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The Impact of Bar-induced Non-Circular Motions on the Measurement of Galactic Rotation Curves

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The standard tilted-ring rotation curve of a barred galaxy is a projection of elliptical gas flows, and when the bar and disk major axes differ by less than about 40 degrees it shows a bar-induced dip that is not present in the true…

desk verdict A credible Δφ-dependent dip in barred-galaxy RCs, with a PHANGS-ALMA census that is suggestive but whose correction rests on an unvalidated transfer from one quadrupole simulation. read the letter →

arxiv 2501.12760 v1 pith:6F7ZQ4NF submitted 2025-01-22 astro-ph.GA

Jie Liu , Zhi Li , Juntai Shen This is my paper · ORCID
classification astro-ph.GA
keywords galacticrotationcurvesbarredgalaxiesnon-circularmotionstilted-ringmethodbar-induceddipfeaturehydrodynamicsimulationsnuclearringgalaxykinematics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that bar-driven non-circular gas motions systematically corrupt rotation curves measured by the standard tilted-ring method, and that the corruption pattern is controlled by the angle between the bar and disk major axes in the face-on plane. For small angles, the measured curve develops a characteristic dip: an inner peak above the true circular speed, a trough below it across the bar, and a recovery outside. The authors find the same dip in hydrodynamic simulations and in a large fraction of observed barred spiral galaxies with molecular-gas kinematics. They explain the dip with a simple geometric model and propose a first-order correction that subtracts a simulation-calibrated deviation profile scaled to each galaxy. If correct, published rotation curves for barred galaxies are biased in a way that can now be approximately undone.

What carries the argument

The central object is the deviation profile $g(R,\Delta\varphi) = (V_{\mathrm{c,tilted,0}}(R,\Delta\varphi) - V_{\mathrm{c,true,0}}(R))/V_{\mathrm{flat,0}}$ measured from the quadrupole-bar hydrodynamic simulation. This profile encodes how the tilted-ring fit overestimates the circular speed in the nuclear ring and underestimates it in the bar when the bar and disk are nearly aligned. The correction procedure takes this dimensionless deviation, rescales it by the target galaxy's flat rotation speed, stretches it to match the galaxy's bar length and the radius of the dip minimum, and subtracts it from the observed tilted-ring rotation curve. The geometric 'misaligned ellipses' model supplies the underlying picture: elliptical gas orbits with constant angular momentum, whose ellipticities and orientations vary with radius, twist from perpendicular to the bar in the nuclear ring to parallel with the bar near the bar end.

What would settle it

Take a barred galaxy whose true circular-speed curve is known independently, for example from a stellar dynamical mass model or from a high-resolution simulation with realistic gas and star formation, measure its tilted-ring rotation curve, and apply the paper's correction; if the corrected curve is not closer to the true curve than the uncorrected one across a set of such cases, the empirical transfer assumption fails.

Watch

Extended reading notes

Core claim

The authors claim that the tilted-ring rotation curve of a barred galaxy is not a direct measurement of the true circular-speed profile $V_{\mathrm{true}}(R)$; it is a $\Delta\varphi$-dependent projection of elliptical, non-circular gas streamlines. For $|\Delta\varphi| \lesssim 40^\circ$, this projection produces a bar-induced 'dip': a central peak above the true curve, a trough below it across the bar region, and a recovery beyond the bar. The dip appears in hydrodynamic simulations with a quadrupole bar potential and is common in the observed sample of barred galaxies. A 'misaligned ellipses' model, in which streamlines rotate from perpendicular to the bar in the nuclear ring to parallel with the bar, reproduces the trend and explains why the nuclear ring boosts $V_{\mathrm{los}}$ while the bar suppresses it. The paper then proposes a first-order correction that subtracts the simulated deviation profile, scaled to each galaxy's flat velocity and bar length.

Load-bearing premise

The correction assumes that the deviation pattern measured in one simulated barred galaxy applies to every real barred galaxy after rescaling by its flat rotation speed and bar length; if that transfer fails, the corrected rotation curves are not closer to the true curve.

Editorial extensions

If this is right

  • Barred galaxies with a small bar-disk angle will have published tilted-ring rotation curves that underestimate rotation speeds across the bar, so mass models and dark-matter fits built on those curves inherit a systematic bias.
  • The sign of the bias flips for bars nearly perpendicular to the disk major axis: the tilted-ring curve overshoots in the bar region instead of undershooting.
  • A decline-rise shape alone is not a bar signature; a massive bulge or strong spiral can produce a similar shape outside the optimal angle range, so identifying a bar-induced dip requires the photometric bar angle and bar length.
  • Applying the first-order correction changes the fitted rotation-curve parameters for the nine galaxies shown, such as lowering the asymptotic speed of NGC 1097 from 328 to 257 km s$^{-1}$, so dynamical inputs for these galaxies shift.
  • Reclassifying several galaxies as barred or unbarred and updating their bar lengths, as the paper does for NGC 4941 and NGC 5248, changes which galaxies are counted as showing the dip.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural test of the method is to build a suite of barred-galaxy simulations spanning different bar strengths, pattern speeds, and disk mass models; if the rescaled deviation profile $g(R,\Delta\varphi)$ does not collapse onto one curve, the correction's error budget is larger than stated.
  • The dip's asymmetry with respect to the sign of $\Delta\varphi$ suggests the shape of the dip could be inverted to estimate the bar's face-on orientation from gas kinematics alone, which would help where photometric bar position angles are uncertain.
  • Because the correction assumes the flat rotation speed is reached at the outermost measured point, galaxies with still-rising outer rotation curves will have the correction amplitude underestimated; applying the method to simulated galaxies with rising outer curves would quantify this effect.
  • The paper's dip classification could be turned into a quantitative classifier (central peak above the true curve, trough below it, recovery before the bar end) and tested on an independent sample of barred and unbarred galaxies with molecular-gas kinematics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript uses two-dimensional hydrodynamical simulations of gas in a quadrupole barred potential, with a Ferrers model as a secondary check, to study how bar-induced non-circular motions bias rotation curves derived with the tilted-ring method. The central simulation result is that RC_tilted deviates from RC_true in a way that depends on the angle Δφ between the bar major axis and the disk major axis in the face-on plane, producing a rise-drop-rise 'dip' feature for |Δφ| ≲ 40°. The paper then identifies decline-rise features in nine PHANGS-ALMA barred galaxies, proposes a qualitative 'misaligned ellipses' model to explain the projection effect, and introduces an empirical correction procedure described by Eqs. (6)-(9) that scales the quadrupole simulation's deviation profile to real galaxies. The overall message is that the tilted-ring rotation curve of a barred galaxy should be interpreted as a Δφ-dependent projection of elliptical gas flows rather than as the true circular-speed profile.

Significance. If the main result holds, the paper provides a systematic, physically motivated explanation for previously noted discrepancies between tilted-ring and true rotation curves in barred galaxies, and it offers a straightforward first-order correction that could be applied to large CO and HI surveys. The study's strengths are the clean forward simulation experiment, the density-threshold test in Appendix A, the use of the homogeneous PHANGS-ALMA sample, and the explicit acknowledgment of many limitations. The principal weakness is that both the observational dip census and the correction procedure rely on transferring the quadrupole simulation's deviation profile g(R, Δφ) to real galaxies without independent validation: the Ferrers model is described as yielding similar effects but is not used to test the correction, and the observational identification cannot verify the full simulation-based definition of a dip because RC_true is unknown. The conclusions are therefore plausible and important, but they are not as firmly established as the abstract's wording suggests.

major comments (3)
  1. [§4.3, Eqs. (6)-(9)] The correction method assumes that the deviation profile g(R, Δφ) measured from a single quadrupole model with one amplitude, one scale length, one pattern speed, and one sound speed applies to all barred galaxies after scaling by V_flat and stretching radii. The Ferrers model is mentioned as producing similar effects but is never used to derive or test a correction profile, and Appendix A's density-threshold test reuses the same quadrupole model. The corrected points in Figure 3 have no propagated uncertainties and are not compared with any independent estimate of RC_true, so the statement that the corrected RCs 'may be closer to RC_true' is an assumption rather than a demonstrated result. I recommend either validating the correction on a second potential or on mock observations with known RC_true, or clearly labeling Figure 3 as an illustrative first-order exercise.
  2. [§3, Figs. 3 and 4] The observational identification of a dip uses only the decline-rise trend in RC_tilted because RC_true is unknown, whereas the simulation-based definition in §2 also requires the central peak to exceed RC_true and the local minimum to lie below it. The |Δφ| ≲ 40° threshold is imported from the quadrupole model without independent calibration, and the paper itself notes that NGC 4321 and NGC 1566 show that a compact bulge can mimic the feature. The claim that dip features are 'very common' in PHANGS is therefore based on a weaker criterion than the full definition, and the 85% agreement statistic inherits this ambiguity. I suggest rewording the observational claim to 'decline-rise features consistent with a bar-induced dip under the assumed Δφ criterion' and adding, if possible, a control comparison with the unbarred sample or an alternative feature-detection statistic.
  3. [§4.2, Fig. 7 and Appendix D] The misaligned-ellipses model takes its ellipticity values (ϵ_ring, ϵ_bar), the radial transition, and the orbit-orientation profile from the same quadrupole simulation whose RC deviation it then reproduces, so it is a compact description of the simulation's kinematics rather than an independent test of the proposed mechanism. Appendix D further shows that when the model is fitted to the simulated V_los map with Eq. (5), the recovered RC still deviates strongly from RC_true. This does not invalidate the qualitative picture, but the text should state more explicitly that the model is illustrative and not a quantitative recovery method.
minor comments (5)
  1. [Abstract] The LaTeX macro \misaell appears unresolved in the abstract; it should be replaced with the intended phrase 'misaligned ellipses'.
  2. [§4.3, Eq. (6)] The subscript in V_c,titled should be V_c,tilted for consistency with the rest of the paper.
  3. [§3] The sentence 'About 85% of the galaxies in our sample align with the expectations from simulations' is not defined: the reader cannot determine which galaxies are counted in the numerator and denominator. Please specify the calculation.
  4. [§4.3] The phrase 'stretching or compressing' refers only to the radial coordinate in Eqs. (7)-(8); the deviation amplitude is not rescaled beyond the V_flat factor. Clarify this to avoid implying an amplitude adjustment.
  5. [§2] The Ferrers model is said to yield 'similar effects,' but no quantitative comparison or figure is provided. If it is not used further, state explicitly that it serves only as a consistency check.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central simulation is a forward numerical experiment, and the correction transfer and dip threshold are openly stated model assumptions rather than hidden reductions.

full rationale

The paper's principal derivation is a forward hydrodynamical experiment: the quadrupole and Ferrers potentials are specified (Eqs. 1–2), the gas response is computed with Athena++, and RC_tilted is obtained by fitting Eq. 3 to the simulated Vlos maps. Nothing in this chain is fitted to the observed RCs, so the central result (a bar-induced dip for |Δϕ|≲40°) is not circular. The two places where one might suspect self-reference are explicitly handled as assumptions rather than hidden reductions. First, the correction in §4.3 is built from the simulation's own g(R,Δϕ) (Eq. 9), and the paper states: 'We assume that the relationship between Δϕ and the deviations of RC, as empirically determined by our simulations in Figure 2, is applicable to all galaxies.' Applying Eq. 6 therefore transfers a modeled bias to real data; whether it truly brings the PHANGS RCs closer to RC_true is an unvalidated calibration question, not a circular derivation, and the Summary concedes that 'developing a single comprehensive model for all galaxies is impractical.' Second, the 'misaligned ellipses' model in §4.2 takes its ellipticity profile from the simulation ('The ellipticity ε_ring is measured directly from the surface density of the simulation') and its velocity scale from RC_true; its successful reproduction of the dip is an internal consistency check of the streamline-projection explanation, and the paper itself reports the quantitative failure of the fitting version ('these outcomes indicate that the “misaligned ellipses” model is inadequate'). The observed dip census shares the simulation's |Δϕ|≲40° threshold; the paper flags the unknown RC_true as a limitation for NGC 4321 and NGC 1566, which is a completeness/robustness caveat rather than a circularity. Self-citations (Li et al. 2015; Qin & Shen 2021) are present but non-load-bearing: the nuclear-ring orientation claim is also supported by Athanassoula, Maciejewski, and Kim et al., and the I2 alternative is only mentioned as an attempted path. The paper is therefore self-contained on its main claims.

Assumptions & free parameters 12 free parameters · 8 assumptions · 0 invented entities

The central claim rests on two layers: forward hydrodynamic simulations that generate the dip feature, and an empirical transfer of that simulated deviation to real galaxies. The simulations themselves require several hand-chosen potential, gas, and projection parameters. The correction adds the strongest assumption: the quadrupole model's deviation profile is universal after normalization. No new physical entities are introduced.

free parameters (12)
  • Quadrupole bar amplitude A = 0.6
    Chosen by hand in Eq. 1 (Section 2) to set bar strength; the deviation profile used for correction depends on it.
  • Quadrupole scale length r_q = 2.0 kpc
    Chosen in Eq. 1 (Section 2); sets the bar length (2 r_q = 4 kpc used as R_bar,0 in Eq. 8).
  • Monopole core scale R_e = 0.1 kpc
    Chosen in Eq. 2 (Section 2); controls central mass concentration. Appendix E shows increasing it to 0.5 kpc removes the nuclear ring and changes the flow pattern, so the dip result is sensitive to this value.
  • Circular velocity scale v_0 = 220 km/s
    Chosen in Section 2; sets V_flat,0 for the simulation and the normalization of deviations.
  • Bar pattern speed Omega_b = 40 km/s/kpc
    Chosen in Section 2; sets co-rotation radius R_CR = 5.5 kpc. The paper states the |Δφ| ≈ 40 degree dip boundary depends on bar strength and pattern speed.
  • Effective sound speed c_s = 10 km/s
    Chosen in Section 2 for the isothermal gas disk; affects shock structure and thus the V_los pattern.
  • Inclination angle i = 45 degrees
    Chosen in Section 2 to construct mock V_los maps; projection factor sin i enters Eq. 3 and the deviation amplitudes.
  • Nuclear ring ellipticity epsilon_ring = 0.29
    Measured from the simulation's surface density in Section 4.2 and used as input to the misaligned ellipses model.
  • Bar ellipticity epsilon_bar = 0.37
    Used in Section 4.2 for the misaligned ellipses model; appears to be chosen or measured from the simulation.
  • Aligned ellipses axis ratio a/b = 1.8
    Chosen by hand in Section 4.1 for the aligned ellipses toy model; later the simulation's nuclear ring axial ratio of roughly 1.5 gives a better match to the simulated deviation.
  • Density threshold Sigma_crit = 0.85 M_sun/pc^2
    Empirical threshold in Appendix A to mimic low signal-to-noise pixels; the dip becomes more prominent after this cut.
  • Dip boundary |Delta_phi| = 40 degrees = 40 degrees
    Empirical criterion from the quadrupole simulations (Section 2), used to classify observed dip features in Section 3. It is not a strict limit and depends on bar properties.
assumptions (8)
  • domain assumption The rotation curve of a barred galaxy is defined as the circular velocity in centrifugal balance with the azimuthally averaged gravitational potential.
    Stated in the introduction: 'We define the RC of a barred galaxy as the circular velocity in centrifugal balance with the azimuthally averaged gravitational potential.' This definition makes RCtrue a specific construction; other definitions are possible.
  • domain assumption Gas in the simulations reaches a quasi-steady flow pattern by t = 1 Gyr and can be modeled as a two-dimensional isothermal disk.
    Section 2 uses a snapshot at t = 1 Gyr after growing the bar for three rotation periods; the results depend on this steady-state assumption.
  • domain assumption The fixed quadrupole plus monopole potential and the Ferrers model are representative of real barred galaxies.
    Sections 2 uses two classical potentials; the paper notes the exact dip range depends on bar strength and pattern speed, so the model is representative rather than universal.
  • domain assumption The tilted-ring model (Eq. 3) is the reduction used for both mock and observed data; any deviation from circular motion contaminates Vc.
    Eq. 3 is the standard method applied to simulated and observed Vlos maps; the entire bias analysis assumes this estimator.
  • domain assumption The measured inclinations and position angles from Salo et al. (2015) and bar lengths and classifications from Querejeta et al. (2021), after the paper's re-evaluations, are accurate.
    Section 3 builds the observed sample on these external measurements; errors in Δφ or bar length directly affect whether a galaxy is classified as having a dip.
  • ad hoc to paper The quadrupole simulation's deviation profile g(R, Δφ) applies to all barred galaxies after scaling by Vflat and stretching radii.
    Section 4.3: 'We assume that the relationship between Δφ and the deviations of RC, as empirically determined by our simulations in Figure 2, is applicable to all galaxies.' This is the load-bearing assumption for the correction method and is explicitly acknowledged as approximate.
  • ad hoc to paper In the toy models, gas follows elliptical orbits with constant angular momentum.
    Sections 4.1 and 4.2 assume Lz = const. Appendix D and Section 4.2 admit this is violated by shocks in the bar region, so the model is only qualitative.
  • domain assumption Decline-rise features in observed RCs with |Δφ| <= 40 degrees are caused by bar-induced non-circular motions rather than bulges or spirals.
    Section 3.1 uses this to identify 9 dip galaxies; the authors explicitly carve out NGC 4321, NGC 1566, and NGC 2997 as non-bar mechanisms, showing the assumption does not always hold.

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Pith. "Pith review of The Impact of Bar-induced Non-Circular Motions on the Measurement of Galactic Rotation Curves." pith.science (2026). https://pith.science/paper/6F7ZQ4NF

@misc{pith2026250112760,
  author       = {Pith},
  title        = {Pith review of: The Impact of Bar-induced Non-Circular Motions on the Measurement of Galactic Rotation Curves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6F7ZQ4NF}},
  note         = {Machine review of arXiv:2501.12760}
}
abstract

We study the impact of bar-induced non-circular motions on the derivation of galactic rotation curves (RCs) using hydrodynamic simulations and observational data from the PHANGS-ALMA survey. We confirm that non-circular motions induced by a bar can significantly bias RCs derived from the conventional tilted-ring method, consistent with previous findings. The shape of the derived RC depends on the position angle difference ($\Delta \phi$) between the major axes of the bar and the disk in the face-on plane. For $\left|\Delta \phi\right|\lesssim40^\circ$, non-circular motions produce a bar-induced "dip" feature (rise-drop-rise pattern) in the derived RC, which shows higher velocities near the nuclear ring and lower velocities in the bar region compared to the true RC (${\mathrm{RC_{true}}}$). We demonstrate convincingly that such dip features are very common in the PHANGS-ALMA barred galaxies sample. Hydrodynamical simulations reveal that the "dip" feature is caused by the perpendicular orientation of the gas flows in the nuclear ring and the bar; at low $\left|\Delta \phi\right|$ streamlines in the nuclear ring tend to enhance $V_\mathrm{los}$, while those in the bar tend to suppress $V_\mathrm{los}$. We use a simple {\misaell} model to qualitatively explain the general trend of RCs from the tilted-ring method (${\mathrm{RC_{tilted}}}$) and the discrepancy between ${\mathrm{RC_{tilted}}}$ and ${\mathrm{RC_{true}}}$. Furthermore, we propose a straightforward method to implement a first-order correction to the RC derived from the tilted-ring method. Our study is the first to systematically discuss the bar-induced "dip" feature in the RCs of barred galaxies combining both simulations and observations.

Figures

Figures reproduced from arXiv: 2501.12760 by the authors.

Figure 1
Figure 1. Clockwise-rotating quadrupole models. Columns 1 and 4 display the projected surface density, with bar directions indicated by red dashed lines. ∆ϕ from 0◦ to ± 90◦ is indicated in the top corner of each plot. Columns 2 and 5 display the constructed Vlos map generated directly from the components Vx and Vy with an inclination (i) of 45◦ . The zero-velocity lines are represented by black dashed lines. Columns 3 and 6 … view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. RCs for real galaxies with a bar-induced “dip” feature. The blue dots with error bars represent RCtilted from Lang et al. (2020), while the blue dashed lines illustrate their best fit of Eq. 10. The red dots are our corrected RCs with the correction procedure described in § 4.3, and fitted using the same equation shown by the red dashed lines. The fitted V0 and rt for the red dots are shown in the bottom of each pan… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: RCs for outlier galaxies with a decline-rise feature. The legend details are similar to those in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Gas streamlines (green) superimposed on the surface density of the quadrupole model. The bar major axis is along the x-axis (RCR = 5.5 kpc). tion of the RCs. We first aim to explain the deviation within the elliptical nuclear ring, where the streamline shapes are relat…
Figure 6
Figure 6. Figure 6: (a) A schematic diagram showing the difference in velocity between elliptical and circular orbits. (b) Vlos at a specific radius (R = 0.8 kpc) as a function of the azimuthal angle, obtained after projecting the velocity of circular (black dashed line) and elliptical (b…
Figure 7
Figure 7. Figure 7: In the upper panel, the first column displays the distribution of orbits in our “misaligned ellipses” model with ∆ϕ = 0◦ , ± 30◦ , projected at an inclination of 45◦ . The black dashed lines indicate the orientation of the bar. The second column presents the contours o…

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