## The difficulty of measuring the local dark matter density

### Hessman, F. V.

**Citable Link (URL):**http://resolver.sub.uni-goettingen.de/purl?gs-1/12436

##### Journal Article (Published version)

##### First published

Astronomy & Astrophysics 2015; 579: Art. A123

##### Abstract

The analysis of the vertical velocity dispersion of disc stars in the local MilkyWay is the most direct astronomical means of estimating
the local dark matter density, DM. Current estimates for DM based on the mid-plane dynamic density use a local baryonic correction
that ignores the non-local e ects of spiral structure and significantly underestimates the amount of dynamically relevant gas now
known to be present in the ISM; the additional gas plus the remaining uncertainties make it practically impossible to measure DM
from mid-plane kinematics alone. The sampling of inhomogeneous tracer populations with di erent scale-heights and scale-lengths
results in a systematic increase in the observed dispersion gradients and changes in the nominal density distributions that, if not
properly considered, can be misinterpreted as a sign of more dark matter. If the disc gravity is modelled locally using an infinite
disc, the local variation in the vertical gravity due to the globally exponential disc components results in an underestimation of
the baryonic contribution by as much as 40%. Given only the assumptions of stationarity, an axially and vertically symmetric
disc, doubly exponential tracer and mass-component density profiles, a phenomenologically justified model for the cross-dispersion
component Rz, and a realistic model for gz(z), it is possible to solve the full vertical Jeans equation analytically for the vertical
dispersion z(z) and hence test the robustness of previous attempts at measuring DM. When the model parameters for Rz are estimated
from SEGUE G dwarf star data, it is still not possible to explain the di erence in behaviour seen in the simple thick- and thin-disc
datasets reported by Buedenbender et al. (2014, MNRAS, submitted). Rather than being a fundamental problem with the kinematical
The analysis of the vertical velocity dispersion of disc stars in the local Milky Way is the most direct astronomical means of estimating the local dark matter density, ρDM. Current estimates for ρDM based on the mid-plane dynamic density use a local baryonic correction that ignores the non-local effects of spiral structure and significantly underestimates the amount of dynamically relevant gas now known to be present in the ISM; the additional gas plus the remaining uncertainties make it practically impossible to measure ρDM from mid-plane kinematics alone. The sampling of inhomogeneous tracer populations with different scale-heights and scale-lengths results in a systematic increase in the observed dispersion gradients and changes in the nominal density distributions that, if not properly considered, can be misinterpreted as a sign of more dark matter. If the disc gravity is modelled locally using an infinite disc, the local variation in the vertical gravity due to the globally exponential disc components results in an underestimation of the baryonic contribution by as much as ~40%. Given only the assumptions of stationarity, an axially and vertically symmetric disc, doubly exponential tracer and mass-component density profiles, a phenomenologically justified model for the cross-dispersion component σRz, and a realistic model for gz(z), it is possible to solve the full vertical Jeans equation analytically for the vertical dispersion σz(z) and hence test the robustness of previous attempts at measuring ρDM. When the model parameters for σRz are estimated from SEGUE G dwarf star data, it is still not possible to explain the difference in behaviour seen in the simple thick- and thin-disc datasets reported by Buedenbender et al. (2014, MNRAS, submitted). Rather than being a fundamental problem with the kinematical model, this effect appears to be a further sign of the difficulty of defining and handling kinematically homogeneous tracer populations.