Evolution Of Galaxy Clusters Research Articles

Galaxy Evolution in Clusters

The galaxy populations in present-day clusters are distinctly different from those of the field, indicating that environment plays a strong role in galaxy evolution. This review discusses some of the recent observations of moderate to high redshift clusters. A consistent picture of galaxy evolution in clusters appears to be emerging, which includes a population of galaxies which formed early in the cluster history, as well as field galaxies which have had their star formation truncated upon falling into the cluster potential. Galaxy interactions probably play an important role in exhausting star formation in some of these galaxies. However, there is significant variation in the populations of different cluster samples, with substantial evidence that some galaxies have their star formation terminated more gradually. This suggests that different mechanisms may dominate in different clusters, perhaps because of the recent merging history of the clusters. We also present a recent analysis of population gradients in clusters which suggests that the observed evolution in cluster populations is consistent with a scenario where changing infall rates drive the fraction of star forming galaxies in clusters, rather than a changing physical mechanism within the cluster. Thus, galaxy populations may provide a fundamental measure of the growth of large scale structure.

Uncovering Additional Clues to Galaxy Evolution. I. Dwarf Irregular Galaxies in the Field

In order to recognize environmental effects on the evolution of dwarf galaxies in clusters of galaxies, it is first necessary to quantify the properties of objects that have evolved in relative isolation. With oxygen abundance as the gauge of metallicity, two key diagnostics of the evolution of dwarf irregular galaxies in the field are reexamined: the metallicity-luminosity relationship and the metallicity–gas fraction relationship. Gas fractions are evaluated from the masses of luminous components only, i.e., constituents of the nucleogenetic pool. Results from new optical spectroscopy obtained for H II regions in five dwarf irregular galaxies in the local volume are incorporated into a new analysis of field dwarfs with [O III] λ4363 detections and good distances. The updated fit to the metallicity-luminosity relationship is consistent with results reported in the literature. The fit to the metallicity–gas fraction relation shows an excellent correlation consistent with expectations of the simple closed box model of chemical evolution. The simplest explanation consistent with the data is that flow rates are zero, although the observations allow for the possibility of modest flows. The derived oxygen yield is one-quarter of the value for the solar neighborhood.

The evolution of active galaxies in clusters

The results of deep radio, sub-mm and X-ray observations of samples of high redshift (z∼1) clusters are presented. These reveal significant excesses of active galaxies associated with the clusters at all three wavelengths. The cluster radio source population shows evolution consistent with the (1+z)3 evolution typical of many AGN classes. A large fraction of the AGN are hosted by apparently passive early-type galaxies, often with a close companion. These results essentially constitute the detection of a counterpart of the Butcher-Oemler effect for both strongly star bursting galaxies and AGN.

Galaxy Populations and Evolution in Clusters. III. The Origin of Low-Mass Galaxies in Clusters: Constraints from Stellar Populations

Low-mass galaxies in nearby clusters are the most numerous galaxy type in the universe, yet their origin and properties remain largely unknown. To study basic questions concerning these galaxies we present the results of a survey designed to constrain the characteristics and properties of the stellar populations in a magnitude complete sample of low-mass cluster galaxies (LMCGs) in the center of the Perseus cluster. Using deep, high-quality WIYN UBR images, we demonstrate that the 53 LMCGs in our sample have a significant scatter about the color-magnitude relationship at M_B > -15. By comparing single-burst stellar population models to our photometry, we argue that stellar populations in LMCGs all have ages > 1 Gyrs, with redder LMCGs having stellar metallicities [Fe/H] > -0.5. By assuming that the colors of LMCGs reflect metallicity, and have co-evolved with the giant ellipticals, we find a wide range of values, from solar to [Fe/H] ~ -3. We argue from this that LMCGs have multiple origins, and fundamentally differ from Local Group dwarf spheroidals/ellipticals. The inferred lower metallicities of the bluer LMCGs implies that these are possibly primordial galaxies formed through self enrichment and stellar feedback provided by winds from supernova. We also investigate several other formation scenarios for these LMCGS, including: self enrichment induced by the confinement of metals in halos by the intracluster medium, in situ formation out of intracluster gas, systems with extreme dark halos, and as remnants of higher mass systems. We conclude that roughly half of all low-mass cluster galaxies have stellar populations and kinematic properties, discussed in previous papers in this series, consistent with being the remnants of stripped galaxies accreted into clusters a few Gyrs ago.

Collisional Evolution of Galaxy Clusters: Fokker–Planck and N-body models

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker–Planck models and self-consistent N-body models. In particular we focus on the growth of the common halos and the development of the central density cusps in the clusters. We find good agreement between the Fokker–Planck and N-body models. At the cluster center the cusp approximated by a power law, ρ(r) ∝ r-α (α ∼ 1), develops. We conclude that this shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness α weakly depends on the relative importance of tidal stripping.

Evolution of Star-forming and Active Galaxies in Nearby Clusters

We have used optical spectroscopy to investigate the active galaxy populations in a sample of 20 nearby Abell clusters. The targets were identified on the basis of 1.4 GHz radio emission, which identifies them as either active galactic nuclei (AGNs) or galaxies forming stars at rates comparable to or greater than that of the Milky Way. The spectra were used to characterize the galaxies via their emission and absorption features. The spectroscopy results reveal a significant population of star-forming galaxies with large amounts of nuclear dust extinction. This extinction eliminates bluer emission lines such as [O II] from the spectra of these galaxies, meaning their star formation could easily be overlooked in studies that focus on such features. Around 20% of the cluster star-forming galaxies have spectra of this type. The radial distributions of active galaxies in clusters show a strong segregation between star-forming galaxies and AGNs, with star-forming galaxies broadly distributed and AGNs preferentially in the cluster cores. The radial distribution of the dusty star-forming galaxies is more centrally concentrated than the star-forming galaxies in general, which argues that they are a consequence of some cluster environmental effect. Furthermore, we note that such galaxies may be identified using their 4000 A break strengths. We find that discrepancies in reported radio luminosity functions for AGNs are likely the result of classification differences. There exists a large population of cluster galaxies whose radio fluxes, far-infrared fluxes, and optical magnitudes suggest their radio emission may be powered by stars yet whose spectra lack emission lines. Understanding the nature of these galaxies is critical to assessing the importance of AGNs in the radio luminosity function at low luminosities. We also find that regardless of this population, the crossover point where the radio luminosity function is composed equally of star-forming galaxies and AGNs occurs at lower luminosities in clusters than in the field. This is likely a simple consequence of the reduction in star formation in cluster galaxies and the morphological mix in clusters compared with the field.

Optical and Near‐Infrared Photometry of Distant Galaxy Clusters

We present optical and near-infrared photometry of 45 clusters of galaxies at 0.1 < z < 1.3. Galaxy catalogs in each cluster were defined at the longest wavelenth available, generally the K-band, down to approximately two magnitudes below M*. We include finding chart images of the band used for catalog definition. The photometry has been used in previously published papers to examine the origin and evolution of galaxies in distant clusters.

An Unexpectedly High Fraction of Active Galactic Nuclei in Red Cluster Galaxies

As part of a program to study the evolution of active galactic nuclei (AGNs) in clusters of galaxies, we present our results for A2104. A deep Chandra observation of this massive, z = 0.154 cluster reveals a significant X-ray point-source excess over the expectations of blank fields, including eight X-ray counterparts with R < 20 mag. Our spectroscopy shows that all six X-ray sources associated with red counterparts are cluster members and their X-ray properties are consistent with all of them being AGNs. Only one of the six has the emission lines characteristic of optically selected AGNs; the remaining five would not have been classified as AGNs based on their optical spectra. This suggests the existence of a large population of obscured, or at least optically unremarkable, AGNs in clusters of galaxies. These six sources correspond to a lower limit of ~5% of the AGN fraction in cluster galaxies with R < 20 mag (rest-frame MV = -19.5 mag) and are comparable to the blue galaxy fraction in the cluster. Such an obscured AGN population in clusters of galaxies has many implications for cluster galaxy evolution, the hidden growth of their central, supermassive black holes, estimates of the star formation rate at infrared and radio wavelengths, and the observed variance in the hard X-ray background.

Abundance and evolution of galaxy clusters in cosmological models with massive neutrino

The time evolution of the number density of galaxy clusters and their mass and temperature functions are used to constrain cosmological parameters in the spatially flat dark matter models containing a fraction of hot particles (massive neutrino) additional to cold and baryonic matter. We test the modified MDM models with cosmic gravitational waves and show that they neither pass the cluster evolution test nor reproduce the observed height of the first acoustic peak in $\Delta T/T$ spectrum, and therefore should be ruled out. The models with a non-zero cosmological constant are in better agreement with observations. We estimate the free cosmological parameters in $\Lambda$MDM with a negligible abundance of gravitational waves, and find that within the parameter ranges $h\in (0.6, 0.7)$, $n\in (0.9, 1.1)$, (i) the value of $\Omega_\Lambda$ is strongly affected by a small fraction of hot dark matter, $f_\nu\equiv\Omega_\nu /\Omega_m\in (0, 0.2)$: $0.45 <\Omega_\Lambda <0.7$ ($1\sigma$ CL), and (ii) the redshift evolution of galaxy clusters alone reveals the following explicit correlation between $\Omega_\Lambda$ and $f_\nu$: $\Omega_\Lambda +0.5f_\nu =0.65\pm 0.1$. The present accuracy of observational data allows only to bound the fraction of hot matter, $f_\nu\in (0, 0.2)$ (the number of massive neutrino species remains undelimited, $N_\nu =1, 2, 3$).

Galaxy Populations and Evolution in Clusters. II. Defining Cluster Populations

This paper presents quantitative techniques for studying, in an unbiased manner, the photometric and structural properties of galaxies in clusters, including a means to identify likely background objects in the absence of redshift information. We develop self-consistent and reproducible measurements of fundamental properties of galaxies such as radius, surface brightness, concentration of light and structural asymmetry. We illustrate our techniques through an application to deep UBR images, taken with the WIYN 3.5m telescope, of the central ~173 arcmin^2 (or 0.3 Mpc * 0.3 Mpc) of the cluster Abell 0146 (Perseus). Our techniques allow us to study the properties of the galaxy population in the center of Perseus down to M_B = -11. Using these methods, we describe and characterize a well-defined relation between absolute magnitude and surface brightness for galaxy cluster members across the entire range of galaxy luminosity from M_B = -20 to M_B = -11. The galaxies that are assigned by our techniques to the background show no such tight relationship between apparent magnitude and surface brightness, with the exception of those we identify as being members of a background cluster of galaxies at z ~ 0.55. We, however, find that at the fainter magnitudes, M_B > -16, there is a large scatter about the underlying color--magnitude relation defined by the brighter galaxies. Our analysis also indicates that the vast majority of Perseus galaxies are `normal', with little evidence for features associated with evolution; we however discuss the detailed properties of a handful of unusual galaxies. Finally, the galaxy luminosity function of the Perseus cluster center is computed, with a derived faint end slope of alpha = -1.44+/-0.04, similar to values found in other nearby clusters.

Collisional Evolution of Galaxy Clusters and the Growth of Common Halos

Abstract We investigated the dynamical evolution of clusters of galaxies in virial equilibrium using Fokker–Planck models and self-consistent $N$-body models. In particular, we focused on the growth of a common halo, which is a cluster-wide halo formed by matter stripped from galaxies, and the development of a central density cusp. The Fokker–Planck models include the effects of two-body gravitational encounters both between galaxies and between galaxies and common halo particles. The effects of tidal mass stripping from the galaxies due to close galaxy–galaxy encounters and accompanying dissipation of the orbital kinetic energies of the galaxies were also taken into account in the Fokker–Planck models. We find that the results of the Fokker–Planck models are in excellent agreement with those of the $N$-body models regarding the growth of the common halo mass and the evolution of the cluster density profiles. In the central region of the cluster, a shallow density cusp, approximated by $\rho (r) \propto r^{-\alpha}$ ($\alpha \sim 1$), develops. This shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness, $\alpha$, weakly depends on the relative importance of the tidal stripping. When the effect of stripping is important, the central velocity dispersion decreases as the central density increases and, consequently, a shallow ($\alpha &amp;lt;2$) cusp is formed. In the limit of no stripping, usual gravothermal core collapse occurs, i.e. the central velocity dispersion increases as the central density increases with a steep ($\alpha \gt 2$) cusp left. We conclude from our consideration of the origin of the cusp demonstrated here that shallow cusps should develop in real galaxy clusters.

Revisiting Brightest Cluster Galaxy Evolution with the Las Campanas Distant Cluster Survey

We investigate the influence of environment on brightest cluster galaxy (BCG) evolution using a sample of 63 clusters at 0.3 ≤ z ≤ 0.9 drawn primarily from the Las Campanas Distant Cluster Survey and follow-up V, I, and K' photometry. The luminosity evolution of the entire BCG sample is not adequately described by a single evolutionary model. Using the integrated light from the cluster detection as a proxy for cluster LX and the suggestion by Burke, Collins, & Mann, we set LX = 2 × 1044 ergs s-1 to be the division between high- and low-luminosity clusters. At high redshift (z > 0.6) BCGs from low-LX clusters are fainter, on average, than those from high-LX clusters and are best modeled as having constant luminosity with redshift. The BCGs from high-LX clusters are best modeled as having a stellar population that formed at large redshift (zform > 5) and is passively evolving. However, for the entire BCG population, the observed V-I and I-K' colors are well described by a single evolutionary model in which the stellar populations have zform > 5 and subsequently passively evolve. We conclude that accretion is proportionally more significant for BCGs in lower mass clusters at these redshifts (a factor of 2-4 increase in mass since z ~ 1 for the low-LX systems; Aragon-Salamanca and coworkers) and that the accreted matter is in the form of systems with evolved stellar populations.

Measuring the redshift evolution of clustering: the Hubble Deep Field South

We present an analysis of the evolution of galaxy clustering in the redshift interval 0<z<4.5 in the HDF-S. The HST optical data are combined with infrared ISAAC/VLT observations, and photometric redshifts are used for all the galaxies brighter than I_AB<27.5. The clustering signal is obtained in different redshift bins using two different approaches: a standard one, which uses the best redshift estimate of each object, and a second one, which takes into account the redshift probability function of each object. This second method makes it possible to improve the information in the redshift intervals where contamination from objects with insecure redshifts is important. With both methods, we find that the clustering strength up to z~3.5 in the HDF-S is consistent with the previous results in the HDF-N. While at redshift lower than z~1 the HDF galaxy population is un/anti-biased (b<1) with respect to the underlying dark matter, at high redshift the bias increases up to b~2-3, depending on the cosmological model. These results support previous claims that, at high redshift, galaxies are preferentially located in massive haloes, as predicted by the biased galaxy formation scenario. The impact of cosmic errors on our analyses has been quantified, showing that errors in the clustering measurements in the HDF surveys are indeed dominated by shot-noise in most regimes. Future observations with instruments like the ACS on HST will improve the S/N by at least a factor of two and more detailed analyses of the errors will be required. In fact, pure shot-noise will give a smaller contribution with respect to other sources of errors, such as finite volume effects or non-Poissonian discreteness effects.

Cluster Galaxy Evolution from a New Sample of Galaxy Clusters at 0.3 &lt;z&lt; 0.9

We analyze photometry and spectroscopy of a sample of 63 clusters at 0.3 ≤ z ≤ 0.9 drawn from the Las Campanas Distant Cluster Survey to empirically constrain models of cluster galaxy evolution. Specifically, (1) by combining I-band photometry of 44 of our clusters with that of 19 clusters from the literature, we parameterize the redshift dependence of M in the observed frame as M = (-21.74 ± 0.12) - (0.88 ± 0.24)z - 5 log h (rms deviation = 0.34) for 0.3 ≤ z ≤ 0.9 (Ω0 = 0.2, ΩΛ = 0); (2) by combining 30 of our clusters and 14 clusters from the literature with V and I data, we parameterize the redshift dependence of the V-I color of the E/S0 red sequence in the observed frames as V-I = (-0.24 ± 0.28) + (7.42 ± 1.03)z - (4.61 ± 0.91)z2 (rms deviation = 0.16) for 0.3 ≤ z ≤ 0.9; and (3) by combining 13 of our clusters with 15 clusters from the literature with I and K' data, we parameterize the redshift dependence of the I-K' color of the E/S0 red sequence in the observed frames as I-K' = (0.66 ± 0.65) + (9.50 ± 3.72)z - (14.72 ± 7.01)z2 + (8.72 ± 4.29)z3 (rms deviation = 0.18) for 0.3 ≤ z ≤ 0.9. Using the peak surface brightness of the cluster detection, Σ, as a proxy for cluster mass, we find no correlation between Σ and M or the location of the red envelope in V-I. We suggest that these observations can be explained with a model in which luminous early-type galaxies (or more precisely, the progenitors of current-day luminous early-type galaxies) form the bulk of their stellar populations at high redshifts (5) and in which many of these galaxies, if not all, accrete mass either in the form of evolved stellar populations or gas that causes only a short-term episode of star formation at lower redshifts (1.5 < z < 2). Our data are too crude to reach conclusions regarding the evolutionary state of any particular cluster or to investigate whether the morphological evolution of galaxies matches the simple scenario that we discuss, but the statistical nature of this study suggests that the observed evolutionary trends are universal in massive clusters.

The morphological and dynamical evolution of simulated galaxy clusters

We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental interest: 1. How does the average cluster morphology depend on the cosmological background model? 2. Is it possible to discriminate between dierent cosmological models using cluster substructure in a statistically signicant way? 3. How is the dynamical state of a cluster, especially its distance from a virial equilibrium, correlated to its visual substructure? To answer these questions, we quantify cluster substructure using a set of morphological order parameters constructed on the basis of the Minkowski valuations (MVs). The dynamical state of a cluster is described using global cluster parameters: in certain spaces of such parameters fundamental band-like structures are forming indicating the emergence of a virial equilibrium. We nd that the average distances from these fundamental structures are correlated to the average amount of cluster substructure for our cluster samples during the time evolution. Furthermore, signicant dierences show up between the high- and the low-m models. We pay special attention to the redshift evolution of morphological characteristics and nd large dierences between the cosmological models even for higher redshifts.

Radial Color Gradients in K + A Galaxies in Distant Clusters of Galaxies

Galaxies in rich clusters with z $\gtrsim$ 0.3 are observed to have a higher fraction of photometrically blue galaxies than their nearby counterparts. This raises the important question of what environmental effects can cause the termination of star formation between z $\approx$ 0.3 and the present. The star formation may be truncated due to ram-pressure stripping, or the gas in the disk may be depleted by an episode of star formation caused by some external perturbation. To help resolve this issue, surface photometry was carried out for a total of 70 early-type galaxies in the cluster Cl1358+62, at z $\sim$ 0.33, using two-color images from the Hubble Archive. The galaxies were divided into two categories based on spectroscopic criteria: 24 are type K+A (e.g., strong Balmer lines, with no visible emission lines), while the remaining 46 are in the control sample with normal spectra. Radial color profiles were produced to see if the K+A galaxies show bluer nuclei in relation to their surrounding disks. Specifically, a linear gradient was fit to the radial color profile of each galaxy. We find that the K+A galaxies on average tend to have slightly bluer gradients towards the center than the normals. A Kolmogorov-Smirnov two-sample test has been applied to the two sets of color gradients. The result of the test indicates that there is only a $\sim$2% probability that the K+A and normal samples are drawn from the same parent distribution. There is a possible complication from a trend in the apparent magnitude vs. color gradient relation, but overall our results favor the centralized star formation scenario as an important process in the evolution of galaxies in dense clusters.

Galaxy Populations and Evolution in Clusters. I. Dynamics and the Origin of Low‐Mass Galaxies in the Virgo Cluster

Early-type dwarfs are the most common galaxy in the local universe, yet their origin and evolution remain a mystery. Various cosmological scenarios predict that dwarf-like galaxies in dense areas are the first to form and hence should be the oldest stellar systems in clusters. By using radial velocities of early-type dwarfs in the Virgo cluster we demonstrate that these galaxies are not an old cluster population but have signatures of production from the infall of field galaxies. Evidence of this includes the combined large dispersions and sub-structure in spatial and kinematic distributions for Virgo early-type dwarfs, and a velocity dispersion ratio with giant ellipticals expected for virialized and accreted populations. We also argue that these galaxies cannot originate from accreted field dwarfs, but must have physically evolved from a precursor population, of different morphology, that fell into Virgo some time in the past.

Cosmological Implications from Observations of Type Ia Supernovae

▪ Abstract Distant type Ia supernovae (SNe Ia) appear fainter than their local counterparts. Independent of what explanation will eventually be found to be correct, this implies a significant change in how we see the distant universe and what we understand of these stellar explosions. The observational characteristics of nearby SNe Ia show some differences from event to event. Despite their considerable range in observed peak luminosity, they can be normalized by their light-curve shape. Through this normalization, SNe Ia can be used as exquisite distance indicators. The Hubble diagram of nearby SNe Ia, demonstrating the linear cosmic expansion at small scales, is the simplest observational proof for the standard character of these objects. Compared with Friedmann models of the universe, the distant SNe are too faint even for a freely coasting, “empty” universe, barring other influences that could dim the events. This result is independent of the absolute calibration of the peak luminosity, which is needed to derive the Hubble constant. Possible noncosmological explanations could be gray dust, with properties that do not change the color of the objects significantly, evolution of the explosions, or deamplification by gravitational lensing. Current indications are that none of these alternatives alone can explain the dimness of the distant SNe. The intrinsic colors of the distant SNe Ia are typically bluer when compared with the local sample. This in itself makes the dust hypothesis less likely. On the other hand, it could be a signature of evolutionary trends that could influence the peak luminosity. This trend is contrary to the observations in the local sample, where bluer objects typically are more luminous. However, current lack of understanding of the explosion physics and the radiation transport of SNe Ia encumbers any investigation of evolutionary changes. Any change in the peak luminosity of SNe Ia must be inferred from indirect observations, such as light-curve shape, colors, and spectral evolution. At the moment, many of the distant SNe do not have the required data set for a detailed investigation of these parameters. The near-uniform light-curve and spectral evolution of SNe Ia can be used as accurate cosmic clocks to demonstrate the time dilation as predicted from expanding world models. The test has been performed through both photometry and spectroscopy, and is fully consistent with the predictions. The supernova (SN) results can be reconciled only with cosmological models that provide some form of acceleration. The simplest such models either include the cosmological constant or refer to a decaying particle field (“quintessence”). Combined with recent measurements of the cosmic microwave background that indicate a flat geometry of the universe, and low-matter density, as derived from bulk flows and the evolution of galaxy clusters, the SNe define a fairly narrow likelihood region for ΩM and ΩΛ. With these new values for the cosmological parameters, the long-standing problem of the dynamical age of the universe appears to be solved. On the other hand, the size of the acceleration, if interpreted as a cosmological constant, is in clear contradiction to predictions from particle theories. In addition, we live in a very privileged period when matter density and the cosmological constant are equal contributors to the cosmic expansion.

Limits on Collisional Dark Matter from Elliptical Galaxies in Clusters

The dynamical evolution of galaxies in clusters would be modified if dark matter were self-interacting. Heat conduction from the hot cluster halo would lead to evaporation of the relatively cooler galactic halos. The stellar distribution would adiabatically expand as it readjusted to the loss of dark matter, reducing the velocity dispersion and increasing the half-light radius. If the dark matter content within that radius was fdm = 25%-50% of the total, as indicated by current observations, the elliptical galaxies in clusters would be offset from the fundamental plane relation beyond observational scatter. The requirement that their halos survive for a Hubble time appears to exclude just that range of the dark matter cross section, 0.3 σp/mp 104 cm2 g-1, thought to be optimal for reducing central halo cusps, unless fdm 1.8. In either case, the problem of central density cusps remains.

Spectroscopic Evolution of Dusty Starburst Galaxies in Distant Clusters

By using a one-zone chemical and spectrophotometric evolution model of a disk galaxy undergoing a dusty starburst, we investigate numerically the optical spectroscopic properties in order to explore galaxy evolution in distant clusters. We adopt an assumption that the degree of dust extinction (represented by AV) depends on the ages of starburst populations in such a way that younger stars have larger AV (originally referred to as selective dust extinction by Poggianti & Wu). In particular, we investigate how the time evolution of the equivalent widths of [O II] λ3727 and Hδ are controlled by the adopted age dependence. This leads to the following three main results: (1) If a young stellar population (with an age of ~106 yr) is more heavily obscured by dust than an old one (>108 yr), the galaxy can show an "e(a)" spectrum characterized by strong Hδ absorption and relatively modest [O II] emission. (2) A dusty starburst galaxy with an e(a) spectrum can evolve into a poststarburst galaxy with an a + k (or k + a) spectrum 0.2 Gyr after the starburst and then into a passive one with a k-type spectrum 1 Gyr after the starburst. This result clearly demonstrates an evolutionary link between galaxies with different spectral classes [i.e., e(b), e(a), a + k, k + a, and k]. (3) A dusty starburst galaxy can show an a + k or k + a spectrum even in the dusty starburst phase if the age-dependence of dust extinction is rather weak; i.e., if young starburst populations with different ages (≤107 yr) are uniformly obscured by dust.