On the Presence of Angular-Velocity Offsets in Disk Galaxies

Abstract

The well-known discrepancy in galactic rotation curves refers to the mismatch between observed rotational velocities and the velocities predicted by baryonic matter. In this study we investigate a potential pattern in the discrepancy, which may point to an underlying pattern in dark-halo distributions. By looking at rotational-velocity curves from an alternate perspective, the angular-velocity curves, it appears that the observed angular velocities and their corresponding baryonic predictions differ by a constant shift. That is, the discrepancy may be reduced to a constant angular-velocity term, independent of the radius. We test the generality of the suggested property by analysing 143 high-quality rotation curves. The property appears significant as it performs equally well (or better) than well-established dark-halo models. Compared to a Burkert profile, it is preferred in 60% of the cases, while relative to a Navarro Frenk White profile (NFW), it is superior in 73% of the cases. Next, by including the new phenomenological property within the dynamical equations, we find an explicit expression for the dark-halo profile. The new single-parameter profile is characterised by a remarkable property: it is intrinsically related to the baryonic distribution. Thus, information regarding the cuspy or cored nature of a particular dark halo, according to this profile, is encoded (and explicitly determined) by the respective baryonic behaviour.

Figures (10)

• Figure 1: Rotation curves and angular-velocity curves of three different galaxies. Top panels: measured rotation curves (black points with error-bars) and their corresponding baryonic contributions (dashed blue lines). Bottom panels: measured angular-velocity curves (black points with error-bars) and their baryonic contributions (dashed blue lines). Apparently, the discrepancy in galactic rotation curves is reduced to a constant offset in this picture. The $\rm M/L$ values: NGC4183: 1, ESO116-G012: 0.5, NGC2841: 0.82. Each baryonic component includes both the stellar disk and the gas contributions.
• Figure 2: Fitting the data of UGC-07089 with the new phenomenological model. The left panel plots the measured angular velocities (black points with error-bars) along with the model's prediction (red line). The baryonic contribution is displayed as a dashed blue line. The right panel presents a corner plot of the two model parameters. Bluer colours in the joint distribution indicate regions with higher likelihood. The complete set of AVC-fittings is available online (see Data-Availability Section).
• Figure 3: A visual representation of the sample's best-fit model parameters. Left panel: A scatter plot of the two parameters. There is a weak but not significant anti-correlation between them ($\rm \rho_{pearson } = -0.1$, $p_{\rm value}=0.26$). Middle panel: Histogram of M/L values. The median value of log(M/L) is $\rm 0.06 \pm 0.04$. There are four outliers in the data with $\rm M/L < 0.1$, but within uncertainties, they are also consistent with higher values. Right Panel: Histogram of $\rm \omega_{0}$ values. The median value of $\rm log(\omega_{0})$ is $-15.97 \pm 0.51$. Eight points with $\rm \omega_{0} < 0$ are not shown, due to the logarithmic nature of the plot, but within uncertainties, they are also consistent with positive values.
• Figure 4: Comparing the phenomenological model with established approaches. Left panel: A histogram of $\rm \Delta BIC$ values, where the comparison is relative to NFW. The median value of the histogram is 3.32 $\pm$ 0.75. The error on the median was calculated by Err = $\rm 1.48 * MAD / \sqrt N$, where N is the number of samples. Central panel: A comparison relative to the Burkert profile. The median value is 0.77 $\pm$ 0.36. Right panel: A comparison relative to MOND. The median value is -0.19 $\pm$ 0.68.
• Figure 5: The observations (black error bars), the Keplerien baryonic contribution (blue line) and the corresponding model (red curve) of NGC-100. Note that the relevant part of the model is given in solid red, while the inner part (dashed red) is presented for clarity. The Keplerian cutoff (as defined in the main text) is indicated by a dashed black line.