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Clustering of noisy image data using an adaptive neuro-fuzzy system

Identification of outliers or noise in a real data set is often quite difficult. A recently developed adaptive fuzzy leader clustering (AFLC) algorithm has been modified to separate the outliers from real data sets while finding the clusters within the data sets. The capability of this modified AFLC algorithm to identify the outliers in a number of real data sets indicates the potential strength of this algorithm in correct classification of noisy real data.

Pemmaraju, Surya↗

Regional and Model-Specific Response Types in A Global Gridded Crop Model Ensemble

Crop models are often employed to project crop yields under changing conditions such as global warming and associated management change for adaptation. Multi-model ensembles are promoted to enhance the robustness of projections, but questions remain on what causes often large differences between projections of individual models. Global Gridded Crop Models (GGCMs) are especially exposed to this question when applied for assessing climate change impacts, adaptation, environmental impacts of agricultural production, because their results are used in downstream analyses, such as in integrated assessment or economic modeling for projecting future land-use change. Even though global gridded crop models are often based on detailed field-scale models or have implemented similar modeling principles in other ecosystem models, global-scale models are subject to substantial uncertainties from both model structure and parametrization as well as from calibration and input data quality. AgMIP’s Global Gridded Crop Model Intercomparison (GGCMI) has thus set out to intercompare GGCMs in order to evaluate model performance, describe model uncertainties, identify inconsistencies within the ensemble and underlying reasons, and to ultimately improve models and modeling capacities. In phase 2 of the GGCMI activities, 12 modeling groups followed a modeling protocol that asked for up to 1404 31-year global simulations at 0.5 arc-degree spatial resolution to assess models’ sensitivities to changes in carbon dioxide (C; 4 different levels) temperature (T; 7 different offset levels), water supply (W; 9 levels), and nitrogen (N; 3 levels), the so-called CTWN experiment (Franke et al. 2020; http://dx.doi.org/10.5194/gmd-13-2315-2020). We here present analyses of model response types using impact response surfaces along the C, T, W, and N dimensions, respectively and collectively. Doing so, we can understand differences in simulated responses per driver rather than aggregated changes in yields. We find that models’ sensitivities to the individual driver dimensions are substantially different and often more different across models than across regions. A cluster analysis finds regional and model-specific patterns. There is some agreement across models with respect to the spatial patterns of response types but strong differences in the distribution of response type clusters across models suggests that models need to undergo further scrutiny. We suggest establishing standards in model process evaluation not only against historical dynamics but also against dedicated experiments across the CTWN dimensions.

crop models↗

Galaxy Cluster Shapes and Systematic Errors in H_0 as Determined by the Sunyaev-Zel'dovich Effect

Imaging of the Sunyaev-Zeldovich (SZ) effect in galaxy clusters combined with cluster plasma x-ray diagnostics promises to measure the cosmic distance scale to high accuracy. However, projecting the inverse-Compton scattering and x-ray emission along the cluster line-of-sight will introduce systematic error's in the Hubble constant, H_0, because the true shape of the cluster is not known. In this paper we present a study of the systematic errors in the value of H_0, as determined by the x-ray and SZ properties of theoretical samples of triaxial isothermal "beta-model" clusters, caused by projection effects and observer orientation relative to the model clusters' principal axes. We calculate three estimates for H_0 for each cluster, based on their large and small apparent angular core radii, and their arithmetic mean. We average the estimates for H_0 for a sample of 25 clusters and find that the estimates have limited systematic error: the 99.7% confidence intervals for the mean estimated H_0 analyzing the clusters using either their large or mean angular core r;dius are within 14% of the "true" (assumed) value of H_0 (and enclose it), for a triaxial beta model cluster sample possessing a distribution of apparent x-ray cluster ellipticities consistent with that of observed x-ray clusters.

Sulkanen, Martin E.↗

A Giant Radio Halo in a Low-Mass Sz-selected Galaxy Cluster: ACT-CLJ0256.5+0006

We present the detection of a giant radio halo (GRH) in the Sunyaev-Zel'dovich (SZ)- selected merging galaxy cluster ACT-CL J0256.5+ 0006 (z = 0.363), observed with the Giant Metrewave Radio Telescope at 325 and 610 MHz. We find this cluster to host a faint (S610 = 5.6 +/- 1.4mJy) radio halo with an angular extent of 2.6 arcmin, corresponding to 0.8 Mpc at the cluster redshift, qualifying it as a GRH. J0256 is one of the lowest mass systems, M500, SZ = (5.0 +/- 1.2) × 10(exp14) M, found to host a GRH. We measure the GRH at lower significance at 325 MHz (S325 = 10.3 +/- 5.3mJy), obtaining a spectral index measurement of α610 325 = 1.0+ 0.7 − 0.9. This result is consistent with the mean spectral index of the population of typical radio haloes, alpha = 1.2 +/- 0.2. Adopting the latter value, we determine a 1.4 GHz radio power of P1.4 GHz = (1.0 +/- 0.3) × 10(exp 24)W/Hz, placing this cluster within the scatter of known scaling relations. Various lines of evidence, including the intracluster medium morphology, suggest that ACT-CL J0256.5+ 0006 is composed of two subclusters. We determine a merger mass ratio of 7:4, and a line-of-sight velocity difference of v⊥ = 1880 +/- 210 km/s. We construct a simple merger model to infer relevant time-scales in the merger. From its location on the P1.4GHz-LX scaling relation, we infer that we observe ACT-CL J0256.5+ 0006 just before first core crossing.

Knowles, Kendra↗

Discovery of intermediate redshift galaxy clusters in the ROSAT NEP field

We report preliminary results from a program to identify optical counterparts of ROSAT sources in the North Ecliptic Pole (NEP) region. The most striking X-ray feature reported by Hasinger et al. (1991) is an extended low surface brightness region of X-ray emission. Within the two X-ray contours of highest count rate we find a cluster of galaxies at a redshift of 0.09 and an early-type galaxy at a redshift of 0.03. X-ray emission from these objects may provide an explanation for the observed X-ray morphology. We also find evidence that other X-ray sources in this region are coincident with clusters or groups of galaxies at redshifts between 0.08 and 0.09. The presence of at least five X-ray detected clusters or groups in this narrow redshift band within a 1.5 deg radius field seems to indicate the existence of a moderate redshift supercluster. The existence of these clusters will have major implications for the study of large-scale structure through X-ray surveys such as ROSAT.

Burg, R.↗

A Giant Radio Halo in a Low-Mass SZ-Selected Galaxy Cluster: ACT-CL J0256.5+0006

We present the detection of a giant radio halo (GRH) in the Sunyaev-Zel'dovich (SZ)-selected merging galaxy cluster ACT-CL J0256.5+0006 (zeta = 0.363), observed with the Giant Metrewave Radio Telescope at 325 MHz and 610 MHz. We find this cluster to host a faint (S(sub 610) = 5.6 +/- 1.4 mJy) radio halo with an angular extent of 2.6 arcmin, corresponding to 0.8 Mpc at the cluster redshift, qualifying it as a GRH. J0256 is one of the lowest-mass systems, M(sub 500,SZ) = (5.0 +/- 1.2) x 10(sup14) solar mass foud to host a GRH. We measure the GRH at lower significance at 325 MHz (S(sub 325) = 10.3 +/- 5.3 mJy), obtaining a spectral index measurement of alpha sup 610 sub 325 = 1.0(sup +0.7)(sub 0.9). This result is consistent with the mean spectral index of the population of typical radio halos, alpha = 1.2 +/- 0.2. Adopting the latter value, we determine a 1.4 GHz radio power of P(sub 1.4GHz) = (1.0 +/- 03) x 10(sup 24) W Hz(sup -1), placing this cluster within the scatter of known scaling relations. Various lines of evidence, including the ICM morphology, suggest that ACT-CL J0256.5+0006 is composed of two subclusters. We determine a merger mass ratio of 7:4, and a line-of-sight velocity difference of perpendicular = 1880 +/- 210 km s(sup -1). We construct a simple merger model of infer relevant time-scales in the merger. From its location on the P1.4GHz-L(sub x) scaling relation, we infer that we observe ACT-CL J0256.5+0006 just before first core crossing.

core crossing↗

On Dark Peaks and Missing Mass: A Weak-Lensing Mass Reconstruction of the Merging Cluster System A520

Merging clusters of galaxies are unique in their power to directly probe and place limits on the self-interaction cross-section of dark matter. Detailed observations of several merging clusters have shown the intracluster gas to be displaced from the centroids of dark matter and galaxy density by ram pressure, while the latter components are spatially coincident, consistent with collisionless dark matter. This has been used to place upper limits on the dark matter particle self-interaction cross-section of order 1 sq cm/g. The cluster A520 has been seen as a possible exception. We revisit A520 presenting new Hubble Space Telescope Advanced Camera for Surveys mosaic images and a Magellan image set. We perform a detailed weak-lensing analysis and show that the weak-lensing mass measurements and morphologies of the core galaxy-filled structures are mostly in good agreement with previous works. There is, however, one significant difference: We do not detect the previously claimed "dark core" that contains excess mass with no significant galaxy overdensity at the location of the X-ray plasma. This peak has been suggested to be indicative of a large self-interaction cross-section for dark matter (at least approx 5alpha larger than the upper limit of 0.7 sq cm/g determined by observations of the Bullet Cluster). We find no such indication and instead find that the mass distribution of A520, after subtraction of the X-ray plasma mass, is in good agreement with the luminosity distribution of the cluster galaxies.We conclude that A520 shows no evidence to contradict the collisionless dark matter scenario.

Clowe, Douglas↗

Atacama Cosmology Telescope measurements of a large sample of candidates from the Massive and Distant Clusters of WISE Survey: Sunyaev-Zeldovich effect confirmation of MaDCoWS candidates using ACT

Context. Galaxy clusters are an important tool for cosmology, and their detection and characterization are key goals for current and future surveys. Using data from the Wide-field Infrared Survey Explorer (WISE), the Massive and Distant Clusters of WISE Survey (MaDCoWS) located 2839 significant galaxy overdensities at redshifts 0.7 . z . 1.5, which included extensive follow-up imaging from the Spitzer Space Telescope to determine cluster richnesses. Concurrently, the Atacama Cosmology Telescope (ACT) has produced large area millimeter-wave maps in three frequency bands along with a large catalog of Sunyaev-Zeldovich (SZ)-selected clusters as part of its Data Release 5 (DR5). Aims. We aim to verify and characterize MaDCoWS clusters using measurements of, or limits on, their thermal SZ effect signatures. We also use these detections to establish the scaling relation between SZ mass and the MaDCoWS-defined richness. Methods. Using the maps and cluster catalog from DR5, we explore the scaling between SZ mass and cluster richness. We do this by comparing cataloged detections and extracting individual and stacked SZ signals from the MaDCoWS cluster locations. We use complementary radio survey data from the Very Large Array, submillimeter data from Herschel, and ACT 224 GHz data to assess the impact of contaminating sources on the SZ signals from both ACT and MaDCoWS clusters. We use a hierarchical Bayesian model to fit the mass-richness scaling relation, allowing for clusters to be drawn from two populations: one, a Gaussian centered on the mass-richness relation, and the other, a Gaussian centered on zero SZ signal. Results. We find that MaDCoWS clusters have submillimeter contamination that is consistent with a gray-body spectrum, while the ACT clusters are consistent with no submillimeter emission on average. Additionally, the intrinsic radio intensities of ACT clusters are lower than those of MaDCoWS clusters, even when the ACT clusters are restricted to the same redshift range as the MaDCoWS clusters. We find the best-fit ACT SZ mass versus MaDCoWS richness scaling relation has a slope of p1 = 1.84+0.15 −0.14, where the slope is defined as M ∝ λ p1 15 and λ15 is the richness. We also find that the ACT SZ signals for a significant fraction (∼57%) of the MaDCoWS sample can statistically be described as being drawn from a noise-like distribution, indicating that the candidates are possibly dominated by low-mass and unvirialized systems that are below the mass limit of the ACT sample. Further, we note that a large portion of the optically confirmed ACT clusters located in the same volume of the sky as MaDCoWS are not selected by MaDCoWS, indicating that the MaDCoWS sample is not complete with respect to SZ selection. Finally, we find that the radio loud fraction of MaDCoWS clusters increases with richness, while we find no evidence that the submillimeter emission of the MaDCoWS clusters evolves with richness. Conclusions. We conclude that the original MaDCoWS selection function is not well defined and, as such, reiterate the MaDCoWS collaboration’s recommendation that the sample is suited for probing cluster and galaxy evolution, but not cosmological analyses. We find a best-fit mass-richness relation slope that agrees with the published MaDCoWS preliminary results. Additionally, we find that while the approximate level of infill of the ACT and MaDCoWS cluster SZ signals (1–2%) is subdominant to other sources of uncertainty for current generation experiments, characterizing and removing this bias will be critical for next-generation experiments hoping to constrain cluster masses at the sub-percent level.

large↗

Einstein x ray observations of the core of the Shapley Supercluster in northern Centaurus

We present Einstein x ray observations of the core of the Shapley Supercluster, one of the richest and densest known mass concentrations in the local (z less than 0.1) universe. We used Imaging Proportional Counter (IPC) observations supplemented with data from the Einstein Slew Survey to determine the locations and structure of mass concentrations in the region. An x ray map composed of IPC observations of the central (10 deg x 10 deg) region of the Shapley Supercluster is presented. We present evidence that the X-ray clusters observed within 5 deg of the core of the supercluster are on average brighter than those of corresponding richness class distributed throughout the sky. However, we measure no significant difference in the galaxy formation efficiency of these cluster of galaxies compared to other, more isolated clusters. We also find one previously uncataloged cluster-sized mass concentration in the core of the Shapley Supercluster. This new cluster, 'SC 1327-312', is relatively x ray bright (F(sub x) = 1.1 + or - 0.2 x 10(exp -11) erg sec(exp -1) cm(exp -2)) and L(sub x) = 1.1 + or - 0.2 x 10(exp 44) erg sec(exp -1) within 10 minutes, assuming z = 0.0477, H(sub 0) = 50, q(sub 0) = 0). As SC 1327-312 lies well within an Abell radius of the richness R = 4 cluster Shapley 8 (A3558), we suggest it may contribute to an artificially high galaxy count and richness classification for shapley 8. From slew data, we estimate an x ray luminosity for Shapley 8 which is just half the mean luminosity of the four other R = 4 clusters observed by the IPC, further suggesting the richness classification to be an overestimate.

Breen, Jeffrey↗

A 4 MPC X-Ray Filament Falling into the Cluster A85

We have completed a first paper confirming the ROSAT observation of a merging filamentary structure associated with the rich cluster A85. We detected a portion of the extended 4 Mpc filament first seen by the ROSAT PSPC. We confirm that there is an extended feature, aligned at the same position angle as the major axis of the central cD, the bright cluster galaxies, and nearby groups and clusters. We find that the X-ray emission from the filament is best described by thermal emission with a temperature of approx. 2 keV, which is significantly lower than the ambient cluster medium, but is significantly higher than anticipated for a gas in a weakly bound extended filament. It is not clear whether this is a filament of diffuse emission, a chain of several groups of galaxies, or stripped gas from the infalling south blob. In conclusion, the XMM-Newton observations confirmed that there really is a highly elongated filamentary like structure extending from the the merging south clump to the south east of Abell-85 along the direction defined by all the structures pointed out by Durret et al. (1998b). The fact that the spatial structure of the X-ray filament detected by XMM-Newton cannot be exactly superimposed to that obtained from ROSAT data shows that it is still difficult to determine exactly its nature. However, the X-ray spectrum from this structure is most likely thermal and its temperature is about 2.0 keV, consistent with that of groups. This value is notably cooler than that of the main cluster: the temperature map by Markevitch et al. (1998) shows the presence of gas at about 3-4 keV in the region at a distance from the cluster center at least as far as the northern part of the ellipse. So, we appear to be seeing cool gas as it enters the cluster core. Another possibility is that the filament is associated with the wake of cool stripped gas left behind by the south blob as it falls onto the cluster. In this case, the 'filament', whether it is diffuse or made of groups, would not really be a filament in the large scale structure formation sense. Besides X-ray observations with a much better signal to noise ratio, which probably will have to wait for the next generation of X-ray satellites, optical data can shed light on this question. With this purpose, we intend to perform wide field imaging in various bands to estimate galaxy photometric redshifts and determine how galaxies are distributed in the 'filament' area.

Forman, William↗

Probing the large-scale velocity field with clusters of galaxies

What is the role of clusters of galaxies in probing the large-scale velocity field of the universe? We investigate the distribution of peculiar velocities of clusters of galaxies in the popular low-density (omega = 0.3) flat cold dark matter (CDM) cosmological model, which best fits many large-scale structure observations. An omega = 1 CDM model is also studied for comparison. We find that clusters of galaxies are efficient tracers of the large-scale velocity field. The clusters exhibit a Maxwellian distribution of peculiar velocities, as expected from Gaussian initial density fluctuations. The cluster three-dimensional velocity distribution for the omega = 0.3 model peaks at nu approximately greater than 400 km/s and extends to high velocities of nu approximately 1200 km/s. The rms peculiar velocity of the clusters is 440 km/s. Approximately 10% of all model clusters move with high peculiar velocities nu greater or equal to 700 km/s. The observed velocity distribution of clusters of galaxies is compared with the predictions from cosmological models. The observed data exhibit a larger velocity tail than seen in the model simulations; however, due to the large observational uncertainties, the data are consistent at approximately equal to 3 sigma level with the odel predictions, and with a Gaussian initial density field. The large peculiar velocities reported for some clusters of galaxies (nu approximately greater than 3000 km/s) are likely to be overestimated, if the current model is viable.

Bahcall, Neta A.↗

AGN-selected clusters as revealed by weak lensing

We discuss the results in light of the cooling flow and the merger/interaction scenarios for triggering and fuelling AGN in clusters, but find that the data do not point unambiguously to neither of the two.

galaxies clusters interactions gravitational lensi↗

Is the M81 fast radio burst host globular cluster special?

We use multiband archival Hubble Space Telescope (HST) observations to measure the photometric and structural parameters of the M81 globular cluster (GC) that hosts the fast radio burst FRB 20200120E. Our best-fitting King model has an effective radius rh = 3.06 pc with a moderate King model concentration of c = 53, and an inferred core radius of 0.81 pc. We revisit the exact astrometric location of the FRB within the cluster, and find that FRB 20200120E is located 1.92 pc from the center, but within the projected half-light radius. We estimate the relative encounter rate of the FRB host, along with the corresponding rates of 210 other GCs in M81, and compare these values with the encounter rates of Galactic GCs. The FRB resides in a GC with an encounter rate that is moderately higher than the median stellar encounter rate in our two comparison samples. While the estimated encounter rate of the FRB host cluster (e.g., ∼50% of a cluster like 47 Tuc) is sufficient to allow the possibility that the FRB formed dynamically, our results do not place strong constraints on this scenario due to the limitations of the available HST data and the possible systematic uncertainties and selection effects in the comparison data.

Kristen C. Dage↗

A New Method to Constrain Supernova Fractions Using X-ray Observations of Clusters of Galaxies

Supernova (SN) explosions enrich the intracluster medium (ICM) both by creating and dispersing metals. We introduce a method to measure the number of SNe and relative contribution of Type Ia supernovae (SNe Ia) and core-collapse supernovae (SNe cc) by directly fitting X-ray spectral observations. The method has been implemented as an XSPEC model called snapec. snapec utilizes a single-temperature thermal plasma code (apec) to model the spectral emission based on metal abundances calculated using the latest SN yields from SN Ia and SN cc explosion models. This approach provides a self-consistent single set of uncertainties on the total number of SN explosions and relative fraction of SN types in the ICM over the cluster lifetime by directly allowing these parameters to be determined by SN yields provided by simulations. We apply our approach to XMM-Newton European Photon Imaging Camera (EPIC), Reflection Grating Spectrometer (RGS), and 200 ks simulated Astro-H observations of a cooling flow cluster, A3112.We find that various sets of SN yields present in the literature produce an acceptable fit to the EPIC and RGS spectra of A3112. We infer that 30.3% plus or minus 5.4% to 37.1% plus or minus 7.1% of the total SN explosions are SNe Ia, and the total number of SN explosions required to create the observed metals is in the range of (1.06 plus or minus 0.34) x 10(exp 9), to (1.28 plus or minus 0.43) x 10(exp 9), fromsnapec fits to RGS spectra. These values may be compared to the enrichment expected based on well-established empirically measured SN rates per star formed. The proportions of SNe Ia and SNe cc inferred to have enriched the ICM in the inner 52 kiloparsecs of A3112 is consistent with these specific rates, if one applies a correction for the metals locked up in stars. At the same time, the inferred level of SN enrichment corresponds to a star-to-gas mass ratio that is several times greater than the 10% estimated globally for clusters in the A3112 mass range.

Observations↗

Search for unresolved sources in the COBE-DMR two-year sky maps

We have searched the temperature maps from the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) first two years of data for evidence of unresolved sources. The high-latitude sky (absolute value of b greater than 30 deg) contains no sources brighter than 192 microKelvin thermodynamic temperature (322 Jy at 53 GHz). The cumulative count of sources brighter than threshold T, N(greater than T), is consistent with a superposition of instrument noise plus scale-invariant spectrum of cosmic temperature fluctuations normalized to Q(sub rms-PS) = 17 microKelvin. We examine the temperature maps toward nearby clusters and find no evidence for any Sunyaev-Zel'dovich effect, delta y less than 7.3 x 10(exp -6) (95% CL) averaged over the DMR beam. We examine the temperature maps near the brightest expected radio sources and detect no evidence of significant emission. The lack of bright unresolved sources in the DMR maps, taken with anisotropy measurements on smaller angular scales, places a weak constraint on the integral number density of any unresolved Planck-spectrum sources brighter than flux density S, n(greater than S) less than 2 x 10(exp 4)/(S/1 Jy)(exp 2)/sr.

Kogut, A.↗

Hot HB Stars in Globular Clusters - Physical Parameters and Consequences for Theory. VI. The Second Parameter Pair M3 and M13

We present the results of spectroscopic analyses of hot horizontal branch (HB) stars in M13 and M3, which form a famous second parameter pair. From the spectra we derived - for the first time in M13 - atmospheric parameters (effective temperature and surface gravity) as well as abundances of helium, magnesium, and iron. Consistent with analyses of hot HB stars in other globular clusters we find evidence for helium depletion and iron enrichment in stars hotter than about 12,000 K in both M3 and M13. Accounting for the iron enrichment substantially improves the agreement with canonical evolutionary models, although the derived gravities and masses are still somewhat too low. This remaining discrepancy may be an indication that scaled-solar metal-rich model atmospheres do not adequately represent the highly non-solar abundance ratios found in blue HB stars with radiative levitation. We discuss the effects of an enhancement in the envelope helium abundance on the atmospheric parameters of the blue HB stars, as might be caused by deep mixing on the red giant branch or primordial pollution from an earlier generation of intermediate mass asymptotic giant branch stars.

Moehler, S.↗

Radio Sources Toward Galaxy Clusters at 30 GHz

Extra-galactic radio sources are a significant contaminant in cosmic microwave background and Sunyaev-Zeldovich effect experiments. Deep interferometric observations with the BIMA and OVRO arrays are used to characterize the spatial, spectral, and flux distributions of radio sources toward massive galaxy clusters at 28.5 GHz. We compute counts of mJy source fluxes from 89 fields centered on known massive galaxy clusters and 8 non-cluster fields. We find that source counts in the inner regions of the cluster fields (within 0.5 arcmin of the cluster center) are a factor of 8.9 (+4.2 to -3.8) times higher than counts in the outer regions of the cluster fields (radius greater than 0.5 arcmin). Counts in the outer regions of the cluster fields are in turn a factor of 3.3 (+4.1 -1.8) greater than those in the noncluster fields. Counts in the non-cluster fields are consistent with extrapolations from the results of other surveys. We compute spectral indices of mJy sources in cluster fields between 1.4 and 28.5 GHz and find a mean spectral index of al[ja = 0.66 with an rms dispersion of 0.36, where flux S varies as upsilon(sup -alpha). The distribution is skewed, with a median spectral index of 0.72 and 25th and 75th percentiles of 0.51 and 0.92, respectively. This is steeper than the spectral indices of stronger field sources measured by other surveys.

Coble, K.↗

A reconsideration of nucleation phenomena in light of recent findings concerning the properties of small clusters, and a brief review of some other particle growth processes

The paper examines mechanisms of nucleation and growth by condensation and coagulation in the light of recent research on properties of small clusters. Homogeneous, hetero-molecular, and heterogeneous nucleation is analyzed, and expressions for the rate of formation of a stable condensed phase and evaluation of the free energy of formation of charged droplets are given. Application of high-pressure mass spectrometry which makes possible a direct determination of intensity spectra for cluster distributions, measurement of the thermodynamic properties of individual ion clusters and determination of cluster entropy and bond energy is discussed. Finally, coagulation of the condensed phase is considered, noting that concentration and mean particle size vary during coagulation, but the shape distribution is time independent, leading to the concept of a self-preserving aerosol size distribution.

Castleman, A. W., Jr.↗