Identifying student and teacher difficulties in interpreting atomic spectra using a quantum model of emission and absorption of radiation

Our study sets out to identify the difficulties that high school students, teachers, and university students encounter when trying to explain atomic spectra. To do so, we identify the key concepts that any quantum model for the emission and absorption of electromagnetic radiation must include to account for the gas spectra and we then design two questionnaires, one for teachers and the other for students. By analyzing the responses, we conclude that (i) teachers lack a quantum model for the emission and absorption of electromagnetic radiation capable of explaining the spectra, (ii) teachers and students share the same difficulties, and (iii) these difficulties concern the model of the atom, the model of radiation, and the model of the interaction between them.

The imprint of the crustal magnetic field on the thermal spectra and pulse profiles of isolated neutron stars

Isolated neutron stars (NSs) show a bewildering variety of astrophysical manifestations, presumably shaped by the magnetic field strength and topology at birth. Here, using state-of-the-art calculations of the coupled magnetic and thermal evolution of NSs, we compute the thermal spectra and pulse profiles expected for a variety of initial magnetic field configurations. In particular, we contrast models with purely poloidal magnetic fields to models dominated by a strong internal toroidal component. We find that, while the former displays double-peaked profiles and very low pulsed fractions, in the latter, the anisotropy in the surface temperature produced by the toroidal field often results in a single pulse profile, with pulsed fractions that can exceed the 50–60 per cent level even for perfectly isotropic local emission. We further use our theoretical results to generate simulated ‘observed’ spectra, and show that blackbody (BB) fits result in inferred radii that can be significantly smaller than the actual NS radius, even as low as ∼1–2 km for old NSs with strong internal toroidal fields and a high absorption column density along their line of sight. We compute the size of the inferred BB radius for a few representative magnetic field configurations, NS ages and magnitudes of the column density. Our theoretical results are of direct relevance to the interpretation of X-ray observations of isolated NSs, as well as to the constraints on the equation of state of dense matter through radius measurements.

Circumstellar emission in Be/X-ray binaries of the Magellanic Clouds and the Milky Way

Aims. We study the optical and near-infrared colour excesses produced by circumstellar emission in a sample of Be/X-ray binaries. Our main goals are exploring whether previously published relations, valid for isolated Be stars, are applicable to Be/X-ray binaries and computing the distance to these systems after correcting for the effects of the circumstellar contamination. Methods. Simultaneous UBVRI photometry and spectra in the 3500−7000 Å spectral range were obtained for 11 optical counterparts to Be/X-ray binaries in the LMC, 5 in the SMC and 12 in the Milky Way. As a measure of the amount of circumstellar emission we used the Hα equivalent width corrected for photospheric absorption. Results. We find a linear relationship between the strength of the Hα emission line and the component of E(B − V) originating from the circumstellar disk. This relationship is valid for stars with emission lines weaker than EW ≈ −15   Å. Beyond this point, the circumstellar contribution to E(B − V) saturates at a value ≈0.17   mag. A similar relationship is found for the (V − I) near infrared colour excess, albeit with a steeper slope and saturation level. The circumstellar excess in (B − V) is found to be about five times higher for Be/X-ray binaries than for isolated Be stars with the same equivalent width EW(Hα), implying significant differences in the physical properties of their circumstellar envelopes. The distance to Be/X-ray binaries (with non-shell Be star companions) can only be correctly estimated by taking into account the excess emission in the V band produced by free-free and free-bound transitions in the circumstellar envelope. We provide a simple method to determine the distances that includes this effect.

Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6×1012G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. None the less, the modelling allows us to place constraints on the system geometry (i.e. the angles ψ and ξ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to 65° ≲ ψ + ξ ≲ 125° or 235° ≲ ψ + ξ ≲ 295°; (b) the temperature contrast between the poles and the equator must be at least a factor of ∼6, and (c) the size of the hottest region ranges between 0.2 and 0.7 km (including uncertainties on the source distance). Lastly, we interpret our findings within the context of internal and external heating models.