arXiv subjects

Romeel Dave

Publications and source records attributed to Romeel Dave.

At least 37 records · Page 2Linked to original sources

arXiv2023

The Three Hundred Project: the evolution of physical baryon profiles

The distribution of baryons provides a significant way to understand the formation of galaxy clusters by revealing the details of its internal structure and changes over time. In this paper, we present theoretical studies on the scaled profiles of physical properties associated with the baryonic components, including gas density, temperature, metallicity, pressure and entropy as well as stellar mass, metallicity and satellite galaxy number density in galaxy clusters from $z=4$ to $z=0$ by tracking their progenitors. These mass-complete simulated galaxy clusters are coming from THE THREE HUNDRED with two runs: GIZMO-SIMBA and Gadget-X. Through comparisons between the two simulations, and with observed profiles which are generally available at low redshift, we find that (1) the agreements between the two runs and observations are mostly at outer radii $r \gtrsim 0.3r_{500}$, in line with the self-similarity assumption. While Gadget-X shows better agreements with the observed gas profiles in the central regions compared to GIZMO-SIMBA; (2) the evolution trends are generally consistent between the two simulations with slightly better consistency at outer radii. In detail, the gas density profile shows less discrepancy than the temperature and entropy profiles at high redshift. The differences in the cluster centre and gas properties imply different behaviours of the AGN models between Gadget-X and GIZMO-SIMBA, with the latter, maybe too strong for this cluster simulation. The high-redshift difference may be caused by the star formation and feedback models or hydrodynamics treatment, which requires observation constraints and understanding.

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arXiv2023

Line Emission Mapper (LEM): Probing the physics of cosmic ecosystems

The Line Emission Mapper (LEM) is an X-ray Probe for the 2030s that will answer the outstanding questions of the Universe's structure formation. It will also provide transformative new observing capabilities for every area of astrophysics, and to heliophysics and planetary physics as well. LEM's main goal is a comprehensive look at the physics of galaxy formation, including stellar and black-hole feedback and flows of baryonic matter into and out of galaxies. These processes are best studied in X-rays, and emission-line mapping is the pressing need in this area. LEM will use a large microcalorimeter array/IFU, covering a 30x30' field with 10" angular resolution, to map the soft X-ray line emission from objects that constitute galactic ecosystems. These include supernova remnants, star-forming regions, superbubbles, galactic outflows (such as the Fermi/eROSITA bubbles in the Milky Way and their analogs in other galaxies), the Circumgalactic Medium in the Milky Way and other galaxies, and the Intergalactic Medium at the outskirts and beyond the confines of galaxies and clusters. LEM's 1-2 eV spectral resolution in the 0.2-2 keV band will make it possible to disentangle the faintest emission lines in those objects from the bright Milky Way foreground, providing groundbreaking measurements of the physics of these plasmas, from temperatures, densities, chemical composition to gas dynamics. While LEM's main focus is on galaxy formation, it will provide transformative capability for all classes of astrophysical objects, from the Earth's magnetosphere, planets and comets to the interstellar medium and X-ray binaries in nearby galaxies, AGN, and cooling gas in galaxy clusters. In addition to pointed observations, LEM will perform a shallow all-sky survey that will dramatically expand the discovery space.

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arXiv2023

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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arXiv2023

How baryons affect halos and large-scale structure: a unified picture from the Simba simulation

Using the state-of-the-art suite of hydrodynamic simulations Simba, as well as its dark-matter-only counterpart, we study the impact of the presence of baryons and of different stellar/AGN feedback mechanisms on large-scale structure, halo density profiles, and on the abundance of different baryonic phases within halos and in the intergalactic medium (IGM). The unified picture that emerges from our analysis is that the main physical drivers shaping the distribution of matter at all scales are star formation-driven galactic outflows at $z>2$ for lower mass halos and AGN jets at $z<2$ in higher mass halos. Feedback suppresses the baryon mass function with time relative to the halo mass function, and it even impacts the halo mass function itself at the ~20% level, particularly evacuating the centres and enhancing dark matter just outside halos. At early epochs baryons pile up in the centres of halos, but by late epochs and particularly in massive systems gas has mostly been evacuated from within the inner halo. AGN jets are so efficient at such evacuation that at low redshifts the baryon fraction within $\sim 10^{12}-10^{13} \, \rm M_{\odot}$ halos is only 25% of the cosmic baryon fraction, mostly in stars. The baryon fraction enclosed in a sphere around such halos approaches the cosmic value $Ω_{\rm b}/Ω_{\rm m}$ only at 10-20 virial radii. As a result, 87% of the baryonic mass in the Universe lies in the IGM at $z=0$, with 67% being in the form of warm-hot IGM ($T>10^5 \, \rm K$).

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arXiv2023

Inferring halo masses with Graph Neural Networks

Understanding the halo-galaxy connection is fundamental in order to improve our knowledge on the nature and properties of dark matter. In this work we build a model that infers the mass of a halo given the positions, velocities, stellar masses, and radii of the galaxies it hosts. In order to capture information from correlations among galaxy properties and their phase-space, we use Graph Neural Networks (GNNs), that are designed to work with irregular and sparse data. We train our models on galaxies from more than 2,000 state-of-the-art simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. Our model, that accounts for cosmological and astrophysical uncertainties, is able to constrain the masses of the halos with a $\sim$0.2 dex accuracy. Furthermore, a GNN trained on a suite of simulations is able to preserve part of its accuracy when tested on simulations run with a different code that utilizes a distinct subgrid physics model, showing the robustness of our method. The PyTorch Geometric implementation of the GNN is publicly available on Github at https://github.com/PabloVD/HaloGraphNet

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arXiv2023

Dusty Starbursts Masquerading as Ultra-high Redshift Galaxies in JWST CEERS Observations

Lyman Break Galaxy (LBG) candidates at z>10 are rapidly being identified in JWST/NIRCam observations. Due to the (redshifted) break produced by neutral hydrogen absorption of rest-frame UV photons, these sources are expected to drop out in the bluer filters while being well detected in redder filters. However, here we show that dust-enshrouded star-forming galaxies at lower redshifts (z<7) may also mimic the near-infrared (near-IR) colors of z>10 LBGs, representing potential contaminants in LBG candidate samples. First, we analyze CEERS-DSFG-1, a NIRCam dropout undetected in the F115W and F150W filters but detected at longer wavelengths. Combining the JWST data with (sub)millimeter constraints, including deep NOEMA interferometric observations, we show that this source is a dusty star-forming galaxy (DSFG) at z~5.1. We also present a tentative 2.6sigma SCUBA-2 detection at 850um around a recently identified z~16 LBG candidate in the same field and show that, if the emission is real and associated with this candidate, the available photometry is consistent with a z~5 dusty galaxy with strong nebular emission lines despite its blue near-IR colors. Further observations on this candidate are imperative to mitigate the low confidence of this tentative submillimeter emission and its positional uncertainty. Our analysis shows that robust (sub)millimeter detections of NIRCam dropout galaxies likely imply z=4-6 redshift solutions, where the observed near-IR break would be the result of a strong rest-frame optical Balmer break combined with high dust attenuation and strong nebular line emission, rather than the rest-frame UV Lyman break. This provides evidence that DSFGs may contaminate searches for ultra high-redshift LBG candidates from JWST observations.

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arXiv2022

Effects of Active Galactic Nucleus Feedback on Cold Gas Depletion and Quenching of Central Galaxies

We investigate the influence of active galactic nucleus (AGN) feedback on the galaxy cold gas content and its connection to galaxy quenching in three hydrodynamical simulations of Illustris, IllustrisTNG and SIMBA. By comparing to the observed atomic and molecular neutral hydrogen measurements for central galaxies, we find that Illustris over-predicts the cold gas masses in star-forming galaxies and significantly under-predicts them for quenched galaxies. IllustrisTNG performs better in this comparison than Illustris, but quenched galaxies retain too much cold gas compared with observations. SIMBA shows good agreement with observations, by depleting the global cold gas reservoir for quenched galaxies. We find that the discrepancies in IllustrisTNG are caused by its weak kinetic AGN feedback that only redistributes the cold gas from the inner disks to the outer regions and reduces the inner cold gas densities. It agrees with observations much better when only the cold gas within the stellar disk is considered to infer the star formation rates. From dependences of cold gas reservoir on the black hole mass and Eddington ratio, we find that the cumulative energy release during the black hole growth is the dominant reason for the cold gas depletion and thus the galaxy quenching. We further measure the central stellar surface density within 1 kpc ($Σ_1$) for the high-resolution run of IllustrisTNG and find a tight correlation between $Σ_1$ and black hole mass. It suggests that the observed decreasing trend of cold gas mass with $Σ_1$ is also a reflection of the black hole growth.

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arXiv2022

Revisiting the [C II]$_{158 μ\text{m}}$ line-intensity mapping power spectrum from the EoR using non-uniform line-luminosity scatter

Detecting the line-intensity mapping (LIM) signal from the galaxies of the Epoch of Reionization is an emerging tool to constrain their role in reionization. Ongoing and upcoming experiments target the signal fluctuations across the sky to reveal statistical and astrophysical properties of these galaxies via signal statistics, e.g., the power spectrum. Here, we revisit the [C II]$_{158 μ\text{m}}$ LIM power spectrum under non-uniform line-luminosity scatter, which has a halo-mass variation of statistical properties. Line-luminosity scatter from a cosmological hydrodynamic and radiative transfer simulation of galaxies at $z=6$ is considered in this study. We test the robustness of different model frameworks that interpret the impact of the line-luminosity scatter on the signal statistics. We use a simple power-law model to fit the scatter and demonstrate that the mean luminosity-halo mass correlation fit cannot preserve the mean intensity of the LIM signal (hence the clustering power spectrum) under non-uniform scatter. In our case, the mean intensity changes by $\sim 48$ per cent compared to the mean correlation fit in contrast to the general case with semi-analytic scatter. However, we find that the prediction for the mean intensity from the most-probable fit can be modelled robustly, considering the generalized and more realistic non-uniform scatter. We also explore the possibility of diminishing luminosity bias under non-uniform scatter, affecting the clustering power spectrum, although this phenomenon might not be statistically significant. Therefore, we should adopt appropriate approaches that can consistently interpret the LIM power spectrum from observations.

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arXiv2022

The Dwarf Galaxy Population at $z\sim 0.7$: A Catalog of Emission Lines and Redshifts from Deep Keck Observations

We present a catalog of spectroscopically measured redshifts over $0 < z < 2$ and emission line fluxes for 1440 galaxies. The majority ($\sim$65\%) of the galaxies come from the HALO7D survey, with the remainder from the DEEPwinds program. This catalog includes redshifts for 646 dwarf galaxies with $\log(M_{\star}/M_{\odot}) < 9.5$. 810 catalog galaxies did not have previously published spectroscopic redshifts, including 454 dwarf galaxies. HALO7D used the DEIMOS spectrograph on the Keck II telescope to take very deep (up to 32 hours exposure, with a median of $\sim$7 hours) optical spectroscopy in the COSMOS, EGS, GOODS-North, and GOODS-South CANDELS fields, and in some areas outside CANDELS. We compare our redshift results to existing spectroscopic and photometric redshifts in these fields, finding only a 1\% rate of discrepancy with other spectroscopic redshifts. We measure a small increase in median photometric redshift error (from 1.0\% to 1.3\%) and catastrophic outlier rate (from 3.5\% to 8\%) with decreasing stellar mass. We obtained successful redshift fits for 75\% of massive galaxies, and demonstrate a similar 70-75\% successful redshift measurement rate in $8.5 < \log(M_{\star}/M_{\odot}) < 9.5$ galaxies, suggesting similar survey sensitivity in this low-mass range. We describe the redshift, mass, and color-magnitude distributions of the catalog galaxies, finding HALO7D galaxies representative of CANDELS galaxies up to \textit{i}-band magnitudes of 25. The catalogs presented will enable studies of star formation (SF), the mass-metallicity relation, SF-morphology relations, and other properties of the $z\sim0.7$ dwarf galaxy population.

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arXiv2022

The black hole population in low-mass galaxies in large-scale cosmological simulations

Recent systematic searches for massive black holes (BHs) in local dwarf galaxies led to the discovery of a population of faint Active Galactic Nuclei (AGN). We investigate the agreement of the BH and AGN populations in the Illustris, TNG, Horizon-AGN, EAGLE, and SIMBA simulations with current observational constraints in low-mass galaxies. We find that some of these simulations produce BHs that are too massive, and that the BH occupation fraction at z=0 is not inherited from the simulation seeding modeling. The ability of BHs and their host galaxies to power an AGN depends on BH and galaxy subgrid modeling. The fraction of AGN in low-mass galaxies is not used to calibrate the simulations, and thus can be used to differentiate galaxy formation models. AGN fractions at z=0 span two orders of magnitude at fixed galaxy stellar mass in simulations, similarly to observational constraints, but uncertainties and degeneracies affect both observations and simulations. The agreement is difficult to interpret due to differences in the masses of simulated and observed BHs, BH occupation fraction affected by numerical choices, and an unknown fraction of obscured AGN. Our work advocates for more thorough comparisons with observations to improve the modeling of cosmological simulations, and our understanding of BH and galaxy physics in the low-mass regime. The mass of BHs, their ability to efficiently accrete gas, and the AGN fraction in low-mass galaxies have important implications for the build-up of the entire BH and galaxy populations with time.

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arXiv2022

\textsc{The Three Hundred} project: The \textsc{Gizmo-Simba} run

We introduce \textsc{Gizmo-Simba}, a new suite of galaxy cluster simulations within \textsc{The Three Hundred} project. \textsc{The Three Hundred} consists of zoom re-simulations of 324 clusters with $M_{200}\gtrsim 10^{14.8}M_\odot$ drawn from the MultiDark-Planck $N$-body simulation, run using several hydrodynamic and semi-analytic codes. The \textsc{Gizmo-Simba} suite adds a state-of-the-art galaxy formation model based on the highly successful {\sc Simba} simulation, mildly re-calibrated to match $z=0$ cluster stellar properties. Comparing to \textsc{The Three Hundred} zooms run with \textsc{Gadget-X}, we find intrinsic differences in the evolution of the stellar and gas mass fractions, BCG ages, and galaxy colour-magnitude diagrams, with \textsc{Gizmo-Simba} generally providing a good match to available data at $z \approx 0$. \textsc{Gizmo-Simba}'s unique black hole growth and feedback model yields agreement with the observed BH scaling relations at the intermediate-mass range and predicts a slightly different slope at high masses where few observations currently lie. \textsc{Gizmo-Simba} provides a new and novel platform to elucidate the co-evolution of galaxies, gas, and black holes within the densest cosmic environments.

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arXiv2022

Rapidly quenched galaxies in the Simba cosmological simulation and observations

A wide range of mechanisms have been put forward to explain the quenching of star formation in galaxies with cosmic time, however, the true balance of responsible mechanisms remains unknown. The identification and study of galaxies that have shut down their star formation on different timescales might elucidate which mechanisms dominate at different epochs and masses. Here we study the population of rapidly quenched galaxies (RQGs) in the SIMBA cosmological hydrodynamic simulation at $0.5<z<2$, comparing directly to observational post-starburst galaxies in the UKIDSS Ultra Deep Survey via their colour distributions and mass functions. We find that the fraction of quiescent galaxies that are rapidly quenched in SIMBA is 59% (or 48% in terms of stellar mass), which is higher than observed. A similar "downsizing" of RQGs is observed in both SIMBA and the UDS, with RQGs at higher redshift having a higher average mass. However, SIMBA produces too many RQGs at $1<z_q<1.5$ and too few low mass RQGs at $0.5<z_q<1$. The precise colour distribution of SIMBA galaxies compared to the observations also indicates various inconsistencies in star formation and chemical enrichment histories, including an absence of short, intense starbursts. Our results will help inform the next generation of galaxy evolution models, particularly with respect to the quenching mechanisms employed.

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arXiv2022

How Well Can We Measure Galaxy Dust Attenuation Curves? The Impact of the Assumed Star-Dust Geometry Model in SED Fitting

One of the most common methods for inferring galaxy attenuation curves is via spectral energy distribution (SED) modeling, where the dust attenuation properties are modeled simultaneously with other galaxy physical properties. In this paper, we assess the ability of SED modeling to infer these dust attenuation curves from broadband photometry, and suggest a new flexible model that greatly improves the accuracy of attenuation curve derivations. To do this, we fit mock SEDs generated from the Simba cosmological simulation with the Prospector SED fitting code. We consider the impact of the commonly-assumed uniform screen model and introduce a new non-uniform screen model parameterized by the fraction of unobscured stellar light. This non-uniform screen model allows for a non-zero fraction of stellar light to remain unattenuated, resulting in a more flexible attenuation curve shape by decoupling the shape of the UV attenuation curve from the optical attenuation curve. The ability to constrain the dust attenuation curve is significantly improved with the use of a non-uniform screen model, with the median offset in UV attenuation decreasing from $-0.30$ dex with a uniform screen model to $-0.17$ dex with the non-uniform screen model. With this increase in dust attenuation modeling accuracy, we also improve the star formation rates (SFRs) inferred with the non-uniform screen model, decreasing the SFR offset on average by $0.12$ dex. We discuss the efficacy of this new model, focusing on caveats with modeling star-dust geometries and the constraining power of available SED observations.

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arXiv2022

Co-evolution of massive black holes and their host galaxies at high redshift: discrepancies from six cosmological simulations and the key role of JWST

The James Webb Space Telescope will have the power to characterize high-redshift quasars at z>6 with an unprecedented depth and spatial resolution. While the brightest quasars at such redshift (i.e., with bolometric luminosity L_bol> 10^46 erg/s) provide us with key information on the most extreme objects in the Universe, measuring the black hole (BH) mass and Eddington ratios of fainter quasars with L_bol= 10^45-10^46 erg/s opens a path to understand the build-up of more normal BHs at z>6. In this paper, we show that the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA large-scale cosmological simulations do not agree on whether BHs at z>4 are overmassive or undermassive at fixed galaxy stellar mass with respect to the M_BH-M_star scaling relation at z=0 (BH mass offsets). Our conclusions are unchanged when using the local scaling relation produced by each simulation or empirical relations. We find that the BH mass offsets of the simulated faint quasar population at z>4, unlike those of bright quasars, represent the BH mass offsets of the entire BH population, for all the simulations. Thus, a population of faint quasars with L_bol= 10^45-10^46 erg/s observed by JWST can provide key constraints on the assembly of BHs at high redshift. Moreover, this will help constraining the high-redshift regime of cosmological simulations, including BH seeding, early growth, and co-evolution with the host galaxies. Our results also motivate the need for simulations of larger cosmological volumes down to z=6, with the same diversity of sub-grid physics, in order to gain statistics on the most extreme objects at high redshift.

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arXiv2022

The Hydrogen Intensity and Real-time Analysis eXperiment: 256-Element Array Status and Overview

The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a radio interferometer array currently in development, with an initial 256-element array to be deployed at the South African Radio Astronomy Observatory (SARAO) Square Kilometer Array (SKA) site in South Africa. Each of the 6m, $f/0.23$ dishes will be instrumented with dual-polarisation feeds operating over a frequency range of 400-800 MHz. Through intensity mapping of the 21 cm emission line of neutral hydrogen, HIRAX will provide a cosmological survey of the distribution of large-scale structure over the redshift range of $0.775 < z < 2.55$ over $\sim$15,000 square degrees of the southern sky. The statistical power of such a survey is sufficient to produce $\sim$7 percent constraints on the dark energy equation of state parameter when combined with measurements from the Planck satellite. Additionally, HIRAX will provide a highly competitive platform for radio transient and HI absorber science while enabling a multitude of cross-correlation studies. In this paper, we describe the science goals of the experiment, overview of the design and status of the sub-components of the telescope system, and describe the expected performance of the initial 256-element array as well as the planned future expansion to the final, 1024-element array.

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arXiv2022

The Circumgalactic Medium from the CAMELS Simulations: Forecasting Constraints on Feedback Processes from Future Sunyaev-Zeldovich Observations

The cycle of baryons through the circumgalactic medium (CGM) is important to understand in the context of galaxy formation and evolution. In this study we forecast constraints on the feedback processes heating the CGM with current and future Sunyaev-Zeldovich (SZ) observations. To constrain these processes, we use a suite of cosmological simulations, the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS), that varies four different feedback parameters of two previously existing hydrodynamical simulations, IllustrisTNG and SIMBA. We capture the dependencies of SZ radial profiles on these feedback parameters with an emulator, calculate their derivatives, and forecast future constraints on these feedback parameters from upcoming experiments. We find that for a DESI-like (Dark Energy Spectroscopic Instrument) galaxy sample observed by the Simons Observatory all four feedback parameters are able to be constrained (some within the $10\%$ level), indicating that future observations will be able to further restrict the parameter space for these sub-grid models. Given the modeled galaxy sample and forecasted errors in this work, we find that the inner SZ profiles contribute more to the constraining power than the outer profiles. Finally, we find that, despite the wide range of AGN feedback parameter variation in the CAMELS simulation suite, we cannot reproduce the tSZ signal of galaxies selected by the Baryon Oscillation Spectroscopic Survey as measured by the Atacama Cosmology Telescope.

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arXiv2022

The CAMELS project: public data release

The Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project was developed to combine cosmology with astrophysics through thousands of cosmological hydrodynamic simulations and machine learning. CAMELS contains 4,233 cosmological simulations, 2,049 N-body and 2,184 state-of-the-art hydrodynamic simulations that sample a vast volume in parameter space. In this paper we present the CAMELS public data release, describing the characteristics of the CAMELS simulations and a variety of data products generated from them, including halo, subhalo, galaxy, and void catalogues, power spectra, bispectra, Lyman-$α$ spectra, probability distribution functions, halo radial profiles, and X-rays photon lists. We also release over one thousand catalogues that contain billions of galaxies from CAMELS-SAM: a large collection of N-body simulations that have been combined with the Santa Cruz Semi-Analytic Model. We release all the data, comprising more than 350 terabytes and containing 143,922 snapshots, millions of halos, galaxies and summary statistics. We provide further technical details on how to access, download, read, and process the data at \url{https://camels.readthedocs.io}.

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arXiv2021

The Three Hundred: Cluster Dynamical States and Relaxation Time Scale

Using the galaxy clusters from The Three Hundred Project, we define a new parameter: $λ_{DS}$ to describe the dynamical state of clusters, which assumes a double-Gaussian distribution in logarithm scale for our mass-complete cluster sample at $z=0$ from the dark-matter-only (DMO) run. Therefore, the threshold for distinguishing relaxed and unrelaxed clusters is naturally determined by the crossing point of the double-Gaussian fitting which has a value of $λ_{DS} = 3.424$. By applying $λ_{DS}$ with the same parameters from the DMO run to the hydro-dynamically simulated clusters (Gadget-X run and GIZMO-SIMBA run), we investigate the effect of baryons on the cluster dynamical state. We find a weak baryon-model dependence for the $λ_{DS}$ parameter. Finally, we study the evolution of $λ_{DS}$ along with clusters mass accretion history. We notice an upper limit of halo mass change $\frac{ΔM_{200}}{M_{200}} \sim 0.12$ that don't alter the cluster dynamical state, i.e. from relaxed to unrelaxed. We define relaxation period (from the most relaxed state to disturb and relaxed again) which reflects how long the dynamical state of a cluster restores its relaxation state, and propose a correlation between this relaxation period and the strength of halo mass change $\frac{ΔM_{200}}{M_{200}}$. With the proposed fitting to such correlation, we verify the relaxation period can be estimated from $\frac{ΔM_{200}}{M_{200}}$ (including multi mass change peaks) with considerably small error.

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