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Register a new userAsymptotic kinematics of Globular Clusters: the emergence of a Tully-Fisher relation
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Using a recent homogeneous sample of 40 high quality velocity dispersion profiles for Galactic globular clusters, we study the low gravitational acceleration regime relevant to the outskirts of these systems. We find that a simple empirical profile having a central Gaussian component and a constant large radius asymptote, $sigma_{infty}$, accurately describes the variety of observed velocity dispersion profiles. We use published population synthesis models, carefully tailored to each individual cluster, to estimate mass to light ratios from which total stellar masses, $M$, are inferred. We obtain a clear scaling, reminiscent of the galactic Tully-Fisher relation of $sigma_{infty}( km s^{-1})= 0.084^{+0.075}_{-0.040} (M/M_{odot})^{0.3 pm 0.051} $, which is interesting to compare to the deep MOND limit of $sigma_{infty} (km s^{-1})=0.2(M/M_{odot})^{0.25}$. Under a Newtonian interpretation, our results constitute a further restriction on models where initial conditions are crafted to yield the outer flattening observed today. Within a modified gravity scheme, as the globular clusters studied are not isolated objects in the deep MOND regime, the results obtained point towards a modified gravity where the external field effect of MOND does not appear, or is much suppressed.
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In this paper we investigate the statistical properties of the Tully-Fisher relation for a sample of 32 galaxies with measured distances from the Cepheid period-luminosity relation and/or TRGB stars. We take advantage of panchromatic photometry in 12 bands (from FUV to 4.5 $mu$m) and of spatially resolved HI kinematics. We use these data together with three kinematic measures ($W^{i}_{50}$, $V_{max}$ and $V_{flat}$) extracted from the global HI profiles or HI rotation curves, so as to construct 36 correlations allowing us to select the one with the least scatter. We introduce a tightness parameter $sigma_{perp}$ of the TFr, in order to obtain a slope-independent measure of the goodness of fit. We find that the tightest correlation occurs when we select the 3.6 $mu$m photometric band together with the $V_{flat}$ parameter extracted from the HI rotation curve.
In a LCDM cosmology, the baryonic Tully-Fisher relation (BTFR) is expected to show significant intrinsic scatter resulting from the mass-concentration relation of dark matter halos and the baryonic-to-halo mass ratio. We study the BTFR using a sample of 118 disc galaxies (spirals and irregulars) with data of the highest quality: extended HI rotation curves (tracing the outer velocity) and Spitzer photometry at 3.6 $mu$m (tracing the stellar mass). Assuming that the stellar mass-to-light ratio (M*/L) is nearly constant at 3.6 $mu$m, we find that the scatter, slope, and normalization of the BTFR systematically vary with the adopted M*/L. The observed scatter is minimized for M*/L > 0.5, corresponding to nearly maximal discs in high-surface-brightness galaxies and BTFR slopes close to ~4. For any reasonable value of M*/L, the intrinsic scatter is ~0.1 dex, below general LCDM expectations. The residuals show no correlations with galaxy structural parameters (radius or surface brightness), contrary to the predictions from some semi-analytic models of galaxy formation. These are fundamental issues for LCDM cosmology.
We study the HI K-band Tully-Fisher relation and the baryonic Tully-Fisher relation for a sample of 16 early-type galaxies, taken from the ATLAS3D sample, which all have very regular HI disks extending well beyond the optical body (> 5 R_eff). We use the kinematics of these disks to estimate the circular velocity at large radii for these galaxies. We find that the Tully-Fisher relation for our early-type galaxies is offset by about 0.5-0.7 magnitudes from the relation for spiral galaxies. The residuals with respect to the spiral Tully-Fisher relation correlate with estimates of the stellar mass-to-light ratio, suggesting that the offset between the relations is mainly driven by differences in stellar populations. We also observe a small offset between our Tully-Fisher relation with the relation derived for the ATLAS3D sample based on CO data representing the galaxies inner regions (< 1 R_eff). This indicates that the circular velocities at large radii are systematically 10% lower than those near 0.5-1 R_eff, in line with recent determinations of the shape of the mass profile of early-type galaxies. The baryonic Tully-Fisher relation of our sample is distinctly tighter than the standard one, in particular when using mass-to-light ratios based on dynamical models of the stellar kinematics. We find that the early-type galaxies fall on the spiral baryonic Tully-Fisher relation if one assumes M/L_K = 0.54 M_sun/L_sun for the stellar populations of the spirals, a value similar to that found by recent studies of the dynamics of spiral galaxies. Such a mass-to-light ratio for spiral galaxies would imply that their disks are 60-70% of maximal. Our analysis increases the range of galaxy morphologies for which the baryonic Tully-Fisher relations holds, strengthening previous claims that it is a more fundamental scaling relation than the classical Tully-Fisher relation.
Galaxies covering several orders of magnitude in stellar mass and a variety of Hubble types have been shown to follow the Radial Acceleration Relation (RAR), a relationship between $g_{rm obs}$, the observed circular acceleration of the galaxy, and $g_{rm bar}$, the acceleration due to the total baryonic mass of the galaxy. For accelerations above $10^{10}~{rm m , s}^{-2}$, $g_{rm obs}$ traces $g_{rm bar}$, asymptoting to the 1:1 line. Below this scale, there is a break in the relation such that $rm g_{rm obs} sim g_{rm bar}^{1/2}$. We show that the RAR slope, scatter and the acceleration scale are all natural consequences of the well-known baryonic Tully-Fisher relation (BTFR). We further demonstrate that galaxies with a variety of baryonic and dark matter (DM) profiles and a wide range of dark halo and galaxy properties (well beyond those expected in CDM) lie on the RAR if we simply require that their rotation curves satisfy the BTFR. We explore conditions needed to break this degeneracy: sub-kpc resolved rotation curves inside of cored DM-dominated profiles and/or outside $gg 100,$kpc could lie on BTFR but deviate in the RAR, providing new constraints on DM.
We validate the baryonic Tully Fisher (BTF) relation by exploring the Tully Fish er (TF) and BTF properties of optically and HI-selected disk galaxies. The data includes galaxies from: Sakai et al. (2000) calibrator sample; McGaugh et al. (2000: MC2000) I-band sample; and 18 newly acquired HI-selected field dwarf galaxies observed with the ANU 2.3m telescope and the ATNF Parkes telescope from Gurovichs thesis sample (2005). As in MC2000, we re-cast the TF and BTF relations as relationships between baryo n mass and W_{20}. First we report some numerical errors in MC2000. Then, we c alculate weighted bi-variate linear fits to the data, and finally we compare the fits of the intrinsically fainter dwarfs with the brighter galaxies of Sakai et al. (2000). With regards to the local calibrator disk galaxies of Sakai et al. (2000), our results suggest that the BTF relation is indeed tighter than the T F relation and that the slopes of the BTF relations are statistically flatter th an the equivalent TF relations. Further, for the fainter galaxies which include the I-band MCG2000 and HI-selected galaxies of Gurovichs thesis sample, we calc ulate a break from a simple power law model because of what appears to be real c osmic scatter. Not withstanding this point, the BTF models are marginally better models than the equivalent TF ones with slightly smaller reduced chi^2.
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