[Paper Review] Measuring the dynamical length of galactic bars

Michael Petersen, Martin D. Weinberg+1 more|arXiv (Cornell University)|May 22, 2023

Stellar, planetary, and galactic studies4 citations

TL;DR

This paper introduces the 'dynamical length' of a galactic bar—defined as the radial extent of the $x_1$ orbits that form the bar's backbone—using a novel velocity-based method from integral field unit (IFU) spectroscopy. The method identifies $x_1$ orbits via the $v_{4\perp}/v_{2\perp}$ Fourier velocity diagnostic, revealing that traditional ellipse-fitting techniques overestimate bar length by 1.5–2.5×, leading to biased inferences about bar mass and pattern speed.

ABSTRACT

We define a physically-motivated measure for galactic bar length, called the dynamical length. The dynamical length of the bar corresponds to the radial extent of the orbits that are the backbone supporting the bar feature. We propose a direct observational technique using integral field unit spectroscopy to measure it. Identifying these orbits and using the dynamical length is a more faithful tracer of the secular evolution and influence of the bar. We demonstrate the success of the metric for recovering the maximal bar-parenting orbit in a range of simulations, and to show its promise we perform its measurement on a real galaxy. We also study the difference between traditionally used ellipse fit approaches to determine bar length and the dynamical length proposed here in a wide range of bar-forming N-body simulations of a stellar disc and dark matter halo. We find that ellipse fitting may severely overestimate measurements of the bar length by a factor of 1.5-2.5 relative to the extent of the orbits that are trapped and actually comprise the bar. This bias leads to overestimates of both bar mass and the ratio of corotation radius to bar length, i.e. the bar speed, affecting inferences about the evolution of bars in the real universe.

Motivation & Objective

• To define a physically motivated bar length metric based on the radial extent of $x_1$ orbits, the dynamical backbone of the bar.
• To address the systematic overestimation of bar length by conventional ellipse-fitting techniques in both simulations and observations.
• To develop and calibrate an observational method using IFU velocity fields to measure the true dynamical length of galactic bars.
• To demonstrate that current bar length measurements bias inferences about bar mass and pattern speed, particularly the $R_{\rm CR}/R_{\rm bar}$ ratio.
• To validate the method on a real galaxy and show its robustness across a range of simulated bar-forming systems.

Proposed method

• Define the dynamical length as the maximum radial extent of $x_1$ orbits, which are the primary structural and dynamical support of the bar.
• Use Fourier decomposition of the stellar velocity field to identify the $v_{4\perp}/v_{2\perp}$ velocity diagnostic, which traces the apocentres of $x_1$ orbits.
• Apply the $x_1$ velocity method to simulated galaxies to calibrate the diagnostic against known $x_1$ orbit extents.
• Compare the dynamical length from the velocity method with bar lengths derived from ellipse fitting across a range of $N$-body simulations.
• Apply the calibrated $x_1$ velocity method to MaNGA IFU data of a real barred galaxy to measure its dynamical bar length.
• Use a brute-force binning approach to test different spatial configurations for the velocity diagnostic, with future work aiming for a continuous function estimator.

Figure 1: Upper panel: The length of the bar in disc scale lengths, measured using four different techniques: maximal $x_{1}$ extent, two different ellipse fits, and our $x_{1}$ velocity diagnostic, versus time. The $x_{1}$ -derived length is the black curve. The simulation ellipse-fit-derived lengt

Experimental results

Research questions

• RQ1 How does the dynamical length, defined by the maximal $x_1$ orbit extent, compare to bar lengths measured via traditional ellipse fitting in simulated barred galaxies?
• RQ2 To what extent do ellipse-fitting techniques overestimate the true radial extent of trapped $x_1$ orbits in barred galaxies?
• RQ3 Can the $v_{4\perp}/v_{2\perp}$ velocity diagnostic reliably identify the apocentres of $x_1$ orbits in both simulations and real IFU data?
• RQ4 How does the bias in ellipse-fitting affect inferences about bar mass and pattern speed, particularly the $R_{\rm CR}/R_{\rm bar}$ ratio?
• RQ5 Can the $x_1$ velocity method be successfully applied to real galaxies, and does it recover a shorter bar length than ellipse fitting?

Key findings

• The dynamical length, based on the maximal $x_1$ orbit turnaround radius, provides a physically grounded and robust measure of bar extent.
• Ellipse-fitting techniques systematically overestimate bar length by a factor of 1.5 to 2.5 compared to the true extent of trapped $x_1$ orbits.
• The $x_1$ velocity method successfully recovers the true dynamical bar length in simulations and correctly identifies a shorter bar length than ellipse fitting in a real galaxy.
• The overestimation from ellipse fitting arises because it includes untrapped, deformed orbits outside the true bar region, which are not dynamically part of the bar.
• The bias in bar length measurement leads to overestimates of both bar mass and the $R_{\rm CR}/R_{\rm bar}$ ratio, distorting inferences about bar evolution and pattern speed.
• The $x_1$ velocity method is robust across different evolutionary phases of barred galaxies and works effectively on real IFU data, offering a reliable alternative to ellipse fitting.

Figure 2: Upper panels: Log surface density, in normalised units, for the three evolutionary phases in the simulation: assembly, growth, and steady-state. Lower panels: The velocity field in the direction tangential to the bar, for the three phases in the upper panels. The white dashed ellipses show