Formation timescales for stellar bars in diverse galactic discs

Abstract

We study the formation of stellar bars using 145 simulations of disc galaxies embedded in live and static dark matter haloes. We use the exponential bar growth timescale, $τ_{\rm bar}$, to quantify how disc structure and kinematics regulate the onset and rate of secular bar formation. We extend previous work to thicker and more turbulent discs, motivated by those observed at high redshift ($z>1$). By revisiting several commonly used disc stability criteria - the Efstathiou-Lake-Negroponte parameter ($ε_{\rm ELN}$), the Ostriker-Peebles ratio ($t_{\rm OP}$), and the disc stellar mass fraction within 2.2 disc scale radii ($f_{\rm disc}$) - we find that $τ_{\rm bar}$, when expressed in terms of the disc's orbital period, follows a tight power law with each criteria. In Milky Way-like discs embedded in live haloes, bars form within a Hubble time if $f_{\rm disc} \geq 0.18$, $t_{\rm OP} \geq 0.27$, and $ε_{\rm ELN} \leq 1.44$. We show discs with higher velocity dispersion experience delayed bar growth and introduce an empirical relation that correctly describes the bar formation timescales of all our live halo models. Bars in static haloes grow at roughly half the rate of those in live haloes and require substantially greater disc instability to do so.

Figures (9)

• Figure 1: The bar strength, $A_{2}^{\rm max}$, is show as a function of time for three example models in the fiducial suite ($Q_{\rm min}=1.5$, $h_{z}=0.1$) with varied $C$. Darker lines indicate discs in more highly concentrated DM haloes, and shorter orbital times. Circles indicate the time at which the bar begins to buckle, and the assembly phase ends. The solid red lines indicate an exponential fit of Eqn. \ref{['eq:taubar']} to the assembly phase for each model, the dotted red lines indicate the extrapolated fit to early times. The horizontal grey dashed line displays the delineation between barred and unbarred galaxies.
• Figure 2: The face-on surface mass density projection of the stellar discs in the live halo fiducial simulation suite at $t = 2.5\,{\rm Gyr}$ for MW-scale. Each row displays a fixed disc-to-halo mass fraction, $M_{\rm d}/M_{\rm h}$, increasing from top to bottom, while each column displays a fixed halo-to-disc scale length fraction, $C$, increasing (decreasing in relative halo concentration) from left to right. All systems are run in a live Hernquist halo. The white horizontal bar indicates a scale of $2R_{\rm d}$.
• Figure 3: The bar strength, $A_{2}^{\rm max}$, as a function of time for the fiducial suite of discs in live haloes (blue) and static haloes (orange). Each row displays a fixed disc-to-halo mass ratio, $M_{\rm d}/M_{\rm h}$, increasing from top to bottom, while each column displays a fixed halo-to-disc scale length ratio, $C$, increasing (decreasing in relative halo concentration) from left to right. The grey dashed line indicates the $A_{2}$ amplitude above which we choose to identify bars. In the top right corner of each panel we indicate with a coloured check-mark if a bar forms within the simulation runtime.
• Figure 4: The normalised bar growth timescale, $\tau_{\rm bar} / t_{\rm orb}$, plotted against the central disc-to-halo mass fraction, $f_{\rm disc}$, the OP1973 criterion, $t_{\rm OP}$, and the ELN1982 criterion, $\epsilon_{\rm ELN}$, from left to right, respectively, shown in log-log space. The dashed horizontal line and grey shaded region at the top of each panel indicate timescales greater than a Hubble time, $\tau_{\rm H}$. Simulations with live haloes are plotted as blue circles, while simulations in static haloes are plotted as orange squares. Fits to the live halo data are shown as thick black lines, with dark shaded regions showing the fit errors. The criteria for disc stability defined by ELN1982, $\epsilon_{\rm ELN} = 1.1$, is shown as a grey vertical line, while those from Syer1998 are plotted as dashed and dotted grey lines. The vertical, solid red lines show the stability threshold below which bars form in our fiducial suite within $\tau_{\rm H}$.
• Figure 5: Overview of the bar growth timescale $\tau_{\rm bar}$ as a function of $f_{\rm disc}$, for the fiducial live halo runs of this work, the runs of Fujii2018 and those of BlandHawthorn2023. The data of BlandHawthorn2023 contains three subsets of different halo masses, which we show using their their three corresponding fits (grey lines). The data from Fujii2018 are shown as pink diamonds, and a similar fit to this data is shown as the black dotted line. This figure does not represent a like-for-like comparison, but illustrates the differences caused by various physical, numerical and post-processing choices (see Section \ref{['ss:comp']}).