1ES 1927+654 is an extreme active galactic nucleus (AGN) that has defied our canonical expectations for how AGN appear across the electromagnetic spectrum and how they vary on short timescales. In 2022, this source began showing a X-ray quasi-periodic oscillation (QPO) at mHz frequencies, along with a newly launched radio jet. Unlike the handful of other known AGN QPOs, the QPO in 1ES 1927+654 showed a significant frequency evolution, spanning from 0.9-2.4 mHz from 2022-2024. In this work, we present the last 1.5 years of monitoring with XMM-Newton (250 ks) up to January 2026, which reveals that the QPO persists but has plateaued at a constant frequency of approximately 2.5 mHz. We perform detailed spectral-timing analyses on this exquisite dataset, consisting of over 900 QPO cycles, more than any AGN QPO to date. Our main findings are: (1) the stacked XMM-Newton power spectra shows no significant second harmonic, (2) a soft (reverberation-like) lag is observed at all frequencies and remains remarkably stable even as the QPO frequency evolved from 2022-2024, and (3) extreme X-ray jumps on the QPO period (up to 80

We report the discovery of complex flaring activity from the galactic nucleus hosting the five-year-old tidal disruption event eRASSt J234402.9−352640 (J2344). With Einstein Probe and XMM-Newton observations, we detected highly structured soft X-ray variability. Through temporal decomposition of the XMM-Newton light curve and time-resolved spectral analysis, we identified broad, thermal flares recurring every ∼12 hours and lasting ∼2 hours, consistent with quasi-periodic eruptions (QPEs). Remarkably, these QPEs are accompanied by an unprecedented crest of hotter shorter flares, each lasting between 5 and 30 minutes. These flares are predominantly found in the rising phases of the QPEs, although they also appear throughout the quiescence. These findings establish J2344 as a new member of the QPE emitter population and uncover a previously unobserved phenomenology that challenges current models of QPEs. In this letter we present the phenomenological properties of this unique source and discuss possible interpretations within the framework of extreme mass ratio inspirals.

In the last few years, short-term X-ray variability (of the order of hours) has been detected in a few supermassive black holes (SMBHs). Given the limited size of the sample, every new addition can bring invaluable information. Within the context of an automated search for X-ray sources showing flux variability in the Chandra archive, we identified peculiar variability patterns in 2MASX J12571076+2724177 (J1257), a SMBH in the Coma cluster, during observations performed in 2020. We investigated the long-term evolution of the flux, together with the evolution of the spectral parameters, throughout the Chandra and XMM-Newton observations, which cover a time span of approximately 20 years. We found that J1257 has repeatedly shown peculiar variability over the last 20 years, on typical timescales of ≃20 − 30 ks. From our spectral analysis, we found hints of a softer-when-brighter behaviour and of two well-separated flux states. We suggest that J1257 might represent a new addition to the ever-growing list of known relatively low-mass SMBHs (M ≃ 106 − 107 M⊙) showing extreme, possibly quasi-periodic X-ray variability on short timescales. The available dataset does not allow for a definitive classification of the nature of the variability. However, given the observed properties, it could either represent a quasi-periodic oscillation at a particularly low frequency or be associated with quasi-periodic eruptions in an active galactic nucleus with peculiar spectral properties.

After 6 years of studies following the discovery of GSN069, a link is starting to appear between the elusive Quasi-Periodic Eruptions (QPEs) and other types of nuclear transients, among which are Tidal Disruption Events (TDEs). As such, observing strategies are adapting, with a current trend focusing on late-time x-ray follow-ups of (optical) TDEs. While these campaigns are so far proving quite successful, the inherent confirmation bias they introduce in our sample could lead the community to hasty, and perhaps erroneous, conclusions. It is thus important to still pursue the search for nuclear transients in other, more agnostic directions. In this work, we focus on the observational aspects of our field, and lay out two different methods that can be deployed in order to reveal new QPE sources. These complementary methods enable the detection of long-term (years) and short term (minutes) transient events, that would have otherwise been missed by the standard detection pipelines. Both of these methods can be used either for data mining in the 25 years worth of XMM-Newton archive, or to trigger real-time follow-ups upon a more recent discovery.

We report the first direct measurement of the period derivative in a quasiperiodic eruption (QPE), finding a smoothly increasing period with P approximate to(1.7 +/- 0.02)& times;10-2 day day-1 in the source ZTF19acnskyy/"Ansky." Most models for QPEs invoke repeated interactions of a stellar-mass orbiting companion around the supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI). In these scenarios, a positive P is surprising, but not impossible to produce. We explore several possible explanations for the observed P , including stable mass-transfer driven by impulsive mass-loss events in an EMRI, velocity kicks at pericenter due to tidal interactions with the SMBH, apparent period changes due either to general relativistic precession effects in an EMRI or light-travel-time delays in a hierarchical SMBH binary, and mass-transfer variations in a thermal/viscous disk instability model. We find that none of the considered models provides a complete explanation for the data, motivating further work on physical explanations for positive period derivatives in QPEs.

Quasiperiodic eruptions (QPEs) are luminous, recurring X-ray outbursts from galactic nuclei, with timescales of hours to days. While their origin remains uncertain, leading models invoke accretion disk instabilities or the interaction of a massive black hole (MBH) with a lower-mass secondary in an extreme mass ratio inspiral (EMRI). EMRI scenarios offer a robust framework for interpreting QPEs by characterizing observational signatures associated with the secondary's orbital dynamics. This, in turn, enables extraction of the MBH/EMRI physical properties and provides a means to test the EMRI scenario, distinguishing models and addressing the question: what can QPE timings teach us about MBHs and EMRIs? In this study, we employ analytic expressions for Kerr geodesics to efficiently resolve the trajectory of the secondary object and perform GPU-accelerated Bayesian inference to assess the information content of QPE timings. Using our inference framework, referred to as QPE-FIT (Fast Inference with Timing; https://github.com/joheenc/QPE-FIT/tree/main), we explore QPE timing constraints on astrophysical parameters, such as EMRI orbital parameters and MBH mass/spin. We find that mild-eccentricity EMRIs (e similar to 0.1-0.3) can constrain MBH mass and EMRI semimajor axis/eccentricity to the 10% level within tens of orbital periods, while MBH spin is unconstrained for the explored semimajor axes >= 100Rg and monitoring baselines O (10-100) orbits. Introducing a misaligned precessing disk generally degrades inference of EMRI orbital parameters, but can constrain disk precession properties within 10%-50%. This work both highlights the prospect of QPE observations as dynamical probes of galactic nuclei and outlines the challenge of doing so in the multimodal parameter space of EMRI-disk collisions.

Quasi-periodic eruptions (QPEs) are a recently identified class of X-ray transient associated with tidal disruption events by supermassive black holes, and for which there are multiple possible explanations. In this paper, we present a simple model which requires the black hole be spinning, be misaligned with the accretion flow (both conditions of which are almost certainly met), and that the accretion rate is a few times the Eddington limit. We speculate that the resulting Lense-Thirring torques force the disc and entrained outflows to precess, leading to increased X-ray flux when the wind-cone is oriented at lower inclinations to the observer. We test the range of parameters for which this model could explain the period and brightness of the QPE events discovered thus far, and make qualitative comparisons between the observed X-ray spectra and light curves to those extracted from general relativistic radiation magnetohydrodynamic simulations. Overall, we find some areas of promising concordance, and identify challenges related to the details of current simulations.

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

Quasi-periodic X-ray eruptions (QPEs) are a new class of repeating nuclear transient in which repeating X-ray flares are observed coming from the nuclei of generally low-mass galaxies. Here, we present a comprehensive summary of the radio properties of 12 bona-fide quasi-periodic eruption sources, including a mix of known tidal disruption events (TDEs) and AGN-like hosts. We include a combination of new dedicated radio observations and archival/previously published radio observations to compile a catalogue of radio observations of each source in the sample. We examine the overall radio properties of the sample and compare to the radio properties of known TDEs, given the apparent link between QPEs and TDEs. Overall we find compact, weak radio sources associated with 5/12 of the QPE sources and no signatures of strong AGN activity via a luminous radio jet. We find no radio variability on hour- to day-timescales corresponding to the X-ray QPEs, but do detect significant changes over year timescales in some sources, implying that the mechanism that produces the X-ray flares does not generate strong radio-emitting outflows. The compactness of the radio sources and lack of correlation between radio luminosity and SMBH mass is very unusual for AGN, but the radio spectra and luminosities are consistent with outflows produced by a recent TDE (or accretion event), in both the known TDE sources and the AGN-like sources in the sample.

Quasi-periodic eruptions (QPEs) are recurring bursts of soft X-ray emission from supermassive black holes, which a growing class of models explains via extreme mass ratio inspirals (EMRIs). QPEs exhibit blackbody-like emission with significant temperature evolution, but the minimal information content of their almost pure-thermal spectra has limited physical constraints. Here we study the recently discovered QPEs in ZTF19acnskyy (“Ansky”), which show absorption-like features evolving dramatically within eruptions and correlating strongly with continuum temperature and luminosity, further probing the conditions underlying the emission surface. The absorption features are well described by dense ionized plasma of column density N H ≳ 10 21 cm −2 , blueshift 0.06 ≲ v / c ≲ 0.4, and either collisional or photoionization equilibrium. With high-resolution spectra, we also detect ionized blueshifted emission lines suggesting a nitrogen overabundance of 21 . 7 − 11.0 + 18.5 × solar. We interpret our results with orbiter–disk collisions in an EMRI system, in which each impact drives a shock that locally heats the disk and expels X-ray-emitting debris undergoing radiation-pressure-driven homologous expansion. We explore an analytical toy model that links the rapid change in absorption lines to the evolution of the ionization parameter and the photosphere radius, and we suggest that ∼10 −3 M ⊙ ejected per eruption with expansion velocities up to v max ∼ 0.15 c can reproduce the absorption features. With these assumptions, we show that a P Cygni profile in a spherical expansion geometry qualitatively matches the observed line profiles. Our work takes a first step toward extending existing physical models for QPEs to address their implications for spectral line formation.

Quasiperiodic eruptions (QPEs) are recurring soft X-ray transients emerging from the vicinity of supermassive black holes in nearby, low-mass galaxy nuclei; about 10 QPE hosts have been identified thus far. Here we report the NICER discovery of QPEs in the optically selected tidal disruption event (TDE) and extreme coronal line emitter (ECLE) AT2022upj, exhibiting a large spread in recurrence times from 0.5–3.5 days, durations from 0.3–1 days, peak luminosities from 10 42.5−43.0 erg s −1 , and erratic flare profiles. A wealth of evidence now links at least some QPEs to the newly formed accretion flows emerging from TDEs; AT2022upj is the third QPE reported in an optically discovered TDE. Marginalizing over the uncertain distributions of QPE peak luminosity, recurrence time, delay after TDE peak, and lifetime, we use the burgeoning sample to make a Bayesian estimate that the fraction of optical TDEs resulting in QPEs within 5 yr post-disruption is 9 − 5 + 9 %. Along with AT2019qiz, AT2022upj also marks the second of the three optical TDE+X-ray QPEs showing coronal line emission, suggesting ECLEs may represent a subset of TDEs particularly efficient at forming QPEs and/or that sustained QPE X-ray emission contributes to coronal line emission in some galactic nuclei.

X-ray quasi-periodic eruptions (QPEs) are intense soft X-ray bursts from the nuclei of nearby low-mass galaxies typically lasting about one hour and repeating every few. Their physical origin remains debated, although so-called impacts models in which a secondary orbiting body pierces through the accretion disc around the primary supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI) system are considered promising. In this work, we study the QPE timing properties of GSN 069, the first galactic nucleus in which QPEs were identified, primarily focusing on Observed minus Calculated (O-C) diagrams. The O-C data in GSN 069 are consistent with a super-orbital modulation on tens of days whose properties do not comply with the impacts model. We suggest that rigid precession of a misaligned accretion disc or, alternatively, the presence of a second SMBH forming a sub-milliparsec binary with the inner EMRI is needed to reconcile the model with the data. In both cases, the quiescent accretion disc emission should also be modulated on similar timescales. Current X-ray monitoring indicates that this might be the case, although a longer baseline of higher-cadence observations is needed to confirm the tentative X-ray flux periodicity on firm statistical grounds. Future dedicated monitoring campaigns will be crucial to test the overall impacts plus modulation model in GSN 069, and to distinguish between the two proposed modulating scenarios. If our interpretation is correct, QPEs in GSN 069 represent the first electromagnetic detection of a short-period EMRI system in an external galaxy, opening the way to future multi-messenger astronomical observations. [abridged]

The Athena mission entered a redefinition phase in July 2022, driven by the imperative to reduce the mission cost at completion for the European Space Agency below an acceptable target, while maintaining the flagship nature of its science return. This notably called for a complete redesign of the X-ray Integral Field Unit (X-IFU) cryogenic architecture towards a simpler active cooling chain. Passive cooling via successive radiative panels at spacecraft level is now used to provide a 50 K thermal environment to an X-IFU owned cryostat. 4.5 K cooling is achieved via a single remote active cryocooler unit, while a multi-stage Adiabatic Demagnetization Refrigerator ensures heat lift down to the 50 mK required by the detectors. Amidst these changes, the core concept of the readout chain remains robust, employing Transition Edge Sensor microcalorimeters and a SQUID-based Time-Division Multiplexing scheme. Noteworthy is the introduction of a slower pixel. This enables an increase in the multiplexing factor (from 34 to 48) without compromising the instrument energy resolution, hence keeping significant system margins to the new 4 eV resolution requirement. This allows reducing the number of channels by more than a factor two, and thus the resource demands on the system, while keeping a 4' field of view (compared to 5' before). In this article, we will give an overview of this new architecture, before detailing its anticipated performances. Finally, we will present the new X-IFU schedule, with its short term focus on demonstration activities towards a mission adoption in early 2027.

Aims. We aim to characterize the X-ray-to-optical/near-infrared(NIR) broad-band emission of luminous quasars (QSOs) in the first gigayear (Gyr) of cosmic evolution in order to decipher whether or not they exhibit differences compared to the lower-z QSO population. Our goal is also to provide a reliable and uniform catalog of derivable properties for these objects (from fitting their spectral energy distribution), such as bolometric and monochromatic luminosities, Eddington ratios, dust extinction, and the strength of the hot dust emission. Methods. We gathered all available photometry -from XMM-Newton proprietary data in X-rays to rest-frame NIR wavelengths- for the 18 QSOs in the HYPERION samples (6.0 <= z <= 7.5). For sources lacking uniform NIR coverage, we conducted NIR observations in the J, H, and K bands. To increase the statistical robustness of our analysis across the UV-to-NIR region, we add 36 additional sources to our sample from the E-XQR-30 sample with 5.7 less than or similar to z less than or similar to 6.6. We characterized the X-ray/UV emission of each QSO using average SEDs from luminous Type 1 sources and calculated bolometric and monochromatic luminosities. Finally, we constructed a mean SED extending from the X-rays to the NIR bands. Results. We find that the UV-optical emission of these QSOs can be modeled with templates of z similar to 2 luminous QSOs. We observe that the bolometric luminosities derived while adopting some bolometric corrections at 3000 & Aring; (BC3000 & Aring;) largely used in the literature are slightly overestimated, by 0.13 dex, as they also include reprocessed IR emission. We estimate a revised value of BC3000 & Aring; = 3.3, which can be used to derive Lbol in z >= 6 QSOs. We provide a subsample of 11 QSOs with rest-frame NIR photometry; these show a broad range of hot dust emission strength, with two sources exhibiting low levels of emission. Despite potential observational biases arising from nonuniform photometric coverage and selection biases, we produce an X-ray-to-NIR mean SED for QSOs at z greater than or similar to 6 that is a good match to templates of lower-redshift, luminous QSOs up to the UV-optical range, with a slightly enhanced contribution from hot dust in the NIR.

Quasiperiodic eruptions (QPEs) are high-amplitude, soft X-ray bursts recurring every few hours, associated with supermassive black holes. Many interpretations for QPEs were proposed since their recent discovery in 2019, including extreme mass ratio inspirals and accretion disk instabilities. But, as of today, their nature still remains debated. We perform the first high-resolution X-ray spectral study of a QPE source using the Reflection Grating Spectrometers' gratings on board XMM-Newton, leveraging nearly 2 Ms of exposure on GSN 069, the first discovered source of this class. We resolve several absorption and emission lines including a strong line pair near the N vii rest-frame energy, resembling the P-Cygni profile. We apply photoionization spectral models and identify the absorption lines as an outflow blueshifted by 1700-2900 km s-1, with a column density of about 1022 cm-2 and an ionization parameter log(xi /erg cm s-1) of 3.9-4.6. The emission lines are instead redshifted by up to 2900 km s-1, and likely originate from the same outflow that imprints the absorption features, and covers the full 4 pi sky from the point of view of GSN 069. The column density and ionization are comparable to the outflows detected in some tidal disruption events, but this outflow is significantly faster and has a strong emission component. The outflow is more highly ionized when the system is in the phase during which QPEs are present, and from the limits, we derive on its location, we conclude that the outflow is connected to the recent complex, transient activity of GSN 069, which began around 2010.

The AXIS Community Science Book represents the collective effort of 592 scientists worldwide to define the transformative science enabled by the Advanced X-ray Imaging Satellite (AXIS), a next-generation X-ray mission selected by NASA's Astrophysics Probe Program for Phase A study. AXIS will advance the legacy of high-angular-resolution X-ray astronomy with 1.5” imaging over a wide 24' field of view and an order of magnitude greater collecting area than Chandra in the 0.3-12 keV band. Combining sharp imaging, high throughput, and rapid response capabilities, AXIS will open new windows on virtually every aspect of modern astrophysics, exploring the birth and growth of supermassive black holes, the feedback processes that shape galaxies, the life cycles of stars and exoplanet environments, and the nature of compact stellar remnants, supernova remnants, and explosive transients. This book compiles 138 community-contributed science cases developed by five Science Working Groups focused on AGN and supermassive black holes, galaxy evolution and feedback, compact objects and supernova remnants, stellar physics and exoplanets, and time-domain and multi-messenger astrophysics. Together, these studies establish the scientific foundation for next-generation X-ray exploration in the 2030s and highlight strong synergies with facilities of the 2030s, such as JWST, Roman, Rubin/LSST, SKA, ALMA, ngVLA, and next-generation gravitational-wave and neutrino networks.

Recent discoveries from time-domain surveys are defying our expectations for how matter accretes onto supermassive black holes (SMBHs). The increased rate of short-timescale, repetitive events around SMBHs, including the recently discovered quasi-periodic eruptions1-5, are garnering further interest in stellar-mass companions around SMBHs and the progenitors to millihertz-frequency gravitational-wave events. Here we report the discovery of a highly significant millihertz quasi-periodic oscillation (QPO) in an actively accreting SMBH, 1ES 1927+654, which underwent a major optical, ultraviolet and X-ray outburst beginning in 20186,7. The QPO was detected in 2022 with a roughly 18-minute period, corresponding to coherent motion on a scale of less than 10 gravitational radii, much closer to the SMBH than typical quasi-periodic eruptions. The period decreased to 7.1 minutes over 2 years with a decelerating period evolution ( P ¨ greater than zero). To our knowledge, this evolution has never been seen in SMBH QPOs or high-frequency QPOs in stellar-mass black holes. Models invoking orbital decay of a stellar-mass companion struggle to explain the period evolution without stable mass transfer to offset angular-momentum losses, and the lack of a direct analogue to stellar-mass black-hole QPOs means that many instability models cannot explain all of the observed properties of the QPO in 1ES 1927+654. Future X-ray monitoring will test these models, and if it is a stellar-mass orbiter, the Laser Interferometer Space Antenna (LISA) should detect its low-frequency gravitational-wave emission.

The detection of blue-shifted absorption lines likely associated with ionized Iron K-shell transitions in the X-ray spectra of many Active Galactic Nuclei (AGN) suggests the presence of a highly ionized gas outflowing with mildly relativistic velocities (0.03c-0.6c), named Ultra-Fast Outflow (UFO). Within the SUBWAYS project we characterized these winds starting from a sample of 22 radio-quiet quasars at 0.1 < z < 0.4, and compared the results with similar studies in the literature on samples of 42 local radio-quiet Seyfert galaxies and 14 high redshift radio-quiet quasars. The scope of our work is a statistical study of UFO parameters and incidence, considering key physical properties of the sources, e.g. supermassive black hole (SMBH) mass, bolometric luminosity, accretion rates and Spectral Energy Distribution, with the aim of gaining new insights into the UFO launching mechanisms. We find indications that highly luminous AGN with steeper X-ray/UV ratio, are more likely to host UFO. The presence of UFO is not significantly related to any other AGN property in our sample. These findings suggest that the UFO phenomenon may be transient. Focusing on AGN with UFO, other important results are: (1) faster UFO have larger ionization parameters and column densities; (2) X-ray radiation plays a more crucial role in driving highly ionized winds compared to UV; (3) the correlation between outflow velocity and luminosity is significantly flatter than what expected for radiatively driven winds; (4) more massive BH experience higher wind mass-losses, suppressing accretion of matter onto the BH; (5) the UFO launching radius is positively correlated with the Eddington ratio. Furthermore, our analysis suggest the involvement of multiple launching mechanisms, including radiation pressure and magneto-hydrodynamic processes, rather than pointing to a single, universally applicable mechanism.

In the past 5 yr, six X-ray quasi-periodic eruption (QPE) sources have been discovered in the nuclei of nearby galaxies. Their origin remains an open question. We present Multi Unit Spectroscopic Explorer integral field spectroscopy of five QPE host galaxies to characterize their properties. We find that 3/5 galaxies host extended emission-line regions (EELRs) up to 10 kpc in size. The EELRs are photoionized by a nonstellar continuum, but the current nuclear luminosity is insufficient to power the observed emission lines. The EELRs are decoupled from the stars both kinematically and in projected sky position, and the low velocities and velocity dispersions (<100 km s −1 and ≲75 km s −1 , respectively) are inconsistent with being driven by active galactic nuclei (AGNs) or shocks. The origin of the EELRs is likely a previous phase of nuclear activity. QPE host galaxies share several similarities with tidal disruption event (TDE) hosts, including an overrepresentation of galaxies with strong Balmer absorption and little ongoing star formation, as well as a preference for a short-lived (the typical EELR lifetime is ∼15,000 yr), gas-rich phase where the nucleus has recently faded significantly. This suggests that QPEs and TDEs may share a common formation channel, disfavoring AGN accretion disk instabilities as the origin of QPEs. If QPEs are related to extreme mass ratio inspiral systems (EMRIs), e.g., stellar-mass objects on bound orbits about massive black holes, the high incidence of EELRs and recently faded nuclei could be used to localize the hosts of EMRIs discovered by low-frequency gravitational-wave observatories.

Quasi-periodic eruptions (QPEs) are repeated X-ray flares from galactic nuclei that recur every few hours to days, depending on the source. Despite some diversity in the recurrence and amplitude of eruptions, their striking regularity has motivated theorists to associate QPEs with orbital systems. Among the known QPE sources, eRO-QPE2 has shown the most regular flare timing and luminosity since its discovery. We report here on its long-term evolution over 3.3 yr from discovery and find that: i) the average QPE recurrence time per epoch has decreased over time, albeit not at a uniform rate; ii) the distinct alternation between consecutive long and short recurrence times found at discovery has not been significant since; iii) the spectral properties, namely flux and temperature of both eruptions and quiescence components, have remained remarkably consistent within uncertainties. We attempted to interpret these results as orbital period and eccentricity decay coupled with orbital and disk precession. However, since gaps between observations are too long, we are not able to distinguish between an evolution dominated by just a decreasing trend, or by large modulations (e.g. due to the precession frequencies at play). In the former case, the observed period decrease is roughly consistent with that of a star losing orbital energy due to hydrodynamic gas drag from disk collisions, although the related eccentricity decay is too fast and additional modulations have to contribute too. In the latter case, no conclusive remarks are possible on the orbital evolution and the nature of the orbiter due to the many effects at play. However, these two cases come with distinctive predictions for future X-ray data: in the case of a decreasing trend, we expect all future observations to show a shorter recurrence time than the latest epoch, while in the case of large-amplitude modulations we expect some future observations to be found with a larger recurrence, hence an apparent temporary period increase.