Effective Velocity Dispersion Research Articles

Toward Implementation of the Pressure-regulated, Feedback-modulated Model of Star Formation in Cosmological Simulations: Methods and Application to TNG

Traditional star formation subgrid models implemented in cosmological galaxy formation simulations, such as that of V. Springel & L. Hernquist (hereafter SH03), employ adjustable parameters to satisfy constraints measured in the local Universe. In recent years, however, theory and spatially resolved simulations of the turbulent, multiphase, star-forming interstellar medium (ISM) have begun to produce new first-principles models, which when fully developed can replace traditional subgrid prescriptions. This approach has advantages of being physically motivated and predictive rather than empirically tuned, and allowing for varying environmental conditions rather than being tied to local-Universe conditions. As a prototype of this new approach, by combining calibrations from the TIGRESS numerical framework with the pressure-regulated feedback-modulated (PRFM) theory, simple formulae can be obtained for both the gas depletion time and an effective equation of state. Considering galaxies in TNG50, we compare the “native” simulation outputs with postprocessed predictions from PRFM. At TNG50 resolution, the total midplane pressure is nearly equal to the total ISM weight, indicating that galaxies in TNG50 are close to satisfying vertical equilibrium. The measured gas scale height is also close to theoretical equilibrium predictions. The slopes of the effective equations of states are similar, but with effective velocity dispersion normalization from SH03 slightly larger than that from current TIGRESS simulations. Because of this and the decrease in PRFM feedback yield at high pressure, the PRFM model predicts shorter gas depletion times than the SH03 model at high densities and redshift. Our results represent a first step toward implementing new, numerically calibrated subgrid algorithms in cosmological galaxy formation simulations.

DWDM-based Effective Group Velocity Dispersion Module for Long-distance Quantum Communication

DWDM-based Effective Group Velocity Dispersion Module for Long-distance Quantum Communication

The origin of massive compact galaxies: lessons from IllustrisTNG

ABSTRACT We investigate the formation and evolution of z = 0 massive compact galaxies (MCGs) in the IllustrisTNG cosmological simulation. We found that, as in observations, MCGs are mainly old (median age ∼10.8 Gyr), have supersolar metallicities (median log Z/Z⊙ ∼ 0.35), and are α-enhanced (median [α/Fe] ∼ 0.25). The age distribution extends to younger ages, however, and a few MCGs are as young as ∼7 Gyr. In general, MCGs assemble their mass early and accrete low angular momentum gas, significantly increasing their mass while growing their size much slower. A small fraction of MCGs follow another evolutionary path, going through a compaction event, with their sizes shrinking by 40 per cent or more. The accretion of low angular momentum gas leads to enhanced supermassive black hole (SMBH) growth, and MCGs reach the threshold SMBH mass of $\log M_\mathrm{BH}\sim 10^{8.5}\ \mathrm{ M}_\odot$ – when kinetic active galactic nucleus feedback kicks in and quenches the galaxy – earlier than non-compact galaxies. Comparing MCGs to a sample of median-sized quiescent galaxies matched in effective velocity dispersion, we find that their accretion histories are very different. 71 per cent of MCGs do not merge after quenching compared to 37 per cent of median-sized quiescent galaxies. Moreover, tracing these populations back in time, we find that at least a third of median-sized quiescent galaxies do not have a compact progenitor, underscoring that both dry mergers and progenitor bias effects are responsible for the differences in the kinematics and stellar population properties of MCGs and median-sized quiescent galaxies.

Distribution and migration of 239,240Pu in soil profiles in North China

The source, vertical distribution and migration behavior of plutonium in five soil profiles (from forest, grassland and desert areas) in northern China were investigated. The average 240Pu/239Pu atomic ratio of 0.184 ± 0.022 observed in these samples is in good agreement with the reported value of global fallout, suggesting that the global fallout is the major source of plutonium in northern China. The 239,240Pu inventories in five soil profiles ranges from 43.3 Bq/m2 to 175 Bq/m2, lying in the reported range for global fallout in the similar latitude band. The effective convection velocity (0.04–0.16 cm/y) and effective dispersion coefficient (0.13–0.41cm2/y) of plutonium in different soil profiles derived using the CDE model varies significantly, attributed to multi-factors including location, topography, climate and soil types. The results showed that the migration of plutonium in grassland soil is significantly slow compared to other type of soil, especially desert soil.

Pressure-regulated, Feedback-modulated Star Formation in Disk Galaxies

The star formation rate (SFR) in galactic disks depends on both the quantity of the available interstellar medium (ISM) gas and its physical state. Conversely, the ISM’s physical state depends on the SFR, because the “feedback” energy and momentum injected by recently formed massive stars is crucial to offsetting losses from turbulent dissipation and radiative cooling. The ISM’s physical state also responds to the gravitational field that confines it, with increased weight driving higher pressure. In a quasi-steady state, it is expected that the mean total pressure of different thermal phases will match each other, that the component pressures and total pressure will satisfy thermal and dynamical equilibrium requirements, and that the SFR will adjust as needed to provide the requisite stellar radiation and supernova feedback. The pressure-regulated, feedback-modulated (PRFM) theory of the star-forming ISM formalizes these ideas, leading to a prediction that the SFR per unit area, ΣSFR, will scale nearly linearly with ISM weight . In terms of the large-scale gas surface density Σgas, stellar plus dark matter density ρ sd, and effective ISM velocity dispersion σ eff, an observable weight estimator is , and this is predicted to match the total midplane pressure P tot. Using a suite of multiphase magnetohydrodynamic simulations run with the TIGRESS computational framework, we test the principles of the PRFM model and calibrate the total feedback yield ϒtot = P tot/ΣSFR ∼ 1000 km s−1, as well as its components. We compare the results from TIGRESS to theory, previous numerical simulations, and observations, finding excellent agreement.

The puzzling origin of massive compact galaxies in MaNGA

ABSTRACT We characterized the kinematics, morphology, and stellar population (SP) properties of a sample of massive compact quiescent galaxies (MCGs, $10\, \lesssim \, \log M_\star$/M$_\odot \, \lesssim \, 11$ and re ∼ 1–3 kpc) in the MaNGA Survey, with the goal of constraining their formation, assembly history, and assessing their relation with non-compact quiescent galaxies. We compared their properties with those of a control sample of median-sized quiescent galaxies (re ∼ 4–8 kpc) with similar effective velocity dispersions. MCGs have elevated rotational support, as evidenced by a strong anticorrelation between the Gauss–Hermite moment h3 and V/σ. In contrast, 30${{\ \rm per\ cent}}$ of control sample galaxies (CSGs) are slow rotators, and fast-rotating CSGs generally show a weak h3–V/σ anticorrelation. MCGs and CSGs have similar ages, but MCGs are more metal-rich and α-enhanced. Both MCGs and CSGs have shallow negative metallicity gradients and flat [α/Fe] gradients. On average, MCGs and CSGs have flat age gradients, but CSGs have a significantly larger dispersion of gradient values. The kinematics and SP properties of MCGs suggest that they experienced highly dissipative gas-rich events, such as mergers, followed by an intense, short, and centrally concentrated burst of star formation, between 4 and 10 Gyr ago (z ∼ 0.4–2), and had a quiet accretion history since then. This sequence of events might be analogous to, although less extreme than, the compaction events that formed compact quiescent galaxies at z ∼ 2. The small sizes of MCGs, and the high efficiency and short duration of their last star formation episode suggest that they are descendants of compact post-starburst galaxies.

WISDOM Project – IX. Giant molecular clouds in the lenticular galaxy NGC 4429: effects of shear and tidal forces on clouds

ABSTRACT We present high spatial resolution (≈12 pc) Atacama Large Millimeter/submillimeter Array 12CO(J = 3–2) observations of the nearby lenticular galaxy NGC 4429. We identify 217 giant molecular clouds within the 450 pc radius molecular gas disc. The clouds generally have smaller sizes and masses but higher surface densities and observed linewidths than those of Milky Way disc clouds. An unusually steep size–linewidth relation ($\sigma \propto R_{\rm c}^{0.8}$) and large cloud internal velocity gradients (0.05–0.91 km s−1 pc−1) and observed virial parameters (〈αobs,vir〉 ≈ 4.0) are found, which appear due to internal rotation driven by the background galactic gravitational potential. Removing this rotation, an internal virial equilibrium appears to be established between the self-gravitational (Usg) and turbulent kinetic (Eturb) energies of each cloud, i.e. $\langle \alpha _{\rm sg,vir}\equiv \frac{2E_{\rm turb}}{\vert U_{\rm sg}\vert }\rangle \approx 1.3$. However, to properly account for both self and external gravity (shear and tidal forces), we formulate a modified virial theorem and define an effective virial parameter $\alpha _{\rm eff,vir}\equiv \alpha _{\rm sg,vir}+\frac{E_{\rm ext}}{\vert U_{\rm sg}\vert }$ (and associated effective velocity dispersion). The NGC 4429 clouds then appear to be in a critical state in which the self-gravitational energy and the contribution of external gravity to the cloud’s energy budget (Eext) are approximately equal, i.e. $\frac{E_{\rm ext}}{\vert U_{\rm sg}\vert }\approx 1$. As such, 〈αeff,vir〉 ≈ 2.2 and most clouds are not virialized but remain marginally gravitationally bound. We show this is consistent with the clouds having sizes similar to their tidal radii and being generally radially elongated. External gravity is thus as important as self-gravity to regulate the clouds of NGC 4429.

The parallelism between galaxy clusters and early-type galaxies

Context. This is the second work dedicated to the observed parallelism between galaxy clusters (GCs) and early-type galaxies (ETGs). The focus is on the distribution of these systems in the scaling relations (SRs) observed when effective radii, effective surface brightness, total luminosities, and velocity dispersions are mutually correlated. Aims. Using the data of the Illustris simulation we speculate on the origin of the observed SRs. Methods. We compare the observational SRs extracted from the database of the WIde-field Nearby Galaxy-cluster Survey with the relevant parameters coming from the Illustris simulations. Then we use the simulated data at different redshift to infer the evolution of the SRs. Results. The comparison demonstrate that GCs at z ∼ 0 follow the same log(L)−​log(σ) relation of ETGs and that both in the log(⟨I⟩e)−​log(Re) and log(Re)−​log(M*) planes the distribution of GCs is along the sequence defined by the brightest and massive early-type galaxies (BCGs). The Illustris simulation reproduces the tails of the massive galaxies visible both in the log(⟨I⟩e)−​log(Re) and log(Re)−​log(M*) planes, but fails to give the correct estimate of the effective radii of the dwarf galaxies that appear too large and those of GCs that are too small. The evolution of the SRs up to z = 4 permits to reveal the complex evolutionary paths of galaxies in the SRs and indicate that the line marking the zone of exclusion, visible in the log(⟨I⟩e)−​log(Re) and the log(Re)−​log(M*) planes, is the trend followed by virialized and passively evolving systems. Conclusions. We speculate that the observed SRs originate from the intersection of the virial theorem and a relation L = L0′σβ where the luminosities depend on the star formation history.

SDSS-IV MaNGA: stellar population correlates with stellar root-mean-square velocity Vrms gradients or total-density-profile slopes at fixed effective velocity dispersion σe

ABSTRACT Galaxy properties are known to correlate most tightly with the galaxy effective stellar velocity dispersion σe. Here, we look for additional trends at fixed σe using 1339 galaxies (M* ≳ 6 × 109 M⊙) with different morphologies in the MaNGA (DR14) sample with integral-field spectroscopy data. We focus on the gradients (γrms ≡ σ(Re/4)/σe) of the stellar root-mean-square velocity ($V_{\rm rms} \equiv \sqrt{V^2 + \sigma ^2}$), which we show traces the total mass density gradient γtot derived from dynamical models and, more weakly, the bulge fraction. We confirm that γrms increases with σe, age, and metallicity. We additionally find that these correlations still exist at fixed σe, where galaxies with larger γrms are found to be older and more metal-rich. It means that mass density gradients contain information of the stellar population which is not fully accounted for by σe. This result puts an extra constraint on our understanding of galaxy quenching. We compare our results with galaxies in the IllustrisTNG hydrodynamical simulations and find that, at fixed σe, similar trends exist with age, the bulge fraction, and the total mass density slope but, unlike observations, no correlation with metallicity can be detected in the simulations.

Numerical simulation of dispersion and nonlinear characteristics of microstructured silica fibres with a thin suspended core in a wide range of their parameters

Dispersion and nonlinear characteristics of microstructured silica fibres with a thin suspended core surrounded by three, four or six air holes have been studied theoretically in the wavelength range 1 – 2 μm. It has been shown that, owing to strong fundamental mode confinement near the core, the Kerr nonlinearity coefficient can exceed the nonlinearity coefficient of standard telecom fibre SMF28e by two orders of magnitude. The large waveguide contribution allows for effective group velocity dispersion management. Estimates are presented that demonstrate the feasibility of using suspended core fibre exhibiting Kerr nonlinearity for generating non-classical light: a state with squeezed quantum fluctuations in one of the quadrature components of a cw laser signal at a wavelength near 1.55 μm.

Enhanced cluster lensing models with measured galaxy kinematics

We present an improved determination of the total mass distribution of three massive clusters from the Cluster Lensing and Supernova Survey with Hubble and Hubble Frontier Fields, MACS J1206.2−0847 (z = 0.44), MACS J0416.1−2403 (z = 0.40), Abell S1063 (z = 0.35). We specifically reconstructed the sub-halo mass component with robust stellar kinematics information of cluster galaxies, in combination with precise strong lensing models based on large samples of spectroscopically identified multiple images. We used integral-field spectroscopy in the cluster cores, from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, to measure the stellar velocity dispersion, σ, of 40−60 member galaxies per cluster, covering four to five magnitudes to mF160W ≃ 21.5. We verified the robustness and quantified the accuracy of the velocity dispersion measurements with extensive spectral simulations. With these data, we determined the normalization and slope of the galaxy L–σ Faber–Jackson relation in each cluster and used these parameters as a prior for the scaling relations of the sub-halo population in the mass distribution modeling. When compared to our previous lens models, the inclusion of member galaxies’ kinematics provides a similar precision in reproducing the positions of the multiple images. However, the inherent degeneracy between the central effective velocity dispersion, σ0, and truncation radius, rcut, of sub-halos is strongly reduced, thus significantly alleviating possible systematics in the measurements of sub-halo masses. The three independent determinations of the σ0 − rcut scaling relation in each cluster are found to be fully consistent, enabling a statistical determination of sub-halo sizes as a function of σ0, or halo masses. Finally, we derived the galaxy central velocity dispersion functions of the three clusters projected within 16% of their virial radius, finding that they are well in agreement with each other. We argue that such a methodology, when applied to high-quality kinematics and strong lensing data, allows the sub-halo mass functions to be determined and compared with those obtained from cosmological simulations.

The fundamental relation between supermassive black holes and their host galaxies

ABSTRACT We study the correlations between supermassive black holes (BHs) and their host galaxies, using a sample of 83 BH masses collected from the most recent and reliable spatially resolved estimates available from the literature. We confirm the mono- and bivariate correlations between SMBHs and the bulges of their host galaxies, confirming that the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality. Instead, pseudo-bulges do not seem to correlate with their SMBHs, probably because their secular evolution is often unable to trigger accretion onto the central BH. We then present a novel approach aimed at finding the fundamental relation between SMBHs and their host galaxies. For the first time, we analytically combine BH masses with the Fundamental Plane (FP), showing that MBH–σe appears to be the fundamental relation rather than a putative ‘BH Fundamental Plane’ of the kind MBH–σe–Re. These results can be explained by a picture which sees the MBH–σe relation as a natural outcome of the change in AGN feedback from momentum-driven to energy-driven. The other scaling relations are then established through the FP.

Six new supermassive black hole mass determinations from adaptive-optics assisted SINFONI observations

Different massive black hole mass – host galaxy scaling relations suggest that the growth of massive black holes is entangled with the evolution of their host galaxies. The number of measured black hole masses is still limited and additional measurements are necessary to understand the underlying physics of this apparent coevolution. We add six new black hole mass (MBH) measurements of nearby fast rotating early-type galaxies to the known black hole mass sample, namely NGC 584, NGC 2784, NGC 3640, NGC 4570, NGC 4281, and NGC 7049. Our target galaxies have effective velocity dispersions (σe) between 170 and 245 km s−1, and thus this work provides additional insight into the black hole properties of intermediate-mass early-type galaxies. We combined high-resolution adaptive-optics SINFONI data with large-scale MUSE, VIMOS and SAURON data from ATLAS3D to derive two-dimensional stellar kinematics maps. We then built both Jeans Anisotropic Models and axisymmetric Schwarzschild models to measure the central black hole masses. Our Schwarzschild models provide black hole masses of (1.3 ± 0.5) × 108 M⊙ for NGC 584, (1.0 ± 0.6) × 108 M⊙ for NGC 2784, (7.7 ± 5) × 107 M⊙ for NGC 3640, (5.4 ± 0.8) × 108 M⊙ for NGC 4281, (6.8 ± 2.0) × 107 M⊙ for NGC 4570, and (3.2 ± 0.8) × 108 M⊙ for NGC 7049 at 3σ confidence level, which are consistent with recent MBH−σe scaling relations. NGC 3640 has a velocity dispersion dip and NGC 7049 a constant velocity dispersion in the center, but we can clearly constrain their lower black hole mass limit. We conclude our analysis with a test on NGC 4570 taking into account a variable mass-to-light ratio (M/L) when constructing dynamical models. When considering M/L variations linked mostly to radial changes in the stellar metallicity, we find that the dynamically determined black hole mass from NGC 4570 decreases by 30%. Further investigations are needed in the future to account for the impact of radial M/L gradients on dynamical modeling.

SDSS-IV MaNGA: Environmental Dependence of the Mgb/ – Relation for Nearby Galaxies

Abstract We use a sample of ∼3000 galaxies from the MaNGA MPL-7 internal data release to study the α abundance distribution within low-redshift galaxies. We use the Lick index ratio Mgb/ as an α abundance indicator to study relationships between the α abundance distribution and galaxy properties such as effective stellar velocity dispersion within 0.3 effective radii (σ *), galaxy environment, and dark matter halo formation time (z f ). We find that (1) all galaxies show a tight correlation between Mgb/ and (2) “old” (Hβ < 3) low-σ * galaxies in high local density environment and inner regions within galaxy groups are enhanced in Mgb/ , while “young” (Hβ > 3) galaxies and high-mass galaxies show no or less environmental dependence; (3) “old” galaxies with high-z f show enhanced Mgb/ over low- and medium-z f ; and (4) Mgb/ gradients are close to zero and show dependence on σ * but no obvious dependence on the environment or z f . Our study indicates that stellar velocity dispersion or galaxy mass is the main parameter driving the Mgb/ enhancement, although environments appear to have modest effects, particularly for low- and medium-mass galaxies.

A quartet of black holes and a missing duo: probing the low end of the MBH–σ relation with the adaptive optics assisted integral-field spectroscopy

We present mass estimates of supermassive black holes in six nearby fast rotating early-type galaxies (NGC4339, NGC4434, NGC4474, NGC4551, NGC4578 and NGC4762) with effective stellar velocity dispersion around 100 km/s. We use near-infrared laser-guide adaptive optics observations with the GEMINI/NIFS to derive stellar kinematics in the galactic nuclei, and SAURON observations from the ATLAS3D Survey for large-scale kinematics. We build axisymmetric Jeans anisotropic models and axisymmetric Schwarzschild dynamical models. Both modelling approaches recover consistent orbital anisotropies and black hole masses within 1-2sigma confidence level, except for one galaxy for which the difference is just above the 3sigma level. Two black holes (NGC4339 and NGC4434) are amongst the largest outliers from the current black hole mass - velocity dispersion relation, with masses of $(4.3^{+4.8}_{-2.3})\times10^7$ and $(7.0^{+2.0}_{-2.8})\times10^7$ M$_\odot$, respectively ($3\sigma$ confidence level). The black holes in NGC4578 and NGC4762 lie on the scaling relation with masses of $(1.9^{+0.6}_{-1.4})\times10^7$ and $(2.3^{+0.9}_{-0.6})\times10^7$ M$_\odot$, respectively (3sigma confidence level). For two galaxies (NGC4474 and NGC4551) we are able to place upper limits on their black holes masses ($<7\times10^6$ and $<5\times10^6$ M$_\odot$, respectively, $3\sigma$ confidence level). The kinematics for these galaxies clearly indicate central velocity dispersion drops within a radius of 35 pc and 80 pc, respectively. These drops cannot be associated with cold stellar structures and our data do not have the resolution to exclude black holes with masses an order of magnitude smaller than the predictions. Parametrizing the orbital distribution in spherical coordinates, the vicinity of the black holes is characterized by isotropic or mildly tangential anisotropy.

Timing the formation and assembly of early-type galaxies via spatially resolved stellar populations analysis

To investigate star formation and assembly processes of massive galaxies, we present here a spatially-resolved stellar populations analysis of a sample of 45 elliptical galaxies (Es) selected from the CALIFA survey. We find rather flat age and [Mg/Fe] radial gradients, weakly dependent on the effective velocity dispersion of the galaxy within half-light radius. However, our analysis shows that metallicity gradients become steeper with increasing galaxy velocity dispersion. In addition, we have homogeneously compared the stellar populations gradients of our sample of Es to a sample of nearby relic galaxies, i.e., local remnants of the high-z population of red nuggets. This comparison indicates that, first, the cores of present-day massive galaxies were likely formed in gas-rich, rapid star formation events at high redshift (z>2). This led to radial metallicity variations steeper than observed in the local Universe, and positive [Mg/Fe] gradients. Second, our analysis also suggests that a later sequence of minor dry mergers, populating the outskirts of early-type galaxies (ETGs), flattened the pristine [Mg/Fe] and metallicity gradients. Finally, we find a tight age-[Mg/Fe] relation, supporting that the duration of the star formation is the main driver of the [Mg/Fe] enhancement in massive ETGs. However, the star formation time-scale alone is not able to fully explain our [Mg/Fe] measurements. Interestingly, our results match the expected effect that a variable stellar initial mass function would have on the [Mg/Fe] ratio.

Sloshing in its cD halo: MUSE kinematics of the central galaxy NGC 3311 in the Hydra I cluster

Context.Early-type galaxies (ETGs) show a strong size evolution with redshift. This evolution is explained by fast “in-situ” star formation at high-zfollowed by a late mass assembly mostly driven by minor mergers that deposit stars primarily in the outer halo.Aims.We aim to identify the main structural components of the Hydra I cD galaxy NGC 3311 to investigate the connection between the central galaxy and the surrounding stellar halo.Methods.We produce maps of the line-of-sight velocity distribution (LOSVD) moments from a mosaic of MUSE pointings covering NGC 3311 out to 25 kpc. Combining deep photometric and spectroscopic data, we model the LOSVD maps using a finite mixture distribution, including four non-concentric components that are nearly isothermal spheroids, with different line-of-sight systemic velocitiesV, velocity dispersionsσ, and small (constant) values of the higher order Gauss-Hermite momentsh3andh4.Results.The kinemetry analysis indicates that NGC 3311 is classified as a slow rotator, although the galaxy shows a line-of-sight velocity gradient along the photometric major axis. The comparison of the correlations betweenh3andh4withV/σwith simulated galaxies indicates that NGC 3311 assembled mainly through dry mergers. Theσprofile rises to ≃ 400 km s-1at 20 kpc, a significant fraction (0.55) of the Hydra I cluster velocity dispersion, indicating that stars there were stripped from progenitors orbiting in the cluster core. The finite mixture distribution modeling supports three inner components related to the central galaxy and a fourth component with large effective radius (51 kpc) and velocity dispersion (327 km s-1) consistent with a cD envelope. We find that the cD envelope is offset from the center of NGC 3311 both spatially (8.6 kpc) and in velocity (ΔV= 204 km s-1), but coincides with the cluster core X-ray isophotes and the mean velocity of core galaxies. Also, the envelope contributes to the broad wings of the LOSVD measured by largeh4values within 10 kpc.Conclusions.The cD envelope of NGC 3311 is dynamically associated with the cluster core, which in Hydra I is in addition displaced from the cluster center, presumably due to a recent subcluster merger.

Regional-scale analysis of karst underground flow deduced from tracing experiments: examples from carbonate aquifers in Malaga province, southern Spain

Tracer concentration data from field experiments conducted in several carbonate aquifers (Malaga province, southern Spain) were analyzed following a dual approach based on the graphical evaluation method (GEM) and solute transport modeling to decipher flow mechanisms in karst systems at regional scale. The results show that conduit system geometry and flow conditions are the principal factors influencing tracer migration through the examined karst flow routes. Solute transport is mainly controlled by longitudinal advection and dispersion throughout the conduit length, but also by flow partitioning between mobile and immobile fluid phases, while the matrix diffusion process appears to be less relevant. The simulation of tracer breakthrough curves (BTCs) suggests that diffuse and concentrated flow through the unsaturated zone can have equivalent transport properties under extreme recharge, with high flow velocities and efficient mixing due to the high hydraulic gradients generated. Tracer mobilization within the saturated zone under low flow conditions mainly depends on the hydrodynamics (rather than on the karst conduit development), which promote a lower longitudinal advection and retardation in the tracer migration, resulting in a marked tailing effect of BTCs. The analytical advection-dispersion equation better approximates the effective flow velocity and longitudinal dispersion estimations provided by the GEM, while the non-equilibrium transport model achieves a better adjustment of most asymmetric and long-tailed BTCs. The assessment of karst underground flow properties from tracing tests at regional scale can aid design of groundwater management and protection strategies, particularly in large hydrogeological systems (i.e. transboundary carbonate aquifers) and/or in poorly investigated ones.

Modulational Instability in Linearly Coupled Asymmetric Dual-Core Fibers

We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. Using coupled-mode equations for this system, we identify MI conditions from the linearization with respect to small perturbations. First, we compare the MI spectra of the asymmetric system and its symmetric counterpart in the case of the anomalous group-velocity dispersion (GVD). In particular, it is demonstrated that the increase of the inter-core linear-coupling coefficient leads to a reduction of the MI gain spectrum in the asymmetric coupler. The analysis is extended for the asymmetric system in the normal-GVD regime, where the coupling induces and controls the MI, as well as for the system with opposite GVD signs in the two cores. Following the analytical consideration of the MI, numerical simulations are carried out to explore nonlinear development of the MI, revealing the generation of periodic chains of localized peaks with growing amplitudes, which may transform into arrays of solitons.

THE VIRIAL RELATION AND INTRINSIC SHAPE OF EARLY-TYPE GALAXIES

Early-type galaxies (ETGs) are supposed to follow the virial relation $M = k_e \sigma_*^2 R_e / G$, with $M$ being the mass, $\sigma_*$ being the stellar velocity dispersion, $R_e$ being the effective radius, $G$ being Newton's constant, and $k_e$ being the virial factor, a geometry factor of order unity. Applying this relation to (a) the ATLAS3D sample of Cappellari et al. (2013) and (b) the sample of Saglia et al. (2016) gives ensemble-averaged factors $\langle k_e\rangle =5.15\pm0.09$ and $\langle k_e\rangle =4.01\pm0.18$, respectively, with the difference arising from different definitions of effective velocity dispersions. The two datasets reveal a statistically significant tilt of the empirical relation relative to the theoretical virial relation such that $M\propto(\sigma_*^2R_e)^{0.92}$. This tilt disappears when replacing $R_e$ with the semi-major axis of the projected half-light ellipse, $a$. All best-fit scaling relations show zero intrinsic scatter, implying that the mass plane of ETGs is fully determined by the virial relation. Whenever a comparison is possible, my results are consistent with, and confirm, the results by Cappellari et al. (2013). The difference between the relations using either $a$ or $R_e$ arises from a known lack of highly elliptical high-mass galaxies; this leads to a scaling $(1-\epsilon) \propto M^{0.12}$, with $\epsilon$ being the ellipticity and $R_e = a\sqrt{1-\epsilon}$. Accordingly, $a$, not $R_e$, is the correct proxy for the scale radius of ETGs. By geometry, this implies that early-type galaxies are axisymmetric and oblate in general, in agreement with published results from modeling based on kinematics and light distributions.