[Paper Review] The distribution of nearby stars in phase space mapped by Hipparcos: I. The potential well and local dynamical mass

M. Crézé, E. Chereul+2 more|arXiv (Cornell University)|Sep 3, 1997

Stellar, planetary, and galactic studies1 references26 citations

TL;DR

Using Hipparcos data, this study maps the phase-space distribution of nearby A-F stars to derive the local galactic potential well and dynamical mass density. It finds a local dynamical density of $\rho_0 = 0.076 \pm 0.015~{}M_\odot~{}\mathrm{pc}^{-3}$, which is consistent with known baryonic matter and rules out a significant disk-shaped dark matter component.

ABSTRACT

Hipparcos data provide the first, volume limited and absolute magnitude limited homogeneous tracer of stellar density and velocity distributions in the solar neighbourhood. The density of A-type stars more luminous than $M_v=2.5$ can be accurately mapped within a sphere of 125 pc radius, while proper motions in galactic latitude provide the vertical velocity distribution near the galactic plane. The potential well across the galactic plane is traced practically hypothesis-free and model-free. The local dynamical density comes out as $ρ_{0}=0.076 \pm0.015~M_{\sun}~{pc}^{-3}$ a value well below all previous determinations leaving no room for any disk shaped component of dark matter.

Motivation & Objective

• To determine the local galactic potential well across the plane using a model- and hypothesis-free approach.
• To measure the local dynamical mass density ($\rho_0$) from the vertical velocity distribution and density profile of nearby stars.
• To test the compatibility of the derived $\rho_0$ with known baryonic matter and assess the necessity of dark matter components.
• To evaluate whether a disk-shaped dark matter component can be accommodated within the observed dynamical constraints.
• To assess the structural parameters of the stellar disc and halo in light of the new dynamical density estimate.

Proposed method

• Utilizes Hipparcos astrometric data for stars within 125 pc, with absolute magnitude limits ($M_V \leq 2.5$) to ensure complete, volume-limited sampling.
• Applies the integral equation (1) linking vertical density $\nu(z)$ and vertical velocity distribution $f(w_0)$ to reconstruct the potential $\phi(z)$ without assuming a specific functional form.
• Employs Poisson's equation (2) to derive the local mass density $\rho_0 = \frac{1}{4\pi G} \frac{d^2\phi}{dz^2}$ from the second derivative of the reconstructed potential.
• Constructs a Galactic mass model including a stellar disc (2.5 kpc scale length, 323 pc scale height), thick disc (3.5 kpc, 656 pc), and a Miyamoto spheroid halo to fit the rotation curve.
• Compares the derived $\rho_0$ with the observed mass density of stars and interstellar matter (0.043 $M_\odot$ pc⁻³ and 0.04 $M_\odot$ pc⁻³ respectively) to assess consistency.
• Tests the feasibility of flatter dark matter distributions by varying halo scale height and mass distribution, under constraints from the observed $\rho_0$.

Experimental results

Research questions

• RQ1 What is the shape of the galactic potential well across the plane, as inferred directly from Hipparcos data without model assumptions?
• RQ2 What is the local dynamical mass density $\rho_0$ derived from the vertical velocity and density distribution of A-F stars?
• RQ3 Is the derived $\rho_0$ consistent with the known mass density of stars and interstellar matter?
• RQ4 Can a disk-shaped component of dark matter be accommodated within the constraints of the observed $\rho_0$?
• RQ5 What are the implications for the structure of the dark matter halo, particularly its flattening and local density?

Key findings

• The potential well across the galactic plane is found to be shallower than previously assumed, based on a model- and hypothesis-free reconstruction from Hipparcos data.
• The local dynamical mass density is measured as $\rho_0 = 0.076 \pm 0.015~{}M_\odot~{}\mathrm{pc}^{-3}$, which is significantly lower than earlier estimates.
• This value is fully consistent with the combined mass density of stars ($0.043~{}M_\odot~{}\mathrm{pc}^{-3}$) and interstellar matter ($0.04~{}M_\odot~{}\mathrm{pc}^{-3}$), leaving no room for additional mass from a disk-shaped dark matter component.
• A spherical or nearly spherical dark matter halo is required to maintain consistency with the observed $\rho_0$, with a local density of $\sim 0.008~{}M_\odot~{}\mathrm{pc}^{-3}$.
• The stellar disc cannot be maximal; even under extreme assumptions, the disc contributes less than half the mass implied by the rotation curve at $R_0 = 8.5$ kpc.
• Any attempt to flatten the dark matter distribution results in a local halo density exceeding the allowed range, making a flat, disk-like dark matter component incompatible with the data.