How Cosmic Background Correlations at Large Angles Relate to Mass Autocorrelations in Space

The Sachs-Wolfe effect is known to produce large angular scale fluctuations in the Cosmic Microwave Background Radiation (CMBR) due to gravitational potential fluctuations. We show how the angular correlation function of the CMBR can be expressed explicitly in terms of the mass autocorrelation function $\xi (r)$ in the Universe. We derive analytic expressions for the angular correlation function and its multipole moments in terms of integrals over $\xi (r)$ or its second moment, $J_3 (r)$, which does not need to satisfy the sort of integral constraint that $\xi (r)$ must. We derive similar expressions for bulk flow velocity in terms of $\xi$ and $J_3$. One interesting result that emerges directly from this analysis is that, for angles $\theta$, there is a substantial contribution to the correlation function from a wide range of distance $r$ and that the radial shape of this contribution does not vary greatly with angle.Comment: 9 pages in Plain TeX and 6 figures appended in 9 pages of uuencoded PostScript. Lick Preprint Number 1

Spitzer, Gaia, and the Potential of the Milky Way

Near-future data from ESA's Gaia mission will provide precise, full phase-space information for hundreds of millions of stars out to heliocentric distances of ~10 kpc. This "horizon" for full phase-space measurements is imposed by the Gaia parallax errors degrading to worse than 10%, and could be significantly extended by an accurate distance indicator. Recent work has demonstrated how Spitzer observations of RR Lyrae stars can be used to make distance estimates accurate to 2%, effectively extending the Gaia, precise-data horizon by a factor of ten in distance and a factor of 1000 in volume. This Letter presents one approach to exploit data of such accuracy to measure the Galactic potential using small samples of stars associated with debris from satellite destruction. The method is tested with synthetic observations of 100 stars from the end point of a simulation of satellite destruction: the shape, orientation, and depth of the potential used in the simulation are recovered to within a few percent. The success of this simple test with such a small sample in a single debris stream suggests that constraints from multiple streams could be combined to examine the Galaxy's dark matter halo in even more detail --- a truly unique opportunity that is enabled by the combination of Spitzer and Gaia with our intimate perspective on the Galaxy.Comment: 6 pages, 5 figures; accepted for publication in ApJ Letter

The Dominance of Metal-Rich Streams in Stellar Halos: A Comparison Between Substructure in M31 and Lambda-CDM Models

Extensive photometric and spectroscopic surveys of the Andromeda galaxy (M31) have discovered tidal debris features throughout M31's stellar halo. We present stellar kinematics and metallicities in fields with identified substructure from our on-going SPLASH survey of M31 red giant branch stars with the DEIMOS spectrograph on the Keck II 10-m telescope. Radial velocity criteria are used to isolate members of the kinematically-cold substructures. The substructures are shown to be metal-rich relative to the rest of the dynamically hot stellar population in the fields in which they are found. We calculate the mean metallicity and average surface brightness of the various kinematical components in each field, and show that, on average, higher surface brightness features tend to be more metal-rich than lower surface brightness features. Simulations of stellar halo formation via accretion in a cosmological context are used to illustrate that the observed trend can be explained as a natural consequence of the observed dwarf galaxy mass-metallicity relation. A significant spread in metallicity at a given surface brightness is seen in the data; we show that this is due to time effects, namely the variation in the time since accretion of the tidal streams' progenitor onto the host halo. We show that in this theoretical framework a relationship between the alpha-enhancement and surface brightness of tidal streams is expected, which arises from the varying times of accretion of the progenitor satellites onto the host halo. Thus, measurements of the alpha-enrichment, metallicity, and surface brightness of tidal debris can be used to reconstruct the luminosity and time of accretion onto the host halo of the progenitors of tidal streams.Comment: 11 pages, 6 figures, published in Ap