Using Velocity Dispersion to Estimate Halo Mass: Is the Local Group in Tension with Λ\LambdaCDM?

Satellite galaxies are commonly used as tracers to measure the line-of-sight velocity dispersion ($\sigma_{\rm LOS}$) of the dark matter halo associated with their central galaxy, and thereby to estimate the halo's mass. Recent observational dispersion estimates of the Local Group, including the Milky Way and M31, suggest $\sigma\sim$50 km/s, which is surprisingly low when compared to the theoretical expectation of $\sigma\sim$100s km/s for systems of their mass. Does this pose a problem for $\Lambda$CDM? We explore this tension using the {\small{SURFS}} suite of $N$-body simulations, containing over 10000 (sub)haloes with well tracked orbits. We test how well a central galaxy's host halo velocity dispersion can be recovered by sampling $\sigma_{\rm LOS}$ of subhaloes and surrounding haloes. Our results demonstrate that $\sigma_{\rm LOS}$ is biased mass proxy. We define an optimal window in $v_{\rm LOS}$ and projected distance ($D_p$) -- $0.5\lesssim D_p/R_{\rm vir}\lesssim1.0$ and $v_{\rm LOS} \lesssim0.5V_{\rm esc}$, where $R_{\rm vir}$ is the virial radius and $V_{\rm esc}$ is the escape velocity -- such that the scatter in LOS to halo dispersion is minimised - $\sigma_{\rm LOS}=(0.5\pm0.1)\sigma_{v,{\rm H}}$. We argue that this window should be used to measure line-of-sight dispersions as a proxy for mass, as it minimises scatter in the $\sigma_{\rm LOS}-M_{\rm vir}$ relation. This bias also naturally explains the results from \cite{mcconnachie2012a}, who used similar cuts when estimating $\sigma_{\rm LOS,LG}$, producing a bias of $\sigma_{\rm LG}=(0.44\pm0.14)\sigma_{v,{\rm H}}$. We conclude that the Local Group's velocity dispersion does not pose a problem for $\Lambda$CDM and has a mass of $\log M_{\rm LG, vir}/M_\odot=12.0^{+0.8}_{-2.0}$.Comment: 8 pages, 7 figures, accepted for publicatio

A mass-dependent density profile for dark matter haloes including the influence of galaxy formation

We introduce a mass-dependent density profile to describe the distribution of dark matter within galaxies, which takes into account the stellar-to-halo mass dependence of the response of dark matter to baryonic processes. The study is based on the analysis of hydrodynamically simulated galaxies from dwarf to Milky Way mass, drawn from the Making Galaxies In a Cosmological Context project, which have been shown to match a wide range of disc scaling relationships. We find that the best-fitting parameters of a generic double power-law density profile vary in a systematic manner that depends on the stellar-to-halo mass ratio of each galaxy. Thus, the quantity M⋆/Mhalo constrains the inner (γ) and outer (β) slopes of dark matter density, and the sharpness of transition between the slopes (α), reducing the number of free parameters of the model to two. Due to the tight relation between stellar mass and halo mass, either of these quantities is sufficient to describe the dark matter halo profile including the effects of baryons. The concentration of the haloes in the hydrodynamical simulations is consistent with N-body expectations up to Milky Way-mass galaxies, at which mass the haloes become twice as concentrated as compared with pure dark matter runs. This mass-dependent density profile can be directly applied to rotation curve data of observed galaxies and to semi-analytic galaxy formation models as a significant improvement over the commonly used NFW profile

The dependence of dark matter profiles on the stellar-to-halo mass ratio: a prediction for cusps versus cores

We use a suite of 31 simulated galaxies drawn from the MaGICC project to investigate the effects of baryonic feedback on the density profiles of dark matter haloes. The sample covers a wide mass range: 9.4×109 <Mhalo/M� <7.8×1011, hosting galaxies with stellarmasses in the range 5.0×105 <M∗/M� < 8.3×1010, i.e. from dwarf to L∗. The galaxies are simulated with blastwave supernova feedback and, for some of them, an additional source of energy from massive stars is included. Within this feedback scheme we vary several parameters, such as the initial mass function, the density threshold for star formation, and energy from supernovae and massive stars. The main result is a clear dependence of the inner slope of the dark matter density profile, α in ρ ∝ rα, on the stellar-to-halo mass ratio, M∗/Mhalo. This relation is independent of the particular choice of parameters within our stellar feedback scheme, allowing a prediction for cusp versus core formation. When M∗/Mhalo is low, �0.01 per cent, energy from stellar feedback is insufficient to significantly alter the inner dark matter density, and the galaxy retains a cuspy profile. At higher stellar-to-halo mass ratios, feedback drives the expansion of the dark matter and generates cored profiles. The flattest profiles form where M∗/Mhalo ∼ 0.5 per cent. Above this ratio, stars formed in the central regions deepen the gravitational potential enough to oppose the supernova-driven expansion process, resulting in cuspier profiles. Combining the dependence of α on M∗/Mhalo with the empirical abundance matching relation between M∗ and Mhalo provides a prediction for how α varies as a function of stellar mass. Further, using the Tully–Fisher relation allows a prediction for the dependence of the dark matter inner slope on the observed rotation velocity of galaxies. The most cored galaxies are expected to have Vrot ∼ 50 km s−1, with α decreasing for more massive disc galaxies: spirals with Vrot ∼ 150 km s−1 have central slopes α ≤−0.8, approaching again the Navarro–Frenk–White profile. This novel prediction for the dependence of α on disc galaxy mass can be tested using observational data sets and can be applied to theoretical modelling of mass profiles and populations of disc galaxies

Development and Validation of a Scale to Explore Pre-Service Teachers’ Sense of Preparedness, Engagement and Self-Efficacy in Classroom Teaching

Raising the quality of initial teacher education can make an important contribution to raising the overall quality of the school system. In Australia, the National Framework for Professional Standards for Teaching is used as a common framework to set standards for the accreditation of teacher education programs. However, institution-wise assessments need to be carried out regularly to explore the quality of preparation pre-service teachers receive and to what extent they feel well prepared to enter teaching. This will enable teacher education programs to implement strategies to strengthen the link between university coursework and professional practice of pre service teachers. This paper discusses the development and validation of a scale to measure pre- service teachers’ perceptions of preparedness to teach, readiness to engage with the teaching profession and self-efficacy in teaching. The study also proposes a model describing the relationship among these variables. Data was collected from 235 final year pre-service teachers using a newly developed questionnaire at an Australian university. Data shows that the Pre service Teacher Professional Experience (PTPE) scale is a theoretically sound, gender invariant and psychometrically valid instrument. The implications of using the scale in teacher education programmes are discussed in the context of the findings