We present a novel approach to estimating the intensity mapping signal of any CO rotational line emitted during the Epoch of Reionization (EoR). Our approach is based on large velocity gradient (LVG) modeling, a radiative transfer modeling technique
that generates the full CO spectral line energy distribution (SLED) for a specified gas kinetic temperature, volume density, velocity gradient, molecular abundance, and column density. These parameters, which drive the physics of CO transitions and ultimately dictate the shape and amplitude of the CO SLED, can be linked to the global properties of the host galaxy, mainly the star formation rate (SFR) and the SFR surface density. By further employing an empirically derived SFR-M relation for high redshift galaxies, we can express the LVG parameters, and thus the specific intensity of any CO rotational transition, as functions of the host halo mass M and redshift z. Integrating over the range of halo masses expected to host CO-luminous galaxies, we predict a mean CO(1-0) brightness temperature ranging from ~0.6 {mu}K at z= 6 to ~0.03 {mu} at z= 10 with brightness temperature fluctuations of $Delta_{CO}^2$ ~ 0.1 and 0.005 {mu}K respectively, at k = 0.1 Mpc$^{-1}$. In this model, the CO emission signal remains strong for higher rotational levels at z = 6, with <T$_{CO}$>~ 0.3 and 0.05 {mu}K for the CO J = 6->5 and CO J = 10->9 transitions respectively. Including the effects of CO photodissociation in these molecular clouds, especially at low metallicities, results in the overall reduction in the amplitude of the CO signal, with the low- and high-J lines weakening by 2-20% and 10-45%, respectively, over the redshift range 4 < z < 10.
We report the detection of far-infrared (FIR) CO rotational emission from nearby active galactic nuclei (AGN) and starburst galaxies, as well as several merging systems and Ultra-Luminous Infrared Galaxies (ULIRGs). Using Herschel-PACS, we have detec
ted transitions in the J$_{upp}$ = 14 - 20 range ($lambda sim$ 130 - 185 $mu$m, $ u sim$ 1612 - 2300 GHz) with upper limits on (and in two cases, detections of) CO line fluxes up to J$_{upp}$ = 30. The PACS CO data obtained here provide the first well-sampled FIR extragalactic CO SLEDs for this range, and will be an essential reference for future high redshift studies. We find a large range in the overall SLED shape, even amongst galaxies of similar type, demonstrating the uncertainties in relying solely on high-J CO diagnostics to characterize the excitation source of a galaxy. Combining our data with low-J line intensities taken from the literature, we present a CO ratio-ratio diagram and discuss its potential diagnostic value in distinguishing excitation sources and physical properties of the molecular gas. The position of a galaxy on such a diagram is less a signature of its excitation mechanism, than an indicator of the presence (or absence) of warm, dense molecular gas. We then quantitatively analyze the CO emission from a subset of the detected sources with Large Velocity Gradient (LVG) radiative transfer models to fit the CO SLEDs. Using both single-component and two-component LVG models to fit the kinetic temperature, velocity gradient, number density and column density of the gas, we derive the molecular gas mass and the corresponding CO-to-H$_2$ conversion factor, $alpha_{CO}$, for each respective source. For the ULIRGs we find $alpha$ values in the canonical range 0.4 - 5 M$_odot$/(K kms$^{-1}$pc$^2$), while for the other objects, $alpha$ varies between 0.2 and 14.} Finally, we compare our best-fit LVG model ..
We simulate the effects of gravitational lensing on the source count of high redshift galaxies as projected to be observed by the Hubble Frontier Fields program and the James Webb Space Telescope (JWST) in the near future. Taking the mass density pro
file of the lensing object to be the singular isothermal sphere (SIS) or the Navarro-Frenk-White (NFW) profile, we model a lens residing at a redshift of z_L = 0.5 and explore the radial dependence of the resulting magnification bias and its variability with the velocity dispersion of the lens, the photometric sensitivity of the instrument, the redshift of the background source population, and the intrinsic maximum absolute magnitude (M_{max}) of the sources. We find that gravitational lensing enhances the number of galaxies with redshifts z >= 13 detected in the angular region theta_E/2 <= theta <= 2theta_E (where theta_E is the Einstein angle) by a factor of ~ 3 and 1.5 in the HUDF (df/d u_0 ~ 9 nJy) and medium-deep JWST surveys (df/d u_0 ~ 6 nJy). Furthermore, we find that even in cases where a negative magnification bias reduces the observed number count of background sources, the lensing effect improves the sensitivity of the count to the intrinsic faint-magnitude cut-off of the Schechter luminosity function. In a field centered on a strong lensing cluster, observations of z >= 6 and z >= 13 galaxies with JWST can be used to infer this cut-off magnitude for values as faint as M_{max} ~ -14.4 and -16.1 mag (L_{min} ~ 2.5*10^{26} and 1.2*10^{27} erg s^{-1} Hz^{-1}) respectively, within the range bracketed by existing theoretical models. Gravitational lensing may therefore offer an effective way of constraining the low-luminosity cut-off of high-redshift galaxies.
