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We investigate galactic winds in the HizEA galaxies, a collection of 46 late-stage galaxy mergers at z = 0.4–0.8, with stellar masses of log (M * / M ⊙) = 10.4 – 11.5 , star formation rates (SFRs) of 20–500 M ⊙ yr−1, and ultra-compact (a few 100 pc) central star-forming regions. We measure their gas kinematics using the Mg ii λ λ 2796,2803 absorption lines in optical spectra from MMT, Magellan, and Keck. We find evidence of outflows in 90% of targets, with maximum outflow velocities of 550–3200 km s−1. We combine these data with ten samples from the literature to construct scaling relations for outflow velocity versus SFR, star formation surface density (ΣSFR), M *, and SFR/ M *. The HizEA galaxies extend the dynamic range of the scaling relations by a factor of ∼2–4 in outflow velocity and an order of magnitude in SFR and ΣSFR. The ensemble scaling relations exhibit strong correlations between outflow velocity, SFR, SFR/ R, and ΣSFR, and weaker correlations with M * and SFR/ M *. The HizEA galaxies are mild outliers on the SFR and M * scaling relations, but they connect smoothly with more typical star-forming galaxies on plots of outflow velocity versus SFR/ R and ΣSFR. These results provide further evidence that the HizEA galaxies' exceptional outflow velocities are a consequence of their extreme star formation conditions rather than hidden black hole activity, and they strengthen previous claims that ΣSFR is one of the most important properties governing the velocities of galactic winds. [ABSTRACT FROM AUTHOR]

We present results on the properties of extreme gas outflows in massive (M * ∼ 1011 M ⊙), compact, starburst (star formation rate, SFR∼ 200 M ⊙ yr−1) galaxies at z = 0.4–0.7 with very high star formation surface densities (ΣSFR ∼ 2000 M ⊙ yr−1 kpc−2). Using optical Keck/HIRES spectroscopy of 14 HizEA starburst galaxies, we identify outflows with maximum velocities of 820–2860 km s−1. High-resolution spectroscopy allows us to measure precise column densities and covering fractions as a function of outflow velocity and characterize the kinematics and structure of the cool gas outflow phase (T ∼ 104 K). We find substantial variation in the absorption profiles, which likely reflects the complex morphology of inhomogeneously distributed, clumpy gas and the intricacy of the turbulent mixing layers between the cold and hot outflow phases. There is not a straightforward correlation between the bursts in the galaxies' star formation histories and their wind absorption line profiles, as might naively be expected for starburst-driven winds. The lack of strong Mg ii absorption at the systemic velocity is likely an orientation effect, where the observations are down the axis of a blowout. We infer high mass outflow rates of ∼50–2200 M ⊙ yr−1, assuming a fiducial outflow size of 5 kpc, and mass loading factors of η ∼ 5 for most of the sample. While these values have high uncertainties, they suggest that starburst galaxies are capable of ejecting very large amounts of cool gas that will substantially impact their future evolution. [ABSTRACT FROM AUTHOR]

Feedback through energetic outflows has emerged as a key physical process responsible for transforming star-forming galaxies into the quiescent systems observed in the local universe. To explore this process, this paper focuses on a sample of massive and compact merger remnant galaxies hosting high-velocity gaseous outflows (km s−1), found at intermediate redshift (z ∼ 0.6). From their mid-infrared emission and compact morphologies, these galaxies are estimated to have exceptionally large star formation rate (SFR) surface densities (ΣSFR ∼ 103M⊙ yr−1 kpc−2), approaching the Eddington limit for radiation pressure on dust grains. This suggests that star formation feedback may be driving the observed outflows. However, these SFR estimates suffer from significant uncertainties. We therefore sought an independent tracer of star formation to probe the compact starburst activity in these systems. In this paper, we present SFR estimates calculated using 1.5 GHz continuum Jansky Very Large Array observations for 19 of these galaxies. We also present updated infrared (IR) SFRs calculated from WISE survey data. We estimate SFRs from the IR to be larger than those from the radio for 16 out of 19 galaxies by a median factor of 2.5. We find that this deviation is maximized for the most compact galaxies hosting the youngest stellar populations, suggesting that compact starbursts deviate from the IR-radio correlation. We suggest that this deviation stems either from free–free absorption of synchrotron emission, a difference in the timescale over which each indicator traces star formation, or exceptionally hot IR-emitting dust in these ultra-dense galaxies. [ABSTRACT FROM AUTHOR]

Feedback processes from active galactic nuclei (AGN) are thought to play a crucial role in regulating star formation in massive galaxies. Previous studies using Herschel have resulted in conflicting conclusions as to whether star formation is quenched, enhanced, or not affected by AGN feedback. We use new deep 850 |$\mu$| m observations from the SCUBA-2 Cosmology Legacy Survey (S2CLS) to investigate star formation in a sample of X-ray selected AGN, probing galaxies up to |$L_{0.5{\!-\!}7~\rm keV} = 10^{46}$| erg s−1. Here, we present the results of our analysis on a sample of 1957 galaxies at 1 < z < 3, using both S2CLS and ancilliary data at seven additional wavelengths (24–500 |$\mu$| m) from Herschel and Spitzer. We perform a stacking analysis, binning our sample by redshift and X-ray luminosity. By fitting analytical spectral energy distributions (SEDs) to decompose contributions from cold and warm dust, we estimate star formation rates (SFRs) for each 'average' source. We find that the average AGN in our sample resides in a star-forming host galaxy, with SFRs ranging from 80 to 600 M⊙ yr−1. Within each redshift bin, we see no trend of SFR with X-ray luminosity, instead finding a flat distribution of SFR across ∼3 orders of magnitude of AGN luminosity. By studying instantaneous X-ray luminosities and SFRs, we find no evidence that AGN activity affects star formation in host galaxies. [ABSTRACT FROM AUTHOR]

We have used the Submillimeter Array (SMA) at 860  $\mu$ m to observe the brightest sources in the Submillimeter Common User Bolometer Array-2 (SCUBA-2) Cosmology Legacy Survey (S2CLS). The goal of this survey is to exploit the large field of the S2CLS along with the resolution and sensitivity of the SMA to construct a large sample of these rare sources and to study their statistical properties. We have targeted 70 of the brightest single-dish SCUBA-2 850  $\mu$ m sources down to S850 ≈  8 mJy, achieving an average synthesized beam of 2.4 arcsec and an average rms of σ860 =  1.5 mJy beam−1 in our primary beam-corrected maps. We searched our SMA maps for 4σ peaks, corresponding to S860 ≳  6 mJy sources, and detected 62, galaxies, including three pairs. We include in our study 35 archival observations, bringing our sample size to 105 bright single-dish submillimetre sources with interferometric follow-up. We compute the cumulative and differential number counts, finding them to overlap with previous single-dish survey number counts within the uncertainties, although our cumulative number count is systematically lower than the parent S2CLS cumulative number count by 14 ±  6 per cent between 11 and 15 mJy. We estimate the probability that a ≳10 mJy single-dish submillimetre source resolves into two or more galaxies with similar flux densities to be less than 15 per cent. Assuming the remaining 85 per cent of the targets are ultraluminous starburst galaxies between z =  2 and 3, we find a likely volume density of ≳400 M⊙ yr−1 sources to be ${\sim }\,3^{+0.7}_{-0.6}\,{\times }\,10^{-7}$  Mpc−3. We show that the descendants of these galaxies could be ≳4 ×  1011 M⊙ local quiescent galaxies, and that about 10 per cent of their total stellar mass would have formed during these short bursts of star formation. [ABSTRACT FROM AUTHOR]

It is thought that a class of broad absorption line (BAL) QSOs, characterized by Fe absorption features in their UV spectra (called 'FeLoBALs'), could mark a transition stage between the end of an obscured starburst event and a youthful QSO beginning to shed its dust cocoon, where Fe has been injected into the interstellar medium by the starburst. To test this hypothesis, we have undertaken deep Submillimetre Common-User Bolometer Array 2 (SCUBA-2) 850 µm observations of a sample of 17 FeLoBAL QSOs with 0.89 ≤ z ≤ 2.78 and -23.31 ≤ MB ≤ -28.50 to directly detect an excess in the thermal emission of the dust which would probe enhanced star formation activity. We find that FeLoBALs are not luminous sources in the sub-mm, none of them are individually detected at 850 μm, nor as a population through stacking (Fs = 1.14 ± 0.58 mJy). Statistical and survival analyses reveal that FeLoBALs have sub-mm properties consistent with BAL and non-BAL QSOs with matched redshifts and magnitudes. An Spectral Energy Distribution fitting analysis shows that the far-infrared emission is dominated by active galactic nuclei activity, and a starburst component is required only in 6/17 sources of our sample; moreover the integrated total luminosity of 16/17 sources is L = 1012 L⊙, high enough to classify FeLoBALs as infrared luminous. In conclusion, we do not find any evidence in support of FeLoBAL QSOs being a transition population between an ultraluminous infrared galaxy (ULIRG) and an unobscured QSO; in particular, FeLoBALs are not characterized by a cold starburst which would support this hypothesis. [ABSTRACT FROM AUTHOR]

We have observed a sample of typical z ∼ 1 star-forming galaxies, selected from the HiZELS survey, with the new K-band Multi-Object Spectrograph (KMOS) near-infrared, multi-integral field unit instrument on the Very Large Telescope (VLT), in order to obtain their dynamics and metallicity gradients. The majority of our galaxies have a metallicity gradient consistent with being flat or negative (i.e. higher metallicity cores than outskirts). Intriguingly, we find a trend between metallicity gradient and specific star formation rate (sSFR), such that galaxies with a high sSFR tend to have relatively metal poor centres, a result which is strengthened when combined with data sets from the literature. This result appears to explain the discrepancies reported between different high-redshift studies and varying claims for evolution. From a galaxy evolution perspective, the trend we see would mean that a galaxy's sSFR is governed by the amount of metal-poor gas that can be funnelled into its core, triggered either by merging or through efficient accretion. In fact, merging may play a significant role as it is the starburst galaxies at all epochs, which have the more positive metallicity gradients. Our results may help to explain the origin of the fundamental metallicity relation, in which galaxies at a fixed mass are observed to have lower metallicities at higher star formation rates, especially if the metallicity is measured in an aperture encompassing only the central regions of the galaxy. Finally, we note that this study demonstrates the power of KMOS as an efficient instrument for large-scale resolved galaxy surveys. [ABSTRACT FROM PUBLISHER]

We use the HiZELS narrow-band Hα survey in combination with CANDELS, UKIDSS and WIRDS near-infrared imaging, to investigate the morphologies, merger rates and sizes of a sample of Hα emitting galaxies in the redshift range z = 0.40–2.23, an epoch encompassing the rise to the peak of the star formation rate density. Merger rates are estimated from space- and ground-based imaging using the M20 coefficient. To account for the increase in the specific star formation rate (sSFR) of the star forming ‘main sequence’ with redshift, we normalize the star formation rates of galaxies at each epoch to the typical value derived from the Hα luminosity function. Once this trend in sSFR is removed we see no evidence for an increase in the number density of star-forming galaxies or the merger rate with redshift. We thus conclude that neither is the main driver of the enhanced star-formation rate density at z ∼ 1–2, with secular processes such as instabilities within efficiently fuelled, gas-rich discs or multiple minor mergers the most likely alternatives. However, we find that ∼40–50 per cent of starburst galaxies, those with enhanced specific star formation at their epoch, are major mergers and this fraction is redshift independent. Finally, we find the surprising result that the typical size of a star-forming galaxy of a given mass does not evolve across the redshift range considered, suggesting a universal size–mass relation. Taken in combination, these results indicate a star-forming galaxy population that is statistically similar in physical size, merger rate and mass over the ∼6 Gyr covered in this study, despite the increase in typical sSFR. [ABSTRACT FROM PUBLISHER]

This paper presents new deep and wide narrow-band surveys undertaken with United Kingdom Infrared Telescope (UKIRT), Subaru and the Very Large Telescope (VLT), a unique combined effort to select large, robust samples of Hα star-forming galaxies at z = 0.40, 0.84, 1.47 and 2.23 (corresponding to look-back times of 4.2, 7.0, 9.2 and 10.6 Gyr) in a uniform manner over ∼2 deg2 in the Cosmological Evolution Survey and Ultra Deep Survey fields. The deep multi-epoch Hα surveys reach a matched 3σ flux limit of ≈3 M⊙ yr−1 out to z = 2.2 for the first time, while the wide area and the coverage over two independent fields allow us to greatly overcome cosmic variance and assemble by far the largest samples of Hα emitters. Catalogues are presented for a total of 1742, 637, 515 and 807 Hα emitters, robustly selected at z = 0.40, 0.84, 1.47 and 2.23, respectively, and used to determine the Hα luminosity function and its evolution. The faint-end slope of the Hα luminosity function is found to be α = −1.60 ± 0.08 over z = 0–2.23, showing no significant evolution. The characteristic luminosity of star-forming galaxies, L*Hα, evolves significantly as log L*Hα(z) = 0.45z + log L*z = 0. This is the first time Hα has been used to trace star formation activity with a single homogeneous survey at z = 0.4–2.23. Overall, the evolution seen with Hα is in good agreement with the evolution seen using inhomogeneous compilations of other tracers of star formation, such as far-infrared and ultraviolet, jointly pointing towards the bulk of the evolution in the last 11 Gyr being driven by a statistically similar star-forming population across cosmic time, but with a strong luminosity increase from z ∼ 0 to ∼2.2. Our uniform analysis allows us to derive the Hα star formation history (SFRH) of the Universe, showing a clear rise up to z ∼ 2.2, for which the simple parametrization log10ρSFR = −2.1(1 + z)−1 is valid over 80 per cent of the age of the Universe. The results reveal that both the shape and normalization of the Hα SFRH are consistent with the measurements of the stellar mass density growth, confirming that our Hα SFRH is tracing the bulk of the formation of stars in the Universe for z < 2.23. The star formation activity over the last ∼11 Gyr is responsible for producing ∼95 per cent of the total stellar mass density observed locally, with half of that being assembled in 2 Gyr between z = 1.2 and 2.2, and the other half in 8 Gyr (since z < 1.2). If the star formation rate density continues to decline with time in the same way as seen in the past ∼11 Gyr, then the stellar mass density of the Universe will reach a maximum which is only 5 per cent higher than the present-day value. [ABSTRACT FROM PUBLISHER]

ABSTRACT This paper presents the results from the first wide and deep dual narrow-band survey to select Hα and [O ii] line emitters at z= 1.47 ± 0.02, exploiting synergies between the United Kingdom Infrared Telescope and the Subaru telescope by using matched narrow-band filters in the H and z′ bands. The Hα survey at z= 1.47 reaches a 3σ flux limit of FHα≈ 7 × 10−17 erg s−1 cm−2 (corresponding to a limiting star formation rate (SFR) in Hα of ≈7 M⊙ yr−1) and detects ≈200 Hα emitters over 0.7 deg2, while the much deeper [O ii] survey reaches an effective flux of ≈7 × 10−18 erg s−1 cm−2 (SFR in [O ii] of ∼1 M⊙ yr−1), detecting ≈1400 z= 1.47 [O ii] emitters in a matched comoving volume of ∼2.5 × 105 Mpc3. The combined survey results in the identification of 190 simultaneous Hα and [O ii] emitters at z= 1.47. Hα and [O ii] luminosity functions are derived and both are shown to evolve significantly from z∼ 0 in a consistent way. The SFR density of the Universe at z= 1.47 is evaluated, with the Hα analysis yielding ρSFR= 0.16 ± 0.05 M⊙ yr−1 Mpc−3 and the [O ii] analysis ρSFR= 0.17 ± 0.04 M⊙ yr−1 Mpc−3. The measurements are combined with other studies, providing a self-consistent measurement of the star formation history of the Universe over the last ∼11 Gyr. By using a large comparison sample at z∼ 0.1, derived from the Sloan Digital Sky Survey (SDSS), [O ii]/Hα line ratios are calibrated as probes of dust extinction. Hα emitters at z∼ 1.47 show on average AHα≈ 1 mag, the same as found by SDSS in the local Universe. It is shown that although dust extinction correlates with SFR, the relation evolves by about ∼0.5 mag from z∼ 1.5 to ∼0, with local relations overpredicting the dust extinction corrections at high z by that amount. Stellar mass is found to be a much more fundamental extinction predictor, with the same relation between mass and dust extinction being valid at both z∼ 0 and ∼1.5, at least for low and moderate stellar masses. The evolution in the extinction-SFR relation is therefore interpreted as being due to the evolution in median specific SFRs over cosmic time. Dust extinction corrections as a function of optical colours are also derived and shown to be broadly valid at both z∼ 0 and ∼1.5, offering simpler mechanisms for estimating extinction in moderately star-forming systems over the last ∼9 Gyr. [ABSTRACT FROM AUTHOR]

This paper presents an environment and stellar mass study of a large sample of star-forming Hα emitters at from the High- z Emission Line Survey (HiZELS), over 1.3 deg split over two fields (COSMOS and UKIDSS UDS). By taking advantage of a truly panoramic coverage of a wide range of environments, from the field to a rich cluster, it is shown that both stellar mass and environment play crucial roles in determining the properties of star-forming galaxies. Specific star formation rates (sSFRs) decline with stellar mass in all environments, and the fraction of Hα star-forming galaxies declines sharply from per cent for galaxies with masses around 10 M to effectively zero above , confirming that mass-downsizing is generally in place by . The fraction of star-forming galaxies is also found to fall sharply as a function of local environmental density from per cent in the field to approaching zero at rich group/cluster densities. When star formation does occur in such high density regions, it is found to be mostly dominated by potential mergers and, indeed, if only non-merging star-forming galaxies are considered, then the environment and mass trends are even stronger and are qualitatively similar at all masses and environments, respectively, as in the local Universe. The median SFR of Hα emitters at is found to increase with density for both field and intermediate (group or cluster outskirts) densities; this is clearly seen as a change in the faint-end slope of the Hα luminosity function from steep , in poor fields, to shallow in groups and clusters. Interestingly, the relation between median SFR and environment is only found for low- to moderate-mass galaxies (with stellar masses below about M, and is not seen for the most massive star-forming galaxies. Overall, these observations provide a detailed view over a sufficiently large range of mass and environment to reconcile previous observational claims: stellar mass is the primary predictor of star formation activity at , but the environment, while initially enhancing the median SFR of (lower mass) star-forming galaxies, is ultimately responsible for suppressing star formation activity in all galaxies above surface densities of 10-30 Mpc (group and cluster environments). [ABSTRACT FROM AUTHOR]

We compare Hα, ultraviolet (UV) and infrared (IR) indicators of star formation rate (SFR) for a well-defined sample of emission-line galaxies from the High- z Emission Line Survey (HiZELS). Using emission-line, optical, IR, radio and X-ray diagnostics, we estimate that 5–11 per cent of Hα emitters at this redshift are active galactic nuclei. We detect 35 per cent of the Hα emitters individually at 24 μm, and stack the locations of star-forming emitters on deep 24-μm Spitzer Space Telescope images in order to calculate the typical SFRs of our Hα-emitting galaxies. These are compared to the observed Hα line fluxes in order to estimate the extinction at , and we find a significant increase in dust extinction for galaxies with higher SFRs. We demonstrate that the relationship between SFR and extinction found in the local Universe is also suitable for our high-redshift galaxies, and attribute the overall increase in the typical dust extinction for galaxies to an increase in the average SFR, rather than to a change in dust properties at higher redshift. We calculate the UV extinction, and find a similar dependence on SFR to the Hα results, but no evidence for a 2175 Å UV bump in the dust attenuation law for high-redshift star-forming galaxies. By comparing Hα and UV indicators, we calculate the conversion between the dust attenuation of nebular and stellar radiation, γ, and show that . The extinction/SFR relationship is shown to be applicable to galaxies with a range of morphologies and bulge-to-disc ratios, to both merging and non-merging galaxies, and to galaxies within high- and low-density environments, implying that it is a fundamental property of star-forming regions. In order to allow future studies to easily correct for a SFR-dependent amount of dust extinction, we present an equation to predict the extinction of a galaxy, based solely on its observed Hα luminosity, and use this to recalculate the Hα luminosity function and SFR density at . [ABSTRACT FROM AUTHOR]

We present IRAM Plateau de Bure Interferometer 3-mm observations of emission in two 24-μm selected starburst galaxies in the outskirts of the rich cluster Cl 0024+16 . The galaxies' inferred far-infrared luminosities place them in the luminous infrared galaxy (LIRG) class , with star formation rates of . Strong emission is detected in both galaxies, and we use the CO line luminosity to estimate the mass of cold molecular gas, . Assuming , we estimate for the two galaxies. We estimate the galaxies' dynamical masses from their CO line widths, , implying large cold gas fractions in the galaxies' central regions. At their current rates, they will complete the assembly of and double their stellar mass within as little as ∼150 Myr. If these galaxies are destined to evolve into S0s, then the short time-scale for stellar mass assembly implies that their major episode of bulge growth occurs while they are still in the cluster outskirts, long before they reach the core regions. Subsequent fading of the disc component relative to the stellar bulge after the gas reservoirs have been exhausted could complete the transformation of spiral-to-S0. [ABSTRACT FROM AUTHOR]

We make use of our “minimal” cold interstellar medium emission line model that predicts the molecular and atomic line emission per unit dense, star-forming gas mass to examine the utility of key line ratios in surveys of the so-called star formation “mode” as traced by ξSF = Mdense(H2)/Mtotal(H2). We argue that ξSF and its proxies provide very sensitive, extinction-free discriminators of rapid starburst/merger-driven versus secular quiescent/disk-like stellar mass assembly, with the most promising diagnostic to be applied in the near-future being CO J(4 → 3)/ [C I](3P1 → 3P0). These lines are accessible across nearly the full range 0 < z < 2 (thus covering the bulk of galaxy evolution) with the Atacama Large Millimeter Array. In addition to their diagnostic power, another advantage of this combination is the similar observed frequencies (Δν0 ≈ 30 GHz) of the lines, resulting in nearly spatially matched beams for a fixed aperture, thus mitigating the effects of resolution/morphology bias in the interpretation of galaxy-averaged line ratios. Finally, we discuss the capability of deep blind redshift surveys with the high-frequency component of the Square Kilometer Array (SKA) in discovering H2-rich galaxies with very low ξSF values. These could be the progenitors of starburst galaxies seen prior to the onset of star formation; such galaxies could be a class of extreme outliers from local (gas surface density)-(star formation rate) scaling laws, which would exclude them from current star formation or stellar-mass-selected samples. Our conservative model suggests that SKA could detect such systems residing at z ∼ 3 at a rate of 20-200 hr–1. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper presents the results from the first wide and deep dual narrow-band survey to select Hα and [O ii] line emitters at z= 1.47 ± 0.02, exploiting synergies between the United Kingdom Infrared Telescope and the Subaru telescope by using matched narrow-band filters in the H and z′ bands. The Hα survey at z= 1.47 reaches a 3σ flux limit of FHα≈ 7 × 10−17 erg s−1 cm−2 (corresponding to a limiting star formation rate (SFR) in Hα of ≈7 M⊙ yr−1) and detects ≈200 Hα emitters over 0.7 deg2, while the much deeper [O ii] survey reaches an effective flux of ≈7 × 10−18 erg s−1 cm−2 (SFR in [O ii] of ∼1 M⊙ yr−1), detecting ≈1400 z= 1.47 [O ii] emitters in a matched comoving volume of ∼2.5 × 105 Mpc3. The combined survey results in the identification of 190 simultaneous Hα and [O ii] emitters at z= 1.47. Hα and [O ii] luminosity functions are derived and both are shown to evolve significantly from z∼ 0 in a consistent way. The SFR density of the Universe at z= 1.47 is evaluated, with the Hα analysis yielding ρSFR= 0.16 ± 0.05 M⊙ yr−1 Mpc−3 and the [O ii] analysis ρSFR= 0.17 ± 0.04 M⊙ yr−1 Mpc−3. The measurements are combined with other studies, providing a self-consistent measurement of the star formation history of the Universe over the last ∼11 Gyr. By using a large comparison sample at z∼ 0.1, derived from the Sloan Digital Sky Survey (SDSS), [O ii]/Hα line ratios are calibrated as probes of dust extinction. Hα emitters at z∼ 1.47 show on average AHα≈ 1 mag, the same as found by SDSS in the local Universe. It is shown that although dust extinction correlates with SFR, the relation evolves by about ∼0.5 mag from z∼ 1.5 to ∼0, with local relations overpredicting the dust extinction corrections at high z by that amount. Stellar mass is found to be a much more fundamental extinction predictor, with the same relation between mass and dust extinction being valid at both z∼ 0 and ∼1.5, at least for low and moderate stellar masses. The evolution in the extinction-SFR relation is therefore interpreted as being due to the evolution in median specific SFRs over cosmic time. Dust extinction corrections as a function of optical colours are also derived and shown to be broadly valid at both z∼ 0 and ∼1.5, offering simpler mechanisms for estimating extinction in moderately star-forming systems over the last ∼9 Gyr. [ABSTRACT FROM AUTHOR]