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At least 451 records · Page 25

Properties of the Prompt Optical Counterpart Arising from the Cooling of Electrons in Gamma-Ray Bursts

This work extends a contemporaneous effort to study the properties of the lower-energy counterpart synchrotron emission produced by the cooling of relativistic gamma-ray burst (GRB) electrons through radiation (synchrotron and self-Compton) emission and adiabatic losses. We derive the major characteristics (pulse duration, lag time after burst, and brightness relative to the burst) of the prompt optical counterpart (POC) occurring during or after the GRB. Depending on the magnetic field lifetime, duration of electron injection, and electron transit time Δt o from hard X-ray (GRB) to optical-emitting energies, a POC may appear during the GRB pulse (of duration δt γ ) or after (delayed OC). The signature of counterparts arising from the cooling of GRB electrons is that POC pulses (Δto < δtγ) last as long as the corresponding GRB pulse (δt o ≃ δt γ ), while delayed OC pulses (Δt o > δt γ ) last as long as the transit time (δt o ≃ Δt o ). If OC variability can be measured, then another signature for this OC mechanism is that the GRB variability is passed on to POCs but not to delayed OCs. Within the GRB electron cooling model for counterparts, POCs should be on average dimmer than delayed ones (consistent with the data), and harder GRB low-energy slopes β LE should be associated more often with the dimmer POCs. The latter sets an observational bias against detecting POCs from (the cooling of electrons in) GRBs with a hard slope β LE , making it more likely that the detected POCs of such bursts arise from another mechanism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Redshift Evolution of the Feedback–Cooling Equilibrium in the Core of 48 SPT Galaxy Clusters: A Joint Chandra–SPT–ATCA Analysis

We analyze the cooling and feedback properties of 48 galaxy clusters at redshifts 0.4 < z < 1.3 selected from the South Pole Telescope (SPT) catalogs to evolve like the progenitors of massive and well-studied systems at z ~ 0. We estimate the radio power at the brightest cluster galaxy (BCG) location of each cluster from an analysis of Australia Telescope Compact Array data. Assuming that the scaling relation between the radio power and active galactic nucleus (AGN) cavity power P cav observed at low redshift does not evolve with redshift, we use these measurements in order to estimate the expected AGN cavity power in the core of each system. We estimate the X-ray luminosity within the cooling radius L cool of each cluster from a joint analysis of the available Chandra X-ray and SPT Sunyaev–Zel'dovich (SZ) data. This allows us to characterize the redshift evolution of the P cav /L cool ratio. When combined with low-redshift results, these constraints enable investigations of the properties of the feedback–cooling cycle across 9 Gyr of cluster growth. We model the redshift evolution of this ratio measured for cool-core clusters by a log-normal distribution Log-N (α + βz, σ 2 ) and constrain the slope of the mean evolution to β = -0.05 ± 0.47. This analysis improves the constraints on the slope of this relation by a factor of two. We find no evidence of redshift evolution of the feedback–cooling equilibrium in these clusters, which suggests that the onset of radio-mode feedback took place at an early stage of cluster formation. High values of P cav /L cool are found at the BCG location of noncool-core clusters, which might suggest that the timescales of the AGN feedback cycle and the cool core–noncool core transition are different. This work demonstrates that the joint analysis of radio, SZ, and X-ray data solidifies the investigation of AGN feedback at high redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

K2 Optical Emission from OJ 287 and Other γ-Ray Blazars on Hours-to-weeks Timescales from 2014 to 2018

We present second observations by K2 of OJ 287 and seven other γ-ray active galactic nuclei (AGNs) obtained in 2017–2018, second and third observations of the lobe-dominated, steep-spectrum quasar 3C 207, and observations of nine additional blazars not previously observed with K2. The AGNs were observed simultaneously with K2 and the Fermi Large Area Telescope for 51–81 days. Our full sample, observed in 2014–2018, contained 16 BL Lacertae objects (BL Lacs), nine flat-spectrum radio quasars (FSRQs), and four other γ-ray AGNs. Twelve BL Lacs and seven FSRQs exhibited fast, jagged light curves, while four BL Lacs and two FSRQs had slow, smooth light curves. Some objects changed their red-noise character significantly between repeated K2 observations. The optical characteristics of OJ 287 derived from the short-cadence K2 light curves changed between observations made before and after the predicted passage of the suspected secondary supermassive black hole through the accretion disk of the primary supermassive black hole. The average slopes of the periodogram power spectral densities of the BL Lacs' and FSRQs' light curves differed significantly, by ≈12%, with the BL Lac slopes being steeper, and a Kolmogorov–Smirnov test with a p-value of 0.039 indicates that these samples probably come from different populations; however, this result is not as strongly supported by power spectral response (PSRESP) analyses. Differences in the origin of the jets from the ergosphere or accretion disk in these two classes could produce such a disparity, as could different sizes or locations of emission regions within the jets.

79 ASTRONOMY AND ASTROPHYSICS↗

Striped Jets in Post–Neutron Star Merger Systems

Abstract Models invoking magnetic reconnection as the particle acceleration mechanism within relativistic jets often adopt a gradual energy dissipation profile within the jet. However, such a profile has yet to be reproduced in first-principles simulations. Here we perform a suite of 3D general relativistic magnetohydrodynamic simulations of post–neutron star merger disks with an initially purely toroidal magnetic field. We explore the variations in both the microphysics (e.g., nuclear recombination, neutrino emission) and system parameters (e.g, disk mass). In all of our simulations, we find the formation of magnetically striped jets. The stripes result from the reversals in the poloidal magnetic flux polarity generated in the accretion disk. The simulations display large variations in the distributions of stripe duration, τ , and power, 〈 P Φ 〉. We find that more massive disks produce more powerful stripes, the most powerful of which reaches 〈 P Φ 〉 ∼ 10 49 erg s −1 at τ ∼ 20 ms. The power and variability that result from the magnetic reconnection of the stripes agree with those inferred in short-duration gamma-ray bursts. We find that the dissipation profile of the cumulative energy is roughly a power law in both radial distance, z , and τ , with a slope in the range of ∼1.7–3; more massive disks display larger slopes.

79 ASTRONOMY AND ASTROPHYSICS↗

New Covariant Density Functionals of Nuclear Matter for Compact Star Simulations

We generate three families of extended covariant density functionals of nuclear matter that have varying slope of symmetry energy and skewness at nuclear saturation density, but otherwise share the same basic parameters (symmetry energy, compressibility, saturation parameters, etc.) with the standard DDME2, DD2, and MPE functionals. Tables of the parameters of these new density functionals are given, which can be straightforwardly used in DDME2, DD2, and MPE parameterization-based codes. Furthermore, we provide tables of a large number of equations of state (81 for each family) that can be used in astrophysical simulations to assess the impact of variations of the not-well-known slope of symmetry energy and skewness of nuclear systems on the astrophysics of compact objects. We also provide tables of computed integral parameters (mass, radius, and tidal deformability) that can be used, e.g., for modeling gravitational waveforms. Finally, for the extended DDME2-based parameterization, we implement a first-order phase transition to quark matter to obtain a family of equations of state that accommodates a phase transition to quark matter. Analogous tables of the equations of state and integral parameters are provided for this case as well.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck Dust Polarization Power Spectra Are Consistent with Strongly Supersonic Turbulence

Abstract The polarization of the cosmic microwave background is rich in information but obscured by foreground emission from the Milky Way’s interstellar medium (ISM). To uncover relationships between the underlying turbulent ISM and the foreground power spectra, we simulated a suite of driven, magnetized, turbulent models of the ISM, varying the fluid properties via the sonic Mach number, M S , and magnetic (Alfvén) Mach number, M A . We measure the power spectra of density ( ρ ), velocity ( v ), magnetic field ( H ), total projected intensity ( T ), parity-even polarization ( E ), and parity-odd polarization ( B ). We find that the slopes of all six quantities increase with M S . Most increase with M A , while the magnetic field spectrum steepens with M A . By comparing spectral slopes of E and B to those measured by Planck, we infer typical values of M S and M A for the ISM. As the fluid velocity increases, M S > 4 , the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of ∼0.5, regardless of the magnetic field strength. We also examine correlation coefficients between projected quantities, and find that r TE ≈ 0.3, in agreement with Planck, for appropriate combinations of M S and M A . Finally, we consider parity-violating correlations r TB and r EB .

Astronomy & Astrophysics↗

Modeling the Far-infrared Polarization Spectrum of a High-mass Star-forming Cloud

The polarization spectrum, or wavelength dependence of the polarization fraction, of interstellar dust emission provides important insights into the grain alignment mechanism of interstellar dust grains. We investigate the far-infrared polarization spectrum of a realistic simulated high-mass star-forming cloud under various models of grain alignment and emission. We find that neither a homogeneous grain alignment model nor a grain alignment model that includes collisional dealignment is able to produce the falling spectrum seen in observations. On the other hand, we find that a grain alignment model with grain alignment efficiency dependent on local temperature is capable of producing a falling spectrum that is in qualitative agreement with observations of OMC-1. For the model most in agreement with OMC-1, we find no correlation between the temperature and the slope of the polarization spectrum. However, we do find a positive correlation between the column density and the slope of the polarization spectrum. We suggest this latter correlation to be the result of wavelength-dependent polarization by absorption.

79 ASTRONOMY AND ASTROPHYSICS↗

A Measurement of Atmospheric Circular Polarization with POLARBEAR

At millimeter wavelengths, the atmospheric emission is circularly polarized owing to the Zeeman splitting of molecular oxygen by the Earth's magnetic field. We report a measurement of the signal in the 150 GHz band using 3 yr of observational data with the POLARBEAR project. Nonidealities of a continuously rotating half-wave plate (HWP) partially convert circularly polarized light to linearly polarized light. While POLARBEAR detectors are sensitive to linear polarization, this effect makes them sensitive to circular polarization. Although this was not the intended use, we utilized this conversion to measure circular polarization. We reconstruct the azimuthal gradient of the circular polarization signal and measure its dependency from the scanning direction and the detector bandpass. We compare the signal with a simulation based on atmospheric emission theory, the detector bandpass, and the HWP leakage spectrum model. We find the ratio of the observed azimuthal slope to the simulated slope is 0.92 ± 0.01(stat) ± 0.07(sys). This ratio corresponds to a brightness temperature of 3.8 mK at the effective band center of 121.8 GHz and bandwidth of 3.5 GHz estimated from representative detector bandpass and the spectrum of Zeeman emission. This result validates our understanding of the instrument and reinforces the feasibility of measuring the circular polarization using the imperfection of continuously rotating HWP. Continuously rotating HWP is popular in ongoing and future cosmic microwave background experiments to modulate the polarized signal. This work shows a method for signal extraction and leakage subtraction that can help measure circular polarization in such experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Luminosity and Stellar Mass Functions of Faint Photometric Satellites around Spectroscopic Central Galaxies from DESI Year-1 Bright Galaxy Survey

We measure the luminosity functions (LFs) and stellar mass functions (SMFs) of photometric satellite galaxies around spectroscopically identified isolated central galaxies (ICGs). The photometric satellites are from the DESI Legacy Imaging Surveys (DR9), while the spectroscopic ICGs are selected from the DESI Year-1 BGS sample. We can measure satellite LFs down to r-band absolute magnitudes of M r,sat ∼ −7, around ICGs as small as 7.1 < log 10 M *,ICG /M ⊙ < 7.8, with the stellar mass of ICGs measured by the DESI Fastspecfit pipeline. The satellite SMF can be measured down to log 10 M *,sat /M ⊙ ~ 5.5. Interestingly, we discover that the faint/low-mass end slopes of satellite LFs/SMFs become steeper with the decrease in the stellar masses of host ICGs, with smaller and nearby host ICGs capable of being used to probe their fainter satellites. The steepest slopes can be −2.298 ± 0.656 and −2.888 ± 0.916 for satellite LF and SMF, respectively. Detailed comparisons are performed between the satellite LFs around ICGs selected from DESI BGS or from the SDSS NYU-VAGC spectroscopic Main galaxies over 7.1 < log 10 M *,ICG /M ⊙ < 11.7, showing reasonable agreement, but we show that differences between DESI and SDSS stellar masses for ICGs play a role to affect the results. We also compare measurements based on DESI Fastspecfit and Cigale stellar masses used to bin ICGs, with the latter including the modeling of active galactic nuclei based on Wide-field Infrared Survey Explorer photometry, and we find good agreements in the measured satellite LFs by using either of the DESI stellar mass catalogs.

79 ASTRONOMY AND ASTROPHYSICS↗

The Dark Matter Content of Milky Way Dwarf Spheroidal Galaxies: Draco, Sextans, and Ursa Minor

The Milky Way Survey of the Dark Energy Spectroscopic Instrument (DESI) has so far observed three classical dwarf spheroidal galaxies (dSphs): Draco, Sextans, and Ursa Minor. Based on the observed line-of-sight velocities and metallicities of their member stars, we apply the axisymmetric Jeans Anisotropic Multi-Gaussian Expansion modeling (JAM) approach to recover their inner dark matter distributions. In particular, both the traditional single-population Jeans model and the multiple population chemodynamical model are adopted. With the chemodynamical model, we divide member stars of each dSph into metal-rich and metal-poor populations. The metal-rich populations are more centrally concentrated and dynamically colder, featuring lower velocity dispersion profiles than the metal-poor populations. We find a diversity of the inner density slopes γ of dark matter halos, with the best constraints by the single-population or chemodynamical models consistent with each other. The inner density slopes are $0.7{1}_{-0.35}^{+0.34}$, $0.2{6}_{-0.12}^{+0.22}$, and $0.3{3}_{-0.16}^{+0.20}$ for Draco, Sextans, and Ursa Minor, respectively. We also present the measured astrophysical J and D factors of the three dSphs. Our results indicate that the study of the dark matter content of dSphs through stellar kinematics is still subject to uncertainties behind both the methodology and the observed data, through comparisons with previous measurements and datasets.

Dark matter↗

Gauging the Impact of Cosmic-ray Feedback on the Stellar Initial Mass Function

Cosmic rays (CRs) drive ionization and influence gas dynamics in molecular clouds (MCs), potentially impacting the resulting star formation outcomes. Although previous simulations of individual star formation have included methods for CR transport (CRT), none have been large enough to resolve the stellar initial mass function (IMF). We conduct numerical simulations following the collapse of a 20,000 M ⊙ MC and the subsequent star formation including CRT, both with and without CRs accelerated by winds from the young massive stars, and compare against a non-CRT simulation. We show that after the first massive stars form, the cavity produced by feedback is more pronounced in the CRT simulations because the external CRs are able to propagate inward and compress the gas into higher-density structures. This increases the subsequent star formation in the cloud; by the end of the simulation, the star formation efficiency (SFE) in the CRT simulation including stellar wind CRs is 43% higher than the non-CRT simulation. The IMF is also top-heavy in comparison, with a slope above 1 M ⊙ that is shallower by ∼20%. These effects are also present in the simulation without wind-accelerated CRs, but they are not as pronounced; the SFE is only 16% higher than the non-CRT simulation, and the IMF high-mass slope is shallower by ∼10%. These results may explain some of the observed top-heavy IMFs, which typically occur in high-CR environments such as the Galactic center.

Fitz Axen, Margot [Oak Ridge National Laboratory (↗

thornado-hydro: A Discontinuous Galerkin Method for Supernova Hydrodynamics with Nuclear Equations of State

This paper describes algorithms for non-relativistic hydrodynamics in the toolkit for high-order neutrino radiation hydrodynamics (thornado), which is being developed for multiphysics simulations of core-collapse supernovae (CCSNe) and related problems with Runge–Kutta discontinuous Galerkin (RKDG) methods. More specifically, thornado employs a spectral type nodal collocation approximation, and we have extended limiters — a slope limiter to prevent non-physical oscillations and a bound-enforcing limiter to prevent non-physical states — from the standard RKDG framework to be able to accommodate a tabulated nuclear equation of state (EoS). To demonstrate the efficacy of the algorithms with a nuclear EoS, we first present numerical results from basic test problems in idealized settings in one and two spatial dimensions, employing Cartesian, spherical-polar, and cylindrical coordinates. Then, we apply the RKDG method to the problem of adiabatic collapse, shock formation, and shock propagation in spherical symmetry, initiated with a 15 M ⊙ progenitor. Herein, we find that the extended limiters improve the fidelity and robustness of the RKDG method in idealized settings. The bound-enforcing limiter improves robustness of the RKDG method in the adiabatic collapse application, while we find that slope limiting in characteristic fields is vulnerable to structures in the EoS — more specifically, in the phase transition from nuclei and nucleons to bulk nuclear matter. The success of these applications marks an important step toward applying RKDG methods to more realistic CCSN simulations with thornado in the future.

Nuclear astrophysics (1129)↗

Hard Synchrotron Spectra from Magnetically Dominated Plasma Turbulence

Synchrotron emission from astrophysical nonthermal sources usually assumes that the emitting particles are isotropic. By means of large-scale two- and three-dimensional particle-in-cell simulations, we demonstrate that the dissipation of magnetically dominated (${\sigma }_{0}\gg 1$) turbulence in pair plasmas leads to strongly anisotropic particle distributions. At Lorentz factors $\sim {\sigma }_{0}{\gamma }_{\mathrm{th}0}$ (here, ${\gamma }_{\mathrm{th}0}$ is the initial Lorentz factor), the particle velocity is preferentially aligned with the local magnetic field; instead, the highest energy particles are preferentially oriented in the plane perpendicular to the field. This energy-dependent anisotropy leads to a synchrotron spectral flux $\nu {F}_{\nu }\propto {\nu }^{s}$ that is much harder than for isotropic particles. Remarkably, for ${\sigma }_{0}\gg 1$ we find that the angle-integrated spectral slope in the slow cooling regime is $s\sim 0.5-0.7$ for a wide range of turbulence fluctuations, $0.25\lesssim \delta {B}_{\mathrm{rms}0}^{2}/{B}_{0}^{2}\lesssim 4$, despite significant variations in the power-law energy spectrum of nonthermal particles. This is because weaker turbulence levels imprint a stronger degree of anisotropy, thereby counteracting the effect of the steeper particle spectrum. The synchrotron spectral slope may be even harder, $s\gtrsim 0.7$, if the observer is in the plane perpendicular to the mean magnetic field. Our results are independent of domain size and dimensionality. Further, our findings may help explain the origin of hard synchrotron spectra of astrophysical nonthermal sources, most notably the radio spectrum of pulsar wind nebulae.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the Jet–Ejecta Interaction in 3D GRMHD Simulations of a Binary Neutron Star Merger Aftermath

Short γ-ray burst (sGRB) jets form in the aftermath of a neutron star merger, drill through disk winds and dynamical ejecta, and extend over four to five orders of magnitude in distance before breaking out of the ejecta. We present the first 3D general-relativistic magnetohydrodynamic sGRB simulations to span this enormous scale separation. They feature three possible outcomes: jet+cocoon, cocoon, and neither. Typical sGRB jets break out of the dynamical ejecta if (i) the bound ejecta's isotropic equivalent mass along the pole at the time of the BH formation is ≲10 -4 M ⊙ , setting a limit on the delay time between the merger and BH formation, otherwise, the jets perish inside the ejecta and leave the jet-inflated cocoon to power a low-luminosity sGRB; (ii) the postmerger remnant disk contains a strong large-scale vertical magnetic field, ≳1015 G; and (iii) if the jets are weak (≲10 50 erg), the ejecta's isotropic equivalent mass along the pole must be small (≲10 -2 M ⊙ ). Generally, the jet structure is shaped by the early interaction with disk winds rather than the dynamical ejecta. As long as our jets break out of the ejecta, they retain a significant magnetization (≲1), suggesting that magnetic reconnection is a fundamental property of sGRB emission. The angular structure of the outflow isotropic equivalent energy after breakout consistently features a flat core followed by a steep power-law distribution (slope ≳3), similar to hydrodynamic jets. In the cocoon-only outcome, the dynamical ejecta broadens the outflow angular distribution and flattens it (slope ~1.5).

Jets↗

SQUID Readout of a High-$Q$ Superconducting $LC$ Resonator

We demonstrate the readout of a superconducting $LC$ resonator, with $Q \approx 2 \times 10^{6}$ at approximately 250 kHz, using a dc SQUID followed by a SQUID series-array amplifier readout chain. We find that $Q$ depends on the SQUID flux-bias point, increasing near the shallow-slope point of the SQUID modulation curve and decreasing near the steep-slope point, consistent with the previously observed SQUID damping effects. From this variation, we infer the SQUID effective input impedance. We further infer the effective temperature of the resonator circuit from the resonance peak in the noise spectrum and show that it also depends on the SQUID flux-bias point, suggesting a possible contribution from SQUID back-action noise. This system provides a working prototype for future experiments based on lumped-element resonators with SQUID readout, in particular low-mass axion searches within the DMRadio program.

FOS: Physical sciences↗

Where does the dust deposited over the Sierra Nevada snow come from?

Abstract. Mineral dust contributes up to one-half of surface aerosol loading in spring over the southwestern United States, posing an environmental challenge that threatens human health and the ecosystem. Using self-organizing map (SOM) analysis with dust deposition and flux data from WRF-Chem and Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), we identify four typical dust transport patterns across the Sierra Nevada, associated with the mesoscale winds, Sierra barrier jet (SBJ), North Pacific High (NPH), and long-range cross-Pacific westerlies, respectively. We find that dust emitted from the Central Valley is persistently transported eastward, while dust from the Mojave Desert and Great Basin influences the Sierra Nevada during mesoscale transport occurring mostly in winter and early spring. Asian dust reaching the mountain range comes either from the west through straight isobars (cross-Pacific transport) or from the north in the presence of the NPH. Extensive dust depositions are found on the west slope of the mountain, contributed by Central Valley emissions and cross-Pacific remote transport. In particular, the SBJ-related transport produces deposition through landfalling atmospheric rivers, whose frequency might increase in a warming climate.

Huang, Huilin (ORCID:0000000273286738)↗

pH dependence of brown-carbon optical properties in cloud water

Abstract. Light-absorbing organic species present in aerosols, collectively called brown carbon (BrC), have important but highly uncertain effects on climate. Clouds likely represent a significant medium for secondary BrC production and for bleaching reactions, though the relative importance of the formation and loss processes in clouds is unknown at present. The acidity (or pH) of atmospheric particles and clouds affects the optical properties of BrC and bleaching rates. Given the wide variability of pH in the atmosphere (pH in particles and clouds ranges from −1 to 8), the optical properties of BrC and its bleaching behavior are expected to vary significantly, and the link between pH and BrC is yet another uncertainty in attempts to constrain its climate forcing effects. In this work, we characterize the pH dependence of BrC optical properties – including light absorption at 365 nm (Abs365), the mass absorption coefficient (MAC365), and the absorption Ångström exponent (AAE) – in bulk cloud water sampled from the summit of Whiteface Mountain, NY. In all samples (n=17), Abs365 and MAC365 increased linearly with increasing pH, highlighting the importance of reporting pH in studies of BrC in aqueous media. There was strong variability in the sensitivity of Abs365 to pH, with normalized slopes that ranged from 5.1 % to 17.2 % per pH unit. The normalized slope decreased strongly with increasing cloud water [K+], suggesting that the non-biomass-burning BrC has optical properties that are more sensitive to pH than BrC associated with biomass burning. AAE also showed a distinct pH dependence as it was relatively flat between pH 1.5–5 and then decreased significantly above pH 5. The cloud water composition was used to inform thermodynamic predictions of aerosol pH upwind and/or downwind of Whiteface Mountain and the subsequent changes in BrC optical properties. Overall, these results show that, in addition to secondary BrC production, photobleaching, and the altitudinal distribution, the climate forcing of BrC is quite strongly affected by its pH-dependent absorption.

54 ENVIRONMENTAL SCIENCES↗

Steady-state mixing state of black carbon aerosols from a particle-resolved model

Abstract. Black carbon (BC) exerts a notable warming effect due to its strong light absorption, largely influenced by its “mixing state”. However, due to computational constraints, the mixing state is challenging to accurately represent in large-scale models. In this study, we employ a particle-resolved model to simulate the evolution of BC mixing state based on field observation. Our result shows that aerosol compositions, coating thickness (CT) distribution, and optical properties of BC aerosols all exhibit a tendency toward a steady state with a characteristic timescale of less than 1 d, considerably shorter than the BC atmospheric lifetime. The rapid attainment of a steady state suggests that it is reasonable to disregard this pre-steady-state period and instead concentrate on the average properties of BC across extensive spatial and temporal scales. The distribution of CT follows an exponential linear distribution and can be characterized by a single slope parameter k. This distribution is independent of the BC core's distribution. In the model simulation, the mean CT, equivalent to the 1/k, is 62 nm, which is consistent with the statistical results indicating a mean CT of 63 nm. Utilizing the slope parameter k, which effectively characterizes the CT distribution under the steady-state simplifying assumption, the BC absorption enhancement closely corresponds to the results obtained via the particle-resolved method. This study simplifies the BC mixing state description and yields a precise evaluation of the BC optical properties, which has the potential utility for modeling efforts in the refinement of the assessment of BC's radiative effects.

Zhang, Zhouyang↗