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Register a new userThe angular momentum-mass relation: a fundamental law from dwarf irregulars to massive spirals
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In a $Lambda$CDM Universe, the specific stellar angular momentum ($j_ast$) and stellar mass ($M_ast$) of a galaxy are correlated as a consequence of the scaling existing for dark matter haloes ($j_{rm h}propto M_{rm h}^{2/3}$). The shape of this law is crucial to test galaxy formation models, which are currently discrepant especially at the lowest masses, allowing to constrain fundamental parameters, e.g. the retained fraction of angular momentum. In this study, we accurately determine the empirical $j_ast-M_ast$ relation (Fall relation) for 92 nearby spiral galaxies (from S0 to Irr) selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample in the unprecedented mass range $7 lesssim log M_ast/M_odot lesssim 11.5$. We significantly improve all previous estimates of the Fall relation by determining $j_ast$ profiles homogeneously for all galaxies, using extended HI rotation curves, and selecting only galaxies for which a robust $j_ast$ could be measured (converged $j_ast(<R)$ radial profile). We find the relation to be well described by a single, unbroken power-law $j_astpropto M_ast^alpha$ over the entire mass range, with $alpha=0.55pm 0.02$ and orthogonal intrinsic scatter of $0.17pm 0.01$ dex. We finally discuss some implications for galaxy formation models of this fundamental scaling law and, in particular, the fact that it excludes models in which discs of all masses retain the same fraction of the halo angular momentum.
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We study the relationship between the H{sc i} specific angular momentum (j$_{rm g}$) and the H{sc i} mass (M$_{rm g}$) for a sample of galaxies with well measured H{sc i} rotation curves. We find that the relation is well described by an unbroken power law jg $propto$ mg$^{alpha}$ over the entire mass range (10$^{7}$-10$^{10.5}$ M$_{odot}$), with $alpha = 0.89 pm 0.05$ (scatter 0.18 dex). This is in reasonable agreement with models which assume that evolutionary processes maintain H{sc i} disks in a marginally stable state. The slope we observe is also significantly different from both the $j propto M^{2/3}$ relation expected for dark matter haloes from tidal torquing models and the observed slope of the specific angular momentum-mass relation for the stellar component of disk galaxies. Our sample includes two H{sc i}-bearing ultra diffuse galaxies, and we find that their angular momentum follows the same relation as other galaxies. The only discrepant galaxies in our sample are early-type galaxies with large rotating H{sc i} disks which are found to have significantly higher angular momentum than expected from the power law relation. The H{sc i} disks of all these early-type galaxies are misaligned or counter-rotating with respect to the stellar disks, consistent with the gas being recently accreted. We speculate that late stage wet mergers, as well as cold flows play a dominant role in determining the kinematics of the baryonic component of galaxies as suggested by recent numerical simulations.
We study the present-day connection between galaxy morphology and angular momentum using the {sc Dark Sage} semi-analytic model of galaxy formation. For galaxies between $ 10^{11}-10^{12} mathrm{M}_{odot}$ in stellar mass, the model successfully predicts the observed trend whereby galaxies with more prominent disks exhibit higher {em stellar} disk specific angular momentum ($j_{rm stellar, disk}$) at fixed stellar mass. However, when we include the gas in the disk, bulge-dominated galaxies have the highest {em total} disk specific angular momentum ($j_{rm total, disk}$). We attribute this to a large contribution from an extended disk of cold gas in typical bulge-dominated galaxies. We find the relationship between $j_{rm dark matter}$ and morphology to be quite complex. Surprisingly, in this stellar mass range, not only do bulge-dominated galaxies tend to live in halos with higher $j_{rm dark matter}$ than disk-dominated galaxies, but intermediate galaxies (those with roughly equal fractions of bulge and disk mass) have the lowest $j_{rm dark matter}$ of all. Yet, when controlling for halo mass, rather than stellar mass, the relationship between $j_{rm dark matter}$ and morphology vanishes. Based on these results, halo mass rather than angular momentum is the main driver of the predicted morphology sequence at high masses. In fact, in our stellar mass range, disk-dominated galaxies live in dark matter halos that are roughly 1/10th the mass of their bulge-dominated counterparts.
Early-type galaxies -- slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars -- define a Fundamental Plane (FP) in the space of half-light radius $R_e$, enclosed surface brightness $I_e$ and velocity dispersion $sigma_e$. Since $I_e$ and $sigma_e$ are distance-independent measurements, the thickness of the FP is often expressed in terms of the accuracy with which $I_e$ and $sigma_e$ can be used to estimate sizes $R_e$. We show that: 1) The thickness of the FP depends strongly on morphology. If the sample only includes E-SRs, then the observed scatter in $R_e$ is $sim 16%$, of which only $sim 9%$ is intrinsic. Removing galaxies with $M_*<10^{11}M_odot$ further reduces the observed scatter to $sim 13%$ ($sim 4%$ intrinsic). The observed scatter increases to the $sim 25%$ usually quoted in the literature if E-FRs and S0s are added. If the FP is defined using the eigenvectors of the covariance matrix of the observables, then the E-SRs again define an exceptionally thin FP, with intrinsic scatter of only $5%$ orthogonal to the plane. 2) The structure within the FP is most easily understood as arising from the fact that $I_e$ and $sigma_e$ are nearly independent, whereas the $R_e-I_e$ and $R_e-sigma_e$ correlations are nearly equal and opposite. 3) If the coefficients of the FP differ from those associated with the virial theorem the plane is said to be `tilted. If we multiply $I_e$ by the global stellar mass-to-light ratio $M_*/L$ and we account for non-homology across the population by using Sersic photometry, then the resulting stellar mass FP is less tilted. Accounting self-consistently for $M_*/L$ gradients will change the tilt. The tilt we currently see suggests that the efficiency of turning baryons into stars increases and/or the dark matter fraction decreases as stellar surface brightness increases.
We study the baryonic Tully-Fisher relation (BTFR) at z=0 using 153 galaxies from the SPARC sample. We consider different definitions of the characteristic velocity from HI and H-alpha rotation curves, as well as HI line-widths from single-dish observations. We reach the following results: (1) The tightest BTFR is given by the mean velocity along the flat part of the rotation curve. The orthogonal intrinsic scatter is extremely small (6%) and the best-fit slope is 3.85+/-0.09, but systematic uncertainties may drive the slope from 3.5 to 4.0. Other velocity definitions lead to BTFRs with systematically higher scatters and shallower slopes. (2) We provide statistical relations to infer the flat rotation velocity from HI line-widths or less extended rotation curves (like H-alpha and CO data). These can be useful to study the BTFR from large HI surveys or the BTFR at high redshifts. (3) The BTFR is more fundamental than the relation between angular momentum and galaxy mass (the Fall relation). The Fall relation has about 7 times more scatter than the BTFR, which is merely driven by the scatter in the mass-size relation of galaxies. The BTFR is already the fundamental plane of galaxy discs: no value is added with a radial variable as a third parameter.
We study the empirical relation between an astronomical objects angular momentum $J$ and mass $M$, $J=beta M^alpha$, the $J-M$ relation, using N-body simulations. In particular, we investigate the time evolution of the $J-M$ relation to study how the initial power spectrum and cosmological model affect this relation, and to test two popular models of its origin - mechanical equilibrium and tidal torque theory. We find that in the $Lambda$CDM model, $alpha$ starts with a value of $sim 1.5$ at high redshift $z$, increases monotonically, and finally reaches $5/3$ near $z=0$, whereas $beta$ evolves linearly with time in the beginning, reaches a maximum and decreases, and stabilizes finally. A three-regime scheme is proposed to understand this newly observed picture. We show that the tidal torque theory accounts for this time evolution behaviour in the linear regime, whereas $alpha=5/3$ comes from the virial equilibrium of haloes. The $J-M$ relation in the linear regime contains the information of the power spectrum and cosmological model. The $J-M$ relations for haloes in different environments and with different merging histories are also investigated to study the effects of a halos non-linear evolution. An updated and more complete understanding of the $J-M$ relation is thus obtained.
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