Testing star formation laws in a starburst galaxy at redshift 3 resolved with ALMA

Aims. In this Virgo Environment Traced in CO (VERTICO) science paper, we aim to study how the star formation process depends on the galactic environment and gravitational interactions in the context of galaxy evolution. We explore the scaling relation between the star formation rate surface density (ΣSFR) and the molecular gas surface density (Σmol), also known as the Kennicutt-Schmidt relation, in a subsample of Virgo cluster spiral galaxies. Methods. We used new Atacama Compact Array and Total Power (ACA+TP) observations from the VERTICO-Atacama Large Millimeter/submillimeter Array (ALMA) Large Program at 720 pc resolution to resolve the molecular gas content, as traced by the 12CO (2 − 1) transition, across the disks of 37 spiral galaxies in the Virgo cluster. In combination with archival UV and IR observations used to determine the star formation rate (SFR), we estimated the parameters of the Kennicutt-Schmidt (KS) relation for the entire ensemble of galaxies, and within individual galaxies. Results. We find the KS slope for the entire population to be N = 0.97 ± 0.07, with a characteristic molecular gas depletion time of 1.86 Gyr for our full sample, which is in agreement with previous work in isolated, nearby star-forming galaxies. In individual galaxies, we find that the KS slope ranges between 0.69 and 1.40, and that typical star formation efficiencies of molecular gas can vary from galaxy to galaxy by a factor of ∼4. These galaxy-to-galaxy variations account for ∼0.20 dex in scatter in the ensemble KS relation, which is characterized by a 0.42 dex scatter. In addition, we find that the HI-deficient galaxies in the Virgo cluster show a steeper resolved KS relation and lower molecular gas efficiencies than HI-normal cluster galaxies. Conclusions. While the molecular gas content in galaxies residing in the Virgo cluster appears – to first order – to behave similarly to that in isolated galaxies, our VERTICO sample of galaxies shows that cluster environments play a key role in regulating star formation. The environmental mechanisms affecting the HI galaxy content also have a direct impact on the star formation efficiency of molecular gas in cluster galaxies, leading to longer depletion times in HI-deficient members.

ABSTRA C T The observational determination of the behaviour of the star formation rate (SFR) with lookback time or redshift has two main weaknesses: (i) the large uncertainty of the dust/extinction corrections, and (ii) that systematic errors may be introduced by the fact that the SFR is estimated using different methods at different redshifts. Most frequently, the luminosity of the Ha emission line, that of the forbidden line [O II] l3727 and that of the far-ultraviolet continuum are used with low-, intermediate- and high-redshift galaxies, respectively. To assess the possible systematic differences among the different SFR estimators and the role of dust, we have compared SFR estimates using Ha ,[ OII] l3727 A ˚ , ultraviolet (UV) and far-infrared (FIR) luminosities [SFR(Ha), SFR(O II), SFR(UV) and SFR(FIR), respectively] of a sample comprising the 31 nearby star-forming galaxies that have high-quality photometric data in the UV, optical and FIR. We review the different ‘standard’ methods for the estimation of the SFR and find that while the standard method provides good agreement between SFR(Ha) and SFR(FIR), both SFR(O II) and SFR(UV) are systematically higher than SFR(FIR), irrespective of the extinction law. We show that the excess in the SFR(O II) and SFR(UV) is mainly due to an overestimation of the extinction resulting from the effect of underlying stellar Balmer absorptions in the measured emission line fluxes. Taking this effect into consideration in the determination of the extinction brings the SFR(O II) and SFR(UV) in line with the SFR(FIR), and simultaneously reduces the internal scatter of the SFR estimations. Based on these results, we have derived ‘unbiased’ SFR expressions for the SFR(UV), SFR(O II) and SFR(Ha). We have used these estimators to recompute the SFR history of the Universe using the results of published surveys. The main results are that the use of the unbiased SFR estimators brings into agreement the results of all surveys. Particularly important is the agreement achieved for the SFR derived from the FIR/millimetre and optical/UV surveys. The ‘unbiased’ star formation history of the Universe shows a steep rise in the SFR from za 0t oza 1 with SFR/O1a zU 4:5 , followed by a decline for z . 2 where SFR/O1a zU 21:5 . Galaxy formation models tend to have a much flatter slope from za 0t o za 1.

We probe the star formation properties of the gas in AzTEC-1 in the COSMOS field, one of the best resolved and brightest starburst galaxies at $z \approx 4.3$, forming stars at a rate > 1000 $\mathrm{M_{\odot}}\,\mathrm{yr^{-1}}$. Using recent ALMA observations, we study star formation in the galaxy nucleus and an off-center star-forming clump and measure a median star formation rate (SFR) surface density of $\Sigma^{\mathrm{nucleus}}_{\mathrm{SFR}} = 270\pm54$ and $\Sigma^{\mathrm{sfclump}}_{\mathrm{SFR}} = 170\pm38\,\mathrm{M_{\odot}}\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$, respectively. Following the analysis by Sharda et al. (2018), we estimate the molecular gas mass, freefall time and turbulent Mach number in these regions to predict $\Sigma_{\mathrm{SFR}}$ from three star formation relations in the literature. The Kennicutt-Schmidt (Kennicutt 1998, KS) relation, which is based on the gas surface density, underestimates the $\Sigma_{\mathrm{SFR}}$ in these regions by a factor 2-3. The $\Sigma_{\mathrm{SFR}}$ we calculate from the single-freefall model of Krumholz et al. 2012 (KDM) is consistent with the measured $\Sigma_{\mathrm{SFR}}$ in the nucleus and the star-forming clump within the uncertainties. The turbulence-regulated star formation relation by Salim et al. 2015 (SFK) agrees slightly better with the observations than the KDM relation. Our analysis reveals that an interplay between turbulence and gravity can help sustain high SFRs in high-redshift starbursts. It can also be extended to other high- and low-redshift galaxies thanks to the high angular resolution and sensitivity of ALMA observations.

We present observational evidence that leakage of ionising photons from star-forming regions can affect the quantification of the star formation rate (SFR) in galaxies. This effect could partially explain the differences between the SFR estimates using the far ultraviolet (FUV) and the Halpha emission. We find that leakage could decrease the SFR(Ha)/SFR(FUV) ratio by up to a 25 per cent. The evidence is based on the observation that the SFR(Ha)/SFR(FUV) ratio is lower for objects showing a shell Halpha structure than for regions exhibiting a much more compact morphology. The study has been performed on three object samples: low luminosity dwarf galaxies from the Local Volume Legacy survey and star-forming regions in the Large Magellanic Cloud and the nearby Local Group galaxy M33. For the three samples we find differences (1.1-1.4sigma) between the SFR(Ha)/SFR(FUV) for compact and shell objects. Although leakage cannot entirely explain the observed trend of SFR(Ha)/SFR(FUV) ratios for systems with low SFR, we show the mechanism can lead to different SFR estimates when using Halpha and FUV luminosities. Therefore, further study is needed to constrain the contribution of leakage to the low SFR(Ha)/SFR(FUV) ratios observed in dwarf galaxies and its impact on the Halpha flux as a SFR indicator in such objects.

Massive galaxies in the distant Universe form stars at much higher rates than today. Although direct resolution of the star forming regions of these galaxies is still a challenge, recent molecular gas observations at the IRAM Plateau de Bure interferometer enable us to study the star formation efficiency on subgalactic scales around redshift z = 1.2. We present a method for obtaining the gas and star formation rate (SFR) surface densities of ensembles of clumps composing galaxies at this redshift, even though the corresponding scales are not resolved. This method is based on identifying these structures in position-velocity diagrams corresponding to slices within the galaxies. We use unique IRAM observations of the CO(3-2) rotational line and DEEP2 spectra of four massive star forming distant galaxies - EGS13003805, EGS13004291, EGS12007881, and EGS13019128 in the AEGIS terminology - to determine the gas and SFR surface densities of the identifiable ensembles of clumps that constitute them. The integrated CO line luminosity is assumed to be directly proportional to the total gas mass, and the SFR is deduced from the [OII] line. We identify the ensembles of clumps with the angular resolution available in both CO and [OII] spectroscopy; i.e., 1-1.5". SFR and gas surface densities are averaged in areas of this size, which is also the thickness of the DEEP2 slits and of the extracted IRAM slices, and we derive a spatially resolved Kennicutt-Schmidt (KS) relation on a scale of ~8 kpc. The data generally indicates an average depletion time of 1.9 Gyr, but with significant variations from point to point within the galaxies.

The Halpha and optical broadband images of 25 nearby Wolf-Rayet (WR) galaxies are presented. The WR galaxies are known to have the presence of a recent ($\le$10 Myr) and massive star formation episode. The photometric Halpha fluxes are estimated, and corrected for extinction and line contamination in the filter pass-bands. The star formation rates (SFRs) are estimated using Halpha images and from the archival data in the far-ultraviolet (FUV), far-infrared (FIR) and 1.4 GHz radio continuum wave-bands. A comparison of SFRs estimated from different wavebands is made after including similar data available in literature for other WR galaxies. The Halpha based SFRs are found to be tightly correlated with SFRs estimated from the FUV data. The correlations also exist with SFRs estimates based on the radio and FIR data. The WR galaxies also follow the radio-FIR correlation known for normal star forming galaxies, although it is seen here that majority of dwarf WR galaxies have radio deficiency. An analysis using ratio of non-thermal to thermal radio continuum and ratio of FUV to Halpha SFR indicates that WR galaxies have lesser non-thermal radio emission compared to normal galaxies, most likely due to lack of supernova from the very young star formation episode in the WR galaxies. The morphologies of 16 galaxies in our sample are highly suggestive of an ongoing tidal interaction or a past merger in these galaxies. This survey strengthens the conclusions obtained from previous similar studies indicating the importance of tidal interactions in triggering star-formation in WR galaxies.

We present measurements of the star formation rate (SFR) in the early-type galaxies (ETGs) of the ATLAS3D sample, based on Wide-field Infrared Survey Explorer (WISE) 22um and Galaxy Evolution Explorer (GALEX) far-ultraviolet emission. We combine these with gas masses estimated from 12CO and HI data in order to investigate the star formation efficiency (SFE) in a larger sample of ETGs than previously available. We first recalibrate (based on WISE data) the relation between old stellar populations (traced at Ks-band) and 22um luminosity, allowing us to remove the contribution of 22um emission from circumstellar dust. We then go on to investigate the position of ETGs on the Kennicutt-Schmidt (KS) relation. Molecular gas-rich ETGs have comparable star formation surface densities to normal spiral galaxy centres, but they lie systematically offset from the KS relation, having lower star formation efficiencies by a factor of ~2.5 (in agreement with other authors). This effect is driven by galaxies where a substantial fraction of the molecular material is in the rising part of the rotation curve, and shear is high. We show here for the first time that although the number of stars formed per unit gas mass per unit time is lower in ETGs, it seems that the amount of stars formed per free-fall time is approximately constant. The scatter around this dynamical relation still correlates with galaxy properties such as the shape of the potential in the inner regions. This leads us to suggest that dynamical properties (such as shear or the global stability of the gas) may be important second parameters that regulate star formation and cause much of the scatter around star-formation relations.

We present a comprehensive study of the physical properties of ∼ 105 galaxies with measurable star formation in the Sloan Digital Sky Survey (SDSS). By comparing physical information extracted from the emission lines with continuum properties, we build up a picture of the nature of star-forming galaxies at z < 0.2. We develop a method for aperture correction using resolved imaging and show that our method takes out essentially all aperture bias in the star formation rate (SFR) estimates, allowing an accurate estimate of the total SFRs in galaxies. We determine the SFR density to be 1.915+0.02−0.01 (random)+0.14−0.42 (systematic) h7010−2 M⊙ yr−1 Mpc−3 at z= 0.1 (for a Kroupa initial mass function) and we study the distribution of star formation as a function of various physical parameters. The majority of the star formation in the low-redshift Universe takes place in moderately massive galaxies (1010–1011 M⊙), typically in high surface brightness disc galaxies. Roughly 15 per cent of all star formation takes place in galaxies that show some sign of an active nucleus. About 20 per cent occurs in starburst galaxies. By focusing on the SFR per unit mass we show that the present to past average SFR, the Scalo b-parameter, is almost constant over almost three orders of magnitude in mass, declining only at M* > 1010 M⊙. The volume averaged b parameter is 0.408+0.005−0.002 (random)+0.029−0.090 (systematic)h−170. We use this value to constrain the star formation history of the Universe. For the concordance cosmology the present-day Universe is forming stars at at least 1/3 of its past average rate. For an exponentially declining cosmic star formation history this corresponds to a time-scale of 7+0.7−1.5 Gyr. In agreement with other work we find a correlation between b and morphological type, as well as a tight correlation between the 4000-Å break (D4000) and b. We discuss how D4000 can be used to estimate b parameters for high-redshift galaxies.

We investigate the nature of the star formation law at low gas surface densities using a sample of 19 low surface brightness (LSB) galaxies with existing HI maps in the literature, UV imaging from the Galaxy Evolution Explorer satellite, and optical images from the Sloan Digital Sky Survey. All of the LSB galaxies have (NUV-r) colors similar to those for higher surface brightness star-forming galaxies of similar luminosity indicating that their average star formation histories are not very different. Based upon four LSB galaxies with both UV and FIR data, we find FIR/UV ratios significantly less than one, implying low amounts of internal UV extinction in LSB galaxies. We use the UV images and HI maps to measure the star formation rate and hydrogen gas surface densities within the same region for all of the galaxies. The LSB galaxy star formation rate surface densities lie below the extrapolation of the power law fit to the star formation rate surface density as a function of the total gas density for higher surface brightness galaxies. Although there is more scatter, the LSB galaxies also lie below a second version of the star formation law in which the star formation rate surface density is correlated with the gas density divided by the orbital time in the disk. The downturn seen in both star formation laws is consistent with theoretical models that predict lower star formation efficiencies in LSB galaxies due to the declining molecular fraction with decreasing density.

We investigate the connection between galactic outflows and star formation using two independent data sets covering a sample of 22 galaxies between 1 ≲ z ≲ 1.5. The Hubble Space Telescope WFC3/G141 grism provides low spectral resolution, high spatial resolution spectroscopy yielding Hα emission-line maps from which we measure the spatial extent and strength of star formation. In the rest-frame near-UV, Keck/DEIMOS observes Fe ii and Mg ii interstellar absorption lines, which provide constraints on the intensity and velocity of the outflows. We compare outflow properties from individual and composite spectra with the star formation rate (SFR) and SFR surface density (ΣSFR), as well as the stellar mass and specific SFR (sSFR). The Fe ii and Mg ii equivalent widths (EWs) increase with both SFR and ΣSFR at ≳3σ significance, while the composite spectra show larger Fe ii EWs and outflow velocities in galaxies with higher SFR, ΣSFR, and sSFR. Absorption-line profiles of the composite spectra further indicate that the differences between subsamples are driven by outflows rather than the interstellar medium. While these results are consistent with those of previous studies, the use of Hα images makes them the most direct test of the relationship between star formation and outflows at z > 1 to date. Future facilities such as the James Webb Space Telescope and the upcoming Extremely Large Telescopes will extend these direct, Hα-based studies to lower masses and SFRs, probing galactic feedback across orders of magnitude in galaxy properties and augmenting the correlations we find here.

We present a [C ii] 158 μm map of the entire M51 (including M51b) grand design spiral galaxy observed with the Far Infrared Field-Imaging Line Spectrometer (FIFI-LS) instrument on board the Stratospheric Observatory For Infrared Astronomy (SOFIA). We compare the [C ii] emission with the total far-infrared (TIR) intensity and star formation rate (SFR) surface density maps (derived using Hα and 24 μm emission) to study the relationship between [C ii] and the star formation activity in a variety of environments within M51 on scales of 16″ corresponding to ∼660 pc. We find that [C ii] and the SFR surface density are well correlated in the central, spiral arm, and inter-arm regions. The correlation is in good agreement with that found for a larger sample of nearby galaxies at kpc scales. We find that the SFR, and [C ii] and TIR luminosities in M51, are dominated by the extended emission in M51's disk. The companion galaxy M51b, however, shows a deficit of [C ii] emission compared with the TIR emission and SFR surface density, with [C ii] emission detected only in the SW part of this galaxy. The [C ii] deficit is associated with an enhanced dust temperature in this galaxy. We interpret the faint [C ii] emission in M51b to be a result of suppressed star formation in this galaxy, while the bright mid- and far-infrared emission, which drive the TIR and SFR values, are powered by other mechanisms. A similar but less-pronounced effect is seen at the location of the black hole in M51's center. The observed [C ii] deficit in M51b suggests that this galaxy is a valuable laboratory to study the origin of the apparent [C ii] deficit observed in ultra-luminous galaxies.

Context. Galaxy evolution has been studied by interpreting the spectral energy distribution of galaxies using spectral synthesis codes. This method has been crucial in discovering different pillars of modern galaxy evolution theories. However, this analysis was mostly carried out using spectral synthesis codes that are purely stellar, that is, they assume that the nebular contribution to the total continuum is negligible. The code FADO is the first publicly available population spectral synthesis tool that treats the contribution from ionised gas to the observed emission self-consistently. This is expected to have a particularly strong effect in star-forming (SF) galaxies. Aims. We study the impact of the nebular contribution on the determination of the star formation rate (SFR), stellar mass, and consequent effect on the star-forming main sequence (SFMS) at low redshift. Methods. We applied FADO to the spectral database of the SDSS to derive the physical properties of galaxies. As a comparison, we used the data in the MPA-JHU catalogue, which contains the properties of SDSS galaxies derived without the nebular contribution. We selected a sample of SF galaxies with Hα and Hβ flux measurements, and we corrected the fluxes for the nebular extinction through the Balmer decrement. We then calculated the Hα luminosity to estimate the SFR. Then, by combining the stellar mass and SFR estimates from FADO and MPA-JHU, the SFMS was obtained. Results. The Hα flux estimates are similar between FADO and MPA-JHU. Because the Hα flux was used as tracer of the SFR, FADO and MPA-JHU agree in their SFR. The stellar mass estimates are slightly higher for FADO than for MPA-JHU on average. However, considering the uncertainties, the differences are negligible. With similar SFR and stellar mass estimates, the derived SFMS is also similar between FADO and MPA-JHU. Conclusions. Our results show that for SDSS normal SF galaxies, the additional modelling of the nebular contribution does not affect the retrieved fluxes and consequentially also does not influence SFR estimators based on the extinction-corrected Hα luminosity. For the stellar masses, the results point to the same conclusion. These results are a consequence of the fact that the vast majority of normal SF galaxies in the SDSS have a low nebular contribution. However, the obtained agreement might only hold for local SF galaxies, but higher-redshift galaxies might show different physical properties when FADO is used. This would then be an effect of the expected increased nebular contribution.

For investigating the relationship between the star formation rate and gas surface density, we develop a Bayesian linear regression method that rigorously treats measurement uncertainties and accounts for hierarchical data structure. The hierarchical Bayesian method simultaneously estimates the intercept, slope and scatter about the regression line of each individual subject (e.g. a galaxy) and the population (e.g. an ensemble of galaxies). Using synthetic data sets, we demonstrate that the method accurately recovers the underlying parameters of both the individuals and the population, especially when compared to commonly employed ordinary least squares techniques, such as the bisector fit. We apply the hierarchical Bayesian method to estimate the Kennicutt–Schmidt (KS) parameters of a sample of spiral galaxies compiled by Bigiel et al. We find significant variation in the KS parameters, indicating that no single KS relationship holds for all galaxies. This suggests that the relationship between molecular gas and star formation differs from galaxy to galaxy, possibly due to the influence of other physical properties within a given galaxy, such as metallicity, molecular gas fraction, stellar mass and/or magnetic fields. In four of the seven galaxies the slope estimates are sublinear, especially for M51, where unity is excluded at the 2σ level. We estimate the mean index of the KS relationship for the population to be 0.84, with 2σ range [0.63, 1.0]. For the galaxies with sublinear KS relationships, a possible interpretation is that CO emission is tracing some molecular gas that is not directly associated with star formation. Equivalently, a sublinear KS relationship may be indicative of an increasing gas depletion time at higher surface densities, as traced by CO emission. The hierarchical Bayesian method can account for all sources of uncertainties, including variations in the conversion of observed intensities to star formation rates and gas surface densities (e.g. the XCO factor), and is therefore well suited for a thorough statistical analysis of the KS relationship.

The processes that regulate star formation within molecular clouds are still not well understood. Various star formation scaling relations have been proposed as an explanation, one of which is to formulate a relation between the star formation rate surface density $\rm \Sigma _{SFR}$ and the underlying gas surface density $\rm \Sigma _{gas}$. In this work, we test various star formation scaling relations, such as the Kennicutt–Schmidt relation, the volumetric star formation relation, the orbital time model, the crossing time model and the multi free-fall time-scale model, towards the North American Nebula and Pelican Nebula and in the cold clumps associated with them. Measuring stellar mass from young stellar objects and gaseous mass from CO measurements, we estimate the mean $\rm \Sigma _{SFR}$, the star formation rate per free-fall time and the star formation efficiency for clumps to be 1.5 $\rm M_{\odot}\, yr^{-1}\, kpc^{-2}$, 0.009 and 2.0 per cent, respectively, while for the whole region covered by both nebulae (which we call the ‘NAN’ complex) the values are 0.6 $\rm M_{\odot}\, yr^{-1}\, kpc^{-2}$, 0.0003 and 1.6 per cent, respectively. For the clumps, we notice that the observed properties are in line with the correlation obtained between $\rm \Sigma _{SFR}$ and $\rm \Sigma _{gas}$, and between $\rm \Sigma _{SFR}$ and $\rm \Sigma _{gas}$ per free-fall time and orbital time for Galactic clouds. At the same time, we do not observe any correlation with $\rm \Sigma _{gas}$ per crossing time and multi free-fall time. Even though we see correlations in the former cases, however, all models agree with each other within a factor of 0.5 dex. It is not possible to discriminate between these models because of the current uncertainties in the input observables. We also test the variation of $\rm \Sigma _{SFR}$ with the dense gas but, because of low statistics, a weak correlation is seen in our analysis.

To investigate the variability of the star formation rate (SFR) of galaxies, we define a star formation change parameter, SFR5 Myr/SFR800 Myr, which is the ratio of the SFR averaged within the last 5 Myr to the SFR averaged within the last 800 Myr. We show that this parameter can be determined from a combination of Hα emission and Hδ absorption, plus the 4000 Å break, with an uncertainty of ∼0.07 dex for star-forming galaxies. We then apply this estimator to MaNGA galaxies, both globally within R e and within radial annuli. We find that the global SFR5 Myr/SFR800 Myr, which indicates by how much a galaxy has changed its specific SFR (sSFR), is nearly independent of its sSFR, i.e., of its position relative to the star formation main sequence (SFMS) as defined by SFR800 Myr. Also, at any sSFR, there are as many galaxies increasing their sSFR as decreasing it, as required if the dispersion in the SFMS is to stay the same. The SFR5 Myr/SFR800 Myr of the overall galaxy population is very close to that expected for the evolving main sequence. Both of these provide a reassuring check on the validity of our calibration of the estimator. We find that galaxies with higher global SFR5 Myr/SFR800 Myr appear to have higher SFR5 Myr/SFR800 Myr at all galactic radii, i.e., that galaxies with a recent temporal enhancement in overall SFR have enhanced star formation at all galactic radii. The dispersion of the SFR5 Myr/SFR800 Myr at a given relative galactic radius and a given stellar mass decreases with the (indirectly inferred) gas depletion time: locations with short gas depletion time appear to undergo bigger variations in their star formation rates on Gyr or less timescales. In Wang et al., we showed that the dispersion in star formation rate surface densities ΣSFR in the galaxy population appears to be inversely correlated with the inferred gas depletion timescale and interpreted this in terms of the dynamical response of a gas-regulator system to changes in the gas inflow rate. In this paper, we can now prove directly with SFR5 Myr/SFR800 Myr that these effects are indeed due to genuine temporal variations in the SFR of individual galaxies on timescales between 107 and 109 yr rather than possibly reflecting intrinsic, non-temporal, differences between different galaxies.