arXiv subjects

Mark A. Fardal

Publications and source records attributed to Mark A. Fardal.

At least 37 records · Page 2Linked to original sources

arXiv2013

Inferring the Andromeda Galaxy's mass from its giant southern stream with Bayesian simulation sampling

M31 has a giant stream of stars extending far to the south and a great deal of other tidal debris in its halo, much of which is thought to be directly associated with the southern stream. We model this structure by means of Bayesian sampling of parameter space, where each sample uses an N-body simulation of a satellite disrupting in M31's potential. We combine constraints on stellar surface densities from the Isaac Newton Telescope survey of M31 with kinematic data and photometric distances. This combination of data tightly constrains the model, indicating a stellar mass at last pericentric passage of log(M_s / Msun) = 9.5+-0.1, comparable to the LMC. Any existing remnant of the satellite is expected to lie in the NE Shelf region beside M31's disk, at velocities more negative than M31's disk in this region. This rules out the prominent satellites M32 or NGC 205 as the progenitor, but an overdensity recently discovered in M31's NE disk sits at the edge of the progenitor locations found in the model. M31's virial mass is constrained in this model to be log(M200) = 12.3+-0.1, alleviating the previous tension between observational virial mass estimates and expectations from the general galactic population and the timing argument. The techniques used in this paper, which should be more generally applicable, are a powerful method of extracting physical inferences from observational data on tidal debris structures.

astro-ph.CO↗

arXiv2012

Unearthing Foundations of a Cosmic Cathedral: Searching the Stars for M33's Halo

We use data from the Pan-Andromeda Archaeological Survey (PAndAS) to search for evidence of an extended halo component belonging to M33 (the Triangulum Galaxy). We identify a population of red giant branch (RGB) stars at large radii from M33's disk whose connection to the recently discovered extended "disk substructure" is ambiguous, and which may represent a "bona-fide" halo component. After first correcting for contamination from the Milky Way foreground population and misidentified background galaxies, we average the radial density of RGB candidate stars over circular annuli centered on the galaxy and away from the disk substructure. We find evidence of a low-luminosity, centrally concentrated component that is everywhere in our data fainter than mu_V ~ 33 mag arcsec^(-2). The scale length of this feature is not well constrained by our data, but it appears to be of order r_exp ~ 20 kpc; there is weak evidence to suggest it is not azimuthally symmetric. Inspection of the overall CMD for this region that specifically clips out the disk substructure reveals that this residual RGB population is consistent with an old population with a photometric metallicity of around [Fe/H] ~ -2 dex, but some residual contamination from the disk substructure appears to remain. We discuss the likelihood that our findings represent a bona-fide halo in M33, rather than extended emission from the disk substructure. We interpret our findings in terms of an upper limit to M33's halo that is a few percent of its total luminosity, although its actual luminosity is likely much less.

astro-ph.CO↗

arXiv2012

A Bayesian Approach to Locating the Red Giant Branch Tip Magnitude (Part II); Distances to the Satellites of M31

In `A Bayesian Approach to Locating the Red Giant Branch Tip Magnitude (PART I),' a new technique was introduced for obtaining distances using the TRGB standard candle. Here we describe a useful complement to the technique with the potential to further reduce the uncertainty in our distance measurements by incorporating a matched-filter weighting scheme into the model likelihood calculations. In this scheme, stars are weighted according to their probability of being true object members. We then re-test our modified algorithm using random-realization artificial data to verify the validity of the generated posterior probability distributions (PPDs) and proceed to apply the algorithm to the satellite system of M31, culminating in a 3D view of the system. Further to the distributions thus obtained, we apply a satellite-specific prior on the satellite distances to weight the resulting distance posterior distributions, based on the halo density profile. Thus in a single publication, using a single method, a comprehensive coverage of the distances to the companion galaxies of M31 is presented, encompassing the dwarf spheroidals Andromedas I - III, V, IX-XXVII and XXX along with NGC147, NGC 185, M33 and M31 itself. Of these, the distances to Andromeda XXIV - XXVII and Andromeda XXX have never before been derived using the TRGB. Object distances are determined from high-resolution tip magnitude posterior distributions generated using the Markov Chain Monte Carlo (MCMC) technique and associated sampling of these distributions to take into account uncertainties in foreground extinction and the absolute magnitude of the TRGB as well as photometric errors. The distance PPDs obtained for each object both with, and without the aforementioned prior are made available to the reader in tabular form...

astro-ph.CO↗

arXiv2012

A spectroscopic survey of Andromeda's Western Shelf

The Andromeda galaxy (M31) shows many tidal features in its halo, including the Giant Southern Stream (GSS) and a sharp ledge in surface density on its western side (the W Shelf). Using DEIMOS on the Keck telescope, we obtain radial velocities of M31's giant stars along its NW minor axis, in a radial range covering the W Shelf and extending beyond its edge. In the space of velocity versus radius, the sample shows the wedge pattern expected from a radial shell, which is detected clearly here for the first time. This confirms predictions from an earlier model of formation of the GSS, which proposed that the W Shelf is a shell from the third orbital wrap of the same tidal debris stream that produces the GSS, with the main body of the progenitor lying in the second wrap. We calculate the distortions in the shelf wedge pattern expected from its outward expansion and angular momentum, and show that these effects are echoed in the data. In addition, a hot, relatively smooth spheroid population is clearly present. We construct a bulge-disk-halo N-body model that agrees with surface brightness and kinematic constraints, and combine it with a simulation of the GSS. From the contrasting kinematic signatures of the hot spheroid and shelf components, we decompose the observed stellar metallicity distribution into contributions from each component using a non-parametric mixture model. The shelf component's metallicity distribution matches previous observations of the GSS superbly, further strengthening the evidence they are connected and bolstering the case for a massive progenitor of this stream.

astro-ph.CO↗

arXiv2012

The SPLASH Survey: Kinematics of Andromeda's Inner Spheroid

The combination of large size, high stellar density, high metallicity, and Sersic surface brightness profile of the spheroidal component of the Andromeda galaxy (M31) within R_proj ~ 20 kpc suggest that it is unlike any subcomponent of the Milky Way. In this work we capitalize on our proximity to and external view of M31 to probe the kinematical properties of this "inner spheroid." We employ a Markov chain Monte Carlo (MCMC) analysis of resolved stellar kinematics from Keck/DEIMOS spectra of 5651 red giant branch stars to disentangle M31's inner spheroid from its stellar disk. We measure the mean velocity and dispersion of the spheroid in each of five spatial bins after accounting for a locally cold stellar disk as well as the Giant Southern Stream and associated tidal debris. For the first time, we detect significant spheroid rotation (v_rot ~ 50 km/s) beyond R_proj ~ 5 kpc. The velocity dispersion decreases from about 140 km/s at R_proj = 7 kpc to 120 km/s at R_proj = 14 kpc, consistent to 2 sigma with existing measurements and models. We calculate the probability that a given star is a member of the spheroid and find that the spheroid has a significant presence throughout the spatial extent of our sample. Lastly, we show that the flattening of the spheroid is due to velocity anisotropy in addition to rotation. Though this suggests that the inner spheroid of M31 more closely resembles an elliptical galaxy than a typical spiral galaxy bulge, it should be cautioned that our measurements are much farther out (2 - 14 r_eff) than for the comparison samples.

astro-ph.GA↗

arXiv2010

Pressure Support vs. Thermal Broadening in the Lyman-alpha Forest I: Effects of the Equation of State on Longitudinal Structure

In the low density intergalactic medium (IGM) that gives rise to the Lyman-alpha forest, gas temperature and density are tightly correlated. The velocity scale of thermal broadening and the Hubble flow across the gas Jeans scale are of similar magnitude (Hlambda_J ~ sigma_th). To separate the effects of gas pressure support and thermal broadening on the Lya forest, we compare spectra extracted from two smoothed particle hydrodynamics (SPH) simulations evolved with different photoionization heating rates (and thus different Jeans scales), imposing different temperature-density relations on the evolved particle distributions. The turnover scales in the flux power spectrum and flux autocorrelation function are determined mainly by thermal broadening rather than pressure. However, the insensitivity to pressure arises partly from a cancellation effect with a sloped temperature-density relation (T ~ rho^{0.6} in our simulations): the high density peaks in the colder, lower pressure simulation are less smoothed by pressure support than in the hotter simulation, and it is this higher density gas that experiences the strongest thermal broadening. Changes in thermal broadening and pressure support have comparably important effects on the flux probability distribution (PDF), which responds directly to the gas overdensity distribution rather than the scale on which it is smooth. Tests on a lower resolution simulation show that our statistical results are converged even at this lower resolution. While thermal broadening generally dominates the longitudinal structure in the Lya forest, we show in Paper II that pressure support determines the transverse coherence of the forest observed towards close quasar pairs. [ABRIDGED]

astro-ph.CO↗

arXiv2010

Pressure Support vs. Thermal Broadening in the Lyman-alpha Forest II: Effects of the Equation of State on Transverse Structure

We examine the impact of gas pressure on the transverse coherence of high-redshift (2 <= z <= 4) Lyman-alpha forest absorption along neighboring lines of sight that probe the gas Jeans scale (projected separation Delta r <= 500 kpc/h comoving; angular separation Delta theta <= 30"). We compare predictions from two smoothed particle hydrodynamics (SPH) simulations that have different photoionization heating rates and thus different temperature-density relations in the intergalactic medium (IGM). We also compare spectra computed from the gas distributions to those computed from the pressureless dark matter. The coherence along neighboring sightlines is markedly higher for the hotter, higher pressure simulation, and lower for the dark matter spectra. We quantify this coherence using the flux cross-correlation function and the conditional distribution of flux decrements as a function of transverse and line-of-sight (velocity) separation. Sightlines separated by Delta theta <= 15" are ideal for probing this transverse coherence. Higher pressure decreases the redshift-space anisotropy of the flux correlation function, while higher thermal broadening increases the anisotropy. In contrast to the longitudinal (line-of-sight) structure of the Lya forest, the transverse structure on these scales is dominated by pressure effects rather than thermal broadening. With the rapid recent growth in the number of known close quasar pairs, paired line-of-sight observations offer a promising new route to probe the IGM temperature-density relation and test the unexpectedly high temperatures that have been inferred from single sightline analyses.

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arXiv2009

Asymmetric Warfare: M31 and its Satellites

Photometric surveys of M31's halo vividly illustrate the wreckage caused by hierarchical galaxy formation. Several of M31's satellites are being disrupted by M31's tidal field, among them M33 and And I, while other tidal structures are the corpses of satellites already destroyed. The extent to which M31's satellites have left battle scars upon it is unknown; to answer this we need accurate orbits and masses of the perturbers. I focus here on M31's 150-kpc-long Giant Southern Stream (GSS) as an example of how these can be determined even in the absence of a visible progenitor. Comparing N-body models to photometric and spectroscopic data, I find this stream resulted from the disruption of a large satellite galaxy by a close passage about 750 Myr ago. The GSS is connected to several other debris structures in M31's halo. Bayesian sampling of the simulations estimates the progenitor's initial mass as log(Mstar/Msun) = 9.5 +- 0.2, showing it was one of the most massive Local Group galaxies until quite recently. The stream model constrains M31's halo mass to be (1.8+-0.5)x10^{12} Msun. While these small uncertainties neglect several important degrees of freedom, they are likely to remain good even with a more complete model. Future work on M31's satellites and streams will provide independent constraints on M31's mass, and reveal the shared history of M31 and its halo components.

astro-ph.CO↗

arXiv2009

The remnants of galaxy formation from a panoramic survey of the region around M31

In hierarchical cosmological models, galaxies grow in mass through the continual accretion of smaller ones. The tidal disruption of these systems is expected to result in loosely bound stars surrounding the galaxy, at distances that reach $10 - 100$ times the radius of the central disk. The number, luminosity and morphology of the relics of this process provide significant clues to galaxy formation history, but obtaining a comprehensive survey of these components is difficult because of their intrinsic faintness and vast extent. Here we report a panoramic survey of the Andromeda galaxy (M31). We detect stars and coherent structures that are almost certainly remnants of dwarf galaxies destroyed by the tidal field of M31. An improved census of their surviving counterparts implies that three-quarters of M31's satellites brighter than $M_V < -6$ await discovery. The brightest companion, Triangulum (M33), is surrounded by a stellar structure that provides persuasive evidence for a recent encounter with M31. This panorama of galaxy structure directly confirms the basic tenets of the hierarchical galaxy formation model and reveals the shared history of M31 and M33 in the unceasing build-up of galaxies.

astro-ph.CO↗

arXiv2008

The impact of mergers on relaxed X-ray clusters - III. Effects on compact cool cores

(Abridged) We use the simulations presented in Poole et al. 2006 to examine the effects of mergers on compact cool cores in X-ray clusters. We propose a scheme for classifying the morphology of clusters based on their surface brightness and entropy profiles. Three dominant morphologies emerge: two hosting compact cores and central temperatures which are cool (CCC systems) or warm (CWC systems) and one hosting extended cores which are warm (EWC systems). We find that CCC states are disrupted only after direct collisions between cluster cores in head-on collisions or during second pericentric passage in off-axis mergers. By the time they relax, our remnant cores have generally been heated to warm core (CWC or EWC) states but subsequently recover CCC states. The only case resulting in a long-lived EWC state is a slightly off-axis 3:1 merger for which the majority of shock heating occurs during the accretion of a low-entropy stream formed from the disruption of the secondary's core. Compression prevents core temperatures from falling until after relaxation thus explaining the observed population of relaxed CWC systems with no need to invoke AGN feedback. The morphological segregation observed in the L_x-T_x and beta-r_c scaling relations is reflected in our simulations as well. However, none of the cases we have studied produce sufficiently high remnant central entropies to account for the most under-luminous EWC systems observed. Lastly, systems which initially host central metallicity gradients do not yield merger remnants with flat metallicity profiles. Taken together, these results suggest that once formed, compact core systems are remarkably stable against disruption from mergers. It remains to be demonstrated exactly how the sizable observed population of extended core systems was formed.

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arXiv2008

Was the Andromeda Stream Produced by a Disk Galaxy?

The halo region of M31 exhibits a startling level of stellar inhomogeneities, the most prominent of which is the "giant southern stream". Our previous analysis indicates that this stream, as well as several other observed features, are products of the tidal disruption of a single satellite galaxy with stellar mass ~10^9 solar masses less than 1 Gyr ago. Here we show that the specific observed morphology of the stream and halo debris favors a cold, rotating, disk-like progenitor over a dynamically hot, non-rotating one. These observed characteristics include the asymmetric distribution of stars along the stream cross-section and its metal-rich core/metal-poor sheath structure. We find that a disk-like progenitor can also give rise to arc-like features on the minor axis at certain orbital phases that resemble the recently discovered minor-axis "streams", even reproducing the lower observed metallicity of these streams. Though interpreted by the discoverers as new, independent tidal streams, our analysis suggests that these minor-axis streams may alternatively arise from the progenitor of the giant southern stream. Overall, our study points the way to a more complete reconstruction of the stream progenitor and its merger with M31, based on the emerging picture that most of the major inhomogeneities observed in the M31 halo share a common origin with the giant stream.

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arXiv2007

The impact of mergers on relaxed X-ray clusters - II. Effects on global X-ray and SZ properties and their scaling relations

We use the suite of simulations presented in Poole et al (2006) to examine global X-ray and Sunyaev-Zel'dovich (SZ) observables for systems of merging relaxed X-ray clusters. In all of the scaling relations generated from the properties we have studied, we observe a generic evolution (in good qualitative agreement with previous authors): a rapid transient roughly along the mass scaling relations, a subsequent slow drift across the scatter until virialization, followed by a slow evolution along and up the mass scaling relations as cooling recovers in the cluster cores. However, this drift is not sufficient to account for the observed scatter in the scaling relations. We also study the effects of mergers on several theoretical temperature measures of the intracluster medium: emission weighted measures (T_ew), the spectroscopic-like measure proposed by Mazzotta et al (2004; T_sl) and plasma model fits to the integrated spectrum of the system (T_spec). We find that T_sl tracks T_spec for the entire duration of our mergers, illustrating that it remains a good tool for observational comparison even for highly disturbed systems. Furthermore, the transient temperature increases produced during first and second pericentric passage are 15-40% larger for T_ew than for T_sl or T_spec. This suggests that the effects of transient temperature increases on sigma_8 and Omega_M derived by Randall et al (2002) are over estimated. Lastly, we examine the X-ray SZ proxy proposed by Kravtsov et al (2006) and find that the tight mass scaling relation they predict remains secure through the entire duration of a merger event, independent of projection effects.

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arXiv2006

The impact of mergers on relaxed X-ray clusters - I. Dynamical evolution and emergent transient structures

We report on the analysis of a suite of SPH simulations (incorporating cooling and star formation) of mergers involving idealised X-ray clusters whose initial conditions resemble relaxed clusters with cool compact cores observed by Chandra and XMM. The simulations sample the most interesting, theoretically plausible, range of impact parameters and progenitor mass ratios. We find that all mergers evolve via a common progression. We illustrate this progression in the projected gas density, X-ray surface brightness, SZ, temperature, and gas entropy maps. Several different classes of transient ``cold front''-like features can arise over the course of a merger. We find that all of these classes are present in Chandra and XMM observations of merging systems and propose a naming scheme for these features: ``comet-like'' tails, bridges, plumes, streams and edges. In none of the cases considered do the initial cool compact cores of the primary and the secondary get destroyed during the course of the mergers. We quantify the evolving morphology of our mergers using centroid variance, power ratios and offset between the X-ray and the projected mass maps. We find that the centroid variance best captures the dynamical state of the cluster. Placing the system at z=0.1, we find that all easily identified observable traces of the secondary disappear from a simulated 50 ks Chandra image following the second pericentric passage. The system, however, takes approximately 2 additional Gyrs to relax and virialize. Temperature fluctuations at the level of 20% can persist in the final systems well past the point of virialization, suggesting that that the existence of temperature fluctuations, in and of themselves, do not necessarily indicate a disturbed or unrelaxed system.

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arXiv2006

On the Evolutionary History of Stars and their Fossil Mass and Light

The total extragalactic background radiation can be an important test of the global star formation history (SFH). Using direct observational estimates of the SFH, along with standard assumptions about the initial mass function (IMF), we calculate the total extragalactic background radiation and the observed stellar density today. We show that plausible SFHs allow a significant range in each quantity, but that their ratio is very tightly constrained. Current estimates of the stellar mass and extragalactic background are difficult to reconcile, as long as the IMF is fixed to the Salpeter slope above 1 Msun. The joint confidence interval of these two quantities only agrees with that determined from the allowed range of SFH fits at the 3-sigma level, and for our best-fit values the discrepancy is about a factor of two. Alternative energy sources that contribute to the background, such as active galactic nuclei (AGN), Population III stars, or decaying particles, appear unlikely to resolve the discrepancy. However, changes to the IMF allow plausible solutions to the background problem. The simplest is an average IMF with an increased contribution from stars around 1.5--4 Msun. A ``paunchy'' IMF of this sort could emerge as a global average if low mass star formation is suppressed in galaxies experiencing rapid starbursts. Such an IMF is consistent with observations of star-forming regions, and would help to reconcile the fossil record of star formation with the directly observed SFH.

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arXiv2005

The Effects of Radiative Cooling on the Entropy Distribution of Intracluster Gas

High resolution X-ray observations indicate that the entropy profiles in the central regions of some massive cooling flow clusters are well approximated by powerlaws. McCarthy and coworkers recently accounted for this trend with an analytic model that includes the detailed effects of radiative cooling. Interestingly, these authors found that cooling (and subsequent inflow of the gas) naturally establishes approximate steady-state powerlaw entropy profiles in the cores of clusters. However, the origin of this behavior and its dependence on initial conditions have yet to be elucidated. In the present study, we explain this trend in the context of the self-similar cooling wave model developed previously by Bertschinger (1989). It is shown that the logarithmic slope of the entropy profile in the cores of relaxed cooling flow clusters is given by a simple analytic function that depends only on the logarithmic slopes of the local gravitational potential and the cooling function. We discuss a number of potentially interesting uses of the above result, including: (1) a way of measuring the shapes of gravitational potentials of cooling flow clusters (which may, for example, be compared with the results of the standard hydrostatic equilibrium method); (2) a simple method for constructing realistic analytic cluster models that include the effects of radiative cooling; and (3) a test of the reliability of cooling routines implemented in analytic models and hydrodynamic simulations.

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arXiv2001

Sub-mm Galaxies in Cosmological Simulations

We study the predicted sub-mm emission from massive galaxies in a Lambda-CDM universe, using hydrodynamic cosmological simulations. Assuming that most of the emission from newly formed stars is absorbed and reradiated in the rest-frame far-IR, we calculate the number of galaxies that would be detected in sub-mm surveys conducted with SCUBA. The predicted number counts are strongly dependent on the assumed dust temperature and emissivity law. With plausible choices for SED parameters (e.g., T=35 K, beta=1.0), the simulation predictions reproduce the observed number counts above ~ 1 mJy. The sources have a broad redshift distribution with median z ~ 2, in reasonable agreement with observational constraints. However, the predicted count distribution may be too steep at the faint end, and the fraction of low redshift objects may be larger than observed. In this physical model of the sub-mm galaxy population, the objects detected in existing surveys consist mainly of massive galaxies (several M_*) forming stars fairly steadily over timescales ~ 10^8-10^9 years, at moderate rates ~100 Msun/yr. The typical descendants of these sub-mm sources are even more massive galaxies, with old stellar populations, found primarily in dense environments. While the resolution of our simulations is not sufficient to determine galaxy morphologies, these properties support the proposed identification of sub-mm sources with massive ellipticals in the process of formation. The most robust and distinctive prediction of this model, stemming directly from the long timescale and correspondingly moderate rate of star formation, is that the far-IR SEDs of SCUBA sources have a relative high 850 micron luminosity for a given bolometric luminosity. [Abridged]

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arXiv2000

Hydrodynamic Simulation of the Cosmological X-ray Background

(Abridged) We use a hydrodynamic simulation of a LambdaCDM model to predict the extragalactic X-ray background (XRB), focussing on emission from the intergalactic medium (IGM). We also include X-rays from point sources associated with galaxies in the simulation, and make maps of the angular distribution of the emission. We find that filaments in the maps are not evident, being diluted by projection. In the soft (0.5-2 keV) band, the mean intensity of radiation from intergalactic and cluster gas is 2.3*10^-12 ergdeg^-2cm^-2s^-1, 35% of the total soft band emission. This is compatible at the ~1 sigma level with estimates of the unresolved soft background from ROSAT and {\it Chandra}. Only 4% of the hard (2-10 keV) emission is associated with the IGM. Relative to AGN flux, the IGM component peaks at a lower redshift (median z~0.45) so its clustering makes an important contribution to that of the total XRB. The angular correlations on 0.1-10 arcmin scales are significant, with an amplitude roughly consistent with an extrapolation of recent ROSAT results to small scales. A cross-correlation of the XRB against nearby galaxies taken from a simulated redshift survey also yields a strong signal from the IGM. Although some recent papers have argued that the expected soft band intensity from gas in galaxy, group, and cluster halos would exceed XRB limits unless much of the gas is expelled by supernova feedback, we obtain reasonable compatibility with current observations in a simulation that incorporates cooling, star formation, and only modest feedback. A prediction of our model is that the unresolved portion of the soft XRB will remain mostly unresolved.

astro-ph↗

arXiv2000

Cooling Radiation and the Lyman-alpha Luminosity of Forming Galaxies

We examine the cooling radiation from forming galaxies in hydrodynamic simulations of the LCDM model (cold dark matter with a cosmological constant), focusing on the Ly-alpha line luminosities of high-redshift systems. Primordial composition gas condenses within dark matter potential wells, forming objects with masses and sizes comparable to the luminous regions of observed galaxies. As expected, the energy radiated in this process is comparable to the gravitational binding energy of the baryons, and the total cooling luminosity of the galaxy population peaks at z ~= 2. However, in contrast to the classical picture of gas cooling from the \sim 10^6 K virial temperature of a typical dark matter halo, we find that most of the cooling radiation is emitted by gas with T < 20,000 K. As a consequence, roughly 50% of this cooling radiation emerges in the Ly-alpha line. While a galaxy's cooling luminosity is usually smaller than the ionizing continuum luminosity of its young stars, the two are comparable in the most massive systems, and the cooling radiation is produced at larger radii, where the Ly-alpha photons are less likely to be extinguished by dust. We suggest, in particular, that cooling radiation could explain the two large (\sim 100 kpc), luminous (L_{Ly-alpha} \sim 10^{44} erg s^{-1}) ``blobs'' of Ly-alpha emission found in Steidel et al.'s (1999) narrow band survey of a z = 3 proto-cluster. Our simulations predict objects of the observed luminosity at about the right space density, and radiative transfer effects can account for the observed sizes and line widths. We discuss observable tests of this hypothesis for the nature of the Ly-alpha blobs, and we present predictions for the contribution of cooling radiation to the Ly-alpha luminosity function of galaxies as a function of redshift.

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