Phase spirals across galactic disks I: Exploring dynamical influences on winding

Abstract

The vertical phase-space spirals in the Milky Way are clear evidence of disequilibrium. However, they are challenging to study because phase mixing signals evolve under the influence of many different dynamical processes and can be driven by many sources of disequilibrium. We characterize phase spirals in two simulations -- one test particle and one N-body -- with basis function expansions, using these to derive winding times ($T_{\rm fit}$). We find that phase spirals in the test particle simulation wind up as expected from pure phase mixing theory while those in the self-consistent simulation do not. Specifically, in the N-body simulation we find that (i) the onset of winding is delayed, (ii) the winding rate is slowed, and (iii) the rate of winding oscillates with time. The extent of these effects depends on the azimuthal action $J_φ$ of the phase spiral region. We build some physical intuition for these effects through 1-D toy models which follow a group of co-moving stars traveling through several different evolving potentials. We find that phase spiral winding can be delayed until the group no longer moves coherently with the midplane of the (perturbed) potential and oscillates with time as the group experiences (e.g.) a breathing mode traveling through the disk. Rates of winding change as the vertical structure of the disk evolves. The modifications to winding are strongest in the inner galaxy where the disk potential dominates. We conclude that in the Milky Way, all calculations of the winding time should be interpreted as lower limits and that the most trustworthy winding times are likely in the outer disk.

Figures (10)

• Figure 1: The orbit of the perturber in both the test particle (left panels) and N-body (right panels) simulations. $T=0$ in these panels corresponds to the time of the disk crossing.
• Figure 2: Two examples of the BFE reconstructions for phase spirals in the test particle (top row) and N-body (bottom row) simulations. In the test particle example, we show the BFE reconstruction for a snapshot taken 0.5 $\mathrm{\,Gyr}$ after the interaction in a region with center $(\theta_{\phi}, J_{\phi}) = (\pi/2 \textrm{ rad}, 2000 \mathrm{\,kpc}\xspace \mathrm{\,km}\xspace \mathrm{\,s}\xspace^{-1})$. In the N-body example, we show the BFE reconstruction for a snapshot taken $\simeq 1$$\mathrm{\,Gyr}$ after the interaction in a region with center $(\theta_{\phi}, J_{\phi}) = (\pi/2 \textrm{ rad}, 2000 \mathrm{\,kpc}\xspace \mathrm{\,km}\xspace \mathrm{\,s}\xspace^{-1})$. In each row, the left panel shows the smoothed (using a 2D gaussian filter with $\sigma=0.2 \: (\mathrm{\,kpc}\xspace \mathrm{\,km}\xspace/\mathrm{\,s}\xspace)^{1/2}$) background-subtracted data from the simulation. The second panel shows the 2D reconstruction from the BFE using the $m=1$ and $m=2$ coefficients. The third panel shows the residual when subtracting the first two panels, divided by the background. For clarity, we only perform the residual calculation for pixels containing more than 5 particles. The rightmost panel shows the combined amplitude of coefficients for each $m$, defined by $\sqrt{\sum_n A_{nm}^2}$ for $n=0,\ldots,19$. The figure demonstrates that the BFEs effectively recover the distribution of particles for different phase space morphologies and separate noise from the signal.
• Figure 3: Left: BFE reconstructions ($m=1$ only) of the phase spiral in the test particle simulation. Each row shows phase spirals at different simulation times, where $T=0$$\mathrm{\,Gyr}$ is the disk crossing time. Each column shows a a different region, with $J_\phi$ increasing from left to right. For each $J_\phi$ we choose the bin with azimuthal center $\theta_\phi=0$. At the same timestep, We see more wound up phase spirals in the inner disk. We gray out the panels where the spiral is too wound up for the resolution of the simulation, leading to an nonphysical reconstruction. Right: The same as the left grid but for the N-body simulation. Here we add an additional column because we have sufficient particles to reconstruct phase spirals out to a larger $J_\phi$. These phase spirals are noisier due to the more complex simulation and interaction. They are also noticeably less wound up than in the test particles case, especially in the inner disk.
• Figure 4: Left:$T_{\rm fit}$ calculated for each bin 0.4 $\mathrm{\,Gyr}$ after the disk crossing in the test particle simulation. Middle: The same as the left panel except that the regions have been rewound to where they were at the time of the interaction. The diagonal ridges of red or blue in the left panel (which would appear as a "macro-spiral" in a face-on view of the disk) unwind into a dipole. This occurs because of differences in when each region experiences the highest amplitude perturbation from the satellite, as explained in Section \ref{['sec:tp_results']} and Gandhi:2022. We note that the perturber crosses the disk at $\theta_\phi = 0$ (or $\pi$), exactly where the dipole split appears. Right: The mean $T_{\rm fit}$ values for each $\theta_\phi$ row in the rewound (middle) plot. The true time since the disk crossing ($0.397 \mathrm{\,Gyr}\xspace$) is denoted with the red dashed line.
• Figure 5: Top left: The $50 \mathrm{\,Myr}\xspace$ moving average of the median $T_{\rm fit}$ value for each $J_\phi$ at each test particle simulation timestep. The dashed black line corresponds to the expected $T_{\rm fit}$ at each timestep from pure phase mixing theory. As discussed in Section \ref{['sec:tp_results']}, the phase spirals in this simulation eventually wind up too much for our resolution to capture them, at which point the $T_{\rm fit}$ calculations are meaningless and fail. This is the reason why some of the curves are not continuous or do not span the entire x-axis. Bottom left: The residual of the top left plot with respect to the expected $T_{\rm fit}$ from pure phase mixing theory. This can also be interpreted as the difference between the derived perturbation time from $T_{\rm fit}$ and the true disk crossing time. Right: The $50 \mathrm{\,Myr}\xspace$ moving average of the median $T_{\rm fit}$ value for each $J_\phi$ at each N-body simulation timestep. In our median calculations, we only include regions with $T_{\rm fit}$ values between 0 and 2 times the value expected from phase mixing theory. We see clearly here that while there are winding delays at all $J_\phi$, the phase spirals in the inner disk are far more affected by n-body interactions. Note: the conversion from $J_\phi$ to $R_G$ in the colorbar is done according to the N-body simulation. The test particle simulation does not have exactly the same scaling (see the two x-axes in Fig. \ref{['fig:tp_dipole']} for a visualization of the test-particle scaling).