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We present new deep ALMA and HST/WFC3 observations of MASOSA and VR7, two luminous Ly$\alpha$ emitters (LAEs) at $z=6.5$, for which the UV continuum level differ by a factor four. No IR dust continuum emission is detected in either, indicating little amounts of obscured star formation and/or high dust temperatures. MASOSA, with a UV luminosity M$_{1500}=-20.9$, compact size and very high Ly$\alpha$ EW$_{0}\approx145$ A, is undetected in [CII] to a limit of L$_{\rm [CII]}, Comment: Main text 19 pages, 16 figures. Appendix tables available in digital format on request. Accepted for publication by ApJ. v3: updated typo in appendix table

A tight relation between the [CII]158$\mu$m line luminosity and star formation rate is measured in local galaxies. At high redshift ($z>5$), though, a much larger scatter is observed, with a considerable (15-20\%) fraction of the outliers being [CII]-deficient. Moreover, the [CII] surface brightness ($\Sigma_{\rm CII}$) of these sources is systematically lower than expected from the local relation. To clarify the origin of such [CII]-deficiency we have developed an analytical model that fits local [CII] data, and has been validated against radiative transfer simulations performed with CLOUDY. The model predicts an overall increase of $\Sigma_{\rm CII}$ with the surface star formation rate ($\Sigma_*$). However, for $\Sigma_* > 1 M_\odot~{\rm yr}^{-1}~{\rm kpc}^{-2}$, $\Sigma_{\rm CII}$ saturates. We conclude that underluminous [CII] systems can result from a combination of three factors: (a) large upward deviations from the Kennicutt-Schmidt relation ($\kappa_s \gg 1$), parameterized by the "burstiness" parameter $\kappa_s$; (b) low metallicity; (c) low gas density, at least for the most extreme sources (e.g. CR7). Observations of [CII] emission alone cannot break the degeneracy among the above three parameters; this requires additional information coming from other emission lines (e.g. [OIII]88$\mu$m, CIII]1909A, CO lines). Simple formulae are given to interpret available data for low and high-$z$ galaxies., Comment: Accepted for publication in MNRAS. 12 pages, 6 Figures. Comments welcome

We study the formation and evolution of a sample of Lyman Break Galaxies in the Epoch of Reionization by using high-resolution ($\sim 10 \,{\rm pc}$), cosmological zoom-in simulations part of the SERRA suite. In SERRA, we follow the interstellar medium (ISM) thermo-chemical non-equilibrium evolution, and perform on-the-fly radiative transfer of the interstellar radiation field (ISRF). The simulation outputs are post-processed to compute the emission of far infrared lines ([CII], [NII], and [OIII]). At $z=8$, the most massive galaxy, `Freesia', has an age $t_\star \simeq 409\,{\rm Myr}$, stellar mass $M_{\star} \simeq 4.2\times 10^9 {\rm M}_{\odot}$, and a star formation rate ${\rm SFR} \simeq 11.5\,{\rm M}_{\odot}{\rm yr}^{-1}$, due to a recent burst. Freesia has two stellar components (A and B) separated by $\simeq 2.5\, {\rm kpc}$; other 11 galaxies are found within $56.9 \pm 21.6 \, {\rm kpc}$. The mean ISRF in the Habing band is $G = 7.9\, G_0$ and is spatially uniform; in contrast, the ionisation parameter is $U = 2^{+20}_{-2} \times 10^{-3}$, and has a patchy distribution peaked at the location of star-forming sites. The resulting ionising escape fraction from Freesia is $f_{\rm esc}\simeq 2\%$. While [CII] emission is extended (radius 1.54 kpc), [OIII] is concentrated in Freesia-A (0.85 kpc), where the ratio $\Sigma_{\rm [OIII]}/\Sigma_{\rm [CII]} \simeq 10$. As many high-$z$ galaxies, Freesia lies below the local [CII]-SFR relation. We show that this is the general consequence of a starburst phase (pushing the galaxy above the Kennicutt-Schmidt relation) which disrupts/photodissociates the emitting molecular clouds around star-forming sites. Metallicity has a sub-dominant impact on the amplitude of [CII]-SFR deviations., Comment: 22 pages, 14 figures, accepted by MNRAS

The intrinsic strength of the Ly$\alpha$ line in young, star-forming systems makes it a special tool for studying high-redshift galaxies. However, interpreting observations remains challenging due to the complex radiative transfer involved. Here, we combine state-of-the-art hydrodynamical simulations of 'Althaea', a prototypical Lyman Break Galaxy (LBG, stellar mass $M_{\star}$$\simeq$ $10^{10}{\rm M}_{\odot})$ at $z=7.2$, with detailed radiative transfer computations of dust/continuum, [CII] 158 $\mu$m, and Ly$\alpha$ to clarify the relation between the galaxy properties and its Ly$\alpha$ emission. Althaea exhibits low ($f_\alpha< 1\%$) Ly$\alpha$ escape fractions and Equivalent Widths, EW $\lesssim 6$ Angstrom for the simulated lines of sight, with a large scatter. The correlation between escape fraction and inclination is weak, as a result of the rather chaotic structure of high-redshift galaxies. Low $f_\alpha$ values persist even if we artificially remove neutral gas around star forming regions to mimick the presence of HII regions. The high attenuation is primarily caused by dust clumps co-located with young stellar clusters. We can turn Althaea into a Lyman Alpha Emitter (LAE) only if we artificially remove dust from the clumps, yielding EWs up to $22$ Angstrom. Our study suggests that the LBG-LAE duty-cycle required by recent clustering measurements poses the challenging problem of a dynamically changing dust attenuation. Finally, we find an anti-correlation between the magnitude of Ly$\alpha$-[CII] line velocity shift and Ly$\alpha$ luminosity., Comment: published in MNRAS

We study the kinematical properties of galaxies in the Epoch of Reionization via the [CII] 158$\mu$m line emission. The line profile provides information on the kinematics as well as structural properties such as the presence of a disk and satellites. To understand how these properties are encoded in the line profile, first we develop analytical models from which we identify disk inclination and gas turbulent motions as the key parameters affecting the line profile. To gain further insights, we use "Althaea", a highly-resolved ($30\, \rm pc$) simulated prototypical Lyman Break Galaxy, in the redshift range $z = 6-7$, when the galaxy is in a very active assembling phase. Based on morphology, we select three main dynamical stages: I) Merger , II) Spiral Disk, and III) Disturbed Disk. We identify spectral signatures of merger events, spiral arms, and extra-planar flows in I), II), and III), respectively. We derive a generalised dynamical mass vs. [CII]-line FWHM relation. If precise information on the galaxy inclination is (not) available, the returned mass estimate is accurate within a factor $2$ ($4$). A Tully-Fisher relation is found for the observed high-$z$ galaxies, i.e. $L_{\rm[CII]}\propto (FWHM)^{1.80\pm 0.35}$ for which we provide a simple, physically-based interpretation. Finally, we perform mock ALMA simulations to check the detectability of [CII]. When seen face-on, Althaea is always detected at $> 5\sigma$; in the edge-on case it remains undetected because the larger intrinsic FWHM pushes the line peak flux below detection limit. This suggests that some of the reported non-detections might be due to inclination effects., Comment: 14 pages, 12 figures, accepted for publication in MNRAS

We present new estimates of AGN accretion and star-formation luminosity in galaxies obtained for the local 12-$\mu$m sample of Seyfert galaxies (12MGS), by performing a detailed broad-band spectral energy distribution (SED) decomposition including the emission of stars, dust heated by star formation and a possible AGN dusty torus. Thanks to the availability of data from the X-rays to the sub-millimetre, we constrain and test the contribution of the stellar, AGN and star-formation components to the SEDs. The availability of Spitzer-IRS low resolution mid-infrared (mid-IR) spectra is crucial to constrain the dusty torus component at its peak wavelengths. The results of SED-fitting are also tested against the available information in other bands: the reconstructed AGN bolometric luminosity is compared to those derived from X-rays and from the high excitation IR lines tracing AGN activity like [Ne V] and [O IV]. The IR luminosity due to star-formation (SF) and the intrinsic AGN bolometric luminosity are shown to be strongly related to the IR line luminosity. Variations of these relations with different AGN fractions are investigated, showing that the relation dispersions are mainly due to different AGN relative contribution within the galaxy. Extrapolating these local relations between line and SF or AGN luminosities to higher redshifts, by means of recent Herschel galaxy evolution results, we then obtain mid- and far-IR line luminosity functions useful to estimate how many star-forming galaxies and AGN we expect to detect in the different lines at different redshifts and luminosities with future IR facilities (e.g., JWST, SPICA)., Comment: 27 pages, 13 figures, 7 tables. MNRAS in press

We study the CO line luminosity ($L_{\rm CO}$), the shape of the CO Spectral Line Energy Distribution (SLED), and the value of the CO-to-$\rm H_2$ conversion factor in galaxies in the Epoch of Reionization (EoR). To this aim, we construct a model that simultaneously takes into account the radiative transfer and the clumpy structure of giant molecular clouds (GMCs) where the CO lines are excited. We then use it to post-process state-of-the-art zoomed, high resolution ($30\, \rm{pc}$), cosmological simulation of a main-sequence ($M_{*}\approx10^{10}\, \rm{M_{\odot}}$, $SFR\approx 100\,\rm{M_{\odot}\, yr^{-1}}$) galaxy, "Alth{\ae}a", at $z\approx6$. We find that the CO emission traces the inner molecular disk ($r\approx 0.5 \,\rm{kpc}$) of Alth{\ae}a with the peak of the CO surface brightness co-located with that of the [CII] 158$\rm \mu m$ emission. Its $L_{\rm CO(1-0)}=10^{4.85}\, \rm{L_{\odot}}$ is comparable to that observed in local galaxies with similar stellar mass. The high ($\Sigma_{gas} \approx 220\, \rm M_{\odot}\, pc^{-2}$) gas surface density in Alth{\ae}a, its large Mach number (\mach$\approx 30$), and the warm kinetic temperature ($T_{k}\approx 45 \, \rm K$) of GMCs yield a CO SLED peaked at the CO(7-6) transition, i.e. at relatively high-$J$, and a CO-to-$\rm H_2$ conversion factor $\alpha_{\rm CO}\approx 1.5 \, \rm M_{\odot} \rm (K\, km\, s^{-1}\, pc^2)^{-1} $ lower than that of the Milky Way. The ALMA observing time required to detect (resolve) at 5$\sigma$ the CO(7-6) line from galaxies similar to Alth{\ae}a is $\approx13$ h ($\approx 38$ h)., Comment: 16 pages, 14 figures, accepted for publication in MNRAS

We present a detailed analysis of the X-ray and molecular gas emission in the nearby galaxy NGC 34, to constrain the properties of molecular gas, and assess whether, and to what extent, the radiation produced by the accretion onto the central black hole affects the CO line emission. We analyse the CO Spectral Line Energy Distribution (SLED) as resulting mainly from Herschel and ALMA data, along with X-ray data from NuSTAR and XMM-Newton. The X-ray data analysis suggests the presence of a heavily obscured AGN with an intrinsic luminosity of L$_{\rm{1-100\,keV}} \simeq 4.0\times10^{42}$ erg s$^{-1}$. ALMA high resolution data ($\theta \simeq 0.2''$) allows us to scan the nuclear region down to a spatial scale of $\approx 100$ pc for the CO(6-5) transition. We model the observed SLED using Photo-Dissociation Region (PDR), X-ray-Dominated Region (XDR), and shock models, finding that a combination of a PDR and an XDR provides the best fit to the observations. The PDR component, characterized by gas density ${\rm log}(n/{\rm cm^{-3}})=2.5$ and temperature $T=30$ K, reproduces the low-J CO line luminosities. The XDR is instead characterised by a denser and warmer gas (${\rm log}(n/{\rm cm^{-3}})=4.5$, $T =65$ K), and is necessary to fit the high-J transitions. The addition of a third component to account for the presence of shocks has been also tested but does not improve the fit of the CO SLED. We conclude that the AGN contribution is significant in heating the molecular gas in NGC 34., Comment: Accepted for publication in MNRAS. 10 pages, 6 figures

We study the photoevaporation of molecular clumps exposed to a UV radiation field including hydrogen-ionizing photons ($h��> 13.6$ eV) produced by massive stars or quasars. We follow the propagation and collision of shock waves inside clumps and take into account self-shielding effects, determining the evolution of clump size and density with time. The structure of the ionization-photodissociation region (iPDR) is obtained for different initial clump masses ($M=0.01 - 10^4\,{\rm M}_\odot$) and impinging fluxes ($G_0=10^2 - 10^5$ in units of the Habing flux). The cases of molecular clumps engulfed in the HII region of an OB star and clumps carried within quasar outflows are treated separately. We find that the clump undergoes in both cases an initial shock-contraction phase and a following expansion phase, which lets the radiation penetrate in until the clump is completely evaporated. Typical evaporation time-scales are $\simeq 0.01$ Myr in the stellar case and 0.1 Myr in the quasar case, where the clump mass is 0.1 ${\rm M}_\odot$ and $10^3\,{\rm M}_\odot$ respectively. We find that clump lifetimes in quasar outflows are compatible with their observed extension, suggesting that photoevaporation is the main mechanism regulating the size of molecular outflows., 13 pages, 12 figures, accepted for publication in MNRAS

We propose a new methodology aimed at finding star-forming galaxies in the phase which immediately follows the star-formation (SF) quenching, based on the use of high- to low-ionization emission line ratios. These ratios rapidly disappear after the SF halt, due to the softening of the UV ionizing radiation. We focus on [O III] $\lambda$5007/H$\alpha$ and [Ne III] $\lambda$3869/[O II] $\lambda$3727, studying them with simulations obtained with the CLOUDY photoionization code. If a sharp quenching is assumed, we find that the two ratios are very sensitive tracers as they drop by a factor $\sim$ 10 within $\sim$ 10 Myr from the interruption of the SF; instead, if a smoother and slower SF decline is assumed (i.e. an exponentially declining star-formation history with $e$-folding time $\tau=$ 200 Myr), they decrease by a factor $\sim$ 2 within $\sim$ 80 Myr. We mitigate the ionization -- metallicity degeneracy affecting our methodology using pairs of emission line ratios separately related to metallicity and ionization, adopting the [N II] $\lambda$6584/[O II] $\lambda$3727 ratio as metallicity diagnostic. Using a Sloan Digital Sky Survey galaxy sample, we identify 10 examples among the most extreme quenching candidates within the [O III] $\lambda$5007/H$\alpha$ vs. [N II] $\lambda$6584/[O II] $\lambda$3727 plane, characterized by low [O III] $\lambda$5007/H$\alpha$, faint [Ne III] $\lambda$3869, and by blue dust-corrected spectra and $(u-r)$ colours, as expected if the SF quenching has occurred in the very recent past. Our results also suggest that the observed fractions of quenching candidates can be used to constrain the quenching mechanism at work and its time-scales., Comment: Accepted for publication in MNRAS; 19 pages, 21 figures, 1 table

We present spectroscopic follow-up observations of CR7 with ALMA, targeted at constraining the infrared (IR) continuum and [CII]$_{158 \mu \rm m}$ line-emission at high spatial resolution matched to the HST/WFC3 imaging. CR7 is a luminous Ly$\alpha$ emitting galaxy at $z=6.6$ that consists of three separated UV-continuum components. Our observations reveal several well-separated components of [CII] emission. The two most luminous components in [CII] coincide with the brightest UV components (A and B), blue-shifted by $\approx 150$ km s$^{-1}$ with respect to the peak of Ly$\alpha$ emission. Other [CII] components are observed close to UV clumps B and C and are blue-shifted by $\approx300$ and $\approx80$ km s$^{-1}$ with respect to the systemic redshift. We do not detect FIR continuum emission due to dust with a 3$\sigma$ limiting luminosity L$_{\rm IR} (T_d = 35 \rm \, K) < 3.1\times10^{10}$ L$_{\odot}$. This allows us to mitigate uncertainties in the dust-corrected SFR and derive SFRs for the three UV clumps A, B and C of 28, 5 and 7 M$_{\odot}$ yr$^{-1}$. All clumps have [CII] luminosities consistent within the scatter observed in the local relation between SFR and L$_{\rm [CII]}$, implying that strong Ly$\alpha$ emission does not necessarily anti-correlate with [CII] luminosity. Combining our measurements with the literature, we show that galaxies with blue UV slopes have weaker [CII] emission at fixed SFR, potentially due to their lower metallicities and/or higher photoionisation. Comparison with hydrodynamical simulations suggests that CR7's clumps have metallicities of $0.1, Comment: 17 pages, accepted for publication in ApJ

To improve our understanding of high-z galaxies we study the impact of H$_{2}$ chemistry on their evolution, morphology and observed properties. We compare two zoom-in high-resolution (30 pc) simulations of prototypical $M_{\star}\sim 10^{10} {\rm M}_{\odot}$ galaxies at $z=6$. The first, "Dahlia", adopts an equilibrium model for H$_{2}$ formation, while the second, "Alth{\ae}a", features an improved non-equilibrium chemistry network. The star formation rate (SFR) of the two galaxies is similar (within 50\%), and increases with time reaching values close to 100 ${\rm M}_{\odot}/\rm yr$ at $z=6$. They both have SFR-stellar mass relation consistent with observations, and a specific SFR of $\simeq 5\, {\rm Gyr}^{-1}$. The main differences arise in the gas properties. The non-equilibrium chemistry determines the H$\rightarrow$ H$_{2}$~transition to occur at densities $> 300\,{cm}^{-3}$, i.e. about 10 times larger than predicted by the equilibrium model used for Dahlia. As a result, Alth{\ae}a features a more clumpy and fragmented morphology, in turn making SN feedback more effective. Also, because of the lower density and weaker feedback, Dahlia sits $3\sigma$ away from the Schmidt-Kennicutt relation; Alth{\ae}a, instead nicely agrees with observations. The different gas properties result in widely different observables. Alth{\ae}a outshines Dahlia by a factor of 7 (15) in [CII]~$157.74\,\mu{\rm m}$ (H$_{2}$~$17.03\,\mu{\rm m}$) line emission. Yet, Alth{\ae}a is under-luminous with respect to the locally observed [CII]-SFR relation. Whether this relation does not apply at high-z or the line luminosity is reduced by CMB and metallicity effects remains as an open question., Comment: 18 pages, 13 Figures 1 Table, accepted for publication in MNRAS

We present a coherent multi-band modelling of the CO Spectral Energy Distribution of the local Seyfert Galaxy NGC7130 to assess the impact of the AGN activity on the molecular gas. We take advantage of all the available data from X-ray to the sub-mm, including ALMA data. The high-resolution (~0.2") ALMA CO(6-5) data constrain the spatial extension of the CO emission down to ~70 pc scale. From the analysis of the archival CHANDRA and NuSTAR data, we infer the presence of a buried, Compton-thick AGN of moderate luminosity, L_2-10keV ~ 1.6x10^{43} ergs-1. We explore photodissociation and X-ray-dominated regions (PDRs and XDRs) models to reproduce the CO emission. We find that PDRs can reproduce the CO lines up to J~6, however, the higher rotational ladder requires the presence of a separate source of excitation. We consider X-ray heating by the AGN as a source of excitation, and find that it can reproduce the observed CO Spectral Energy Distribution. By adopting a composite PDR+XDR model, we derive molecular cloud properties. Our study clearly indicates the capabilities offered by current-generation of instruments to shed light on the properties of nearby galaxies adopting state-of-the art physical modelling., Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letters

We derive the CO luminosity function (LF) for different rotational transitions (i.e. (1-0), (3-2), (5-4)) starting from the Herschel LF by Gruppioni et al. and using appropriate $L'_{\rm CO} - L_{\rm IR}$ conversions for different galaxy classes. Our predicted LFs fit the data so far available at $z\approx0$ and $2$. We compare our results with those obtained by semi-analytical models (SAMs): while we find a good agreement over the whole range of luminosities at $z\approx0$, at $z\approx1$ and $z\approx2$ the tension between our LFs and SAMs in the faint and bright ends increases. We finally discuss the contribution of luminous AGN ($L_{X}>10^{44}\,\rm{erg\,s^{-1}}$) to the bright end of the CO LF concluding that they are too rare to reproduce the actual CO luminosity function at $z\approx2$., 5 pages, 3 figures, accepted for publication in MNRAS Letters

By combining high resolution, radiative transfer cosmological simulations of z~6 galaxies with a sub-grid multi-phase model of their interstellar medium we derive the expected intensity of several far infrared (FIR) emission lines ([C II] 158 micron, [O I] 63 micron, and [N II] 122 micron) for different values of the gas metallicity, Z. For Z = Z_sun the [C II] spectrum is very complex due to the presence of several emitting clumps of individual size < 3 kpc; the peak is displaced from the galaxy center by ~100 km/s. While the [O I] spectrum is also similarly displaced, the [N II] line comes predominantly from the central ionized regions of the galaxy. When integrated over ~500 km/s, the [C II] line flux is 185 mJy km/s; 95% of such flux originates from the cold (T~250 K) H I phase, and only 5% from the warm (T~5000 K) neutral medium. The [O I] and [N II] fluxes are ~6 and ~90 times lower than the [C II] one, respectively. By comparing our results with observations of Himiko, the most extended and luminous Lyman Alpha Emitter (LAE) at z = 6.6, we find that the gas metallicity in this source must be sub-solar. We conclude that the [C II] line from z~6 galaxies is detectable by the ALMA full array in 1.9 < t_ON < 7.7 hr observing time, depending on Z.

We present the analysis of deep HST multi-band imaging of the BDF field specifically designed to identify faint companions around two of the few Ly-alpha emitting galaxies spectroscopically confirmed at z~7 (Vanzella et al. 2011). Although separated by only 4.4 proper Mpc these galaxies cannot generate HII regions large enough to explain visibility of their Ly-alpha line, thus requiring a population of fainter ionizing sources in their vicinity. We use deep HST and VLT-Hawk-I data to select z~7 Lyman break galaxies around the emitters. We select 6 new robust z~7 LBGs at Y~26.5-27.5 whose average spectral energy distribution is consistent with the objects being at the redshift of the close-by Ly-alpha emitters. The resulting number density of z~7 LBGs in the BDF field is a factor ~3-4 higher than expected in random pointings of the same size. We compare these findings with cosmological hydrodynamic plus radiative transfer simulations of a universe with a half neutral IGM: we find that indeed Ly-alpha emitter pairs are only found in completely ionized regions characterized by significant LBG overdensities. Our findings match the theoretical prediction that the first ionization fronts are generated within significant galaxy overdensities and support a scenario where faint, "normal" star-forming galaxies are responsible for reionization., Comment: Accepted for publication in The Astrophysical Journal Letters. 6 pages, 5 figures

We present a novel method to simultaneously characterize the star formation law and the interstellar medium properties of galaxies in the epoch of reionization (EoR) through the combination of [C ii] 158 μm (and its known relation with star formation rate) and C iii] λ1909 Å emission line data. The method, based on a Markov chain Monte Carlo algorithm, allows us to determine the target galaxy average density, n, gas metallicity, Z, and ‘burstiness’ parameter, κs, quantifying deviations from the Kennicutt–Schmidt relation. As an application, we consider COS-3018 (z = 6.854), the only EoR Lyman Break Galaxy so far detected in both [C ii] and C iii]. We show that COS-3018 is a moderate starburst (κs ≈ 3), with $Z \approx 0.4 \, \mathrm{Z}_{\odot }$, and $n \approx 500\, {\rm cm^{-3}}$. Our method will be optimally applied to joint ALMA and James Webb Space Telescope targets.

We present Atacama Large Millimiter/submillimiter Array (ALMA) observations of eight highly excited CO (J$_{\rm up}>8$) lines and continuum emission in two $z\sim6$ quasars: SDSS J231038.88+185519.7 (hereafter J2310), for which CO(8-7), CO(9-8), and CO(17-16) lines have been observed, and ULAS J131911.29+095951.4 (J1319), observed in the CO(14-13), CO(17-16) and CO(19-18) lines. The continuum emission of both quasars arises from a compact region ($< 0.9$ kpc). By assuming a modified black-body law, we estimate dust masses of Log$(M_{\rm dust}/M_{\odot})=8.75\pm0.07$ and Log$(M_{\rm dust}/M_{\odot})=8.8\pm0.2$ and dust temperatures of $T_{\rm dust}=76\pm3~{\rm K}$ and $T_{\rm dust}=66^{+15}_{-10}~{\rm K}$, respectively for J2310 and J1319. Only CO(8-7) and CO(9-8) in J2310 are detected, while $3��$ upper limits on luminosities are reported for the other lines of both quasars. The CO line luminosities and upper limits measured in J2310 and J1319 are consistent with those observed in local AGN and starburst galaxies, and other $z\sim 6$ quasars, except for SDSS J1148+5251 (J1148), the only quasar at $z=6.4$ with a previous CO(17-16) line detection. By computing the CO SLEDs normalised to the CO(6-5) line and FIR luminosities for J2310, J1319, and J1149, we conclude that different gas heating mechanisms (X-ray radiation and/or shocks) may explain the different CO luminosities observed in these $z\sim6$ quasar. Future J$_{\rm up}>8$ CO observations will be crucial to understand the processes responsible for molecular gas excitation in luminous high-$z$ quasars., 13 pages, 9 figures, 3 tables; MNRAS journal