arXiv subjects

Qing-Hua Tan

Publications and source records attributed to Qing-Hua Tan.

15 recordsLinked to original sources

arXiv2025

The MALATANG survey: star formation, dense gas, and AGN feedback in NGC 1068

We aim to investigate the interplay between dense molecular gas, star formation, and active galactic nucleus (AGN) feedback in the luminous infrared galaxy (LIRG) NGC 1068 at sub-kiloparsec scales. We present the HCN (4-3) and HCO$^+$ (4-3) maps of NGC 1068, obtained with JCMT as part of the Mapping the dense molecular gas in the strongest star-forming galaxies (MALATANG) project, and perform spatially resolved analyses of their correlations with infrared luminosity and soft X-ray emission. Spatially resolved relations between the luminosities of infrared dust emission and dense molecular gas tracers ($L_{\rm IR}-L'_{\rm dense}$) are found to be nearly linear, without clear evidence of excess contributions from AGN activity. The spatially resolved X-ray emission ($L^{\rm gas}_{0.5-2\,\mathrm{keV}}$) displays a radially-dependent twofold correlation with the star formation rate (SFR), suggesting distinct gas-heating mechanisms between the galaxy center and the outer regions. A super-linear scaling is obtained in galactic center regions with SFR surface density ($Σ_{\rm SFR}$) $>$ 8.2 $\times$ 10$^{-6}$ $M_\odot$ yr$^{-1}$ kpc$^{-2}$: log($L^{\rm gas}_{0.5-2\,\mathrm{keV}}$/erg s$^{-1}$) = 2.2 log(SFR/$M_\odot$ yr$^{-1}$) + 39.1. We further found a statistically significant super-linear correlation ($β= 1.34$ $\pm$ 0.86) between $L^{\rm gas}_{0.5-2\,\mathrm{keV}}$/SFR and HCN(4-3)/CO(1-0) intensity ratio, whereas no such trend is seen for HCO$^+$(4-3)/CO(1-0) or CO(3-2)/CO(1-0). These findings indicate that AGN feedback does not dominate star formation regulation on sub-kiloparsec scales, and that the excitation of dense gas traced by HCN (4-3) may be more directly influenced by high-energy feedback processes compared to HCO$^+$ (4-3) and CO (3-2).

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arXiv2025

Under the glare of a luminous quasar, the FIR continuum is still an excellent tracer of the ISM down to the central kiloparsec

Contamination-free assessments of the interstellar medium and star formation in quasar host galaxies, particularly based on the far-infrared, offer insights into the role of supermassive black holes in galaxy evolution. Motivated by predictions of quasar heating of dust on both nuclear and galaxy-wide scales, we perform two-component (host galaxy + point source) modeling of high-resolution (~0.1") ALMA observations of the FIR continuum in Band 5 (lambda_rest~500 um) of three highly luminous quasars (L_bol~10^47 erg/s), powered by supermassive black holes having M_BH~10^9 M_sun, at z=2. We include Band 9 (lambda_rest~154 um; 0.06" and 0.3") data at high S/N which places further constraints on the unresolved nuclear component in two cases. To break the degeneracy between quasar and stellar heating, we use CO (J=5-4), observed in Band 5, to gauge the expected contribution of star formation to the infrared luminosity. We find very good agreement between the strength and spatial distribution of the extended continuum component and its prediction based on CO (J=5-4). This is supported by the location of our three quasars along the L_(CO 5-4)-L_(IR, SFR) luminosity relation for inactive star-forming galaxies. As a consequence, there is no evidence for additional continuum emission on extended scales which could be attributed to quasar-heated dust. As expected, the nuclear (i.e., torus) contribution is present and subdominant (12% in Band 9 for one quasar with a typical star-forming host) or non-existent (<8% in Band 9 for the starbursting host). Based on the continuum and CO, the presence of substantial levels of ongoing star formation agrees with previous estimates from unresolved ALMA continuum observations which finds SFRs consistent with star-forming main-sequence galaxies. Therefore, our results do not provide evidence for a quasar-mode feedback, even for the most luminous cases at z=2.

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arXiv2025

The MALATANG survey: Dense gas distribution on sub-kiloparsec scales across the disk of M82

We present observations of HCN J=4-3 and HCO^+ J=4-3 lines obtained with the James Clerk Maxwell Telescope as part of the MALATANG survey, combined with archival HCN J=1-0 and HCO^+ J=1-0 data from the Green Bank Telescope, to study the spatial distribution and excitation conditions of dense molecular gas in the disk of M82. We detect HCN J=4-3 and HCO^+ J=4-3 emission within the central region (< 500 pc) of the galaxy, while the J=1-0 emission lines exhibit a more extended spatial distribution (> 700 pc). The dense gas shows a clear double-lobed structure in both spatial distribution and kinematics, with the HCN and HCO^+ J=4-3 lines in the southwest lobe blueshifted by ~ 40 km/s relative to the J=1-0 lines. The HCN J=4-3/1-0 and HCO^+ J=4-3/1-0 line-luminosity ratios range from 0.09 to 0.53 and from 0.14 to 0.87, respectively, with mean values of 0.18 +/- 0.04 and 0.36 +/- 0.06. The HCN ratio is lower than the typical average observed in nearby star-forming galaxies, whereas the HCO^+ ratio is comparatively higher, suggesting that the high-J HCN emission in M82 is significantly sub-thermally excited. Spatially, the peak values of the J=4-3/1-0 ratios are found in the northwest region of M82, coinciding with the galaxy-scale outflow. Elevated HCN/HCO^+ ratios are also detected in roughly the same area, potentially tracing local excitation enhancements driven by the outflow. The HCN/HCO^+ J=4-3 ratio across all detected regions ranges from 0.19 to 1.07 with a mean value of 0.41 +/- 0.11, which is significantly lower than the average J=1-0 ratio of 0.76 +/- 0.08. Both ratios are significantly lower than the average values observed in nearby star-forming galaxies, which could be related to the relatively low gas density and the presence of an extended photo-dissociation region in M82.

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arXiv2024

CO-CHANGES II: spatially resolved IRAM 30M CO line observations of 23 nearby edge-on spiral galaxies

Molecular gas, as the fuel for star formation, and its relationship with atomic gas are crucial for understanding how galaxies regulate their star forming (SF) activities. We conducted IRAM 30m observations of 23 nearby spiral galaxies from the CHANG-ES project to investigatet the distribution of molecular gas and the Kennicutt-Schmidt law. Combining these results with atomic gas masses from previous studies, we aim to investigate the scaling relations that connect the molecular and atomic gas masses with stellar masses and the baryonic Tully-Fisher relation. Based on spatially resolved observations of the three CO lines, we calculated the total molecular gas masses, the ratios between different CO lines, and derived physical parameters such as temperature and optical depth. The median line ratios for nuclear/disk regions are 8.6/6.1 (^{12}\mathrm{CO}/^{13}\mathrm{CO}\ J=1{-}0) and 0.53/0.39 (^{12}\mathrm{CO}\ J=2{-}1/J=1{-}0). Molecular gas mass derived from ^{13}\mathrm{CO} is correlated but systematically lower than that from ^{12}\mathrm{CO}. Most galaxies follow the spatially resolved SF scaling relation with a median gas depletion timescale of approximately 1 Gyr, while a few exhibit shorter timescales of approximately 0.1 Gyr. The molecular-to-atomic gas mass ratio correlates strongly with stellar mass, consistent with previous studies. Galaxies with lower stellar masses show an excess of atomic gas, indicating less efficient conversion to molecular gas. Most galaxies tightly follow the baryonic Tully-Fisher relation, but NGC 2992 and NGC 4594 deviate from the relation due to different physical factors. We find that the ratio of the cold gas (comprising molecular and atomic gas) to the total baryon mass decreases with the gravitational potential of the galaxy, as traced by rotation velocity, which could be due to gas consumption in SF or being heated to the hot phase.

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arXiv2024

The first exploration of the correlations between \textit{WISE} 12 \micron\ and CO emission in early-type galaxies

We present the analysis of a comprehensive sample of 352 early-type galaxies using public data, to investigate the correlations between CO luminosities and mid-infrared luminosities observed by \textit{Wide-field Infrared Survey Explorer} (\textit{WISE}). We find strong correlations between both CO (1-0) and CO (2-1) luminosities and 12 \micron\ luminosity, boasting a correlation coefficient greater than 0.9 and an intrinsic scatter smaller than 0.1 dex. The consistent slopes observed for the relationships of CO (1-0) and CO (2-1) suggest that the line ratio R21 lacks correlation with mid-infrared emission in early-type galaxies, which is significantly different from star-forming galaxies. Moreover, the slopes of $L_{\rm CO (1-0)}$--$L_{\mbox{12\micron}}$ and $L_{\rm CO (2-1)}$--$L_{\mbox{12\micron}}$ relations in early-type galaxies are steeper than those observed in star-forming galaxies. Given the absence of correlation with color, morphology or sSFR, the correlation between deviations and the molecular gas mass surface density could be eliminated by correcting the possible 12 \micron\ emission from old stars or adopting a systematically different $α_{\rm CO}$. The latter, on average, is equivalent to adding an constant CO brightness density, specifically ${2.8{_{-0.6}}\!\!\!\!\!\!\!\!\!^{+0.8}}~[\mathrm{K~km~s^{-1}}]$ and ${4.4{_{-1.4}}\!\!\!\!\!\!\!\!\!^{+2.2}}~[\mathrm{K~km~s^{-1}}]$ for CO (1-0) and (2-1) respectively. These explorations will serve as useful tools for estimating the molecular gas content in gas-poor galaxies and understanding associated quenching processes.

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arXiv2024

In-Situ Spheroid Formation in Distant Submillimeter-Bright Galaxies

The majority of stars in today's Universe reside within spheroids, which are bulges of spiral galaxies and elliptical galaxies. Their formation is still an unsolved problem. Infrared/submm-bright galaxies at high redshifts have long been suspected to be related to spheroids formation. Proving this connection has been hampered so far by heavy dust obscuration when focusing on their stellar emission or by methodologies and limited signal-to-noise ratios when looking at submm wavelengths. Here we show that spheroids are directly generated by star formation within the cores of highly luminous starburst galaxies in the distant Universe. This follows from the ALMA submillimeter surface brightness profiles which deviate significantly from those of exponential disks, and from the skewed-high axis-ratio distribution. The majority of these galaxies are fully triaxial rather than flat disks: the ratio of the shortest to the longest of their three axes is half, on average, and increases with spatial compactness. These observations, supported by simulations, reveal a cosmologically relevant pathway for in-situ spheroid formation through starbursts likely preferentially triggered by interactions (and mergers) acting on galaxies fed by non-co-planar gas accretion streams.

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arXiv2024

Sub-kiloparsec scaling relations between hot gas, dense gas and star formation rate in five nearby star-forming galaxies

Based on the newly acquired dense gas observations from the JCMT MALATANG survey and X-ray data from Chandra, we explore the correlation between hot gas and HCN $J=4 \rightarrow 3$, HCO$^+\ J=4 \rightarrow 3$ emission for the first time at sub-kiloparsec scale of five nearby star-forming galaxies, namely M82, M83, IC 342, NGC 253, and NGC 6946. We find that both HCN $J=4 \rightarrow 3$ and HCO$^+\ J=4 \rightarrow 3$ line luminosity show a statistically significant correlation with the 0.5${-}$2 keV X-ray emission of the diffuse hot gas ($L_{\rm 0.5 - 2\,keV}^{\rm gas}$). The Bayesian regression analysis gives the best fit of ${\rm log}(L_{\rm 0.5-2\,keV}^{\rm gas} /{\rm erg\,s^{-1}})=2.39\,{\rm log}(L'_{\rm HCN(4-3)} /{\rm K\,km\,s^{-1}\,pc^{2}})+24.83$ and ${\rm log}(L_{\rm 0.5-2\,keV}^{\rm gas} /{\rm erg\,s^{-1}})=2.48\,{\rm log}(L'_{\rm HCO^{+}(4-3)} /{\rm K\,km\,s^{-1}\,pc^{2}})+23.84$, with dispersion of $\thicksim$0.69 dex and 0.54 dex, respectively. At the sub-kiloparsec scale, we find that the power-law index of the $L_{\rm 0.5 - 2\,keV}^{\rm gas}$ ${-}$ star formation rate (SFR) relation is ${\rm log}(L_{\rm 0.5-2\,keV}^{\rm gas} /{\rm erg\,s^{-1}})=1.80\,{\rm log} ({\rm SFR} /M_\odot\,{\rm yr}^{-1})+39.16$, deviated from previous linear relations at global scale. This implies that the global property of hot gas significantly differs from individual resolved regions, which is influenced by the local physical conditions close to the sites of star formation.

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arXiv2024

The Dust Attenuation Scaling Relation of Star-Forming Galaxies in the EAGLE Simulations

Dust attenuation in star-forming galaxies (SFGs), as parameterized by the infrared excess (IRX $\equiv L_{\rm IR}/L_{\rm UV}$), is found to be tightly correlated with star formation rate (SFR), metallicity and galaxy size, following a universal IRX relation up to $z=3$. This scaling relation can provide a fundamental constraint for theoretical models to reconcile galaxy star formation, chemical enrichment, and structural evolution across cosmic time. We attempt to reproduce the universal IRX relation over $0.1\leq z\leq 2.5$ using the EAGLE hydrodynamical simulations and examine sensitive parameters in determining galaxy dust attenuation. Our findings show that while the predicted universal IRX relation from EAGLE approximately aligns with observations at $z\leq 0.5$, noticeable disparities arise at different stellar masses and higher redshifts. Specifically, we investigate how modifying various galaxy parameters can affect the predicted universal IRX relation in comparison to the observed data. We demonstrate that the simulated gas-phase metallicity is the critical quantity for the shape of the predicted universal IRX relation. We find that the influence of the infrared luminosity and infrared excess is less important while galaxy size has virtually no significant effect. Overall, the EAGLE simulations are not able to replicate some of the observed characteristics between IRX and galaxy parameters of SFGs, emphasizing the need for further investigation and testing for our current state-of-the-art theoretical models.

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arXiv2023

Fitting pseudo-S${\rm \acute{e}}$rsic(Spergel) light profiles to galaxies in interferometric data: the excellence of the $uv$-plane

Modern (sub)millimeter interferometers, such as ALMA and NOEMA, offer high angular resolution and unprecedented sensitivity. This provides the possibility to characterize the morphology of the gas and dust in distant galaxies. To assess the capabilities of current softwares in recovering morphologies and surface brightness profiles in interferometric observations, we test the performance of the Spergel model for fitting in the $uv$-plane, which has been recently implemented in the IRAM software GILDAS (uv$\_$fit). Spergel profiles provide an alternative to the Sersic profile, with the advantage of having an analytical Fourier transform, making them ideal to model visibilities in the $uv$-plane. We provide an approximate conversion between Spergel index and Sersic index, which depends on the ratio of the galaxy size to the angular resolution of the data. We show through extensive simulations that Spergel modeling in the $uv$-plane is a more reliable method for parameter estimation than modeling in the image-plane, as it returns parameters that are less affected by systematic biases and results in a higher effective signal-to-noise ratio (S/N). The better performance in the $uv$-plane is likely driven by the difficulty of accounting for correlated signal in interferometric images. Even in the $uv$-plane, the integrated source flux needs to be at least 50 times larger than the noise per beam to enable a reasonably good measurement of a Spergel index. We characterise the performance of Spergel model fitting in detail by showing that parameters biases are generally low (< 10%) and that uncertainties returned by uv$\_$fit are reliable within a factor of two. Finally, we showcase the power of Spergel fitting by re-examining two claims of extended halos around galaxies from the literature, showing that galaxies and halos can be successfully fitted simultaneously with a single Spergel model.

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arXiv2023

JWST and ALMA imaging of dust-obscured, massive substructures in a typical $z \sim 3$ star-forming disk galaxy

We present an identification of dust-attenuated star-forming galactic-disk substructures in a typical star-forming galaxy (SFG), UDF2, at $z = 2.696$. To date, substructures containing significant buildup of stellar mass and actively forming stars have yet to be found in typical (i.e., main-sequence) SFGs at $z > 2$. This is due to the strong dust attenuation common in massive galaxies at the epoch and the scarcity of high-resolution, high-sensitivity extinction-independent imaging. To search for disk substructures, we subtracted the central stellar-mass disk from the JWST/NIRCam rest-frame 1.2 $μ$m image ($0.13''$ resolution) and subtracted, in the visibility plane, the central starburst disk from ALMA rest-frame 240 $μ$m observations ($0.03''$ resolution). The residual images revealed substructures at rest-frame 1.2 $μ$m co-located with those found at rest-frame 240 $μ$m, $\simeq 2$ kpc away from the galactic center. The largest substructure contains $\simeq20$% of the total stellar mass and $\simeq5$% of the total SFR of the galaxy. While UDF2 exhibits a kinematically-ordered velocity field of molecular gas consistent with a secularly evolving disk, more sensitive observations are required to characterize the nature and the origin of this substructure (spiral arms, minor merger, or other types of disk instabilities). UDF2 resides in an overdense region ($N \geqslant 4$ massive galaxies within 70 kpc projected distance at $z=2.690-2.697$) and the substructures may be associated with interaction-induced instabilities. Importantly, a statistical sample of such substructures identified with JWST and ALMA could play a key role in bridging the gap between the bulge-forming starburst and the rest of the galaxy.

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arXiv2022

The correlation between WISE 12 $μ$m emission and molecular gas tracers on sub-kpc scales in nearby star-forming galaxies

We complement the MALATANG sample of dense gas in nearby galaxies with archival observations of $^{12}\rm CO$ and its isotopologues to determine scaling relations between Wide-field Infrared Survey Explorer (WISE) 12 $μ$m emission and molecular gas tracers at sub-kiloparsec scales. We find that 12 $μ$m luminosity is more tightly correlated with $^{12}\rm CO$ than it is with $^{13}\rm CO$ or dense gas tracers. Residuals between predicted and observed $^{12}\rm CO$ are only weakly correlated with molecular gas mass surface density ($Σ_{\rm mol}$) in regions where $Σ_{\rm mol}$ is very low ($\sim 10~{\rm M_{\odot}~pc^{-2}}$). Above this limit, the $^{12}\rm CO$ residuals show no correlations with physical conditions of molecular gas, while $^{13}\rm CO$ residuals depend on the gas optical depth and temperature. By analyzing differences from galaxy to galaxy, we confirm that the $^{12}\rm CO$-12 $μ$m relation is strong and statistically robust with respect to star forming galaxies and AGN hosts. These results suggest that WISE 12 $μ$m emission can be used to trace total molecular gas instead of dense molecular gas, likely because polycyclic aromatic hydrocarbons (PAHs, a major contributor to WISE 12 $μ$m~emission) may be well-mixed with the gas that is traced by $^{12}\rm CO$. We propose that WISE 12 $μ$m luminosity can be used to estimate molecular gas surface density for statistical analyses of the star formation process in galaxies.

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arXiv2022

The Physical Properties of Star-Forming Galaxies with Strong [O III] Lines at z=3.25

We present an analysis of physical properties of 34 [O III] emission-line galaxies (ELGs) at z=3.254$\pm$0.029 in the Extended Chandra Deep Field South (ECDFS). These ELGs are selected from deep narrow H2S(1) and broad Ks imaging of 383 arcmin$^{2}$ obtained with CFHT/WIRCam. We construct spectral energy distributions (SEDs) from U to Ks to derive the physical properties of ELGs. These [O III] ELGs are identified as starburst galaxies with strong [O III] lines of L([O III]) ~ 10$^{42.6}$ - 10$^{44.2}$ erg s$^{-1}$, and have stellar masses of M* ~ 10$^{9.0}$-10$^{10.6}$ M$_\odot$ and star formation rates of ~ 10-210 M$_\odot$ yr$^{-1}$. Our results show that 24% of our sample galaxies are dusty with Av > 1 mag and EW(OIII)$_{rest}$ ~ 70-500 $Å$, which are often missed in optically selected [O III] ELG samples. Their rest-frame UV and optical morphologies from HST/ACS and HST/WFC3 deep imaging reveal that these [O III] ELGs are mostly multiple-component systems (likely mergers) or compact. And 20% of them are nearly invisible in the rest-frame UV owing to heavy dust attenuation. Interestingly, we find that our samples reside in an overdensity consisting of two components: one southeast (SE) with an overdensity factor of $δ_{gal}$ ~ 41 over a volume of 13$^{3}$ cMpc$^{3}$ and the other northwest (NW) with $δ_{gal}$ ~ 38 over a volume of 10$^{3}$ cMpc$^{3}$. The two overdense substructures are expected to be virialized at z=0 with a total mass of ~ 1.1 x 10$^{15}$ M$_\odot$ and ~ 4.8 x 10$^{14}$ M$_\odot$, and probably merge into a Coma-like galaxy cluster.

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arXiv2021

Deep Observations of CO and Free-Free Emission in Ultraluminous Infrared QSO IRAS F07599+6508

Infrared quasi-stellar objects (IR QSOs) are a rare subpopulation selected from ultraluminous infrared galaxies (ULIRGs) and have been regarded as promising candidates of ULIRG-to-optical QSO transition objects. Here we present NOEMA observations of the CO(1-0) line and 3 mm continuum emission in an IR QSO IRAS F07599+6508 at $z=0.1486$, which has many properties in common with Mrk 231. The CO emission is found to be resolved with a major axis of $\sim$6.1 kpc that is larger than the size of $\sim$4.0 kpc derived for 3 mm continuum. We identify two faint CO features located at a projected distance of $\sim$11.4 and 19.1 kpc from the galaxy nucleus, respectively, both of which are found to have counterparts in the optical and radio bands and may have a merger origin. A systematic velocity gradient is found in the CO main component, suggesting that the bulk of molecular gas is likely rotationally supported. Based on the radio-to-millimeter spectral energy distribution and IR data, we estimate that about 30$\%$ of the flux at 3 mm arises from free-free emission and infer a free-free-derived star formation rate of 77 $M_\odot\ {\rm yr^{-1}}$, close to the IR estimate corrected for the AGN contribution. We find a high-velocity CO emission feature at the velocity range of about -1300 to -2000 km s$^{-1}$. Additional deep CO observations are needed to confirm the presence of a possible very high-velocity CO extension of the OH outflow in this IR QSO.

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arXiv2019

Resolving the Interstellar Medium in Ultraluminous Infrared QSO Hosts with ALMA

We present ALMA observations of the CO(1-0) line and 3-mm continuum emission in eight ultraluminous infrared (IR) quasi-stellar objects (QSOs) at z = 0.06-0.19. All eight IR QSO hosts are clearly resolved in their CO molecular gas emission with a median source size of 3.2 kpc, and seven out of eight sources are detected in 3-mm continuum, which is found to be more centrally concentrated with respect to molecular gas with sizes of 0.4-1.0 kpc. Our observations reveal a diversity of CO morphology and kinematics for the IR QSO systems which can be roughly classified into three categories, rotating gas disk with ordered velocity gradient, compact CO peak with disturbed velocity, and multiple CO distinct sources undergoing a merger between luminous QSO and a companion galaxy separated by a few kpc. The molecular gas in three of IR QSO hosts are found to be rotation-dominated with the ratio of the maximum rotation velocity to the local velocity dispersion of $V_{\rm rot}/σ=4-6$. Basic estimates of the dynamical masses within the CO-emitting regions give masses between $7.4\times10^9$ and $6.9\times10^{10}$ $M_\odot$. We find an increasing trend between BH mass accretion rate and star formation rate (SFR) over three orders of magnitude in far-IR luminosity/SFR, in line with the correlation between QSO bolometric luminosity and SF activity, indicative of a likely direct connection between AGN and SF activity over galaxy evolution timescales.

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arXiv2018

The MALATANG Survey: the L_gas-L_IR correlation on sub-kiloparsec scale in six nearby star-forming galaxies as traced by HCN J=4-3 and HCO^+ J=4-3

We present HCN J=4-3 and HCO^+ J=4-3 maps of six nearby star-forming galaxies, NGC 253, NGC 1068, IC 342, M82, M83, and NGC 6946, obtained with the James Clerk Maxwell Telescope as part of the MALATANG survey. All galaxies were mapped in the central 2 arcmin $\times$ 2 arcmin region at 14 arcsec (FWHM) resolution (corresponding to linear scales of ~ 0.2-1.0 kpc). The L_IR-L'_dense relation, where the dense gas is traced by the HCN J=4-3 and the HCO^+ J=4-3 emission, measured in our sample of spatially-resolved galaxies is found to follow the linear correlation established globally in galaxies within the scatter. We find that the luminosity ratio, L_IR/L'_dense, shows systematic variations with L_IR within individual spatially resolved galaxies, whereas the galaxy-integrated ratios vary little. A rising trend is also found between L_IR/L'_dense ratio and the warm-dust temperature gauged by the 70 μm/100 μm flux ratio. We find the luminosity ratios of IR/HCN(4-3) and IR/HCO^+(4-3), which can be taken as a proxy for the efficiency of star formation in the dense molecular gas (SFE_dense), appears to be nearly independent of the dense-gas fraction (f_dense) for our sample of galaxies. The SFE of the total molecular gas (SFE_mol) is found to increase substantially with f_dense when combining our data with that on local (ultra)luminous infrared galaxies and high-z quasars. The mean L'_HCN(4-3)/L'_HCO^+(4-3) line ratio measured for the six targeted galaxies is 0.9+/-0.6. No significant correlation is found for the L'_HCN(4-3)/L'_HCO^+(4-3) ratio with the SFR as traced by L_IR, nor with the warm-dust temperature, for the different populations of galaxies.

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