Secular Evolution Research Articles

Dust Drift Timescales in Protoplanetary Disks at the Cusp of Gravitational Instability

Millimeter emitting dust grains have sizes that make them susceptible to drift in protoplanetary disks due to the difference between their orbital speed and that of the gas. The characteristic drift timescale depends on the surface density of the gas. By comparing disk radius measurements from Atacama Large Millimeter/submillimeter Array CO and continuum observations at millimeter wavelengths, the gas surface density profile and dust drift time can be self-consistently determined. We find that profiles which match the measured dust mass have very short drift timescales, an order of magnitude or more shorter than the stellar age, whereas profiles for disks that are on the cusp of gravitational instability, defined via the minimum value of the Toomre parameter, Qmin∼1−2 , have drift timescales comparable to the stellar lifetime. This holds for disks with masses of dust ≳5 M ⊕ across a range of absolute ages from less than 1 Myr to over 10 Myr. The inferred disk masses scale with stellar mass as Mdisk≈M*/5Qmin . This interpretation of the gas and dust disk sizes simultaneously solves two long standing issues regarding the dust lifetime and exoplanet mass budget, and suggests that we consider millimeter wavelength observations as a window into an underlying population of particles with a wide size distribution in secular evolution with a massive planetesimal disk.

Underplating-induced trans-crustal melting and maturation of Neoarchean continental crust in the North China Craton

A global change in granitoid compositions from early predominantly sodic tonalite-trondhjemite-granodiorites (TTGs) to later TTGs and more potassic granites occurred during the late Archean, coupled with a major period of crustal maturation. However, the detailed relationship between granitoid chemical evolution and the maturing crustal process remains enigmatic. Successive granitoid magmatism including late Neoarchean TTGs and high-K granites occurred in the Western Shandong Province granite-greenstone belt (WSP) of the North China Craton and thus preserves crucial clues of the crustal maturation process. In this study, petrology, whole-rock geochemistry, and zircon U-Pb and Lu-Hf isotopes are reported for the late Neoarchean TTG gneisses, monzogranites, and minor metabasaltic to andesitic rocks from the WSP. The ca. 2560−2540 Ma TTG gneisses show low MgO, K2O/Na2O, but high (La/Yb)N, Sr/Y, and absence of Eu anomalies, indicating their derivation from partial melting of the thickened lower mafic crust. The ca. 2530−2500 Ma monzogranites are characterized by systematically high SiO2 and K2O/Na2O, but low MgO and Sr/Y, and moderately negative Eu anomalies, revealing they were formed by intracrustal reworking of local TTGs and sedimentary rocks in the middle to upper crust. Geochemical variations of these crustal-derived granitoids suggest that they were formed by melting at gradually higher crustal levels with the melt zone moved gradationally from the eclogite stability field into the plagioclase stability field. The ca. 2530−2500 Ma calc-alkaline metabasaltic to andesitic rocks sourced from metasomatized mantle outline roles of mantle-derived magma underplating in contributions of heating and trans-crustal melting magmatism. The long-term melting processes facilitated the upward movement of volatiles and heat-producing elements from deep to shallow crustal levels, and introduced K-enriched monzogranites into the upper crust, leaving a refractory, strengthening, and tectonically stable lower crust. Secular compositional evolution of crustal-derived granitoids reveals that continuous crustal reworking drove lithosphere differentiation and paved the way for the maturation of the Archean continental crust.

The Galactic population of canonical pulsar. II. Taking into account several evolutionary paths: Interstellar medium interaction, Galactic potential, and a death valley

Pulsars are highly magnetised rotating neutron stars, emitting in a broad electromagnetic energy range. These objects were discovered more than 55 years ago and are astrophysical laboratories for studying physics at extreme conditions. Reproducing the observed pulsar population helps refine our understanding of their formation and evolution scenarios, as well as their radiation processes and geometry. In this paper, we improve our previous population synthesis by focusing on both the radio and gamma -ray pulsar populations, investigating the impact of the Galactic gravitational potential and of the radio emission death line. To elucidate the necessity of a death line, we implemented our refined initial distributions of the spin period and spacial position at birth. This approach allowed us to elevate the sophistication of our simulations to the most recent state-of-the-art approaches. The motion of each individual pulsar was tracked in the Galactic potential by a fourth-order symplectic integration scheme. Our pulsar population synthesis took into account the secular evolution of the force-free magnetosphere and magnetic field decay simultaneously and self-consistently. Each pulsar was evolved from birth to the present time. The radio and gamma -ray emission locations were modelled by the polar cap geometry and striped wind model, respectively. By simulating ten million pulsars, we found that including a death line allows us to better reproduce the observational trend. However, when simulating one million pulsars, we obtained an even more realistic $P- P $ diagram, whether or not a death line was included. This suggests that the ages of the detected pulsars might be overestimated and so, it sets the need for a death line in pulsar population studies into question. Kolmogorov-Smirnov tests confirm the statistical similarity between the observed and simulated $P- P $ diagram. Additionally, simulations with increased gamma -ray telescope sensitivities hint at a significant contribution coming from the gamma -ray pulsars to the GeV excess in the Galactic centre.

Modified method of round Gaussian rings. Application to the two-planetary problem

A scheme of the modified method of round Gaussian rings, designed to study the secular evolution of orbits in systems consisting of a central star and two planets, is presented. The reason for the secular evolution of the nodes and inclinations of the orbits of the planets is their mutual gravitational attraction. The orbits of the planets are modeled by homogeneous round Gaussian rings, to which the masses, sizes and angles of inclination of the orbits, as well as orbital angular momenta of the planets, are transferred. The method takes into account the fact that, in general, the ascending nodes of the orbits may not coincide. The mutual gravitational energy of the rings 𝑊𝑚𝑢𝑡 is represented as a series in the quadratic approximation in powers of small inclination angles. Using this function 𝑊𝑚𝑢𝑡, a closed system of four differential equations describing the secular evolution of the planets’ orbits is composed. The solution to the equations is obtained in finite analytic form, which simplifies the interpretation of the investigated planetary motions. The method was tested on the example of the Sun-Jupiter-Saturn system; for it, in particular, the difference in the longitudes of the nodes of the orbits of Jupiter and Saturn was calculated as a function of time. New approach is also used to study the precession of nodes in the exoplanetary system K2-36; graphs of all unknown quantities are obtained. It has been established that in the course of evolution the mutual inclination angle of the orbits remains constant, and the librations of the orbits in the inclination angle and in the motion of the nodes occur synchronously.

Gaseous Dynamical Friction on Elliptical Keplerian Orbits

We compute the gaseous dynamical friction force experienced by massive perturbers on elliptical Keplerian orbits. Using linear perturbation theory, we investigate the density wake morphology, dynamical friction force, and secular orbital evolution for massive single perturbers as well as equal-mass binaries embedded in a homogeneous, static medium. In all cases, the rate of change in the semimajor axis is found to be negative (as expected), whereas the rate of change in eccentricity is negative for strictly subsonic trajectories and positive for strictly supersonic trajectories. Transonic orbits can experience both positive and negative torques during the course of an orbit, with some growing in eccentricity and others circularizing. We observe all initial orbits becoming highly supersonic and eccentric (over sufficiently long timescales) due to a relentless semimajor axis decay increasing the Mach number and subsequent eccentricity driving. We compare our findings to previous studies for rectilinear and circular motion while also making our data for the evolution of Keplerian orbits available.

A Comprehensive Comparison of Spin-up and Spin-down Episodes of 4U 1538-522 Observed with NuSTAR

4U 1538-522 is a persistent high-mass X-ray binary that exhibits secular spin evolution. In 2019, it underwent a torque reversal from spinning up to spinning down. We performed an extensive study using four NuSTAR observations to compare temporal and spectral properties during different states. We observed no abrupt change in luminosity associated with the torque reversal. In addition, the pulse profile, the spectral shape, and the power spectrum remained unchanged before and after the torque reversal. The orbital and superorbital modulation profiles also showed no significant changes. We discuss possible mechanisms for the torque reversal and conclude that it is unlikely to be caused by interactions between the accretion disk and the magnetosphere. Instead, the transition of accretion modes in spherical accretion may be a plausible explanation.

Long-term changes in the Western Pacific Warm Pool upper-water structure over the last 4 Ma

Earth's climate underwent secular structural evolution and cooling since the Pliocene Warmth, punctuated by increasing thermal gradients between the Western Pacific Warm Pool (WPWP) and the surrounding cooler regions of Eastern Pacific Cold Tongue and extra-tropics. One key mechanism for deciphering the climate evolution since Pliocene is the shoaling of the ocean thermocline, but much remains unknown about the upper-water structure of the western Pacific Warm Pool, the heat engine of the climate system, and its linkage to global ocean circulations. Here, by a newly made series of millennial-resolved δ18O and δ13C records of paired mixed-layer and thermocline dwelling planktonic foraminifera from IODP Site U1489 drilled in the center of WPWP, the trends of cooling and respired carbon content decreasing in the WPWP thermocline since ∼4 Ma are revisited and diagnosed. Our data allows us to propose that, the tropical Pacific upper-water circulation cell had shoaled and shrunk and the vertical mixing from deeper waters may have increased, since the Pliocene. Development towards a modern-style Warm Pool was initially onset at ∼3.1 and finalized at ∼0.7 Ma, respectively.

Earth’s metamorphic secular evolution accessed by rutile

Rutile provides crucial insights into the evolution of plate tectonics and variations in tectonomagmatic modes over Earth’s history primarily because rutile predominantly tracks higher-pressure metamorphism (>1.0–1.2 GPa). Comparison of rutile age and compositional data with diverse proxies tracks the presence of low temperature/pressure (T/P) metamorphic conditions, enabling the tracing of plate tectonics onset and evolution. We present a new compilation of rutile U-Pb ages that lag zircon ages by approximately 50 Myr, potentially indicating cooling ages of metamorphic belts. The earliest rutile age peak (ca. 1.8 Ga) aligns with the oldest evidence for low T/P metamorphic conditions. This coincides with a shift in the T/P distribution of rutile whereas the T/P of Archean rutile forms a tight normal distribution. In the Paleoproterozoic, the rutile T/P distribution is skewed to lower T/P, following the broader pattern of the full metamorphic record. The degree of lower T/P skew increases through time until the lower T/P population dominates the rutile record from the Neoproterozoic to the present. These data further highlight shifts in dominant metamorphic modes that can be tied to the evolution of the tectonic system, with early Archean metamorphism being associated with plume-driven vertical tectonics or hot, shallow subduction and post-Archean metamorphism being associated with progressive less plume-driven vertical tectonics and colder, steeper subduction. Although the frequency of rutile is lower during the Mesoproterozoic, the rutile T/P during this time follows the progressive skewing pattern from the Paleoproterozoic to the present and is likely inconsistent with a phase of interrupted tectonics characterized by stagnant lid.

Closing the gap: secular evolution of bar-induced dark gaps in the presence of thick discs

ABSTRACT The presence of dark gaps, a preferential light deficit along the bar minor axis, is observationally well known. The properties of dark gaps are thought to be associated with the properties of bars, and their spatial locations are often associated with bar resonances. However, a systematic study, testing the robustness and universality of these assumptions, is still largely missing. Here, we investigate the formation and evolution of bar-induced dark gaps using a suite of N-body models of (kinematically cold) thin and (kinematically hot) thick discs with varying thick disc mass fractions and different thin-to-thick disc geometries. We find that dark gaps are a natural consequence of the trapping of disc stars by the bar. The properties of dark gaps (such as strength and extent) are well correlated with the properties of bars. For stronger dark gaps, the fractional mass-loss along the bar minor axis can reach up to ${\sim} 60\!-\!80$ per cent of the initial mass contained, which is redistributed within the bar. These trends hold true irrespective of the mass fraction in the thick disc and the assumed disc geometry. In all our models harbouring slow bars, none of the resonances (corotation, inner Lindblad resonance, and 4:1 ultraharmonic resonance) associated with the bar correspond to the location of dark gaps, thereby suggesting that the location of dark gaps is not a universal proxy for these bar resonances, in contrast with earlier studies.

Detailed study of a rare hyperluminous rotating disk in an Einstein ring 10 billion years ago

Hyperluminous infrared galaxies (HyLIRGs) are the rarest and most extreme starbursts and found only in the distant Universe (z ≳ 1). They have intrinsic infrared (IR) luminosities LIR ≥ 1013 L⊙ and are commonly found to be major mergers. Recently, the Planck All-Sky Survey to Analyze Gravitationally-lensed Extreme Starbursts project (PASSAGES) searched ~104 deg2 of the sky and found ~20 HyLIRGs. We describe a detailed study of PJ0116-24, the brightest (μLIR ≈ 2.6 × 1014 L⊙, magnified with μ ≈ 17) Einstein-ring HyLIRG in the southern sky, at z = 2.125, with observations from the near-IR integral-field spectrograph VLT/ERIS and the submillimetre interferometer ALMA. We detected Hα, Hβ, [N ii] and [S ii] lines and obtained an extreme Balmer decrement (Hα/Hβ ≈ 8.73 ± 1.14). We modelled the molecular-gas and ionized-gas kinematics with CO(3–2) and Hα data at ~100–300 pc and (sub)kiloparsec delensed scales, respectively, finding consistent regular rotation. We found PJ0116-24 to be highly rotationally supported (vrot/σ0, mol. gas ≈ 9.4) with a richer gaseous substructure than other known HyLIRGs. Our results imply that PJ0116-24 is an intrinsically massive (Mbaryon ≈ 1011.3 M⊙) and rare starbursty disk (star-formation rate, SFR = 1,490 M⊙ yr−1) probably undergoing secular evolution. This indicates that the maximal SFR (≳1,000 M⊙ yr−1) predicted by simulations could occur during a galaxy’s secular evolution, away from major mergers.

Importance of Initial Condition on Bar Secular Evolution: Role of Halo Angular Momentum Distribution Discontinuity

The dark matter halo properties, for example, mass, spin, and concentration, play a significant role in the formation and evolution of bars in disk galaxies. This study highlights the importance of a new parameter: the dark matter halo angular momentum distribution in the disk’s central region. We experiment with N-body galaxy models having a disk and dark matter similar to Milky Way–type galaxies. In these models, we vary the discontinuity of the angular momentum distribution of the halo (the total spin is the same for all models). Our N-body experiments suggest that bar forms in all models after a few Gyr of disk evolution. However, in the secular evolution of the bar, as we evolve these models until 9.78 Gyr, the bar gains its strength in the model with the most continuous halo angular momentum distribution, and the bar loses strength for the most discontinuous halo angular momentum distribution. The secular evolution of the bar suggests that box/peanut/x-shaped bulges similar to those found in the Milky Way disk should be more pronounced in halos with continuous halo angular momentum distributions. This study demonstrates the importance of the initial condition setup of galaxy systems, namely the discontinuity in the dark matter halo angular momentum distribution for a given density distribution, on the bar secular evolution in the disk galaxy simulations. Further, this study helps reconcile the conflicting results of bar secular evolution in a high-spinning halo of the recent literature.

Secular Evolution and Stability of Rings Around Rotationally Asymmetrical Bodies. Revision of the Problem

Secular Evolution and Stability of Rings Around Rotationally Asymmetrical Bodies. Revision of the Problem

A Complete 16 μm Selected Galaxy Sample at z ∼ 1. II. Morphological Analysis

We present a morphological analysis of the 16 μm flux-density-limited galaxy sample at 0.8 < z < 1.3 from Huang et al. (2021). At the targeted redshift, the 16 μm emission corresponds to the polycyclic aromatic hydrocarbon feature from intense star formation, or dust heated by active galactic nuclei (AGN). Our sample of 479 galaxies are dominated by luminous infrared galaxies (LIRGs; 67%) in three CANDLES fields (Extended Groth Strip, ​​​​Great Observatories Origins Deep Survey North and South fields), and are further divided into AGN-dominated, star-forming dominated, composite, and blue compact galaxies by their spectral energy distribution types. The majority of our sample (71%) have disk morphologies, with the few AGN-dominated galaxies being more bulge-dominated than the star-forming-dominated and composite galaxies. The distribution of our sample on the Gini versus M 20 plane is consistent with previous studies, where the Sérsic index n shows an increasing trend toward the smaller M 20 and higher Gini region below the dividing line for mergers. The subsample of ultraluminous infrared galaxies (ULIRGs) follows a steep size–mass relation that is closer to the early-type galaxies. In addition, as the 4.5 μm luminosity excess ( L4.5exc , proxy for AGN strength) increases, our sample appears to be more bulge dominated (i.e., higher n). Based on the specific star formation rate and compactness ( log10Σ1.5,Σ1.5=M*/Re1.5 ) diagram, the majority of our LIRG-dominated galaxy sample follows a secular evolution track, and their distribution can be explained without involving any merging activities. Out of the 16 ULIRGs in our sample, six are compact with strong AGN contributions, likely evolving along the fast track from more violent activities.

Potassium isotopes trace the formation of juvenile continental crust

Constraining the processes associated with the formation of new (juvenile) continental crust from mantle-derived (basaltic) sources is key to understanding the origin and evolution of Earth’s landmasses. Here we present high-precision measurements of stable isotopes of potassium (K) from Earth’s most voluminous plagiogranites, exposed near El-Shadli in the Eastern Desert of Egypt. These plagiogranites exhibit a wide range of δ41K values (–0.31‰ ± 0.06‰ to 0.36‰ ± 0.05‰; 2 SE, standard error) that are significantly higher (isotopically heavier) than mantle values (–0.42‰ ± 0.08‰). Isotopic (87Sr/86Sr and 143Nd/144Nd) and trace element data indicate that the large variation in δ41K was inherited from the basaltic source rocks of the El-Shadli plagiogranites, consistent with an origin through partial melting of hydrothermally-altered mid-to-lower oceanic crust. These data demonstrate that K isotopes have the potential to better constrain the source of granitoid rocks and thus the secular evolution of the continental crust.

Geochronology and Sr-Nd-Pb-Hf-O isotopes of Neoproterozoic orthogneisses in the Jiamusi Block, NE China: Implications for tectonic origin and secular crustal evolution

There is a considerable debate as to when and how the continental crust has evolved to its present state. Existing studies of crustal evolution have focused on large cratons, whereas microcontinents within accretionary orogenic belts have been conspicuously neglected. The controversial definition of tectonic origins and lack of Precambrian basement rocks of microcontinents, lead to an equivocal issue of their secular crustal evolution processes. Here we present zircon U-Pb ages and Hf-O isotopes, as well as whole-rock elemental and Sr-Nd-Pb-Hf isotopic data for the newly discovered Neoproterozoic orthogneisses from the Jiamusi Block of NE China in the easternmost Central Asian Orogenic Belt (CAOB). LA-ICP-MS U-Pb dating of zircons from the orthogneisses recorded two episodes of magmatism at 896–886 Ma and 752–726 Ma. Combined with zircon Hf-O isotopes and REE patterns, the peak of the late Pan-African metamorphism is proved to occur at 566–565 Ma, demonstrating the linkage between the Jiamusi Block and the Kuunga-Pinjarra interior orogen of East Gondwana. In conjunction with compiled zircon U-Pb-Hf isotopic data of Neoproterozoic-Mesozoic granitoids, a new crustal evolution model has been established for the Jiamusi Block, which defines a continuous rather than an episodic crustal growth pattern during the Neoarchean to Neoproterozoic, as well as four stages of crustal reworking at 940–880 Ma, 780–660 Ma, 560–460 Ma, and 340–240 Ma. The enhanced and reduced rates of crustal growth during the progressive period are related to the assembly-breakup and collision phases of supercontinent cycles, respectively. Our study along with previous researches on eastern CAOB not only highlights that the Phanerozoic accretionary orogen underwent diverse forms of crustal growth with most of the continental crust formed during the Precambrian, but also provides an example to show the heterogeneity of the lower continent and the complexity of global secular crustal evolution.

Simulating nearby disc galaxies on the main star formation sequence

Past studies have long emphasised the key role played by galactic stellar bars in the context of disc secular evolution, via the redistribution of gas and stars, the triggering of star formation, and the formation of prominent structures such as rings and central mass concentrations. However, the exact physical processes acting on those structures, as well as the timescales associated with the building and consumption of central gas reservoirs are still not well understood. We are building a suite of hydro-dynamical RAMSES simulations of isolated, low-redshift galaxies that mimic the properties of the PHANGS sample. The initial conditions of the models reproduce the observed stellar mass, disc scale length, or gas fraction, and this paper presents a first subset of these models. Most of our simulated galaxies develop a prominent bar structure, which itself triggers central gas fuelling and the building of an over-density with a typical scale of 100−1000 pc. We confirm that if the host galaxy features an ellipsoidal component, the formation of the bar and gas fuelling are delayed. We show that most of our simulations follow a common time evolution, when accounting for mass scaling and the bar formation time. In our simulations, the stellar mass of 1010 M⊙ seems to mark a change in the phases describing the time evolution of the bar and its impact on the interstellar medium. In massive discs (M⋆ ≥ 1010 M⊙), we observe the formation of a central gas reservoir with star formation mostly occurring within a restricted starburst region, leading to a gas depletion phase. Lower-mass systems (M⋆ &lt; 1010 M⊙) do not exhibit such a depletion phase, and show a more homogeneous spread of star-forming regions along the bar structure, and do not appear to host inner bar-driven discs or rings. Our results seem to be supported by observations, and we briefly discuss how this new suite of simulations can help our understanding of the secular evolution of main sequence disc galaxies.

UV radiation-induced peptides in frog skin confer protection against cutaneous photodamage through suppressing MAPK signaling.

Overexposure to ultraviolet light (UV) has become a major dermatological problem since the intensity of ultraviolet radiation is increasing. As an adaption to outside environments, amphibians gained an excellent peptide-based defense system in their naked skin from secular evolution. Here, we first determined the adaptation and resistance of the dark-spotted frogs (Pelophylax nigromaculatus) to constant ultraviolet B (UVB) exposure. Subsequently, peptidomics of frog skin identified a series of novel peptides in response to UVB. These UV-induced frog skin peptides (UIFSPs) conferred significant protection against UVB-induced death and senescence in skin cells. Moreover, the protective effects of UIFSPs were boosted by coupling with the transcription trans-activating (TAT) protein transduction domain. In vivo, TAT-conjugated UIFSPs mitigated skin photodamage and accelerated wound healing. Transcriptomic profiling revealed that multiple pathways were modulated by TAT-conjugated UIFSPs, including small GTPase/Ras signaling and MAPK signaling. Importantly, pharmacological activation of MAPK kinases counteracted UIFSP-induced decrease in cell death after UVB exposure. Taken together, our findings provide evidence for the potential preventive and therapeutic significance of UIFSPs in UV-induced skin damage by antagonizing MAPK signaling pathways. In addition, these results suggest a practicable alternative in which potential therapeutic agents can be mined from organisms with a fascinating ability to adapt.

Bulk Rock and Olivine Chemistry and Isotopes of 106–58 Ma Basalts from Liaodong Peninsula and its Adjacent Areas: Implications for Secular Evolution of the Big Mantle Wedge in Eastern China

Abstract The subducting Pacific slab stagnates in the mantle transition zone and creates a big mantle wedge (BMW) system in East Asia. A similar BMW structure may have already existed since the Early Cretaceous (&amp;gt;120 Ma), but how such a structure evolved from Early Cretaceous to the present day remains unclear. We address this issue by comparing compositions and source heterogeneity of the 106–58 Ma basalts from Liaodong Peninsula and its adjacent areas (LPAA) in eastern China, with those formed in the modern BMW setting. The LPAA basalts display oceanic island basalts–like trace element patterns. Elemental and isotopic compositions of these basalts and their olivine phenocrysts point to peridotite and two recycled components in their source. One recycled component is altered lower oceanic crust given the low δ18Oolivine (2.8–5.2‰) of the ~99 Ma Liaoyuan alkali basalts. The second component consists of altered upper oceanic crust and pelagic sediments indicated by high δ18Oolivine (&amp;gt;6.0‰), represented by the ~58 Ma Luanshishanzi alkali basalts. The depleted mantle-like isotopes of these two components suggest derivation from a young HIMU source with characteristics of the Izanagi plate (e.g. Indian Ocean-type Sr-Nd-Pb-Hf isotopes), which may have resided in the mantle transition zone at that time. Our results reveal strong similarities between chemical and source characteristics of the mantle sampled by the 106–58 Ma LPAA basalts and those derived from the modern BMW. This implies that the BMW structure has been present since the Early Cretaceous, probably having lasted more than 120 Myr, and modulating the chemical properties of the upper mantle and influencing a variety of geological processes.

SECULARISM AND RELIGIOUS FREEDOM: EXPLORING THE DYNAMICS OF COEXISTENCE

This research paper explores the intricate interplay between secularism and religious freedom, analysing their impact on societal coexistence. Beginning with a historical overview, the paper traces the evolution of secularism and the development of concepts related to religious freedom, providing a foundational understanding for the subsequent discussions. Various theoretical frameworks, including laïcité, multiculturalism, and secular humanism, are examined to gain insights into how different approaches to secular governance influence religious rights and freedoms. Case studies from countries such as France, the United States, and India are analysed to illustrate practical implications and challenges in achieving coexistence between secularism and religious freedom. The paper highlights the importance of understanding these dynamics for fostering mutual respect, tolerance, and inclusivity within pluralistic societies. The conclusion emphasizes the significance of this study in addressing societal dynamics, governance structures, and individual rights. It underscores the need for nuanced policy interventions and societal dialogues to navigate the complexities of secularism and religious freedom in contemporary contexts.

Landau Tidal Damping and Major-Body Clustering in Solar and Extrasolar Subsystems

Major (exo)planetary and satellite bodies seem to concentrate at intermediate areas of the radial distributions of all the objects orbiting in each (sub)system. We show that angular-momentum transport during secular evolution of (exo)planets and satellites necessarily results in the observed intermediate accumulation of the massive objects. We quantify the ‘middle’ as the mean of mean motions (orbital angular velocities) when three or more massive objects are involved. Radial evolution of the orbits is expected to be halted when the survivors settle near mean-motion resonances and angular-momentum transfer between them ceases (gravitational Landau damping). This dynamical behavior is opposite in direction to what has been theorized for viscous and magnetized accretion disks, in which gas spreads out and away from either side of any conceivable intermediate area. We present angular momentum transfer calculations in few-body systems, and we also calculate the tidal dissipation timescales and the physical properties of the mean tidal field in planetary and satellite (sub)systems.