Knots in Four Dimensions and the Fundamental Group

This paper is an introduction to knotted spheres in four dimensions (analogous to knotted circles in three dimensions). We define what a knotted sphere is and describe a to visually represent them, via movies. The fundamental group of the complement of a knot is a powerful invariant and we describe this invariant in detail giving a convenient algorithm for computing it. Lots of examples are given, including the simplest non-trivial locally flat knot

Evidence for non-stellar rest-frame near-IR emission associated with increased star formation in galaxies at z∼1z \sim 1

We explore the presence of non-stellar rest-frame near-IR ($2-5 \ \mu \mathrm{m}$) emission in galaxies at $z \sim 1$. Previous studies identified this excess in relatively small samples and suggested that such non-stellar emission, which could be linked to the $3.3 \ \mu \mathrm{m}$ polycyclic aromatic hydrocarbons feature or hot dust emission, is associated with an increased star formation rate (SFR). In this Letter, we confirm and quantify the presence of an IR excess in a significant fraction of galaxies in the 3D-HST GOODS catalogs. By constructing a matched sample of galaxies with and without strong non-stellar near-IR emission, we find that galaxies with such emission are predominantly star-forming galaxies. Moreover, star-forming galaxies with an excess show increased mid- and far-IR and H$\alpha$ emission compared to other star-forming galaxies without. While galaxies with a near-IR excess show a larger fraction of individually detected X-ray active galactic nuclei (AGNs), an X-ray stacking analysis, together with the IR-colors and H$\alpha$ profiles, shows that AGNs are unlikely to be the dominant source of the excess in the majority of galaxies. Our results suggest that non-stellar near-IR emission is linked to increased SFRs and is ubiquitous among star-forming galaxies. As such, the near-IR emission might be a powerful tool to measure SFRs in the era of the James Webb Space Telescope.Comment: 6 pages, 5 figures, accepted for publication in ApJ

Ages of massive galaxies at 0.5<z<2.00.5 < z < 2.0 from 3D-HST rest-frame optical spectroscopy

We present low-resolution near-infrared stacked spectra from the 3D-HST survey up to $z=2.0$ and fit them with commonly used stellar population synthesis models: BC03 (Bruzual & Charlot, 2003), FSPS10 (Flexible Stellar Population Synthesis, Conroy & Gunn 2010), and FSPS-C3K (Conroy, Kurucz, Cargile, Castelli, in prep). The accuracy of the grism redshifts allows the unambiguous detection of many emission and absorption features, and thus a first systematic exploration of the rest-frame optical spectra of galaxies up to $z=2$. We select massive galaxies ($\rm log(M_{*} / M_{\odot}) > 10.8$), we divide them into quiescent and star-forming via a rest-frame color-color technique, and we median-stack the samples in 3 redshift bins between $z=0.5$ and $z=2.0$. We find that stellar population models fit the observations well at wavelengths below $\rm 6500 \AA$ rest-frame, but show systematic residuals at redder wavelengths. The FSPS-C3K model generally provides the best fits (evaluated with a $\chi^2_{red}$ statistics) for quiescent galaxies, while BC03 performs the best for star-forming galaxies. The stellar ages of quiescent galaxies implied by the models, assuming solar metallicity, vary from 4 Gyr at $z \sim 0.75$ to 1.5 Gyr at $z \sim 1.75$, with an uncertainty of a factor of 2 caused by the unknown metallicity. On average the stellar ages are half the age of the Universe at these redshifts. We show that the inferred evolution of ages of quiescent galaxies is in agreement with fundamental plane measurements, assuming an 8 Gyr age for local galaxies. For star-forming galaxies the inferred ages depend strongly on the stellar population model and the shape of the assumed star-formation history.Comment: 13 pages, 15 figures, accepted for publication in Ap

Predicting Quiescence: The Dependence of Specific Star Formation Rate on Galaxy Size and Central Density at 0.5<z<2.5

In this paper, we investigate the relationship between star formation and structure, using a mass-complete sample of 27,893 galaxies at $0.5<z<2.5$ selected from 3D-HST. We confirm that star-forming galaxies are larger than quiescent galaxies at fixed stellar mass (M$_{\star}$). However, in contrast with some simulations, there is only a weak relation between star formation rate (SFR) and size within the star-forming population: when dividing into quartiles based on residual offsets in SFR, we find that the sizes of star-forming galaxies in the lowest quartile are 0.27$\pm$0.06 dex smaller than the highest quartile. We show that 50% of star formation in galaxies at fixed M$_{\star}$ takes place within a narrow range of sizes (0.26 dex). Taken together, these results suggest that there is an abrupt cessation of star formation after galaxies attain particular structural properties. Confirming earlier results, we find that central stellar density within a 1 kpc fixed physical radius is the key parameter connecting galaxy morphology and star formation histories: galaxies with high central densities are red and have increasingly lower SFR/M$_{\star}$, whereas galaxies with low central densities are blue and have a roughly constant (higher) SFR/M$_{\star}$ at a given redshift. We find remarkably little scatter in the average trends and a strong evolution of $>$0.5 dex in the central density threshold correlated with quiescence from $z\sim0.7-2.0$. Neither a compact size nor high-$n$ are sufficient to assess the likelihood of quiescence for the average galaxy; rather, the combination of these two parameters together with M$_{\star}$ results in a unique quenching threshold in central density/velocity.Comment: 20 pages, 15 figures, and 2 tables; Accepted for publication in the Astrophysical Journa

Quiescent Galaxies in the 3D-HST Survey: Spectroscopic Confirmation of a Large Number of Galaxies with Relatively Old Stellar Populations at z~2

Quiescent galaxies at z~2 have been identified in large numbers based on rest-frame colors, but only a small number of these galaxies have been spectroscopically confirmed to show that their rest-frame optical spectra show either strong Balmer or metal absorption lines. Here, we median stack the rest-frame optical spectra for 171 photometrically-quiescent galaxies at 1.4 < z < 2.2 from the 3D-HST grism survey. In addition to Hbeta (4861A), we unambiguously identify metal absorption lines in the stacked spectrum, including the G-band (4304A), Mg I (5175A), and Na I (5894A). This finding demonstrates that galaxies with relatively old stellar populations already existed when the universe was ~3 Gyr old, and that rest-frame color selection techniques can efficiently select them. We find an average age of 1.3^0.1_0.3 Gyr when fitting a simple stellar population to the entire stack. We confirm our previous result from medium-band photometry that the stellar age varies with the colors of quiescent galaxies: the reddest 80% of galaxies are dominated by metal lines and have a relatively old mean age of 1.6^0.5_0.4 Gyr, whereas the bluest (and brightest) galaxies have strong Balmer lines and a spectroscopic age of 0.9^0.2_0.1 Gyr. Although the spectrum is dominated by an evolved stellar population, we also find [OIII] and Hbeta emission. Interestingly, this emission is more centrally concentrated than the continuum with L_[OIII] = 1.7 +/- 0.3 x 10^40 erg s^-1, indicating residual central star formation or nuclear activity.Comment: 6 pages, 4 figures, accepted for publication in the Astrophysical Journal Letter

Direct measurements of dust attenuation in z~1.5 star-forming galaxies from 3D-HST: Implications for dust geometry and star formation rates

The nature of dust in distant galaxies is not well understood, and until recently few direct dust measurements have been possible. We investigate dust in distant star-forming galaxies using near-infrared grism spectra of the 3D-HST survey combined with archival multi-wavelength photometry. These data allow us to make a direct comparison between dust around star-forming regions ($A_{V,\mathrm{HII}}$) and the integrated dust content ($A_{V,\mathrm{star}}$). We select a sample of 163 galaxies between $1.36\le{}z\le1.5$ with H$\alpha$ signal-to-noise ratio $\ge5$ and measure Balmer decrements from stacked spectra to calculate $A_{V,\mathrm{HII}}$. First, we stack spectra in bins of $A_{V,\mathrm{star}}$, and find that $A_{V,\mathrm{HII}}=1.86\,A_{V,\mathrm{star}}$, with a significance of $\sigma=1.7$. Our result is consistent with the two-component dust model, in which galaxies contain both diffuse and stellar birth cloud dust. Next, we stack spectra in bins of specific star formation rate ($\log\,\mathrm{SSFR}$), star formation rate ($\log\,\mathrm{SFR}$), and stellar mass ($\log{}M_*$). We find that on average $A_{V,\mathrm{HII}}$ increases with SFR and mass, but decreases with increasing SSFR. Interestingly, the data hint that the amount of extra attenuation decreases with increasing SSFR. This trend is expected from the two-component model, as the extra attenuation will increase once older stars outside the star-forming regions become more dominant in the galaxy spectrum. Finally, using Balmer decrements we derive dust-corrected H$\alpha$ SFRs, and find that stellar population modeling produces incorrect SFRs if rapidly declining star formation histories are included in the explored parameter space.Comment: Accepted for publication in the Astrophysical Journal (13 pages, 9 figures

A Massive Galaxy in its Core Formation Phase Three Billion Years After the Big Bang

Most massive galaxies are thought to have formed their dense stellar cores at early cosmic epochs. However, cores in their formation phase have not yet been observed. Previous studies have found galaxies with high gas velocity dispersions or small apparent sizes but so far no objects have been identified with both the stellar structure and the gas dynamics of a forming core. Here we present a candidate core in formation 11 billion years ago, at z=2.3. GOODS-N-774 has a stellar mass of 1.0x10^11 Msun, a half-light radius of 1.0 kpc, and a star formation rate of 90[+45-20]Msun/yr. The star forming gas has a velocity dispersion 317+-30 km/s, amongst the highest ever measured. It is similar to the stellar velocity dispersions of the putative descendants of GOODS-N-774, compact quiescent galaxies at z~2 and giant elliptical galaxies in the nearby Universe. Galaxies such as GOODS-N-774 appear to be rare; however, from the star formation rate and size of the galaxy we infer that many star forming cores may be heavily obscured, and could be missed in optical and near-infrared surveys.Comment: To appear in Natur

Exploring the chemical link between local ellipticals and their high-redshift progenitors

We present Keck/MOSFIRE K-band spectroscopy of the first mass-selected sample of galaxies at $z\sim2.3$. Targets are selected from the 3D-HST Treasury survey. The six detected galaxies have a mean [NII]$\lambda$6584/H$\alpha$ ratio of $0.27\pm0.01$, with a small standard deviation of 0.05. This mean value is similar to that of UV-selected galaxies of the same mass. The mean gas-phase oxygen abundance inferred from the [NII]/H$\alpha$ ratios depends on the calibration method, and ranges from 12+log(O/H)$_{gas}=8.57$ for the {Pettini} & {Pagel} (2004) calibration to 12+log(O/H)$_{gas}= 8.87$ for the {Maiolino} {et~al.} (2008) calibration. Measurements of the stellar oxygen abundance in nearby quiescent galaxies with the same number density indicate 12+log(O/H)$_{stars}= 8.95$, similar to the gas-phase abundances of the $z\sim2.3$ galaxies if the {Maiolino} {et~al.} (2008) calibration is used. This suggests that these high-redshift star forming galaxies may be progenitors of today's massive early-type galaxies. The main uncertainties are the absolute calibration of the gas-phase oxygen abundance and the incompleteness of the $z\sim2.3$ sample: the galaxies with detected H$\alpha$ tend to be larger and have higher star formation rates than the galaxies without detected H$\alpha$, and we may still be missing the most dust-obscured progenitors.Comment: 7 pages, 5 figures. Accepted for publication in ApJ

First results from the VIRIAL survey: the stellar content of UVJUVJ-selected quiescent galaxies at 1.5<z<21.5 < z < 2 from KMOS

We investigate the stellar populations of 25 massive, galaxies ($\log[M_\ast/M_\odot] \geq 10.9$) at $1.5 < z < 2$ using data obtained with the K-band Multi-Object Spectrograph (KMOS) on the ESO VLT. Targets were selected to be quiescent based on their broadband colors and redshifts using data from the 3D-HST grism survey. The mean redshift of our sample is $\bar{z} = 1.75$, where KMOS YJ-band data probe age- and metallicity-sensitive absorption features in the rest-frame optical, including the $G$ band, Fe I, and high-order Balmer lines. Fitting simple stellar population models to a stack of our KMOS spectra, we derive a mean age of $1.03^{+0.13}_{-0.08}$ Gyr. We confirm previous results suggesting a correlation between color and age for quiescent galaxies, finding mean ages of $1.22^{+0.56}_{-0.19}$ Gyr and $0.85^{+0.08}_{-0.05}$ Gyr for the reddest and bluest galaxies in our sample. Combining our KMOS measurements with those obtained from previous studies at $0.2 < z < 2$ we find evidence for a $2-3$ Gyr spread in the formation epoch of massive galaxies. At $z < 1$ the measured stellar ages are consistent with passive evolution, while at $1 < z \lesssim2$ they appear to saturate at $\sim$1 Gyr, which likely reflects changing demographics of the (mean) progenitor population. By comparing to star-formation histories inferred for "normal" star-forming galaxies, we show that the timescales required to form massive galaxies at $z \gtrsim 1.5$ are consistent with the enhanced $\alpha$-element abundances found in massive local early-type galaxies.Comment: 6 pages, 5 figures, accepted for publication in ApJ