Local Mass Density Research Articles

New limits on dark photons from solar emission and keV scale dark matter

We provide updates to the limits on solar emission of dark photons, or more generally any light vector particle coupled to the electron vector current. The recent 2019 and 2020 electronic recoil data from XENON1T now provides more stringent constraints on these models than stellar energy loss in the sub-keV mass region. We also show that solar emission of dark photons does not provide a good fit to the recent XENON1T excess in the 2-5 keV energy bins. In contrast, the absorption of 2-4 keV mass dark photons that saturate the local dark matter mass density does provide a good fit to the excess, for mixing angles in the range $\epsilon \in (4-12)\times 10^{-16}$, while satisfying astrophysical constraints. Similarly, other models utilizing the vector portal can fit the excess, including those with operators that directly couple the dark photon field strength to electron spin.

Accretion History of AGNs. III. Radiative Efficiency and AGN Contribution to Reionization

Abstract The cosmic history of supermassive black hole (SMBH) growth is important for understanding galaxy evolution, reionization, and the physics of accretion. Recent NuSTAR, Swift-BAT, and Chandra hard X-ray surveys have provided new constraints on the space density of heavily obscured active galactic nuclei (AGNs). Using the new X-ray luminosity function derived from these data, we here estimate the accretion efficiency of SMBHs and their contribution to reionization. We calculate the total ionizing radiation from AGNs as a function of redshift, based on the X radiation and distribution of obscuring column density, converted to ultraviolet (UV) wavelengths. Limiting the luminosity function to unobscured AGNs only, our results agree with current UV luminosity functions of unobscured AGNs. For realistic assumptions about the escape fraction, the contribution of all AGNs to cosmic reionization is ∼4 times lower than the galaxy contribution (23% at z ∼ 6). Our results also offer an observationally constrained prescription that can be used in simulations or models of galaxy evolution. To estimate the average efficiency with which SMBHs convert mass to light, we compare the total radiated energy, converted from X-ray light using a bolometric correction, with the most recent local black hole mass density. The most likely value, η ∼ 0.3–0.34, approaches the theoretical limit for a maximally rotating Kerr black hole, η = 0.42, implying that on average growing SMBHs are spinning rapidly.

Effects of environment on stellar metallicity profiles of late-type galaxies in the CALIFA survey

Aims. We explore the effects of environment in the evolution of late-type galaxies by studying the radial profiles of light- and mass-weighted metallicities of galaxies in two discrete environments: field and groups. Methods. We used a sample of 167 late-type galaxies with stellar masses of 9 ≤ log(M⋆/M⊙) ≤ 12 drawn from the Calar Alto Legacy Integral Field Area (CALIFA) survey. Firstly, we obtained light- and mass-weighted stellar metallicity profiles and stellar mass density profiles of these galaxies using publicly available data. We then classified them according to their environment into field and group galaxies. Finally, we studied the metallicity of galaxies in these two environments, including a comparison of the metallicity as a function of radius, at a characteristic scale, and as a function of stellar mass surface density. As metallicity depends on galaxy mass, we took special care throughout the study to compare, in all cases, subsamples of galaxies in groups and in the field that have similar masses. Results. We find significant differences between group and field late-type galaxies in terms of their metallicity: group galaxies are systematically higher in metallicity than their field counterparts. We find that field galaxies, in general, have metallicity profiles that show a negative gradient in their inner regions and a shallower profile at larger radii. This is in contrast to the metallicity profiles of galaxies in groups, which tend to be flat in the inner regions and to have a negative gradient in the outer parts. Regarding the metallicity at the characteristic radius of the luminosity profiles, we consistently find that it is higher for group galaxies irrespective of galaxy mass. At fixed local stellar surface mass density, group galaxies are again higher in metallicity, also the dependence of metallicity on surface density is less important for group galaxies. Conclusions. The evidence of a clear difference in metallicity between group and field galaxies as a function of mass, spatial scale, and local stellar mass density is indicative of the different evolutionary paths followed by galaxies in groups and in the field. We discuss some possible implications of the observed differences.

Dynamics of DiskMass Survey galaxies in refracted gravity

We aim to verify whether refracted gravity (RG) is capable of describing the dynamics of disk galaxies without resorting to the presence of dark matter. RG is a classical theory of gravity in which the standard Poisson equation is modified with the introduction of the gravitational permittivity, which is a universal monotonic function of the local mass density. We used the rotation curves and the radial profiles of the stellar velocity dispersion perpendicular to the galactic disks of 30 disk galaxies from the DiskMass Survey (DMS) to determine the gravitational permittivity. RG describes the rotation curves and the vertical velocity dispersions by requiring galaxy mass-to-light ratios that are in agreement with stellar population synthesis models, and disk thicknesses that are in agreement with observations, once observational biases are taken into account. Our results rely on setting the three free parameters of the gravitational permittivity for each individual galaxy. However, we show that the differences of these parameters from galaxy to galaxy can, in principle, be ascribed to statistical fluctuations. We adopted an approximate procedure to estimate a single set of parameters that may properly describe the kinematics of the entire sample and suggest that the gravitational permittivity is indeed a universal function. Finally, we showed that the RG models of the individual rotation curves can only partly describe the radial acceleration relation (RAR) between the observed centripetal acceleration derived from the rotation curve and the Newtonian gravitational acceleration originating from the baryonic mass distribution. Evidently, the RG models underestimate the observed accelerations by 0.1 to 0.3 dex at low Newtonian accelerations. An additional problem that ought to be considered is the strong correlation, at much more than 5σ, between the residuals of the RAR models and three radially-dependent properties of the galaxies, whereas the DMS data show a considerably less significant correlation, at more than 4σ, for only two of these quantities. These correlations might be the source of the non-null intrinsic scatter of the RG models: this non-null scatter is at odds with the observed intrinsic scatter of other galaxy samples different from DMS, which is consistent with zero. Further investigations are required to assess whether these discrepancies in the RAR originate from the DMS sample, which might not be ideal for deriving the RAR, or whether they are genuine failures of RG.

An Improved STEM/EDX Quantitative Method for Dopant Profiling at the Nanoscale.

In this paper, an improved quantification technique for STEM/EDX measurements of 1D dopant profiles based on the Cliff-Lorimer equation is presented. The technique uses an iterative absorption correction procedure based on density models correlating the local mass density and composition of the specimen. Moreover, a calibration and error estimation procedure based on linear regression and error propagation is proposed in order to estimate the total measurement error in the dopant density. The proposed approach is applied to the measurement of the As profile in a nanodevice test structure. For the calibration, two crystalline Si specimens implanted with different As doses have been used, and the calibration of the Cliff-Lorimer coefficients has been carried out using Rutherford Back Scattering measurements. The As profile measurement has been carried out on an FinFET test structure, showing that quantitative results can be obtained in the nanometer scale and for dopant atomic densities lower than 1%. Using the proposed approach, the measurement error and detection limit for our experimental setup are calculated and the possibility to improve this limit by increasing the observation time is discussed.

Diagnosing the Role of Alfvén Waves in Global Field‐Aligned Current System Dynamics During Southward IMF: Swarm Observations

AbstractField‐aligned currents (FACs) are a primary signature of magnetosphere‐ionosphere coupling (MIC). However, establishing FACs requires the propagation of Alfvén waves. Large‐scale quasi‐static FACs are well‐organized into large‐scale Region 1 (R1) and Region 2 (R2) systems during intervals of southward interplanetary magnetic field (IMF); however, the scale‐dependent spatiotemporal variability and related electrodynamics are less well understood. Using the electric and magnetic field data from Swarms A and C, we examine the role of Alfvén waves in MIC at a range of scales during two auroral crossings during southward IMF on May 16, 2016. Interspacecraft techniques reveal large amplitude small‐scale (10s km) non‐stationary magnetic fields inconsistent with a quasi‐static formulation. Cross‐phase techniques reveal a frequency‐dependent E/B ratio and E‐B phase difference consistent with an Alfvén wave interpretation, validated using the Lysak (1991, https://doi.org/10.1029/90JA02154) ionospheric Alfvén resonator model constrained by inferred local Swarm plasma mass density. Local large amplitude E and B fields indicate the importance of Alfvénic energy transport at small scales. Evidence for Poynting flux concentration at the boundary between large‐scale upward and downward FACs is also presented. Our results suggest that cross‐scale FAC characteristics can be explained by a single Alfvén wave paradigm: quasi‐static large‐scale FACs representing the ω → 0 limit of a broader continuum of spatial scales associated with MIC. Future work should assess in more detail the energetic significance of small scales and the potential localization of large amplitude small‐scale disturbances at large scale FAC boundaries and assess related scale‐dependent MIC including Alfvénic ionospheric feedback.

Formation of the mass density peak at the magnetospheric equator triggered by EMIC waves

We report a simultaneous observation of two band electromagnetic ion cyclotron (EMIC) waves and toroidal Alfvén waves by the Van Allen Probe mission. Through wave frequency analyses, the mass density <i>ρ</i> is found to be locally peaked at the magnetic equator. Perpendicular fluxes of ions (&lt; 100 eV) increase simultaneously with the appearances of EMIC waves, indicating a heating of these ions by EMIC waves. In addition, the measured ion distributions also support the equatorial peak formation, which accords with the result of the frequency analyses. The formation of local mass density peaks at the equator should be due to enhancements of equatorial ion concentrations, which are triggered by EMIC waves’ perpendicular heating on low energy ions.

Constraining black hole–galaxy scaling relations and radiative efficiency from galaxy clustering

The masses of supermassive black holes are observed to increase with either the total mass or the mean (random) velocity of the stars in their host galaxies. The origin of these correlations remains elusive due to observational systematics and biases that severely limit our knowledge of the local demography of supermassive black holes. Here, we show that the large-scale spatial distribution of local active galactic nuclei (AGN) can constrain the shape and normalization of the black hole–stellar mass relation, thus bypassing resolution-related observational biases. In turn, our results can set more stringent constraints on the AGN radiative efficiency, e. For currently accepted values of the AGN obscured fractions and bolometric corrections, our estimated local supermassive black hole mass density favours mean e values of ~10–20%, suggesting that the vast majority of supermassive black holes are spinning moderately to rapidly. With large-scale AGN surveys coming online, our methodology will enable even tighter constraints on the fundamental parameters that regulate the growth of supermassive black holes. The large-scale spatial distribution of local active galactic nuclei can constrain the black hole–stellar mass relation and their mean radiative efficiency to 10–20%, suggesting moderate to high spins for the vast majority of supermassive black holes.

Dark matter capture by the Sun: revisiting velocity distribution uncertainties

Among the different strategies aiming to detect WIMP dark matter (DM), a neutrino signal coming from the Sun would be a smoking gun. This possibility relies on the DM capture by the Sun driven by the local DM distribution assumptions: the local mass density and the velocity distribution. In this context, we revisit those astrophysical hypotheses (also relevant for direct detection). We focus especially on the DM velocity distribution considering different possibilities beyond the popular Maxwellian distribution. Namely, some alternatives can be considered through analytical approaches and by looking into cosmological simulations of spiral galaxies. Most of the fitting formulas used to constrain the local velocity distribution function fail to describe the peak and the high velocity tail of the velocity distribution observed in simulations, the latter being improved when adding the local escape velocity of DM into the benchmark fitting models. In addition we test the predictions by the Eddington inversion method and also illustrate the importance of the galactic dynamical history. We estimate the resulting uncertainties on the DM capture rate by the Sun and conclude that different velocity distributions will affect the capture rate of DM by the Sun up to a 15–20%. On top of that, the calculation of the intrinsic variance of the capture rate leads to poorly controlled uncertainties especially for high WIMP masses (>30 GeV) raising concerns about the capture scenario.

A comparison of methods for adapting dose-voxel-kernels to tissue inhomogeneities

In radionuclide therapies, dosimetry is used for determining patient-individual dose burden. Standard approaches provide whole organ doses only. For assessing dose heterogeneity inside organs, voxel-wise dosimetry based on 3D SPECT/CT imaging could be applied. Often, this is achieved by convolving voxel-wise time-activity-curves with appropriate dose-voxel-kernels (DVK). The DVKs are meant to model dose deposition, and can be more accurate if modelled for the specific tissue type under consideration. In literature, DVKs are often not adapted to these inhomogeneities, or simple approximation schemes are applied.For 26 patients, which had previously undergone a -PSMA or -DOTATOC therapy, decay maps, mass-density maps as well as tissue-type maps were derived from SPECT/CT acquisitions. These were used for a voxel-based dosimetry based on convolution with DVKs (each of size ) obtained by four different DVK methods proposed in literature. The simplest only considers a spatially constant soft-tissue DVK (herein named ‘constant’), while others either take into account only the local density of the center voxel of the DVK (herein named ‘center-voxel’) or scale each voxel linearly according to the proper mass density deduced from the CT image (herein named ‘density’) or considered both the local mass density as well as the direct path between the center voxel and any voxel in its surrounding (herein named ‘percentage’). Deviations between resulting dose values and those from full Monte-Carlo simulations (MC simulations) were compared for selected organs and tissue-types.For each DVK method, inter-patient variability was considerable showing both under- and over-estimation of energy dose compared to the MC result for all tissue densities higher than soft tissue. In kidneys and spleen, ‘constant’ and ‘density’-scaled DVKs achieved estimated doses with smallest deviations to the full MC gold standard (∼ underestimation). For low and high density tissue types such as lung and adipose or bone tissue, alternative DVK methods like ‘center-voxel’- and ‘percentage’- scaled achieved superior results, respectively. Concerning computational load, dose estimation with the DVK method ‘constant’ needs about 1.1 s per patient, center-voxel scaling amounts to 1.2 s, density scaling needs 1.4 s while percentage scaling consumes 860.3 s per patient.In this study encompassing a large patient cohort and four different DVK estimation methods, no single DVK-adaption method was consistently better than any other in case of soft tissue kernels. Hence in such cases the simplest DVK method, labeled ‘constant’, suffices. In case of tumors, often located in tissues of low (lung) or high (bone) density, more sophisticated DVK methods excel. The high inter-patient variability indicates that for evaluating new algorithms, a sufficiently large patient cohort needs to be involved.

The clustering of undetected high-redshift black holes and their signatures in cosmic backgrounds

ABSTRACT There exist hitherto unexplained fluctuations in the cosmic infrared background on arcminute scales and larger. These have been shown to cross-correlate with the cosmic X-ray background, leading several authors to attribute the excess to a high-redshift growing black hole population. In order to investigate potential sources that could explain this excess, in this paper, we develop a new framework to compute the power spectrum of undetected sources that do not have constant flux as a function of halo mass. In this formulation, we combine a semi-analytic model for black hole growth and their simulated spectra from hydrodynamical simulations. Revisiting the possible contribution of a high-redshift black hole population, we find that too much black hole growth is required at early epochs for z &amp;gt; 6 accretion to explain these fluctuations. Examining a population of accreting black holes at more moderate redshifts, z ∼ 2–3, we find that such models produce a poor fit to the observed fluctuations while simultaneously overproducing the local black hole mass density. Additionally, we rule out the hypothesis of a missing Galactic foreground of warm dust that produces coherent fluctuations in the X-ray via reflection of Galactic X-ray binary emission. Although we firmly rule out accreting massive black holes as the source of these missing fluctuations, additional studies will be required to determine their origin.

The formation and evolution of low-surface-brightness galaxies

Our statistical understanding of galaxy evolution is fundamentally driven by objects that lie above the surface-brightness limits of current wide-area surveys (mu ~ 23 mag arcsec^-2). While both theory and small, deep surveys have hinted at a rich population of low-surface-brightness galaxies (LSBGs) fainter than these limits, their formation remains poorly understood. We use Horizon-AGN, a cosmological hydrodynamical simulation to study how LSBGs, and in particular the population of ultra-diffuse galaxies (UDGs; mu > 24.5 mag arcsec^-2), form and evolve over time. For M* > 10^8 MSun, LSBGs contribute 47, 7 and 6 per cent of the local number, mass and luminosity densities respectively (~85/11/10 per cent for M* > 10^7 MSun). Today's LSBGs have similar dark-matter fractions and angular momenta to high-surface-brightness galaxies (HSBGs; mu < 23 mag arcsec^-2), but larger effective radii (x2.5 for UDGs) and lower fractions of dense, star-forming gas (more than x6 less in UDGs than HSBGs). LSBGs originate from the same progenitors as HSBGs at z > 2. However, LSBG progenitors form stars more rapidly at early epochs. The higher resultant rate of supernova-energy injection flattens their gas-density profiles, which, in turn, creates shallower stellar profiles that are more susceptible to tidal processes. After z ~ 1, tidal perturbations broaden LSBG stellar distributions and heat their cold gas, creating the diffuse, largely gas-poor LSBGs seen today. In clusters, ram-pressure stripping provides an additional mechanism that assists in gas removal in LSBG progenitors. Our results offer insights into the formation of a galaxy population that is central to a complete understanding of galaxy evolution, and which will be a key topic of research using new and forthcoming deep-wide surveys.

Insights into interphase thickness characterization for graphene/epoxy nanocomposites: a molecular dynamics simulation.

This work presents a molecular dynamics simulation study on the interfacial characterization of graphene/epoxy nanocomposites. In polymeric nanocomposites, the thermo-mechanical properties of a system strongly depend on the characteristics of the interphase region between the matrix and the inclusions. The first step in the characterization of this interphase is to distinguish its border limit (i.e., the interphase thickness). Here, we present a methodology to systematically quantify the interphase thickness based on analyzing the variation of the local mass density profile. To this end, three functions (average accumulated mass density, accumulated standard deviation (ASD) and its first derivative) are successively applied on the local mass density profile. Using this procedure, the interphase limit can be easily detected regardless of the oscillatory nature of the local mass density. The effect of the epoxy crosslinking density and number of graphene layers on the interphase thickness is then investigated, and the results are analyzed by studying the interaction energies, polymer dynamics and distribution quality of reacted and unreacted components, as well as conformational changes of the polymer chains in the interphase region. The results reveal that the crosslinking density is the most influential parameter on the interphase thickness: the higher the crosslinking degree, the thicker the interphase region. To a lower extent, the interaction energy has also an effect on the interphase thickness since there is an inverse relationship between the interaction energy and the crosslinking density in our case study. Overall, the reported findings highlight useful insights into the detection and properties of the interphase region in thermoset composites.

Early science with the Large Millimetre Telescope: An LMT/AzTEC 1.1 mm Survey of dense cores in the Monoceros R2 giant molecular cloud

We present a 1.1~mm census of dense cores in the Mon~R2 Giant Molecular Cloud with the AzTEC instrument on the Large Millimeter Telescope (LMT). We detect 295 cores (209 starless, and 86 with protostars) in a two square degree shallow survey. We also carry out a deep follow-up survey of 9 regions with low to intermediate ($3<A_V<7$) gas column densities and detect 60 new cores in the deeper survey which allows us to derive a completeness limit. After performing corrections for low signal-to-noise cores, we find a median core mass of $\sim 2.1 \text{M}_{\odot}$ and a median size of $ 0.08$~pc. $46\%$ of the cores (141) have masses exceeding the local Bonor-Ebert mass for cores with T=12K, suggesting that in the absence of supporting non-thermal pressure, these regions are unstable to gravitational collapse. We present the core mass function (CMF) for various subdivisions of the core sample. We find that cores with masses $>$10~$M_{\odot}$ are exclusively found in regions with high core number densities and that the CMF of the starless cores has an excess of low-mass cores ($<$5~$M_{\odot}$) compared to the CMF of protostellar cores. We report a power law correlation of index $1.99 \pm 0.03$ between local core mass density and gas column density (as traced by Herschel) over a wide range of size scales (0.3-5~pc). This power law is consistent with that predicted for thermal fragmentation of a self-gravitating sheet.

Plasticity of spacetime as an alternative to dark matter

We propose an alternative to the dark matter hypothesis that would explain why the effects of a curvature of spacetime are measured in regions where no electromagnetic radiation is observed. The problem could be solved, assuming a plasticity of spacetime that, in some conditions, can allow a region to remain locally curved even when the mass density has gone away from that region. This way we can observe curvature also in the absence of a local mass density. We apply this idea in a very simple way to the rotation curve of Milky Way showing an agreement between the prediction of the theory and the experimental data. We propose also a different scenario that gives as a result a flat rotation curve. At this stage, our approach is just an idea, not an already complete theory, so many problems remain still unsolved.

Mapping spiral waves and other radial features in Saturn’s rings

We have analyzed the highest-quality images to be obtained by Cassini of Saturn’s main rings after the Saturn Orbit Insertion (SOI) and before the Ring Grazing Orbits (RGO) and Grand Finale (GF). These images are comparable to those of SOI in fidelity, though not in nominal resolution, due to their high signal-to-noise. We have systematically searched for radial structure in these images by reducing them to a single dimension (distance from Saturn’s center) and using the continuous wavelet transform technique. We discuss the resonant theory of spiral waves and discuss the proper method for deriving the local surface mass density from the wavelet signature of a spiral wave. We present 1) individual features of interest found in our data, including several classes of waves that have not previously been reported; 2) a radial profile of surface mass density in Saturn’s rings, which is more definitive for the A ring than any previously presented and which corrects some errors in previous profiles; and 3) an atlas of resonant features that indicates whether each feature is or is not expressed in the rings and that is organized graphically by resonance strength.

Surface plasmon resonance sensing: from purified biomolecules to intact cells.

Surface plasmon resonance (SPR) has become a well-recognized label-free technique for measuring the binding kinetics between biomolecules since the invention of the first SPR-based immunosensor in 1980s. The most popular and traditional format for SPR analysis is to monitor the real-time optical signals when a solution containing ligand molecules is flowing over a sensor substrate functionalized with purified receptor molecules. In recent years, rapid development of several kinds of SPR imaging techniques have allowed for mapping the dynamic distribution of local mass density within single living cells with high spatial and temporal resolutions and reliable sensitivity. Such capability immediately enabled one to investigate the interaction between important biomolecules and intact cells in a label-free, quantitative, and single cell manner, leading to an exciting new trend of cell-based SPR bioanalysis. In this Trend Article, we first describe the principle and technical features of two types of SPR imaging techniques based on prism and objective, respectively. Then we survey the intact cell-based applications in both fundamental cell biology and drug discovery. We conclude the article with comments and perspectives on the future developments. Graphical abstract Recent developments in surface plasmon resonance (SPR) imaging techniques allow for label-free mapping the mass-distribution within single living cells, leading to great expansions in biomolecular interactions studies from homogeneous substrates functionalized with purified biomolecules to heterogeneous substrates containing individual living cells.

Influence of the local mass density variation on the fracture behavior of fiber network materials

The fracture process in two fiber network materials, a low- and a high-density paper, is analyzed experimentally and numerically. The high-density paper is able to localize continued fracture to very small defects while a rather large defect is required in the low-density paper. Whereas the high-density paper has a homogeneous and limited variation in local mass density, the low-density paper is substantially more heterogeneous and has a higher local mass density variation. It is hypothesized that these fairly large regions of lower mass density govern the fracture process in paper and similar fiber network materials. A nonlocal fracture model is applied to describe and capture this length scale phenomenon and intents to simulate forces bridged over distant regions in the material via connected fibers. The suggested fracture hypothesis is consistent with experiments and hence offers an explanation to why network materials with different mass density variation may fracture differently.

SDSS-IV MaNGA: What Shapes the Distribution of Metals in Galaxies? Exploring the Roles of the Local Gas Fraction and Escape Velocity

Abstract We determine the local metallicity of the ionized gas for more than 9.2 × 105 star-forming regions (spaxels) located in 1023 nearby galaxies included in the Sloan Digital Sky Survey-IV MaNGA integral field spectroscopy unit survey. We use the dust extinction derived from the Balmer decrement and the stellar template fitting in each spaxel to estimate the local gas and stellar mass densities, respectively. We also use the measured rotation curves to determine the local escape velocity (V esc). We then analyze the relationships between the local metallicity and both the local gas fraction (μ) and V esc. We find that metallicity decreases with both increasing μ and decreasing V esc. By examining the residuals in these relations we show that the gas fraction plays a more primary role in the local chemical enrichment than does V esc. We show that the gas-regulator model of chemical evolution provides a reasonable explanation of the metallicity on local scales. The best-fit parameters for this model are consistent with the metal loss caused by momentum-driven galactic outflows. We also argue that both the gas fraction and the local escape velocity are connected to the local stellar surface density, which in turn is a tracer of the epoch at which the dominant local stellar population formed.

The front location in branching Brownian motion with decay of mass

We augment standard branching Brownian motion by adding a competitive interaction between nearby particles. Informally, when particles are in competition, the local resources are insufficient to cover the energetic cost of motion, so the particles’ masses decay. In standard BBM, we may define the front displacement at time tt as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the local mass density drops from Θ(1)Θ(1) to o(1)o(1). We show that one can find arbitrarily large times tt for which this occurs at a distance Θ(t1/3)Θ(t1/3) behind the front displacement for standard BBM.