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Weighing the Galactic disk using phase-space spirals: II. Most stringent constraints to a thin dark disk using Gaia EDR3

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 Added by Axel Widmark
 Publication date 2021
  fields Physics
and research's language is English




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Using the method that was developed in the first paper of this series, we measure the vertical gravitational potential of the Galactic disk from the time-varying structure of the phase-space spiral, using data from Gaia as well as supplementary radial velocity information from legacy spectroscopic surveys. For eleven independent data samples, we inferred gravitational potentials that were in good agreement, despite the data samples varied and substantial selection effects. Using a model for the baryonic matter densities, we inferred a local halo dark matter density of $0.0085 pm 0.0039$ M$_odot$/pc$^3 = 0.32 pm 0.15$ GeV/cm$^3$. We were also able to place the most stringent constraint to the surface density of a thin dark disk with a scale height $leq 50$ pc: an upper 95 % confidence limit of roughly 5 M$_odot$/pc$^2$ (compared to previous limit of roughly 10 M$_odot$/pc$^2$, given the same scale height). For the inferred halo dark matter density and thin dark disk surface density, the uncertainties are dominated by the baryonic model. With this level of precision, our method is highly competitive with traditional methods that rely on the assumption of a steady state. In a general sense, this illustrates that time-varying dynamical structures are not solely obstacles to dynamical mass measurements, but can also be regarded as assets containing useful information.



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We infer the gravitational potential of the Galactic disk by analysing the phase-space densities of 120 stellar samples in 40 spatially separate sub-regions of the solar neighbourhood, using Gaias second data release (DR2), in order to quantify spatially dependent systematic effects that bias this type of measurement. The gravitational potential was inferred under the assumption of a steady state in the framework of a Bayesian hierarchical model. We performed a joint fit of our stellar tracers three-dimensional velocity distribution, while fully accounting for the astrometric uncertainties of all stars. The inferred gravitational potential is compared, post-inference, to a model for the baryonic matter and halo dark matter components. We see an unexpected but clear trend for all 40 spatially separate sub-regions: Compared to the potential derived from the baryonic model, the inferred gravitational potential is significantly steeper close to the Galactic mid-plane (<60 pc), but flattens such that the two agree well at greater distances (~400 pc). The inferred potential implies a total matter density distribution that is highly concentrated to the Galactic mid-plane and decays quickly with height. Apart from this, there are discrepancies between stellar samples, implying spatially dependent systematic effects which are, at least in part, explained by substructures in the phase-space distributions. In terms of the inferred matter density distribution, the very low matter density that is inferred at greater heights is inconsistent with the observed scale height and matter distribution of the stellar disk, which cannot be explained by a misunderstood density of cold gas or other hidden mass. Our interpretation is that these results must be biased by a time-varying phase-space structure, possibly a breathing mode, that is large enough to affect all stellar samples in the same manner.
We update the method of the Holmberg & Flynn (2000) study, including an updated model of the Milky Ways interstellar gas, radial velocities, an updated reddening map, and a careful statistical analysis, to bound the allowed surface density and scale height of a dark disk. We pay careful attention to the self-consistency of the model, including the gravitational influence of the dark disk on other disk components, and to the net velocity of the tracer stars. We find that the data set exhibits a non-zero bulk velocity in the vertical direction as well as a displacement from the expected location at the Galactic midplane. If not properly accounted for, these features would bias the bound toward low dark disk mass. We therefore perform our analysis two ways. In the first, traditional method, we subtract the mean velocity and displacement from the tracers phase space distributions. In the second method, we perform a non-equilibrium version of the HF method to derive a bound on the dark disk parameters for an oscillating tracer distribution. Despite updates in the mass model and reddening map, the traditional method results remain consistent with those of HF2000. The second, non-equilibrium technique, however, allows a surface density as large as $14, M_odot,{rm pc}^{-2}$ (and as small as 0), demonstrating much weaker constraints. For both techniques, the bound on surface density is weaker for larger scale height. In future analyses of Gaia data, it will be important to verify whether the tracer populations are in equilibrium.
We discuss the physical mechanism by which pure vertical bending waves in a stellar disc evolve to form phase space spirals similar to those discovered by Antoja et al. ( arXiv:1804.10196) in Gaia Data Release 2. These spirals were found by projecting Solar Neighbourhood stars onto the $z-v_z$ plane. Faint spirals appear in the number density of stars projected onto the $z-v_z$ plane, which can be explained by a simple model for phase wrapping. More prominent spirals are seen when bins across the $z-v_z$ plane are coloured by median $v_R$ or $v_phi$. We use both toy model and fully self-consistent simulations to show that the spirals develop naturally from vertical bending oscillations of a stellar disc. The underlying physics follows from the observation that the vertical energy of a star (essentially, its radius in the $z-v_z$ plane) correlates with its angular momentum or, alternatively, guiding radius. Moreover, at fixed physical radius, the guiding radius determines the azimuthal velocity. Together, these properties imply the link between in-plane and vertical motion that lead directly to the Gaia spirals. We show that the cubic $R-z$ coupling term in the effective potential is crucial for understanding the morphology of the spirals. This suggests that phase space spirals might be a powerful probe of the Galactic potential. In addition, we argue that self-gravity is necessary to properly model the evolution of the bending waves and their attendant phase space spirals.
146 - Giovanni Carraro 2018
In this note I show how the recently suggested membership of the open cluster Gaia 1 to the Galactic thick disk is based on incorrect assumptions about the structure of the disk itself, and neglect well-known observational evidences on the disk warp and flare.
116 - R. da Silva , B. Lemasle , G. Bono 2015
We present new accurate abundances for five neutron-capture (Y, La, Ce, Nd, Eu) elements in 73 classical Cepheids located across the Galactic thin disk. Individual abundances are based on high spectral resolution (R ~ 38,000) and high signal-to-noise ratio (S/N ~ 50-300) spectra collected with UVES at ESO VLT for the DIONYSOS project. Taking account for similar Cepheid abundances provided either by our group (111 stars) or available in the literature, we end up with a sample of 435 Cepheids covering a broad range in iron abundances (-1.6 < [Fe/H] < 0.6). We found, using homogeneous individual distances and abundance scales, well defined gradients for the above elements. However, the slope of the light s-process element (Y) is at least a factor of two steeper than the slopes of heavy s- (La, Ce, Nd) and r- (Eu) process elements. The s to r abundance ratio ([La/Eu]) of Cepheids shows a well defined anticorrelation with of both Eu and Fe. On the other hand, Galactic field stars attain an almost constant value and only when they approach solar iron abundance display a mild enhancement in La. The [Y/Eu] ratio shows a mild evidence of a correlation with Eu and, in particular, with iron abundance for field Galactic stars. We also investigated the s-process index - [hs/ls] - and we found a well defined anticorrelation, as expected, between [La/Y] and iron abundance. Moreover, we found a strong correlation between [La/Y] and [La/Fe] and, in particular, a clear separation between Galactic and Sagittarius red giants. Finally, the comparison between predictions for low-mass asymptotic giant branch stars and the observed [La/Y] ratio indicate a very good agreement over the entire metallicity range covered by Cepheids. However, the observed spread, at fixed iron content, is larger than predicted by current models.
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