One of the major challenges in astrophysics is understanding how much dark matter exists and how it is distributed. In the case of our galaxy, the Milky Way, to study this problem, we start with observations of the distribution of stars and gas and their velocity field.
Thanks to data from the Gaia satellite, it is now possible to analyze large samples of stars for which both the three-dimensional position and the three components of velocity are known. From these observations, it is possible to reconstruct the velocity field in three dimensions, allowing us to characterize the kinematics of the Milky Way.
To connect kinematics to dynamics, we must assume that the galaxy has reached a steady equilibrium, where stars move in closed circular orbits and the entire system is stable and does not change over time.
Today, we know that this assumption is only approximately correct, as stars exhibit coherent non-circular motions over large distances.
Neglecting these out-of-equilibrium effects, we can connect the circular velocity of stars at different distances from the center of the galaxy—i.e., the galaxy’s rotation curve—to the mass distribution.
In this way, it has been understood that stars orbit at velocities that are too high compared to the luminous mass we can measure from observations.
As a result, there must be a portion of dark matter: the problem is determining how much there is and how it is distributed.
The classical hypothesis, adopted since the 1980s, is that dark matter is distributed in a spherical halo around the galactic disk. This implies that not only does dark matter have different spatial properties compared to luminous matter (i.e., a spherical distribution instead of a flat disk), but also that its velocity distribution is completely different.
In fact, for dark matter particles to be in equilibrium in a spherical volume, the halo, they must not have a coherent rotational velocity like stars in the disk. On the contrary, their velocity distribution must be isotropic, meaning they move in all directions without a coherent average motion.
Under this assumption, the amount of required dark matter is about 10-20 times what is observed in the form of stars and gas.
An alternative mass model, which we introduced a few years ago, hypothesizes that dark matter is distributed within the disk, following the distribution of neutral hydrogen. The latter can be observed with radio telescopes through its 21 cm line emission. Thus, the hypothesis is that for every observed hydrogen atom emitting at 21 cm, there are about ten others that do not emit.
The reason why they do not emit observable radiation could be due to various causes: for instance, it could be extremely cold hydrogen or some other form of matter that does not emit radiation (even the dark matter hypothesized in the halo model does not emit radiation!).
We like to think that dark matter is in the form of very cold ordinary matter (with a temperature below 10 Kelvin).
In any case, and regardless of the type of dark matter, the amount needed to explain the rotation curves is much smaller if it is located in the galactic disk rather than in a spherical halo—only a factor of two instead of a factor of 10-20.
Usually, the rotation curve is determined on the galactic plane. In this article, we determine it off the galactic plane, at different distances from it. In this way, we can construct the generalized rotation curve.
We then show that the generalized rotation curve is better explained by a model where all the matter resides in the disk rather than a model where the luminous matter is in the disk and the dark matter is in a spherical halo.
| Comments: | 16 pages, 13 figure, The Astrophysical Journal in the press (2024) |
| Subjects: | Astrophysics of Galaxies (astro-ph.GA) |
| Cite as: | arXiv:2410.14307 [astro-ph.GA] |
| (or arXiv:2410.14307v1 [astro-ph.GA] for this version) | |
| https://doi.org/10.48550/arXiv.2410.14307Focus to learn more |
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The circular velocity curve traced by stars provides a direct means of investigating the potential and mass distribution of the Milky Way. Recent measurements of the Galaxy’s rotation curve have revealed a significant decrease in velocity for galactic radii larger than approximately 15 kpc. While these determinations have primarily focused on the Galactic plane, the Gaia DR3 data also offer information about off-plane velocity components. By assuming the Milky Way is in a state of Jeans equilibrium, we derived the generalized rotation curve for radial distances spanning from 8.5 kpc to 25 kpc and vertical heights ranging from -2 kpc to 2 kpc. These measurements were employed to constrain the matter distribution using two distinct mass models. The first is the canonical NFW halo model, while the second, the dark matter disk (DMD) model, posits that dark matter is confined to the Galactic plane and follows
the distribution of neutral hydrogen. The best-fitting NFW model yields a virial mass of $M_{\text{vir}} = (6.5 \pm 0.5) \times 10^{11} M_\odot$, whereas the DMD model indicates a total mass of $M_{\text{DMD}} = (1.7 \pm 0.2) \times 10^{11} M_\odot$. Our findings indicate that the DMD model generally shows a better fit to both the on-plane and off-plane behaviors at large radial distances of the generalized rotation curves when compared to the NFW model. We
emphasize that studying the generalized rotation curves at different vertical heights has the potential to provide better constraints on the geometrical properties of the dark matter distribution.
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Francesco Sylos Labini 