Further evidence for a population of dark-matter-deficient dwarf galaxies

TL;DR

This paper presents evidence for a population of dwarf galaxies that appear to be dominated by baryons rather than dark matter, challenging standard cosmological models of galaxy formation.

Contribution

It reports 19 dwarf galaxies with baryon dominance beyond their half-light radii, including 14 isolated ones, providing new observational evidence against existing dark matter dominance assumptions.

Findings

19 dwarf galaxies with baryon-dominated outskirts

14 isolated dwarf galaxies free from environmental effects

Challenges to standard galaxy formation theories

Abstract

In the standard cosmological model, dark matter drives the structure formation and constructs potential wells within which galaxies may form. The baryon fraction in dark halos can reach the universal value (15.7%) in massive clusters and decreases rapidly as the mass of the system decreases. The formation of dwarf galaxies is sensitive both to baryonic processes and the properties of dark matter owing to the shallow potential wells in which they form. In dwarf galaxies in the Local Group, dark matter dominates the mass content even within their optical-light half-radii (r_e ~ 1 kpc). However, recently it has been argued that not all dwarf galaxies are dominated by dark matter. Here we report 19 dwarf galaxies that could consist mainly of baryons up to radii well beyond r_e, at which point they are expected to be dominated by dark matter. Of these, 14 are isolated dwarf galaxies, free from the influence of nearby bright galaxies and high dense environments. This result provides observational evidence that could challenge the formation theory of low-mass galaxies within the framework of standard cosmology. Further observations, in particular deep imaging and spatially-resolved kinematics, are needed to constrain the baryon fraction better in such galaxies.

Equations

$$w_{20}=\sqrt[]{w_{20,raw}^2-(\delta s{)}^2}$$

$${\mathrm{M}}_{\mathrm{HI}}=2.36\times 10^5{d}^2\int \mathrm{F}\mathrm{d}\mathrm{v}[{\mathrm{M}}_{\odot }]$$

$${\log }_{10}(M/L)=a_{\lambda }+b_{\lambda }\times ({\mathrm{M}}_g-{\mathrm{M}}_r).$$

$$\mathrm{lo}{\mathrm{g}}_{10}{\mathrm{r}}_{\mathrm{HI}}=(0.506\pm 0.003)\mathrm{lo}{\mathrm{g}}_{10}{\mathrm{M}}_{\mathrm{HI}}-(3.293\pm 0.009)-\mathrm{lo}{\mathrm{g}}_{10}2$$

$$\sin (\mathrm{i})=\sqrt[]{\frac{1-(\frac{b}{a}{)}^2}{1-q_0^2}}$$

$${\mathrm{M}}_{\mathrm{dyn}}(<{\mathrm{r}}_{\mathrm{HI}})$$

$$=4\pi {\rho }_0{R}_s^3\left[\ln \left(\frac{R_s+r_{\mathrm{HI}}}{R_s}\right)-\frac{r_{\mathrm{HI}}}{R_s+r_{\mathrm{HI}}}\right],$$

$${\mathrm{M}}_{\mathrm{vir}}={\int }_0^{{\mathrm{R}}_{\mathrm{vir}}}4\pi {\mathrm{r}}^2\rho (\mathrm{r})\mathrm{dr}=4\pi {\rho }_0{\mathrm{R}}_{\mathrm{s}}^3\left[\ln \left(1+\mathrm{c}\right)-\frac{\mathrm{c}}{1+\mathrm{c}}\right],$$

$${\rho }_0=\frac{200{\rho }_{\mathrm{cr}}}{3}\frac{{\mathrm{c}}^3}{\ln (1+\mathrm{c})-\frac{\mathrm{c}}{1+\mathrm{c}}},$$

$$\mathrm{lo}{\mathrm{g}}_{10}\mathrm{c}=0.905-0.101({\mathrm{lo}{\mathrm{g}}_{10}\mathrm{M}}_{\mathrm{vir}}/10^{12}{\mathrm{h}}^{-1}{\mathrm{M}}_{\odot }).$$

$${\mathrm{M}}_{\mathrm{dyn}}(<{\mathrm{r}}_{\mathrm{HI}})$$

$$=2\pi {\rho }_0{r}_0^3\left[\ln \left(1+\frac{r_{\mathrm{HI}}}{r_0}\right)+\frac{1}{2}\ln \left(1+\frac{r_{\mathrm{HI}}^2}{r_0^2}\right)-arctan(\frac{r_{\mathrm{HI}}}{r_0})\right],$$

$$\mathrm{lo}{\mathrm{g}}_{10}(r_0/\mathrm{kpc})=0.66-0.58({\mathrm{lo}{\mathrm{g}}_{10}\mathrm{M}}_{\mathrm{vir}}/10^{11}{M}_{\odot }),$$

Full text

{affiliations}

National Astronomical Observatories, Chinese Academy of Science, 20A Datun Road, Chaoyang District, Beijing, 100101, China

University of Chinese Academy of Sciences, No. 19 A Yuquan Road, Beijing, 100049, China

Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China

Key Laboratory of The Five-hundred-meter Aperture Spherical radio Telescope, National Astronomical Observatories, Chinese Academy of Sciences

Key Laboratory of Optical Astronomy, National Astronomical Observatories, Beijing, 100101, China

Physics Department and Tsinghua Center for Astrophysics, Tsinghua University, Beijing 100084, China

Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China

In the standard cosmology8, dark matter contributes around 26.6% of the Universe, while baryons only occupy 4.9%. The baryonic fraction is about the universal value, 15.7%, in galaxy clusters, and decreases rapidly towards lower masses. In low mass systems, the potential wells are shallow so that various baryonic processes, including background UV ionization and stellar feedback, could either prevent gas infall or expel gas out of the systems, leading to a low baryonic fraction. Observationally, it infers a typical mass-to-light ratio of 10–1000, using stellar dynamics of the dwarf satellite galaxies in the Local Group9, 10. Such values are supported by modern simulations11. However, recently two dwarf galaxies were found to have baryonic mass comparable to the dark matter mass up to several kiloparsecs using the dynamics of their HI gas12, 7. Similar results were reported for two ultra-diffuse dwarf galaxies in the NGC1052 group 5, 6 using the dynamics of their globular clusters, of which the NGC1052-DF4 dwarfs may have almost no dark matter at all. Such relation between dark matter and baryons is also revealed in the population of tidal dwarf galaxies13, 14. In all cases, these galaxies reside in (relatively) high density regions, and the environmental stripping/interaction might play a role.

Here we search for baryon dominated dwarf galaxies (r-band absolute magnitude, M${}_{\rm r}>-18$) in the field, using the catalogue of Arecibo Legacy Fast ALFA (ALFALFA) $\alpha$.4015, which matches the HI selected galaxies to the Seventh Data Release of Sloan Digital Sky Survey (SDSS DR7)16 PhotoPrimary optical catalogue. Signal-to-noise cut at HI spectrum, SNR${}_{\rm HI}>10$, is imposed. We further remove sources with suspicious optical images and HI spectra, and sources which have multiple Galaxy Evolution Explorer(GALEX)17 images. The photometric and geometric properties are re-calculated for low surface brightness galaxies for SDSS DR7 pipeline systematically over-estimate the sky background for such systems18, 19. In the lack of HI image, we use the r-band b/a ratio to correct for the inclination. In order to minimize the mis-alignment effect between the HI content and the r-band image, we select galaxies with r-band b/a ratio between 0.3 and 0.6, leading to a final parent sample of 324 galaxies. The stellar mass of each galaxy is derived from the optical photometry from SDSS and the distance measured by the ALFALFA20. Dynamical mass is estimated using the circular velocity VHI which is derived from 20% of the HI line width (w20), and the HI radius (rHI, defined at HI surface density = 1M*⊙pc-2*) which is converted from the HI mass based on the tight relation between HI radius and HI mass21. We verify the accuracy of such defined rHI and VHI using dwarf galaxies in the Local Irregulars That Trace Luminosity Extremes The HI Nearby Galaxy Survey (LITTLE THINGS), where the HI images have been well resolved and HI dynamics been detailed analyzed. Details are given in the Method.

Figure 1 shows images and spectra of two example dwarf galaxies: AGC 213086 and AGC 8915. The r-band luminosity of AGC 213086 is $3.07\times 10^{42}$ erg s*-1*, corresponding to a stellar mass of $5.51_{-2.32}^{+4.02}\times 10^{8}$M*⊙. The HI mass is $2.45_{-0.09}^{+0.11}\times 10^{9}$M⊙, corresponding to a radius of r${}_{\rm HI}=14.37\pm 1.023$ kpc. This radius is much larger than the half light radius in the optical wavelength, r${}_{\rm e}\sim 3.39$ kpc, extending to the dark matter dominated region if AGC 213086 were a typical dwarf galaxy. The total baryonic mass (Mbary) within rHI is $3.82_{-0.32}^{+0.34}\times 10^{9}$M⊙. The circular velocity is $43.47\pm 2.40$ km/s and the dynamical mass (Mdyn) enclosed within the rHI is $6.31_{-0.77}^{+0.89}\times 10^{9}$ M⊙. Error bars account for various uncertainties in the data and in the method for the mass estimation. Assuming a typical NFW profile22 the virial mass (Mhalo, the total mass within the virial radius, Rvir, within which the mean density is 200 times the critical density) is $1.41\times 10^{10}$M⊙, and is $1.01\times 10^{10}$M⊙ if assuming a Burkert profile23. The ratio between Mdyn($<$rHI) and Mbary($<$rHI) is less than 2, suggesting baryon dominates over dark matter within rHI. The baryonic fraction within Rvir is 0.271 (and 0.376 if assuming a Burkert profile), well above the universal value. In comparison, we show at the bottom a ‘typical’ dwarf galaxies, AGC 8915. It has Mbary($<$rHI) = Mgas($<$rHI) + Mstar ($<$rHI)= $3.14_{-0.17}^{+0.18}\times 10^{9}$M${}_{\odot}\ll$ Mdyn($<$rHI)= $2.647_{-0.18}^{+0.20}\times 10^{10}$ M⊙* and M${}_{\rm halo}=$ $1.83\times 10^{11}$ M*⊙* (NFW profile ) / $1.04\times 10^{11}$ M*⊙* (Burkert profile). Its Mdyn-to-Mbary ratio within rHI is $\sim$10, and the baryonic fraction within Rvir is 0.0171 (NFW profile) / 0.0301 (Burkert profile), well below the universal value.

The main statistical results are presented in Figure 2. We find 19 dwarf galaxies out of 324 parent dwarf galaxies, a non-negligible fraction, with Mdyn($<$rHI) $<$ 2 $\times$ Mbary($<$rHI), i.e. MDM($<$rHI) $<$Mbary($<$rHI). These 19 dwarf galaxies have more extended re distribution and rHI distribution compared to the parent sample. For each of them, rHI is much larger than re, suggesting its dynamics is estimated at rather large radius where dark matter is expected to be dominant.

The median Mdyn($<$rHI)/Mbary($<$rHI) (here after Mdyn/Mbary) of the parent sample is 7.36 with the one-$\sigma$ dispersion of [3.85, 11.03], well below the the typical values found in the dwarf galaxies in the Local Group (right panel of Figure 2). There is a clear excess of the baryonic dominated dwarf galaxies (here after BDDGs) compared to a Gaussian distribution in the log Mdyn/Mbary, suggesting BDDGs to be a distinct galaxy population rather than statistical outliers.

Figure 3 shows that as the parent sample, for most BDDGs Mdyn($<$rHI) is dominated by gas masses, so that the potential mis-matching between the optical and HI sources could not affect the results substantially. The parent sample generally follows the same Tully-Fisher relation as spiral galaxies, yet BDDGs tends to have much lower circular velocities for given luminosities. It is the low circular velocities rather than systemic uncertainties (e.g. geometric structures, distance estimates and etc.) that leads to their small Mdyn/Mbary values. Assuming the NFW profile, we find the BDDGs reside in halos as small as $\rm 10^{9}\sim 10^{11}$ M*⊙* (Figure 4), consistent with the mass range if assuming the Burkert profile. Their baryon fractions within Rvir are mostly well above the universal value. This is unexpected for these systems have rather shallow potential well and are thus harder to maintain their baryons against various feedback. Hydro-dynamical simulations of galaxy formation show that interactions of galaxies at high density region could be responsible for the formation of baryonic dominated tidal dwarf galaxies, and the environmental stripping could play a role in forming the BDDGs around clusters26, 27. However, only 5 of the 19 BDDGs are within/close to groups/clusters. The rest of the 14 BDDGs reside at distances farther than 3 times the virial radii of any surrounding groups/clusters (right panel in Figure 4). This makes the environmental stripping and origin from interaction of galaxies very unlikely. Our results suggest that a population of dwarf galaxies could form in a particular way such that much less dark matter is required than for those in the Local Group and those found in simulations.

One possible channel is that, under extreme conditions, strong supernova feedback could flatten the potential well by expelling gas. Along with this procedure dark matter could be removed to the outer region, in response to the gravity of the expelled gas. Further fueling cold gas might reach the potential well along filaments(cold flow), while dark matter grow in a more smooth and steady way. Under such special circumstance, it is possible to form BDDGs. Further studies with high resolution simulations are required to explore such possibility. A warm dark matter model could also likely lead to a relatively low density in the inner region of a given halo and thus could probably be more in line with the existence of the BDDGs.

Alternatively, the systematic errors in inclination may lead to an under-estimate of the circular velocity and thus an under-estimate of the dynamical mass, for there could be mis-alignment between the optical inclination and the inclination of the HI kinematic field. Applying the same mis-alignment distribution between the optical images28 and the HI dynamics from the LITTLE THINGS and those from the most up-to-data simulations29 to our sample, we find similar distributions of the Mdyn/Mbary, suggesting the existence of the BDDGs. In addition, most of our BDDGs are field dwarf galaxies for which less mis-alignment effect is expected. There could also exist systematic errors in optical inclinations, i.e. galaxies with high axis ratios could be bars in face-on disks. Recent work 30 shows a fraction of 10% of such cases for dwarf galaxies, thought the fraction could be lower in low dense environments where most of our BDDGs are found. Detailed HI interferometric mapping of these galaxies in the future are required to rule out such possibilities.

METHODS

T ALFALFA.

The Arecibo Legacy Fast ALFA (Arecibo L-band Feed Array) survey(ALFALFA)1, 2, 3 is a blind extragalactic HI survey, covering a wide area of 7000 deg2 of the sky at high Galactic latitudes. The beam size is about 3.5 arcmin. It has HI line spectra of more than 30,000 extragalactic sources with radial velocities $<$ 18000 km s*-1*. The spectral resolution4 is $\sim$10 km s*-1*, enabling reliable measurements of $\sim$ 20 km s*-1*, the typical velocity of dwarf galaxies. Here we use $\alpha$.4015, a catalog which covers 40$\%$ of the full ALFALFA survey area, including the northern hemisphere spring region: 07h30${}^{m}<$ ra $<$ 16h30m, +04${}^{\circ}<$ dec $<$ +16*∘, and +24${}^{\circ}<$ dec $<$ +28∘, and the northern hemisphere autumn region: 22h00${}^{m}<$ ra $<$ 03h00m*, +14${}^{\circ}<$ dec $<$ +16*∘, and +24${}^{\circ}<$ dec $<$ +32∘*. There are 15855 HI detected sources, among which 15041 are extragalactic objects and the rest 814 are more likely Galactic high velocity cloud (HVC).

The catalogue provides w50, 50% peak width of HI spectrum, and the corresponding errors. However, we find that in most cases, the edge of neither side of the spectrum has a cut-off feature. Instead, the flux at each side drops gradually. Calculations based on w50 could lead to underestimates of the dynamical masses enclosed in rHI. w20, 20% peak width of the HI spectrum, is a better indicator of the gas velocity. In practice, we treat systems with one peak and two peaks in their HI spectra differently. For those with one peak, wavelengths at which the fluxes are 20% of the peak values are identified to determine the w20,raw, while for those with two peaks, the 20%-fluxes are calculated for both peak values and the corresponding characteristic wavelengths are identified at each rising side of the spectrum to determine the w20,raw. We perform Gaussian/Lorentzian fitting at each rising side. The results are consistent with those using polynomial fits. For each source, we generate 10000 realizations using the rms given by the ALFALFA catalogue, and adopt the corresponding 1-$\sigma$ range as the uncertainty in $\rm w_{\rm 20}$( $\rm w_{\rm 20,err}$). Then, we subtract the instrumental broadening as following5

[TABLE]

where $\delta s$ is the final velocity resolution after smoothing and we adopted the value of 10 km/s.

U SDSS DR7.

The optical galaxy catalogue is based on SDSS DR716, but with an independent set of improvement in sky-background subtraction. SDSS DR7 contains images and spectra for millions of galaxies, centered at z $\sim$ 0.1. The photometric data completes at 24 r-band apparent magnitude and the extinction-corrected spectroscopy data are complete at 17.72.

It is found that the SDSS photometric pipeline systematically overestimated the sky backgrounds of galaxies with extended low surface brightness by $\sim$ 0.5 mag6, 7, 18. The surface brightness of dwarf galaxies is usually very low and their luminosities could thus be very sensitive to the sky subtraction. Here we select a sub-sample of low surface brightness galaxy (central surface brightness in the B band $\rm\mu_{\rm 0}$(B)$\rm>22.5$ mag arcsec-2)8 and use the g-band and r-band SDSS mosaic images from the Twelfth Data Releases of the Sloan Digital Sky Survey(SDSS DR12)9 to re-calculate their photometry19. The method is summarized as following: we first use SEXtractor10 to extract and mask all sources above $2\sigma$ local background variation using the r-band/g-band image and then unmask the target galaxy by visual inspection. We grow the masks using the IDL function DILATE with a square shape operator, whose size is proportional to the size of the mask. Stars on top of our target galaxies are removed and filled with the average value of pixels around the star. We fit each galaxy’s ellipticity profile using the ELLIPSE task in IRAF and use the ellipticity of the largest fitted ellipse to calculate the r-band axis ratio b/a. The Petrosian flux is then calculated by summing up all fluxes within 2 times the elliptical Petrosian radius11, 12. For those with smaller surface brightness, we simply adopt the Petrosian magnitudes, and use exponential axes ratio expABr (or de Vaucouleurs axes ratio deVABr) if the likelihood fraction of de Vaucouleurs model fracDeV${}_{\rm r}<$ 0.5 (fracDeV${}_{\rm r}>$ 0.5) as the b/a value from the released SDSS DR7 catalogue.

There are 12423 galaxies with optical counterparts (OCs) in the HI and optical cross-matched catalogue15. Here we focus on dwarf galaxies with absolute magnitude M${}_{\rm r}>-18$ and high signal-to-noise ratio in HI spectra: SNR${}_{\rm HI}>10$. To avoid significant bias caused by inclination, we further require the r-band b/a to be within 0.3 and 0.6, corresponding to the inclination angle range of [54.7, 76.8] degree. The final parent sample consists of 324 galaxies.

V LITTLE THINGS.

“Local Irregulars That Trace Luminosity Extremes, The HI Nearby Galaxy Survey”(LITTLE THINGS)28 is a high resolution, very large array HI survey with angular resolution of $\sim$6 arcsec and velocity resolution of $<$2.6 km s*-1*, aiming to obtain deep HI-line maps of dwarf galaxies. The high resolution enable a reliable measurement of the rotation curve12. In practice, Oh et al.12 fitted a 2D tilted-ring model to the 2D bulk velocity fields extracted from the HI data. This provides geometric and kinematic parameters for each galaxy, including central position, position angle, inclination, systemic velocity and rotation velocity. The asymmetric drift is then made to improve the rotation curve measurement by taking into account the dynamical support due to random motions. In combination with Spitzer 3.6 $\mu$m and optical U, B, and V images, the rotation curve is then used to analyze the dynamical contributions by baryons and dark matter. They found the inner slope of the dark matter density profiles deviate significantly from the cusp-like mass distribution predicted by dark matter only simulations, but in line with those predicted by $\rm\Lambda$CDM + hydro-dynamical simulations, for which the baryon feedback process could change the inner profile.

W Mass algorithm.

Four kinds of masses are used in this work, including stellar mass, HI mass, dynamical mass, and dark halo virial mass. Here we describe briefly how each of the mass is derived.

Gas mass. Gas in galaxies mainly consists of HI and Helium. The HI mass is calculated following Roberts (1962)13

[TABLE]

where F is the HI flux in Jy km s*-1*, and v is the receding velocity. d is the distance15 of the HI detected galaxies estimated using d = cz/H0 for galaxies with cz$>$6000 km/s, where H0 is the Hubble constant, 70km s*-1*, and c is the speed of light. For galaxies with cz$<$6000 km/s, the distance is derived adopting the local universe peculiar velocity model14, using a combination of primary distances form the literature and secondary distances from the Tully-Fisher relation. The total gas mass is derived by assuming the same Helium-HI ratio as that derived from the Big Bang nucleosynthesis: M${}_{\rm gas}=1.33\times$MHI (Y${}_{\rm P}^{\rm BBN}=0.247$)8, where Y${}_{\rm P}^{\rm BBN}$ is the primordial He abundance from Planck in $\Lambda$CDM.

Stellar mass. For a given galaxy, we calculate the absolute magnitude in g and r band, using the photometry as described above and the distance from $\alpha.$ 40. Following Bell’s algorithm, we have

[TABLE]

Here we adopt a Kroupa initial mass function(IMF)15 with $a_{\rm r}=-0.306-0.15$ and $b_{\rm r}=1.097$. The final error bars accounts for both observational errors in photometry and distance, and the method error of 0.1 dex as suggested by Bell20.

Dynamical mass. With the velocity and radius of the HI component, we calculate the dynamical mass enclosed in rHI by assuming a spherical symmetry: Mdyn ($<$rHI) =V${}^{2}_{\rm HI}$rHI/G, where G is the gravitational constant. Previous work21 found that there is a tight relation between the HI mass and the HI radius rHI, defined at a surface density of 1M⊙ pc*-2*.

[TABLE]

This relation has been proven successful in describing the rHI and MHI relation for various galaxies types21. In particular, we apply this rHI vs. MHI relation to the dwarf galaxies from LITTLE THINGS (Left panel of Extended Data Figure 1) and find they agree very well with the direct measurement using the resolved HI images.

The velocity VHI is estimated using w20: VHI = w20/2/sin(i), where i is the inclination angel.

[TABLE]

The parameter q0 is the intrinsic axial ratio of a galaxy seen edge-on. The value of q0 could depend on galaxy morphology16, 17. Here we use 0.2 as usually adopted in the literature. w20 is a good indicator of the circular velocity given sharp edges at both sides of the given spectrum. However, for dwarf galaxies, velocity dispersion could contribute a non-negligible fraction to the total kinematic energy of the systems. This is reflected by the shape of the spectrum that at both sides the spectrum decline gradually, lacking the feature of a sharp cut-off. w20 could thus carry both information of the circular velocity and of the velocity dispersion. We test the choice of using w20 as an indicator of the asymmetric drift-corrected circular velocity using dwarf galaxies in the LITTLE THINGS (Middle panel of Extended Data Figure 1). It shows the w20 is a good indicator of the corrected circular velocity, while w50 usually under-estimates the corrected circular velocity. We then test the full method by performing the same analysis as for our BDDGs on the LITTLE THINGS galaxies and find the derived Mdyn are consistent with the estimates using the tilted-ring model (Right panel in Extended Data Figure 1).

Note for we do not have HI images, we use the inclination angels estimated in the optical r-band. There could be mis-alignment between r-band image and HI velocity field, leading to biased estimate of the circular velocity. We restrict our parent sample to have r-band b/a between [0.3, 0.6] in order to avoid severe deviation of the derived velocities from the true ones. Using dwarf galaxies in the LITTLE THINGS, we show in the left panel of Extended Data Figure 2 the distribution of the angle between r-band image and the HI velocity filed. It shows that in most cases the mis-alignment is below 20 degree, thought there is a tail towards large angle. We apply the same distribution of the mis-alignment to our parent sample and generate 10000 realization for each parent galaxy. The resulting Mdyn/Mbary distribution is shown in the right panel of Extended Data Figure 2. It shows there is still an apparent excess of BDDGs at the low Mdyn/Mbary end. The existence of BDDGs is also supported when applying the same distribution of the mis-alignment as those in the simulations18.

If the BDDGs were very compact dwarf galaxies, it would be possible to have baryon mass dominated in the compact region. We compare the r-band re and rHI of the BDDGs and those of the parent dwarf galaxies and find that the BDDGs are slightly more extended than the parent dwarf galaxies, both in the optical and in the HI contents (Extended Data Figure 3). In addition, rHI is larger than re for all the BDDGs. Both the baryonic masses and dynamical masses are measured at radii within which it is expected to be dominated by dark matter if the BDDGs were typical dwarf galaxies.

Halo mass. Assuming a typical NFW profile22, rHI and Mdyn($<$r${}_{\rm HI})$ are related as

[TABLE]

where Rs is a free parameter. Given rHI and Mdyn($<$r${}_{\rm HI})$, for each galaxy, we obtain the corresponding Rs. The virial mass is expressed as

[TABLE]

[TABLE]

where $\rm\rho_{0}$ is a characteristic density, $\rm\rho_{cr}$ is the critical density, and c is the concentration parameter which relates to Rs and Rvir via c = $\frac{\rm R_{\rm vir}}{\rm R_{s}}$. The concentration parameter follows a tight halo mass-concentration relation19.

[TABLE]

Here h = H0/(100 km s*-1* Mpc*-1*)=0.7. Inserting Eq. 9 to Eq. 7, one could obtain the Mvir.

Assuming a Burkert profile23, rHI and Mdyn($<$r${}_{\rm HI})$ are related as

[TABLE]

where r0 and $\rho_{0}$ are free parameters. With the relation between r0 and Mvir20

[TABLE]

one could derive Mvir for any given combination of rHI and Mdyn($<$r${}_{\rm HI})$.

X Galaxy clusters.

The galaxies groups and clusters catalogues are created based on the SDSS DR129 and the 2MASS Redshift Survey (2MRS)21, using a friends-of-friends group finder algorithm22. Various observational biases have been taken into account, including Malmquist bias, the ‘Fingers of God’ and etc. The groups/clusters mass depends on the total luminosity, the luminosity distance, the velocity dispersion, the group radius and the number of detected group members. This method has been carefully calibrated and optimized on wide-angle mock catalogues from the Millennium simulation23, 24. For any group/cluster included in these catalogues, where available, group parameters in the published literature are adopted primarily.

The properties of the 19 BDDGs are summarized in Extend Data Table 1.