Clustering Of Lyman-break Galaxies Research Articles

Strong Clustering of Lyman Break Galaxies around Luminous Quasars at Z ∼ 4* †

Abstract In the standard picture of structure formation, the first massive galaxies are expected to form at the highest peaks of the density field, which constitute the cores of massive proto-clusters. Luminous quasars (QSOs) at z ∼ 4 are the most strongly clustered population known, and should thus reside in massive dark matter halos surrounded by large overdensities of galaxies, implying a strong QSO–galaxy cross-correlation function. We observed six z ∼ 4 QSO fields with VLT/FORS, exploiting a novel set of narrow-band filters custom designed to select Lyman Break Galaxies (LBGs) in a thin redshift slice of , mitigating the projection effects that have limited the sensitivity of previous searches for galaxies around QSOs. We find that LBGs are strongly clustered around QSOs, and present the first measurement of the QSO–LBG cross-correlation function at z ∼ 4, on scales of (comoving). Assuming a power-law form for the cross-correlation function , we measure for a fixed slope of . This result is in agreement with the expected cross-correlation length deduced from measurements of the QSO and LBG auto-correlation function, and assuming a deterministic bias model. We also measure a strong auto-correlation of LBGs in our QSO fields, finding for a fixed slope of , which is ∼4 times larger than the LBG auto-correlation length in blank fields, providing further evidence that QSOs reside in overdensities of LBGs. Our results qualitatively support a picture where luminous QSOs inhabit exceptionally massive ( ) dark matter halos at z ∼ 4.

Understanding the non-linear clustering of high-redshift galaxies

We incorporate the non-linear clustering of dark matter halos, as modelled by Jose et al. (2016) into the halo model to better understand the clustering of Lyman break galaxies (LBGs) in the redshift range $z=3-5$. We find that, with this change, the predicted LBG clustering increases significantly on quasi-linear scales ($0.1 \leq r\,/\,h^{-1} \,{\rm Mpc} \leq 10$) compared to that in the linear halo bias model. This in turn results in an increase in the clustering of LBGs by an order of magnitude on angular scales $5" \leq \theta \leq 100"$. Remarkably, the predictions of our new model on the whole remove the systematic discrepancy between the linear halo bias predictions and the observations. The correlation length and large scale galaxy bias of LBGs are found to be significantly higher in the non-linear halo bias model than in the linear halo bias model. The resulting two-point correlation function retains an approximate power-law form in contrast with that computed using the linear halo bias theory. We also find that the non-linear clustering of LBGs increases with increasing luminosity and redshift. Our work emphasizes the importance of using non-linear halo bias in order to model the clustering of high-z galaxies to probe the physics of galaxy formation and extract cosmological parameters reliably.

The clustering and halo occupation distribution of Lyman-break galaxies atz ∼ 4

We investigate the clustering of Lyman-break galaxies (LBGs) at $z\sim4$. Using the hierarchical galaxy formation model GALFORM, we predict, for the first time using a semi-analytical model with feedback from active galactic nuclei (AGN), the angular correlation function (ACF) of LBGs and find agreement within $3\,\sigma$ with new measurements of the ACF from surveys including the Hubble eXtreme Deep Field (XDF) and CANDELS field. Our simulations confirm the conclusion reached using independent models that although the predicted ACFs reproduce the trend of increased clustering with luminosity, the dependence is less strong than observed. We find that for the detection limits of the XDF field central LBGs at $z\sim 4$ predominantly reside in haloes of mass $\sim 10^{11}-10^{12}h^{-1}M_{\rm \odot}$ and that satellites reside in larger haloes of mass $\sim 10^{12}-10^{13}h^{-1}M_{\rm \odot}$. The model predicts fewer bright satellite LBGs at $z\sim4$ than is inferred from measurements of the ACF at small scales. By analysing the halo occupation distribution (HOD) predicted by the model, we find evidence that AGN feedback affects the HOD of central LBGs in massive haloes. This is a new high-redshift test of this important feedback mechanism. We investigate the effect of photometric errors in the observations on the ACF predictions. We find that the observational uncertainty in the galaxy luminosity reduces the clustering amplitude and that this effect increases towards faint galaxies, particularly on small scales. To compare properties of model with observed LBGs this uncertainty must be considered.

Are z ∼ 5 quasars found in the most massive high-redshift overdensities?★

Luminous high-redshift QSOs are thought to exist within the most massive dark matter haloes in the young Universe. As a consequence they are likely to be markers for biased, over-dense regions where early galaxies cluster, regions that eventually grow into the groups and clusters seen in the lower redshift universe. In this paper we explore the clustering of galaxies around z ~ 5 QSOs as traced by Lyman Break Galaxies (LBGs). We target the fields of three QSOs using the same optical imaging and spectroscopy techniques used in the ESO Remote Galaxy Survey (ERGS, Douglas et al. 2009, 2010), which was successful in identifying individual clustered structures of LBGs. We use the statistics of the redshift clustering in ERGS to show that two of the three fields show significant clustering of LBGs at the QSO redshifts. Neither of these fields is obviously over-dense in LBGs from the imaging alone; a possible reason why previous imaging-only studies of high-redshift QSO environments have given ambiguous results. This result shows that luminous QSOs at z ~ 5 are typically found in over-dense regions. The richest QSO field contains at least nine spectroscopically confirmed objects at the same redshift including the QSO itself, seven LBGs and a second fainter QSO. While this is a very strong observational signal of clustering at z ~ 5, it is of similar strength to that seen in two structures identified in the 'blank sky' ERGS fields. This indicates that, while over-dense, the QSO environments are not more extreme than other structures that can be identified at these redshifts. The three richest structures discovered in this work and in ERGS have properties consistent with that expected for proto-clusters and likely represent the early stages in the build-up of massive current-day groups and clusters.

Close galaxy pairs atz= 3: a challenge to UV luminosity abundance matching

We use a sample of z ∼ 3 Lyman-break galaxies (LBGs) to examine close pair clustering statistics in comparison to Λ cold dark matter (ΛCDM)-based models of structure formation. Samples are selected by matching the LBG number density, ng, and by matching the observed LBG 3D correlation function of LBGs over the two-halo term region. We show that ultraviolet (UV) luminosity abundance matching cannot reproduce the observed data, but if subhaloes are chosen to reproduce the observed clustering of LBGs we are able to reproduce the observed LBG pair fraction (Nc) defined as the average number of companions per galaxy. This model suggests an overabundance of LBGs by a factor of ∼5 over those observed, suggesting that only one in five haloes above a fixed mass hosts a galaxy with LBG-like UV luminosity detectable via LBG selection techniques. This overdensity is in agreement with the results of a Millennium 2 analysis and with the discrepancies noted by previous authors using different types of simulations. We find a total observable close pair fraction of 23 ± 0.6 per cent (17.7 ± 0.5 per cent) using a prototypical cylinder radius in our overdense fiducial model and 8.3 ± 0.5 per cent (5.6 ± 0.2 per cent) in an abundance matched model (impurity corrected). For the matched spectroscopic slit analysis, we find and 5.1 ± 0.2 (1.68 ± 0.02) per cent, the average number of companions observed serendipitously in randomly aligned spectroscopic slits, for fiducial slits (abundance matched), whereas the observed fraction of serendipitous spectroscopic close pairs is 4.7 ± 1.5 per cent using the full LBG sample and 7.1 ± 2.3 per cent for a subsample with higher signal-to-noise ratio. We conduct the same analysis on a sample of dark matter haloes from the Millennium 2 simulation and find similar results. From the results and an analysis of the observed LBG 2D correlation functions, we show that the standard method of halo assignment fails to reproduce the break, or up turn, in the LBG close pair behaviour at small scale (≲20 h−1 kpc physical). To reconcile these discrepancies we suggest that a plausible fraction of LBGs in close pairs with lower mass (higher density) than our sample experience interaction-induced enhanced star formation that boosts their luminosity sufficiently to be detected in observational sample but are not included in the abundance matched simulation sample.

Galaxy statistics in pencil-beam surveys at high redshifts

Surveys of faint galaxies at high redshifts often result in a "pencil-beam" geometry that is much longer along the line-of-sight than across the sky. We explore the effects of this geometry on the abundance and clustering of Lyman-break galaxies (LBGs) and Lyman-alpha emitters (LAEs) in current and future surveys based on cosmological N-body simulations which adequately describe the nonlinear growth of structure on small scales and compare to linear theory. We find that the probability distribution of the LBG abundance is skewed toward low values since the narrow transverse dimension of the survey is more likely to probe underdense regions. Over a range that spans 1--2 orders of magnitude in galaxy luminosities, the variance in the number of objects differs from the commonly used analytic prediction and is not dominated by Poisson noise. Additionally, nonlinear bias on small scales results in a one-dimensional power spectrum of LAEs using a James Webb Space Telescope field-of-view that is relatively flat, markedly different from the expectation of linear perturbation theory. We discuss how these results may affect attempts to measure the UV background at high redshifts, estimate the relationship between halo mass and galaxy luminosity, and probe reionization by measuring the power-modulating effect of ionized regions.

Where are z= 4 Lyman Break Galaxies? Results from conditional luminosity function models of luminosity-dependent clustering★

Using the conditional luminosity function (CLF) - the luminosity distribution of galaxies in a dark matter halo - as a way to model galaxy statistics, we study how z = 4 Lyman Break Galaxies (LBGs) are distributed in dark matter haloes. For this purpose, we measure luminosity-dependent clustering of LBGs in the Subaru/XMM-Newton Deep Field by separating a sample of 16 920 galaxies to three magnitude bins in i' band between 24.5 and 27.5. Our model fits to data show a possible trend for more-luminous galaxies to appear as satellites in more-massive haloes; the minimum halo mass in which satellites appear is 3.9 +4.1 -3.5 x 10 12 , 6.2 +3.8 -4.9 × 10 12 and 9.6 +7.0 -4.6 x 10 12 M ⊙ (1σ errors) for galaxies with 26.5 < i' < 27.5, 25.5 < i' < 26.5 and 24.5 < i' < 25.5 mag, respectively. The satellite fraction of galaxies at z = 4 in these magnitude bins is 0.13-0.3, 0.09-0.22 and 0.03-0.14, respectively, where the 1σ ranges account for differences coming from two different estimates of the z = 4 LF from the literature. To jointly explain the LF and the large-scale linear bias factor of z = 4 LBGs as a function of rest UV luminosity requires central galaxies to be brighter in UV at z = 4 than present-day galaxies in same dark matter mass haloes. Moreover, UV luminosity of central galaxies in haloes with total mass greater than roughly 10 12 M ⊙ must decrease from z = 4 to today by an amount more than the luminosity change for galaxies in haloes below this mass. This mass-dependent luminosity evolution is preferred at more than 3σ confidence level compared to a pure-luminosity evolution scenario where all galaxies decrease in luminosity by the same amount from z = 4 to today. The scenario preferred by the data is consistent with the 'downsizing' picture of galaxy evolution.

Dynamical virial masses of Lyman-break galaxy haloes at z = 3

Abstract We improve on our earlier dynamical estimate of the virial masses of the haloes of Lyman-break galaxies (LBGs) at redshift z= 3 by accounting for the effects of seeing, slit width and observational uncertainties. From an analysis of the small number of available rotation curves for LBGs we determine a relation Vc7= (1.9 ± 0.2)σ between circular velocity at a radius of 7 kpc, Vc7, and central line velocity width, σ. We use this relation to transform the measured velocity widths of 32 LBGs to the distribution of circular velocities, Vc7, for the population of LBGs brighter than . We compare this distribution against the predicted distribution for the ‘massive-halo’ model in which LBGs pinpoint all of the highest mass dark matter haloes at that epoch. The observed LBG circular velocities are smaller than the predicted circular velocities by a factor of &amp;gt;1.4 ± 0.15. This is a lower limit, as we have ignored any increase of circular velocity caused by baryonic dissipation. The massive-halo model predicts a median halo virial mass of 1012.3 M⊙, and a small spread of circular velocities, Vc7. Our median estimated dynamical mass is &amp;lt;1011.6±0.3 M⊙, which is significantly smaller; furthermore, the spread of our derived circular velocities is much larger than the massive-halo prediction. These results are consistent with a picture which leaves some of the most massive haloes available for occupation by other populations which do not meet the LBG selection criteria. Our new dynamical mass limit is a factor of 3 larger than our earlier estimate which neglected the effects of seeing and slit width. The median halo mass recently estimated by Adelberger et al. from the measured clustering of LBGs is 1011.86±0.3 M⊙. Our dynamical analysis appears to favour lower masses and to be more in line with the median mass predicted by the collisional starburst model of Somerville et al., which is 1011.3 M⊙.

The Clustering of Galaxies around Threez∼ 3 Damped Lyα Absorbers

We present our results on the cross-correlation of Lyman break galaxies (LBGs) around three damped Ly? absorbers (DLAs) at zabs 3 from deep [?I,AB(sky) 27.6 mag arcsec-2] UBVI KPNO 4 m/MOSAIC images. The large area of the MOSAIC images, 0.31 deg2 or ~65 ? 65 h Mpc comoving at redshift z = 3, allows us to probe the clustering of LBGs on scales up to 20 Mpc comoving. Our survey covers a total of 1 deg2 and contains ~3000 LBGs with photometric redshifts between 2.8 and 3.5. Using the redshift likelihood distributions with mI as a prior, we selected LBGs within a redshift slice of width Wz = 0.15 (corresponding to ?z, the uncertainty in photometric redshifts) centered on the redshift of the absorbers. Within that redshift slice, we find that the DLA-LBG cross-correlation wdg is wdg = (1.62 ? 1.32) ? wgg, where wgg is the LBG autocorrelation. This corresponds to a correlation length of r0 = 5 ? 4.5 h-1 (comoving) (or r0 = 7 ? 6.8 h Mpc). The cross-correlation is most significant on scales 5-10 Mpc. Through Monte Carlo simulations, we find that wdg is significantly greater than zero at the greater than 95% level. In three other redshift slices that do not contain a DLA, we do not find any evidence of clustering. A larger sample will enable us to discriminate between wdg/wgg 1, i.e., to test whether DLA halos are more or less massive than LBG halos.

Clustering of Galaxies atz ∼ 3 around the Probable Damped Lyα Absorber toward QSO APM 08279+5255

We present results on the clustering of Lyman break galaxies (LBGs) around a probable damped Ly? absorption line cloud (DLA) at zabs = 2.974 from deep UBVI images of the field containing the quasar APM 08279+5255 (zem = 3.91). The large area covered by our images, 0.31 deg2 or ~40 ? 40 Mpc comoving at redshift z = 3, and their depth, ?I,AB(sky) 27.6 mag arcsec-2, allow us to identify ~450 LBG candidates brighter than IAB = 24.80 at 2.75 < z < 3.25 both close (50 kpc) to the DLA line of sight and up to 20 Mpc (comoving) from the DLA, i.e., physically unrelated. LBG candidates were identified using photometric redshift techniques that include the I magnitude as a prior estimate in addition to the colors. The two are combined using Bayes's theorem. This helps to break the degeneracies that occur in a pure spectral template fitting scheme. The overall rms is ?z 0.15 at z ~ 3 based on our analysis of photometric redshifts in the HDF-N. From the redshift likelihood distributions, we selected LBG galaxies within a redshift slice of width Wz = 0.15( ?z) centered on the redshift of the DLA zabs. Within that redshift slice, we find an enhancement of galaxies near the DLA using both the surface density (?/?g 3) and an estimator of the three-dimensional spatial overdensity (n/g ~ 5 ? 3). The surface overdensity ?/?g is significant at the more than 95% significance level on scales 2.5 < r? < 5 Mpc comoving. The overdensity cannot be related to the QSO environment since the QSO is at zem = 3.91. These results imply that some DLA could reside in high-density regions. We search within 45'' from the line of sight for galaxies responsible for the DLA and find one candidate with zphot = 3.03 that is 26'' (145 kpc physical) away. From its magnitude I = 24.65 ? 0.2, its luminosity is MI,AB = -21.35. Due to its large impact parameter, however, this galaxy is not a likely candidate for the absorber.

Galaxy halo occupation at high redshift

We discuss how current and future data on the clustering and number density of Lyman-break galaxies (LBGs) can be used to constrain their relationship to dark matter haloes. We explore a three-parameter model in which the number of LBGs per dark halo scales like a power law in the halo mass: for . Here, Mmin is the minimum mass halo that can host an LBG, M1 is a normalization parameter, associated with the mass above which haloes host more than one observed LBG, and S determines the strength of the mass-dependence. We show how these three parameters are constrained by three observable properties of LBGs: the number density, the large-scale bias and the fraction of objects in close pairs. Given these three quantities, the three unknown model parameters may be estimated analytically, allowing a full exploration of parameter space. As an example, we assume a ΛCDM cosmology and consider the observed properties of a recent sample of spectroscopically confirmed LBGs. We find that the favoured range for our model parameters is , , and . The preferred region in Mmin expands by an order of magnitude, and slightly shallower slopes are acceptable if the allowed range of bg is permitted to span all recent observational estimates. We also discuss how the observed clustering of LBGs as a function of luminosity can be used to constrain halo occupation, although because of current observational uncertainties we are unable to reach any strong conclusions. Our methods and results can be used to constrain more realistic models that aim to derive the occupation function N(M) from first principles, and offer insight into how basic physical properties affect the observed properties of LBGs.

NIR Narrow- and Broad-Band Study of the SSA 22 Field

Abstract Deep narrow- and broad-band near-infrared imaging observations of the central $ {2{}^{\mathrm {\prime }}} \times {2{}^{\mathrm {\prime }}}$ region of the SSA 22 field were made with the near-infrared camera (CISCO) attached to the Subaru Telescope. Using a narrow-band filter centered at $2.033\, {\mu \mathrm {m}}$, [O III] $\lambda~5007$ emitters at $z \sim 3.06 \pm 0.02$ were searched to examine star-forming activities in an over-density region where a clustering of Lyman Break Galaxies (LBGs) and Lyman $ \alpha$ emitter candidates around $ z = 3.09$ was reported, though the targeted redshift is slightly different from that of the peak of the over-density region. Although one emitter candidate at $ z = 3.06$ was detected, it is likely to be located at a redshift of between 1 and 2 judged based on multi-band photometry. Another emission-line object was detected in another narrow-band filter (“off band” filter) centered at $ 2.120\, {\mu \mathrm {m}}$, which is identified with a galaxy at $ z = 0.132$ (the emission line is Paschen $\alpha$). The $ K^{\prime}$-band imaging data revealed the presence of 12 Extremely Red Objects (EROs) with $I_{814}-K^{\prime} \geq4$. The distribution of the EROs does not seem to coincide with that of Lyman Break Galaxies or Lyman $\alpha $ emitters at $ z \sim3$. The magnitudes and colors of the EROs are not consistent with those of passively evolving massive elliptical galaxies at $ z \sim3$. Candidates for counterparts of the submm sources detected with SCUBA are found; no EROs around the submm sources are found in our magnitude limit.

Theoretical predictions on the clustering of SCUBA galaxies and implications for small-scale fluctuations at submillimetre wavelengths

This paper investigates the clustering properties of Submillimetre Common User Bolometric Array (SCUBA) selected galaxies within the framework of a unifying scheme relating the formation of quasi-stellar objects and spheroids. The theoretical angular correlation function is derived for different bias functions, corresponding to different values of the ratio Mhalo/Msph between the mass of the dark halo and the final mass in stars. SCUBA sources are predicted to be strongly clustered, with a clustering strength increasing with mass. We show that the model accounts for the clustering of Lyman-break galaxies, seen as the optical counterpart of low- to intermediate-mass primeval spheroidal galaxies, and is also consistent with the observed angular correlation function of extremely red objects. Best agreement is obtained for Mhalo/Msph=100. We also consider the implications for small-scale fluctuations observed at submillimetre wavelengths by current or forthcoming experiments aimed at mapping the cosmic microwave background (CMB). The predicted amplitude of the clustering signal in the 350-GHz channel of the Planck mission strongly depends on the halo-to-bulge mass ratio and may be of comparable amplitude to primary CMB anisotropies for multipole numbers l≳50.

Clustering Segregation with Ultraviolet Luminosity in Lyman Break Galaxies atz∼3 and Its Implications

We report on the clustering properties of Lyman break galaxies (LBGs) at z ~ 3. The correlation length of flux-limited samples of LBGs depends on their rest-frame ultraviolet (UV) luminosity at λ ~ 1700 Å, with fainter galaxies being less strongly clustered in space. We have used three samples with progressively fainter flux limits: two extracted from our ground-based survey and one from the Hubble Deep Fields (both North and South). The correlation length decreases by a factor of ≈3 over the range of limiting magnitudes that we have probed, namely, 25 ≲ ≲ 27, suggesting that samples with a fainter UV luminosity limit include galaxies with smaller mass. We have compared the observed scaling properties of the clustering strength with those predicted for cold dark matter (CDM) halos and found that (1) the clustering strength of LBGs follows, within the errors, the same scaling law with the volume density as the halos; and (2) the scaling law predicted for the galaxies using the halo mass spectrum and a number of models for the relationship that maps the halos' mass into the galaxies' UV luminosity depends only on how tightly mass and UV luminosity correlate but is otherwise insensitive to the details of the models. We interpret these results as additional evidence that the strong spatial clustering of LBGs is due to galaxy biasing, supporting the theory of biased galaxy formation and gravitational instability as the primary physical mechanism for the formation of structure. We have also fitted models of the mass-UV luminosity relationship to the data to reproduce simultaneously from the CDM halo mass spectrum the dependence of the correlation length with the UV luminosity and the luminosity function. We have found that (1) a scale invariant relationship between mass and UV luminosity (e.g., a power law) is not supported by the observations, suggesting that the properties of star formation of galaxies change along the mass spectrum of the observed LBGs; (2) the scatter of the UV luminosity of LBGs of given mass must be relatively small for massive LBGs, suggesting that the mass is an important parameter in regulating the activity of star formation in these systems; and (3) the fraction of massive halos at z ~ 3 that are not observed in UV-selected surveys is not large. From the fits, for a given choice of the cosmology, one can assign a scale of mass to the LBGs. For example, if Ω = 0.3 and ΩΛ = 0.7, the average mass of galaxies with luminosity = 23, 25.5, and 27.0 is = 2.5, 0.9, and 0.4 × 1012 M☉, respectively. The numbers are ≈2 times larger and ≈10 times smaller in an open universe with Ω = 0.2 and ΩΛ = 0 and in the Einstein-de Sitter cosmologies, respectively.

The Clustering of High‐Redshift Galaxies in the Cold Dark Matter Scenario

We investigate the clustering of high-redshift galaxies in five variants of the cold dark matter (CDM) scenario, using hydrodynamic cosmological simulations that resolve the formation of systems with circular velocities vc ≥ 100 km s-1 (Ω = 1) or vc ≥ 70 km s-1 (Ω = 0.4). Although the five models differ in their cosmological parameters and in the shapes and amplitudes of their mass power spectra, they predict remarkably similar galaxy clustering at z = 2, 3, and 4. The galaxy correlation functions show almost no evolution over this redshift range, even though the mass correlation functions grow steadily in time. Despite the fairly low circular velocity threshold of the simulations, the high-redshift galaxies are usually highly biased tracers of the underlying mass distribution; the bias factor evolves with redshift and varies from model to model. Predicted correlation lengths for the resolved galaxy population are 2-3 h-1 Mpc (comoving) at z = 3. More massive galaxies tend to be more strongly clustered. These CDM models have no difficulty in explaining the strong observed clustering of Lyman-break galaxies, and some may even predict excessive clustering. Because the effects of bias obscure differences in mass clustering, it appears that Lyman-break galaxy clustering will not be a good test of cosmological models but will instead provide a tool for constraining the physics of galaxy formation.

The Power Spectrum of Mass Fluctuations Measured from the Lyα Forest at Redshiftz = 2.5

We measure the linear power spectrum of mass-density fluctuations at redshift z = 2.5 from the Lyα forest absorption in a sample of 19 QSO spectra, using the method introduced by Croft et al. The P(k) measurement covers the range 2π/k ~ 450-2350 km s-1 (2-12 comoving h-1 Mpc for Ω = 1), limited on the upper end by uncertainty in fitting the unabsorbed QSO continuum and on the lower end by finite spectral resolution (0.8-2.3 A FWHM) and by nonlinear dynamical effects. We examine a number of possible sources of systematic error and find none that are significant on these scales. In particular, we show that spatial variations in the UV background caused by the discreteness of the source population should have negligible effect on our P(k) measurement. We estimate statistical errors by dividing the data set into ten subsamples. The statistical uncertainty in the rms mass-fluctuation amplitude, σ [P(k)]1/2, is ~20%, and is dominated by the finite number of spectra in the sample. We obtain consistent P(k) measurements (with larger statistical uncertainties) from the high- and low-redshift halves of the data set, and from an entirely independent sample of nine QSO spectra with mean redshift z = 2.1. A power-law fit to our results yields a logarithmic slope n = -2.25 ± 0.18 and an amplitude Δ2ρ(kp) = 0.57+0.26-0.18, where Δ2ρ is the contribution to the density variance from a unit interval of ln k and kp = 0.008(km s-1)-1. Direct comparison of our mass P(k) to the measured clustering of Lyman break galaxies shows that they are a highly biased population, with a bias factor b ~ 2-5. The slope of the linear P(k), never previously measured on these scales, is close to that predicted by models based on inflation and cold dark matter (CDM). The P(k) amplitude is consistent with some scale-invariant, COBE-normalized CDM models (e.g., an open model with Ω0 = 0.4) and inconsistent with others (e.g., Ω = 1). Even with limited dynamic range and substantial statistical uncertainty, a measurement of P(k) that has no unknown bias factors offers many opportunities for testing theories of structure formation and constraining cosmological parameters.

The structure and clustering of Lyman-break galaxies

The number density and clustering properties of Lyman-break galaxies (LBGs) are consistent with them being the central galaxies of the most massive dark haloes present at z ̃ 3. This conclusion holds in all currently popular hierarchical models for structure formation, and is almost independent of the global cosmological parameters. We examine whether the sizes, luminosities, kinematics and star formation rates of LBGs are also consistent with this identification. Simple formation models tuned to give good fits to low-redshift galaxies can predict the distribution of these quantities in the LBG population. The LBGs should be small (with typical half-light radii of 0.6–2 h−1kpc), should inhabit haloes of moderately high circular velocity (180–290 km s−1) but have low stellar velocity dispersions (70–120 km s−1) and should have substantial star formation rates (15–100 M⊙ yr−1). The numbers here refer to the predicted median values in the LBG sample of Adelberger et al.; the first number assumes an ω0=1 universe and the second number a flat universe with ω0=0.3. For either cosmology these predictions are consistent with the current (rather limited) observational data. Following the work of Kennicutt, we assume stars to form more rapidly in gas of higher surface density. This predicts that LBG samples should preferentially contain objects with low angular momentum, and therefore small size, for their mass. In contrast, samples of damped Ly α systems (DLSs) should be biased towards objects with large angular momentum. Bright LBGs and DLSs may therefore form distinct populations, with very different sizes and star formation rates, LBGs being smaller and more metal-rich than DLSs of similar mass and redshift.

The Angular Clustering of Lyman‐Break Galaxies at Redshiftz∼ 3

We have measured the angular correlation function w(?) for a sample of 871 Lyman-break galaxies (LBGs) in five fields at redshift z ~ 3. Fitting the power law Aw ?-? to a weighted average of w(?) from the five fields over the range 12'' ? 330'', we find Aw ~ 2 arcsec? and ? ~ 0.9. The slope is, within the errors, the same as for galaxy samples in the local and intermediate-redshift universe, and a slope ? = 0.25 or shallower is ruled out by the data at the 99.9% confidence level. Because N(z) of LBGs is well determined from 376 spectroscopic LBG redshifts, the real-space correlation function can be accurately derived from the angular one through the Limber transform. The inversion of w(?) is rather insensitive to the still relatively large uncertainties on A? and ?, and the spatial correlation length is much more tightly constrained than either of these parameters. We estimate r -->0=3.3 -->+ 0.7?0.6(2.1 -->+ 0.4?0.5) h-1 Mpc (comoving) for q0 = 0.1 (0.5) at the median redshift of the survey, ${u{z}{7016}}$ -->=3.04 (h is in units of 100 km s-1 Mpc-1 throughout this paper). The observed comoving correlation length of LBGs at z ~ 3 is comparable to that of present-day spiral galaxies and is only ~50% smaller than that of present-day ellipticals; it is as large or larger than any measured in recent intermediate-redshift galaxy samples (0.3 z 1). By comparing the observed galaxy correlation length to that of the mass predicted from cold dark matter (CDM) theory, we estimate a linear bias for LBGs of b ~ 1.5 (4.5) for q0 = 0.1 (0.5), in broad agreement with our previous estimates based on preliminary spectroscopy. The strong clustering and the large bias of the LBGs are consistent with biased galaxy formation theories and provide additional evidence that these systems are associated with massive dark matter halos. The results of the clustering of LBGs at z ~ 3 emphasize that apparent evolution in the clustering properties of galaxies may be due as much to variations in effective light-to-mass bias parameter among different galaxy samples as to evolution in the mass distribution through gravitational instability.

The clustering of Lyman-break galaxies

We calculate the statistical clustering of Lyman-break galaxies predicted in a selection of currently-fashionable structure formation scenarios. These models are all based on the cold dark matter model, but vary in the amount of dark matter, the initial perturbation spectrum, the background cosmology and in the presence or absence of a cosmological constant term. If Lyman-break galaxies form as a result of hierarchical merging, the amplitude of clustering depends quite sensitively on the minimum halo mass that can host such a galaxy. Interpretation of the recent observations by Giavalisco et al. (1998) would therefore be considerably clarified by a direct determination of the relevant halo properties. For a typical halo mass around $10^{11} h^{-1} M_\odot$ the observations do not discriminate strongly between cosmological models, but if the appropriate mass is larger, say $10^{12} ~h^{-1} M_\odot$ (which seems likely on theoretical grounds), then the data strongly favour models with a low matter-density.

Confronting Cold Dark Matter Cosmologies with Strong Clustering of Lyman Break Galaxies at [CLC][ITAL]z[/ITAL][/CLC] ∼ 3

We perform a detailed analysis of the statistical significance of a concentration of Lyman break galaxies at z~3 recently discovered by Steidel et al., using a series of N-body simulations with N=256 -->3 particles in a (100 h-1 Mpc)3 comoving box. While the observed number density of Lyman break galaxies at z~3 implies that they correspond to systems with dark matter halos of 1012 M☉, the resulting clustering of such objects on average is not strong enough to be reconciled with the concentration if it is fairly common; we predict one similar concentration approximately per 6-10 fields in three representative cold dark matter models. Considering the current observational uncertainty of the frequency of such clustering at z~3, it would be premature to rule out the models, but the future spectroscopic surveys in a dozen fields could definitely challenge all the existing cosmological models a posteriori fitted to the z=0 universe.