Modeling accretion columns in accretion-powered pulsars

II. Directly observable column emission

¹ Dr. Karl Remeis-Observatory & ECAP, University of Erlangen-Nuremberg, Sternwartstr. 7, 96049 Bamberg, Germany
² NASA Goddard Space Flight Center, Astrophysics Science Division, Greenbelt, MD 20771, USA
³ CRESST, Department of Astronomy, University of Maryland, College Park, MD 20742, USA
⁴ Sternberg Astronomical Institute, M. V. Lomonosov Moscow State University, Universitetskij pr., 13 Moscow 119992, Russia
⁵ Boston Fusion Corp., 70 Westview, Suite 100 Lexington, MA 02421, USA
⁶ CRESST and Center for Space Science and Technology, UMBC, Baltimore, MD 21250, USA
⁷ European Space Astronomy Center (ESA/ESAC), Science Operations Department, Villanueva de la Cañada, 28691 Madrid, Spain
⁸ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
⁹ Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352, USA
¹⁰ Department of Physics & Astronomy, George Mason University, Fairfax, VA 22030-4444, USA
¹¹ International Space Science Institute, Hallerstrasse 6, 3012 Bern, Switzerland
¹² Physikalisches Institut, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
¹³ ISDC, Department of Astronomy, University of Geneva, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
¹⁴ INAF, Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate, Italy
¹⁵ Astronomy and Astrophysics Dept., University of California San Diego, La Jolla, CA 92075, USA
¹⁶ Institut für Astronomie und Astrophysik, Universität Tübingen, Sand 1, 72076 Tübingen, Germany

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Received: 31 December 2024
Accepted: 9 April 2026

Abstract

Context. Modeling the observed emission from highly magnetized accreting neutron stars is essential for interpreting their X-ray spectra and variability. This task is challenging due to the dynamic, multidimensional nature of the accretion columns and the strong gravitational field. Radiation propagation outside the column, within the neutron star’s gravitational field, significantly shapes the observed emission and its variability with rotational phase. Geometry – the location of the magnetic poles and the observer’s inclination – is one of the key factors influencing the observables due to the anisotropy of the problem.

Aims. In this work, we study how visibility effects in the gravitational field of the neutron star influence the direct emission from an accretion column, highlighting their importance when interpreting plasma parameters from observed spectra.

Methods. Building on the physical model from the previous paper in this series, we investigate the directly observable X-ray flux from one and two columns with fan-beam wall emission, down-boosted by the bulk flow, focusing on the impact of geometry.

Results. We find that the observed flux strongly depends on the geometrical setup, which we illustrate across various observables. Particularly notable are special geometries in which a column on the far side of the neutron star aligns with the line of sight. In these cases, shadowing and strong light bending produce a narrow intense peak in pulse profiles at soft energies and a pronounced dip at higher energies (≳20 keV). The combination of shadowing and height dependence of emission also leads to spectral softening. Flux-derived luminosities can be overestimated by up to a factor of 10. The fundamental cyclotron resonant scattering feature (CRSF) appears predominantly in emission across geometries, and we discuss possible causes.

Conclusions. Our results demonstrate that geometry has a major impact on pulse profiles, phase-averaged spectra, phase–energy maps, and the anisotropy factor relevant for luminosity estimates. Future studies should include the reflected component in addition to the direct emission considered here, and account for a more accurate treatment of resonant redistribution in the CRSF-forming region.