arXiv subjects

Guilin Liu

Publications and source records attributed to Guilin Liu.

At least 91 records · Page 5Linked to original sources

arXiv2017

SDSS J1640+1932: a spectacular galaxy-quasar strong lens system

We present Canada-France-Hawaii Telescope (CFHT) MegaCam observations of a galaxy-quasar strong gravitational lens system, SDSS J1640+1932. This system, located at z=0.195 (foreground elliptical galaxy) and z=0.778 (background quasar), was first visually identified by us in the Sloan Digital Sky Survey (SDSS) database. Our CFHT imaging with an angular resolution of 0.7$^{\prime \prime}$ clearly resolves 4 lensed images and a nearly complete Einstein ring. Modeling the system with a singular isothermal ellipsoid (SIE) total mass distribution, we find an Einstein radius of ${2.49^{\prime \prime}}_{-0.049}^{+0.063}$ enclosing a inferred mass of $7.25_{-0.29}^{+0.37}\times10^{11} M_{\odot}$. The quasar and its host galaxy have been magnified by a factor of 23, and the time delay relative to the leading image is determined to be 23.4-25.2 days. These parameters vary minimally when our model is fitted to the {\it{g}}-, {\it{r}}- or {\it{i}}-band images.

astro-ph.GA↗

arXiv2017

Variation of ionizing continuum: the main driver of Broad Absorption Line Variability

We present a statistical analysis of the variability of broad absorption lines (BALs) in quasars using the large multi-epoch spectroscopic dataset of the Sloan Digital Sky Survey Data Release 12 (SDSS DR12). We divide the sample into two groups according to the pattern of the variation of C iv BAL with respect to that of continuum: the equivalent widths (EW) of the BAL decreases (increases) when the continuum brightens (dims) as group T1; and the variation of EW and continuum in the opposite relation as group T2. We find that T2 has significantly (P_T<10-6 , Students T Test) higher EW ratios (R) of Si iv to C iv BAL than T1. Our result agrees with the prediction of photoionization models that C +3 column density increases (decreases) if there is a (or no) C +3 ionization front while R decreases with the incident continuum. We show that BAL variabilities in at least 80% quasars are driven by the variation of ionizing continuum while other models that predict uncorrelated BAL and continuum variability contribute less than 20%. Considering large uncertainty in the continuum flux calibration, the latter fraction may be much smaller. When the sample is binned into different time interval between the two observations, we find significant difference in the distribution of R between T1 and T2 in all time-bins down to a deltaT < 6 days, suggesting that BAL outflow in a fraction of quasars has a recombination time scale of only a few days.

astro-ph.GA↗

arXiv2017

Zooming into local active galactic nuclei: The power of combining SDSS-IV MaNGA with higher resolution integral field unit observations

Ionised gas outflows driven by active galactic nuclei (AGN) are ubiquitous in high luminosity AGN with outflow speeds apparently correlated with the total bolometric luminosity of the AGN. This empirical relation and theoretical work suggest that in the range L_bol ~ 10^43-45 erg/s there must exist a threshold luminosity above which the AGN becomes powerful enough to launch winds that will be able to escape the galaxy potential. In this paper, we present pilot observations of two AGN in this transitional range that were taken with the Gemini North Multi-Object Spectrograph Integral Field Unit (IFU). Both sources have also previously been observed within the Sloan Digital Sky Survey-IV (SDSS) Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. While the MaNGA IFU maps probe the gas fields on galaxy-wide scales and show that some regions are dominated by AGN ionization, the new Gemini IFU data zoom into the centre with four times better spatial resolution. In the object with the lower L_bol we find evidence of a young or stalled biconical AGN-driven outflow where none was obvious at the MaNGA resolution. In the object with the higher L_bol we trace the large-scale biconical outflow into the nuclear region and connect the outflow from small to large scales. These observations suggest that AGN luminosity and galaxy potential are crucial in shaping wind launching and propagation in low-luminosity AGN. The transition from small and young outflows to galaxy-wide feedback can only be understood by combining large-scale IFU data that trace the galaxy velocity field with higher resolution, small scale IFU maps.

astro-ph.GA↗

arXiv2016

Symmetry-aware Depth Estimation using Deep Neural Networks

Due to the abundance of 2D product images from the Internet, developing efficient and scalable algorithms to recover the missing depth information is central to many applications. Recent works have addressed the single-view depth estimation problem by utilizing convolutional neural networks. In this paper, we show that exploring symmetry information, which is ubiquitous in man made objects, can significantly boost the quality of such depth predictions. Specifically, we propose a new convolutional neural network architecture to first estimate dense symmetric correspondences in a product image and then propose an optimization which utilizes this information explicitly to significantly improve the quality of single-view depth estimations. We have evaluated our approach extensively, and experimental results show that this approach outperforms state-of-the-art depth estimation techniques.

cs.CV↗

arXiv2016

Extremely Red Quasars from SDSS, BOSS and WISE: Classification of Optical Spectra

Quasars with extremely red infrared-to-optical colours are an interesting population that can test ideas about quasar evolution as well as orientation, obscuration and geometric effects in the so-called AGN unified model. To identify such a population we match the quasar catalogues of the Sloan Digital Sky Survey (SDSS), the Baryon Oscillation Spectroscopic Survey (BOSS) to the Wide-Field Infrared Survey Explorer (WISE) to identify quasars with extremely high infrared-to-optical ratios. We identify 65 objects with r(AB)-W4(Vega)>14 mag (i.e., F_nu(22um)/F_nu(r) > ~1000). This sample spans a redshift range of 0.28 2.6 objects that are detected in the W4-band but not W1 or W2 (i.e., W1W2-dropouts). The SDSS/BOSS spectra show that the majority of the objects are reddened Type 1 quasars, Type 2 quasars (both at low and high redshift) or objects with deep low-ionization broad absorption lines (BALs) that suppress the observed r-band flux. In addition, we identify a class of Type 1 permitted broad-emission line objects at z~2-3 which are characterized by emission line rest-frame equivalent widths (REWs) of >~150Ang , much larger than those of typical quasars. In particular, 55% (45%) of the non-BAL Type 1s with measurable CIV in our sample have REW(CIV) > 100 (150)Ang, compared to only 5.8% (1.3%) for non-BAL quasars in BOSS. These objects often also have unusual line ratios, such as very high NV/Ly-alpha ratios. These large REWs might be caused by suppressed continuum emission analogous to Type 2 quasars; however, there is no obvious mechanism in standard Unified Models to suppress the continuum without also obscuring the broad emission lines.

astro-ph.GA↗

arXiv2016

Towards a comprehensive picture of powerful quasars, their host galaxies and quasar winds at z ~ 0.5

Luminous type-2 quasars in which the glow from the central black hole is obscured by dust are ideal targets for studying their host galaxies and the quasars' effect on galaxy evolution. Such feedback appears ubiquitous in luminous obscured quasars where high velocity ionized nebulae have been found. We present rest-frame yellow-band (~5000 Angstroms) observations using the Hubble Space Telescope for a sample of 20 luminous quasar host galaxies at 0.2 < z < 0.6 selected from the Sloan Digital Sky Survey. For the first time, we combine host galaxy observations with geometric measurements of quasar illumination using blue-band HST observations and [OIII] integral field unit observations probing the quasar winds. The HST images reveal bright merger signatures in about half the galaxies; a significantly higher fraction than in comparison inactive ellipticals. We show that the host galaxies are primarily bulge-dominated, with masses close to M*, but belong to < 30% of elliptical galaxies that are highly star-forming at z ~ 0.5. Ionized gas signatures are uncorrelated with faint stellar disks (if present), confirming that the ionized gas is not concentrated in a disk. Scattering cones and [OIII] ionized gas velocity field are aligned with the forward scattering cones being co-spatial with the blue-shifted side of the velocity field, suggesting the high velocity gas is indeed photo-ionized by the quasar. Based on the host galaxies' high star-formation rates and bright merger signatures, we suggest that this low-redshift outbreak of luminous quasar activity is triggered by recent minor mergers. Combining these novel observations, we present new quasar unification tests, which are in agreement with expectations of the orientation-based unification model for quasars.

astro-ph.GA↗

arXiv2015

Giant scattering cones in obscured quasars

We analyze Hubble Space Telescope observations of scattering regions in 20 luminous obscured quasars at $0.24<z<0.65$ (11 new observations and 9 archival ones) observed at rest-frame $\sim 3000$Å. We find spectacular $5-10$ kpc-scale scattering regions in almost all cases. The median scattering efficiency at this wavelength (the ratio of observed to estimated intrinsic flux) is 2.3\%, and 73\% of the observed flux at this wavelength is due to scattered light, which if unaccounted for may strongly bias estimates of quasar hosts' star formation rates. Modeling these regions as illuminated dusty cones, we estimate the radial density distributions of the interstellar medium as well as the geometric properties of circumnuclear quasar obscuration -- inclinations and covering factors. Small derived opening angles (median half-angle and standard deviation 27\dg$\pm$9\dg) are inconsistent with a 1:1 type 1 / type 2 ratio. We suggest that quasar obscuration is patchy and that the observer has a $\sim 40\%$ chance of seeing a type 1 source even through the obscuration. We estimate median density profile of the scattering medium to be $n_{\rm H}=0.04-0.5$ $(1{\rm kpc}/r)^2$ cm$^{-3}$, depending on the method. Quasars in our sample likely exhibit galaxy-wide winds, but if these consist of optically thick clouds then only a small fraction of the wind mass ($\la 10\%$) contributes to scattering.

astro-ph.GA↗

arXiv2015

Integral Field Spectroscopy of AGN Absorption Outflows: Mrk 509 and IRAS F04250-5718

Ultravoilet (UV) absorption lines provide abundant spectroscopic information enabling the probe of the physical conditions in AGN outflows, but the outflow radii (and the energetics consequently) can only be determined indirectly. In this paper, we present the first direct test of these determinations using integral field unit (IFU) spectroscopy. We have conducted Gemini IFU mapping of the ionized gas nebulae surrounding two AGNs, whose outflow radii have been constrained by UV absorption line analyses. In Mrk 509, we find a quasi-spherical outflow with a radius of 1.2 kpc and a velocity of $\sim290$ km s$^{-1}$, while IRAS F04250$-$5718 is driving a biconical outflow extending out to 2.9 kpc, with a velocity of $\sim580$ km s$^{-1}$ and an opening angle of $\sim70^{\circ}$. The derived mass flow rate is $\sim5$ and $>1$ M$_{\odot}$ yr$^{-1}$, respectively, and the kinetic luminosity is $\gtrsim1\times10^{41}$ erg s$^{-1}$ for both. Adopting the outflow radii and geometric parameters measured from IFU, absorption line analyses would yield mass flow rates and kinetic luminosities in agreement with the above results within a factor of $\sim2$. We conclude that the spatial locations, kinematics and energetics revealed by this IFU emission-line study are consistent with pre-existing UV absorption line analyses, providing a long-awaited direct confirmation of the latter as an effective approach for characterizing outflow properties.

astro-ph.GA↗

arXiv2015

Similarity of ionized gas nebulae around unobscured and obscured quasars

Quasar feedback is suspected to play a key role in the evolution of massive galaxies, by removing or reheating gas in quasar host galaxies and thus limiting the amount of star formation. In this paper we continue our investigation of quasar-driven winds on galaxy-wide scales. We conduct Gemini Integral Field Unit spectroscopy of a sample of luminous unobscured (type 1) quasars, to determine the morphology and kinematics of ionized gas around these objects, predominantly via observations of the [O III]5007 emission line. We find that ionized gas nebulae extend out to ~13 kpc from the quasar, that they are smooth and round, and that their kinematics are inconsistent with gas in dynamical equilibrium with the host galaxy. The observed morphological and kinematic properties are strikingly similar to those of ionized gas around obscured (type 2) quasars with matched [O III] luminosity, with marginal evidence that nebulae around unobscured quasars are slightly more compact. Therefore in samples of obscured and unobscured quasars carefully matched in [O III] luminosity we find support for the standard geometry-based unification model of active galactic nuclei, in that the intrinsic properties of quasars, of their hosts and of their ionized gas appear to be very similar. Given the apparent ubiquity of extended ionized regions, we are forced to conclude that either the quasar is at least partially illuminating pre-existing gas or that both samples of quasars are seen during advanced stages of quasar feedback. In the latter case, we may be biased by our [O III]-based selection against quasars in the early "blow-out" phase, for example due to dust obscuration.

astro-ph.GA↗

arXiv2014

Near Infrared Spectra and Intrinsic Luminosities of Candidate Type II Quasars at 2 < z < 3.4

We present JHK near-infrared (NIR) spectroscopy of 25 candidate Type II quasars selected from the Sloan Digital Sky Survey, using Triplespec on the Apache Point Observatory 3.5m telescope, FIRE at the Magellan/Baade 6.5m telescope, and GNIRS on Gemini. At redshifts of 2 < z < 3.4, our NIR spectra probe the rest-frame optical region of these targets, which were initially selected to have strong lines of CIV and Ly alpha, with FWHM<2000 km/s from the SDSS pipeline. We use the [OIII]5007 line shape as a model for the narrow line region emission, and find that \halpha\ consistently requires a broad component with FWHMs ranging from 1000 to 7500 km/s. Interestingly, the CIV lines also require broad bases, but with considerably narrower widths of 1000 to 4500 km/s. Estimating the extinction using the Balmer decrement and also the relationship in lower-z quasars between rest equivalent width and luminosity in the [OIII] line, we find typical A_V values of 0-2 mag, which naturally explain the attenuated CIV lines relative to Halpha. We propose that our targets are moderately obscured quasars. We also describe one unusual object with three distinct velocity peaks in its [OIII] spectrum.

astro-ph.GA↗

arXiv2014

Gemini Long-slit Observations of Luminous Obscured Quasars: Further Evidence for an Upper Limit on the Size of the Narrow-Line Region

We examine the spatial extent of the narrow-line regions (NLRs) of a sample of 30 luminous obscured quasars at $0.4 < z < 0.7$ observed with spatially resolved Gemini-N GMOS long-slit spectroscopy. Using the [OIII]$\lambda5007$ emission feature, we estimate the size of the NLR using a cosmology-independent measurement: the radius where the surface brightness falls to 10$^{-15}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$. We then explore the effects of atmospheric seeing on NLR size measurements and conclude that direct measurements of the NLR size from observed profiles are too large by 0.1 - 0.2 dex on average, as compared to measurements made to best-fit Sérsic or Voigt profiles convolved with the seeing. These data, which span a full order of magnitude in IR luminosity ($\log{(L_{8 μ\mathrm{m}} / \mathrm{erg\, s}^{-1})} = 44.4 - 45.4$) also provide strong evidence that there is a flattening of the relationship between NLR size and AGN luminosity at a seeing-corrected size of $\sim 7$ kpc. The objects in this sample have high luminosities which place them in a previously under-explored portion of the size-luminosity relationship. These results support the existence of a maximal size of the narrow-line region around luminous quasars; beyond this size either there is not enough gas, or the gas is over-ionized and does not produce enough [OIII]$\lambda5007$ emission.

astro-ph.GA↗

arXiv2013

Extinction and Dust Geometry in M83 HII Regions: A Hubble Space Telescope/WFC3 Study

We present HST/WFC3 narrow-band imaging of the starburst galaxy M83 targeting the hydrogen recombination lines (H$β$, H$α$ and Pa$β$), which we use to investigate the dust extinction in the HII regions. We derive extinction maps with 6 parsec spatial resolution from two combinations of hydrogen lines (H$α$/H$β$ and H$α$/Pa$β$), and show that the longer wavelengths probe larger optical depths, with $A_V$ values larger by $\gtrsim$1 mag than those derived from the shorter wavelengths. This difference leads to a factor $\gtrsim$2 discrepancy in the extinction-corrected H$α$ luminosity, a significant effect when studying extragalactic HII regions. By comparing these observations to a series of simple models, we conclude that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground "dust screen" assumption. However, most data points are bracketed by the foreground screen and a model where dust and emitters are uniformly mixed. When averaged over large ($\gtrsim$100--200 pc) scales, the extinction becomes consistent with a "dust screen", suggesting that other geometries tend to be restricted to more local scales. Moreover, the extinction in any region can be described by a combination of the foreground screen and the uniform mixture model with weights of 1/3 and 2/3 in the center ($\lesssim$2 kpc), respectively, and 2/3 and 1/3 for the rest of the disk. This simple prescription significantly improves the accuracy of the dust extinction corrections and can be especially useful for pixel-based analyses of galaxies similar to M83.

astro-ph.CO↗

arXiv2013

Observations of Feedback from Radio-Quiet Quasars - II. Kinematics of Ionized Gas Nebulae

The prevalence and energetics of quasar feedback is a major unresolved problem in galaxy formation theory. In this paper, we present Gemini Integral Field Unit observations of ionized gas around eleven luminous, obscured, radio-quiet quasars at z~0.5 out to ~15 kpc from the quasar; specifically, we measure the kinematics and morphology of [O III]5007 emission. The round morphologies of the nebulae and the large line-of-sight velocity widths (with velocities containing 80% of the emission as high as 1000 km/s combined with relatively small velocity difference across them (from 90 to 520 km/s) point toward wide-angle quasi-spherical outflows. We use the observed velocity widths to estimate a median outflow velocity of 760 km/s, similar to or above the escape velocities from the host galaxies. The line-of-sight velocity dispersion declines slightly toward outer parts of the nebulae (by 3% per kpc on average). The majority of nebulae show blueshifted excesses in their line profiles across most of their extents, signifying gas outflows. For the median outflow velocity, we find a kinetic energy flow between 4x10^{44} and 3x10^{45} erg/s and mass outflow rate between 2000 and 20000 Msun/yr. These values are large enough for the observed quasar winds to have a significant impact on their host galaxies. The median rate of converting bolometric luminosity to kinetic energy of ionized gas clouds is ~2%. We report four new candidates for "super-bubbles" -- outflows that may have broken out of the denser regions of the host galaxy.

astro-ph.CO↗

arXiv2013

Candidate Type II Quasars at 2 < z < 4.3 in the Sloan Digital Sky Survey III

At low redshifts, dust-obscured quasars often have strong yet narrow permitted lines in the rest-frame optical and ultraviolet, excited by the central active nucleus, earning the designation Type II quasars. We present a sample of 145 candidate Type II quasars at redshifts between 2 and 4.3, encompassing the epoch at which quasar activity peaked in the universe. These objects, selected from the quasar sample of the Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey III, are characterized by weak continuum in the rest-frame ultraviolet (typical continuum magnitude of i \approx 22) and strong lines of CIV and Ly α, with Full Width at Half Maximum less than 2000 kms-1. The continuum magnitudes correspond to an absolute magnitude of -23 or brighter at redshift 3, too bright to be due exclusively to the host galaxies of these objects. Roughly one third of the objects are detected in the shorter-wavelength bands of the WISE survey; the spectral energy distributions (SEDs) of these objects appear to be intermediate between classic Type I and Type II quasars seen at lower redshift. Five objects are detected at rest frame 6μm by Spitzer, implying bolometric luminosities of several times 10^46 erg s-1. We have obtained polarization measurements for two objects; they are roughly 3% polarized. We suggest that these objects are luminous quasars, with modest dust extinction (A_V ~ 0.5 mag), whose ultraviolet continuum also includes a substantial scattering contribution. Alternatively, the line of sight to the central engines of these objects may be partially obscured by optically thick material.

astro-ph.CO↗

arXiv2013

Star Formation On Sub-kpc Scale Triggered By Non-linear Processes In Nearby Spiral Galaxies

We report a super-linear correlation for the star formation law based on new CO($J$=1-0) data from the CARMA and NOBEYAMA Nearby-galaxies (CANON) CO survey. The sample includes 10 nearby spiral galaxies, in which structures at sub-kpc scales are spatially resolved. Combined with the star formation rate surface density traced by H$α$ and 24 $μ$m images, CO($J$=1-0) data provide a super-linear slope of $N$ = 1.3. The slope becomes even steeper ($N$ = 1.8) when the diffuse stellar and dust background emission is subtracted from the H$α$ and 24 $μ$m images. In contrast to the recent results with CO($J$=2-1) that found a constant star formation efficiency (SFE) in many spiral galaxies, these results suggest that the SFE is not independent of environment, but increases with molecular gas surface density. We suggest that the excitation of CO($J$=2-1) is likely enhanced in the regions with higher star formation and does not linearly trace the molecular gas mass. In addition, the diffuse emission contaminates the SFE measurement most in regions where star formation rate is law. These two effects can flatten the power law correlation and produce the apparent linear slope. The super linear slope from the CO($J$=1-0) analysis indicates that star formation is enhanced by non-linear processes in regions of high gas density, e.g., gravitational collapse and cloud-cloud collisions.

astro-ph.CO↗

arXiv2013

The Paα Luminosity Function of HII Regions in Nearby Galaxies from HST/NICMOS

The HII region luminosity function (LF) is an important tool for deriving the birthrates and mass distribution of OB associations, and is an excellent tracer of the newly formed massive stars and associations. To date, extensive work (predominantly in Hα) has been done from the ground, which is hindered by dust extinction and the severe blending of adjacent (spatially or in projection) HII regions. Reliably measuring the properties of HII regions requires a linear resolution <40 pc, but analyses satisfying this requirement have been done only in a handful of galaxies, so far. As the first space-based work using a galaxy sample, we have selected 12 galaxies from our HST NICMOS Paα survey and studied the luminosity function and size distribution of HII regions both in individual galaxies and cumulatively, using a virtually extinction-free tracer of the ionizing photon rate. The high angular resolution and low sensitivity to diffuse emission of NICMOS also offer an advantage over ground-based imaging by enabling a higher degree of de-blending of the HII regions. We do not confirm the broken power-law LFs found in ground-based studies. Instead, we find that the LFs, both individual and co-added, follow a single power law dN(L)/dlnL ~ L^-1, consistent with the mass function of star clusters in nearby galaxies, and in agreement with the results of the existing analyses with HST data. The individual and co-added size distribution of HII regions are both roughly consistent with dN(D)/dlnD ~ D^-3, but the power-law scaling is probably contaminated by blended regions or complexes.

astro-ph.CO↗

arXiv2013

Observations of Feedback from Radio-Quiet Quasars: I. Extents and Morphologies of Ionized Gas Nebulae

Black hole feedback -- the strong interaction between the energy output of supermassive black holes and their surrounding environments -- is routinely invoked to explain the absence of overly luminous galaxies, the black hole vs. bulge correlations and the similarity of black hole accretion and star formation histories. Yet direct probes of this process in action are scarce and limited to small samples of active nuclei. We present Gemini IFU observations of the distribution of ionized gas around luminous, obscured, radio-quiet (RQ) quasars at z~0.5. We detect extended ionized gas nebulae via [O III]5007 emission in every case, with a mean diameter of 28 kpc. These nebulae are nearly perfectly round. The regular morphologies of nebulae around RQ quasars are in striking contrast with lumpy or elongated nebulae seen around radio galaxies at low and high redshifts. We present the uniformly measured size-luminosity relationship of [O III] nebulae around Seyfert 2 galaxies and type 2 quasars spanning 6 orders of magnitude in luminosity and confirm the flat slope of the correlation (R ~ L^{0.25+/-0.02}). We find a universal behavior of the [O III]/H-beta ratio in our entire RQ quasar sample: it persists at a constant value (~10) in the central regions, until reaching a "break" isophotal radius ranging from 4 to 11 kpc where it starts to decrease. We propose a model of clumpy nebulae in which clouds that produce line emission transition from being ionization-bounded at small distances from the quasar to being matter-bounded in the outer parts of the nebula, which qualitatively explains the observed line ratio and surface brightness profiles. It is striking that we see such smooth and round large-scale gas nebulosities in this sample, which are inconsistent with illuminated merger debris and which we suggest may be the signature of accretion energy from the nucleus reaching gas at large scales.

astro-ph.CO↗

arXiv2012

Star Formation Laws: the Effects of Gas Cloud Sampling

Recent observational results indicate that the functional shape of the spatially-resolved star formation-molecular gas density relation depends on the spatial scale considered. These results may indicate a fundamental role of sampling effects on scales that are typically only a few times larger than those of the largest molecular clouds. To investigate the impact of this effect, we construct simple models for the distribution of molecular clouds in a typical star-forming spiral galaxy, and, assuming a power-law relation between SFR and cloud mass, explore a range of input parameters. We confirm that the slope and the scatter of the simulated SFR-molecular gas surface density relation depend on the size of the sub-galactic region considered, due to stochastic sampling of the molecular cloud mass function, and the effect is larger for steeper relations between SFR and molecular gas. There is a general trend for all slope values to tend to ~unity for region sizes larger than 1-2 kpc, irrespective of the input SFR-cloud relation. The region size of 1-2 kpc corresponds to the area where the cloud mass function becomes fully sampled. We quantify the effects of selection biases in data tracing the SFR, either as thresholds (i.e., clouds smaller than a given mass value do not form stars) or backgrounds (e.g., diffuse emission unrelated to current star formation is counted towards the SFR). Apparently discordant observational results are brought into agreement via this simple model, and the comparison of our simulations with data for a few galaxies supports a steep (>1) power law index between SFR and molecular gas.

astro-ph.GA↗