How Do Disk Galaxies Form?

Abstract

In both observed and simulated galaxies, disk morphologies become more prevalent at higher masses and lower redshifts. To elucidate the physical origin of this trend, we develop a simple analytical model in which galaxy morphology is governed by the competition between rotational support and turbulence in a gravitational potential of a dark matter halo and the galaxy itself, and a disk forms when the potential steepens due to the accumulation of baryons in the halo center. The minimum galaxy mass required for this transition decreases with an increasing dark matter contribution within the galaxy, making more concentrated halos more prone to forming disks. Our model predicts that galaxy sizes behave qualitatively differently before and after disk formation: after disks form, sizes are governed by the halo spin, in agreement with classical models, whereas before disk formation, sizes are larger and set by the scale on which turbulent motions, which dominate over rotation, can be contained. We validate our model against the results of the TNG50 cosmological simulation and, despite the simplicity of the model, find remarkable agreement. In particular, our model explains the increase with redshift in the critical halo mass for disk formation, reported in both simulations and observations, as a consequence of the evolution of the halo mass-concentration and baryonic mass-halo mass relations. This redshift trend therefore supports the recent proposal that it is the steepening of the gravitational potential that causes disk formation, while other effects discussed in the literature, such as potential deepening and hot gaseous halo formation, can still play important roles in the transition from early turbulent to dynamically cold disks.

Figures (11)

• Figure 1: Schematic illustration of the disk formation scenarios and the role played by the gravitational potential (or the shape of the rotation curve). Top: a disk forms when the scale on which baryons settle into rotational support, $r_{\rm circ}$, is larger than the scale on which the turbulent motions are contained by the gravitational potential, $r_{\rm turb}$. With the definitions described in the text, this criterion, $r_{\rm circ}/r_{\rm turb} > 1$, is equivalent to $v_{\rm rot}/\sigma > 1$. Bottom: the transition from non-disks ($r_{\rm circ}/r_{\rm turb} < 1$) to disks ($r_{\rm circ}/r_{\rm turb} > 1$) can be achieved either by decreasing $\sigma$ relative to $v_{\rm vir}$, or by making the potential steep, resulting in a peaked rotation curve.
• Figure 2: Rotation curves of an NFW dark matter halo with different concentrations $c$. The corresponding scale-radius, $r_{\rm s}/r_{\rm vir} = 1/c$, is shown with the vertical ticks. As a proxy for the galaxy size, the red vertical lines show the range of halo spin parameters, $\lambda$, with the mean value of 0.035 and 0.22 dex of scatter. For a pure dark matter halo, $v_{\rm c}/v_{\rm vir}$ evaluated at $x \sim \lambda$ is usually $< 1$, implying shallowly rising potential and therefore a dispersion-dominated system ($v_{\rm rot}/\sigma < 1$, or $r_{\rm circ}/r_{\rm turb} < 1$).
• Figure 3: The contribution of baryons (including stars and gas) to the gravitation potential in the halo center can produce a sufficiently steep potential to trigger disk formation. Different colors show rotation curves assuming that the $f_{\rm b} = 0.2$ fraction of available baryons is concentrated at the center, with three different half-mass radii ($x_{\rm b}$; also shown with the vertical ticks), with the smaller $x_{\rm b}$ leading to more peaked rotation curves. Different line styles show the total (thick) and individual contributions of baryons (thin) and dark matter (dashed). The top panel shows $v_{\rm c}(r)$ assuming that the dark halo remains fixed (with the concentration $c = 5$, which is typical for $M_{\rm vir} \sim 10^{11} {\rm \;M_\odot}$ at $z \sim 2$), while the bottom panel also accounts for the adiabatic contraction of the halo (AC; see Section \ref{['sec:model:profile:ac']}). The markers show the value of $v_{\rm c}/v_{\rm vir}$ at $x_{\rm b}$. According to our criterion ($v_{\rm c}(x_{\rm b})/v_{\rm vir} > 1$), without AC, only the smallest of $x_{\rm b}$ can produce a steep enough potential to trigger disk formation, while with AC, all three values satisfy this condition.
• Figure 4: Distinction between disks and non-disks in the plane of the galaxy baryon-half-mass size, $x_{\rm b}$, and mass fraction, $f_{\rm b}$. Top: The potential steepness parameter ($v_{\rm c}(x_{\rm b})/v_{\rm vir}$) as a function of $x_{\rm b}$ and $f_{\rm b}$, for an NFW halo with concentration $c = 5$. For reference, the dotted line shows the half-mass radius of the NFW profile, while solid and dashed black horizontal lines show the typical values of the halo spin parameter, $\lambda$, with $x_{\rm b} \sim \lambda$ being the typical size of a galaxy in full rotational support. If a galaxy with velocity dispersion $\sigma \sim v_{\rm vir}$ (see Section \ref{['sec:model:idea:assumptions']}) is in a shallow potential ($v_{\rm c}(x_{\rm b})/v_{\rm vir} < 1$; red color), its size will expand until the scale on which this $\sigma$ can be contained, i.e., until $x_{\rm b}$ at which $v_{\rm c}(x_{\rm b})/v_{\rm vir} \sim 1$ (see Section \ref{['sec:model:transition']}). Conversely, if the potential is steep ($v_{\rm c}(x_{\rm b})/v_{\rm vir} > 1$), the galaxy size will approach $x_{\rm b} \sim \lambda$ at which the gravity is balanced by the centrifugal force. These two attractors are indicated with the thick purple line corresponding to "non-disks" and "disk" parts, respectively. Bottom: The transition between non-disks and disks depends on the halo concentration, so that for higher $c$, the fraction of baryons $f_{\rm b}$ needed to produce the steep potential becomes smaller, and these baryons need to be concentrated on a smaller scale. This relation is shown by the purple line, which traces the turnover point on the critical line $v_{\rm c}(x_{\rm b})/v_{\rm vir} = 1$, shown for a set of $c$ values. This relation enables one to formulate a criterion for disk formation with non-disks exhibiting low $c$, low $f_{\rm b}$, and large $x_{\rm b}$, while disks correspond to high $c$, high $f_{\rm b}$, and small $x_{\rm b}$ (see Section \ref{['sec:model:criterion']}).
• Figure 5: Evolution of the MW-like galaxies from TNG50 in the plane of the baryon half-mass size, $x_{\rm b}$, and galaxy mass fraction, $f_{\rm b}$. Large circles show the final locations of these galaxies at $z=0$ (when these analogs are identified; see Section \ref{['sec:results:methods:tng50']}), while small circles show their locations in preceding snapshots out to $z \sim 12$. The points are colored according to the rotational support of the star-forming disk ($v_{\rm rot}/\sigma$; top panel) and the potential steepness parameter ($v_{\rm c}(x_{\rm b})/v_{\rm vir}$; bottom panel). The purple line shows the transition from non-disks (above the line) to disks (below the line) predicted by our model (see Figure \ref{['fig:fbxb-model']}). Despite the drastic differences in mass assembly histories, disk-formation timing, and the presence of destructive galaxy mergers semenov23a, our model describes disk formation in this galaxy sample remarkably well. The comparison of colors between the two panels shows that the disk formation is associated with the steepening of the gravitational potential in agreement with our formal criterion (see Section \ref{['sec:model:criterion']}).