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Cosmological implications of the Gaia Milky Way declining rotation curve

Even Coquery, Alain Blanchard

TL;DR

The paper tests whether Milgrom's MOND can explain Gaia's observed decline in the Milky Way rotation curve, versus a ΛCDM framework with an NFW halo. Using a B2-based baryonic model, it computes the rotation curve under both paradigms and fits the decline with an NFW halo, finding a good match only with a high concentration parameter; MOND cannot reproduce the decline with standard baryons, yielding a best-fit $a_0$ around $2.4×10^{-10}$ m s$^{-2}$ but with poor statistics. Allowing greater freedom in the baryonic components via MCMC shows MOND can accommodate the data only with unusually large disk masses and/or $a_0$ values far from the canonical one, or even $a_0≈0$ if a heavy disk is present, which would imply a baryon-dominated or disk-dominated mass distribution rather than MOND effects. Across all variants, an upper limit of $a_0<0.53×10^{-10}$ m s$^{-2}$ (95%) strongly disfavors MOND as a universal explanation for the Milky Way’s outer RC, favoring a DM halo interpretation for the Gaia decline and highlighting tension between MOND and other galaxies’ RCs.

Abstract

Although the existence of dark matter has been widely acknowledged in the cosmology community, it is as yet unknown in nature, despite decades of research, which questions its very existence. This never-ending search for dark matter leads to consider alternatives. Since increasing the enclosed mass is the only way to explain the flat appearance of galaxies' rotation curves in a Newtonian framework, the MOND theory proposed to modify Newton's dynamics when the acceleration is around or below a threshold value, $a_0$. Observed rotation curves, generally flat at large distances, are then usually well reproduced by MOND with $a_0 \sim 1.2 10^{-10}$ m/s$^{2}$. However, the recent Gaia evidence of a decline in the Milky Way rotation curve is a distinct behavior. Therefore, we examine whether MOND can accommodate the Gaia declining rotation curve of the Milky Way. We first depict a standard model to describe the Milky Way's baryonic components. Secondly, we show that a NFW (Navarro, Frenk, \& White ) model is able to fit the decline, assuming a scale radius $R_s$ of the order of $4$ kpc. In a third step, we show that the usual MOND paradigm is not able to reproduce the declining part for a standard baryonic model. Finally, we examine whether the MOND theory can accommodate the declining part of the rotation curve when relaxing the characteristics of the baryonic components. To do so we use a MCMC method on the characteristics of the stellar and the HI disk, including their mass. We found that the stellar disk should be massive, of the order of $10^{11}$ M$_{\odot}$. The HI disk mass is capped at nearly 1.8 $ 10^{11}$ M$_{\odot}$ but could also be negligible. Finally, $a_0$ is consistent with 0, with an upper limit of $0.53 10^{-10}$ m/s$^{2}$ (95\%), a value much lower than the above mentioned value usually advocated to explain standard flat rotation curves in MOND theory.

Cosmological implications of the Gaia Milky Way declining rotation curve

TL;DR

The paper tests whether Milgrom's MOND can explain Gaia's observed decline in the Milky Way rotation curve, versus a ΛCDM framework with an NFW halo. Using a B2-based baryonic model, it computes the rotation curve under both paradigms and fits the decline with an NFW halo, finding a good match only with a high concentration parameter; MOND cannot reproduce the decline with standard baryons, yielding a best-fit around m s but with poor statistics. Allowing greater freedom in the baryonic components via MCMC shows MOND can accommodate the data only with unusually large disk masses and/or values far from the canonical one, or even if a heavy disk is present, which would imply a baryon-dominated or disk-dominated mass distribution rather than MOND effects. Across all variants, an upper limit of m s (95%) strongly disfavors MOND as a universal explanation for the Milky Way’s outer RC, favoring a DM halo interpretation for the Gaia decline and highlighting tension between MOND and other galaxies’ RCs.

Abstract

Although the existence of dark matter has been widely acknowledged in the cosmology community, it is as yet unknown in nature, despite decades of research, which questions its very existence. This never-ending search for dark matter leads to consider alternatives. Since increasing the enclosed mass is the only way to explain the flat appearance of galaxies' rotation curves in a Newtonian framework, the MOND theory proposed to modify Newton's dynamics when the acceleration is around or below a threshold value, . Observed rotation curves, generally flat at large distances, are then usually well reproduced by MOND with m/s. However, the recent Gaia evidence of a decline in the Milky Way rotation curve is a distinct behavior. Therefore, we examine whether MOND can accommodate the Gaia declining rotation curve of the Milky Way. We first depict a standard model to describe the Milky Way's baryonic components. Secondly, we show that a NFW (Navarro, Frenk, \& White ) model is able to fit the decline, assuming a scale radius of the order of kpc. In a third step, we show that the usual MOND paradigm is not able to reproduce the declining part for a standard baryonic model. Finally, we examine whether the MOND theory can accommodate the declining part of the rotation curve when relaxing the characteristics of the baryonic components. To do so we use a MCMC method on the characteristics of the stellar and the HI disk, including their mass. We found that the stellar disk should be massive, of the order of M. The HI disk mass is capped at nearly 1.8 M but could also be negligible. Finally, is consistent with 0, with an upper limit of m/s (95\%), a value much lower than the above mentioned value usually advocated to explain standard flat rotation curves in MOND theory.
Paper Structure (10 sections, 9 equations, 5 figures, 3 tables)

This paper contains 10 sections, 9 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Milky Way's rotation curve
  3. Modeling the baryonic components of the Milky Way
  4. Rotation curve under $\Lambda$CDM
  5. Rotation velocity under MOND
  6. Relaxing the baryonic components to fit the decline with MOND
  7. Methodology
  8. Results
  9. More freedom on the baryonic components.
  10. Discussion and conclusion

Figures (5)

  • Figure 1: Rotation curve decline example using NFW with $\rho_{0,NFW}=1.8\times10^8$ M$_{\odot}$/kpc$^3$, $R_s^{thin}=3.97$ kpc, $R_s^{thin+thick}=3.98$ kpc. The parameters for the baryonic components are those of the B2 model in Table \ref{['b2_params']} taken from jiao_detection_2023. We also provide the rotation curve (grey lines) with two disks, one thin and one thick (see section 2.1).
  • Figure 2: Decline fit under the MOND paradigm. $a_0^{thin}=2.417\times10^{-10}$ m/s$^2$, $a_0^{thin+thick}=2.429\times10^{-10}$ m/s$^2$. The parameters for the baryonic components are the same than in Figure \ref{['fig:nfw_decline']}.
  • Figure 3: MCMC contours for $r_d=2.35$ kpc and $r_d=3.1$ kpc. The stellar disk mass and $a_0$ are left as free parameters. The red cross indicates the observed values of $M^{stellar}$ and the standard value of $a_0$ with their respective uncertainty (see text).
  • Figure 4: Fits using MCMC results (Table \ref{['tab:mcmc_results']}. The parameters for the other baryonic components are the same as in Figure \ref{['fig:mond_classic']}.
  • Figure 5: MCMC contours with a free stellar disk mass, free Hi disk mass, free $a_0$, free scale radius and free scale height.