The expected area of the filled planar Brownian loop is Pi/5

Let B_t be a planar Brownian loop of time duration 1 (a Brownian motion conditioned so that B_0 = B_1). We consider the compact hull obtained by filling in all the holes, i.e. the complement of the unique unbounded component of R^2\B[0,1]. We show that the expected area of this hull is Pi/5. The proof uses, perhaps not surprisingly, the Schramm Loewner Evolution (SLE). Also, using the result of Yor about the law of the index of a Brownian loop, we show that the expected areas of the regions of non-zero index n equal 1/(2 Pi n^2). As a consequence, we find that the expected area of the region of index zero inside the loop is Pi/30; this value could not be obtained directly using Yor's index description.Comment: 15 pages, 3 figure

Exploring the formation of spheroidal galaxies out to z ∼ 1.5 in GOODS

The formation of massive spheroidal galaxies is studied on a visually classified sample extracted from the Advanced Camera for Surveys/Hubble Space Telescope (ACS/HST) images of the Great Observatories Origins Deep Survey north and south fields, covering a total area of 360 arcmin . The sample size (910 galaxies brighter than i = 24) allows us to explore in detail the evolution over a wide range of redshifts (0.4 10 M galaxies by a factor of 2 between z = 1 and 0, in contrast with a factor of ∼50 for lower mass galaxies (10 <M / M <10 ). One-quarter of the whole sample of early types are photometrically classified as blue galaxies. On a volume-limited sample out to z <0.7, the average stellar mass of the blue ellipticals is 5 × 10 M compared to 4 × 10 M for red ellipticals. On a volume-limited subsample out to z = 1.4 probing the brightest galaxies (M <-21), we find the median redshift of blue and red early types: 1.10 and 0.85, respectively. Blue early types only amount to 4 per cent of this sample (compared to 26 per cent in the full sample). The intrinsic colour distribution correlates overall bluer colours with blue cores (positive radial gradients of colour), suggesting an inside-out process of formation. The redshift evolution of the observed colour gradients is incompatible with a significant variation in stellar age within each galaxy. The slope of the Kormendy relation in the subsample of massive galaxies does not change over 0.4 <z <1.4 and is compatible with z = 0 values. The 'zero-point' of the Kormendy relation (i.e. the surface brightness at a fixed half-light radius) is 1 mag fainter (in the B band) for the subsample of low-mass (M <3.5 × 10 M ) early types.Peer reviewe

Does environment affect the star formation histories of early-type galaxies?

Differences in the stellar populations of galaxies can be used to quantify the effect of environment on the star formation history. We target a sample of early-type galaxies from the Sloan Digital Sky Survey in two different environmental regimes: close pairs and a general sample where environment is measured by the mass of their host dark matter halo. We apply a blind source separation technique based on principal component analysis, from which we define two parameters that correlate, respectively, with the average stellar age (eta) and with the presence of recent star formation (zeta) from the spectral energy distribution of the galaxy. We find that environment leaves a second order imprint on the spectra, whereas local properties - such as internal velocity dispersion - obey a much stronger correlation with the stellar age distribution.Comment: 5 pages, 2 figures. Proceedings of JENAM 2010, Symposium 2: "Environment and the formation of galaxies: 30 years later

SPIDER X - Environmental effects in central and satellite early-type galaxies through the stellar fossil record

A detailed analysis of how environment affects the star formation history of early-type galaxies (ETGs) is undertaken via high signal to noise ratio stacked spectra obtained from a sample of 20,977 ETGs (morphologically selected) from the SDSS-based SPIDER survey. Two major parameters are considered for the study: the central velocity dispersion (sigma), which relates to local drivers of star formation, and the mass of the host halo, which relates to environment-related effects. In addition, we separate the sample between centrals (the most massive galaxy in a halo) and satellites. We derive trends of age, metallicity, and [alpha/Fe] enhancement, with sigma. We confirm that the major driver of stellar population properties in ETGs is velocity dispersion, with a second-order effect associated to the central/satellite nature of the galaxy. No environmental dependence is detected for satellite ETGs, except at low sigma - where satellites in groups or in the outskirts of clusters tend to be younger than those in the central regions of clusters. In contrast, the trends for centrals show a significant dependence on halo mass. Central ETGs in groups (i.e. with a halo mass >10^12.5 M_Sun) have younger ages, lower [alpha/Fe], and higher internal reddening, than "isolated" systems (i.e. centrals residing in low-mass, <10^12.5 M_Sun, halos). Our findings imply that central ETGs in groups formed their stellar component over longer time scales than "isolated" centrals, mainly because of gas-rich interactions with their companion galaxies.Comment: 22 pages, 19 figures, accepted for publication in MNRA

Survey for Galaxies Associated with z~3 Damped Lyman alpha Systems I: Spectroscopic Calibration of u'BVRI Photometric Selection

We present a survey for z~3 Lyman break galaxies (LBGs) associated with damped Lyman alpha systems (DLAs) with the primary purpose of determining the DLA-LBG cross-correlation. This paper describes the acquisition and analysis of imaging and spectroscopic data of 9 quasar fields having 11 known z~3 DLAs covering an area of 465 arcmin^2. Using deep u'BVRI images, 796 LBG candidates to an apparent R_AB magnitude of 25.5 were photometrically selected from 17,343 sources detected in the field. Spectroscopic observations of 529 LBG candidates using Keck LRIS yielded 339 redshifts. We have conservatively identified 211 z>2 objects with =3.02+/-0.32. We discuss our method of z~3 LBG identification and present a model of the u'BVRI photometric selection function. We use the 339 spectra to evaluate our u'BVRI z~3 Lyman break photometric selection technique.Comment: 26 pages, 6 tables, 11 figures, accepted for publication in Ap

IMF and [Na/Fe] abundance ratios from optical and NIR Spectral Features in Early-type Galaxies

We present a joint analysis of the four most prominent sodium-sensitive features (NaD, NaI8190, NaI1.14, and NaI2.21), in the optical and Near-Infrared spectral range, of two nearby, massive (sigma~300km/s), early-type galaxies (named XSG1 and XSG2). Our analysis relies on deep VLT/X-Shooter long-slit spectra, along with newly developed stellar population models, allowing for [Na/Fe] variations, up to 1.2dex, over a wide range of age, total metallicity, and IMF slope. The new models show that the response of the Na-dependent spectral indices to [Na/Fe] is stronger when the IMF is bottom heavier. For the first time, we are able to match all four Na features in the central regions of massive early-type galaxies, finding an overabundance of [Na/Fe], in the range 0.5-0.7dex, and a bottom-heavy IMF. Therefore, individual abundance variations cannot be fully responsible for the trends of gravity-sensitive indices, strengthening the case towards a non-universal IMF. Given current limitations of theoretical atmosphere models, our [Na/Fe] estimates should be taken as upper limits. For XSG1, where line strengths are measured out to 0.8Re, the radial trend of [Na/Fe] is similar to [Mg/Fe] and [C/Fe], being constant out to 0.5Re, and decreasing by 0.2-0.3dex at 0.8Re, without any clear correlation with local metallicity. Such a result seems to be in contrast with the predicted increase of Na nucleosynthetic yields from AGB stars and TypeII SNe. For XSG1, the Na-inferred IMF radial profile is consistent, within the errors, with that derived from TiO features and the Wing-Ford band, presented in a recent paper.Comment: 22 pages, 8 figure, accepted for publication in MNRAS. The new Na-enhanced models will be available soon at http://miles.iac.es

Predicting spectral features in galaxy spectra from broad-band photometry

We explore the prospects of predicting emission line features present in galaxy spectra given broad-band photometry alone. There is a general consent that colours, and spectral features, most notably the 4000 A break, can predict many properties of galaxies, including star formation rates and hence they could infer some of the line properties. We argue that these techniques have great prospects in helping us understand line emission in extragalactic objects and might speed up future galaxy redshift surveys if they are to target emission line objects only. We use two independent methods, Artifical Neural Neworks (based on the ANNz code) and Locally Weighted Regression (LWR), to retrieve correlations present in the colour N-dimensional space and to predict the equivalent widths present in the corresponding spectra. We also investigate how well it is possible to separate galaxies with and without lines from broad band photometry only. We find, unsurprisingly, that recombination lines can be well predicted by galaxy colours. However, among collisional lines some can and some cannot be predicted well from galaxy colours alone, without any further redshift information. We also use our techniques to estimate how much information contained in spectral diagnostic diagrams can be recovered from broad-band photometry alone. We find that it is possible to classify AGN and star formation objects relatively well using colours only. We suggest that this technique could be used to considerably improve redshift surveys such as the upcoming FMOS survey and the planned WFMOS survey.Comment: 10 pages 7 figures summitted to MNRA