High-resolution Simulations Research Articles

MAGICS. II. Seed Black Holes Stripped of Their Surrounding Stars Do Not Sink

Abstract Massive black hole (MBH) seed mergers are expected to be among the loudest sources of gravitational waves detected by the Laser Interferometer Space Antenna, providing a unique window into the birth and early growth of MBHs. We present the MAGICS-II simulation suite, which consists of six galaxy mergers that result in MBH seed mergers identified in the cosmological simulation ASTRID. With the enhanced resolution (mass resolution: 500 M ⊙; softening length: 5 pc), improved subgrid models for the MBH dynamics and accretion, and the accurate regularized gravity integrator included in KETJU, we trace MBH seed dynamics down to 0.1 pc. After evolving all the systems for ≈1.2 Gyr in three stages (MAGICS-2000, MAGICS-500, and MAGICS-K), we find in four of the six systems that the MBHs stall at separations Δr ≳ 200 pc. Only in two systems, the MBHs manage to sink further, and only in one of them a bound binary forms. In the sinking systems, the MBH retains a population of bound stars. The final separation between the MBH is related to the surrounding unstripped stellar (and/or dark matter) mass: if more than 90% of the surrounding stellar system is stripped away, the MBHs stall. Besides the unstripped stars from the original host galaxy, we find that newly formed stars bound to the MBH significantly contribute to its sinking. Resolving the stellar system around MBH seeds, and its induced tidal interactions and dynamical friction is key for accurately capturing MBH dynamics. For this, high-resolution simulations are required. In a companion paper (MAGICS-III), we resimulate the central regions of these systems with an increased resolution to model directly the effects of actual star clusters around MBHs.

Accurate space-based NOx emission estimates with the flux divergence approach require fine-scale model information on local oxidation chemistry and profile shapes

Abstract. The flux divergence approach (FDA) is a popular technique for deriving NOx emission estimates from tropospheric NO2 columns measured by the TROPOspheric Monitoring Instrument (TROPOMI) satellite sensor. An attractive aspect of the FDA is that the method simplifies three-dimensional atmospheric chemistry and transport processes into a two-dimensional (longitude–latitude) steady-state continuity equation for columns that balances local NOx emissions with the net outflow and chemical loss of NOx. Here we test the capability of the FDA to reproduce known NOx emissions from synthetic NO2 column retrievals generated with the LOTOS-EUROS chemistry transport model over the Netherlands at high spatial resolution of about 2×2 km during summer. Our results show that the FDA captures the magnitude and spatial distribution of the NOx emissions to high accuracy (absolute bias <9 %), provided that the observations represent the NO2 column in the boundary layer, that wind speed and direction are representative for the boundary layer (PBL) column, and that the high-resolution spatiotemporal variability of the NO2 lifetimes and NOx:NO2 ratio is accounted for in the inversion instead of using single fixed values. The FDA systematically overestimates NOx emissions by 15 %–60 % when using tropospheric NO2 columns as the driving observation, while using PBL NO2 columns largely overcomes this systematic error. This merely reflects the fact that the local balance between emissions and sinks of NOx occurs in the boundary layer, which is decoupled from the NO2 in the free troposphere. Based on the recommendations from this sensitivity test, we then applied the FDA using observations of NO2 columns from TROPOMI, corrected for contributions from free-tropospheric NO2, between 1 June and 31 August 2018. The NOx emissions derived from the default TROPOMI retrievals are biased low over cities and industrialized areas. However, when the coarse 1×1° TM5-MP NO2 profile used in the retrieval is replaced by the high-resolution profile of LOTOS-EUROS, the TROPOMI NOx emissions are enhanced by 22 % and are in better agreement with the inventory for the Netherlands. This emphasizes the importance of using realistic high-resolution a priori NO2 profile shapes in the TROPOMI retrieval. We conclude that accurate quantitative NOx emissions estimates are possible with the FDA, but they require sophisticated, fine-scale corrections for both the NO2 observations driving the method and the estimates of the NO2 chemical lifetime and NOx:NO2 ratio. This information can be obtained from high-resolution chemistry transport model simulations at the expense of the simplicity and applicability of the FDA.

Understanding the Mechanisms Behind the Distribution of Galactic Metals

Abstract The evolution and distribution of metals within galaxies are critical for understanding galactic evolution and star formation processes, but the mechanisms responsible for shaping this distribution remain uncertain. In this study we carry out high-resolution simulations of an isolated Milky Way-like galaxy, including a star-by-star treatment of both feedback and element injection. We include seven key isotopes of observational and physical interest, and which are distributed across different nucleosynthetic channels—primarily AGB stars (N, Ba, Ce), supernovae (O, Mg, S), and Wolf-Rayet stars (C)show measurably different correlation statistics in space and time and their fluctuations. This difference arises from the distinct ejection mechanisms associated with each nucleosynthetic process. The large-scale properties ensure that different elements, despite having different nucleosynthetic origins, are highly correlated with one another (>0.85 for all, >0.99 for same origins), and their spatial correlations vary together in time. However small-scale variations naturally break elements into distinct nucleosynthetic familiars, with elements originating from the same channels correlating better with each other than with elements from different origins. Our findings suggest both challenges and opportunities for ongoing efforts to use chemical measurements of gas and stars to unravel the history and physics of galaxy assembly.

AEOS: Star-by-star Cosmological Simulations of Early Chemical Enrichment and Galaxy Formation

Abstract The Aeos project introduces a series of high-resolution cosmological simulations that model star-by-star chemical enrichment and galaxy formation in the early Universe, achieving 1 pc resolution. These simulations capture the complexities of galaxy evolution within the first ~300 Myr by modeling individual stars and their feedback processes. By incorporating chemical yields from individual stars, Aeos generates galaxies with diverse stellar chemical abundances, linking them to hierarchical galaxy formation and early nucleosynthetic events. These simulations underscore the importance of chemical abundance patterns in ancient stars as vital probes of early nucleosynthesis, star formation histories, and galaxy formation. We examine the metallicity floors of various elements resulting from Population III enrichment, providing best-fit values for eight different metals (e.g., [O/H] = −4.0) to guide simulations without Population III models. Additionally, we identify galaxies that begin star formation with Population II after external enrichment and investigate the frequency of carbon-enhanced metal-poor stars at varying metallicities. The Aeos simulations offer detailed insights into the relationship between star formation, feedback, and chemical enrichment. Future work will extend these simulations to later epochs to interpret the diverse stellar populations of the Milky Way and its satellites.

Evaluation of high-resolution snowpack simulations from global datasets and comparison with Sentinel-1 snow depth retrievals in the Sierra Nevada, USA

Abstract. The spatial distribution of mountain snow water equivalent (SWE) is key information for water management. We implement a tool to simulate snowpack properties at high resolution (100 m) by using only global datasets of meteorology, land cover and elevation. The meteorological data are obtained from ERA5, which makes the method applicable in near real time (5 d latency). We evaluate the output using 49 SWE maps derived from airborne lidar surveys in the Sierra Nevada. We find very good agreement at the catchment scale using uncalibrated lapse rates. Larger biases at the model grid scale are especially evident at high elevation but do not alter the catchment-scale snow mass accuracy. We additionally compare the simulated snow depth to Sentinel-1 retrievals and find a similar accuracy with respect to synchronous airborne lidar surveys. However, Sentinel-1 snow depth products are sparse and often masked during the melt season, whereas ERA5–SnowModel provides a spatially and temporally continuous SWE.

Tidal energetics in the eddying South China Sea from a high-resolution numerical simulation

Tidal energetics in the eddying South China Sea from a high-resolution numerical simulation

Bay of Bengal river plume response to a tropical cyclone in high-resolution numerical simulations

Bay of Bengal river plume response to a tropical cyclone in high-resolution numerical simulations

Reflection-driven turbulence in the super-Alfvénic solar wind

In magnetized, stratified environments such as the Sun's corona and solar wind, Alfvénic fluctuations ‘reflect’ from background gradients, enabling nonlinear interactions that allow their energy to dissipate into heat. This process, termed ‘reflection-driven turbulence’, likely plays a key role in coronal heating and solar-wind acceleration, explaining a range of detailed observational correlations and constraints. Building on previous works focused on the inner heliosphere, here we study the basic physics of reflection-driven turbulence using reduced magnetohydrodynamics in an expanding box – the simplest model that can capture local turbulent plasma dynamics in the super-Alfvénic solar wind. Although idealized, our high-resolution simulations and simple theory reveal a rich phenomenology that is consistent with a diverse range of observations. Outwards-propagating fluctuations, which initially have high imbalance (high cross-helicity), decay nonlinearly to heat the plasma, becoming more balanced and magnetically dominated. Despite the high imbalance, the turbulence is strong because Elsässer collisions are suppressed by reflection, leading to ‘anomalous coherence’ between the two Elsässer fields. This coherence, together with linear effects, causes the growth of ‘anastrophy’ (squared magnetic potential) as the turbulence decays, forcing the energy to rush to larger scales and forming a ‘ $1/f$ -range’ energy spectrum in the process. Eventually, expansion overcomes the nonlinear and Alfvénic physics, forming isolated, magnetically dominated ‘Alfvén vortices’ with minimal nonlinear dissipation. These results can plausibly explain the observed radial and wind-speed dependence of turbulence imbalance (cross-helicity), residual energy, fluctuation amplitudes, plasma heating and fluctuation spectra, as well as making a variety of testable predictions for future observations.

Dynamical imprints on precipitation cluster statistics across a hierarchy of high-resolution simulations

Abstract. Tropical precipitation cluster area and intensity distributions follow power laws, but the physical processes responsible for this macroscopic behavior remain unknown. We analyze global simulations at 10 km horizontal resolution that are configured to have drastically varying degrees of realism, ranging from global radiative–convective equilibrium to fully realistic atmospheric simulations, to investigate how dynamics influence precipitation statistics. We find the presence of stirring and large-scale vertical overturning, as associated with substantial planetary- and synoptic-scale variability, to be key to having cluster statistics approach power laws. The presence of such large-scale dynamics is reflected in steep vertical velocity spectra. Large-scale rising and sinking modulate the column water vapor and temperature field, leading to a heterogeneous distribution of moist and dry patches and regions of strong mass flux, in which large precipitation clusters form. Our findings suggest that power laws in Earth's precipitation cluster statistics stem from the robust power laws of atmospheric motions.

Jetted Seyfert Galaxies at z = 0: Simulating Feedback Effects on Galactic Morphology and Beyond

Abstract We use high-resolution cosmological zoom-in simulations to model feedback from Seyfert-type supermassive black hole (SMBH) jets onto galaxies with identical dark matter (DM) halos of log M/M ⊙ ∼ 11.8. The low-mass, ∼106 M ⊙, seed SMBHs have been introduced when the parent DM halos have reached log M/M ⊙ ∼ 11. In a controlled experiment, we vary only the efficiency of the SMBH accretion and focus on galaxies and their immediate environment properties. Our results show that the active galactic nucleus jet feedback has a substantial effect on the basic properties of Seyfert-type galaxies, such as morphology, gas fraction and distribution, star formation rate and distribution, B/D ratio, DM halo baryon fraction, and properties of the circumgalactic medium and beyond. These have been compared to a galaxy with supernovae only feedback. We focus on the energy deposition by the jet in the interstellar medium (ISM) and intergalactic gas medium, and follow the expansion of the multiple jet cocoons to ∼2 Mpc. We find that the jet–ISM interaction gradually pushes the star formation to larger radii with increasing accretion efficiency, which results in increased mass of the outer stellar disk, which is best fit as a double-exponential disk. Furthermore, we compare our galaxies and their properties with the observed nearby Seyfert galaxies, including the scaling relations, and find a close agreement, although statistical analysis of observed Seyferts is currently missing. In a forthcoming paper, we focus on the evolution of these objects at z ≲ 10 and study the effect of the SMBH seeding redshift.

AGN feedback in isolated galaxies with a SMUGGLE multiphase ISM

Abstract Feedback from active galactic nuclei (AGN) can strongly impact the host galaxies by driving high-velocity winds that impart substantial energy and momentum to the interstellar medium (ISM). In this work, we study the impact of these winds in isolated galaxies using high-resolution hydrodynamics simulations. Our simulations use the explicit ISM and stellar evolution model called Stars and MUltiphase Gas in GaLaxiEs (SMUGGLE). Additionally, using a super-Lagrangian refinement scheme, we resolve AGN feedback coupling to the ISM at ∼10-100 pc scales. We find that AGN feedback efficiently regulates the growth of SMBHs. However, its effect on star formation and outflows depends strongly on the relative strengths of AGN vs local stellar feedback and the geometrical structure of the gas disk. When the energy injected by AGN is subdominant to that of stellar feedback, there are no significant changes in the star formation rates or mass outflow rates of the host galaxy. Conversely, when the energy budget is dominated by the AGN, we see a significant decline in the star formation rates accompanied by an increase in outflows. Galaxies with thin gas disks like the Milky Way allow feedback to escape easily into the polar directions without doing much work on the ISM. In contrast, galaxies with thick and diffuse gas disks confine the initial expansion of the feedback bubble within the disk, resulting in more work done on the ISM. Phase space analysis indicates that outflows primarily comprise hot and diffuse gas, with a lack of cold and dense gas.

Understanding the atmospheric dynamics over high-altitude glaciated regions in the central Himalaya using high-resolution numerical simulations

Abstract The atmospheric dynamics over the higher Himalaya play a crucial role in controlling glacier variability and ultimately regulating downstream water availability. However, the paucity of station observations makes exploring these atmospheric dynamics challenging. To address these issues, we employed a high-resolution configuration of the Weather Research and Forecasting (WRF) model with a 2-km convection-permitting grid scale to simulate atmospheric variables over the central Himalaya. We analyze the atmospheric variables over three high-altitude glaciated regions, namely the Langtang, Rolwaling, and Everest regions, in the central Himalaya. The model reproduces precipitation and temperature seasonality well, with the model precipitation displaying better agreement with the station data and outperforming the satellite observations. Furthermore, we investigate the spatial variability of precipitation during the monsoon and winter seasons and explore the associated dynamics by computing the vertically integrated moisture transport (VIMT) and vertically integrated moisture flux divergence (VIMFD). The VIMT and VIMFD analysis reveal that the valleys that meridionally dissect the Himalaya transport the moisture from the Indo-Gangetic plains to the higher Himalaya, and the sharp rise in elevation results in moisture convergence and precipitation, with the results that the ridges and windward slopes accumulate more precipitation than the leeward slopes and valleys. The orographic effect on moisture convergence, cloud formation, and precipitation consequently controls the glacier energy balance. During the monsoon season, the enhancement of net radiation by thick monsoon cloud cover, coupled with added latent heat and reduced albedo from the dominant liquid precipitation below 5,000 m amsl, increases the melt energy, promoting glacier melt.

Revisiting the Last Ice Area projections from a high-resolution Global Earth System Model

The Last Ice Area—located to the north of Greenland and the northern Canadian Arctic Archipelago—is expected to persist as the central Arctic Ocean becomes seasonally ice-free within a few decades. Projections of the Last Ice Area, however, have come from relatively low resolution Global Climate Models that do not resolve sea ice export through the waterways of the Canadian Arctic Archipelago and Nares Strait. Here we revisit Last Ice Area projections using high-resolution numerical simulations from the Community Earth System Model, which resolves these narrow waterways. Under a high-end forcing scenario, the sea ice of the Last Ice Area thins and becomes more mobile, resulting in a large export southward. Under this potentially worst-case scenario, sea ice of the Last Ice Area could disappear a little more than one decade after the central Arctic Ocean has reached seasonally ice-free conditions. This loss would have profound impacts on ice-obligate species.

Long-term variability and trends in the Agulhas Leakage and its impacts on the global overturning

Abstract. Agulhas Leakage transports relatively warm and salty Indian Ocean waters into the Atlantic Ocean and as such is an important component of the global ocean circulation. These waters are part of the upper limb of the Atlantic meridional overturning circulation (AMOC), and Agulhas Leakage variability has been linked to AMOC variability. Agulhas Leakage is expected to increase under a warming climate due to a southward shift in the Southern Hemisphere westerlies, which could further influence the AMOC dynamics. This study uses a set of high-resolution preindustrial control, historical and transient simulations with the Community Earth System Model (CESM) with a nominal horizontal resolution of 0.1° for the ocean and sea ice and 0.25° for the atmosphere and land. At these resolutions, the model represents the necessary scales to investigate Agulhas Leakage transport variability and its relation to the AMOC. The simulated Agulhas Leakage transport of 19.7 ± 3 Sv lies well within the observed range of 21.3 ± 4.7 Sv. A positive correlation between the Agulhas Current and the Agulhas Leakage is shown, meaning that an increase of the Agulhas Current transport leads to an increase in Agulhas Leakage. The Agulhas Leakage impacts the strength of the AMOC through Rossby wave dynamics that alter the cross-basin geostrophic balance with a time lag of 2–3 years. Furthermore, the salt transport associated with the Agulhas Leakage influences AMOC dynamics through the salt–advection feedback by reducing the AMOC's freshwater transport at 34° S. The Agulhas Leakage transport indeed increases under a warming climate due to strengthened and southward-shifting winds. In contrast, the Agulhas Current transport decreases due to a decrease in the Indonesian Throughflow and the strength of the wind-driven subtropical gyre. The increase in the Agulhas Leakage is accompanied by a higher salt transport into the Atlantic Ocean, which could play a role in the stability of the AMOC via the salt–advection feedback.

Dominant inflation of the Arctic Ocean’s Beaufort Gyre in a warming climate

The Arctic Ocean’s Beaufort Gyre, the largest Arctic freshwater reservoir, plays a crucial role for climate and marine ecosystems. Understanding how it changes in a warming climate is therefore essential. Here, using high-resolution simulations and Coupled Model Intercomparison Project phase 6 data, we find that the Beaufort Gyre will increasingly accumulate freshwater, elevate sea level, and spin up its circulation as the climate warms. These changes, collectively referred to as inflation, are more pronounced in the Beaufort Gyre region than in other Arctic areas, amplifying the spatial asymmetry of the Arctic Ocean. The inflation is driven by increased surface freshwater fluxes and intensified surface stress from wind strengthening and sea ice decline. Current climate models tend to underestimate this inflation, which could be alleviated by high-resolution ocean models and improved atmospheric circulation simulations. The inflation of the Beaufort Gyre underscores its growing importance in a warming climate.

Understanding observational characteristics of solar flare current sheets

The elongated bright structures above solar flare loops are suggested to be current sheets, where magnetic reconnection takes place. Observations have revealed various characteristics of the current sheet; however, their physical origin remains to be ascertained. In this study we aim to reveal the relations of observational characteristics of current sheets with the fundamental processes of magnetic reconnection. Using high-resolution 3D magnetohydrodynamic simulations of turbulent magnetic reconnection within a solar flare current sheet, we synthesized the remote-sensing observations of the current sheet and determined their physical properties. Turbulent magnetic reconnection can significantly broaden the apparent width of the current sheet, which is much larger than the realistic physical width because of the superposition effect. The differential emission measures of the current sheet have two peaks; the high-temperature component is spatially related to confirmed small-scale reconnection sites, showing that the current sheet is directly heated by reconnection. Moreover, we demonstrate that strong turbulence can cause the nonthermal broadening of spectral lines at both the current sheet and flare loop-top regions. A strong correlation between them in time is also observed. Our 3D turbulent magnetic reconnection flare model can be used to interpret primary observational characteristics of the elongated bright current sheets of solar flares.

Effect of soft sediments modeling on the seismic response of a 3D mid-rise RC building: high-resolution physics-based ground-motion simulations and empirical factors

Ground-motion simulations have progressively become a key resource in earthquake engineering. Nevertheless, the challenge of accurately simulating ground motions in regions with low shear-wave velocities, such as basins and shallow sediments, persists and is often constrained by the associated computational demands. Motivated by the potential unavailability of suites of simulations resolving low velocities for a specific region or site of interest, this work assesses the implications of using different approaches for modeling low shear-wave velocities on structural response. Two methods are investigated: one relies on simulation models capable of resolving low shear-wave velocities, while the other combines simulations that resolve high shear-wave velocities with empirical site amplification factors. An M7 Hayward Fault strike-slip earthquake in the San Francisco Bay Area and a three-dimensional ten-story reinforced concrete building are used as case study. Findings from this work demonstrate significant differences in the prediction of ground-motion intensities and building responses (from moderate to extensive damage) when different modeling methods are employed. Such differences manifest at sites with low shear-wave velocities as well as at stiff sites in their vicinity. This is caused by the concurrent effect of the specificity of the seismic velocity structure for the considered region and wave propagation, which is adequately captured only by the simulation model incorporating the (target) low shear-wave velocity. Evidence from this study indicates that empirical factors should be used and processed (i.e., transfer functions tapering) with consideration for the specific geological characteristics of the domain of interest, especially in regions lacking representation in the databases of historical records, such as the San Francisco Bay Area. From a structural engineering perspective, these insights contribute to a better understanding of the complexities involved in soft sediment modeling and its implications in structural engineering applications.

Quantifying Lyman-α emissions from reionization fronts

Abstract During reionization, intergalactic ionization fronts (I-fronts) are sources of Lyα line radiation produced by collisional excitation of hydrogen atoms within the fronts. In principle, detecting this emission could provide direct evidence for a reionizing intergalactic medium (IGM). In this paper, we use a suite of high-resolution one-dimensional radiative transfer simulations run on cosmological density fields to quantify the parameter space of I-front Lyα emission. We find that the Lyα production efficiency — the ratio of emitted Lyα flux to incident ionizing flux driving the front — depends mainly on the I-front speed and the spectral index of the ionizing radiation. IGM density fluctuations on scales smaller than the typical I-front width produce scatter in the efficiency, but they do not significantly boost its mean value. The Lyα flux emitted by an I-front is largest if 3 conditions are met simultaneously: (1) the incident ionizing flux is large; (2) the incident spectrum is hard, consisting of more energetic photons; (3) the I-front is traveling through a cosmological over-density, which causes it to propagate more slowly. We present a convenient parameterization of the efficiency in terms of I-front speed and incident spectral index. We make these results publicly available as an interpolation table and we provide a simple fitting function for a representative ionizing background spectrum. Our results can be applied as a sub-grid model for I-front Lyα emissions in reionization simulations with spatial and/or temporal resolutions too coarse to resolve I-front structure. In a companion paper, we use our results to explore the possibility of directly imaging Lyα emission around neutral islands during the last phases of reionization.

Testing the robustness of the BAO determination in the presence of massive neutrinos

We study the robustness of the Baryon Acoustic Oscillation (BAO) feature in the large-scale structure in the presence of massive neutrinos. In the standard BAO analysis pipeline a reference cosmological model is assumed to boost the BAO peak through the so-called reconstruction technique and in the modelling of the BAO feature to extract the cosmological information. State-of-the art spectroscopic BAO measurements, such as the Dark Energy Spectroscopic Instrument claim an aggregate precision of 0.52% on the BAO scale, with a systematic error of 0.1% associated to the assumption of a reference cosmology when measuring and analyzing the BAO feature. While the systematic effect induced by this arbitrary choice of fiducial cosmology has been studied for a wide range of ΛCDM-like models, it has not yet been tested for reference cosmologies with massive neutrinos with the precision afforded by next generation surveys. In this context, we employ the Quijote high-resolution dark-matter simulations with haloes above a mass of M ∼ 2×1013 h -1 M ⊙, with different values for the total sum of neutrinos masses, ∑mν [eV] = 0, 0.1, 0,2, 0.4 to study and quantify the impact of the pipeline's built-in assumption of massless neutrinos on the measurement of the BAO signal, with a special focus on the BAO reconstruction technique. We determine that any additional systematic bias introduced by the assumption of massless neutrinos is no greater than 0.1% (0.2%) for the isotropic (anisotropic) measurement. We expect these conclusions also hold for galaxies provided that neutrino properties do not alter the galaxy-halo connection.

Everything hot everywhere all at once: neutrinos and hot dark matter as a single effective species

Observational cosmology is rapidly closing in on a measurement of the sum Mν of neutrino masses, at least in the simplest cosmologies, while opening the door to probes of non-standard hot dark matter (HDM) models. By extending the method of effective distributions, we show that any collection of HDM species, with arbitrary masses, temperatures, and distribution functions, including massive neutrinos, may be represented as a single effective HDM species. Implementing this method in the FlowsForTheMasses non-linear perturbation theory for free-streaming particles, we study non-standard HDM models that contain thermal QCD axions or generic bosons in addition to standard neutrinos, as well as non-standard neutrino models wherein either the distribution function of the neutrinos or their temperature is changed. Along the way, we substantially improve the accuracy of this perturbation theory at low masses, bringing it into agreement with the high-resolution TianNu neutrino N-body simulation to ≈ 2% at k = 0.1 h/Mpc and to ≤ 21% over the range k ≤ 1 h/Mpc. We accurately reproduce the results of simulations including axions and neutrinos of multiple masses. Studying the differences between the normal, inverted, and degenerate neutrino mass orderings on their non-linear power, we quantify the error in the common approximation of degenerate masses. We release our code publicly at http://github.com/upadhye/FlowsForTheMassesII.