CPT symmetry and antimatter gravity in general relativity

The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is self-attractive, the interaction between matter and antimatter might be either attractive or repulsive. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion, i.e. antigravity appears as a prediction of general relativity when CPT is applied. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter repulsive interaction.Comment: 6 pages, to be published in EPL (http://epljournal.edpsciences.org/

Scale in education research: towards a multi-scale methodology

This article explores some theoretical and methodological problems concerned with scale in education research through a critique of a recent mixed-method project. The project was framed by scale metaphors drawn from the physical and earth sciences and I consider how recent thinking around scale, for example in ecosystems and human geography might offer helpful points and angles of view on the challenges of thinking spatially in education research. Working between the spatial metaphors of ecology scholars and the critiques of the human geographers, for example the hypercomplex social space in Lefebvre’s political-economic thinking and the fluid, simultaneous, multiple spatialities of Massey’s post-structuralism, I problematize space and scale in education research. Interweaving these geographical ideas with Giddens’ structuration and Bourdieu’s theory of practice, both of which employed what might be termed scale-bridging to challenge social science’s entrenched paradigms, leads me to reconsider what is possible and desirable in the study of education systems. Following the spatial turn in the social sciences generally, there is an outstanding need to theorise multi-scale methodology for education research

On the relevance of the mathematics curriculum to young people

In this paper we draw upon focus group data from a large study of learner trajectories through 14-19 mathematics education to think about the notion of relevance in the mathematics curriculum. Drawing on data from three socially distanced sites we explore how different emphases on what might be termed practical, process and/or professional forms of relevance affect the experiences and aspirations of learners of mathematics. We consider whether an emphasis on practical relevance in schools serving relatively disadvantaged communities might aid the reproduction of students’ social position. This leads us to suggest that a fourth category of curriculum relevance – political relevance – is largely missing from classrooms

Exoplanets or Dynamic Atmospheres? The Radial Velocity and Line Shape Variations of 51 Pegasi and Tau Bootis

Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in Tau Boo. For 51 Peg, our upper limit for line shape variations with 4.23-day periodicity is small enough to exclude with 10 sigma confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray (1997) are also not seen, but in this case with marginal (2 sigma) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation, because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes' data and for our own. Tau Boo's large radial velocity amplitude and v*sin(i) make it easier to test for pulsations in this star. Again we find no evidence for periodic line-shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.Comment: 44 pages, 19 figures, plain TeX, accepted to ApJS (companion to letter astro-ph/9712279

HAT-P-4b: A metal-rich low-density transiting hot Jupiter

We describe the discovery of HAT-P-4b, a low-density extrasolar planet transiting BD+36 2593, a V = 11.2 mag slightly evolved metal-rich late F star. The planet's orbital period is 3.056536+/-0.000057 d with a mid-transit epoch of 2,454,245.8154 +/- 0.0003 (HJD). Based on high-precision photometric and spectroscopic data, and by using transit light curve modeling, spectrum analysis and evolutionary models, we derive the following planet parameters: Mp= 0.68 +/- 0.04 MJ, Rp= 1.27 +/- 0.05 RJ, rho = 0.41 +/- 0.06 g cm-3 and a = 0.0446 +/- 0.0012 AU. Because of its relatively large radius, together with its assumed high metallicity of that of its parent star, this planet adds to the theoretical challenges to explain inflated extrasolar planets.Comment: 5 pages, accepted for publication in ApJ

HAT-P-3b: A heavy-element rich planet transiting a K dwarf star

We report the discovery of a Jupiter-size planet transiting a relatively bright (V = 11.56) and metal-rich early K dwarf star with a period of about 2.9 days. On the basis of follow-up photometry and spectroscopy we determine the mass and radius of the planet, HAT-P-3b, to be M_p = 0.599 +/- 0.026 M_Jup and R_p = 0.890 +/- 0.046 R_Jup. The relatively small size of the object for its mass implies the presence of about 75 Earth masses worth of heavy elements (1/3 of the total mass) based on current theories of irradiated extrasolar giant planets, similar to the mass of the core inferred for the transiting planet HD 149026b. The bulk density of HAT-P-3b is found to be rho_p = 1.06 +/- 0.17 g/cm^3, and the planet orbits the star at a distance of 0.03894 AU. Ephemerides for the transit centers are T_c = 2,454,218.7594 +/- 0.0029 + N (2.899703 +/- 0.000054) (HJD).Comment: To appear in ApJ

Three-neutron resonance trajectories for realistic interaction models

Three-neutron resonances are investigated using realistic nucleon-nucleon interaction models. The resonance pole trajectories are explored by first adding an additional interaction to artificially bind the three-neutron system and then gradually removing it. The pole positions for the three-neutron states up to J=5/2 are localized in the third energy quadrant-Im (E)<=0, Re (E)<=0-well before the additional interaction is removed. Our study shows that realistic nucleon-nucleon interaction models exclude any possible experimental signature of three-neutron resonances.Comment: 13 pages ; 8 figs ; 5 table

HAT-P-17b,c: A Transiting, Eccentric, Hot Saturn and a Long-period, Cold Jupiter

We report the discovery of HAT-P-17b,c, a multi-planet system with an inner transiting planet in a short-period, eccentric orbit and an outer planet in a 4.8 yr, nearly circular orbit. The inner planet, HAT-P-17b, transits the bright V = 10.54 early K dwarf star GSC 2717-00417, with an orbital period P = 10.338523 +/- 0.000009 d, orbital eccentricity e = 0.346 +/- 0.007, transit epoch T_c = 2454801.16945 +/- 0.00020, and transit duration 0.1691 +/- 0.0009 d. HAT-P-17b has a mass of 0.530 +/- 0.018 M_J and radius of 1.010 +/- 0.029 R_J yielding a mean density of 0.64 +/- 0.05 g cm^-3. This planet has a relatively low equilibrium temperature in the range 780-927 K, making it an attractive target for follow-up spectroscopic studies. The outer planet, HAT-P-17c, has a significantly longer orbital period P_2 = 1797^+58_-89 d and a minimum mass m_2 sin i_2 = 1.4^+1.1_-0.4 M_J. The orbital inclination of HAT-P-17c is unknown as transits have not been observed and may not be present. The host star has a mass of 0.86 +/- 0.04 M_Sun, radius of 0.84 +/- 0.02, effective temperature 5246 +/- 80 K, and metallicity [Fe/H] = 0.00 +/- 0.08. HAT-P-17 is the second multi-planet system detected from ground-based transit surveys.Comment: Submitted to ApJ, 13 pages, 6 figures, 6 table

HAT-P-18b and HAT-P-19b: Two Low-Density Saturn-Mass Planets Transiting Metal-Rich K Stars

We report the discovery of two new transiting extrasolar planets. HAT-P-18b orbits the V=12.759 K2 dwarf star GSC 2594-00646, with a period P=5.508023+-0.000006 d, transit epoch Tc=2454715.02174+-0.00020 (BJD), and transit duration 0.1131+-0.0009 d. The host star has a mass of 0.77+-0.03 Msun, radius of 0.75+-0.04 Rsun, effective temperature 4803+-80 K, and metallicity [Fe/H]=+0.10+-0.08. The planetary companion has a mass of 0.197+-0.013 Mjup, and radius of 0.995+-0.052 Rjup yielding a mean density of 0.25+-0.04 g cm-3. HAT-P-19b orbits the V=12.901 K1 dwarf star GSC 2283-00589, with a period P=4.008778+-0.000006 d, transit epoch Tc=2455091.53417+-0.00034 (BJD), and transit duration 0.1182+-0.0014 d. The host star has a mass of 0.84+-0.04 Msun, radius of 0.82+-0.05 Rsun, effective temperature 4990+-130 K, and metallicity [Fe/H]=+0.23+-0.08. The planetary companion has a mass of 0.292+-0.018 Mjup, and radius of 1.132+-0.072 Rjup yielding a mean density of 0.25+-0.04 g cm-3. The radial velocity residuals for HAT-P-19 exhibit a linear trend in time, which indicates the presence of a third body in the system. Comparing these observations with theoretical models, we find that HAT-P-18b and HAT-P-19b are each consistent with a hydrogen-helium dominated gas giant planet with negligible core mass. HAT-P-18b and HAT-P-19b join HAT-P-12b and WASP-21b in an emerging group of low-density Saturn-mass planets, with negligible inferred core masses. However, unlike HAT-P-12b and WASP-21b, both HAT-P-18b and HAT-P-19b orbit stars with super-solar metallicity. This calls into question the heretofore suggestive correlation between the inferred core mass and host star metallicity for Saturn-mass planets.Comment: 18 pages, 11 figures, 9 tables. Replaced with version accepted for publication in Ap