Back and forth between accretion and rotation power: tackling the diversity of millisecond pulsars across the spectrum

This thesis explores the intricate behaviors of millisecond pulsars (MSPs), the fastest-spinning neutron stars (NSs) in the Universe. These pulsars achieve their millisecond spin period through a Gyr-long accretion phase, when a low-mass donor star transfers matter and angular momentum to the NS surface, causing the system to shine as a bright low-mass X-ray binary. Once the mass accretion rate ceases, the NS shifts to a radio pulsar state powered by the gradual loss of its rotational energy. MSPs provide crucial clues for unraveling the complex mechanisms behind mass accretion and ejection, as well as the processes related to magnetospheric particle acceleration. The first part of this research project focuses on accreting MSPs (AMSPs), transient systems that predominantly persist in quiescence but can suddenly exhibit mass accretion outbursts lasting weeks or months, marked by a considerable increase in X-ray luminosity. By studying the temporal evolution of their X-ray pulsations throughout the outburst, we can gain insights into the pulsar’s behavior and the accretion torques acting on it while accreting. Additionally, long-term studies on orbital period and spin frequency evolution further reveal the pulsar’s dynamics during extended periods of inactivity. Following Chapters 1, 2, and 3, which provide an overview of pulsars, the main telescopes, and the primary analysis techniques used throughout this thesis, Chapter 4 is dedicated to the prototype of AMSPs, SAX J1808.4−3658, and the timing analysis of X-ray pulsations during its latest outburst in 2022. The long-term spin derivative of ∼10−15 Hz s−1, consistent with the spin-down torque from a ∼108 G rotating magnetic dipole, supports the hypothesis that a rotation-powered pulsar could turn on during quiescence. For the first time in the last twenty years, the orbital phase evolution shows evidence of a decrease in the orbital period. I discuss the observed evolution in terms of a coupling between the orbit and variations in the mass quadrupole of the companion star. In addition to timing analysis, X-ray spectra offer another crucial tool for investigating the accretion flow and its geometry near the NS. Chapter 5 focuses on the X-ray spectral properties of the AMSP IGR J17498−2921 during its 2023 outburst. As typically observed for these sources, the broad-band spectral emission is well described by an absorbed Comptonized emission presumably originated from the accretion columns over the NS surface, plus a disk reflection component. The broadening of the disk reflection spectral features, including a prominent iron emission line, is consistent with the relativistic motion of disk matter. I also present the timing analysis throughout the outburst, with a specific focus on a sudden jump in the pulse phase observed halfway through the accretion event. This jump may be related to a change in the accretion geometry, potentially involving a reconfiguration of the magnetic field lines. Chapter 6 centers on the recently discovered AMSP SRGA J144459.2−604207. This part outlines the steps taken following the detection of a new source in the context of an international collaboration, starting from its localization and the determination of its spin and orbital parameters. We also report the discovery of significant polarized X-ray emission from an AMSP for the first time, confirming theoretical expectations and strengthening the prospects of using X-ray polarimetry to measure the NS geometrical parameters and eventually constrain their mass and radius through pulse profile modeling. In the second part of this thesis, I shift the focus to transitional MSPs (tMSPs), intriguing objects that bridge the long-sought evolutionary gap between accretionpowered and rotation-powered states. Remarkably, tMSPs swing back and forth between these two emission mechanisms on time scales as short as a few weeks. All tMSPs have also been caught in an intermediate condition, referred to as the sub-luminous disk state. The most defining feature of this state is the variable X-ray emission, which unpredictably oscillates between two distinct intensity levels, dubbed ‘high’ and ‘low’ modes, along with occasional flares. The prototype of tMSPs in the sub-luminous disk state, PSR J1023+0038, was recently observed to pulse not only in the X-rays but also in optical and UV bands, challenging our understanding of their underlying emission mechanisms. In Chapter 7, I investigate the proposed scenario where X-ray, UV, and optical pulsations originate from synchrotron radiation in a shock formed where the particle wind ejected from a rotation-powered pulsar encounters matter from the inner accretion disk at ∼100 km from the pulsar. To test this model, I present a detailed study of the time lags between optical and X-ray pulsations based on (quasi-)simultaneous observations over five years with various instruments. This analysis demonstrates that the pulsations in the two bands remain in phase over time, with phase shifts consistent with the differing synchrotron emission timescales for optical and X-ray photons. To further investigate the mode switching phenomena across different wavelengths, I organized the first high-time resolution multi-wavelength campaign on a promising candidate tMSP in the sub-luminous disk state, 3FGL J1544.6−1125. The results of this campaign are presented in Chapter 8, reinforcing the classification of this source as a very promising candidate and supporting the hypothesis that most of the optical emission originates in the same region of X-rays, namely in the shock between the pulsar wind and the accretion disk. Motivated by the discovery of optical pulsations from PSR J1023+0038 and the striking similarities between this confirmed tMSP and the promising candidate 3FGL J1544.6−1125, in Chapter 9 I review our ongoing efforts to search for optical pulsed signals from the latter and present the most stringent upper limits to date. Lastly, in Chapter 10, I summarize the main findings and conclusions of this work. Overall, this thesis highlights the paramount role of multi-wavelength temporal and spectral analysis in disentangling the complexity of MSPs across their different observed states, with particular emphasis on accreting and transitional systems. While many results presented here support and strengthen existing theoretical frameworks, others underscore many unresolved questions. These open topics offer promising avenues for advancing our understanding of the evolution and interplay between the many facets of MSPs, as well as the potential coexistence or alternation between accretion-powered and rotation-powered states.