichis both unlikely and incompatible with the observed in-tensity maps, as illustrated in Figure 1, with an ellipseshowing the inclination that the galaxy would need tobe on the BTFR. Third, non-circular motions are notstrong enough to solve the observed discrepancy: re-gardless of the mode(s), their order, phase or amplitude,harmonic non-circular motions do not bias V rot towardslower values systematically, as long as the viewing an-gle of the galaxy is random (Oman et al. 2019, theirFig. 7), and the symmetry of the approaching and re-ceding sides of our PV-diagrams suggests the absenceof anharmonic components. We also investigated with Barolo the presence of radial motions, but no clearevidence for this was found, although higher-resolutionobservations are needed to further confirm this. ff the btfr: a population of baryon-dominated udg s Figure 3.
Circular velocity versus baryonic mass plane. Galaxies from the SPARC, SHIELD and LITTLE THINGS sampleslie on top of the BTFR. The pink area is the 99% confidence interval of an orthogonal distance regression to the SPARC sample.H i –rich UDGs are clear outliers of the BTFR, and in a position consistent with having no “missing baryons”. Finally, it is worth to mention that the observed ve-locity gradients cannot be attributed to H i winds: inthat case the gas velocity dispersion would be muchhigher than observed, and the galaxies would need veryhigh star formation rate densities, opposite to what ismeasured (Leisman et al. 2017).Previous studies already suggested the existence of out-liers in the BTFR, or at least an increase in its scatterat low V circ (e.g. Geha et al. 2006). Sometimes, how-ever, the robustness of the measurements of the rotationvelocities (usually estimated from the global H i profile)and inclinations of such outliers were unclear (cf. Omanet al. 2016 and references therein).Based on the discussion above, we conclude that thepositions of H i –rich UDGs in the M bar − V circ planederived here are robust, and our UDGs do not followthe BTFR . This suggests that the distribution of late-type systems in such plane is broader than previouslyobserved, and may have important implications for thescatter in the BTFR, which is a strong constraint for It is worth to notice that the two outliers close to our UDGs,DDO 50 and UGC 7125, also have relatively large effective radiiand/or low surface brightness. cosmological models. Despite the small scatter previ-ously reported (e.g. Lelli et al. 2016a; Ponomareva etal. 2017), our findings open the possibility for a scenariowhere the parameter space in the M bar − V circ planebetween the UDGs presented here and the BTFR ispopulated by LSB galaxies whose resolved H i kinemat-ics have not been studied yet, and which are not in oursample due to sharp selection effects. This may increasethe error budget of the intrinsic scatter of the relation,but to properly understand the magnitude of this effecta more complete census of the relative abundances ofthese galaxies is required.A second result emerges when comparing the positionof our galaxies with the curves in Figure 3. The blackdashed curve is the relation between the circular velocityat the virial radius and the virial mass of dark matterhaloes (M vir / M (cid:12) ≈ . × (V vir / km s − ) , for∆ c = 100, cf. McGaugh 2012). If M vir is multiplied bythe cosmological baryon fraction (f bar ≈ Pavel E. Mancera Pi˜na et al. sition for galaxies with a baryon fraction equal to f bar5 .Unexpectedly, our UDGs lie on top this curve, mean-ing that they are consistent with having no “missingbaryons”.Posti et al. (2019) recently discovered that somemassive spirals have virtually no “missing baryons”.There is, however, a substantial difference between ourUDGs and these massive spirals, as the former areH i –dominated and have very shallow potential wellscompared to the latter. How, then, is it possible thatthey retained all of their gas? One intriguing possibilityis that they have not experienced strong episodes of gasejection: feedback processes must have been relativelyweak and the shallow gravitational potentials managedto retain (or promptly re-accrete) all of their baryons.We surmise that this could be related to the low gasvelocity dispersions we find for our sample, which sug-gest a currently weak heating of the gas. This may beanalogous to the “failed feedback problem” of Posti etal. (2019), although in their case feedback has failed atlimiting the star formation efficiency of massive spiralgalaxies.Extremely efficient feedback has been invoked to solvedifferent discrepancies between observations and ΛCDMpredictions (see Tulin & Yu 2018 and Bullock & Boylan-Kolchin 2017 for a review, including limitations of suchsolutions), as well as to explain the formation of UDGsvia feedback-driven outflows resulting from bursty starformation histories (e.g. Di Cintio et al. 2017). Thesenew observations seem to present a challenge to thesemodels.An alternative scenario could be that our galaxiesreside in haloes with V circ ≈
80 km s − but very lowconcentration, such that their rotation curves are stillrising at our outermost measured radii. However, thisdoes not seem feasible since the concentration param-eter needed for this is c ≈
1, instead of the expected c ≈
10 (Ludlow et al. 2014), making the existence ofsuch galaxies within the volume of the Universe basi-cally impossible.Figure 4 shows the ratio between baryonic and dynam-ical mass of our UDGs, with a dynamical mass esti-mated as M dyn ( < R out ) = V R out / G, with R out theradius of the outermost point of the rotation curve. Bothour sample and LITTLE THINGS galaxies have a meanR out / R d ≈
4, with R d the optical disc-scale length. Note that this assumes V circ ≈ V vir , but in general V circ tendsto be slightly larger for massive galaxies (V circ ≈ . vir ). Thiswould flatten the grey curve at high V circ values. log(M dyn / M fl ) l og ( M b a r / M d y n ) DF − − − LITTLE THINGSHI − rich UDGs f DM = 0f DM = 0 . DM = 0 . Figure 4.
Baryonic to dynamical mass ratio as a functionof the dynamical mass, measured inside ≈ d . The solid,dashed and dotted lines show the position where galaxieswith 0%, 50% and 90% dark matter lie, respectively. LIT-TLE THINGS galaxies (Iorio et al. 2017) are shown for com-parison, as well as two estimates for DF–2 (Danieli et al.2019, D+19 and Trujillo et al. 2019, T+19) and DF–4 vanDokkum et al. (2019), for which we assume M bar = M (cid:63) . Even if our H i –rich UDGs have a baryon fractionequal to the cosmological average, their dynamics couldbe dark matter-dominated at all radii, as other galax-ies of similar V circ , but this is does not seem to bethe case, since M bar (R < R out ) ≈ M dyn (R < R out ). Al-though more precise values of M bar and M dyn shouldbe determined with better data, Figure 4 indicates thatthese galaxies have much less dark matter within theextent of their discs than other dwarfs and LSB galax-ies, and that, inside their discs, the baryonic componentdominates.The dynamical properties here shown resemble thoseof tidal dwarf galaxies (Hunter et al. 2000; Lelli et al.2015). However, given the isolation (mean distance tonearest neighbor ∼ ff the btfr: a population of baryon-dominated udg s CONCLUSIONSWe have analyzed a set of interferometric H i line ob-servations of gas–dominated UDGs. Using a 3D fittingtechnique we obtain robust measurements of their circu-lar velocities, allowing us to place them in the circularvelocity–baryonic mass plane.We find that our six galaxies lie well above the BTFR,with rotation velocities too low given their baryonicmasses. Their position in the circular velocity–baryonicmass plane implies that they have a baryon fractionwithin their virial radius equal or close to the cosmo-logical value, and we speculate that this could be due toextremely inefficient feedback, challenging our currentunderstanding of feedback processes in dwarfs. Addi-tionally, the dynamics of these galaxies are dominatedby the baryonic component out to the outermost mea-sured radii, and they have very low dark matter fractionsinside such radii, suggesting a broader distribution in thedark matter content of galaxies than previously thought.The fact that galaxies with these properties had notbeen reported before is perhaps because interferometricH i observations are usually targeted based on previousoptical studies. Since UDGs are an extremely optically faint population, it is not particularly surprising thatthis galaxy population has not been identified before.With the advent of large H i interferometric surveys weexpect this hidden population to come to light. We appreciate the careful revision and useful commentsmade by an anonymous referee. We thank Giuliano Iorioand Andrew McNichols for their clarifications on LITTLETHINGS and SHIELD data, respectively. We would alsolike to thank Anastasia Ponomareva, Arianna Di Cintio andFederico Lelli for interesting discussions.PEMP and FF are supported by the Netherlands Re-search School for Astronomy (Nederlandse Onderzoekschoolvoor Astronomie, NOVA), Phase-5 research programme Net-work 1, Project 10.1.5.6. EAKA is supported by the WISEresearch programme, which is financed by the NetherlandsOrganization for Scientific Research (NWO). KAO receivedsupport from VICI grant 016.130.338 of NWO. LP acknowl-edges support from the Centre National d’´Etudes Spatiales(CNES). MPH is supported by grants NSF/AST-1714828and from the Brinson Foundation. This work has been sup-ported in part by NSF grant AST-1625483 to KLR, and byThe National Radio Astronomy Observatory (The NationalRadio Astronomy Observatory is a facility of the NationalScience Foundation operated under cooperative agreementby Associated Universities, Inc.). We have made an exten-sive use of SIMBAD and ADS services, for which we arethankful.
REFERENCES
Bacchini, C., Fraternali, F., Iorio, G., Pezzulli, G., 2019,A&A, 622, 64Bullock J. S., Boylan-Kolchin M., 2017, ARAA, 55, 343Dalcanton, J. et al. 1997, ApJ, 482, 659den Heijer M. et al. 2015, A&A, 581, A98Danieli S., van Dokkum P., Conroy C., Abraham R.,RomanowskyA. J., 2019, ApJ, 874, 12de Blok, W. J. G. 1997, PhD thesis, University ofGroningenDi Cintio, A. et al. 2017, MNRAS, 466, 1Di Cintio, A. et al. 2019, MNRAS, 486, 2535Di Teodoro, E. & Fraternali, F., 2015, MNRAS, 451, 3021Di Teodoro, E. M., Fraternali, F., & Miller, S. H. 2016,A&A, 594, A77Dutton, A. A., 2012, MNRAS, 424, 3123Fattahi, A., Navarro, J. F., Sawala, T. et al. 2016,MNRAS,457, 844Geha, M., Blanton, M. R., Masjedi, M., & West, A. A.2006, ApJ, 653, 240Giovanelli, R., Haynes, M. P., Kent, B. R. et al. 2005, AJ,130, 2598 Governato, F. et al. 2007, MNRAS, 374, 1479Herrmann K. A., Hunter D. A., Zhang H.-X., Elmegreen B.G., 2016, AJ, 152, 17Hunter, D. A., Hunsberger, S. D., & Roye, E. W. 2000,ApJ, 542, 137Iorio G., Fraternali F., Nipoti C., Di Teodoro E., Read J. I.,Battaglia G., 2017, MNRAS, 466, 415Impey C., Bothun G., Malin D. 1988, ApJ, 330, 634Janowiecki, S. et al. 2019, MNRAS, DOI:10.1093/mnras/stz1868Jones, M. G. et al. 2018, A&A, 614, 21Leisman L. et al. 2017, ApJ, 842, 13Lelli, F. et al. 2015, A&A, 584, A113Lelli, F., McGaugh, S. S., Schombert, J. M., 2016a, ApJ,816, 14Lelli F., McGaugh S. S., Schombert J. M., 2016b, AJ, 152,15Ludlow A. D. et al. 2014, MNRAS, 441,378Mancera Pi˜na, P. E., Aguerri, J.A.L., Peletier, R.F.,Venhola, A., Trager, S., Choque Challapa, N., 2019,MNRAS, 485, 1036