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Yueying Ni

Publications and source records attributed to Yueying Ni.

At least 55 records · Page 3Linked to original sources

Efficient Reionization in a Large Hydrodynamic Galaxy Formation Simulation

Accuracy in the topology and statistics of a simulated Epoch of Reionization (EoR) are vital to draw connections between observations and physical processes. While full radiative transfer models produce the most accurate reionization models, they are highly computationally expensive, and are infeasible for the largest cosmological simulations. Instead, large simulations often include EoR models that are pre-computed via the initial density field, or post-processed where feedback effects are ignored. We introduce Astrid-ES, a resimulation of the Astrid epoch of reionisation $20 > z > 5.5$ which includes an on-the-fly excursion-set reionization algorithm. Astrid-ES produces more accurate reionization histories without significantly impacting the computational time. This model directly utilises the star particles produced in the simulation to calculate the EoR history and includes a UV background which heats the gas particles after their reionization. We contrast the reionization topology and statistics in Astrid-ES with the previously employed parametric reionisation model, finding that in Astrid-ES, ionised regions are more correlated with galaxies, and the 21cm power-spectrum shows an increase in large scale power. We calculate the relation between the size of HII regions and the UV luminosity of the brightest galaxy within them. Prior to the overlap phase, we find a power-law fit of $\mathrm{log} (R) = -0.314 M_\mathrm{UV} - 2.550 \mathrm{log}(1+z) + 7.408$ with a standard deviation $σ_R < 0.15 \mathrm{dex}$ across all mass bins. We also examine the properties of halos throughout reionization, finding that while the properties of halos in the simulation are correlated with the redshift of reionisation, they are not greatly affected by reionisation itself.

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Cosmological baryon spread and impact on matter clustering in CAMELS

We quantify the cosmological spread of baryons relative to their initial neighboring dark matter distribution using thousands of state-of-the-art simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. We show that dark matter particles spread relative to their initial neighboring distribution owing to chaotic gravitational dynamics on spatial scales comparable to their host dark matter halo. In contrast, gas in hydrodynamic simulations spreads much further from the initial neighboring dark matter owing to feedback from supernovae (SNe) and Active Galactic Nuclei (AGN). We show that large-scale baryon spread is very sensitive to model implementation details, with the fiducial \textsc{SIMBA} model spreading $\sim$40\% of baryons $>$1\,Mpc away compared to $\sim$10\% for the IllustrisTNG and \textsc{ASTRID} models. Increasing the efficiency of AGN-driven outflows greatly increases baryon spread while increasing the strength of SNe-driven winds can decrease spreading due to non-linear coupling of stellar and AGN feedback. We compare total matter power spectra between hydrodynamic and paired $N$-body simulations and demonstrate that the baryonic spread metric broadly captures the global impact of feedback on matter clustering over variations of cosmological and astrophysical parameters, initial conditions, and galaxy formation models. Using symbolic regression, we find a function that reproduces the suppression of power by feedback as a function of wave number ($k$) and baryonic spread up to $k \sim 10\,h$\,Mpc$^{-1}$ while highlighting the challenge of developing models robust to variations in galaxy formation physics implementation.

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Robust Field-level Likelihood-free Inference with Galaxies

We train graph neural networks to perform field-level likelihood-free inference using galaxy catalogs from state-of-the-art hydrodynamic simulations of the CAMELS project. Our models are rotational, translational, and permutation invariant and do not impose any cut on scale. From galaxy catalogs that only contain $3$D positions and radial velocities of $\sim 1, 000$ galaxies in tiny $(25~h^{-1}{\rm Mpc})^3$ volumes our models can infer the value of $Ω_{\rm m}$ with approximately $12$ % precision. More importantly, by testing the models on galaxy catalogs from thousands of hydrodynamic simulations, each having a different efficiency of supernova and AGN feedback, run with five different codes and subgrid models - IllustrisTNG, SIMBA, Astrid, Magneticum, SWIFT-EAGLE -, we find that our models are robust to changes in astrophysics, subgrid physics, and subhalo/galaxy finder. Furthermore, we test our models on $1,024$ simulations that cover a vast region in parameter space - variations in $5$ cosmological and $23$ astrophysical parameters - finding that the model extrapolates really well. Our results indicate that the key to building a robust model is the use of both galaxy positions and velocities, suggesting that the network have likely learned an underlying physical relation that does not depend on galaxy formation and is valid on scales larger than $\sim10~h^{-1}{\rm kpc}$.

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Fly-by galaxy encounters with multiple black holes produce star-forming linear wakes

We look for simulated star-forming linear wakes such as the one recently discovered by van Dokkum et al. (2023) in the cosmological hydrodynamical simulation ASTRID. Amongst the runaway black holes in ASTRID, none are able to produce clear star-forming wakes. Meanwhile, fly-by encounters, typically involving a compact galaxy (with a central black hole) and a star-forming galaxy (with a duo of black holes) reproduce remarkably well many of the key properties (its length and linearity; recent star formation, etc.) of the observed star-forming linear feature. We predict the feature to persist for approximately 100 Myr in such a system and hence constitute a rare event. The feature contains a partly stripped galaxy (with $M_{\rm gal}=10^9 \sim 10^{10}M_\odot$) and a dual BH system ($M_{\rm BH}=10^5 \sim 10^7\,M_\odot$) in its brightest knot. X-ray emission from AGN in the knot should be detectable in such systems. After $100\sim 200\,{\rm Myrs}$ from the first fly-by, the galaxies merge leaving behind a triple black hole system in a (still) actively star-forming early-type remnant of mass $\sim 5\times 10^{10}\,M_\odot$. Follow-up JWST observations may be key for revealing the nature of these linear features by potentially detecting the older stellar populations constituting the bright knot. Confirmation of such detections may therefore help discriminate a fly-by encounter from a massive BH wake to reveal the origin of such features.

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AI-assisted super-resolution cosmological simulations III: Time evolution

In this work, we extend our recently developed super-resolution (SR) model for cosmological simulations to produce fully time consistent evolving representations of the particle phase-space distribution. We employ a style-based constrained generative adversarial network (Style-GAN) where the changing cosmic time is an input style parameter to the network. The matter power spectrum and halo mass function agree well with results from high-resolution N-body simulations over the full trained redshift range ($10 \le z \le 0$). Furthermore, we assess the temporal consistency of our SR model by constructing halo merger trees. We examine progenitors, descendants and mass growth along the tree branches. All statistical indicators demonstrate the ability of our SR model to generate satisfactory high-resolution simulations based on low-resolution inputs.

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Cosmology with one galaxy? -- The ASTRID model and robustness

Recent work has pointed out the potential existence of a tight relation between the cosmological parameter $Ω_{\rm m}$, at fixed $Ω_{\rm b}$, and the properties of individual galaxies in state-of-the-art cosmological hydrodynamic simulations. In this paper, we investigate whether such a relation also holds for galaxies from simulations run with a different code that made use of a distinct subgrid physics: Astrid. We find that also in this case, neural networks are able to infer the value of $Ω_{\rm m}$ with a $\sim10\%$ precision from the properties of individual galaxies while accounting for astrophysics uncertainties as modeled in CAMELS. This tight relationship is present at all considered redshifts, $z\leq3$, and the stellar mass, the stellar metallicity, and the maximum circular velocity are among the most important galaxy properties behind the relation. In order to use this method with real galaxies, one needs to quantify its robustness: the accuracy of the model when tested on galaxies generated by codes different from the one used for training. We quantify the robustness of the models by testing them on galaxies from four different codes: IllustrisTNG, SIMBA, Astrid, and Magneticum. We show that the models perform well on a large fraction of the galaxies, but fail dramatically on a small fraction of them. Removing these outliers significantly improves the accuracy of the models across simulation codes.

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The CAMELS project: Expanding the galaxy formation model space with new ASTRID and 28-parameter TNG and SIMBA suites

We present CAMELS-ASTRID, the third suite of hydrodynamical simulations in the Cosmology and Astrophysics with MachinE Learning (CAMELS) project, along with new simulation sets that extend the model parameter space based on the previous frameworks of CAMELS-TNG and CAMELS-SIMBA, to provide broader training sets and testing grounds for machine-learning algorithms designed for cosmological studies. CAMELS-ASTRID employs the galaxy formation model following the ASTRID simulation and contains 2,124 hydrodynamic simulation runs that vary 3 cosmological parameters ($Ω_m$, $σ_8$, $Ω_b$) and 4 parameters controlling stellar and AGN feedback. Compared to the existing TNG and SIMBA simulation suites in CAMELS, the fiducial model of ASTRID features the mildest AGN feedback and predicts the least baryonic effect on the matter power spectrum. The training set of ASTRID covers a broader variation in the galaxy populations and the baryonic impact on the matter power spectrum compared to its TNG and SIMBA counterparts, which can make machine-learning models trained on the ASTRID suite exhibit better extrapolation performance when tested on other hydrodynamic simulation sets. We also introduce extension simulation sets in CAMELS that widely explore 28 parameters in the TNG and SIMBA models, demonstrating the enormity of the overall galaxy formation model parameter space and the complex non-linear interplay between cosmology and astrophysical processes. With the new simulation suites, we show that building robust machine-learning models favors training and testing on the largest possible diversity of galaxy formation models. We also demonstrate that it is possible to train accurate neural networks to infer cosmological parameters using the high-dimensional TNG-SB28 simulation set.

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Orbital and Radiative Properties of Wandering Intermediate-Mass Black Holes in the ASTRID Simulation

Intermediate-Mass Black Holes (IMBHs) of $10^3-10^6 \, M_\odot$ are commonly found at the center of dwarf galaxies. Simulations and observations convincingly show that a sizable population of IMBHs could wander off-center in galaxies. We use the cosmological simulation ASTRID to study the orbital and radiative properties of wandering IMBHs in massive galaxies at $z\sim3$. We find that this population of black holes has large orbital inclinations ($60^\circ\pm22^\circ$) with respect to the principal plane of the host. The eccentricity of their orbits is also significant ($0.6\pm0.2$) and decreases with time. Wandering IMBHs undergo spikes of accretion activity around the pericenter of their orbits, with rates $10^{-3}-10^{-5}$ times the Eddington rate and a median accretion duty cycle of $\sim 12\%$. Their typical spectral energy distribution peaks in the infrared at $\sim 11 \, μ\rm m$ rest-frame. Assuming a standard value of $10\%$ for the matter-to-energy radiative efficiency, IMBHs reach $2-10$ keV X-ray luminosities $>10^{37} \, \mathrm{erg\,s^{-1}}$ for $\sim10\%$ of the time. This luminosity corresponds to fluxes $>10^{-15} \, \mathrm{erg \, s^{-1} \, cm^{-2}}$ within $10$ Mpc. They could be challenging to detect because of competing emissions from X-ray binaries and the interstellar medium. X-ray luminosities $> 10^{41} \, \mathrm{erg \, s^{-1}}$, in the hyper-luminous X-ray sources (HLXs) regime, are reached by $\sim 7\%$ of the IMBHs. These findings suggest that HLXs are a small subset of the wandering IMBH population, which is characterized by luminosities $10^3-10^4$ times fainter. Dedicated surveys are needed to assess the demographics of this missing population of black holes.

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Triple and Quadruple Black Holes in the ASTRID Simulation at $z \sim 2$

We use the ASTRID cosmological hydrodynamic simulation to investigate the properties and evolution of triple and quadruple Massive Black Hole (MBH) systems at $z = 2-3$. Only a handful of MBH tuple systems have been detected to date. In ASTRID, we find $4\%$ of the $M_{\rm BH}>10^7\,M_\odot$ are in tuples with $Δr_{\rm max} < 200\,{\rm kpc}$. The tuple systems span a range of separations with the majority of the observable AGN systems at $Δr \sim 50-100$ kpc. They include some of the most massive BHs (up to $10^{10} \,M_\odot$) but with at least one of the components of $M_{\rm BH} \sim 10^7 \,M_\odot$. Tuples' host galaxies are typically massive with $M_* \sim 10^{10-11} \,M_\odot$. We find that $>10\%$ massive halos with $M_{\rm halo} > 10^{13} M_\odot$ host MBH tuples. Following the subsequent interactions between MBHs in tuples, we found that in $\sim 5\%$ of the triplets all three MBHs merge within a Gyr, and $15\%$ go through one merger. As a by-product of the complex multi-galaxy interaction of these systems, we also find that up to $\sim 5\%$ of tuples lead to runaway MBHs. In ASTRID, virtually all of the ultramassive black holes ($>10^{10} \,M_\odot $) have undergone a triple quasar phase while for BHs with $M_{\rm BH} \sim 10^9 \,M_\odot$ this fraction drops to $50\%$.

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A universal equation to predict $Ω_{\rm m}$ from halo and galaxy catalogues

We discover analytic equations that can infer the value of $Ω_{\rm m}$ from the positions and velocity moduli of halo and galaxy catalogues. The equations are derived by combining a tailored graph neural network (GNN) architecture with symbolic regression. We first train the GNN on dark matter halos from Gadget N-body simulations to perform field-level likelihood-free inference, and show that our model can infer $Ω_{\rm m}$ with $\sim6\%$ accuracy from halo catalogues of thousands of N-body simulations run with six different codes: Abacus, CUBEP$^3$M, Gadget, Enzo, PKDGrav3, and Ramses. By applying symbolic regression to the different parts comprising the GNN, we derive equations that can predict $Ω_{\rm m}$ from halo catalogues of simulations run with all of the above codes with accuracies similar to those of the GNN. We show that by tuning a single free parameter, our equations can also infer the value of $Ω_{\rm m}$ from galaxy catalogues of thousands of state-of-the-art hydrodynamic simulations of the CAMELS project, each with a different astrophysics model, run with five distinct codes that employ different subgrid physics: IllustrisTNG, SIMBA, Astrid, Magneticum, SWIFT-EAGLE. Furthermore, the equations also perform well when tested on galaxy catalogues from simulations covering a vast region in parameter space that samples variations in 5 cosmological and 23 astrophysical parameters. We speculate that the equations may reflect the existence of a fundamental physics relation between the phase-space distribution of generic tracers and $Ω_{\rm m}$, one that is not affected by galaxy formation physics down to scales as small as $10~h^{-1}{\rm kpc}$.

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High-redshift supermassive black hole mergers in simulations with dynamical friction modelling

In the near future, projects like LISA and Pulsar Timing Arrays are expected to detect gravitational waves from mergers between supermassive black holes, and it is crucial to precisely model the underlying merger populations now to maximize what we can learn from this new data. Here we characterize expected high-redshift (z > 2) black hole mergers using the very large volume Astrid cosmological simulation, which uses a range of seed masses to probe down to low-mass BHs, and directly incorporates dynamical friction so as to accurately model the dynamical processes which bring black holes to the galaxy center where binary formation and coalescence will occur. The black hole populations in Astrid include black holes down to 10$^{4.5}$ M$_\odot$, and remain broadly consistent with the TNG simulations at scales > 10$^6$ M$_\odot$ (the seed mass used in TNG). By resolving lower-mass black holes, the overall merger rate is ~5x higher than in TNG. However, incorporating dynamical friction delays mergers compared to a recentering scheme, reducing the high-z merger rate mass-matched mergers by a factor of ~2x. We also calculate the expected LISA Signal-to-Noise values, and show that the distribution peaks at high SNR (>100), emphasizing the importance of implementing a seed mass well below LISA's peak sensitivity (10$^6$ M$_\odot$) to resolve the majority of LISA's GW detections.

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Inferring the impact of feedback on the matter distribution using the Sunyaev Zel'dovich effect: Insights from CAMELS simulations and ACT+DES data

Feedback from active galactic nuclei and stellar processes changes the matter distribution on small scales, leading to significant systematic uncertainty in weak lensing constraints on cosmology. We investigate how the observable properties of group-scale halos can constrain feedback's impact on the matter distribution using Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS). Extending the results of previous work to smaller halo masses and higher wavenumber, $k$, we find that the baryon fraction in halos contains significant information about the impact of feedback on the matter power spectrum. We explore how the thermal Sunyaev Zel'dovich (tSZ) signal from group-scale halos contains similar information. Using recent Dark Energy Survey (DES) weak lensing and Atacama Cosmology Telescope (ACT) tSZ cross-correlation measurements and models trained on CAMELS, we obtain $10\%$ constraints on feedback effects on the power spectrum at $k \sim 5\, h/{\rm Mpc}$. We show that with future surveys, it will be possible to constrain baryonic effects on the power spectrum to $\mathcal{O}(<1\%)$ at $k = 1\, h/{\rm Mpc}$ and $\mathcal{O}(3\%)$ at $k = 5\, h/{\rm Mpc}$ using the methods that we introduce here. Finally, we investigate the impact of feedback on the matter bispectrum, finding that tSZ observables are highly informative in this case.

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A vast population of wandering and merging IMBHs at cosmic noon

Massive black holes in the centers of galaxies today must have grown by several orders of magnitude from seed black holes formed at early times. Detecting a population of intermediate mass black holes (IMBHs) can provide constraints on these elusive BH seeds. Here we use the large volume, cosmological hydrodynamical simulation Astrid, which includes IMBH seeds and dynamical friction to investigate the population of IMBH seeds. Dynamical friction is largely inefficient at sinking and merging seed IMBHs at high-z. This leads to an extensive population (several hundred per galaxy) of wandering IMBHs in large halos at z~2. A small fraction of these IMBHs are detectable as HLXs, Hyper Luminous X-ray sources. Importantly, at z ~ 2, IMBHs mergers produce the peak of GW events. We find close to a million GW events in Astrid between z=2-3 involving seed IMBH mergers. These GW events (almost all detectable by LISA) at cosmic noon should provide strong constraints on IMBH seed models and their formation mechanisms. At the center of massive galaxies, where the number of IMBHs can be as high as 10-100, SMBH-IMBH pairs can form. These Intermediate mass ratio inspirals (IMRIs) and extreme mass ratio inspirals (EMRIs), will require the next generation of milli-muHz space-based GW interferometers to be detected. Large populations of IMBHs around massive black holes will probe their environments and MBH causal structure.

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Super-resolution simulation of the Fuzzy Dark Matter cosmological model

AI super-resolution, combining deep learning and N-body simulations has been shown to successfully reproduce the large scale structure and halo abundances in the Lambda Cold Dark Matter cosmological model. Here, we extend its use to models with a different dark matter content, in this case Fuzzy Dark Matter (FDM), in the approximation that the difference is encoded in the initial power spectrum. We focus on redshift z = 2, with simulations that model smaller scales and lower masses, the latter by two orders of magnitude, than has been done in previous AI super-resolution work. We find that the super-resolution technique can reproduce the power spectrum and halo mass function to within a few percent of full high resolution calculations. We also find that halo artifacts, caused by spurious numerical fragmentation of filaments, are equally present in the super-resolution outputs. Although we have not trained the super-resolution algorithm using full quantum pressure FDM simulations, the fact that it performs well at the relevant length and mass scales means that it has promise as technique which could avoid the very high computational cost of the latter, in some contexts. We conclude that AI super-resolution can become a useful tool to extend the range of dark matter models covered in mock catalogs.

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Robust field-level inference with dark matter halos

We train graph neural networks on halo catalogues from Gadget N-body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogues contain $\lesssim$5,000 halos with masses $\gtrsim 10^{10}~h^{-1}M_\odot$ in a periodic volume of $(25~h^{-1}{\rm Mpc})^3$; every halo in the catalogue is characterized by several properties such as position, mass, velocity, concentration, and maximum circular velocity. Our models, built to be permutationally, translationally, and rotationally invariant, do not impose a minimum scale on which to extract information and are able to infer the values of $Ω_{\rm m}$ and $σ_8$ with a mean relative error of $\sim6\%$, when using positions plus velocities and positions plus masses, respectively. More importantly, we find that our models are very robust: they can infer the value of $Ω_{\rm m}$ and $σ_8$ when tested using halo catalogues from thousands of N-body simulations run with five different N-body codes: Abacus, CUBEP$^3$M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer $Ω_{\rm m}$ also works when tested on thousands of state-of-the-art CAMELS hydrodynamic simulations run with four different codes and subgrid physics implementations. Using halo properties such as concentration and maximum circular velocity allow our models to extract more information, at the expense of breaking the robustness of the models. This may happen because the different N-body codes are not converged on the relevant scales corresponding to these parameters.

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Ultramassive black holes formed by triple quasar mergers at $z\sim 2$

The origin of rare and elusive ultramassive black holes (UMBH, with MBH > 1e10 Msun) is an open question. Using the large volume cosmological hydrodynamic simulation ASTRID, we report on the formation of an extremely massive UMBH with MBH ~ 1e11 Msun at z~2. The UMBH is assembled as a result of two successive mergers of massive galaxies each with stellar mass M* > 3e11 Msun that also produces a bright, rare triple quasar system powered by three ~10^9 Msun black holes. The second merger of supermassive black holes (SMBHs) follows the first after 150 Myrs. The merger events lead to sustained Eddington accretion onto the central SMBH, forming an UMBH in the center of a massive compact stellar core with M* > 2e12 Msun. The strong feedback of the UMBH quenches the surrounding star formation to < 10 Msun/yr in the inner 50 kpc/h region. There are two more UMBHs with MBH > 5e10 Msun at z>2 in ASTRID which are also produced by major mergers of galaxies, and their progenitors can be observed as quasar triplets of lower luminosity. The rarely observed quasar multiples can be the cradle of UMBHs at high redshift, and likely end up in the center of the most massive clusters.

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The BlueTides Mock Image Catalogue: Simulated observations of high-redshift galaxies and predictions for JWST imaging surveys

We present a mock image catalogue of ~100,000 MUV=-22.5 to -19.6 mag galaxies at z=7-12 from the BlueTides cosmological simulation. We create mock images of each galaxy with the James Webb (JWST), Hubble, Roman, and Euclid Space Telescopes, as well as Subaru, and VISTA, with a range of near- and mid-infrared filters. We perform photometry on the mock images to estimate the success of these instruments for detecting high-z galaxies. We predict that JWST will have unprecedented power in detecting high-z galaxies, with a 95% completeness limit at least 2.5 magnitudes fainter than VISTA and Subaru, 1.1 magnitudes fainter than Hubble, and 0.9 magnitudes fainter than Roman, for the same wavelength and exposure time. Focusing on JWST, we consider a range of exposure times and filters, and find that the NIRCam F356W and F277W filters will detect the faintest galaxies, with 95% completeness at m=27.4 mag in 10ks exposures. We also predict the number of high-z galaxies that will be discovered by upcoming JWST imaging surveys. We predict that the COSMOS-Web survey will detect ~1000 MUV<-20.1 mag galaxies at 6.5<z<7.5, by virtue of its large survey area. JADES-Medium will detect almost 100% of MUV<-20 mag galaxies at z<8.5 due to its significant depth, however with its smaller survey area it will detect only ~100 of these galaxies at 6.5<z<7.5. Cosmic variance results in a large range in the number of predicted galaxies each survey will detect, which is more evident in smaller surveys such as CEERS and the PEARLS NEP and GOODS-S fields.

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Properties and Evolution of Dual and Offset AGN in the ASTRID Simulation at $z \sim 2$

We examine the dual (both BHs active) and offset (one BH active) AGN population (comprising $\sim$ 2000 pairs at $0.5\,\text{kpc}\lesssimΔr<30\,\text{kpc}$) at $z=2\sim3$ in the ASTRID simulation covering (360 cMpc)${^3}$. The dual (offset) AGN make up $3.0(2.2)\%$ of all AGN at $z=2$. The dual fraction is roughly constant while the offset fraction increases by a factor of ten from $z=4\sim2$. Compared with the full AGN population, duals are characterized by a low $M_\text{BH}/M_*$ ratio, a high specific star-formation rate (sSFR) of $\sim 1\,\text{Gyr}^{-1}$, and a high Eddington ratio ($\sim 0.05$, double that of single AGN). The dual AGN are formed in major galaxy mergers (typically involving $M_\text{halo}<10^{13}\,M_\odot$), with BHs that have similar masses. At small separations (when their host galaxies are in the late phase of the merger) duals become $2\sim8$ times brighter (albeit more obscured) than at larger separations. $80\%$ of these bright, close duals merge in the simulation within $\sim500\,\text{Myrs}$. Notably, the initially less-massive BH in duals frequently becomes the brighter AGN during the galaxy merger. In offset AGN, the active BH is typically $\gtrsim 10$ times more massive than its non-active counterpart and than most BHs in duals. Offsets are predominantly formed in minor galaxy mergers with the active BH residing in the center of massive halos ($ M_\text{ halo}\sim 10^{13-14}\,M_\odot$). In these deep potentials, gas stripping is common and the secondary quickly deactivates. The stripping also leads to inefficient orbital decay amongst offsets, which stall at $Δr\sim5\,\text{kpc}$ for a few hundred Myrs.

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