The rotation speed of the spiral pattern in the Milky Way galaxy

TL;DR

The paper addresses the problem of determining the Milky Way's spiral pattern rotation speed $\Omega_p$ and corotation radius $R_{\rm cor}$ from maser kinematics measured with VLBI parallaxes. It introduces two least-squares–based methods: a direct fit for spiral-wave perturbations $f_R$ and $f_\theta$, and a two-step approach that first fits the Galactic rotation curve parameters $(\Omega_0,\Omega'_0,\Omega''_0)$ and then applies spectral analysis to extract $i$, $\chi_\odot$, $f_R$, and $f_\theta$, including a vertical perturbation $W$. The results reveal a strong $\Omega_p$–$R_{\rm cor}$ degeneracy, with $\Omega_p$ around $25.8$ or $35.4$ km s$^{-1}$ kpc$^{-1}$ and $R_{\rm cor}$ around $9.1$ or $6.8$ kpc depending on the relative signs of $f_R$ and $f_\theta$, and confirm a vertical perturbation with $\lambda_W\approx1.9$ kpc. These findings underscore substantial uncertainties in spiral pattern speed estimates and highlight the importance of including vertical wave components in modeling the Galactic disk.

Abstract

For a sample of masers, the basic kinematic equations were solved by including the Galactic rotation parameters and the peculiar velocity of the Sun as the unknown variables. Based on spectral analysis, the following estimates were obtained: $|f|_{R,θ}=(7.0,5.1)\pm(1.2,1.4)$ km s$^{-1}$ and the corresponding wavelengths $λ_{R,θ}=(1.9,1.7)\pm(0.4,0.7)$ kpc, as well as $χ_\odot=-140^\circ\pm15^\circ$. The presence of periodic perturbations in the vertical velocities of masers with an amplitude of $|f|_W=3.1\pm1.4$ km s$^{-1}$ and a wavelength of $λ=1.9\pm0.8$ kpc was confirmed. It is shown that the velocities $f_R$ and $f_θ$ can have both the same and different signs. Therefore, we obtained a large scatter of estimates. Thus, if $f_R$ and $f_θ$ have the same signs, then $Ω_p=25.8\pm2.0$ km s$^{-1}$ kpc$^{-1}$ and $R_{cor}=9.1\pm0.8$ kpc. And when $f_R$ and $f_θ$ have different signs, then $Ω_p=35.4\pm2.0$ km s$^{-1}$ kpc$^{-1}$ and $R_{cor}=6.8\pm0.8$ kpc.

Figures (3)

• Figure 1: Dependences of the velocities $V_R$ and $\Delta V_{circ}$ on $R$ according to the linear theory of density waves of Lin, Shu (1964), constructed using the data of Fig. 21 from the monograph by Rolfs (1977) for the case $\Omega_p<\Omega(R)$, where the $R$ axis is directed from the center of the Galaxy towards the Sun, and the radial phase $\chi$ is directed toward the center of the Galaxy.
• Figure 2: Radial $V_R$ (a), residual tangential $\Delta V_{circ}$ (b) and vertical $W$ (c) maser velocities as a function of distance $R$, red lines are periodic curves found based on spectral analysis, orange lines are smoothed averages.
• Figure 3: Power spectra of radial (a), residual tangential (b) and vertical (c) velocities of masers.