The stellar mass-halo mass relation of isolated field dwarfs: a critical test of Λ\LambdaCDM at the edge of galaxy formation

We fit the rotation curves of isolated dwarf galaxies to directly measure the stellar mass-halo mass relation ($M_*-M_{200}$) over the mass range $5 \times 10^5 < M_{*}/{\rm M}_\odot < 10^{8}$. By accounting for cusp-core transformations due to stellar feedback, we find a monotonic relation with little scatter. Such monotonicity implies that abundance matching should yield a similar $M_*-M_{200}$ if the cosmological model is correct. Using the 'field galaxy' stellar mass function from the Sloan Digital Sky Survey (SDSS) and the halo mass function from the $\Lambda$ Cold Dark Matter Bolshoi simulation, we find remarkable agreement between the two. This holds down to $M_{200} \sim 5 \times 10^9$M$_\odot$, and to $M_{200} \sim 5 \times 10^8$M$_\odot$ if we assume a power law extrapolation of the SDSS stellar mass function below $M_* \sim 10^7$M$_\odot$. However, if instead of SDSS we use the stellar mass function of nearby galaxy groups, then the agreement is poor. This occurs because the group stellar mass function is shallower than that of the field below $M_* \sim 10^9$M$_\odot$, recovering the familiar 'missing satellites' and 'too big to fail' problems. Our result demonstrates that both problems are confined to group environments and must, therefore, owe to 'galaxy formation physics' rather than exotic cosmology. Finally, we repeat our analysis for a $\Lambda$ Warm Dark Matter cosmology, finding that it fails at 68% confidence for a thermal relic mass of $m_{\rm WDM} < 1.25$keV, and $m_{\rm WDM} < 2$keV if we use the power law extrapolation of SDSS. We conclude by making a number of predictions for future surveys based on these results.Comment: 22 pages; 2 Tables; 10 Figures. This is the version accepted for publication in MNRAS. Key changes: (i) added substantially more information on the surveys used to measure the stellar mass functions; (ii) added tests of the robustness of our results. Results and conclusions unchanged from previously. Minor typos corrected from previous versio

Valuing PSS outputs and quality changes

The Gershon review of efficiency recommended that target improvements in efficiency should be met both through financial savings and through improvements in quality of outputs. This paper reports on a pilot project designed to feed into an approach for local authorities to quantify in monetary terms quality gains in the provision of personal social services (PSS), with a specific application to the provision of home care for older people. There are a number of practical and theoretical problems with attributing monetary values to aspects of quality. The approach described here builds on ongoing work into the measurement of PSS outputs for the purposes of National Accounts and measuring changes in productivity and efficiency more widely. This approach distinguishes what services could provide (capacity for benefit) from the quality of what is provided in practice. By attaching a financial valuation to capacity for benefit we are able to attribute a monetary valuation to changes in the quality of provision measured (in the case of home care) through service user experiences of their care. Capacity for benefit (CfB) is defined in terms of eight domains of outcome that services address and four levels of need (no needs, all needs met, low needs, high needs) within these domains. In addition we identify whether people are living in their own homes, as a key attribute of care provision. The characteristics of the service (in terms of domains of outcome and whether living at home) and service users (in terms of level of need that need to be met) determine the CfB of a given service

Simultaneous Exoplanet Characterization and deep wide-field imaging with a diffractive pupil telescope

High-precision astrometry can identify exoplanets and measure their orbits and masses, while coronagraphic imaging enables detailed characterization of their physical properties and atmospheric compositions through spectroscopy. In a previous paper, we showed that a diffractive pupil telescope (DPT) in space can enable sub-microarcsecond accuracy astrometric measurements from wide-field images by creating faint but sharp diffraction spikes around the bright target star. The DPT allows simultaneous astrometric measurement and coronagraphic imaging, and we discuss and quantify in this paper the scientific benefits of this combination for exoplanet science investigations: identification of exoplanets with increased sensitivity and robustness, and ability to measure planetary masses to high accuracy. We show how using both measurements to identify planets and measure their masses offers greater sensitivity and provides more reliable measurements than possible with separate missions, and therefore results in a large gain in mission efficiency. The combined measurements reliably identify potentially habitable planets in multiple systems with a few observations, while astrometry or imaging alone would require many measurements over a long time baseline. In addition, the combined measurement allows direct determination of stellar masses to percent-level accuracy, using planets as test particles. We also show that the DPT maintains the full sensitivity of the telescope for deep wide-field imaging, and is therefore compatible with simultaneous scientific observations unrelated to exoplanets. We conclude that astrometry, coronagraphy, and deep wide-field imaging can be performed simultaneously on a single telescope without significant negative impact on the performance of any of the three techniques.Comment: 15 pages, 6 figures. This second paper, following the paper describing the diffractive pupil telescope (DPT) astrometric technique, shows how simultaneous astrometry and coronagraphy observations, enabled by the DPT concept, constrain the orbital parameters and mass of exoplanet

The Photoeccentric Effect and Proto-Hot Jupiters I. Measuring photometric eccentricities of individual transiting planets

Exoplanet orbital eccentricities offer valuable clues about the history of planetary systems. Eccentric, Jupiter-sized planets are particularly interesting: they may link the "cold" Jupiters beyond the ice line to close-in hot Jupiters, which are unlikely to have formed in situ. To date, eccentricities of individual transiting planets primarily come from radial velocity measurements. Kepler has discovered hundreds of transiting Jupiters spanning a range of periods, but the faintness of the host stars precludes radial velocity follow-up of most. Here we demonstrate a Bayesian method of measuring an individual planet's eccentricity solely from its transit light curve using prior knowledge of its host star's density. We show that eccentric Jupiters are readily identified by their short ingress/egress/total transit durations -- part of the "photoeccentric" light curve signature of a planet's eccentricity --- even with long-cadence Kepler photometry and loosely-constrained stellar parameters. A Markov Chain Monte Carlo exploration of parameter posteriors naturally marginalizes over the periapse angle and automatically accounts for the transit probability. To demonstrate, we use three published transit light curves of HD 17156 b to measure an eccentricity of e = 0.71 +0.16/-0.09, in good agreement with the discovery value e = 0.67+/-0.08 based on 33 radial-velocity measurements. We present two additional tests using actual Kepler data. In each case the technique proves to be a viable method of measuring exoplanet eccentricities and their confidence intervals. Finally, we argue that this method is the most efficient, effective means of identifying the extremely eccentric, proto hot Jupiters predicted by Socrates et al. (2012).Comment: ApJ, 756, 122. Received 2012 April 5; accepted 2012 July 9; published 2012 August 2

Education’s not black and white, it’s vibrant grey

This paper offers a learner’s eye-view of a journey through education, written in an auto-narrative style. Sarah’s story spans from Secondary School to College and through University finishing at the point of Graduation. Revealed in this open and honest account is an insight to coping with home life whilst navigating the trials of the Education system. Sarah makes criticisms of her peers at every level reminding us how competitive some students have to be to get on and achieve success in their education. Critical judgements are also made about Sarah’s School teachers and University lecturers, which are at times as rewarding as they are uncomfortable, but always truthful. Consequently, there is much to learn by both academics and students from this sensitive and vulnerable personal revelation. Sarah’s evidence in turn points to some fundamental questions about the genuine outcomes of the Educational system, e.g. what are we actually teaching young people to be like? And do we like the product in terms of their values, beliefs and motives? A concluding message from Sarah’s perspective is that greater independence in learning, freedom in thinking and equipping people to reason, judge and make decisions in whatever realm, may be defining steps towards becoming educated

Application of parameter estimation to aircraft stability and control: The output-error approach

The practical application of parameter estimation methodology to the problem of estimating aircraft stability and control derivatives from flight test data is examined. The primary purpose of the document is to present a comprehensive and unified picture of the entire parameter estimation process and its integration into a flight test program. The document concentrates on the output-error method to provide a focus for detailed examination and to allow us to give specific examples of situations that have arisen. The document first derives the aircraft equations of motion in a form suitable for application to estimation of stability and control derivatives. It then discusses the issues that arise in adapting the equations to the limitations of analysis programs, using a specific program for an example. The roles and issues relating to mass distribution data, preflight predictions, maneuver design, flight scheduling, instrumentation sensors, data acquisition systems, and data processing are then addressed. Finally, the document discusses evaluation and the use of the analysis results

Kramers-Kronig constrained variational analysis of optical spectra

A universal method of extraction of the complex dielectric function $\epsilon(\omega)=\epsilon_{1}(\omega)+i\epsilon_{2}(\omega)$ from experimentally accessible optical quantities is developed. The central idea is that $\epsilon_{2}(\omega)$ is parameterized independently at each node of a properly chosen anchor frequency mesh, while $\epsilon_{1}(\omega)$ is dynamically coupled to $\epsilon_{2}(\omega)$ by the Kramers-Kronig (KK) transformation. This approach can be regarded as a limiting case of the multi-oscillator fitting of spectra, when the number of oscillators is of the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry {\it etc.}, done on different types of samples, including thin films and anisotropic crystals.Comment: 10 pages, 7 figure