Very Thin Disc Galaxies in The SDSS Catalog of Edge-on Galaxies
D. V. Bizyaev, S. J. Kautsch, N. Ya. Sotnikova, V. P. Reshetnikov, A. V. Mosenkov
aa r X i v : . [ a s t r o - ph . GA ] D ec MNRAS , 1–11 (2016) Preprint 6 December 2016 Compiled using MNRAS L A TEX style file v3.0
Very Thin Disc Galaxies in The SDSS Catalog of Edge-onGalaxies
D. V. Bizyaev , ⋆ , S. J. Kautsch , N. Ya. Sotnikova , V. P. Reshetnikov ,and A. V. Mosenkov , , Apache Point Observatory and New Mexico State University, Sunspot, NM, 88349, USA Sternberg Astronomical Institute, Moscow State University, Moscow, Russia Nova Southeastern University, Fort Lauderdale, FL, 33314, USA St.Petersburg State University, 7/9 Universitetskaya nab., St.Petersburg, 199034 Russia Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium Central Astronomical Observatory, Russian Academy of Sciences, 65/1 Pulkovskoye chaussee, St.Petersburg, 196140 Russia
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We study the properties of galaxies with very thin discs using a sample of 85objects whose stellar disc radial-to-vertical scale ratio determined from photometricdecomposition, exceeds nine. We present evidences of similarities between the verythin disc galaxies (VTD galaxies) and low surface brightness (LSB) disc galaxies, andconclude that both small and giant LSB galaxies may reveal themselves as VTD, edge-on galaxies. Our VTD galaxies are mostly bulgeless, and those with large radial scalelength tend to have redder colors. We performed spectral observations of 22 VTDgalaxies with the Dual Imaging Spectrograph on the 3.5m telescope at the ApachePoint Observatory. The spectra with good resolution (R ∼ M ⊙ /pc , which we observe in thecase of very thin, rotationally supported galactic discs. Key words: galaxies: structure, galaxies: edge-on, galaxies: LSB
Extremely thin galaxies with large major-to-minor axes ratio a/b (typically, determined directly from images) have beennoticed in large catalogs of edge-on galaxies since a long timeago, e.g., (Vorontsov-Velyaminov 1967; Karachentsev et al.1993; Kautsch et al. 2006). Edge-on galaxies with largeaxis ratio, e.g. a/b >
9, are often called superthin galax-ies (Goad & Roberts 1979, 1981). Only a few superthingalaxies have been studied thoroughly, such as UGC 7321(Matthews et al. 1999; Matthews 2000; Matthews & Wood2001; Uson & Matthews 2003). A few more large superthingalaxies were studied spectroscopically (Goad & Roberts1981). Several spiral galaxies with large a/b ratio andwithout bulges were observed in HI (Matthews & van Driel2000). A large sample of flat and superthin disc galaxies was ⋆ E-mail: [email protected] analyzed and reviewed by Kautsch (2009) using data of op-tical photometry. The axis ratio a/b used for the superthinselection in the previous studies was often estimated usingfaint outer isophotes in images, sometimes visually, makingthe a/b axial ratio dependent of used photometric depth ofthe images (Karachentsev et al. 1993, 1999). The axis ratioestimated this way also can be biased by the presence of abulge. In this paper we use the radial-to-vertical scale ra-tio ( h/z ), which was automatically determined for a largesample of verified edge-on galaxies by Bizyaev et al. (2014)(”Edge-on disk Galaxies In SDSS”, hereafter EGIS ). Sincesome large low surface brightness (LSB) galaxies with no-ticeable bulges are suspected to have thin LSB discs, wedo not limit this study to bulgeless galaxies only. Instead,we call a galaxy as VTD, i.e. having a very thin disc, if http://users.apo.nmsu.edu/ ∼ dmbiz/EGIS/c (cid:13) Bizyaev et al. its stellar disc’s radial-to-vertical scale ratio h/z is greaterthan 9, independent of the bulge contribution. Below weoutline general properties of our sample of VTD galaxies,consider their connection to cosmological environment, andestimate properties of their very thin discs, which may helpunderstand the marginal star formation conditions necessaryto form disc galaxies. The cosmological framework adoptedthroughout this paper is H = 72 km s − Mpc − , Ω m =0.3, and Ω Λ = 0.7. The large sample of verified edge-on galaxies collected byEGIS (Bizyaev et al. 2014) allows us to select a subsam-ple of VTD galaxies large enough for statistical analysis. Adisadvantage of the EGIS analysis is using a fixed, averagegaussian Point Spread Function (PSF) for all galaxies. Atthe same time, using correct PSF is important in the case ofedge-on galaxies, especially for the objects whose thicknessis comparable to the PSF size. We incorporated the corre-sponding SDSS PSF information to the EGIS data release,and re-ran the photometric profile analysis pipeline with re-alistic PSFs. As a result, we selected 82 galaxies with h/z > r -band).The 1D analysis underestimates the radial-to-verticalscale ratio h/z in the presence of a significant bulge: thescale ratio is biased 10% or more if the bulge-to-total ratiois greater than 0.4 (Mosenkov et al. 2015). In order to findpossible missing galaxies with large bulges and very thindiscs, we formed a subsample of objects with large h/z ra-tios, which are based on the 3D analysis from EGIS. Some ofthose galaxies have been selected by our 1D approach. Theimages of the rest of the objects were visually inspected. Theobjects with noticeable curvature of the galactic midplane,or with small-scale structural elements that can confuse the3D analysis (e.g. edge-on rings or spiral arms) were removedfrom the sample.The resulting sample comprised 14 galaxies with largebulges and visually thin discs. All the galaxies were pro-cessed through the 1D EGIS pipeline again, while theregion for the analysis was adjusted to avoid effects ofthe large bulges. Also, since we expect that stellar andthe dust discs in VTD galaxies have comparable thickness(Dalcanton et al. 2004), in which the 3D structure analy-sis performed by EGIS was not reliable, the thickness of thedust layer was set equal to that of the stellar disc, and the 3Dpipeline was re-run for the selected group of objects. Neitherof these objects showed large enough h/z to be qualified asVTD, so we left the subsample of 82 VTD galaxies unmodi-fied. A well-studied ”prototype”superthin galaxy UGC 7321,and two more large thin galaxies IC 2233 and UGC 711, wereadded to the sample for comparison purposes, despite theirformally determined inverse scale ratio h/z is less than nine.Our final sample comprises 85 VTD galaxies.Our sample is presented in Table 1, which shows EGISname, radial and vertical scales in kpc, the scale ratio, andthe quality flag. The latter indicates ’Y’ if the radial veloc-ity of the galaxy was within the reasonable range (between0 and 30,000 km/s), and also if the galactic color ( r − i )was reported in EGIS. The flag ’N’ indicates that the spa- tial scales are incorrect, whereas the scale ratios calculatedfrom the angular values of the scales are right. Note that theobjects with wrong radial velocities have zeros in the scalecolumns in Table 1. Systematic study of the properties of VTD galaxies is a diffi-cult task without dedicated spectroscopic observations. Justa few galaxies from our sample have information about theirmaximum of rotation curve in the HyperLeda database. Wefind that only 63% of VTD galaxies from our sample haveradial velocities reported by HyperLeda or SDSS .We observed a sample of 24 objects with the Dual Imag-ing Spectrograph (DIS) on the 3.5m telescope at the ApachePoint Observatory (APO). The observing time was issued inhalf-night blocks, and between December 2014 and August2015 we were granted 8 such observing blocks. We observedin a high-resolution mode (B1200/R1200 grating), whichprovides the spectra resolution of about 5000. In many caseswe detect major emission lines, other than H α , available inour optical range (H β , [OIII]4959,5007˚A, [NII]6548,6583˚A,& [SII]6713,6731˚A).Typically, each galaxy was observed with 3 exposuresfrom 5 to 20 minutes long. During the observing nights weobtained a set of biases and dome flats. A Helium-Neon-Argone wavelength calibration lamp was observed immedi-ately after each galaxy at the same position in the sky. Spec-trophotometric standard stars were observed every night.The data reduction was performed with IRAF standardtools, including bias subtraction, flat fielding, wavelengthcalibration, sky line and sky background subtraction, cosmicray removal, and flux calibration. We estimated the heliocen-tric radial velocity of the galactic centre and the maximumrotation velocity V from the spectra for each galaxy. Weused the Hα emission line for it, except for two galaxies inwhich we did not detect any emission lines. In those cases weused the weak NaD absorption lines at 5893˚A and assumedthat we estimate the lower limit of the maximum rotationalvelocity from it.The typical accuracy of the radial velocity and V is 15and 10 km/s, respectively, except for the galaxies withoutthe emission lines, where only a lower limit constraint on themaximum rotational velocity is available. Fourteen galaxiesfrom Table 2 have radial velocities reported by the NEDdatabase . The mean difference between the NED and ourradial velocities is 9 km/s, and the r.m.s. is 23 km/s for thissample of fourteen galaxies. Table 2 shows the object name(in the EGIS catalog), date of observations, total exposuretime, our heliocentric radial velocity, and the amplitude ofthe rotation curve. http://leda.univ-lyon1.fr http://skyserver.sdss.org https://ned.ipac.caltech.edu MNRAS , 1–11 (2016) ery Thin Disc Galaxies Table 1.
Selected Sample of Very Thin Disc GalaxiesEGIS Name h ,kpc z ,kpc h/z (r-i) QualityEON 2.694 -0.892 10.01 0.81 11.0 0.315 YEON 6.305 13.538 0.00 0.00 10.5 0.369 NEON 7.069 24.845 0.00 0.00 11.4 0.403 NEON 8.366 -11.103 16.66 0.81 23.6 0.336 YEON 8.452 -9.540 0.00 0.00 11.3 0.383 N...The table is published in its entirety in the electronic edition.The columns show the galaxy name according to the EGIS catalog (which contains coarse decimal RA and Dec coordinates), the radialscale length, the vertical scale height, the scale ratio, integral color, and the quality flag (see text).
Table 2.
Spectral Observations of Very Thin Disc GalaxiesObject Date Exposure RV V max min km/s km/sEON 2.694 -0.892 11 Aug 2015 35 11452 152EON 17.154 1.641 21 Jun 2015 15 1964 79EON 17.275 19.605 16 Aug 2015 45 12498 96EON 19.768 -0.139 16 Aug 2015 35 5230 141EON 31.087 6.852 11 Aug 2015 40 23516 191EON 44.216 5.686 16 Aug 2015 45 11150 132EON 65.268 18.389 14 Dec 2014 20 16175 232EON 119.500 17.903 14 Mar 2015 60 45001 334 b EON 126.544 1.747 14 Mar 2015 60 16773 162EON 132.574 3.497 14 Mar 2015 45 8519 298EON 175.741 9.394 21 Mar 2015 50 25275 272EON 194.909 6.446 21 Mar 2015 45 6363 107EON 200.709 19.691 a
21 Mar 2015 35 6733 194EON 205.922 54.952 14 Dec 2014 40 19734 317EON 211.189 2.896 21 Mar 2015 50 49931 205 c EON 233.587 57.953 21 Mar 2015 35 29628 301EON 237.173 21.870 a
21 May 2015 45 2160 197EON 253.776 39.578 21 May 2015 45 20885 213EON 266.042 55.180 21 Jun 2015 35 22872 174EON 267.275 64.367 18 May 2015 55 16244 193EON 310.213 -6.850 21 May 2015 50 8555 113 d EON 332.464 7.430 21 Jun 2015 40 3955 92EON 341.857 -1.255 16 Aug 2015 50 26184 202EON 344.455 14.189 21 Jun 2015 45 25896 215 a Not a VTD galaxy, the h/z ratio is close to 6. Used for comparison purposes. b,c No H α line in the spectrum. A line identified as NaD absorption is used. d Raising rotation curve with ring-like features.
The subsample of VTD galaxies is different in both the stel-lar disc scale length and the stellar disc scale height in com-parison to the main sample from EGIS. Figure 1 shows thatthe scale length of VTD discs spans a wide range and isbiased towards larger values (h = 11.6 ± ± z = 1.0 ± z = 1.3 ± MNRAS , 1–11 (2016)
Bizyaev et al.
Figure 1.
The radial scale length (top) and the vertical scaleheight (bottom) of all EGIS galaxies (dashed curve and greyshaded histohram) and of VTD subsample (solid curve). The his-togram for VTD galaxies is arbitrary scaled in the Y-directionin order to better show the plot (the tallest bins have 6 and 13objects in the top and bottom panels, respectively).
Figure 2.
The central face-on surface brightness in the r -bandfor all EGIS galaxies (open histogram) and for the VTD subsam-ple (filled histogram). The VTD galaxies are mostly LSB galaxieswith about 1.5 mag dimmer surface brightness than regular galax-ies in the EGIS catalog. cally significant sample of thin edge-on galaxies will allowus to update the sample of VTD galaxies in the near future. The broad-band colors of our VTD galaxies do not differsignificantly from the main EGIS sample in the color-colordiagram, see Figure 4. The colors of VTD galaxies span therange typical for the regular galaxies. As it is seen in Fig-ure 4, red VTD galaxies tend to have larger scale length.The galaxies in the blue corner of the diagram have shorterscalelength, whereas the smaller galaxies occupy mostly the
Figure 3.
The bulge-to-total ratio in the main EGIS sample(open histogram) in the comparison with the VTD subsample(filled histogram).
Figure 4.
The SDSS colors ( g − r ) and ( r − i ) of the mainEGIS sample (grey) and of the VTD galaxies (red bullets). Thecolors are corrected for the reddening in the Milky Way, but notcorrected for the internal extinction. The symbol size designatesthe galaxy scale length. The open circles denote the galaxies withunknown redshift and physical size. lower left corner of the ( g − r ) - ( r − i ) diagram. The scalelength of the VTD galaxies (ranges from 1.6 to 28 kpc) is de-noted by the symbol size in Figure 4. It may suggest that theselected sample of VTD galaxies is a mix of different typesof objects, including those blue and underevolved, similar toUGC 7321, and large red LSB galaxies like Malin 2 or otherlarge LSB systems (Beijersbergen et al. 1999; O’Neil et al.2000). Note that the colors are corrected for the reddeningin our Galaxy using Schlegel et al. (1998) maps, but are notcorrected for internal extinction. MNRAS , 1–11 (2016) ery Thin Disc Galaxies Figure 5.
The relative fraction of the h and z is shown for thesame samples as in Figure 1, with the VTD galaxies subdivided bythe blue and red subsamples (see text). The grey filled histogramshows regular EGIS galaxies. The blue and red subsamples aredesignated by the blue and red colors, respectively. We split the sample of our VTD galaxies into blue andred subsamples (divided by the color ( r − i ) =0.23 mag),and redraw the first figure in the paper. Figure 5 shows thedistribution of the scale length h and scale height z of theVTD galaxies for the separate ”blue” and ”red” subsamples.The VTD galaxies are not typical, as it is seen fromtheir location on the color-size diagram in Figure 6. Theyhave bluer color, on average, for the same size as regu-lar EGIS galaxies. The colors of very thin galaxies can bepartly or completely attributed to the low dust extinction inthem (MacLachlan et al. 2011, see also discussion below), aswell as to underevolved stellar population in LSB galaxies(Vorobyov et al. 2009). The higher extinction in the regularedge-on galaxies can help explain the color difference be-tween the normal and VTD objects in Figure 6. It is worthnoting that Figure 6 is qualitatively similar to the size-colorplot from Beijersbergen et al. (1999) made for LSB galaxies,which also supports the analogy between the VTD and LSBgalaxies.The internal extinction is low in LSB galaxies(Matthews & Wood 2001). MacLachlan et al. (2011) cameto a conclusion that small and thin LSB galaxies have lowoverall dust extinction. Their face-on optical depth is muchless than unity. The dust scale height in those galaxies iscomparable to their stellar scale height. By analogy, we ex-pect that our VTD galaxies also have low dust extinction.While the H α line is detected in the majority of our objectsfrom Table 2, only 11 galaxies have measurable H β lines. Weintegrated the hydrogen line fluxes all over the galaxies inorder to increase the signal-to-noise and estimate the over-all extinction from the H α /H β ratio (Charlot & Longhetti2001). We noticed that the background stellar populationspectrum is not detected in majority of the galaxies or Figure 6.
The integral (r-i) color of EGIS galaxies (grey) inthe comparison with their radial scale length expressed in kpc.VTD galaxies from our spectroscopic sample with detected H α emission are designated by the blue bullets. The red circles markall other VTD galaxies from our list in Table 2. The red barin the lower right corner shows the average uncertainty of theradial scale length for the sample of VTD galaxies. The colors arecorrected for the reddening in the Milky Way. looks extremely weak, and the correction for the underly-ing absorption does not affect the estimated fluxes. Fig-ure 7 shows the overall extinction A V corrected for theforeground Milky Way reddening (Schlegel et al. 1998) plot-ted for the galaxies with different thickness. We also in-clude two regular EGIS galaxies (EON 200.709 19.691 andEON 237.173 21.870) that did not meet the ”very thin disc”threshold. The bullets designate the small galaxies with lowamplitude of rotation curve, V max ≤
110 km/s. The circlesshow the galaxies with V max >
110 km/s. The VTD galax-ies in Figure 7 indicate low dust extinction, which suggeststheir low dust content (see also Matthews & Wood 2001;MacLachlan et al. 2011).
Cosmological simulations suggest that the formation of LSBgalaxies may require special cosmological conditions: in gen-eral, LSB galaxies are born in 15% less concentrated darkmatter halos than high surface brightness galaxies (e.g.,Maccio et al. 2007). Karachentsev et al. (2016) found thatvery thin galaxies tend to have smaller number of satellitesthan regular spiral galaxies. We investigate if VTD galaxiescorrelate with elements of the large-scale structure, such asvoids, superclusters, and filaments.A catalog of filaments identified in SDSS data byTempel et al. (2014) allows us to find the minimum distancefrom a galaxy in the EGIS catalog to a filament. We filteredthe EGIS catalog and left only the objects within the sameredshift range as our sample of VTD galaxies.We also lim-
MNRAS , 1–11 (2016)
Bizyaev et al.
Figure 7.
The overall dust extinction A V in the V band esti-mated from the H α /H β emission flux ratio for those 11 galaxies inwhich the H α and H β fluxes were available from our spectroscopy.The blue bullets designate the galaxies with V max ≤
110 km/s,the red circles show larger galaxies. The A V is corrected for thereddening in the Milky Way. ited the maximum radial velocity in both samples by 25,000km/s since the majority of VTD galaxies are have lower ra-dial velocities. Note that the conclusions presented belowdo not change if the maximum radial velocity is limited byslightly different value (e.g. 30,000 km/s.) In this case theKolmogorov-Smirnov test suggests that the probability thatthe distances in the two subsamples are drawn from thesame distribution equals to 0.77. Then we estimated three-dimensional distances to the filaments from Tempel et al.(2014) for the objects from both samples.We observe significant difference in how the VTD andregular galaxies associate with the filaments. Figure 8 showsthe fraction of galaxies that are farther than certain distancefrom filaments for three groups of objects: all non-thin discgalaxies, all VTD galaxies, and those from the latter groupwhose scale length is shorter than 4.5 kpc. Here the fractionthat equals to 1 means that there are no objects closer thanthis distance from the filament, and the fraction of 0 meansthat all objects of this kind are located closer than certaindistance to the nearby filament.It is seen that within a certain distance from filamentswe observe a smaller fraction of VTD galaxies than regularEGIS objects. The fraction of non-associated supethins ismore than twice as large than that of the regular edge-ongalaxies starting with a few Mpc from filaments.Interesting to notice that LSB galaxies also tend toavoid the inner regions in filaments ( ∼ inner 5 Mpc), andprefer to reside in the outer regions there (Mo et al. 1994;Rosenbaum & Bomans 2004). Since large and small galax-ies tend to have different colors (Figure 4), which may re-veal different evolution scenarios, we also check if the radialscale length affects the fraction of the galaxies associated with filaments. The dash-dotted blue curve in Figure 8 des-ignates relatively small VTD galaxies defined as those withthe scalelength h ≤ The main ingredients of known VTD galaxies are massivedark matter halos and LSB stellar discs (Matthews et al.1999; Uson & Matthews 2003; Bizyaev & Mitronova 2002;Bizyaev & Kajsin 2004; Sotnikova & Rodionov 2006;Bizyaev & Mitronova 2009; Karachentsev et al. 2016).The gas fraction is also high in some VTD galaxies(Matthews & van Driel 2000; Uson & Matthews 2003;Banerjee et al. 2009). It was found that the gravitationalpotential of dark matter halo dominates at all radii in aVTD galaxy UGC 7321 (Banerjee et al. 2009).
A massive dark halo is a necessary but not sufficient con-dition: Saha (2014) found that a galaxy has to avoid form-
MNRAS , 1–11 (2016) ery Thin Disc Galaxies Figure 8.
The fraction of edge-on galaxies that reside fartherthan certain distance from filaments. The solid green curve des-ignates regular EGIS galaxies, while the dashed red curve showsour VTD galaxies. The dash-dotted blue curve denotes our smallVTD galaxies with h < Figure 9.
The distance to filaments versus the scale length of thegalaxy. The sample of regular, non VTD galaxies is designated bygrey dots. The VTD galaxies are marked with the red bullets. ing a bar or prominent spirals during its evolution to be aVTD. Banerjee & Jog (2013) analyzed the halo concentra-tion parameter in two galaxies and concluded that a com-pact dark matter halo with its scale less the radial scale-length of the stellar disc is required to assemble a VTDgalaxy. Sotnikova & Rodionov (2006) concluded that thepresence of a compact, not necessarily massive bulge in aspiral galaxy may be enough to suppress the bending in- stability and to keep the stellar disc very thin. This findingsupports the conclusions by Banerjee & Jog (2013), becauseSotnikova & Rodionov (2006) noticed that the gravitationalpotential of a compact bulge has the same effect as the po-tential of a compact dark halo. Khoperskov et al. (2010) si-multaneously modeled rotation curves and thickness of sev-eral galaxies, including three very thin ones. They found thatdark halos dominate by mass in the galaxies with very thinstellar discs. The presence of a compact dark halo in galaxieswith very thin discs is not confirmed by Khoperskov et al.(2010). Instead, the results of Khoperskov et al. (2010) in-dicate that stellar discs must have a low surface density tokeep them very thin.An interesting example comes from the dynamicalanalysis of components of a giant LSB galaxy Malin 2:Kasparova et al. (2014) confirm a low surface brightnessstellar disc in Malin 2, and also a very massive dark halo. Thestellar disc thickness estimated from dynamical equilibriumreasons is of the order of 1 kpc in Malin 2 (A. Kasparova,private communication), so the galaxy can be considered asa VTD, with a large scale ratio h/z ∼
20. The halo scalelength was estimated by Kasparova et al. (2014), and theconclusion is opposite to that by Banerjee & Jog (2013): anextended and spread-out halo is required to make a giantLSB (and VTD) galaxy. Thus we suspect that the halo con-centration parameter may work different ways in the evolu-tion of small and large VTD galaxies, but in all cases a lowsurface density stellar disc is required.
The marginal conditions for star formation in galactic discscan be explored and quantified with the help of VTD galax-ies. VTDs exhibit low-density discs and gravitationally dom-inating dark halos. This brings them close to the minimumconditions, which are necessary for starting the star forma-tion. Therefore, VTD galaxies provide an additional tool,the disc thickness, which cannot be infinitely small. The one-dimensional gas velocity dispersion is of the order of 6 km/sin the star forming media (see e.g., Kennicutt 1989), and thestellar disc formed from the gas cannot decrease its verticalvelocity dispersion being collisionless.A toy model of an exponential stellar disc embed-ded into a spherical gravitational potential brings upsimple equations to estimate the relative disc thick-ness (Zasov et al. 1991, 2002; Kregel & van der Kruit 2005;Sotnikova & Rodionov 2006; Bizyaev & Mitronova 2009;Khoperskov et al. 2010). We assume that the disc mass is M d = 2 π Σ h , and the total mass of the galaxy within fourdisc scale lengths is M t = 4 V h/G . Here Σ is the centralsurface density of the stellar disc, V is the circular veloc-ity, which can be assumed as constant in the case of a flatrotation curve, and G is the gravitational constant. We con-sider the discs are in equilibrium in the vertical direction,with their vertical scaleheight z determined via the verticalequilibrium condition for the isothermal slab (Spitzer 1942): σ z = π G Σ( R ) z , where σ z is the vertical stellar or gasvelocity dispersion.The radial stellar velocity dispersion σ R in a disc thatis marginally stable against axisymmetric perturbations inits plane, is σ R = 3 . G Σ( R ) /κ (Toomre 1964), where κ MNRAS , 1–11 (2016)
Bizyaev et al. is the epicyclic frequency. If we take into account the non-axisymmetric perturbations and a finite layer thickness, theminimum radial dispersion should be greater than σ R ≥ Q . G Σ( R ) /κ , where Q > Q usually has a wide minimum with the value Q ≈ . . − h in the marginally stablediscs (see, e.g., numerical simulations by Khoperskov et al.2003). The value of Q ≈ . Q is a constant at inter-mediate distances to the galactic centre. The epicyclic fre-quency at the region of the flat rotation curve is κ = √ V /R ,and we get z ∼ ( M d /M t ) h . At R = 2 h the total-to-discmass ratio is M t /M d & . σ z /σ R ) ( h/z ) ( Q/ . .The low vertical dispersion in disc galaxies allowsus to introduce a few more simplifications. Note that ifwe consider early epochs of the galaxy formation, thediscs should be assumed mostly gaseous, for which σ R = π G Q Σ( R ) /κ (Safronov 1960) and ( σ z /σ R ) = 1. In gen-eral, considering the instability of multi-component galacticdiscs (Jog & Solomon 1984; Rafikov 2001; Romeo & Falstad2013) as well as finite gas and stellar layer thickness (e.g.,Bogelman & Shlosman 2009) should introduce correctionsto the stability criterion. Fortunately, the proximity of thevertical velocity dispersion in the stellar and gas discs, aswell as the small disc thickness, make the pure gas disc sta-bility criterion equation well applicable in the case of theVTD discs. In this case M t /M d & . h/z ) ( Q/ . . (1)Formally, equation (1) does not put any constraints on thestellar disc thickness and if M t /M d → ∞ , the ratio h/z grows infinitely, too.Although we considered a purely gaseous disc in ourtoy model, the stellar component inevitably emerges inreal galaxies. It is worth noticing that if we apply atwo-component stability criterion (Jog & Solomon 1984;Efstathiou 2000) in which the stellar velocity dispersion isequal or higher than that in the gas, we obtain a higher crit-ical density necessary to make the disc (stellar and gaseoustogether, in this case) unstable. The stellar or gas discs canbe stable if considered taken apart, but their combinationcan be unstable, at the same time. In this case our approx-imation of purely gaseous disc at the beginning, when thestar formation just started, constrains the lower limit of thecritical density necessary for starting the disc fragmentation.One more limitation to the disc thickness comes fromthe inability to make vertical component of the velocity dis-persion arbitrary small. We assume that one-dimensional gasvelocity dispersion is limited by (10/ √
3) km/s, and that thestellar population cannot inherit the vertical velocity dis-persion less than this value. Starting with equation (1), wesubstitute σ z = 10 / √ µ = M t /M d , Q = 1 .
4, and R = 2 h in it, and get h/z = 2 V / ( µ e ), where e is thebase of the natural logarithm. In more convenient designa-tion this can be written h/z . (81 /µ ) V , (2)where V = V /
100 km/s. Equation (2) predicts verythin discs ( h/z .
20 for V ∼
1) for galaxieswith massive dark halos ( µ ∼
4) (Bizyaev & Mitronova
Figure 10.
The rotation curve maximum V versus the scalelength diagram for nine galaxies with published data (the redopen circles) and for the sample from Table 2 (the blue bullets).The diagram suggests that the majority of the galaxies follow thesame trend. The three galaxies with the lower limit estimationsfor V (see text) are marked with arrows. One of these galaxiesshould have much higher V than the lower limit. V > µ = M t /M d would help partly “fix” equation (2): Mosenkov et al.(2010) report slightly higher maximum values of µ up to 8,but it will not prevent equation (2) from displaying veryhigh ratios h/z for large galaxies with V > h ∼ V . ,as follows from Courteau et al. (2007); Hall et al. (2012).The coefficient in the equation can be calibrated usingexisting kinematic measurements available for several VTDgalaxies from our sample, see the next section. In this caseequation (1) can be written h/z = 107 V . / Σ ,c . (3)Here V is expressed in km/s, and Σ ,c in M ⊙ /pc ; Q = 1 . σ z /σ R = 1. In this case we expect h/z ∼
10 for small galax-ies like UGC 7321, and h/z &
15 for giant LSB galaxies likeMalin 2 (given a proper value of Σ ,c ).Since equations (2) and (3) have different functional de-pendence of the rotation curve amplitude V , we can distin-guish between the two cases considered above. The thinnestdiscs in the VTD galaxies should highlight the cases of thelowest vertical stellar velocity dispersion and lowest stellardensity.Figure 10 demonstrates the relation between the rota- MNRAS , 1–11 (2016) ery Thin Disc Galaxies tion curve maximum V and the radial scale length h fornine galaxies with data from HYPERLEDA (open circles)and for the galaxies observed by us (filled circles). The trendcorresponds to the h ∼ V . dependency. The arrows indi-cate the two cases of the lack of emission lines in spectra,when NaD absorption line was used to constrain the V , andone more case of purely raising rotation curve with ring-likebrightness distribution in the H α rotation curve. The latterindicates that we observe emission from a gas ring in thegalaxy, whereas the outer regions can rotate faster than gasin the ring. Figure 11 shows the comparison between h/z and V for ourVTD galaxies. The open circles designate the galaxies withthe rotation curve maximum V found in literature (HYPER-LEDA), while the filled circles show our APO/DIS measure-ments ( § V , same as in Figure 10.The solid and dashed lines correspond to equations (3)and (2) with µ = 4, respectively. The observing point al-location in Figure 11 strongly favors the case of a star for-mation threshold surface density. Since all galaxies (not onlyVTDs) are located above the solid line because the thresholdshould prevent them from moving below this line), the lowestpoints help determine the “envelope” line that correspondsto certain lowest Σ ,c . We determine that the solid curve inFigure 11 corresponds to Σ ,c = 88 M ⊙ /pc . As it followsfrom the assumed initial conditions and assumptions for theequations, this is the stellar and gas surface density summedtogether. It is interesting to notice that the upper left cor-ner in Fig. 11 in Matthews & van Driel (2000) demonstratesa similar “envelope” feature and confirms our finding, al-though the definition of a/b ratio in Matthews & van Driel(2000) comes from a visual estimate, therefore it is hard tocompare it quantitatively to our results. Kregel et al. (2005)show this “envelope” feature in their h/z versus V plots aswell. Note that the predictions of our toy model are in qual-itative agreement with N-body simulations of UGC 7321,which suggest that the central surface density in the stel-lar disc ranges between 50 (Banerjee & Jog 2013) and 200M ⊙ /pc (Khoperskov et al. 2010).The galaxies that are located above both the solid anddashed lines in Figure 11 have their disc surface densityabove the threshold and the stellar velocity dispersion abovethe minimum value. It does not mean that galaxies withlower surface density and, hence, lower surface brightnesscannot exist: galaxies can have a lower central surface den-sity, but their discs will be thick and have a relatively highvertical stellar velocity dispersion, i.e. they will be morepressure supported and less rotationally supported. In thelatter sense they will resemble Irr/Im galaxies rather thanSd. The minimum central surface density that we observein the large, rotationally supported disc galaxies, may be amanifestation of the disc formation regulating processes viathe spin angular momentum parameter λ (Peebles 1969;Dalcanton et al. 1997): LSB galaxies with massive dark ha-los tend to have large λ and a low dark matter halo con-centration index (Maccio et al. 2007). Since we assumed themarginal stability of galactic discs to evaluate equation (1),this threshold density is an additional threshold, indepen- Figure 11.
The rotation curve maximum V versus the inversestellar disc thickness h/z . The two lines, solid and dashed, corre-spond to the cases of a surface density threshold, and no thresh-old, respectively. The red open circles show the data available forseveral VTD galaxies from literature. The blue bullets designateour sample with APO/DIS spectral observations. dent of the Toomre-Kennicutt large scale instability crite-rion (Kennicutt 1989).Our toy model uses several simplifications and assump-tions. “Typical” values of numerical coefficients may notwork well in all cases of the extreme conditions, whichwe consider. The modelling of real galaxy rotation curveswith the application of additional constraints from thestellar disc thickness for a larger sample of VTD galax-ies should help to better understand their dynamical sta-tus and the star formation threshold. The essential trans-parency of the dust layer in the galaxies is an additionalfeature, which should simplify the estimation of the param-eters of the galactic components from the rotation curvemodelling (e.g., as shown in Zasov & Khoperskov (2003);Kregel & van der Kruit (2005)). The properties of VTD galaxies resemble those of LSB discgalaxies. Both classes of galaxies have low surface brightness,both are relatively deficient in dust, and prefer to resideoutside the core filament regions. VTD galaxies possess largefraction of dark matter, similar to many LSB galaxies. Wecan conclude that VTD galaxies are mostly LSB galaxies,but the opposite is incorrect, in general: not all LSB galaxiesare VTD, as well as not all LSB galaxies have massive darkhalos (Graham 2002). Moreover, extreme LSB galaxies witha surface density below ∼
90 M ⊙ /pc should have moderate(less than nine) radial-to-vertical disc scale ratios and thestellar velocity dispersion close to that in the galactic gasmedium. Additional studies of statistically large samples ofVTD galaxies are needed to verify our conclusions. MNRAS , 1–11 (2016) Bizyaev et al.
We select 85 VTD galaxies with large radial-to-verticalscale ratios h/z from the EGIS catalog of edge-on galaxies(Bizyaev et al. 2014). The VTD galaxies have larger scalelengths and shorter scale heights than regular EGIS objectsin general. The objects with large radial and vertical scalestend to have redder colors, whereas smaller VTD galaxieshave bluer colors.VTD galaxies are mostly LSB stellar systems with lowdust extinction. They may possess bulges, but a large frac-tion of VTD galaxies have very small bulges (bulge-to-totalluminosity ratio is less than 0.1) or no bulges at all.VTD galaxies from our sample avoid large-scale fila-ments twice as frequent than regular EGIS objects, thussuggesting that the VTDs are located in more isolated en-vironment. At the same time, VTD galaxies possess verymassive and spread out dark matter halos, which makes thedark-to-luminous mass ratio several times greater than thatin regular spiral galaxies. Further studies of correlations be-tween the properties of the dark halos around VTD galaxiesand cosmological structures in which they reside should helpidentify specific cosmological conditions necessary to createVTD, dark matter dominated disc galaxies.Correlation between the scale ratio h/z and maximumrotational velocity, as well as the lack of very thin and low-massive galaxies, suggests that the formation of the disccomponent in galaxies is regulated by a threshold surfacedensity. Using kinematic data available for a sample of VTDgalaxies observed with the Dual Imaging Spectrograph atthe Apache Point Observatory, we conclude that the min-imum central surface density in the VTD galaxies is 88M ⊙ /pc . Galaxies with less central surface density indicatea small h/z ratio (i.e. they are not VTD), and they are lessrotationally supported systems. ACKNOWLEDGEMENTS
DB is supported by RSF grants RSCF-14-50-00043 (spec-tra acquisition and reduction) and RSCF-14-22-00041 (datainterpretation and modeling.) AM is a beneficiary of a mo-bility grant from the Belgian Federal Science Policy Office.We acknowledge partial financial support from the RFBRgrants 14-02-00810 and 14-22-03006-ofi. Based on observa-tions obtained with the Apache Point Observatory 3.5-metertelescope, which is owned and operated by the AstrophysicalResearch Consortium.We appreciate valuable suggestions by Heinz Andernach(Univ. Guanajuato) for his help in increasing our sample ofEGIS galaxies with known parameters. We thank DmitryMakarov (SAO RAS) and Vasily Belokurov (University ofCambridge) for comments on many individual galaxies inthe EGIS catalog. We thank anonymous referee for helpfulconstructive comments that improved the paper.We acknowledge the usage of the HyperLeda database.This research has made use of the NASA/IPAC Extragalac-tic Database (NED) which is operated by the Jet Propul-sion Laboratory, California Institute of Technology, undercontract with the National Aeronautics and Space Admin-istration.
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