Investigating the origin of optical and X-ray pulsations of the transitional millisecond pulsar PSR J1023+0038

¹ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00076 Monteporzio Catone, RM, Italy
e-mail: giulia.illiano@inaf.it
² Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133 Roma, Italy
³ INAF-Istituto di Astrofisica e Planetologia Spaziali, Via Fosso del Cavaliere 100, 00133 Rome, Italy
⁴ Sapienza Universitá di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
⁵ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain
⁶ Institut d’Estudis Espacials de Catalunya (IEEC), Carrer Gran Capitá 2-4, 08034 Barcelona, Spain
⁷ INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, LC, Italy
⁸ INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁹ INAF-Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Florence, Italy
¹⁰ INAF-Fundación Galileo Galilei, Rambla José Ana Fernández Pérez, 7, 38712 Santa Cruz de Tenerife, Spain
¹¹ INAF-Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Napoli, Italy
¹² Department of Physics and Astronomy, University of Padova, Via F. Marzolo 8, 35131 Padova, Italy
¹³ Dipartimento di Fisica e Astronomia, Università di Catania, Sezione Astrofisica, Via S. Sofia 78, 95123 Catania, Italy
¹⁴ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys, 23, 08010 Barcelona, Spain
¹⁵ Norwegian University of Science and Technology (NTNU), Høgskoleringen 1, 7491 Trondheim, Norway

Received: 29 July 2022
Accepted: 16 November 2022

Abstract

Context. PSR J1023+0038 is the first millisecond pulsar that was ever observed as an optical and UV pulsar. So far, it is the only optical transitional millisecond pulsar. The rotation- and accretion-powered emission mechanisms hardly individually explain the observed characteristics of optical pulsations. A synergistic model, combining these standard emission processes, was proposed to explain the origin of the X-ray/UV/optical pulsations.

Aims. We study the phase lag between the pulses in the optical and X-ray bands to gain insight into the physical mechanisms that cause it.

Methods. We performed a detailed timing analysis of simultaneous or quasi-simultaneous observations in the X-ray band, acquired with the XMM-Newton and NICER satellites, and in the optical band, with the fast photometers SiFAP2 (mounted at the 3.6 m Telescopio Nazionale Galileo) and Aqueye+ (mounted at the 1.8 m Copernicus Telescope). We estimated the time lag of the optical pulsation with respect to that in the X-rays by modeling the folded pulse profiles with two harmonic components.

Results. Optical pulses lag the X-ray pulses by ∼150 μs in observations acquired with instruments (NICER and Aqueye+) whose absolute timing uncertainty is much smaller than the measured lag. We also show that the phase lag between optical and X-ray pulsations lies in a limited range of values, δϕ ∈ (0 − 0.15), which is maintained over timescales of about five years. This indicates that both pulsations originate from the same region, and it supports the hypothesis of a common emission mechanism. Our results are interpreted in the shock-driven mini pulsar nebula scenario. This scenario suggests that optical and X-ray pulses are produced by synchrotron emission from the shock that formed within a few light cylinder radii away (∼100 km) from the pulsar, where its striped wind encounters the accretion disk inflow.