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Lee Armus

Publications and source records attributed to Lee Armus.

At least 109 records · Page 6Linked to original sources

A controlled study of cold dust content in galaxies from $z=0-2$

At $z=1-3$, the formation of new stars is dominated by dusty galaxies whose far-IR emission indicates they contain colder dust than local galaxies of a similar luminosity. We explore the reasons for the evolving IR emission of similar galaxies over cosmic time using: 1) Local galaxies from GOALS $(L_{\rm IR}=10^{11}-10^{12}\,L_\odot)$; 2) Galaxies at $z\sim0.1-0.5$ from the 5MUSES ($L_{\rm IR}=10^{10}-10^{12}\,L_\odot$); 3) IR luminous galaxies spanning $z=0.5-3$ from GOODS and Spitzer xFLS ($L_{\rm IR}>10^{11}\,L_\odot$). All samples have Spitzer mid-IR spectra, and Herschel and ground-based submillimeter imaging covering the full IR spectral energy distribution, allowing us to robustly measure $L_{\rm IR}^{\rm\scriptscriptstyle SF}$, $T_{\rm dust}$, and $M_{\rm dust}$ for every galaxy. Despite similar infrared luminosities, $z>0.5$ dusty star forming galaxies have a factor of 5 higher dust masses and 5K colder temperatures. The increase in dust mass is linked with an increase in the gas fractions with redshift, and we do not observe a similar increase in stellar mass or star formation efficiency. $L_{160}^{\rm\scriptscriptstyle SF}/L_{70}^{\rm\scriptscriptstyle SF}$, a proxy for $T_{\rm dust}$, is strongly correlated with $L_{\rm IR}^{\rm\scriptscriptstyle SF}/M_{\rm dust}$ independently of redshift. We measure merger classification and galaxy size for a subsample, and there is no obvious correlation between these parameters and $L_{\rm IR}^{\rm \scriptscriptstyle SF}/M_{\rm dust}$ or $L_{160}^{\rm\scriptscriptstyle SF}/L_{70}^{\rm\scriptscriptstyle SF}$. In dusty star forming galaxies, the change in $L_{\rm IR}^{\rm\scriptscriptstyle SF}/M_{\rm dust}$ can fully account for the observed colder dust temperatures, suggesting that any change in the spatial extent of the interstellar medium is a second order effect.

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A Herschel Space Observatory Spectral Line Survey of Local Luminous Infrared Galaxies from 194 to 671 Microns

We describe a Herschel Space Observatory 194-671 micron spectroscopic survey of a sample of 121 local luminous infrared galaxies and report the fluxes of the CO $J$ to $J$-1 rotational transitions for $4 \leqslant J \leqslant 13$, the [NII] 205 um line, the [CI] lines at 609 and 370 um, as well as additional and usually fainter lines. The CO spectral line energy distributions (SLEDs) presented here are consistent with our earlier work, which was based on a smaller sample, that calls for two distinct molecular gas components in general: (i) a cold component, which emits CO lines primarily at $J \lesssim 4$ and likely represents the same gas phase traced by CO (1-0), and (ii) a warm component, which dominates over the mid-$J$ regime ($4 < J < 10$) and is intimately related to current star formation. We present evidence that the CO line emission associated with an active galactic nucleus is significant only at $J > 10$. The flux ratios of the two [CI] lines imply modest excitation temperatures of 15 to 30 K; the [CI] 370 um line scales more linearly in flux with CO (4-3) than with CO (7-6). These findings suggest that the [CI] emission is predominately associated with the gas component defined in (i) above. Our analysis of the stacked spectra in different far-infrared (FIR) color bins reveals an evolution of the SLED of the rotational transitions of water vapor as a function of the FIR color in a direction consistent with infrared photon pumping.

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IROCKS: Spatially resolved kinematics of z~1 star forming galaxies

We present results from IROCKS (Intermediate Redshift OSIRIS Chemo-Kinematic Survey) for sixteen z~1 and one z~1.4 star-forming galaxies. All galaxies were observed with OSIRIS with the laser guide star adaptive optics system at Keck Observatory. We use rest-frame nebular Ha emission lines to trace morphologies and kinematics of ionized gas in star-forming galaxies on sub-kiloparsec physical scales. We observe elevated velocity dispersions (sigma > 50 km/s) seen in z > 1.5 galaxies persist at z~1 in the integrated galaxies. Using an inclined disk model and the ratio of v/sigma, we find that 1/3 of the z~1 sample are disk candidates while the other 2/3 of the sample are dominated by merger-like and irregular sources. We find that including extra attenuation towards HII regions derived from stellar population synthesis modeling brings star formation rates (SFR) using Ha and stellar population fit into a better agreement. We explore properties of compact Ha sub-component, or "clump," at z~1 and find that they follow a similar size-luminosity relation as local HII regions but are scaled-up by an order of magnitude with higher luminosities and sizes. Comparing the z~1 clumps to other high-redshift clump studies, we determine that the clump SFR surface density evolves as a function of redshift. This may imply clump formation is directly related to the gas fraction in these systems and support disk fragmentation as their formation mechanism since gas fraction scales with redshift.

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ALMA Resolves the Nuclear Disks of Arp 220

We present 90 mas (37 pc) resolution ALMA imaging of Arp 220 in the CO (1-0) line and continuum at $λ= 2.6$ mm. The internal gas distribution and kinematics of both galactic nuclei are well-resolved for the first time. In the West nucleus, the major gas and dust emission extends out to 0.2\arcsec radius (74 pc); the central resolution element shows a strong peak in the dust emission but a factor 3 dip in the CO line emission. In this nucleus, the dust is apparently optically thick ($τ_{\rm 2.6mm} \sim1$) at $λ= 2.6$ mm with a dust brightness temperature $\sim147$ K. The column of ISM at this nucleus is $\rm N_{H2} \geq 2\times10^{26}$ cm$^{-2}$, corresponding to $\sim$900 gr cm$^{-2}$. The East nucleus is more elongated with radial extent 0.3\arcsec or $\sim111$ pc. The derived kinematics of the nuclear disks provide a good fit to the line profiles, yielding the emissivity distributions, the rotation curves and velocity dispersions. In the West nucleus, there is evidence of a central Keplerian component requiring a central mass of $8\times10^8$ \msun. The intrinsic widths of the emission lines are $Δ\rm v (FWHM)$ = 250 (West) and 120 (East) \kms. Given the very short dissipation timescales for turbulence ($\lesssim10^5$ yrs), we suggest that the line widths may be due to semi-coherent motions within the nuclear disks. The symmetry of the nuclear disk structures is impressive -- implying the merger timescale is significantly longer than the rotation period of the disks.

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SPIRITS: Uncovering Unusual Infrared Transients With Spitzer

We present an ongoing, systematic search for extragalactic infrared transients, dubbed SPIRITS --- SPitzer InfraRed Intensive Transients Survey. In the first year, using Spitzer/IRAC, we searched 190 nearby galaxies with cadence baselines of one month and six months. We discovered over 1958 variables and 43 transients. Here, we describe the survey design and highlight 14 unusual infrared transients with no optical counterparts to deep limits, which we refer to as SPRITEs (eSPecially Red Intermediate Luminosity Transient Events). SPRITEs are in the infrared luminosity gap between novae and supernovae, with [4.5] absolute magnitudes between -11 and -14 (Vega-mag) and [3.6]-[4.5] colors between 0.3 mag and 1.6 mag. The photometric evolution of SPRITEs is diverse, ranging from < 0.1 mag/yr to > 7 mag/yr. SPRITEs occur in star-forming galaxies. We present an in-depth study of one of them, SPIRITS 14ajc in Messier 83, which shows shock-excited molecular hydrogen emission. This shock may have been triggered by the dynamic decay of a non-hierarchical system of massive stars that led to either the formation of a binary or a proto-stellar merger.

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The Local [CII] 158 um Emission Line Luminosity Function

We present, for the first time, the local [CII] 158 um emission line luminosity function measured using a sample of more than 500 galaxies from the Revised Bright Galaxy Sample (RBGS). [CII] luminosities are measured from the Herschel PACS observations of the Luminous Infrared Galaxies in the Great Observatories All-sky LIRG Survey (GOALS) and estimated for the rest of the sample based on the far-IR luminosity and color. The sample covers 91.3% of the sky and is complete at S_60 um > 5.24 Jy. We calculated the completeness as a function of [CII] line luminosity and distance, based on the far-IR color and flux densities. The [CII] luminosity function is constrained in the range ~10^(7-9) (Lo) from both the 1/V_max and a maximum likelihood methods. The shape of our derived [CII] emission line luminosity function agrees well with the IR luminosity function. For the CO(1-0) and [CII] luminosity functions to agree, we propose a varying ratio of [CII]/CO(1-0) as a function of CO luminosity, with larger ratios for fainter CO luminosities. Limited [CII] high redshift observations as well as estimates based on the IR and UV luminosity functions are suggestive of an evolution in the [CII] luminosity function similar to the evolution trend of the cosmic star formation rate density. Deep surveys using ALMA with full capability will be able to confirm this prediction.

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The Spatially Resolved [CII] Cooling Line Deficit in Galaxies

We present [CII] 158um measurements from over 15,000 resolved regions within 54 nearby galaxies of the KINGFISH program to investigate the so-called [CII] "line cooling deficit" long known to occur in galaxies with different luminosities. The [CII]/TIR ratio ranges from above 1% to below 0.1% in the sample, with a mean value of 0.48+-0.21%. We find that the surface density of 24um emission dominates this trend, with [CII]/TIR dropping as nuInu{24um} increases. Deviations from this overall decline are correlated with changes in the gas phase metal abundance, with higher metallicity associated with deeper deficits at a fixed surface brightness. We supplement the local sample with resolved [CII] measurements from nearby luminous infrared galaxies and high redshift sources from z=1.8-6.4, and find that star formation rate density drives a continuous trend of deepening [CII] deficit across six orders of magnitude in SFRD. The tightness of this correlation suggests that an approximate star formation rate density can be estimated directly from global measurements of [CII]/TIR, and a relation is provided to do so. Several low-luminosity AGN hosts in the sample show additional and significant central suppression of [CII]/TIR, but these deficit enhancements occur not in those AGN with the highest X-ray luminosities, but instead those with the highest central starlight intensities. Taken together, these results demonstrate that the [CII] cooling line deficit in galaxies likely arises from local physical phenomena in interstellar gas.

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The InfraRed Imaging Spectrograph (IRIS) for TMT: latest science cases and simulations

The Thirty Meter Telescope (TMT) first light instrument IRIS (Infrared Imaging Spectrograph) will complete its preliminary design phase in 2016. The IRIS instrument design includes a near-infrared (0.85 - 2.4 micron) integral field spectrograph (IFS) and imager that are able to conduct simultaneous diffraction-limited observations behind the advanced adaptive optics system NFIRAOS. The IRIS science cases have continued to be developed and new science studies have been investigated to aid in technical performance and design requirements. In this development phase, the IRIS science team has paid particular attention to the selection of filters, gratings, sensitivities of the entire system, and science cases that will benefit from the parallel mode of the IFS and imaging camera. We present new science cases for IRIS using the latest end-to-end data simulator on the following topics: Solar System bodies, the Galactic center, active galactic nuclei (AGN), and distant gravitationally-lensed galaxies. We then briefly discuss the necessity of an advanced data management system and data reduction pipeline.

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Providing stringent star formation rate limits of z$\sim$2 QSO host galaxies at high angular resolution

We present integral field spectrograph (IFS) with laser guide star adaptive optics (LGS-AO) observations of z=2 quasi-stellar objects (QSOs) designed to resolve extended nebular line emission from the host galaxy. Our data was obtained with W. M. Keck and Gemini-North Observatories using OSIRIS and NIFS coupled with the LGS-AO systems. We have conducted a pilot survey of five QSOs, three observed with NIFS+AO and two observed with OSIRIS+AO at an average redshift of z=2.15. We demonstrate that the combination of AO and IFS provides the necessary spatial and spectral resolutions required to separate QSO emission from its host. We present our technique for generating a PSF from the broad-line region of the QSO and performing PSF subtraction of the QSO emission to detect the host galaxy. We detect H$α$ and [NII] for two sources, SDSS J1029+6510 and SDSS J0925+06 that have both star formation and extended narrow-line emission. Assuming that the majority of narrow-line H$α$ is from star formation, we infer a star formation rate for SDSS J1029+6510 of 78.4 M$_\odot$yr$^{-1}$ originating from a compact region that is kinematically offset by 290 - 350 km/s. For SDSS J0925+06 we infer a star formation rate of 29 M$_\odot$yr$^{-1}$ distributed over three clumps that are spatially offset by $\sim$ 7 kpc. The null detections on three of the QSOs are used to infer surface brightness limits and we find that at 1.4 kpc distance from the QSO that the un-reddened star formation limit is $<$ 0.3 M$_\odot$yr$^{-1}$kpc$^{-2}$. If we assume a typical extinction values for z=2 type-1 QSOs, the dereddened star formation rate for our null detections would be $<$ 0.6 M$_\odot$yr$^{-1}$kpc$^{-2}$. These IFS observations indicate that if star formation is present in the host it would have to occur diffusely with significant extinction and not in compact, clumpy regions.

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ALMA Imaging of the CO(6-5) Line Emission in NGC 7130

In this paper, we report our high-resolution ($0^{\prime\prime}.20\times0^{\prime\prime}.14$ or $\sim$$70\times49$ pc) observations of the CO(6-5) line emission, which probes warm and dense molecular gas, and the 434 $μ$m dust continuum in the nuclear region of NGC 7130, obtained with the Atacama Large Millimeter Array (ALMA). The CO line and dust continuum fluxes detected in our ALMA observations are $1230\pm74$ Jy km s$^{-1}$ and $814\pm52$ mJy, respectively, which account for 100% and 51% of their total respective fluxes. We find that the CO(6-5) and dust emissions are generally spatially correlated, but their brightest peaks show an offset of $\sim$70 pc, suggesting that the gas and dust emissions may start decoupling at this physical scale. The brightest peak of the CO(6-5) emission does not spatially correspond to the radio continuum peak, which is likely dominated by an Active Galactic Nucleus (AGN). This, together with our additional quantitative analysis, suggests that the heating contribution of the AGN to the CO(6-5) emission in NGC 7130 is negligible. The CO(6-5) and the extinction-corrected Pa-$α$ maps display striking differences, suggestive of either a breakdown of the correlation between warm dense gas and star formation at linear scales of $<$100 pc or a large uncertainty in our extinction correction to the observed Pa-$α$ image. Over a larger scale of $\sim$2.1\,kpc, the double-lobed structure found in the CO(6-5) emission agrees well with the dust lanes in the optical/near-infrared images.

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Spatially resolved dust emission of extremely metal poor galaxies

We present infrared (IR) spectral energy distributions (SEDs) of individual star-forming regions in four extremely metal poor (EMP) galaxies with metallicity Z around Zsun/10 as observed by the Herschel Space Observatory. With the good wavelength coverage of the SED, it is found that these EMP star-forming regions show distinct SED shapes as compared to those of grand design Spirals and higher metallicity dwarfs: they have on average much higher f70um/f160um ratios at a given f160um/f250um ratio; single modified black-body (MBB) fittings to the SED at λ>= 100 um still reveal higher dust temperatures and lower emissivity indices compared to that of Spirals, while two MBB fittings to the full SED with a fixed emissivity index (beta = 2) show that even at 100 um about half of the emission comes from warm (50 K) dust, in contrast to the cold (~20 K) dust component. Our spatially resolved images further reveal that the far-IR colors including f70um/f160um, f160um/f250um and f250um/f350um are all related to the surface densities of young stars as traced by far-UV, 24 um and SFRs, but not to the stellar mass surface densities. This suggests that the dust emitting at wavelengths from 70 um to 350 um is primarily heated by radiation from young stars.

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Next Generation Very Large Array Memo No. 7 Science Working Group 2: "Galaxy Ecosystems": The Matter Cycle in and Around Galaxies

This white paper discusses how a "next-generation" Very Large Array (ngVLA) operating in the frequency range 1-116 GHz could be a groundbreaking tool to study the detailed astrophysics of the "matter cycle" in the Milky Way and other galaxies. If optimized for high brightness sensitivity, the ngVLA would bring detailed microwave spectroscopy and modeling of the full radio spectral energy distribution into regular use as survey tools at resolutions of 0.1- 1 arcseconds. This wavelength range includes powerful diagnostics of density, excitation, and chemistry in the cold ISM, as well as multiple tracers of the rate of recent star formation, the magnetic field, shocks, and properties of the ionized ISM. We highlight design considerations that would make this facility revolutionary in this area, the foremost of which is a large amount of collecting area on ~km-length baselines. We also emphasize the strong case for harnessing the large proposed collecting area of the ngVLA for very long baseline applications as part of the core design. This would allow measurements of the three dimensional space motions of galaxies to beyond the Local Group and mapping of the Milky Way out to the far side of the disk. Finally, we discuss the gains from the proposed combination of very high resolution and sensitivity to thermal emission, which include observing the feeding of black holes and resolving forming protoclusters.

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The role of star-formation and AGN in dust heating of z = 0.3-2.8 galaxies - I. Evolution with redshift and luminosity

We characterize infrared spectral energy distributions of 343 (Ultra) Luminous Infrared Galaxies from $z=0.3-2.8$. We diagnose the presence of an AGN by decomposing individual Spitzer mid-IR spectroscopy into emission from star-formation and an AGN-powered continuum; we classify sources as star-forming galaxies (SFGs), AGN, or composites. Composites comprise 30% of our sample and are prevalent at faint and bright $S_{24}$, making them an important source of IR AGN emission. We combine spectroscopy with multiwavelength photometry, including Herschel imaging, to create three libraries of publicly available templates (2-1000 $μ$m). We fit the far-IR emission using a two temperature modified blackbody to measure cold and warm dust temperatures ($T_c$ and $T_w$). We find that $T_c$ does not depend on mid-IR classification, while $T_w$ shows a notable increase as the AGN grows more luminous. We measure a quadratic relationship between mid-IR AGN emission and total AGN contribution to $L_{\rm IR}$. AGN, composites, and SFGs separate in $S_8/S_{3.6}$ and $S_{250}/S_{24}$, providing a useful diagnostic for estimating relative amounts of these sources. We estimate that >40% of IR selected samples host an AGN, even at faint selection thresholds ($S_{24}$>100 $μ$Jy). Our decomposition technique and color diagnostics are relevant given upcoming observations with the James Webb Space Telescope.

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Following Black Hole Scaling Relations Through Gas-Rich Mergers

We present black hole mass measurements from kinematic modeling of high-spatial resolution integral field spectroscopy of the inner regions of 9 nearby (ultra-)luminous infrared galaxies in a variety of merger stages. These observations were taken with OSIRIS and laser guide star adaptive optics on the Keck I and Keck II telescopes, and reveal gas and stellar kinematics inside the spheres of influence of these supermassive black holes. We find that this sample of black holes are overmassive ($\sim10^{7-9}$ M$_{Sun}$) compared to the expected values based on black hole scaling relations, and suggest that the major epoch of black hole growth occurs in early stages of a merger, as opposed to during a final episode of quasar-mode feedback. The black hole masses presented are the dynamical masses enclosed in $\sim$25pc, and could include gas which is gravitationally bound to the black hole but has not yet lost sufficient angular momentum to be accreted. If present, this gas could in principle eventually fuel AGN feedback or be itself blown out from the system.

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The Weak Carbon Monoxide Emission In An Extremely Metal Poor Galaxy, Sextans A

Carbon monoxide (CO) is one of the primary coolants of gas and an easily accessible tracer of molecular gas in spiral galaxies but it is unclear if CO plays a similar role in metal poor dwarfs. We carried out a deep observation with IRAM 30 m to search for CO emission by targeting the brightest far-IR peak in a nearby extremely metal poor galaxy, Sextans A, with 7% Solar metallicity. A weak CO J=1-0 emission is seen, which is already faint enough to place a strong constraint on the conversion factor (a_CO) from the CO luminosity to the molecular gas mass that is derived from the spatially resolved dust mass map. The a_CO is at least seven hundred times the Milky Way value. This indicates that CO emission is exceedingly weak in extremely metal poor galaxies, challenging its role as a coolant in these galaxies.

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Measuring Star-formation Rate and Far-Infrared Color in High-redshift Galaxies Using the CO (7-6) and [NII] 205 micron Lines

To better characterize the global star formation (SF) activity in a galaxy, one needs to know not only the star formation rate (SFR) but also the rest-frame, far-infrared (FIR) color (e.g., the 60-to-100 $μ$m color, $C(60/100)$] of the dust emission. The latter probes the average intensity of the dust heating radiation field and scales statistically with the effective SFR surface density in star-forming galaxies including (ultra-)luminous infrared galaxies [(U)LIRGs]. To this end, we exploit here a new spectroscopic approach involving only two emission lines: CO\,(7$-$6) at 372 $μ$m and [NII] at 205 $μ$m. For local (U)LIRGs, the ratios of the CO (7$-$6) luminosity ($L_{\rm CO\,(7-6)}$) to the total infrared luminosity ($L_{\rm IR}$; 8$-$1000 $μ$m) are fairly tightly distributed (to within $\sim$0.12 dex) and show little dependence on $C(60/100)$. This makes $L_{\rm CO\,(7-6)}$ a good SFR tracer, which is less contaminated by active galactic nuclei (AGN) than $L_{\rm IR}$ and may also be much less sensitive to metallicity than $L_{\rm CO\,(1-0)}$. Furthermore, the logarithmic [NII] 205 $μ$m to CO (7$-$6) luminosity ratio is fairly steeply (at a slope of $\sim$$-1.4$) correlated with $C(60/100)$, with a modest scatter ($\sim$0.23 dex). This makes it a useful estimator on $C(60/100)$ with an implied uncertainty of $\sim$0.15 [or $\lesssim$4 K in the dust temperature ($T_{\rm dust}$) in the case of a graybody emission with $T_{\rm dust} \gtrsim 30$ K and a dust emissivity index $β\ge 1$]. Our locally calibrated SFR and $C(60/100)$ estimators are shown to be consistent with the published data of (U)LIRGs of $z$ up to $\sim$6.5.

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Shocked Gas in IRAS F17207-0014: ISM Collisions and Outflows

We combine optical and near-infrared AO-assisted integral field observations of the merging ULIRG IRAS F17207-0014 from the Wide-Field Spectrograph (WiFeS) and Keck/OSIRIS. The optical emission line ratios [N II]/H$α$, [S II]/H$α$, and [O I]/H$α$ reveal a mixing sequence of shocks present throughout the galaxy, with the strongest contributions coming from large radii (up to 100% at $\sim$5 kpc in some directions), suggesting galactic-scale winds. The near-infrared observations, which have approximately 30 times higher spatial resolution, show that two sorts of shocks are present in the vicinity of the merging nuclei: low-level shocks distributed throughout our field-of-view evidenced by an H$_{2}$/Br$γ$ line ratio of $\sim$0.6-4, and strong collimated shocks with a high H$_{2}$/Br$γ$ line ratio of $\sim$4-8, extending south from the two nuclear disks approximately 400 pc ($\sim$0.5 arcsec). Our data suggest that the diffuse shocks are caused by the collision of the interstellar media associated with the two progenitor galaxies and the strong shocks trace the base of a collimated outflow coming from the nucleus of one of the two disks.

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Early Science with the Large Millimeter Telescope: Exploring the Effect of AGN Activity on the Relationships Between Molecular Gas, Dust, and Star Formation

The molecular gas, H$_2$, that fuels star formation in galaxies is difficult to observe directly. As such, the ratio of $L_{\rm IR}$ to $L^\prime_{\rm CO}$ is an observational estimation of the star formation rate compared with the amount of molecular gas available to form stars, which is related to the star formation efficiency and the inverse of the gas consumption timescale. We test what effect an IR luminous AGN has on the ratio $L_{\rm IR}/L^\prime_{\rm CO}$ in a sample of 24 intermediate redshift galaxies from the 5 mJy Unbiased Spitzer Extragalactic Survey (5MUSES). We obtain new CO(1-0) observations with the Redshift Search Receiver on the Large Millimeter Telescope. We diagnose the presence and strength of an AGN using Spitzer IRS spectroscopy. We find that removing the AGN contribution to $L_{\rm IR}^{\rm tot}$ results in a mean $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$ for our entire sample consistent with the mean $L_{\rm IR}/L^\prime_{\rm CO}$ derived for a large sample of star forming galaxies from $z\sim0-3$. We also include in our comparison the relative amount of polycyclic aromatic hydrocarbon emission for our sample and a literature sample of local and high redshift Ultra Luminous Infrared Galaxies and find a consistent trend between $L_{6.2}/L_{\rm IR}^{\rm SF}$ and $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$, such that small dust grain emission decreases with increasing $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$ for both local and high redshift dusty galaxies.

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