Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to form in the radiative shock in the accretion column. High-luminosity NSs show a smooth anti-correlation between the cyclotron-line centroid ($E_{CRSF}$) and X-ray luminosity ($L_X$). The observed $E_{CRSF}-L_X$ smooth anti-correlation has been in tension with the theoretically predicted one by the radiative shock model. Since there is no other candidate site for the cyclotron-line formation, we re-examine the predicted rate of change of the cyclotron-line energy with luminosity at the radiative shock, taking a closer look at the Physics involved. We developed a purely analytical model describing the overall dependence of the observed cyclotron energy centroid on the shock front's height, including the relativistic boosting effect due to the mildly relativistic motion of the accreting plasma upstream with respect to the shock's reference frame and the gravitational redshift. We find that the CRSF energy varies with a) the shock height due to the dipolar magnetic field, b) the Doppler boosting between the shock and bulk-motion frames, and c) the gravitational redshift. We show that the relativistic effects noticeably weaken the predicted $E_{CRSF}-L_X$ anti-correlation. We use our model to fit the data of the X-ray source V0332+53 and demonstrate that the model fits the data impressively well, alleviating the tension between observations and theory. The reported $E_{CRSF}-L_X$ weak anti-correlation in the supercritical accretion regime may be explained by the combination of the variation of the magnetic-field strength along the accretion column, the effect of Doppler boosting, and the gravitational redshift. Thus, the actual magnetic field on the NS surface may be a factor of $\sim 2$ larger than the naively inferred value from the observed CRSF.
We report the discovery and validation of HD 21520 b, a transiting planet found with TESS and orbiting a bright G dwarf (V=9.2, $T_{eff} = 5871 \pm 62$ K, $R_{\star} = 1.04\pm 0.02\, R_{\odot}$). HD 21520 b was originally alerted as a system (TOI-4320) consisting of two planet candidates with periods of 703.6 and 46.4 days. However, our analysis supports instead a single-planet system with an orbital period of $25.1292\pm0.0001$ days and radius of $2.70 \pm 0.09\, R_{\oplus}$. Three full transits in sectors 4, 30 and 31 match this period and have transit depths and durations in agreement with each other, as does a partial transit in sector 3. We also observe transits using CHEOPS and LCOGT. SOAR and Gemini high-resolution imaging do not indicate the presence of any nearby companions, and MINERVA-Australis and CORALIE radial velocities rule out an on-target spectroscopic binary. Additionally, we use ESPRESSO radial velocities to obtain a tentative mass measurement of $7.9^{+3.2}_{-3.0}\, M_{\oplus}$, with a 3-$\sigma$ upper limit of 17.7 $M_{\oplus}$. Due to the bright nature of its host and likely significant gas envelope of the planet, HD 21520 b is a promising candidate for further mass measurements and for atmospheric characterization.
The nitrogen isotope ratio 14N/15N is a powerful tool to trace Galactic stellar nucleosynthesis and constraining Galactic chemical evolution. Previous observations have found lower 14N/15N ratios in the Galactic center and higher values in the Galactic disk. This is consistent with the inside-out formation scenario of our Milky Way. However, previous studies mostly utilized double isotope ratios also including 12C/13C, which introduces additional uncertainties. Here we therefore present observations of C14N and its rare isotopologue, C15N, toward a sample of star forming regions, measured by the IRAM 30 m and/or the ARO 12 m telescope at $\lambda$ ~3 mm wavelength. For those 35 sources detected in both isotopologues, physical parameters are determined. Furthermore we have obtained nitrogen isotope ratios using the strongest hyperfine components of CN and C15N. For those sources showing small deviations from Local Thermodynamical Equilibrium and/or self-absorption, the weakest hyperfine component, likely free of the latter effect, was used to obtain reliable 14N/15N values. Our measured 14N/15N isotope ratios from C14N and C15N measurements are compatible with those from our earlier measurements of NH3 and 15NH3 (Paper I), i.e., increasing ratios to a Galacticentric distance of ~9 kpc. The unweighted second order polynomial fit yields $\frac{{\rm C^{14}N}}{{\rm C^{15}N}} = (-4.85 \pm 1.89)\;{\rm kpc^{-2}} \times R_{\rm GC}^{2} + (82.11 \pm 31.93) \;{\rm kpc^{-1}} \times R_{\rm GC} - (28.12 \pm 126.62)$. Toward the outer galaxy, the isotope ratio tends to decrease, supporting an earlier finding by H13CN/HC15N. Galactic chemical evolution models are consistent with our measurements of the 14N/15N isotope ratio, i.e. a rising trend from the Galactic center region to approximately 9 kpc, followed by a decreasing trend with increasing $R_{\rm GC}$ toward the outer Galaxy.