Central Light Concentration Research Articles

The morphological mix of dwarf galaxies in the nearby Universe

ABSTRACT We use a complete, unbiased sample of 257 dwarf (10$^{8}\, {\rm M}_{\odot } \lt M_{\rm {\star }} \lt 10^{9.5}\, {\rm M}_{\odot }$) galaxies at z < 0.08, in the COSMOS field, to study the morphological mix of the dwarf population in low-density environments. Visual inspection of extremely deep optical images and their unsharp-masked counterparts reveals three principal dwarf morphological classes. 43 per cent and 45 per cent of dwarfs exhibit the traditional ‘early-type’ (elliptical/S0) and ‘late-type’ (spiral) morphologies, respectively. However, 10 per cent populate a ‘featureless’ class, that lacks both the central light concentration seen in early-types and any spiral structure – this class is missing in the massive-galaxy regime. 14 per cent, 27 per cent, and 19 per cent of early-type, late-type, and featureless dwarfs respectively show evidence for interactions, which drive around 20 per cent of the overall star formation activity in the dwarf population. Compared to their massive counterparts, dwarf early-types show a much lower incidence of interactions, are significantly less concentrated and share similar rest-frame colours as dwarf late-types. This suggests that the formation histories of dwarf and massive early-types are different, with dwarf early-types being shaped less by interactions and more by secular processes. The lack of large groups or clusters in COSMOS at z < 0.08, and the fact that our dwarf morphological classes show similar local density, suggests that featureless dwarfs in low-density environments are created via internal baryonic feedback, rather than by environmental processes. Finally, while interacting dwarfs can be identified using the asymmetry parameter, it is challenging to cleanly separate early and late-type dwarfs using traditional morphological parameters, such as ‘CAS’, M20, and the Gini coefficient (unlike in the massive-galaxy regime).

Integral Field Spectroscopy of 13 Tidal Disruption Event Hosts from the Zwicky Transient Facility Survey

The host galaxies of tidal disruption events (TDEs) have been shown to possess peculiar properties, including high central light concentrations, unusual star formation histories, and “green” colors. The ubiquity of these large-scale galaxy characteristics among TDE host populations suggests that they may serve to boost the TDE rate in such galaxies by influencing the nuclear stellar dynamics. We present the first population study of integral field spectroscopy for 13 TDE host galaxies across all spectral classes and X-ray brightnesses with the purpose of investigating their large-scale properties. We derive the black hole masses via stellar kinematics (i.e., the M–σ relation) and find masses in the range , with a distribution dominated by black holes with M BH ∼ 106 M ⊙. We find one object with M BH ≳ 108 M ⊙, above the “Hills mass”, which if the disrupted star was of solar type, allows a lower limit of a ≳ 0.16 to be placed on its spin, lending further support to the proposed connection between featureless TDEs and jetted TDEs. We also explore the level of rotational support in the TDE hosts, quantified by (V/σ) e , a parameter that has been shown to correlate with the stellar age and may explain the peculiar host-galaxy preferences of TDEs. We find that the TDE hosts exhibit a broad range in (V/σ) e following a similar distribution as E + A galaxies, which have been shown to be overrepresented among TDE host populations.

Study of central light concentration in nearby galaxies

We propose a novel technique to estimate the masses of super massive black holes (SMBHs) residing at the centres of massive galaxies in the nearby Universe using simple photometry. Aperture photometry using SEXTRACTOR is employed to determine the central intensity ratio (CIR) at the optical centre of the galaxy image for a sample of 49 nearby galaxies with SMBH mass estimations. We find that the CIR of ellipticals and classical bulges is strongly correlated with SMBH masses whereas pseudo bulges and ongoing mergers show significant scatter. Also, the CIR of low luminosity AGNs in the sample shows significant connection with the 5 GHz nuclear radio emission suggesting a stronger link between the former and the SMBH evolution in these galaxies. In addition, it is seen that various structural and dynamical properties of the SMBH host galaxies are correlated with the CIR making the latter an important parameter in galaxy evolution studies. Finally, we propose the CIR to be an efficient and simple tool not only to distinguish classical bulges from pseudo bulges but also to estimate the mass of the central SMBH.

A new population of recently quenched elliptical galaxies in the SDSS

We use the Sloan Digital Sky Survey to investigate the properties of massive elliptical galaxies in the local Universe (z\leq0.08) that have unusually blue optical colors. Through careful inspection, we distinguish elliptical from non-elliptical morphologies among a large sample of similarly blue galaxies with high central light concentrations (c_r\geq2.6). These blue ellipticals comprise 3.7 per cent of all c_r\geq2.6 galaxies with stellar masses between 10^10 and 10^11 h^{-2} {\rm M}_{\sun}. Using published fiber spectra diagnostics, we identify a unique subset of 172 non-star-forming ellipticals with distinctly blue urz colors and young (< 3 Gyr) light-weighted stellar ages. These recently quenched ellipticals (RQEs) have a number density of 2.7-4.7\times 10^{-5}\,h^3\,{\rm Mpc}^{-3} and sufficient numbers above 2.5\times10^{10} h^{-2} {\rm M}_{\sun} to account for more than half of the expected quiescent growth at late cosmic time assuming this phase lasts 0.5 Gyr. RQEs have properties that are consistent with a recent merger origin (i.e., they are strong `first-generation' elliptical candidates), yet few involved a starburst strong enough to produce an E+A signature. The preferred environment of RQEs (90 per cent reside at the centers of < 3\times 10^{12}\,h^{-1}{\rm M}_{\sun} groups) agrees well with the `small group scale' predicted for maximally efficient spiral merging onto their halo center and rules out satellite-specific quenching processes. The high incidence of Seyfert and LINER activity in RQEs and their plausible descendents may heat the atmospheres of small host halos sufficiently to maintain quenching.

The supermassive black hole mass–Sérsic index relations for bulges and elliptical galaxies

Scaling relations between supermassive black hole mass, M_BH, and host galaxy properties are a powerful instrument for studying their coevolution. A complete picture involving all of the black hole scaling relations, in which each relation is consistent with the others, is necessary to fully understand the black hole-galaxy connection. The relation between M_BH and the central light concentration of the surrounding bulge, quantified by the S\'ersic index n, may be one of the simplest and strongest such relations, requiring only uncalibrated galaxy images. We have conducted a census of literature S\'ersic index measurements for a sample of 54 local galaxies with directly measured M_BH values. We find a clear M_BH - n relation, despite an appreciable level of scatter due to the heterogeneity of the data. Given the current M_BH - L_sph and the L_sph - n relations, we have additionally derived the expected M_BH - n relations, which are marginally consistent at the 2 sigma level with the observed relations. Elliptical galaxies and the bulges of disc galaxies are each expected to follow two distinct bent M_BH - n relations due to the S\'ersic/core-S\'ersic divide. For the same central light concentration, we predict that M_BH in the S\'ersic bulges of disc galaxies are an order magnitude higher than in S\'ersic elliptical galaxies if they follow the same M_BH - L_sph relation.

Internal kinematics of spiral galaxies in distant clusters

(Abridged) We trace the interaction processes of galaxies at intermediate redshift by measuring the irregularity of their ionized gas kinematics, and investigate these irregularities as a function of the environment (cluster versus field) and of morphological type (spiral versus irregular). Our sample consists of 92 distant galaxies. 16 cluster (z~0.3 and z~0.5) and 29 field galaxies (mean z=0.44) of these have velocity fields with sufficient signal to be analyzed. We find that the fraction of galaxies that have irregular gas kinematics is remarkably similar in galaxy clusters and in the field at intermediate redshifts. The distribution of the field and cluster galaxies in (ir)regularity parameters space is also similar. On the other hand galaxies with small central concentration of light, that we see in the field sample, are absent in the cluster sample. We find that field galaxies at intermediate redshifts have more irregular velocity fields as well as more clumpy and less centrally concentrated light distributions than their local counterparts. Comparison with a SINS sample of 11 z ~ 2 galaxies shows that these distant galaxies have more irregular gas kinematics than our intermediate redshift cluster and field sample. We do not find a dependence of the irregularities in gas kinematics on morphological type. We find that two different indicators of star formation correlate with irregularity in the gas kinematics. More irregular gas kinematics, also more clumpy and less centrally concentrated light distributions of spiral field galaxies at intermediate redshifts in comparison to their local counterparts indicate that these galaxies are probably still in the process of building their disks via mechanisms such as accretion and mergers. On the other hand, they have less irregular gas kinematics compared to galaxies at z ~ 2.

A Comparison of Hα and Stellar Scale Lengths in Virgo and Field Spirals

The scale lengths of the old stars and ionized gas distributions are compared for similar samples of Virgo Cluster members and field spiral galaxies via Hα and broad R-band surface photometry. While the R-band and Hα scale lengths are, on average, comparable for the combined sample, we find significant differences between the field and cluster samples. While the Hα scale lengths of the field galaxies are a factor of 1.14 ± 0.07 longer, on average, than their R-band scale lengths, the Hα scale lengths of Virgo Cluster members are, on average, 20% smaller than their R-band scale lengths. Furthermore, in Virgo, the scale length ratios are correlated with the size of the star-forming disk: galaxies with smaller overall Hα extents also show steeper radial falloff of star formation activity. At the same time, we find no strong trends in scale length ratio as a function of other galaxy properties, including galaxy luminosity, inclination, morphological type, central R-band light concentration, or bar type. Our results for Hα emission are similar to other results for dust emission, suggesting that Hα and dust have similar distributions. The environmental dependence of the Hα scale length places additional constraints on the evolutionary process(es) that cause gas depletion and a suppression of the star formation rate in clusters of galaxies.

GHASP: an Hα kinematic survey of spiral and irregular galaxies - IV. 44 new velocity fields. Extension, shape and asymmetry of Hα rotation curves

We present Fabry–Perot observations obtained in the frame of the GHASP survey (Gassendi HAlpha survey of SPirals). We have derived the Hα map, the velocity field and the rotation curve for a new set of 44 galaxies. The data presented in this paper are combined with the data published in the three previous papers providing a total number of 85 of the 96 galaxies observed up to now. This sample of kinematical data has been divided into two groups: isolated (ISO) and softly interacting (SOFT) galaxies. In this paper, the extension of the Hα discs, the shape of the rotation curves, the kinematical asymmetry and the Tully–Fisher relation have been investigated for both ISO and SOFT galaxies. The Hα extension is roughly proportional to R25 for ISO as well as for SOFT galaxies. The smallest extensions of the ionized disc are found for ISO galaxies. The inner slope of the rotation curves is found to be correlated with the central concentration of light more clearly than with the type or the kinematical asymmetry, for ISO as well as for SOFT galaxies. The outer slope of the rotation curves increases with the type and with the kinematical asymmetry for ISO galaxies but shows no special trend for SOFT galaxies. No decreasing rotation curve is found for SOFT galaxies. The asymmetry of the rotation curves is correlated with the morphological type, the luminosity, the (B−V) colour and the maximal rotational velocity of galaxies. Our results show that the brightest, the most massive and the reddest galaxies, which are fast rotators, are the least asymmetric, meaning that they are the most efficient with which to average the mass distribution on the whole disc. Asymmetry in the rotation curves seems to be linked with local star formation, betraying disturbances of the gravitational potential. The Tully–Fisher relation has a smaller slope for ISO than for SOFT galaxies.

Near-Infrared Adaptive Optics Imaging of the Central Regions of Nearby S[CLC]c[/CLC] Galaxies. II. NGC 247 and NGC 2403

J, H, and K' images obtained with the Canada-France-Hawaii Telescope adaptive optics system are used to investigate the star-forming histories of the central regions of the Sc galaxies NGC 247 and NGC 2403. The brightest resolved red stars within 15'' of the nucleus of each galaxy are red supergiants (RSGs), indicating that the central few hundred parsecs of these galaxies experienced star formation within the last ~0.1 Gyr. While there are indications of galaxy-to-galaxy differences in the recent (t ≤ 0.1 Gyr) star-forming histories, a comparison of the K luminosity functions of stars near the centers of NGC 2403 and M33 indicates that, when averaged over gigayear timescales, the star-forming histories of the inner disks of these galaxies have been remarkably similar. This is consistent with suggestions that the long-term evolution of disks is defined by local characteristics such as mass density. It is demonstrated that NGC 247 and NGC 2403, like M33, harbor nuclear star clusters with stellar contents that differ from the surrounding central light concentrations, which in turn have near-infrared spectral energy distributions that are similar to old stellar systems. The nucleus of NGC 2403 is significantly bluer than that of the other two galaxies. If the nuclei of NGC 247, NGC 2403, and M33 are subject to similar amounts of extinction, then this indicates that NGC 2403 harbors the youngest nuclear star cluster in the sample. The K-band surface brightnesses near the centers of NGC 247 and NGC 2403 are 1–2 mag arcsec-2 lower than in M33. Finally, it is noted that young or intermediate-age nuclear star clusters are a common occurrence in nearby spirals, indicating that nuclear star formation in these objects is either continuous or episodic on timescales of 0.1–1 Gyr. This is consistent with models that have been proposed to explain the properties of the Galactic center.

Galaxy Light Concentration. I. Index Stability and the Connection with Galaxy Structure, Dynamics, and Supermassive Black Holes

We explore the stability of diUerent galaxy light concentration indices as a function of the outermost observed galaxy radius. With a series of analytical light-pro—le models, we show mathematically how varying the radial extent to which one measures a galaxys light can strongly aUect the derived galaxy concentration. The ii mean concentration index,ˇˇ often used for parameterizing high-redshift galaxies, is shown to be horribly unstable, even when modeling one-component systems such as elliptical, dwarf elliptical, and pure exponential disk galaxies. The concentration index performs considerably better C 31 but is also heavily dependent on the radial extent, and hence exposure depth, of any given galaxy. We show that the recently de—ned central concentration index is remarkably stable against changes to the outer radius and observational errors and provides a both meaningful and reliable estimate of galaxy concentration. The index n from the r1@n models is shown to be monotonically related with the Sec rsic central concentration of light, giving the index n a second and perhaps more tangible meaning. With a sample of elliptical and dwarf elliptical galaxies, we present correlations between the central light concen- tration and the global parameters: luminosity (Pearsons r \( 0.82), eUective radius (r 0.67), central surface brightness (r \( 0.88), and velocity dispersion (r 0.80). The more massive elliptical galaxies are shown to be more centrally concentrated. We speculate that the physical mechanism behind the recently observed correlation between the central velocity dispersion (mass) of a galaxy and the mass of its central supermassive black hole may be connected with the central galaxy concentration. That is, we hypothesize that it may not simply be the amount of mass in a galaxy but rather how that mass is distributed that controls the mass of the central black hole.

Near-Infrared Adaptive Optics Imaging of the Central Regions of Nearby S[CLC]c[/CLC] Galaxies. I. M33

Near-infrared images obtained with the Canada-France-Hawaii Telescope (CFHT) Adaptive Optics Bonnette (AOB) are used to investigate the stellar content within 18 arcsec of the center of the Local Group spiral galaxy M33. AGB stars with near-infrared spectral-energy distributions similar to those of giants in the solar neighborhood and Baade's Window are detected over most of the field. The bolometric luminosity function (LF) of these stars has a discontinuity near M_{bol} = -5.25, and comparisons with evolutionary tracks suggest that most of the AGB stars formed in a burst of star formation 1 - 3 Gyr in the past. The images are also used to investigate the integrated near-infrared photometric properties of the nucleus and the central light concentration. The nucleus is bluer than the central light concentration, in agreement with previous studies at visible wavelengths. The CO index of the central light concentration 0.5 arcsec from the galaxy center is 0.05, which corresponds to [Fe/H] = -1.2 for simple stellar systems. Hence, the central light concentration could not have formed from the chemically-enriched material that dominates the present-day inner disk of M33.

Environmental Extremists in the Virgo Cluster

Many types of galaxy interactions have been posited to occur in clusters, although it remains unclear which processes actually occur, and which ones might help explain the tendency for early type galaxies to inhabit high density environments, or cause the rapid evolution of cluster galaxies (e.g., Dressler et al. 1997). With these questions in mind, we have been conducting an environmental inventory of galaxies in the Virgo Cluster. Our approach is to combine surveys of spirals and S0s with detailed studies of the most interesting and peculiar galaxies. In this paper, we describe two main points. 1.) There is a population of spiral galaxies in the Virgo cluster with the small central light concentrations (bulge-to-disk ratios, or B/D's) characteristic of isolated Sb and Sc galaxies, but global star formation rates lower than those of isolated spirals of any Hubble class (Sa-Sc). These Virgo galaxies are generally classified as “early type” (e.g. Sa), and thus contribute to the morphology-density relationship. 2.) There areseveral typesof environmental interactions occurring in Virgo, including low velocity tidal interactions and mergers, high velocity tidal interactions and collisions, HI accretion, and ICM-ISM stripping. We discuss examples of some of these interactions.

The Influence of Environment on the Star Formation Rates of Galaxies

We have used a sample of 15,749 galaxies taken from the Las Campanas Redshift Survey to investigate the effects of environment on the rate of star formation in galaxies. For each galaxy, we derive a measure of the star formation rate (SFR) based on the strength of the [O II] emission line and a measure of galactic structure based on the central concentration of the galaxy's light, which is used to decouple the effect of morphology-environment relation from the SFR. Galactic environment is characterized both by the three-space local density of galaxies and by membership in groups and clusters. The size and homogeneity of this data set allows us to sample, for the first time, the entire range of galactic environments, from the lowest density voids to the richest clusters, in a uniform manner. Thus, we could expand our research from the conventional cluster versus field comparison to a new environmental investigation by decoupling the local galaxy density from the membership in associations. This decoupling is crucial for constraining the physical processes responsible for the observed environmental dependencies of star formation. On the other hand, the use of an automatic measure of galactic structure (concentration index) rather than Hubble type, which is a subjective and star formation-contaminated estimate of galactic morphology, allows us to separate cleanly the morphological component from the SFR-environment relationship. We find that, when a cluster/field comparison is made, cluster galaxies exhibit reduced star formation for the same concentration index. This result supports several previous studies based on Hubble type reporting similar suppression of star formation among cluster galaxies for the same Hubble type. We did not find any qualitatively different responses to environments between early- and late-type spirals, which were also previously reported. On the other hand, a further division of clusters by richness reveals a new possible excitation of starbursts in groups and poor clusters. Meanwhile, a more general environmental investigation shows that the star formation rate of galaxies with a given concentration index is sensitive to local galaxy density and shows a continuous correlation with the local density, in such a way that galaxies show higher levels of star formation in lower density environments. Interestingly, this trend is also observed both inside and outside of clusters, implying that physical processes responsible for this correlation might not operate intrinsically in the cluster environment. Furthermore, a more complex facet of the dependence of SFR on local density is also revealed; galaxies with differing levels of star formation appear to respond differently to the local density. Low levels of star formation, corresponding to those expected in normal members of the Hubble sequence, are more sensitive to environment inside than outside of clusters. In contrast, high levels of star formation, identified as starbursts, are at least as sensitive to local density in the field as in clusters. We conclude that at least two separate processes are responsible for the environmental sensitivity of the SFR and tentatively identify gas removal processes as responsible for the variation with density of the SFR of normal galaxies and galaxy-galaxy interactions as responsible for the prevalence of starbursts in intermediate density environments.

The Trouble with Hubble Types in the Virgo Cluster

Quantitative measures of central light concentration and star formation activity are derived from R and Hα surface photometry of 84 bright S0-Scd Virgo Cluster and isolated spiral galaxies. For isolated spirals, there is a good correlation between these two parameters and assigned Hubble types. In the Virgo Cluster, the correlation between central light concentration and star formation activity is significantly weaker. Virgo Cluster spirals have systematically reduced global star formation with respect to isolated spirals, with severe reduction in the outer disk, but normal or enhanced activity in the inner disk. Assigned Hubble types are thus inadequate to describe the range in morphologies of bright Virgo Cluster spirals. In particular, spirals with reduced global star formation activity are often assigned misleading spiral classifications, irrespective of their central light concentrations; 45%±25% of the galaxies classified as Sa in the Virgo Cluster sample have central light concentrations more characteristic of isolated Sb-Sc galaxies. The misleading classification of low-concentration galaxies with low star formation rates as spirals may account for part of the excess of early-type spiral galaxies in clusters. Thus, the morphology-density relationship is not all due to a systematic increase in the bulge-to-disk ratio with environmental density.

The Published Extended Rotation Curves of Spiral Galaxies: Confrontation with Modified Dynamics

A sample of 22 spiral galaxy rotation curves, measured in the 21 cm line of neutral hydrogen, is considered in the context of Milgrom's modified dynamics (MOND). Combined with the previous, highly selected sample of Begeman et al., this constitutes the current total sample of galaxies with published (or available) extended rotation curves and photometric observations of the light distribution. This is the observational basis of present quantitative understanding of the discrepancy between the visible mass and classical dynamical mass in galaxies. It is found that the gravitational force calculated from the observed distribution of luminous material and gas by use of the simple MOND formula can account for the overall shape and amplitude of these 22 rotation curves, and in some cases, the predicted curve agrees with the observed rotation curve in detail. The fitted rotation curves have, in 13 cases, only one free parameter, which is the mass-to-light ratio of the luminous disk; in nine cases, there is an additional free parameter, which is M/L of a central bulge or light concentration. The values of the global M/L (bulge plus disk) are reasonable and, when the gas mass is also included, show a scatter consistent with that in the Tully-Fisher relation. The success of the MOND prescription in predicting the rotation curves in this larger, less stringently selected sample lends further support to the idea that dynamics or gravity is non-Newtonian in the limit of low acceleration and that it is unnecessary to invoke the presence of large quantities of unseen matter.

Galaxy morphology to I=25 mag in the Hubble Deep Field

The morphological properties of galaxies between $21 {\rm~mag} < I < 25 {\rm~mag}$ in the {\em Hubble Deep Field} are investigated using a quantitative classification system based on measurements of the central concentration and asymmetry of galaxian light. The class distribution of objects in the {\em Hubble Deep Field} is strongly skewed towards highly asymmetric objects, relative to distributions from both the {\em HST Medium Deep Survey} at $I < 22 {\rm~mag}$ and an artificially redshifted sample of local galaxies. The steeply rising number count-magnitude relation for irregular/peculiar/merging systems at $I < 22 {~\rm mag}$ reported in Glazebrook \etal\ (1995a) continues to at least $I=25~{\rm mag}$. Although these peculiar systems are predominantly blue at optical wavelengths, a significant fraction also exhibit red $U-B$ colours, which may indicate they are at high redshift. Beyond Glazebrook \etal 's magnitude limit the spiral counts appear to rise more steeply than high-normalization no-evolution predictions, whereas those of elliptical/S0 galaxies only slightly exceed such predictions and may turn-over beyond $I \sim 24~{\rm mag}$. These results are compared with those from previous investigations of faint galaxy morphology with HST and the possible implications are briefly discussed. The large fraction of peculiar/irregular/merging systems in the {\em Hubble Deep Field} suggests that by $I\sim 25 {\rm~mag}$ the conventional Hubble system no longer provides an adequate description of the morphological characteristics of a high fraction of field galaxies.

The morphologies of distant galaxies. 1: an automated classification system

We describe an automated morphological classification system that is useful for the study of faint objects detected on CCD frames. The fundamental parameter in our system is the central concentration of light. This parameter traces both the disk-to-bulge ratio and the effective radius of the galactic bulge component. We show that our classification system is less sensitive to seeing degradation than the Hubble system. The fundamental parameter of our classification system is of physical interest as a tracer of stellar population. In some respects our system might be regarded as an automated version of Morgan's Yerkes system. Our classification scheme is illustrated by using wide-field CCD data of the core of the galaxy cluster Abell 957. Many of the galaxies in the core of this cluster are poorly described by the Hubble system, but are well described by a classification system based on central concentration of light. We have also artificially redshifted our wide- field CCD image to mimic the appearance of an intermediate-redshift cluster seen under excellent seeing conditions, and show that our procedure makes it possible to morphologically classify faint galaxies out to z ~ 0.5 using ground-based data. Monte Carlo simulations are used to quantify the statistical uncertainties inherent in our morphological classifications.

Shock excitation, nuclear activity, and star formation in NGC 6240

Observations of the IR-excess object NGC 6240 are presented, including (1) broadband BVR, Gunn z, i, H-alpha, forbidden N II (658.3-nm), and K images obtained at ESO and KPNO; (2) 350-690-nm and 550-1100-nm long-slit spectra obtained at La Palma and ESO; and (3) 628.0-697.5-nm fiber-array spectra of the inner region obtained with the 4-m Mayall telescope at KPNO. The results are presented graphically and characterized in detail. Strong optical line emission is attributed to shocks between clouds in large-scale chaotic motion, and evidence found for an active Seyfert-1-type nucleus. There is only a moderate amount of star formation, and two central light concentrations are interpreted as the remnant nuclei of merging galaxies. It is suggested that the observed luminosity of NGC 6240 could be maintained for tens of Myr (without dominant starburst activity) by the energy stored in gas motion, assuming that the proportion of ionized gas is less than 0.0001. 41 refs.

An Application of Bessel Functions to a Problem in Optical Resolution

Whatever theory is finally adopted for the propagation of light, there will always remain the interesting fundamental problem as to how far an object is exactly reproduced by an optical system. In this paper, the enquiry will be considered in its simplest form, and only the simplest types of objects can be considered. Taking the wave theory, let us consider the reproduction of an infinitely distant self-luminous point source, such as a star, through an optical system, such as a telescope. Sir George Airy investigated this case in 1834 ; he shewed what W. Herschel had recorded in 1782, that the image in the focal plane f of the optical system consisted of a central concentration of light, surrounded by light rings of rapidly diminishing intensity (see Fig 2), and gave formulae to shew the falling off in intensity of the light away from the centre of the image. This disc of light, then, is the approximation to the point-image of geometrical optics. The deformation is due to the distortion of the sphericity of the light waves making the image by diffraction at the aperture of the system. As in the propagation of wireless waves, however, diffraction is not the only cause of distortion.