Dwarf Galaxies in the Local Volume

TL;DR

This paper reviews observational data on about 1000 dwarf galaxies within 11 Mpc, highlighting their properties, distribution, and significance for testing cosmological models and understanding local universe structures.

Contribution

It provides a comprehensive overview of Local Volume dwarf galaxies, emphasizing their role in testing the $ m f extit{ extLambda CDM}$ paradigm and their use as tracers for mass estimation.

Findings

Dwarf galaxies constitute 5/6 of the Local Volume sample.

Approximately 40% of these dwarfs have precise distance measurements from Hubble.

LV dwarfs are crucial for understanding galaxy formation and local mass distribution.

Abstract

We review observational data about a sample of Local Volume objects containing about 1000 galaxies within 11 Mpc of the Milky Way. Dwarf galaxies with stellar masses $M_*/M_{\odot} < 9$ dex make up 5/6 of the sample. Almost 40% of them have their distances measured with high precision using the Hubble Space Telescope. Currently, the LV is the most representative and least selection-affected sample of dwarf galaxies suitable for testing the standard $\Lambda$CDM paradigm at the shortest cosmological scales. We discuss the H II properties of dwarf galaxies in different environments and the star formation rates in these systems as determined from $FUV$ - and H$\alpha$-survey data. We also pay certain attention to the baryonic Tully-Fisher relation for low-mass dwarf galaxies. We also point out that LV dwarfs are important `tracers' for determining the total masses of nearby groups and the nearest Virgo cluster.

Equations

$$M_T=16\pi G^{-1}⟨\Delta V^2{R}_p⟩,$$

$$(M_{\mathrm{H}\mathrm{I}}/M_{\odot })=2.36\times 10^5{D}^2{F}_{\mathrm{H}\mathrm{I}},$$

$$\log (SFR)=2.78+2\log D-0.4m_{FUV}^c,$$

$$\log SFR=8.98+2\log D+\log F_c(\mathrm{H}\alpha ),$$

$$\begin{array}[]{rcl}P&=&\log(SFR\times T_{0}/M_{*}),\\ F&=&\log(1.85M_{\rm H\,I}/SFR\times T_{0})\end{array}$$

$$\log (M_{\mathrm{bar}})=2.59\log (W_{50})+3.84,$$

$$M_T=({\pi }^2/8G)R_0^3{H}_0^2/f^2({\Omega }_m),$$

$$(M_T/M_{\odot })=2.12\times 10^{12}(R_0/\mathrm{Mpc}{)}^3.$$

Full text

1 INTRODUCTION

When compiling catalogs of galaxies astronomers usually limit the sample by a certain limiting magnitude or a certain smallest angular diameter of objects. Theoreticians modeling the evolution of the large-scale structure of the Universe need volume limited catalogs compare their computations with observations. Because of the enormous variety of galaxies in terms of size (by a factor of 1000) and luminosity (by a factor of a million), magnitude- and distance-limited samples have very few objects in common.

A distance-limited sample contains a much higher fraction of low-luminosity objects (dwarfs) than usual catalogs. However, to compile such a sample one needs accurate data about the individual distances to galaxies. For distant galaxies their redshift $z$ is quite a suitable distance indicator. At the same time, in the nearby volume, where dwarfs systems can be discerned, Hubble distances $D=cz/H_{0}$ are not reliable because of the peculiar velocities. Kraan-Korteweg and Tammann kra1979:Karachentsev_n_en were the first to attempt compiling a catalog of nearby galaxies. They composed a list of 179 galaxies across the entire sky except for he virial domain of Virgo cluster with Local-Group reference frame radial velocities $V_{\rm LG}<500$ km s*-1*.

Compiling a representative sample of nearby galaxies became a feasible task after the launch of the Hubble Space Telescope (HST). In HST images taken in two colors galaxies are seen resolved into stars, making it possible to determine the position of the tip of the red-giant branch (TRGB) and use it to estimate the distance to the galaxy with an accuracy of 5–10%. This method is applicable to practically all galaxies containing stellar population older than 2 billion years. Exposures fitting into one orbital period of the satellite allow TRGB distances to be measured to galaxies located out to 11 Mpc from the Sun. The volume of the region of this radius is usually referred to as the Local Volume (LV). Our brief review focuses on the main properties of low-luminosity galaxies within $D=11$ Mpc.

As is evident from an analysis of the disk galaxies of increasingly lower stellar mass, the signs of the spiral structure in these objects begin to get fuzzy at masses $M_{*}\leq 1\times 10^{9}M_{\odot}$. Such a mass is intermediate between those of the two Milky-Way satellites—the Large and Small Magellanic Clouds. At the same time, below this critical mass galaxies loose signs of the central starlike core, which is usually associated with a massive black holes. Galaxies with masses smaller than $10^{9}M_{\odot}$ are usually called dwarf stellar systems. The maximum amplitude of rotation velocity in these systems, $V_{m}\leq 50$ km s*-1*, exceeds only slightly the characteristic velocity of turbulent motions of gas clouds. In other words, random chaotic events play an important part in the world of dwarf galaxies.

Van den Bergh vanB1959:Karachentsev_n_en carried out a systematic search for dwarf galaxies on (POSS-I) images. A total of 243 dwarf galaxies got DDO designations. Later, Karachentseva kara1968:Karachentsev_n_en explored the same POSS-I images to find 318 more dwarf galaxies (KDG) with $2^{\rm m}$–$3^{\rm m}$ lower luminosities and surface brightness compared to DDO objects. Karachentseva and Sharina kara1988:Karachentsev_n_en combined the above lists with the results of the searches for dwarf galaxies performed by other authors including the searches carried out in Southern-sky images (ESO/SERC), to compile the "Catalog of Low Surface Brightness Dwarf galaxies’’, which included 1500 objects distributed across the entire sky.

After the release of the Second Palomar Observatory Sky Survey (POSS-II) carried out on fine-grain plates Karachentseva and her colleagues performed systematic searches and found 600 more dwarf galaxies with typical surface brightness levels lower than 25m/\Box\hbox{{}^{\prime\prime}} kara1998:Karachentsev_n_en ; kara1999:Karachentsev_n_en ; kara2000:Karachentsev_n_en ; kar2000:Karachentsev_n_en ; huch2001a:Karachentsev_n_en . Follow-up 21-cm line radial-velocity measurements of these objects showed that most of them are nearby dwarf systems huch2000:Karachentsev_n_en ; huch2001b:Karachentsev_n_en ; huch2003:Karachentsev_n_en .

Many new dwarf galaxies were resolved into stars on images taken with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences, making it possible to estimate the distances to these galaxies from the luminosities of their brightest blue and red supergiants maka1997:Karachentsev_n_en ; geo1997:Karachentsev_n_en ; tik1998:Karachentsev_n_en ; sha1999:Karachentsev_n_en . The researchers from the Special Astrophysical Observatory of the Russian Academy of Sciences found three new members of the Local group among many nearby objects: LGS-3 kara1976:Karachentsev_n_en ; mil2001:Karachentsev_n_en , Cas dSph, and Peg dSph tik1999:Karachentsev_n_en . Note, just for fun, that several dozen dwarf galaxies found by Karachentseva, were later rediscovered and renamed by other authors. The most recent example is the diffuse dwarf system KKSG4 kar2000:Karachentsev_n_en , which was rediscovered by van-Dokkum et al. vanD2018:Karachentsev_n_en , which they named NGC 1052-DF2.

Modern large-area CCD surveys: SDSS aba2009:Karachentsev_n_en , Pan-STARRS1 cha2016:Karachentsev_n_en , and blind 21-cm surveysHIPASS zwa2003:Karachentsev_n_en ; kor2004:Karachentsev_n_en and ALFALFA gio2005:Karachentsev_n_en ; hay2011:Karachentsev_n_en brought about the discovery of many gas-rich dwarf galaxies. Dedicated CCD surveys of the vicinity of the neighboring Andromeda galaxy M 31 iba2007:Karachentsev_n_en , Magellanic Clouds drl2015:Karachentsev_n_en , and also the neighborhoods of other nearby massive galaxies—M 81, Cen A, M 101, M 106 chi2009:Karachentsev_n_en ; mul2017:Karachentsev_n_en ; vanD2014:Karachentsev_n_en ; kim2011:Karachentsev_n_en —proved to be very productive.

In the immediate vicinity of the Milky Way and the Andromeda galaxy several dozen ultrafaint dwarf systems were found that could be resolved into stars and whose sizes (about $10$ pc) and stellar masses (about $10^{5}M_{\odot}$) are comparable with those of globular clusters. Zwicky zwi1957:Karachentsev_n_en proposed to call them ‘‘pygmy’’ galaxies, but this term did not take hold in present-day literature.

Note that besides large telescopes small instruments with apertures of 1 m or less are also successfully used to search for faint satellites of massive nearby galaxies mar2014:Karachentsev_n_en ; kar2015a:Karachentsev_n_en ; jav2016:Karachentsev_n_en . Several dozen hours long exposures on small telescopes made it possible to discover dwarf satellites with surface brightness below $26^{\rm m}$/\Box\hbox{{}^{\prime\prime}}.

Dedicated efforts of different observing teams brought about a rapid increase of the number of known dwarf galaxies in the LV. In 2004 ‘‘A Catalog of Neighboring Galaxies’’ contained 450 objects within 10 Mpc kar2004:Karachentsev_n_en . A decade later, the ‘‘Updated Nearby Galaxy Catalog’’ kar2013a:Karachentsev_n_en already contained 869 galaxies with estimated distances $D<11$ Mpc. As of now, the regularly updated LV galaxy database kai2012:Karachentsev_n_en contains 1170 candidate members of the LV sample. Various data about these galaxies are available at http://www.sao.ru/lv/lvgdb. Dwarf galaxies with $M_{*}<9$ dex make up about 85% of this sample.

2 BASIC PROPERTIES OF THE SAMPLE OF GALAXIES IN THE LOCAL VOLUME

We included a galaxy into the LV if its distance estimated using some method did not exceed 11 Mpc. In the cases where only the radial velocity of the galaxy was known it had to be $V_{\rm LG}<600$ km s*-1* for the galaxy to be included into the LV sample. Figure 1 shows the picture of the Hubble flow of galaxies in the LV.

The distances $D$ of the galaxies are measured with respect to the observer and the radial velocities $V_{\rm LG}$ are corrected for the motion of the observer relative to the mass center of the Local group kar1996:Karachentsev_n_en .

Galaxies with distance estimates obtained using different methods are shown by differ symbols. About 90% galaxies within $D<6$ Mpc have precise photometric distance estimates based on TRGB, supernovae (SN), Cepheids (Cep), or surface-brightness fluctuations (SBF) and accurate to at least within 10%. More than half of all TRGB based measurements use HST observations performed within the framework of programs proposed by the staff members of the Special Astrophysical Observatory of the Russian Academy of Sciences. Most of the distances near the far boundary of the LV are estimated via the Tully–Fisher (TF) method, fundamental plane (FP), from the planetary nebula luminosity function (PNLF), of based on the magnitudes of the brightest stars (BS). The accuracy of these methods is not better than 20%. We adopted kinematic (Hubble) distances for some of the galaxies with $V_{\rm LG}<600$ km s*-1*. The dispersion of galaxy velocities at small distances $D$ is due to the virial motions of galaxies in groups. At $D>7$ Mpc effects of coherent streams begin to show up: fall of galaxies toward the nearest massive attractor in Virgo cluster and the motion of galaxies away from the center of the Local cosmic void (the so-called phenomenon of ‘‘local velocity anomaly’’). It follows from these data that selecting LV galaxies only by condition $V_{\rm LG}<600$ km s*-1* would introduce significant distortions in the local Hubble flow pattern. On the average, the slope of the ‘‘velocity–distance’’ relation in Fig. 1 can be described quite well by the Hubble parameter $H_{0}=73$ km s*-1* Mpc*-1*.

Figure 2 shows the distribution of LV galaxies in the $K$-band luminosity–distance $D$ plane. The designations of galaxies by different symbols are the same as in Fig. 1. Given the $M_{*}/L_{K}\!=\!1.0M_{\odot}/L_{\odot}$ bel2003:Karachentsev_n_en mass-to-luminosity ratio, luminosity $L_{K}$ can be used as a proxy of the stellar mass of the galaxy. The dashed line separates dwarf galaxies ($M_{*}\!<\!1\times 10^{9}M_{\odot}$) from luminous galaxies. The solid line corresponds to the apparent magnitude m_{K}=15\hbox{,.!!^{\rm m}}0, which approximately corresponds to the photometric limit for all-sky searches for LV galaxies. The distribution of galaxies relative to this curve is indicative of a significant loss of ultrafaint objects with masses $\log(M_{*}/M_{\odot})<6$ at the outskirts of the volume.

Figure 3 shows the distribution of average $B$-band surface brightness values of galaxies of our sample. The circles and asterisks show late-type ($T=9$ and $10$) dwarf and late-type ($T=5$, $6$, $7$, and $8$) spiral galaxies, respectively. Most of the galaxies have their average surface brightness levels in the $SB=[22;26]$ m/\Box\hbox{{}^{\prime\prime}} interval, which corresponds to 100% and 3% moonless night-sky brightness level, respectively. The broadest surface-brightness interval, $SB=[21;30]$ m/\Box\hbox{{}^{\prime\prime}}, is spanned by the satellites of the Milky Way and Andromeda galaxy. Most of these galaxies were discovered only when they were resolved into individual stars. We can now extrapolate the situation in the Local group to the entire LV assuming that about half of all very low surface-brightness dwarf galaxies are lost in distant parts of the LV. Some ultracompact dwarf galaxies like UCD 320, UCD 330 can also be missed because of their almost starlike appearance.

3 SPACE DISTRIBUTION OF NEARBY DWARFS

About 52% of dwarf galaxies reside in regions of gravitational influence of luminous galaxies like the Milky Way and M31 and form groups with sizes of about 200–300 kpc around these large galaxies. The remaining nearby dwarfs are distributed among groups clustering into diffuse filamentary and flat structures. On the whole, dwarf and normal galaxies concentrate toward the plane of the Local supercluster centered on Virgo cluster of galaxies.

The two panels in Fig. 4 show the distribution of galaxies in the nearby part of the LV within the radius $D=8$ Mpc. The left panel shows the distribution of galaxies in the plane of the Local supercluster without objects at high latitudes $|SGZ|>2$ Mpc. Massive and dwarf galaxies are shown by circles of different size. Besides well-defined compact groups around M 81 and Cen A, a diffuse Canes Venatici cloud can be seen at the top of the figure, which consists mostly of dwarf galaxies. As is evident from the figure, groups of galaxies are not distributed randomly, but associate into filaments. Dwarf galaxies inside groups are often arranged into flat structures with signs of coherent motions iba2013:Karachentsev_n_en ; mul2018:Karachentsev_n_en .

In the edge-on view of the Local ‘‘wall’’ (Fig. 4b) a large empty region can be seen toward the north pole of the supercluster at $|SGZ|>2$ Mpc populated by only a few dwarf galaxies. According to Tully tul1988:Karachentsev_n_en , this Local cosmic void extends for more than 20 Mpc. An analysis of the radial velocities of galaxies shows that the entire flat structure at $|SGZ|<2$ Mpc moves toward ‘‘$-SGZ$’’ from the center of the Local void at a velocity of about 280 km s*-1* tul2008:Karachentsev_n_en .

Dwarf galaxies can be used as ‘‘tracers’’ to determine the mass of the central luminous galaxy. We assume that satellites move in randomly oriented orbits with an average eccentricity of $\langle e^{2}\rangle=1/2$ to obtain the following estimate for the total mass:

[TABLE]

where $\Delta V$ and $R_{p}$ are the difference of the radial velocities of the satellite and the main galaxy and its projected separation from the main galaxy, respectively, and $G$ is the gravitational constant.

Inside the LV at Galactic latitudes |b|>15\hbox{{}^{\circ}} there are a total of 21 galaxies with stellar masses $\log(M_{*}/M_{\odot})\geq 10.5$. The data about these galaxies are listed in Table 1: the first column gives the name of the galaxy; the second and third columns, its distance and radial velocity, respectively; the fourth and the fifth columns, the magnitude and total (orbital) mass of the galaxy111For completeness, the parameters of other three massive galaxies are given, which are located at low Galactic latitudes and whose data are not quite reliable because of strong extinction.. About half of the dwarf population of the LV are located inside the regions of influence of these giant galaxies. It follows from the data presented here that the typical total-to-stellar mass ratio is $M_{T}/M_{*}\simeq 32$. A detailed analysis of the statistics of the $M_{T}/M_{*}$ ratios galaxies of different morphological types can be found in kar2014a:Karachentsev_n_en ; kar2014b:Karachentsev_n_en .

Note that the dwarf galaxies in groups (suites) around massive galaxies are mostly of the dSph type with almost total lack of gas and young stellar population. The dwarf galaxy population of the general field, on the contrary, is dominated by irregular (dIr) and blue compact galaxies (BCD), in the stage of ongoing star formation. Dwarf galaxies with their ‘‘shallow’’ potential wells are believed to easily loose gas while moving through the halo of their massive neighbor thereby exhausting the potential for further star formation. However, recently, ‘‘dead’’ spheroidal galaxies KKR 25 kar2001:Karachentsev_n_en ; mak2012:Karachentsev_n_en , Apples 1 pas2005:Karachentsev_n_en , KKs 3 kar2015b:Karachentsev_n_en , and KK 258 kar2014c:Karachentsev_n_en have been found located quite far from their nearest neighbors. The cause of their suppressed activity so far remains unclear.

4 H I-PROPERTIES OF DWARF GALAXIES IN DIFFERENT ENVIRONMENTS

The morphology of dwarf galaxies is to a significant degree determined by the availability of large reserves of gas, which determine the possibility of further star formation detected by H$\alpha$ emission flux or in far ultraviolet.

Table 2 gives a clue as to extent to which LV dwarfs have been studied in the HI 21-cm line and in other parts of the electromagnetic spectrum. The top row of the table gives the total number of galaxies in the LV and separately the number of dIr $(T=10)$, Im+BCD $(T=9)$, and dSph+dE-type $(T<0)$ dwarf galaxies. Objects located in the zone of strong Galactic extinction (A_{B}>3\hbox{,.!!^{\rm m}}0), and those located outside $D=11.0$ Mpc are excluded. The second and third rows of the table give the numbers of galaxies of the above types that were observed and detected in the H I line. As is evident from the Table, H I-surveys cover 75% of all LV galaxies. The detection levels are equal to 90% and 94% for dIr and Im+BCD type galaxies and only 16% for dSph+dE type galaxies. The small observed number of undetected irregular dwarfs and the small number detected spheroidal dwarfs is due to the presence of the population of dwarf ‘‘transient’’ systems (Tr) with morphology intermediate between dIr and dSph. Another example of such objects, which cannot be clearly classified, is LGS-3—a peripheral satellite of the Andromeda galaxy.

The hydrogen mass of a late-type galaxy determined by the formula

[TABLE]

where $F_{\rm H\,I}$ is the H I line flux in Jy km s*-1*, correlates quite closely with the stellar mass of the galaxy.

Figure 5 reproduces the distribution of the number of late-type dwarf (circles) and spiral (asterisks) LV galaxies by their hydrogen and stellar masses. The straight line corresponds to the condition $M_{\rm H\,I}=M_{*}$. The galaxies with upper $F_{\rm H\,I}$ flux limits are shown by open circles. These data imply the existence of many dwarf systems where the hydrogen mass has not yet been transformed into stellar mass. Such cases occur most often among the least luminous galaxies. On the contrary, disks of luminous spiral galaxies mostly consist of the stellar component, i.e., they show a more advanced evolutionary stage.

We already pointed out above that the closer the dwarf galaxy is to its massive neighbor, the lower is its gas content. The effect of the ambient density on the relative content of hydrogen mass in LV galaxies was analyzed in detail in kar2018a:Karachentsev_n_en . To estimate the ambient density, the above authors used three different dimensionless parameters: $\Theta_{1}$, the relative local density created by the most important neighbor in terms of mass and distance; $\Theta_{5}$, the relative density created by the five most important neighbors, and $\Theta_{j}$, the relative $K$-luminosity density inside the sphere of radius 1 Mpc in the units of the average global luminosity density. All three parameters are expressed in logarithmic scale.

Figure 6 shows the behavior of the $M_{\rm H\,I}/M_{*}$ ratio for late-type dwarf and spiral galaxies depending on tidal index $\Theta_{1}$. Objects where only the upper $F_{\rm H\,I}$ flux limit is measured are shown by open circles. The domain of negative $\Theta_{1}$ corresponds to isolated galaxies and the right-hand side, where $\Theta_{1}>0$, is populated by satellites of primary galaxies in groups. The scatter of $M_{\rm HI}/M_{*}$ ratios is rather large and amounts to three orders of magnitude. In extreme cases—BST 1047+1156, And-IV and ESO 215-009—the hydrogen mass of the dwarf galaxy is one order of magnitude higher than its stellar mass. The average $M_{\rm H\,I}/M_{*}$ ratio decreases slightly from isolated galaxies to group members. This tendency becomes more pronounced if we take into account the fact that the $\Theta_{1}>0$ domain contains many spheroidal dwarfs, which were not detected in the H I line. A detailed analysis of these data is difficult to perform because of the low resolution of the radio telescopes: the H I flux of many dwarfs in groups can hardly been distinguished against the background flux of the more massive neighbor.

The small drift of $M_{\rm H\,I}/M_{*}$ on $\Theta_{1}$ indicates that the hydrogen-to-stellar mass ratio in late- type galaxies is primarily determined by their internal processes and only secondly to ambient density.

5 STAR FORMATION RATE IN DWARFS IN GROUPS AND IN THE FIELD

The far ultraviolet survey of galaxies carried out with GALEX gil2007:Karachentsev_n_en orbital telescope detected $FUV$-fluxes in a large number of galaxies located outside the Milky Way zone. According to lee2009:Karachentsev_n_en ; lee2011:Karachentsev_n_en , the integrated star-formation rate in the units of $(M_{\odot}\,{\rm yr}^{-1}$) can be written as

[TABLE]

where $m^{c}_{FUV}$ is the apparent $FUV$-band magnitude of the galaxy corrected for Galactic and internal extinction. The main contributors to the $FUV$-flux are young stars with characteristic age of about 100 Myr.

It follows from Table 2 that GALEX survey area covers 85% of LV galaxies and 72% them were actually detected in the $FUV$ band. The fraction of detected galaxies among dIr and Im+BCD-type dwarfs was equal to 88% and 99%, respectively, whereas only 28% of objects among dSph+dE-type galaxies exhibited appreciable $FUV$ flux. Note that $FUV$-band fluxes of some of the spheroidal galaxies with large angular sizes may be false because of projected background sources.

Figure 7a shows the distribution of late-type dwarf $(T=9,\leavevmode\nobreak\ 10)$ and spiral $(T=5$–$8)$ galaxies by star-formation rate and stellar mass. The dwarf and spiral galaxies are shown by circles and asterisks, respectively. The cases where only the upper flux limits were measured are shown by open circles. The dashed line corresponds to the cosmological time of 13.7 Gyr during which the galaxy reproduces the observed stellar mass with the observed rate of star formation. Hence dwarf and spiral galaxies obey the same relation and the current rate of star formation in most of the galaxies is quite sufficient to reproduce their stellar mass.

Figure 7b shows the distribution of late-type LV galaxies by star-formation rate and hydrogen mass. Designations are the same as in the top panel. The straight line corresponds to the slope of 1.4 known as the Schmidt–Kennicutt relation for individual sites of star formation in galaxies. The data presented show that integrated hydrogen mass and integrated rate of star formation of late-type galaxies follow quite well the dependence established for sites of star formation located inside them.

In late-type galaxies star-formation rate closely correlates with stellar mass and therefore specific star-formation rate $sSFR=SFR/M_{*}$ referred to unit stellar mass is usually employed to characterize the star-forming activity of these systems.

Figure 8 shows the distribution of late-type LV galaxies by $sSFR$ and tidal index $\Theta_{1}$. Galaxies with upper $FUV$ flux limits are shown by open circles. Note that parameter $sSFR$ has the dimension of yr*-1*, which coincides with that of the Hubble parameter $H_{0}=13.7$ Gyr*-1*. Galaxies with $sSFR=H_{0}$ (the dashed line) are capable of reproducing their stellar mass with the observed rate of star formation during the cosmological time $H_{0}^{-1}$. It follows from these data that the scatter of $sSFR$ values increases from isolated dwarfs to group members. This pattern is due to the increase of the fraction of objects in groups with low star-formation rates because of the likely ‘‘expulsion’’ of gas from the dwarf galaxy as it moves through dense intergalactic medium. Unlike the blurry lower boundary of the distribution of galaxies by $sSFR$, the upper boundary appears rather sharp with the limit $sSFR_{\rm max}\simeq-9.4$ dex, which depends only slightly on ambient density kar2013b:Karachentsev_n_en ; kar2018a:Karachentsev_n_en . Only a few dwarf galaxies of the LV (Mrk 36, NGC 1592) at the stage of ongoing star formation are located slightly above this limit. The existence of this limit, which is similar to the Eddington limit of stellar luminosity, is indicative of hard feedback of the process: the stronger the ‘‘epidemics’’ of star formation in the galaxy, the less resources of gas remain to sustain it. The value of this limit $sSFR_{\rm max}\simeq 5.5\times H_{0}$ may serve as an important characteristic of the process of star formation at the present epoch $(z=0)$.

It is evident from Fig. 8 that the amplitude of the drop of the average $sSFR$ from isolated dwarfs to group members is small compared to the dispersion of the specific rate of star formation. This indicates that the variety of observed star formation rates in late-type dwarf galaxies is primarily determined by their internal parameters and not by the ambient effects.

Measurements of the integrated H$\alpha$-flux of a galaxy can be used to determine the star-formation rate on a characteristic time scale on the order of 10 Myr. According to ken1998:Karachentsev_n_en ,

[TABLE]

where $SFR$ is in the units of ($M_{\odot}\,{\rm yr}^{-1}$), and the flux (in erg cm2 s*-1*) is corrected for Galactic and internal extinction. The most extensive H$\alpha$ survey of LV galaxies was performed with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. During the last ten years homogeneous H$\alpha$-images were obtained for more than 400 galaxies (see kai2019:Karachentsev_n_en and references therein). Combined with the data by other authors, H$\alpha$-images are currently available for 61% of LV galaxies. Among them H$\alpha$ emission was detected in 85% of irregular dwarfs, 95% of Im+BCD-type objects, and in 41% of spheroidal (dSph+dE) systems. Curiously, some classical dSph dwarfs, e.g., DDO 44, contain small sites of star formation, which can be seen in H$\alpha$ kar2011:Karachentsev_n_en .

A comparison of the $SFR$ estimates inferred from H$\alpha$-line and $FUV$-band fluxes gives the idea of the variations of star-formation rates in dwarf galaxies on a time scale on the order of 10–100 Myr. Figure 9 reproduces $SFR({\rm H}\alpha)/SFR(FUV)$—the distribution of the ratio for late-type galaxies as a function of stellar mass. The above data lead us to conclude that:

• (a) Mutual calibration of the empirical $SFR({\rm H}\alpha)$ and $SFR(FUV)$ values by formulas (3) and (4) is quite good for late-type spiral galaxies, which are dominated by disks.
• (b) The $SFR({\rm H}\alpha)/SFR(FUV)$ ratio on the average decreases from spirals to progressively less massive dwarfs. Various causes of this pattern were discussed in pfl2009:Karachentsev_n_en ; wei2012:Karachentsev_n_en ; fum2011:Karachentsev_n_en , however, it is still not entirely clear why H$\alpha$-flux-determined star-formation rates in dwarfs are underestimated.
• (c) The dispersion of the $SFR({\rm H}\alpha)/SFR(FUV)$ ratio increases significantly with decreasing mass of the galaxy. This can be naturally explained by starburst activity, which becomes relatively more pronounced in low-mass objects.

Dependence of the $SFR({\rm H}\alpha)/SFR(FUV)$ ratio on other parameters—apparent axial ratio of the galaxy, its morphological type, ambient density—were analyzed in kar2018a:Karachentsev_n_en .

The evolutionary state of the ensemble of LV dwarf galaxies can be conveniently characterized by the ‘‘Past–Future’’ (PF) diagnostic diagram where dimensionless parameters

[TABLE]

do not depend on the errors of the estimated distance to the galaxy kar2007:Karachentsev_n_en ; kar2013b:Karachentsev_n_en .

Here parameter $P$ is the specific star-formation rate normalized to cosmological time $T_{0}=13.7$ Gyr. Parameter $F$ characterizes the time (in the units of $T_{0}$) during which the galaxy exhausts its available reserves of gas at the observed star-formation rate $SFR$. The coefficient 1.85 is introduced to take into account the contribution of He and $H_{2}$ to the total mass of gas fuk2004:Karachentsev_n_en . Note that a galaxy with the coordinates $P=0$, $F=0$ is capable of reproducing its observed stellar mass during time $T_{0}$ and has sufficient reserves of gas to sustain the observed star-formation rate over yet another time interval $T_{0}$.

Figure 10 shows the PF diagram for late-type $(T=9,\leavevmode\nobreak\ 10)$ LV dwarf galaxies. The centroid of the dwarf distribution is located near the coordinate origin. Hence the typical observed star-formation rate in dwarfs is quite sufficient for reproducing their observed stellar masses, and, on the whole, the population of dwarf galaxies is halfway in processing its gas into stars.

Another important feature of the PF diagram is that the diagonal extent of the distribution of dwarfs in parameters $P$ and $F$. This is evidently due to the starburst activity. During a starburst dwarf galaxies like Mrk 36, Mrk 475 find themselves in the bottom right part of the PF diagram and as the starburst fades they move to the top left quadrant where passive dwarfs like DDO 120 and KDG 52 reside. The proportion of dwarfs in quadrants [$P>0$, $F<0$] and [$P<0$, $F>0$] is of about 3:1, which indicates that dwarf galaxies spend more time in the quiescent phase compared to the starburst phase. The presence of ‘‘dead’’ dwarfs of dSph and dE types, which are not represented in Fig. 10, increases this ratio even further.

It is important that such interpretation is based on the assumption that the galaxy evolves in the ‘‘closed box’’ mode. The inflow of intergalactic gas observed in some galaxies may have appreciable effect on the evolutionary tracks of galaxies in the PF diagram.

6 BARYONIC TULLY–FISHER RELATION

It follows from the data in Figs. 5 and 6 that about 40% of late-type dwarf galaxies in the LV have hydrogen masses greater than their stellar masses. Given the presence of He and H2, gas-rich dwarfs are the dominating population of the LV.

The classical Tully–Fisher relation tul1977:Karachentsev_n_en expresses linear relationship between the logarithm of the width of the H I-line, $W_{50}$, and absolute magnitude (or logarithm of the stellar mass) of the galaxy. In the domain of dwarf galaxies the linearity of the TF relation systematically breaks down because of the contribution of the gaseous component to the total baryonic mass of the galaxy. This was first noted by McGaugh mcg2005:Karachentsev_n_en ; mcg2012:Karachentsev_n_en .

The abundance of LV galaxies with accurately measured distances made it possible to extend the baryonic Tully–Fisher relation (bTF) to the domain of low masses down to $\log(M_{\rm bar}/M_{\odot})\simeq 6$. According to kar2017:Karachentsev_n_en , the bTF relation for 330 galaxies in the LV has the form shown in Fig. 11. The regression line in this figure is described by the following formula:

[TABLE]

where the baryonic mass is in $M_{\odot}$ and the width of the H I at half maximum, in km s*-1*. In addition to galaxies with accurately measured distances we also show in Fig. 11 objects with distances estimated based on their membership in known groups.

The standard deviation on the bTF diagram is equal to 0.39 dex, making it possible to estimate the distances of other gas-rich dwarf galaxies with a typical error of 0.195 dex. The main contributor to this error are $W_{50}$ measurement errors and photometric errors. The error of the bTF distance estimates for galaxies with accurate observational data can be reduced down to 0.10 dex. Further analysis shows kar2017:Karachentsev_n_en that incorporating a second parameter into equation (6), such as surface brightness of the galaxy or the $M_{\rm H\,I}/M_{*}$, decreases only slightly the scatter on the diagram.

7 DWARF GALAXIES AND LOCAL DISTRIBUTION OF DARK MATTER

The presence of dwarf satellites with accurately measured radial velocities and distances around nearby massive galaxies made it possible to determine the total (orbital) masses on the scale length of virial radius $R_{\rm vir}\simeq 250$ kpc. These estimates for 21 principal LV galaxies are listed above in Table 1.

Lynden–Bell lyn1981:Karachentsev_n_en proposed an independent method for determining the total mass of a group (cluster).

A galaxy group as overdensity distorts the Hubble flow of surrounding galaxies slowing down their velocities. As a result, the zero-velocity surface forms around the group, which separates the collapsing region from the zone of cosmic expansion. In the spherically symmetric case the radius $R_{0}$ of the zero-velocity surface is related to the total mass $M_{T}$ of the group by the formula:

[TABLE]

where dimensionless factor $f$ depends on the average mass density and varies from 1 to 2/3 with $\Omega_{m}$ varying from 0 to 1. In the standard $\Lambda$CDM model with $\Omega_{m}=0.24$, $\Omega_{\lambda}=0.76$, and $H_{0}=73$ km s*-1* Mpc*-1* from spe2007:Karachentsev_n_en the $M_{T}(R_{0})$ formula acquires the form:

[TABLE]

The distribution of velocities and distances of dwarf galaxies within 3 Mpc of the centroid of the Local group was analyzed repeatedly by a number of authors ekh2001:Karachentsev_n_en ; kar2002:Karachentsev_n_en ; kar2009:Karachentsev_n_en . Figure 12 shows the most complete version of this diagram (Fig. 4a from kas2018:Karachentsev_n_en ). Non-isolated ($\Theta_{1}>0$) galaxies burdened with virial velocities are excluded. The Hubble regression line crosses the zero-velocity line at the level of $R_{0}\!=\!(0.95\!\pm\!0.03)$ Mpc kas2018:Karachentsev_n_en , which corresponds to the Local group mass of $M_{T}\!=\!(1.8\!\pm\!0.2)\!\times\!10^{12}\,M_{\odot}$. This estimate proved to be somewhat below the total mass of the Milky Way and Andromeda galaxy: $M({\rm MW}+{\rm M\,31})=2.87\times 10^{12}M_{\odot}$.

Fairly high accuracy of the $R_{0}$ and the total mass of the LG based on external motions of galaxies is due to ‘‘coldness’’ of the Local Hubble flow where the dispersion of radial velocities is only $\sigma_{V}=42$ km s*-1*kas2018:Karachentsev_n_en .

Kashibadze and Karachentsev kas2018:Karachentsev_n_en joined suites of dwarfs surrounding other dominating galaxies of the LV—M 81, Cen A, NGC 4736, M 101, etc.—to estimate the radius $R_{0}$ of the ‘‘synthetic’’ LV group. The $R_{0}=(0.92\pm 0.02)$ Mpc value determined from a combined sample of 14 groups corresponds to the total synthetic group mass of about $1.7\times 10^{12}M_{\odot}$, which is about 60% of the typical virial mass of nearby groups. The fact that the estimate of the total mass based on external motions of galaxies is made on a scale length that is 3–4 times greater than the virial radius led Kashibadze and Karachentsev kas2018:Karachentsev_n_en to conclude that there is no appreciable amount of dark matter in the outskirts of the Local group and other neighboring groups of galaxies.

A similar approach to determining the total mass was also applied to the nearest Virgo cluster of galaxies located at a distance of 16.5 Mpc. Between the Local group and Virgo cluster there are about 30 dwarf galaxies with the distances measured using observations made with the Hubble Space Telescope kar2014d:Karachentsev_n_en ; kar2018b:Karachentsev_n_en .

The radius of the LV is equal to 2/3 of the distance to Virgo cluster. Such an extent of the LV allows tracing the effect of the fall of galaxies onto the cluster and determine the radius $R_{0}$ with high accuracy. Figure 13 shows the pattern of the Hubble flow of galaxies relative to the center of Virgo cluster. Galaxies with accurately measured velocities are shown by circles. The domain of virial motions inside the cluster proper is shown by grey color. The lack of observational data about the tangential components of galaxy velocities makes it necessary to adopt certain assumptions concerning their dominating motion pattern. The two panels of the figure correspond to the extreme assumptions about the pattern of motions of galaxies near the cluster: the case of a minor attractor, when Hubble expansion prevails, and major attractor dominated by radial motions toward the cluster center. According to these data with the uncertainty of the pattern of galaxy motions taken into account, the radius of the zero-velocity sphere around Virgo is $R_{0}=(7.32\pm 0.28)$ Mpc, which corresponds to the total cluster mass of $M_{T}=(8.3\pm 0.9)\times 10^{14}M_{\odot}$. This estimate agrees well within the quoted errors with the virial mass of Virgo cluster $7.5\times 10^{14}M_{\odot}$ based on the data adopted from tul1984:Karachentsev_n_en . Shaya et al. sha2017:Karachentsev_n_en obtained practically the same estimate of the total mass of Virgo by numerically modeling galaxy trajectories.

Karachentsev and Telikova kar2018c:Karachentsev_n_en used the most complete available data about the distances and halo masses of nearby galaxies to reconstruct the distribution of visible and dark matter in the LV. Figure 14a shows the integrated stellar-mass profile in the units of critical density. The lower line corresponds to the contribution of the principal LV galaxies listed in Table 1 and the upper line, the contribution of the entire LV population to the luminosity density. The horizontal line fixes the average cosmic density of stellar mass according to fuk2004:Karachentsev_n_en . As is evident from the figure, the LV exhibits excess of stellar density over its global value on all scales out to the distance of 11 Mpc.

Figure 14b, which shows the distribution of the dark-matter density, demonstrates a totally different pattern. Here the lower line shows the contribution of the halos of the principal galaxies from Table 1, and the middle and upper line correspond to the total contribution of all galaxies computed assuming (1) that the $M_{T}/M_{*}=32$ kar2014b:Karachentsev_n_en ratio is the same for all galaxies or (2) that $M_{T}/M_{*}$ for field galaxies increases toward groups and dwarf galaxies tul2015:Karachentsev_n_en . Differences between the three lines are small because the main contributors to the matter density in the LV are two dozen most massive galaxies. It is remarkable that the average density of dark matter within 11 Mpc is equal to only $\Omega_{m}=0.17$, i.e., the LV is a low-density region in terms of this parameter.

This strange result also shows up in a much greater volume. Makarov and Karachentsev mak2011:Karachentsev_n_en analyzed the local distribution of visible and dark (virial) mass based on their catalog of groups of galaxies. The sequences of asterisks in the panels of Fig. 15 show the profiles of stellar and virial mass according to the data of the above authors. The average density values in the LV are shown by the diamond signs. It follows from the data in the top panel that the average local density of visible matter shows a small excess compared to the global value out to a distance of 40 Mpc. However, the density of dark matter proves to be rather low smoothly decreasing down to $\Omega_{m}=0.09\pm 0.03$ at the distance of 40 Mpc. A similar value, $\Omega_{m}=0.12$–$0.14$, was recently inferred by Kourkchi and Tully kou2017:Karachentsev_n_en from the data in a catalog of groups of galaxies organized in accordance with a different algorithm. The low value of the local density of dark matter compared to its global value ($\Omega_{m}=0.24$–$0.31$) leads one to conclude that the bulk of the mass of the cosmic dark matter is not concentrated in groups and clusters but scattered in the intergalactic space between them.

8 CONCLUSIONS

In recent years comprehensive study of galaxies in the near Universe crystallized into a separate branch of observational cosmology. Numerical simulation of the dynamical evolution of galaxies in terms of the standard $\Lambda$CDM-model has reached the spatial resolution on the scale of the sizes and masses of dwarf galaxies. In the process, the cosmology on small scales has run into well-known problems: observed deficit of low- and very low-mass galaxies, observed lack of the central ‘‘cusps’’ in the rotation curves of dwarf galaxies, and abundance of thin flat structures made of dwarf satellites around massive galaxies. A review of these and other problems of the standard paradigm can be found in kro2016:Karachentsev_n_en . The problems of standard models, which became apparent in studies of dwarf galaxies, provide a powerful stimulus for refining the theoretical scenarios of the formation and evolution of galaxies.

Precise measurements of the radial velocities and distances to galaxies make it possible to determine their peculiar velocities and use these velocities to reconstruct the locations and masses of surrounding attractors. Numerous precise measurements of galaxy distances with the Hubble Space Telescope made the LV a unique laboratory for validating cosmological models as foreseen by Pebbles pee1993:Karachentsev_n_en .

Where is the bulk of the dark mass located: in systems of galaxies or in the space between them? So far, we have no a straight answer to this question. The ever increasing density of data about peculiar velocities in the LV will serve as the most suitable observational material for solving this problem.

Acknowledgements.

We are grateful to the staff members of the Laboratory of Extragalactic Astrophysics and Cosmology of the Special Astrophysical Observatory of the Russian Academy of Sciences S. S. Kaisin, O. G. Kashibadze, G. G. Korotkova, D. I. Makarov, L. N. Makarova, M. E. Sharina, and V. E. Karachentseva for their long-continued assistance in performing this work.

FUNDING

This work was supported by the Russian Foundation for Basic Research (grant no. 18–02-00005).

CONFLICT OF INTEREST

The authors declare that there is no conflict of interest regarding the publication of this article.