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Register a new userAstrometric mock observations for determining the local dark matter density
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To determine the local dark matter density (LDMD) of the solar system is a classical problem in astronomy. Recently, a novel method of determining the LDMD from stellar distribution and vertical velocity dispersion profiles perpendicular to the Galactic plane was devised. This method has the advantage of abolishing conventional approximations and using only a few assumptions. Our aims are to carefully scrutinize this method and to examine influences by uncertainties of astrometric observations. We discuss how the determinations of the LDMD vary with observational precisions on parallax, proper motion, and line-of-sight velocity measurements. To examine the influences by the observational imprecision, we created mock observation data for stars that are dynamical tracers based on an analytical galaxy model and applied parametrized observational errors to the mock data. We evaluated the accuracy of determining the LDMD by applying the method to the mock data. In addition, we estimated a sample size and observational precision required to determine the LDMD with accuracy. We find that the method is capable of determining the LDMD with accuracy if the sample size and observational precisions are satisfactory. The random errors of parallaxes and proper motions can cause systematic overestimation of the LDMD. We estimate the required precisions of the parallax measurements to be approximately 0.1-0.3 milliarcseconds at 1 kpc away from the Sun; the proper motion precisions do not seem to be as important as the parallaxes. From these results, we expect that using the Hipparcos catalog would overestimate the LDMD because of the imprecise parallax measurements if this method is applied; however, we emphasize the capability of the method. We expect that Gaia will provide data precise enough to determine the LDMD.
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Measurement of the local dark matter density plays an important role in both Galactic dynamics and dark matter direct detection experiments. However, the estimated values from previous works are far from agreeing with each other. In this work, we provide a well-defined observed sample with 1427 G & K type main-sequence stars from the LAMOST spectroscopic survey, taking into account selection effects, volume completeness, and the stellar populations. We apply a vertical Jeans equation method containing a single exponential stellar disk, a razor thin gas disk, and a constant dark matter density distribution to the sample, and obtain a total surface mass density of $rm {78.7 ^{+3.9}_{-4.7} M_{odot} pc^{-2}}$ up to 1 kpc and a local dark matter density of $0.0159^{+0.0047}_{-0.0057},rm M_{odot},rm pc^{-3}$. We find that the sampling density (i.e. number of stars per unit volume) of the spectroscopic data contributes to about two-thirds of the uncertainty in the estimated values. We discuss the effect of the tilt term in the Jeans equation and find it has little impact on our measurement. Other issues, such as a non-equilibrium component due to perturbations and contamination by the thick disk population, are also discussed.
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