Tully-Fisher Research Articles

Scaling relations between mass components and rotational velocity in disk galaxies

Abstract In this study, we re-evaluate the baryonic Tully–Fisher relation (BTFR) by analyzing the correlations between maximum rotational velocity and various mass components, including stellar mass, atomic hydrogen (H i) mass, baryonic mass, and dark matter mass in a sample of 141 disk galaxies from the SPARC (Spitzer Photometry and Accurate Rotation Curves) database, augmented by recent data on stellar and dark matter masses. We apply multiple statistical methods, including Monte Carlo orthogonal distance regression (MCODR), Monte Carlo least-squares (MCLS), and traditional least-squares (LS), to assess the impact of different fitting techniques on the derived scaling relations between the mass components (stellar, H i, and dark matter) and maximum rotational velocities of these galaxies. We find that the selection of statistical methods significantly influences the derived slopes and intercepts the relation between maximum rotational velocity and mass components. The MCODR method that accounts for errors in both variables consistently produces steeper slopes, suggesting a stronger correlation between stellar mass and rotational dynamics compared to other methods. In contrast, the MCLS method tends to yield flatter slopes, highlighting the sensitivity of this approach to outliers. Despite the variations in slope and intercept across different methods, the fundamental relation between baryonic mass and rotational velocity remains robust. We have also compared dark matter mass derived from different halo models [NFW (Navarro–Frenk–White) versus combined NFW + Dekel–Zhao profiles] and noted that the slope from the NFW profile is slightly steeper than that from the combined profile, highlighting the sensitivity of scaling relations to the selection of halo model. Overall, this study reinforces the robustness of the BTFR across different mass components in disk galaxies while emphasizing the critical role of statistical methods and dark matter profiles in analyzing galactic dynamics.

Photometry and kinematics of dwarf galaxies from the Apertif HI survey

Understanding the dwarf galaxy population in low density environments (in the field) is crucial for testing the current Lambda Cold Dark Matter cosmological model. The increase in diversity toward low-mass galaxies is seen as an increase in the scatter of scaling relations, such as the stellar mass--size and the baryonic Tully-Fisher relation (BTFR), and is also demonstrated by recent in-depth studies of an extreme sub-class of dwarf galaxies with low surface brightnesses but large physical sizes called ultra-diffuse galaxies (UDGs). We aim to select dwarf galaxies independent of their stellar content and to make a detailed study of their gas and stellar properties. We selected galaxies from the APERture Tile In Focus (Apertif) survey and applied a constraint on their $i$-band absolute magnitude in order to exclude high-mass systems. The sample consists of 24 galaxies, 22 of which are resolved in by at least three beams, and they span mass ranges of 8.6 $ lesssim 9.7 and a stellar mass range of 8.0 $ lesssim 9.7 (with only three galaxies having log ( msun)>9). We determined the geometrical parameters of the and stellar disks, built kinematic models from the data using and extracted surface brightness profiles in the g-, r- and i- bands from the Pan-STARRS 1 photometric survey. We used these measurements to place our galaxies on the stellar mass--size relation and the BTFR, and we compared them with other samples from the literature. We find that at a fixed stellar mass, our dwarfs have larger optical effective radii than isolated optically selected dwarfs from the literature, and we found misalignments between the optical and morphologies for some of our sample. For most of our galaxies, we used the morphology to determine their kinematics, and we stress that deep optical observations are needed to trace the underlying stellar disks. Standard dwarfs in our sample follow the same BTFR of high-mass galaxies, whereas UDGs are slightly offset toward lower rotational velocities, in qualitative agreement with results from previous studies. Finally, our sample features a fraction (25<!PCT!>) of dwarf galaxies in pairs that is significantly larger with respect to previous estimates based on optical spectroscopic data.

The role of active galactic nucleus feedback on the evolution of dwarf galaxies from cosmological simulations

Aims. Recent observational studies suggest that feedback from active galactic nuclei (AGNs) may play an important role in the formation and evolution of dwarf galaxies, an issue that has received little attention from a theoretical perspective. Methods. We investigated this using two sets of 12 cosmological magnetohydrodynamic simulations of the formation of dwarf galaxies (108.3M⊙ ≤ M* ≤ 109.8M⊙): one set using a version of the AURIGA galaxy formation physics model including AGN feedback and a parallel set with AGN feedback turned off. Results. We show that the full-physics AGN runs satisfactorily reproduce several scaling relations, including the black-hole-to-stellar mass (MBH-M⋆), the black-hole-to-sigma (MBH-σ⋆), and the baryonic Tully-Fisher relation. We find that the global star formation (SF) of galaxies run with an AGN is reduced compared to the one in which the AGN has been turned off, suggesting that AGN feedback is a viable way of suppressing SF in dwarf galaxies, even though none of our galaxies is completely quenched by z = 0. Furthermore, we find a tight correlation between the median SF rates and the MBH/M⋆ ratio in our simulated dwarfs. Star formation is suppressed due to gas heating in the vicinity of the AGN: less HI gas is available in AGN runs, though the total amount of gas is preserved across the two settings within each galaxy. This indicates that the main effect of AGN feedback in our dwarfs is to heat up and push the gas away from the galaxy’s centre rather than expelling it completely. Finally, we show that the two galaxies harbouring the largest supermassive black holes have suffered a considerable (up to ∼65%) reduction in their central dark matter density, pinpointing the role of AGNs in determining the final dark matter mass distribution within dwarf galaxies. This pilot paper highlights the importance of modelling AGN feedback at the lowest mass scales and the impact this can have on dwarf galaxy evolution.

Retardation theory of eleven galaxies

Abstract The missing mass problem has been with us since the 1970s, as Newtonian gravity using baryonic mass cannot account for various observations. We investigate the viability of retardation theory, an alternative to the Dark Matter paradigm (DM) which does not seek to modify the General Principal of Relativity but to improve solutions within it by exploring its weak field approximation to solve the said problem in a galactic context. This approach have yielded satisfactory results, with respect to galactic rotation curves, the Tully-Fisher relation and missing mass derived from gravitational lensing. Recently it was able to introduce a necessary correction to the virial theorem explaining mass excess in clusters of galaxies. The current work presents eleven rotation curves calculated using Retardation Theory. The calculated rotation curves are compared with observed rotation curves. Values for the change in mass flux to mass ratio are extracted from the fitting process as a free fitting parameter. Those quantities are interpreted here and in previous works using galactic processes. Retardation Theory was able to successfully reproduce rotation curves and a preliminary correlation with star birthrate index is seen, suggesting a possible link between galactic winds and observed rotation curves. Retardation Theory shows promising results within current observations. More research is needed to elucidate the suggested mechanism and the processes which contribute to it. Galactic mass outflows carried by galactic winds may affect rotation curves.

Tully-Fisher relation of late-type galaxies at 0.6 ≤ z ≤ 2.5

We present a study of the stellar and baryonic Tully-Fisher relation within the redshift range of 0.6 ≤ z ≤ 2.5, utilizing observations of star-forming galaxies. This dataset comprises of disk-like galaxies spanning a stellar mass range of 8.89 ≤ log(Mstar [M⊙]) ≤ 11.5, a baryonic mass range of 9.0 ≤ log(Mbar [M⊙]) ≤ 11.5, and a circular velocity range of 1.65 ≤ log(Vc [km/s]) ≤ 2.85. We estimated the stellar masses of these objects using spectral energy distribution fitting techniques, while the gas masses were determined via scaling relations. Circular velocities were directly derived from the rotation curves (RCs), after meticulously correcting for beam smearing and pressure support. Our analysis confirms that our sample adheres to the fundamental mass-size relations of galaxies and reflects the evolution of velocity dispersion in galaxies, in line with previous findings. This reaffirms the reliability of our photometric and kinematic parameters (i.e., Mstar and Vc), thereby enabling a comprehensive examination of the Tully-Fisher relation. To attain robust results, we employed a novel orthogonal likelihood fitting technique designed to minimize intrinsic scatter around the best-fit line, as required at high redshifts. For the stellar Tully-Fisher relation, we obtained a slope of α = 3.03 ± 0.25, an offset of β = 3.34 ± 0.53, and an intrinsic scatter of ζint = 0.08 dex. Correspondingly, the baryonic Tully-Fisher relation yielded α = 3.21 ± 0.28, β = 3.16 ± 0.61, and ζint = 0.09 dex. Our findings indicate a subtle deviation in the stellar and baryonic Tully-Fisher relation with respect to local studies, which is most likely due to the evolutionary processes governing disk formation.

Dark halos and Tully–Fisher relation testing modified gravity

In this paper, we involve the galactic halo observational data to test the weak field General Relativity involving the cosmological constant. By using the data for 15 hydrogen (Hi) VLA super spirals and the Tully–Fisher relation, we obtain constraints for each galaxy. The results are consistent with previous results for spiral galaxies, as well as with the scaling relations for the halos, thus confirming the efficiency of the use of dark halo data and Tully–Fisher relation, including the baryonic Tully–Fisher index (BTFR), for testing modified gravity models.

Gas-rich "ultra-diffuse" galaxies are consistent with the baryonic Tully-Fisher relation and with Milgromian dynamics

Some gas-rich ``ultra-diffuse'' galaxies (UDGs), which are extreme examples of low surface brightness (LSB) dwarf galaxies, have been reported to lack dark matter and to be offset from the baryonic Tully-Fisher relation (BTFR). If confirmed, these UDGs would represent a serious challenge for both Lambda CDM galaxy-formation models and Milgromian dynamics. Here I demonstrate that these conclusions are very dubious due to underestimated uncertainties on inclinations and/or distances. First, I show that UDGs are offset from the BTFR in the same way as usual face-on LSB dwarfs due to systematic biases at low inclinations. Next, I analyze the two UDGs with the best available rotation-curve data. The first (AGC\,242019) is ideally inclined for kinematic studies; MOND can fit the observed rotation curve with a distance of 12.5pm 0.6 Mpc, which is consistent with Virgocentric flow models. The second UDG (AGC\,114905) is close to face-on, so not ideal for kinematic studies; MOND can fit the observed rotation curve with a distance of 68pm 13 Mpc and inclination of circ circ $, which are consistent with existing data. In particular, I show that the disk inclination is more uncertain than previously estimated due to significant asymmetries (lopsidedness) in the stellar distribution. In conclusion, there is no strong evidence that gas-rich UDGs and gas-rich LSB dwarfs are distinct galaxy populations with different dynamical properties; instead, UDGs seem to be a subset of LSB dwarf galaxies biased toward face-on systems.

BreakBRD Galaxies: Evolutionary Clues through an Analysis of Gas Content

By combining newly obtained deep Green Bank Telescope 21 cm observations with optical spectroscopic data, we present an analysis of the gas content of break bulges in red disks (breakBRD) galaxies, a population denoted by their blue star-forming centers and red quenched disks that do not appear to follow the typical inside-out evolution of spiral galaxies. We confirm previous results that the neutral atomic hydrogen (H i) gas fractions of breakBRDs are, on average, lower than those of typical galaxies on the star-forming sequence (SFS), and find that their H i fractions are generally higher than green valley (GV) galaxies. H i depletion times for breakBRDs are roughly an order of magnitude lower than those of SFS galaxies, in stark contrast with GV galaxies that typically have much longer depletion times than SFS galaxies. The nuclear gas-phase metallicities of breakBRDs have a broader distribution than SFS galaxies and are skewed toward slightly above-average values. BreakBRDs are systematically offset from the baryonic Tully–Fisher relation toward lower baryonic mass at a given rotation velocity. They also have higher typical H i asymmetries than SFS galaxies, and of those galaxies with spatially resolved gas velocity fields from the Sloan Digital Sky Survey IV Mapping Nearby Galaxies at Apache Point Observatory survey, two-thirds are either highly distorted or completely misaligned relative to the stellar disk. Evidence supports a scenario where breakBRDs are in an early phase of quenching, and there is mixed evidence that their behavior is related to past merger activity.

Galaxy dynamics tracing quantum cosmology beyond [formula omitted]CDM below the de Sitter scale of acceleration

It is proposed that the baryonic Tully–Fisher relation (bTFR) and JWST ’Impossible galaxies’ at cosmic dawn are unified in weak gravity by the trace J of the Schouten tensor below the Sitter scale of acceleration adS=cH, where c is the velocity of light and H is the Hubble parameter. Across adS, J parametrizes short-period galaxy rotation curves and fast gravitational collapse beyond the predictions of ΛCDM. The sensitivity of weak gravitation to J=16R, where R is the Ricci scalar tensor, is derived in infrared gravitation from a consistent limit to quantum gravity, reducing to general relativity in the limit of a small Planck constant. For the first time, it identifies the exact relation a0=c2J/2π of the Milgrom parameter across all redshifts, accounting for the bTFR and early galaxy formation accelerated by a factor ∼J1/8. It predicts a0′(0)<0 at the present epoch.

Galaxy and Mass Assembly (GAMA): Stellar-to-dynamical Mass Relation. II. Peculiar Velocities

Empirical correlations connecting starlight to galaxy dynamics (e.g., the fundamental plane (FP) of elliptical/quiescent (Q) galaxies and the Tully–Fisher relation of spiral/star-forming (SF) galaxies) provide cosmology-independent distance estimation and are central to local Universe cosmology. In this work, we introduce the mass hyperplane (MH), which is the stellar-to-dynamical mass relation (M ⋆/M dyn) recast as a linear distance indicator. Building on recent FP studies, we show that both SF and Q galaxies follow the same empirical MH, then use this to measure the peculiar velocities (PVs) for a sample of 2496 galaxies at z < 0.12 from GAMA. The limiting precision of MH-derived distance/PV estimates is set by the intrinsic scatter in size, which we find to be ≈0.1 dex for both Q and SF galaxies (when modeled independently) and ≈0.11 dex when all galaxies are modeled together, showing that the MH is as good as the FP. To empirically validate our framework and distance/PV estimates, we compare the inferred distances to groups as derived using either Q or SF galaxies. A good agreement is obtained with no discernible bias or offset, having a scatter of ≈0.05 dex ≈12% in distance. Further, we compare our PV measurements for the Q galaxies to the previous PV measurements of the galaxies in common between GAMA and the Sloan Digital Sky Survey, which shows similarly good agreement. Finally, we provide comparisons of PV measurements made with the FP and the MH, then discuss possible improvements in the context of upcoming surveys such as the 4MOST Hemisphere Survey.

Overview and public data release of the augmented Auriga Project: cosmological simulations of dwarf and Milky Way-mass galaxies

ABSTRACT We present an extended suite of the Auriga cosmological gravo-magnetohydrodynamical ‘zoom-in’ simulations of 40 Milky Way-mass haloes and 26 dwarf galaxy–mass haloes run with the moving-mesh code arepo. Auriga adopts the Lambda cold dark matter cosmogony and includes a comprehensive galaxy formation physics model following the coupled cosmic evolution of dark matter, gas, stars, and supermassive black holes which has been shown to produce numerically well-converged galaxy properties for Milky Way-mass systems. We describe the first public data release of this augmented suite of Auriga simulations, which includes raw snapshots, group catalogues, merger trees, initial conditions, and supplementary data, as well as public analysis tools with worked examples of how to use the data. To demonstrate the value and robustness of the simulation predictions, we analyse a series of low-redshift global properties that compare well with many observed scaling relations, such as the Tully–Fisher relation, the star-forming (SF) main sequence, and H i gas fraction/disc thickness. Finally, we show that SF gas discs appear to build rotation and velocity dispersion rapidly for $z\gtrsim 3$ before they ‘settle’ into ever-increasing rotation-dispersion ratios ($V/\sigma$). This evolution appears to be in rough agreement with some kinematic measurements from H$\alpha$ observations, and demonstrates an application of how to utilize the released data.

Indefinitely Flat Circular Velocities and the Baryonic Tully–Fisher Relation from Weak Lensing

We use a new deprojection formula to infer the gravitational potential around isolated galaxies from weak gravitational lensing. The results imply circular velocity curves that remain flat for hundreds of kiloparsecs, greatly extending the classic result from 21 cm observations. Indeed, there is no clear hint of a decline out to 1 Mpc, well beyond the expected virial radii of dark matter halos. Binning the data by mass reveals a correlation with the flat circular speed that closely agrees with the baryonic Tully–Fisher relation known from kinematic data. These results apply to both early- and late-type galaxies, indicating a common universal behavior.

The Baryonic Tully–Fisher Relation. I. WISE/Spitzer Photometry

We present Wide-field Infrared Survey Explorer (WISE) W1 photometry of the Spitzer Photometry and Accurate Rotation Curves sample. The baseline of near-IR fluxes is established for use by stellar mass models, a key component to the baryonic Tully–Fisher relation and other kinematic galaxies scaling relations. We focus this paper on determination of the characteristics of the W1 fluxes compared to IRAC 3.6 μm fluxes, internal accuracy limitations from photometric techniques, external accuracy by comparison to other work in the literature and the range of W1 to IRAC 3.6 μm colors. We outline the behavior of SDSS g, W1 and IRAC 3.6 colors with respect to underlying spectral energy distribution features. We also note a previously unknown correlation between WISE colors and the central surface brightness, probably related to the low metallicity of low-surface-brightness dwarfs.

WALLABY pilot survey: the Tully–Fisher relation in the NGC 4808, Vela, and NGC 5044 fields

ABSTRACT The Tully–Fisher Relation (TFR) is a well-known empirical relationship between the luminosity of a spiral galaxy and its circular velocity, allowing us to estimate redshift independent distances. Here we use high signal-to-noise H i 21-cm integrated spectra from the second pilot data release (PDR2, 180 deg2) of the Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY). In order to prepare for the full WALLABY survey, we have investigated the TFR in phase 2 of the pilot survey with a further three fields. The data were obtained with wide-field Phased Array Feeds on the Australian Square Kilometre Array Pathfinder (ASKAP) and have an angular resolution of 30 arcsec and a velocity resolution of $\sim$4 km s−1. Galaxy luminosities have been measured from the Wide-field Infrared Survey Explorer, and optical galaxy inclinations from the Dark Energy Camera Legacy Survey. We present TFRs for wavelengths from 0.8 to 3.4 μm. We examine sources of galaxy inclination data and investigate magnitudes from the DECam Local Volume Exploration Survey and DENIS catalogues and the 4HS target catalogue based on the VISTA Hemisphere Survey. We consider the baryonic TFR. These are all of interest for TFR using the full WALLABY survey of 200 000 galaxies. We demonstrate that WALLABY TFR distances can take their place among state-of-the-art studies of the local velocity field.

Universal Basic Mass Density inside Dark Matter Halos

Abstract In this work we propose a universal basic mass density and a universal basic metric inside dark matter halos in the framework of Einstein equations providing an analytical ground for learning about dark matter. In a previous work the authors have proposed a simplified model for galaxies: a Schwarzschild black hole (that contains all the baryonic matter of the galaxy) immersed inside a dark matter halo. The solution solved the Einstein equations perturbatively and successfully gave the flat rotation curve and the baryonic Tully-Fisher relation, the two signatures of spiral galaxies. In this work we take the black hole mass (the baryonic mass) of the solution to be zero in order to focus our study on the dark matter halo exclusively. Among the results (1) is the prediction of a universal basic mass density of dark matter, ρ = a_0/2πGr, where a_0 ≈ 2.8×10^{-11} m/s^2 is a universal constant whose value was deduced from observations, (2) we show that the mass and velocity curve of the dark halo agree excellently with observational data at intermediate distances where the baryonic matter contribution is negligible, (3) we show that the constant a0is the origin of the constant surface density of dark matter and the origin of the scale-radius/scale-density scaling relation of the Navarro-Frenk-White profile (4) we show how the inclusion of baryonic matter in our model solves the core-cusp problem.&amp;#xD;

Geometric interpretation of Tensor-Vector-Scalar theory in a Kaluza–Klein reference fluid

Gravitational alternatives to dark matter require additional fields or assumptions beyond general relativity while continuing to agree with tight solar system constraints. Modified Newtonian Dynamics (MOND), for example, predicts the Tully–Fisher relation for galaxies more accurately than dark matter models while limiting to Newtonian gravity in the solar system. On the other hand, MOND does a poor job predicting larger scale observations such as the cosmic microwave background and Matter Power Spectra. Tensor-Vector-Scalar (TeVeS) theory is a relativistic generalization of MOND that accounts for these observations without dark matter. In this paper, a generalized TeVeS from Kaluza–Klein theory in one extra dimension is derived as a consequence of n = 0 Kaluza–Klein modes. In the KK theory, MOND is a special case of a slicing condition in the 5D Arnowitt–Deser–Misner formalism enforced by a reference fluid as in the Isham-Kuchař method which may arise from a broken displacement symmetry. This has two benefits: first is means that TeVeS is compatible with Kaluza–Klein dark matter theory, which is a strong candidate for Weakly Interacting Massive Particles, the other is that it provides an elegant mechanism for the scalar and vector fields. It constrains most of the freedom in the definition of TeVeS which does not have a field theoretic motivation. This is important because the Kaluza–Klein theory predicts that spin-2 tensor modes must propagate at the speed of light, in agreement with observation, from theoretical constraints while TeVeS has to match this observation empirically. Furthermore, it provides a symmetry breaking motivation for the interpolating function in MOND.

Large-scale motions and growth rate from forward-modelling Tully–Fisher peculiar velocities

ABSTRACT Peculiar velocities are an important probe of the mass distribution in the Universe and the growth rate of structure, directly measuring the effects of gravity on the largest scales and providing a test for theories of gravity. Comparing peculiar velocities predicted from the density field mapped by a galaxy redshift survey with peculiar velocities measured using a distance estimator such as the Tully–Fisher relation yields the growth factor for large-scale structure. We present a method for forward modelling a sample of galaxy magnitudes and velocity widths that simultaneously determines the parameters of the Tully–Fisher relation and the peculiar velocity field. We apply this to the Cosmicflows-4 Tully–Fisher data set, using the peculiar velocities predicted from the 2M++ redshift survey. After validating the method on mock surveys, we measure the product of the growth rate and mass fluctuation amplitude to be fσ8 = 0.35 ± 0.03 at an effective redshift of z = 0.017. This is consistent at 3σ with the Planck CMB prediction, even though the uncertainty does not fully account for all sources of sample variance. We find the residual bulk flow from gravitational influences outside the 2M++ survey volume to be |V| = 227 ± 11 km s−1, (l, b) = (303°, −1°) in Galactic polar coordinates and the CMB frame. Using simulations, we show that applying our methodology to the large new sample of Tully–Fisher peculiar velocities expected from the WALLABY H I survey of the southern sky can improve the constraints on the growth rate by a factor of 2–3.

KAOSS: turbulent, but disc-like kinematics in dust-obscured star-forming galaxies at z ∼ 1.3–2.6

ABSTRACT We present spatially resolved kinematics of 27 ALMA-identified dust-obscured star-forming galaxies (DSFGs) at z ∼ 1.3–2.6, as traced by Hα emission using VLT/KMOS near-infrared integral field spectroscopy from the ‘KMOS-ALMA Observations of Submillimetre Sources’ (KAOSS) Large Programme. We derive Hα rotation curves and velocity dispersion profiles for the DSFGs, and find that among the 27 sources with bright, spatially extended Hα emission, 24 display evidence for disc-like kinematics. We measure a median inclination-corrected velocity at 2.2 Rd of vrot = 190 ± 40 km s−1 and intrinsic velocity dispersion of σ0 = 87 ± 6 km s−1 for these disc-like sources. The kinematics yield median circular velocities of vcirc = 230 ± 20 km s−1 and dynamical masses within 2Re (∼ 7 kpc radius) of Mdyn = (1.1 ± 0.2) × 1011 M⊙. Compared to less actively star-forming galaxies, KAOSS DSFGs are both faster rotating with higher intrinsic velocity dispersions, but have similar vrot/σ0 ratios, median v/σ0 = 2.5 ± 0.5. We suggest that the kinematics of the DSFGs are primarily rotation supported but with a non-negligible contribution from pressure support, which may be driven by star formation or mergers/interactions. We estimate the normalization of the stellar mass Tully–Fisher relation (sTFR) for the disc-like DSFGs and compare it with local studies, finding no evolution at fixed slope between z ∼ 2 and z ∼ 0. Finally, we show that the kinematic properties of the DSFG population are consistent with them evolving into massive early-type galaxies, the dominant z ∼ 0 population at these masses.

Kinematic Properties of the Gaseous Stellar Dynamics Using the Tully-Fisher Relation in the Different Types of Spiral Galaxies

The goal of this paper is to show the kinematic characteristics of gaseous stellar dynamics using scaling coefficient relationships (such as Tully-Fisher) in different spiral galaxies. We selected a sample of types of spiral morphology (116 early, 150 intermediate, and 146 late) from previous literature work, and used statistical software (statistic-win-program) to find out the associations of multiple factors under investigation, such as the main kinematic properties of the gaseous-stellar (mass, luminosity, rotational speed, and baryons) in different types of spiral galaxies. We concluded that there is a robust positive connection between Log Vrot.max.) and Log Mstar(B-V), as well as between Log Vrot.max. and Log Mbar (B-V) in three types of spiral galaxies (early, intermediate, and late), with a sharply negative relationship found between and Log MB in addition to the relationship between Log Mbar (B-V) and Log MB, with the partial correlation coefficient (R ≈ - 0.85) in all the different types of spiral galaxies. Our results indicated that for early and intermediate kinds of spiral galaxies, the baryonic disk mass and the maximum rotational speed fit best with the formula Mbar (B-V) ≈ 60V4rot.max., but this relationship seems to be stronger in late-type spiral galaxies with Mbar (B-V) ~ 60 V5rot.max . Whenever the observable stars and atomic hydrogen gas were taken into account, several scientific facts show that additional extremely massive baryon stores are virtually probably present in late spiral galaxies.

Comment on “The Tully-Fisher law and dark matter effects derived via modified symmetries” by Arraut Ivan

Comment on “The Tully-Fisher law and dark matter effects derived via modified symmetries” by Arraut Ivan