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

TeV Gamma-Ray Sources from a Survey of the Galactic Plane with Milagro

A survey of Galactic gamma-ray sources at a median energy of ~20 TeV has been performed using the Milagro Gamma Ray Observatory. Eight candidate sources of TeV emission are detected with pre-trials significance $>4.5\sigma$ in the region of Galactic longitude $l\in[30^\circ,220^\circ]$ and latitude $b\in[-10^\circ,10^\circ]$. Four of these sources, including the Crab nebula and the recently published MGRO J2019+37, are observed with significances $>4\sigma$ after accounting for the trials involved in searching the 3800 square degree region. All four of these sources are also coincident with EGRET sources. Two of the lower significance sources are coincident with EGRET sources and one of these sources is Geminga. The other two candidates are in the Cygnus region of the Galaxy. Several of the sources appear to be spatially extended. The fluxes of the sources at 20 TeV range from ~25% of the Crab flux to nearly as bright as the Crab.Comment: Submitted to Ap

Milagro Constraints on Very High Energy Emission from Short Duration Gamma-Ray Bursts

Recent rapid localizations of short, hard gamma-ray bursts (GRBs) by the Swift and HETE satellites have led to the observation of the first afterglows and the measurement of the first redshifts from this type of burst. Detection of >100 GeV counterparts would place powerful constraints on GRB mechanisms. Seventeen short duration (< 5 s) GRBs detected by satellites occurred within the field of view of the Milagro gamma-ray observatory between 2000 January and 2006 December. We have searched the Milagro data for >100 GeV counterparts to these GRBs and find no significant emission correlated with these bursts. Due to the absorption of high-energy gamma rays by the extragalactic background light (EBL), detections are only expected for redshifts less than ~0.5. While most long duration GRBs occur at redshifts higher than 0.5, the opposite is thought to be true of short GRBs. Lack of a detected VHE signal thus allows setting meaningful fluence limits. One GRB in the sample (050509b) has a likely association with a galaxy at a redshift of 0.225, while another (051103) has been tentatively linked to the nearby galaxy M81. Fluence limits are corrected for EBL absorption, either using the known measured redshift, or computing the corresponding absorption for a redshift of 0.1 and 0.5, as well as for the case of z=0.Comment: Accepted for publication in the Astrophysical Journa

HAT-P-6b: A Hot Jupiter transiting a bright F star

In the ongoing HATNet survey we have detected a giant planet, with radius 1.33 +/- 0.06 RJup and mass 1.06 +/- 0.12 MJup, transiting the bright (V = 10.5) star GSC 03239-00992. The planet is in a circular orbit with period 3.852985 +/- 0.000005 days and mid-transit epoch 2,454,035.67575 +/- 0.00028 (HJD). The parent star is a late F star with mass 1.29 +/- 0.06 Msun, radius 1.46 +/- 0.06 Rsun, Teff ~ 6570 +/- 80 K, [Fe=H] = -0.13 +/- 0.08 and age ~ 2.3+/-^{0.5}_{0.7}Gy. With this radius and mass, HAT-P-6b has somewhat larger radius than theoretically expected. We describe the observations and their analysis to determine physical properties of the HAT-P-6 system, and briefly discuss some implications of this finding.Comment: Accepted for publication in ApJL, 5 pages, minor changes compared to V

The CORALIE survey for southern extra-solar planets. X. A Hot Jupiter orbiting HD73256

Recent radial-velocity measurements obtained with the CORALIE spectrograph on the 1.2-m Euler Swiss telescope at La Silla unveil the presence of a new Jovian-mass Hot Jupiter around HD 73256. The 1.85-M_Jup planet moves on an extremely short-period (P=2.5486 d), quasi-circular orbit. The best Keplerian orbital solution is presented together with an unsuccessful photometric planetary-transit search performed with the SAT Danish telescope at La Silla. Over the time span of the observations, the photometric follow-up of the candidate has nevertheless revealed a P=14-d photometric periodicity corresponding to the rotational period of the star. This variation as well as the radial-velocity jitter around the Keplerian solution are shown to be related to the fair activity level known for HD 73256.Comment: 7 pages, 7 figures. Accepted in A&

Discovery of Localized Regions of Excess 10-TeV Cosmic Rays

An analysis of 7 years of Milagro data performed on a 10-degree angular scale has found two localized regions of excess of unknown origin with greater than 12 sigma significance. Both regions are inconsistent with gamma-ray emission with high confidence. One of the regions has a different energy spectrum than the isotropic cosmic-ray flux at a level of 4.6 sigma, and it is consistent with hard spectrum protons with an exponential cutoff, with the most significant excess at ~10 TeV. Potential causes of these excesses are explored, but no compelling explanations are found.Comment: Submitted to PhysRevLet

HAT-P-49b: A 1.7 M_J Planet Transiting a Bright 1.5 M_S F-Star

We report the discovery of the transiting extrasolar planet HAT-P-49b. The planet transits the bright (V = 10.3) slightly evolved F-star HD 340099 with a mass of 1.54M_S and a radius of 1.83 R_S. HAT-P-49b is orbiting one of the 25 brightest stars to host a transiting planet which makes this a favorable candidate for detailed follow-up. This system is an especially strong target for Rossiter- McLaughlin follow-up due to the fast rotation of the host star, 16 km/s. The planetary companion has a period of 2.6915 d, mass of 1.73 M_J and radius of 1.41 R_J. The planetary characteristics are consistent with that of a classical hot Jupiter but we note that this is the fourth most massive star to host a transiting planet with both M_p and R_p well determined.Comment: Accepted to the Astronomical Journa

The Intrinsic Origin of Spin Echoes in Dipolar Solids Generated by Strong Pi Pulses

In spectroscopy, it is conventional to treat pulses much stronger than the linewidth as delta-functions. In NMR, this assumption leads to the prediction that pi pulses do not refocus the dipolar coupling. However, NMR spin echo measurements in dipolar solids defy these conventional expectations when more than one pi pulse is used. Observed effects include a long tail in the CPMG echo train for short delays between pi pulses, an even-odd asymmetry in the echo amplitudes for long delays, an unusual fingerprint pattern for intermediate delays, and a strong sensitivity to pi-pulse phase. Experiments that set limits on possible extrinsic causes for the phenomena are reported. We find that the action of the system's internal Hamiltonian during any real pulse is sufficient to cause the effects. Exact numerical calculations, combined with average Hamiltonian theory, identify novel terms that are sensitive to parameters such as pulse phase, dipolar coupling, and system size. Visualization of the entire density matrix shows a unique flow of quantum coherence from non-observable to observable channels when applying repeated pi pulses.Comment: 24 pages, 27 figures. Revised from helpful referee comments. Added new Table IV, new paragraphs on pages 3 and 1