© ESO 2020

1. Introduction

Galaxy interactions and mergers play important roles in the formation and evolution of galaxies; they are able to trigger massive starbursts (SBs) and also feed super massive black holes (SMBHs). The study of active galactic nuclei (AGNs) and starburst phenomena is key to our understanding of the relationship between star formation and AGN activity in galaxies.

The presence of powerful outflows is believed to play an important role in the evolution of galaxies. These are able to regulate both star formation and the growth of the SMBH through “positive” or “negative” feedback in young galaxies (e.g., Hopkins et al. 2009; Cresci et al. 2015). Recently, evidence of massive molecular outflows in AGN and SB galaxies has been found, strongly supporting the study of outflowing molecular gas as a process able to quickly remove from the galaxy the gas that would otherwise be available for star formation (negative feedback on star formation; Sakamoto et al. 2009; Alatalo et al. 2011; Chung et al. 2011; Sturm et al. 2011; Spoon et al. 2013; Cicone et al. 2014; García-Burillo et al. 2014).

The molecular gas plays not only a key role as fuel in the activity process but should also, in turn, be strongly affected by the activity. Depending on the evolutionary phase of the activity, different physical processes can be involved, changing the excitation conditions and the chemistry: strong ultraviolet (UV) radiation coming from young massive stars (i.e., the photon-dominated region or PDR; e.g., Wolfire et al. 2010), highly energetic X-ray photons coming from an AGN (i.e., X-ray dominated region (XDR); Meijerink et al. 2006), as well as shocks and outflows and inflows (see Flower et al. 2010). X-rays can penetrate more deeply into the interstellar medium (ISM) than UV photons (Maloney et al. 1996; Maloney 1999; Meijerink & Spaans 2005): X-rays are able to heat the gas more efficiently, but not the dust, and they are less effective in dissociating molecules (Meijerink et al. 2013). On the other hand, PDRs are more efficient than XDRs in heating the dust. For this reason, AGNs are suspected to create excitation and chemical conditions for the surrounding molecular gas that are spatially quite different from those in SB environments. Knowledge of the composition and properties of the molecular gas in such environments is essential to characterize the activity itself, and to differentiate between AGN and SB mechanisms.

We focus our analysis on the nearby (D  ∼  3.8 Mpc; Karachentsev et al. 2007), almost edge-on (i = 78°) galaxy, NGC 4945, known to be a remarkable prototype AGN–SB composite galaxy. Its proximity (1″ ∼ 19 pc) makes this object an excellent target for studies of molecular gas at the center of an active galaxy. It is also one of the closest galaxies in the local universe that hosts both an AGN and a starburst. The black hole mass estimated from the velocity dispersion of 150 km s⁻¹ obtained from the water maser is around ∼10⁶ M_⊙, similar to that of our own Galaxy and a factor of ten smaller than the black hole hosted in the Sy2 galaxy NGC 1068 (1.5 × 10⁷ M_⊙; Greenhill & Gwinn 1997). Together with Circinus, it contains a highly obscured Seyfert 2 nucleus (Iwasawa et al. 1993; Marinucci et al. 2012; Puccetti et al. 2014) with associated dense molecular clouds, bright infrared emission, compact (arcsec) radio source, bright H₂O “megamaser” (∼15 mas; Greenhill et al. 1997), a strong Fe 6.4 KeV line, and variable X-ray emission (Schurch et al. 2002). These observations reveal a Compton-thick spectrum with an absorbing column density of N_H ∼ 2.4−4  ×  10²⁴ cm⁻² (Guainazzi et al. 2000; Itoh et al. 2008). The nucleus of NGC 4945 is one of the brightest extragalactic sources at 100 keV (Done et al. 1996), and the brightest Seyfert 2 AGN at > 20 keV (Itoh et al. 2008), whose emission is only visible through its reflected emission below 10 keV due to the large column density that completely absorbs the primary nuclear emission. The emission at higher energy is still visible, though heavily affected by Compton scattering and photoelectric absorption. The nuclear emission between 2 and 10 keV is enclosed in a region of 12″ × 6″, consistent with the SB ring observed using molecular gas tracers (e.g., Moorwood et al. 1996; Marconi et al. 2000; Curran et al. 2001; Schurch et al. 2002).

From IRAS observations we know that about 75% of the total infrared luminosity of the galaxy (L_IR = 2.4 × 10¹⁰ L_⊙) is generated within an elongated region of < 12″ × 9″ centered on the nucleus (Brock et al. 1988). This structure, as shown in high-resolution HST-NICMOS observations of the Paα line, is consistent with a nearly edge-on SB ring of ∼5″–10″ (100–200 pc; radius ∼2.5″–5″, Marconi et al. 2000).

Recently, the very inner regions of NGC 4945 were studied in radio by Henkel et al. (2018), who find a complex structure composed of a nuclear disk of 10″ × 2″ enclosing a spatially unresolved molecular core of ≲2″, consistent with the X-ray source size observed with Chandra (Marinucci et al. 2012). According to the results obtained by Marinucci et al. (2012), the nuclear emission between 2 and 10 keV enclosed in a region of 12″ × 6″ (i.e., “cold X-ray reflector”) is in good agreement with the molecular disk observed by Henkel et al. (2018). Furthermore, using high-density gas tracers (e.g., HCN, CS), these latter authors also observed two bending spiral-like arms connected by a thick bar-like structure extending in the east–west direction from galactocentric radii of ∼100 pc out to 300 pc.

A conically shaped wind-blown cavity has been observed to the northwest at different wavelengths, extending out of the galaxy plane from the nucleus and probably produced by a SB-driven wind (Moorwood et al. 1996). In particular, it has been detected at soft X-ray (i.e., the “plume”¹), optical, and infrared (IR) wavelengths (Nakai 1989; Moorwood et al. 1996; Schurch et al. 2002; Mingozzi et al. 2019). The extension of the outflow ranges from ≳2″ in the X-ray band from Chandra (Marinucci et al. 2012) reaching ∼30″ in the optical band, observed with MUSE/VLT (Venturi et al. 2017), and in the X-ray band (Schurch et al. 2002).

Figure 1 (left panel) shows a composite view of this galaxy using optical and X-ray emission from Marinucci et al. (2012). The right panel of Fig. 1 shows a sketch of the observed structures in the inner regions of NGC 4945 at different wavelengths.

Fig. 1. Left: combined image of X-ray emission from Chandra (low energy: magenta, high energy: blue) overlaid on an optical image from ESO. Credits from NASA/CXC/Univ degli Studi Roma Tre/Marinucci et al. (2012), Optical: ESO/VLT & NASA/STScI. Right: cartoon of the central region (<1 kpc) of NGC 4945. The optical image shown in the left panel is used as the background. The size (diameter) of the different components observed in the (soft and hard) X-ray, NIR, and radio bands are highlighted: the limb-brightening “plume” in soft X-rays as well as the nuclear hard X-ray emission region (Marinucci et al. 2012), the starburst ring in Paα (Marconi et al. 2000), and the nuclear molecular disk along with the unresolved molecular core (Henkel et al. 2018).

Here, we study the molecular composition as well as the excitation temperature and column density of the ISM in the nucleus of NGC 4945. We apply a local thermodynamic equilibrium (LTE) multi-transition analysis to a dataset of several molecules observed using the Heterodyne Instrument for the Far Infrared (HIFI) onboard Herschel satellite and the single dish Atacama Pathfinder EXperiment (APEX; diameter D = 12 m; Güsten et al. 2006) antenna. The LTE analysis was also applied to 2D imaging spectroscopy of ¹²CO data obtained with the Photoconductor Array Camera and Spectrometer (PACS) and the Spectral and Photometric Imaging REceiver (SPIRE). We focus on the LTE analysis applied using the whole sub-millimeter (sub-mm) and far-infrared (FIR) range for studying ¹²CO, which allows us to characterize the distribution of the heating at different spatial scales: from large (35″, ∼ 700 pc) down to small scales (9.4″, ∼ 200 pc). The aim of this work is to characterize the thermal and density structures at different spatial scales in NGC 4945. Furthermore, the determination of the dominant heating mechanism and the origin of the observed heating pattern in the inner regions of this object are also analyzed. The photometric data allow us to derive the mass of dust and the corresponding mass of gas (once assumed a specific gas-to-dust ratio) and compare with the expectations from the heating mechanisms inferred from the ¹²CO analysis.

The paper is organized as follows: in Sect. 2 we introduce the observations and the data analysis applied for each instrument. In Sect. 3 we present the spectral energy distribution (SED) results derived from analyzing photometric data obtained from different instruments, from the FIR to sub-mm wavelengths. Section 4 is dedicated to the derivation of the column densities and the excitation temperatures obtained using the high-spectral-resolution HIFI and APEX data for all molecules (¹²CO, ¹³CO, HCN, HNC, HCO⁺, CS, [CI], CH) for spatial scales between 20″ and 30″ (∼400–700 pc). In Sect. 5 we focus our analysis on the thermal and column density structures of ¹²CO using 2D imaging spectroscopy: from SPIRE (≳700 pc) down to smaller spatial scales using PACS (≲200 pc). Section 6 is devoted to a discussion of the results in order to understand the origin of both gas- and dust-heating mechanisms. Our main conclusions are summarized in Sect. 7. Appendix A presents detailed information on the derivation of the flux densities used in the SED fitting analysis (Sect. 3). Throughout the paper we consider H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_M = 0.27 and Ω_Λ = 0.73.

2. Observations and data analysis

2.1. Observations

2.1.1. Heterodyne Instrument for the Far Infrared and the Atacama Pathfinder EXperiment

The HIFI observations are taken in the pointed dual beam switch (DBS) mode covering the frequency range between 480 GHz and 1270 GHz (band 1–5; see Jackson & Rueda 2005) and from 1410 GHz up to 1910 GHz² (bands 6 and 7; see Cherednichenko et al. 2002) at high spectral resolution (R = 10⁶–10⁷). The half-power beam width (HPBW) of the telescope was 37″ and 12″ at 572 GHz and 1892 GHz, respectively. The HIFI Wide Band Spectrometer (WBS) was used with an instantaneous frequency coverage of 4 GHz and an effective spectral resolution of 1.1 MHz. Two orthogonal polarizations (horizontal, H, and vertical, V) were recorded and then combined together to end up with a higher signal-to-noise ratio (S/N). We used the standard Herschel pipeline Level 2.5 which provides fully calibrated spectra (de Graauw et al. 2010; see Table 1). In particular, the HIFI Level 2.5 pipeline combines the Level 2 products into final products. Single-point data products are stitched spectra for each of the polarizations and backends applicable to the observation. The spectra were produced using the pipeline version Standard Product Generation (SPG) v14.1.0 within HIPE. For further information see Shipman et al. (2017).

In addition to the HIFI data we obtained sub-mm data of lower transitions (J_up = 3, 4) of ¹²CO, ¹³CO, HCN, HNC and HCO⁺ using the FLASH+³ receiver at 345 GHz at APEX (see Table 2). The HPWB ranges from 21″ down to 17″ at 272 and 354 GHz, respectively. The spectral resolution provided by a Fourier Transform Spectrometer (FTS) was smoothed to a velocity resolution of 20 MHz. The data reduction was initially performed using CLASS⁴ and then imported in MADCUBA⁵ (Rivilla et al. 2016; Martín et al. 2019).

2.1.2. Photoconductor Array Camera and Spectrometer (PACS)

PACS is a photometer and a medium-resolution spectrometer⁶. In imaging dual-band photometry, PACS simultaneously images the wavelength ranges 60–90 μm, 90–130 μm, and 130–210 μm over a field of view (FoV) of 1.75′ × 3.5′. Its grating imagining spectrometer covers the 55–210 μm spectral range with a spectral resolution between 75 and 300 km s⁻¹ over a FoV of 47″ × 47″, resolved into 5 × 5 spaxels, each with an aperture of 9.4″.

PACS data were provided from the Herschel archive⁷ using Level 2 and 2.5 products (see Table 1). The PACS Level-2 spectroscopy products can be used for scientific analysis. Processing to this level involves actual spectra and is highly dependent on the observing mode. The result is an image of cube products (for further details see Poglitsch et al. 2010). The Level-2.5 photometric products are maps (produced with JScanam, Unimap and the high-pass filter pipelines) generated by combining scan and cross-scan observations taken on the same sky field. The PACS products were produced using the pipeline version SPGv14.2.2 within HIPE.

2.1.3. Spectral and Photometric Imaging REceiver (SPIRE)

SPIRE consists of a three-band imaging photometer and an imaging Fourier Transform Spectrometer (FTS). The photometer carries out broadband photometry (λ/Δλ ≈ 3) in three spectral bands centered on approximately 250, 350, and 500 μm with an angular resolution of about 18″, 24″ and 35″, respectively (see Table 3). The spectroscopy is carried out by a FTS that uses two overlapping bands to cover 194–671 μm (447–1550 GHz) simultaneously, the SSW short-wavelength band (190–313 μm; 957–1577 GHz) and SLW long-wavelength band (303–650 μm; 461–989 GHz). The SPIRE–FTS is a low-spatial- and spectral (1.2 GHz)-resolution mapping spectrometer. In particular, the beam full width at half-maximum (FWHM) of the SSW bolometers is 18″, approximately constant with frequency. The beam FWHM of the SLW bolometers varies between ∼30″ and 42″ with a complicated dependence on frequency (Swinyard et al. 2010).

We use SPIRE Level-2 spectroscopic and photometric products for our analysis. These data are processed to such a level that scientific analysis can be performed. The SPIRE Level-2 photometer products (maps) are calibrated in terms of in-beam flux density (Jy beam⁻¹)⁸. The photometric and spectroscopic SPIRE data Level-2 were produced using the pipeline version SPGv14.1.0 within HIPE.

Our data have been achieved with an intermediate spatial sampling: in such a case, the pixel size for the SLW and SSW bolometers are 35″ and 19″, respectively. The ¹²CO ladder (from J_up = 4 to 13) is the most prominent spectral feature in this frequency range. These mid-J¹²CO emission lines probe warm molecular gas (upper-level energies ranging from 55 K to 500 K above the ground state) that can be heated by ultraviolet photons, shocks, or X-rays originating from the AGN or in young star-forming regions. In the SPIRE–FTS range, besides the ¹²CO transitions we also detected the prominent [CI]492 μm, [CI]809 μm, and [NII]205 μm transitions across the entire system along with several molecular species observed in absorption (see Fig. 2). A baseline (continuum) subtraction of second or third order has been applied to these spectra. Detailed information on the SPIRE observations is summarized in Table 1.

Fig. 2. SLW (upper panel) and SSW SPIRE (lower panel) spectra corresponding to the peak emission in the same FoV in the rest-frame frequency. 12CO lines are shown in blue while fine structure lines, such as [CI] and [NII], are indicated in red. Other molecular species observed in emission and/or absorption are shown in green.

2.2. Data analysis

Using high-spectral-resolution HIFI and APEX data, we carried out a multi-line analysis of ¹²CO, ¹³CO, HCN, HCN, HCO⁺, CS, [CI], and CH, which were all detected in emission. Other molecules such as NH, NH₂, OH⁺, HF, and H₂O were detected in absorption and they will be analyzed in a future study. HIFI and APEX products are calibrated in antenna temperature ($T_{\text{A}}^{\star }$). This was converted to main beam temperature (T_MB) according to the relation:

$$\begin{array}{c}\hfill T_{\mathrm{MB}}=\frac{{\eta }_{\mathrm{f}}}{{\eta }_{\mathrm{MB}}}{T}_{\mathrm{A}}^{\star },\end{array}$$(1)

where η_f is the forward efficiency⁹ of the telescope and η_MB is the main beam efficiency. For the HIFI data, η_MB ranges from 0.69 to 0.76 with η_f = 0.96, while for the APEX data we used η_MB = 0.73 and η_f ¹⁰ = 0.97. The main beam temperature T_MB has been corrected for beam dilution according to the relation:

$$\begin{array}{c}\hfill T_{\mathrm{MB}}^{\prime }=\left(\frac{{\theta }_{\mathrm{s}}^2+{\theta }_{\mathrm{b}}^2}{{\theta }_{\mathrm{s}}^2}\right)T_{\mathrm{MB}},\end{array}$$(2)

where θ_s and θ_b are the source size and the beam size¹¹, respectively. For this object a source size of 20″ has been considered (Wang et al. 2004).

The HIFI spectra were smoothed to a resolution of 20 km s⁻¹. When needed, further smoothing and baseline corrections were applied to the spectra to improve the S/N.

The molecular emission was modeled with the SLIM¹² package within MADCUBA (Martín et al. 2019). In the model, SLIM fits the synthetic LTE line profiles to the observed spectra. The fit is performed in the parameter space of molecular column density N_mol, excitation temperature T_ex, velocity v_LSR, and width of the line (FWHM) to the line profile and source size. SLIM allows the presence of different components (“multi Gaussian fit”), which can be differentiated using different physical parameters (e.g., column density, excitation temperature, velocity). In cases where multiple transitions are fit, two (or more) T_ex can also be assumed (“multiple excitation temperature”, see Sect. 3.3.2 in Martín et al. 2019). To properly account for the beam dilution factor, a source size was fixed as an input parameter.

3. Continuum analysis

3.1. Intrinsic source size of the dust emission from PACS and SPIRE photometry

Here we present the intrinsic (deconvolved) size of the different components of the dust emission in NGC 4945, as small and large grains along with polyaromatic hydrocarbons (PAHs; Lisenfeld et al. 2002; da Cunha et al. 2008), which we derived using the photometric data from PACS (70, 100, 160 μm) and SPIRE (250, 350, 500 μm). These photometric images were retrieved from the Herschel archive (see Table 1). We measured the FWHM sizes of the peak emission and deconvolved them with the relevant PSF sizes assuming Gaussian shapes for both. At these moderate resolutions the galaxy shows the presence of a compact source plus a disk component: at these wavelengths the contribution of the compact source emission dominates over the disk component within the beam. The results of the intrinsic source size are listed in Table 4.

We then computed the flux density enclosed in the observed source size. For the PACS data the maps are in units of [Jy pixel⁻¹] while the SPIRE maps (point source calibrated) are in units of [Jy beam⁻¹]. Therefore, to compute the total flux density included in the (observed) source size, we treated the two dataset as follows: for the PACS data we simply sum all fluxes of each pixel within the estimated source size while for the SPIRE data we multiply the sum of all values within the source size by a factor of (pixel size/PSF)² at the corresponding wavelength (Table 4). From these results the emission of NGC 4945 is resolved in both directions at all but one PACS and SPIRE wavelength: in particular, at 500 μm the emission is resolved in one direction and unresolved in the perpendicular direction. The photometric PACS and SPIRE maps are shown in Fig. 3.

Fig. 3. Photometric images of NGC 4945 at the PACS (70, 100 and 160 μm; top) and SPIRE (250, 350 and 500 μm; bottom) wavelengths. The flux units have been converted to Jansky for both the PACS and SPIRE data (see text for details). The black circle in each panel identifies a beam of 40″ × 40″. From PACS 70 μm to SPIRE 500 μm wavelengths, an aperture of 40″ corresponds to 25, 25, 12.5, 6.7, 4, and 3 pixels, respectively. The black cross represents the peak emission in each band.

3.2. Spectral energy distribution of NCG 4945

We derived the SED combining PACS and SPIRE data with those obtained at sub-mm wavelengths from Weiß et al. (2008) using Large APEX Bolometer Camera (LABOCA) and from Chou et al. (2007) using the Submillimeter Array (SMA) within an aperture of 40″ × 40″ (see Fig. 4). This is a reasonable value to consider most of the emission from the inner regions of the galaxy at all wavelengths: the aperture considered is shown in Fig. 3 for both PACS and SPIRE bands. The flux density obtained in Weiß et al. (2008) in an aperture of 80″ × 80″ has been scaled to our aperture, deriving a flux density of 9.05 (±1.3) Jy (see Appendix A for details). We also added one FIR data point from MSX at ∼20 μm. Other data at shorter wavelengths were available from MSX, IRAC, and 2MASS catalogs but they were not included in this analysis because their emission (in the range ∼3–17 μm) is strongly affected by several emission features from PAH molecules (see Povich et al. 2007; Pérez-Beaupuits et al. 2018). In Table 5 the derived flux densities are shown.

Fig. 4. SED-fitting results for NGC 4945. The best-fit solution (red solid line) is obtained when two dust components with temperatures of 28 K (blue MBB) and 50 K (green MBB) are needed, assuming a source size of 20″ × 10″. The total dust mass obtained from the fit is ≲107 M⊙. The SPIRE and PACS data are shown using red and violet squares, respectively. Additional data used in the fit are shown in filled black squares. In particular, at shorter frequencies the SMA (Chou et al. 2007) and LABOCA (Weiß et al. 2008) data were added (see text for details) obtaining a β parameter of 2.0. At higher frequencies the MSX data point is considered in the fit while two IRAC data points are only shown for completeness (in gray).

From the SED fitting we are able to constrain the source size, Ω_s, the dust temperature, T_d, and the total mass of dust, M_dust (as done in Weiß et al. 2008). To properly fit the dust emission an attenuated black body function (i.e., modified black body) is considered. The source function, S_ν, of the dust is related to the Planck’s blackbody function (B_ν) at the dust temperature (T_d), the dust opacity (τ_ν) and the source solid angle (Ω_s) according to the formula:

$$\begin{array}{c}\hfill S_{\nu }=B_{\nu }(\nu ,T_{\mathrm{d}})\times (1-e^{-\tau (\nu )})\times {\mathrm{\Omega }}_{\mathrm{s}},\end{array}$$(3)

while the dust optical depth was computed as

$$\begin{array}{c}\hfill {\tau }_{\nu }={\kappa }_{\mathrm{d}}(\nu )\times \frac{M_{\mathrm{dust}}}{D^2{\mathrm{\Omega }}_{\mathrm{s}}},\end{array}$$(4)

where D is the distance to the source and κ_d(ν) is the dust absorption coefficient in units of m² kg⁻¹ (Krugel & Siebenmorgen 1994). Here, κ_d(ν) is related to the β parameter according to the relation: κ_d(ν) = 0.04 × (ν/250 GHz)^β. In this work, β was computed using SPIRE, LABOCA, and SMA data, obtaining a value of 2.0 from the linear fit. A source size of 20″ × 10″ was assumed.

In Fig. 4 the best-fit SED (${\chi }_{\min }^2~4.6$; red solid line) is derived when two component temperatures are considered in the dust model: a cold dust component at 28 K to fit the shorter frequencies and a warm component at 50 K to fit the higher frequencies. A total mass of dust of ∼8 × 10⁶ M_⊙ is derived. Assuming a gas-to-dust ratio between 100 and 150 (see Weiß et al. 2008), we derived a total gas mass of 7.6–11.4 × 10⁸ M_⊙.

We found good agreement with the results obtained from previous works. Indeed, Weiß et al. (2008) derived a total mass of gas in the central region using an aperture of 80″ × 80″ of 1.6 × 10⁹ M_⊙. Comparing the results of these latter authors with ours, we can conclude that most of the total emission (70%) is included in a region of 40″ × 40″.

On the other hand, Chou et al. (2007) estimated the mass of molecular gas from the inferred dust emission at 1.3 mm (i.e., 1 Jy; see Fig. 4), assuming a gas-to-dust ratio of 100. These latter authors assumed a dust temperature T_dust ∼ 40 K as inferred from FIR measurements (Brock et al. 1988), then deriving M_gas ≈ 3.6 × 10⁸ M_⊙ according to their Eq. (1), which corresponds to a mass of dust in the range ∼2.4–3.6 × 10⁶ M_⊙. The mass of dust derived by Chou et al. (2007) is a factor of between two and three lower than that derived here, and can be considered as a lower limit. The results of our SED modeling are summarized in Table 6.

4. Density and temperature determination. Resolved spectra from HIFI and APEX

4.1. LTE results using MADCUBA

We apply the LTE analysis using MADCUBA (Martín et al. 2019) to ¹²CO, ¹³CO, HCN, HNC, HCO⁺, CS, [CI], and CH molecules observed using the high-spectral-resolution HIFI and APEX data. A source size of θ = 20″ was assumed (see Sect. 2.2). The observed spectra and the simulated emission from the LTE model are shown in Fig. 5. All molecules except ¹²CO were properly fitted using one temperature component. Indeed, in the specific case of ¹²CO, the emission was fitted using two temperature components (top left panel in Fig. 5): one cold and more dense, and the other warm and less dense. The cold component (∼20 K; in blue) dominates the emission characterizing the low J transitions while the warm one (∼90 K; in green) dominates the emission at higher J. The need for two different (LTE) excitation temperatures T_ex to fit all the line profiles is a clear indication of NLTE excitation due to temperature and/or density gradients. The physical conditions required to explain the molecular excitation are discussed in the following section.

Fig. 5. High resolution molecular spectra from APEX and HIFI for all molecules analyzed in this work. The observed spectra and LTE fit obtained using MADCUBA are shown in black and red, respectively. For the 12CO molecule, we highlight a cold (blue) and a hot (green) component because two temperature components were needed to properly fit the emission. For each APEX (Jup ≤ 4) and HIFI (Jup≥ 5–9) spectrum, the J transitions are identified. Other detected molecular species like CH, 13CH and 12CO (in the image band) are shown in green. For each molecule the range in temperature is the same for all J (APEX and HIFI) transitions with the exception of 12CO and HCN, which show different ranges to better appreciate the fainter emission of the HIFI data. The emission is shown in main beam temperature (TMB) in kelvin.

The combination of low rotational transitions (J = 3–2 or 4–3) from APEX with higher rotational transitions from HIFI (J = 5–4 up to 9–8) allows us to better constrain the molecular column density N_mol and excitation temperature T_ex parameters for each species (see Sect. 2.2). The typical value of N_mol derived for ¹²CO with MADCUBA ranges from 4 × 10¹⁶ cm⁻² up to 3.2 × 10¹⁷ cm⁻², for the warm and cold components, respectively. The N_mol and T_ex values for the different molecules are shown in Fig. 6.

Fig. 6. LTE results derived with MADCUBA for each individual molecular species. From left to right: excitation temperature, Tex, in kelvin, along with the molecular column density, Nmol, in units of cm−2.

According to the LTE analysis, we derived the following results (see Table 7) for all molecules:

1. We found three distinct kinematic components for all molecules: these identify the nuclear bulk (∼560 km s⁻¹) and the rotating disk structures which show one blueshifted (∼450 km s⁻¹) and one redshifted (∼690 km s⁻¹) component. Our result is an agreement with the kinematics derived in previous works (e.g., Ott et al. 2001; Henkel et al. 2018).

2. All species except ¹²CO and [CI] were properly fitted using a single excitation temperature of about 20 K. ¹²CO needs two components with excitation temperatures of 20 K and 90 K while [CI]¹³ needs one component with a high excitation temperature, T_ex ∼ 150 K.

3. The typical value of N_mol derived for low-density gas tracers such as ¹²CO, ¹³CO, [CI] ranges from 3 × 10¹⁶ cm⁻² up to 5 × 10¹⁷ cm⁻². For the low-density tracer CH the lowest column density is achieved (N_mol ∼ 10¹⁴ cm⁻²). The derived N_mol for the high-density gas tracers such as HCN, HNC, HCO⁺ and CS has a lower value of the order of 10¹³ cm⁻². If a smaller source size were considered (i.e., θ_s = 10″), as in Henkel et al. 2018, the column density values would be increased by a factor of ≲3.

4.2. NLTE results using the RADEX code

As mentioned above, the need for two different LTE excitation temperatures T_ex to fit all the ¹²CO line profiles (from J_up = 3 up to 9) is a clear indication of a NLTE excitation of this molecule. We therefore applied the NLTE RADEX code to derive the volume gas density of the collisional patter, n(H₂), in NGC 4945 for each molecular species¹⁴, and to confirm the molecular column densities, N_mol, and the excitation temperature, T_ex, values derived with MADCUBA LTE analysis, restricted to the rotational J transitions of the specific molecule involved in the analysis (Sect. 4.1).

The RADEX code is based on a NLTE analysis taking advantage of the velocity gradient (i.e., N_mol/Δv, the ratio between the column density, in cm⁻², and line width, in km s⁻¹). This code was used to predict the line emission from all molecules using all lines simultaneously, and considering a kinetic temperature of 200 K. This assumption is based on the T_ex derived for CO and [CI] (i.e., ∼150 K; see previous section). In fact, in the case of ¹²CO, we carried out the analysis for two different kinematic temperatures: T_kin = 50 K when fitting the cold component and T_kin = 200 K for the warm component. A lower T_kin would not be able to properly reproduce the line profiles of the ¹²CO transitions at higher frequencies (e.g., J = 6–5). For most of the transitions observed in this work, except those involving ¹²CO levels with energies below 50 K, the choice of the T_kin has a marginal effect on the derived H₂ densities and the molecular column densities.

To derive the H₂ densities and the molecular column densities, N_mol, from RADEX we tried to fit all the observed ¹²CO lines with an isothermal and uniform cloud but did not find a unique solution. At least two clouds with different densities and/or temperatures were needed to fit all the lines. These results indicate the presence of molecular clouds with a range of densities and temperatures within the beam, as expected for the complexity of the NGC 4945 nucleus. The predicted NLTE ¹²CO column densities for the two different H₂ density regimes are similar to those derived from the LTE analysis. The comparison of the predicted NLTE T_ex with the derived LTE values is more complicated as there is no single NLTE T_ex but a range of T_ex depending on the excitation requirements for each transition. The situation is even more complicated for the case of a nonuniform molecular cloud with H₂ density gradients exciting different ¹²CO lines in different regions. As illustrated by the NLTE analysis, lower J lines will be more sensitive to low densities than the high-J lines. We subsequently compared the average of the predicted NLTE T_ex with the LTE T_ex for the range of transitions that dominates the ¹²CO emission. We find a reasonable agreement between both temperatures for the low- and the high-J lines corresponding to the low- and high-density components, respectively.

As expected from the typical density of the ISM in galaxies over the scales of hundreds of parsecs, most of the high-dipole-moment molecules (e.g., HCN, CS, HCO⁺) usually have a critical density much larger than the average H₂ density of the ISM. We then derived subthermal excitation (T_kin >  T_ex) for all density gas tracers.

According to our results, we derive a moderate volume gas density n(H₂) for most of the molecules, in the range 10³ cm⁻³ up to 10⁶ cm⁻³. Lower densities are obtained when considering the low-density gas tracers (e.g., ¹²CO, [CI]), while higher densities are derived when studying the high-density gas tracers, such as HCN, HNC, HCO⁺ and CS (see Table 8). We reproduce the intensities of all transitions for each molecule with RADEX reasonably well; this is also the case when considering a nonuniform cloud (i.e., two H₂ densities), in agreement with the results derived using MADCUBA, as in the case of the two-component model applied to ¹²CO.

5. Thermal and column density structures from the ¹²CO emission at different scales

We study the distribution of the thermal balance and the column density distribution at different spatial scales using the 2D PACS and SPIRE data through the analysis of the ¹²CO emission over a wide range of rotational transitions. In particular, the ¹²CO transitions at wavelengths from 55 μm to 650 μm were covered: this molecule is the most abundant in the ISM after H₂ and therefore considered a good tracer of the properties of the bulk of the molecular gas phase. As shown from the analysis of a limited number of ¹²CO transitions (Sect. 4.1), the wide range of physical properties expected in the nucleus of NGC 4945 cannot be described by either LTE or simple NLTE modeling. To deal with the full range of ¹²CO transitions and the wide range of spatial scales addressed in this work, in what follows we will apply a “transition-limited” LTE analysis to a given range of transitions sampling specific physical conditions (density and temperatures) of the molecular gas. This analysis will allow us to derive the spatial distribution of transition-limited T_ex and N_mol, which describes the different phases of the molecular gas in NGC 4945.

5.1. Mid-J¹²CO at large spatial scale (700 pc–2 kpc)

In this section, we study the warm component using the mid- and high-J of ¹²CO rotational transitions from SPIRE long wavelengths (SLW; transitions from J_up = 4 to 8), and from SPIRE short wavelengths (SSW; J_up = 9–13). For our study we mainly focus on the very central regions of the whole FoV, where the strongest ¹²CO emission is observed. In particular, a maximum region of 3 × 3 spaxels at a resolution of 35″ (∼2 × 2 kpc²; see left panel in Fig. 7) in the SLW map is considered. For each SLW spectrum we combined the contribution at higher frequencies of 3 × 3 SSW spectra at a resolution of 19″ (∼1 × 1 kpc²) to match the beam of the SLW spectrum (middle panel in Fig. 7).

Fig. 7. From left to right: schematic view of the different FoVs involved in the analysis of SLW, SSW SPIRE, and PACS data. Left: in the SLW SPIRE map the green square highlights the FoV considered in the analysis (∼100″). These data are characterized by a beam of 35″ identified by the yellow small square. Middle: in the SSW SPIRE map the yellow square represents the 3 × 3 spaxels area involved in the analysis. The map is characterized by a beam of 19″ (small black square). Right: in the PACS map the black square identifies a FoV of ∼19″ (i.e., one SSW SPIRE spaxel) while the yellow square identifies a FoV of ∼35″. The star symbols represent those spaxels where the 12CO emission is observed: in particular, white stars highlight the spaxels characterized by stronger 12CO emission than that observed in the remaining spaxels marked using yellow stars. PACS data are characterized by a beam of 9.4″.

When applying the LTE analysis to all SPIRE data, we derived the excitation temperature and column density for each (combined) spectrum at the resolution of 35″ (∼700 pc). From this analysis, we found higher T_ex in the center and in the north part of the galaxy possibly affected by the presence of the outflow at large scales (see Sect. 1). Lower temperatures are found in the remaining regions. The column density peaks in the center showing higher values in the south (middle panels in Fig. 8). At this spatial resolution the LTE analysis gives good results when using one temperature component¹⁵.

Fig. 8. Left:12CO(8–7) emission map showing a FoV of 3 × 3 spaxels (35″ each; light green square) considered when combining the SSW and SLW SPIRE data at the same resolution (i.e., 35″, large spatial scale). The peak emission (in red) and a ring of one spaxel width around that maximum (green area) are identified. Middle: excitation temperatures (Tex) and the (logarithmic) column densities (NCO) are derived for each spaxel using the rotational diagrams. The yellow boxes represent the spectra characterized by high Tex and NCO values. Right:12CO/IR flux ratios computed for the different J transitions in the SPIRE domain. In red are shown the values derived at the position of the flux density peak (spaxel #5 in the left panel) while in green the ratios derived integrating the emission in the ring. The ratio between the maximum peak and the ring for each transition is also shown (i.e., “peak-to-ring ratio”, in blue) divided by 100 (a factor of 100 has to be applied to obtain the real values). The dashed gray lines identify the lower and upper limit values of the peak-to-ring ratios computed within the errors. Higher 12CO/IR values are derived for high J (Jup ≥ 11–10) in the ring structure, implying lower (≲1) peak-to-ring ratios.

In order to study the spatial distribution of the heating in this galaxy we compare the emission in the peak with the emission integrated in an annular ring around the peak (one spaxel width) using the same beam for all transitions. We computed the ratio between the ¹²CO flux density peak and the corresponding IR continuum emission at each frequency of the ¹²CO as a function of J (hereafter referred to as CO/IR) as shown in Fig. 8 (right panel). For a spectroscopically unresolved line, as in this case, the flux density peak (given in W m⁻² Hz⁻¹, or Jy) is proportional to its line total flux (W m⁻²). We then multiply the IR flux density by the spectral resolution to derive the total integrated IR continuum flux at the wavelength of each line. As all ¹²CO transitions have similar line widths¹⁶, CO/IR corresponds to the flux ratio of each emission line: i.e., Flux(CO)/Flux(IR Continuum). Thus, the ratio is a dimensionless quantity. Instead of using the total IR flux, as is usually considered in the literature (see Meijerink et al. 2013), we consider the continuum underlying each ¹²CO transition to characterize the ¹²CO/IR ratio at the specific continuum value and specific frequency to take into account changes in the shape of the SED.

We find that the CO/IR values derived in the peak position are higher (of a factor of ≲2, within the errors) than those derived in the ring for all rotational transitions up to J_up = 10. This trend changes for J_up > 11 transitions where the emission in the ring becomes higher (or similar) than that of the peak. This result suggests the presence of mechanisms able to increase the emission of ¹²CO at higher frequencies. In what follows, we study this issue in detail using higher resolution data, moving from intermediate to small scales in order to unveil the origin of this mechanism.

5.2. Mid- and high-J¹²CO data within the inner 700 pc (large to intermediate scales)

We now combine SPIRE (SSW and SLW) and PACS data at a resolution of 35″ (∼700 pc). These instruments have different PSFs (19″ and 35″ for SPIRE SSW and SLW data, respectively, and 9.4″ for PACS). To properly analyze all the ¹²CO spectra over the whole frequency range we smoothed all data to the largest PSF (35″). The reference spectrum in the SLW SPIRE data cube is the one corresponding to the ¹²CO peak emission (central spaxel).

The SPIRE data were combined as explained in the previous section while for the PACS data we only combined the emission observed in eight¹⁷ spaxels. Figure 9 shows the SPIRE and PACS¹²CO spectra (rotational transition from J_up = 4 up to J_up = 20) of the central spaxel at a resolution of 35″.

Fig. 9. Top: averaged SLW, SSW SPIRE (Jup = 4 up to 13), and PACS12CO spectra (Jup = 15 up to 20) of the central region combined together at the same resolution (35″). The original spectra are shown in black while the total simulated 12CO emission obtained from the LTE approach is shown in blue. Other molecular species like [CI] and OH are identified in emission (green). Bottom: table from MADCUBA showing the output parameter values (i.e., column density NCO, excitation temperature Tex, vLSR, FWHM of the line as well as the source size) deriving different source sizes for the cold and hot components.

The LTE analysis accurately reproduces the observed ¹²CO emission (see Fig. 9 and table below), giving rise to the following results:

1. Two temperature components are needed to properly fit the spectra: one warm at ∼80 K and the other hot at 330 K. The hottest temperature is characterized by the lowest molecular column density (N_CO ∼ 5.2 × 10¹⁶ cm⁻²) while the warm component is characterized by a higher column density value (N_CO ∼ 9 × 10¹⁶ cm⁻²).

2. Two different source sizes characterize the warm and hot components: for the warm component a source size of 20″ was assumed (see Sect. 2.2) while for the hot component a source size of ∼7″ was derived from the fit.

5.3. Heating at intermediate scales (360 pc–1 kpc) from SSW SPIRE and PACS data

In this section we first focus on the analysis of the emission observed at intermediate scales described using SSW SPIRE data. At these scales the differences in ¹²CO/IR found in the ring (0.36–1 kpc, or 19″–57″) and those derived in the central spaxel (<360 pc) become significant. A FoV of 3 × 3 spaxels (∼1′ × 1′) is considered, which corresponds to the observed extension of the high-J¹²CO emission in this galaxy (mainly found in the disk plane). The ¹²CO/IR distribution in each¹⁸ spaxel is shown in Fig. 10: an increase in ¹²CO/IR is apparent in the central spaxel (spaxel #5) and in the northwest direction (spaxel #3) for the rotational transitions J_up = 9 and 10. This increase at higher J seems to follow the direction of the outflow observed in the X-ray band by Chandra (see Sect. 1). Assuming that the X-ray outflow is responsible for such an increase in these directions, we normalize the emission of each spaxel to the central one. In the ring we then derived the highest ¹²CO/IR in the disk plane of the galaxy for J_up = 12 (i.e., northeastern (#1), western (#6) and southern (#8) spaxels; see Fig. 10 right panel). At these spatial scales the increased emission at higher frequencies (J_up ≥ 11–12) suggests that other mechanisms, like shocks, could also be at work. In principle, we excluded the (pure) PDR process as responsible for this increase at such high frequencies (see Sect. 6.1 for further details).

Fig. 10. Bottom left:SPIRE SSW12CO emission maps showing the nine spaxels involved in the analysis. Top left: hard (green) and soft (red) X-ray emission from Chandra from Marinucci et al. (2012) of the outflow observed in the central region (∼1′ × 1′) in NGC 4945. Middle:12CO/IR results obtained using SSW SPIRE data (19″ beam) numbered following the scheme shown in the bottom-left panel. Right:12CO/IR results normalized to the emission of the central spaxel (red square).

In the next step, we combine the SSW SPIRE spectra with those from PACS at higher frequencies, smoothing the PACS data to the SSW SPIRE resolution (beam 19″). In this case, for each SSW spectrum we combined (averaged) ∼3–4 PACS spectra. Unfortunately, only half of the PACS spectra presented detections to be considered in the data. In particular, for the spaxels #1, #5, and #8, the ¹²CO emission from SPIRE and PACS were considered, while for the remaining spectra (#3, #4 and #6) we only considered the SPIRE emission (Fig. 11, bottom). For all of them we applied the LTE analysis which allowed us to derive the T_ex and N_mol parameters in each spaxel (Fig. 11, top panel) at the resolution of 19″. From this analysis we found high T_ex in the disk and in the south direction where a maximum value is found. For these spaxels (#1, #5 and #8), two component temperatures are needed to properly fit the spectra.

Fig. 11. LTE results derived combining SSW SPIRE and PACS spectra. Top: distribution of the excitation temperature (Tex, top left) and column density (NCO, top right) derived applying MADCUBA to the combined SSW SPIRE and PACS spectra. The FoV covered by 3 × 3 spaxels (∼1′ × 1′) is the same as that shown in Fig. 10. Bottom: observed (black) and simulated (blue) 12CO emission spectra from combining SSW SPIRE and PACS. The spaxels are identified using the same number used in the top panel. For spaxels #3 and #6 only SPIRE data are available while for spaxels #1, #5 (central), and #8 SSW SPIRE and PACS data are combined together. The 12CO emission is found in the inner region (3 × 3 spaxels) and mainly located in the disk, with some contribution in the perpendicular direction.

The column density N_CO shows a maximum in the central spaxel for both the warm and hot components (N_CO = 5 × 10¹⁶ and 6.3 × 10¹⁷ cm⁻²) and slightly lower values in the south (N_CO = 10¹⁶ and 2 × 10¹⁷ cm⁻²). In the disk plane column densities ≲10¹⁶ cm⁻² are derived.

5.4. Heating and density distribution at small scales (≲200 pc) using PACS

We now focus our attention on the ¹²CO emission observed at higher frequencies with PACS. At this resolution (9.4″) we are covering spatial scales of the order of ≲200 pc. The observed PACS spectra along with the simulated LTE results obtained with MADCUBA¹⁹ are shown in Fig. 12. From the rotational diagrams (Fig. 13) we obtained the T_ex and N_mol for each spaxel²⁰. From this analysis we found that the highest temperatures (846 K and 871 K) are not found in the nucleus but in two spaxels located closed to the nucleus in the northern and southern spaxels. These are mainly located in the disk plane of the galaxy. On the other hand, the nucleus is characterized by T_ex ∼ 360 K. Lower T_ex are found above and below the disk plane (from ∼240 K up to ∼330 K).

Fig. 12. Left: observed 12CO PACS spectra (black) along with the simulated Gaussian fit results (blue). The respective rotational transition (J + 1 → J) is shown for each spectrum. The flux emission is shown in main beam temperature (TMB). The OH emission lines close to the 12CO(16–15) transition are also observed (see Fig. 9).

Fig. 13. Rotational diagrams derived for PACS data. The excitation temperatures (Tex) and the (logarithmic) column densities (NCO) with their respective uncertainties are derived for each spaxel.

According to this result, mechanical heating seems the most probable mechanism able to explain the spatial distribution of the excitation temperature at this scale. Indeed, if the X-ray emission were dominating the nuclear region one would expect the highest excitation temperature in the nucleus. In order to exclude the presence of a XDR in the central spaxel, we derived the intrinsic excitation temperature, correcting the observed T_ex for the nuclear extinction. We thus apply the extinction law:

$$\begin{array}{c}\hfill I_{\lambda }^{\mathrm{int}}=I_{\lambda }^{\mathrm{obs}}\times e^{{\tau }_{\lambda }},\end{array}$$(5)

where τ_λ can be derived following the relation:

$$\begin{array}{c}\hfill {\tau }_{\lambda }={\tau }_{100\mu \mathrm{m}}\times {\left(\frac{100\mu \mathrm{m}}{\lambda }\right)}^{\beta }.\end{array}$$(6)

The optical depth τ_100 μm is derived at 100 μm from the continuum SED fitting (i.e., τ_100 μm ∼ 1.2) with β = 2.0 (Sect. 3.2), assuming that the gas is homogeneously mixed with the dust. For each PACS spectrum of the nuclear spaxel we applied the extinction law associated to the specific wavelength. The corrected excitation temperature of the central spaxel is ∼470 K, far below the values obtained in the surrounding regions (∼850 K). We therefore deduce that the dust opacity does not play an important role in our overall conclusions. Even the AGN interaction does not seem to have a strong impact on the thermal structure of the source at large spatial scales.

According to the results obtained from large to small scales we summarize the distribution of T_ex in Fig. 14 (top panel). The excitation temperature distribution of PACS data is in good agreement with that derived using SSW SPIRE data.

Fig. 14. Excitation temperature and (logarithmic) column density distributions at different spatial scales as derived using SPIRE (SLW, SSW) and PACS data. The yellow squares identify the spaxels with high values for each parameter.

For what concerns the molecular column density N_CO, the highest values are found in the nucleus corresponding to moderate excitation temperatures, while lower column densities are found to correspond to maximum temperatures in the disk. In Fig. 14 (bottom panel) we report the distribution of N_CO at different spatial scales. In Table 9 we summarize all the excitation temperature T_ex and column density N_CO values derived at different spatial scales.

5.5. The dust and gas in a multi-phase ISM

The trend we find in our ¹²CO column densities, N_CO, as a function of the rotational levels J involved in the LTE analysis shows a gradient in both the H₂ density and the kinetic temperature, and a decreasing column density of the hot gas for increasing J, as expected from a multi-phase molecular clumpy medium. As the quantum number J of the transitions used in the analysis increases, the physical conditions required for their excitation change according to their critical densities and the energy above the ground state of the levels involved in our study. Indeed, we see large changes in temperature from 20 K for the mid-J to 400 K for the high-J transitions (see Table 9). This is consistent with the picture of the multi-phase molecular ISM described above. Therefore, the ¹²CO column densities, N_CO, will decrease from the HIFI to the PACS data analysis because the amount of dense and hot gas measured by the high-J transitions is much smaller than the cold-warm gas measured from the low-J transitions.

We could use the ratios between the column densities from the different instruments to roughly estimate the fraction of the warm-hot molecular component to the cold component. In particular, the cold–warm component at ∼20 K is characterized by N(¹²CO_{cold − warm}) = 10^17.6 cm⁻², the warm component at 90 K shows N(¹²CO_warm) ≲ 10¹⁷ cm⁻², while the hot component at ∼370 K is characterized by N(¹²CO_hot) ∼ 10¹⁵ cm⁻². In addition, the coldest component traced by the J = 1–0 and J = 2–1 transitions has a ¹²CO column density of 9.6 × 10¹⁸ cm⁻² for a source size of 20″ × 20″ (Wang et al. 2004), about one order of magnitude larger than the cold–warm component. Thus, the ratio between the cold–warm (CW) and hot (H) components with respect to the cold (C) component is CW/C = 0.05 and H/C = 10⁻⁴: these values correspond to a larger column density of the cold–warm component than that of the hot component (CW/H) by a factor of ∼500.

From our results we can also estimate the total molecular hydrogen column densities, N(H₂). From the SED fitting analysis we derived a total molecular mass of 7.6 10⁸ M_⊙ for the typical GDR = 100. Furthermore, the N_H2 obtained for the size of the dust emission of 20″ × 10″ corresponds to N_H2 ∼ 7 × 10²³ cm⁻². To properly account for the total column density N_CO we need to consider the ¹²CO column densities derived for all the components discussed above and scale them (i.e., multiply by a factor of approximately two) to the size of the dust emission of 20″ × 10″. After the correction for the different source sizes, the total ¹²CO column density is ∼2 × 10¹⁹ cm⁻² which translates into a molecular hydrogen column density of N_H2 ∼ 2 × 10²³ cm⁻² for the ¹²CO fractional abundance of 10⁻⁴. This is a factor of approximately three lower than that derived from the SED fitting analysis which is likely within the uncertainties in the sizes, the dust absorption coefficient, the fractional abundance of ¹²CO, and the GDR we have considered. Assuming the standard conversion:

$$\begin{array}{c}\hfill N_{{\mathrm{H}}_2}=9.4\times {10}^{20}{A}_V[{\mathrm{cm}}^{-2}],\end{array}$$(7)

from Bohlin et al. (1978) (see also Kauffmann et al. 2008; Lacy et al. 2017), we derive very large visual extinction in both cases (>200 mag) as a result of the derived column densities.

We therefore find that the hydrogen column densities derived from the SED fitting approach and ¹²CO analysis are in good agreement. These values are higher than those derived for some local AGN- and starburst-dominated galaxies like NGC 1068 (García-Burillo et al. 2014; Viti et al. 2014) and NGC 253 (Pérez-Beaupuits et al. 2018), but similar to those derived for Compton-thick type 2 Seyfert galaxies like Mrk 3 and NGC 3281 (Sales et al. 2014).

Furthermore, the typical molecular fractional abundances observed in starburst galaxies derived using high-density gas tracers like [HCN]/[H₂] (=X_HCN) are of the order of 10⁻⁸ (see Wang et al. 2004; Martín et al. 2006). The derived column densities between ¹²CO and HCN from our LTE analysis are of the order of N_CO/N_HCN ∼ 10¹⁷/10¹³ ∼ 10⁴. This is the same ratio as that obtained when considering the fractional abundances relative to H₂: X_CO = 10⁻⁴ and X_HCN = 10⁻⁸ (see Martín et al. 2006).

6. Discussion

6.1. Gas heating mechanisms

Distinguishing among the heating mechanisms, such as for example the photoelectric effect by UV photons (PDRs) or XDRs and mechanical processes like shocks, stellar winds, and outflows, is not straightforward, and in most cases a number of mechanisms coexist with different contributions depending on the spatial scale. Many works have addressed this issue by modeling the effect of different mechanisms and comparing the predictions with ¹²CO observations of galaxies with different types of activity like SB galaxies, such as M 82 (Panuzzo et al. 2010; Kamenetzky et al. 2012) and NGC 253 (Rosenberg et al. 2014a; Pérez-Beaupuits et al. 2018), AGN-dominated galaxies, such as NGC 1068 (Spinoglio et al. 2012; Hailey-Dunsheath et al. 2012) and Mrk 231 (van der Werf et al. 2010; Mashian et al. 2015), and composite AGN–SB galaxies, like NGC 6240 (e.g., Meijerink et al. 2013). The ¹²CO emission is strongly affected by the specific mechanism(s) (or by the combinations of them) at work in each galaxy, and some differences can be highlighted between them. For example, when PDRs dominate the emission, the ¹²CO emission increases up to rotational transition J_up = 5 and then decreases. In the presence of XDRs or shocks the contribution of the ¹²CO emission increases up to high (J_up >  10) frequencies.

The ¹²CO spectral line energy distribution (hereafter, ¹²CO SLED) for a large variety of systems has been used in the literature as a powerful tool to derive the physical parameters characterizing the molecular gas phase. The left panel of Fig. 15 shows the ¹²CO SLEDs for different kinds of galaxies; most of the ¹²CO fluxes shown are taken from the work by Mashian et al. (2015, and references therein). This plot can be used for direct comparison of the ¹²CO SLEDs of the different systems up to high J transitions.

Fig. 15. Left: comparison of 12CO SLEDs (normalized to the 12CO(1–0) flux of each specific source) obtained from different sources. Starburst, AGN, and AGN–SB sources have been considered. A 12CO SLED of a SMG at high-z analyzed by Cañameras et al. (2018) is also shown. Different colors identify the galaxies while different symbols indicate the types of objects. In each group, the following galaxies have been selected: M82 and NGC 253 as SB, NGC 6240 and NGC 4945 as AGN–SB composite galaxies, and NGC 1068 and Mrk 231 as AGN-dominated galaxies. The galaxy G244.8+54.9 has been chosen as representative of SMG at high-z, for which the authors derived log ngas ∼ 5.1 cm−3 and log G0 ∼ 3.7 (Habing units). Right: results of the 12CO SLED of NGC 4945 from J = 1–0 through 20–19 applying the Kazandjian et al. (2015) mechanical heating models. The black points are the observed 12CO fluxes obtained from ground-based observations (Hitschfeld et al. 2008) while in green are the data from this work. The fit was constrained to three PDR models, all of them with some contribution of mechanical heating (mPDR), displayed in green, magenta, and blue. Dashed gray lines show the other best-fit results for the three PDRs. The dashed blue line is also shown to represent a model with the same ngas and G0 parameters as those characterizing the PDRIII model but with no mechanical heating contribution (α = 0). The red line represents the best fit with the minimum ${\chi }_{\text{red}}^2$ (∼0.8) while the light red area shows the combination of other best fits with slightly higher χ2 (<1.4). The H2 density (i.e., ngas in log cm−3), G0 (log Habing flux), and percentage of mechanical heating α values are shown in the legend for the three best-fit components.

We selected three different kinds of galaxies for comparison: (1) AGN-dominated, (2) SB-dominated, and (3) AGN–SB composite galaxies. Among the AGN-dominated systems, we selected the prototype (Sy2) NGC 1068 and (Sy1) Mrk 231. The former shows strong ¹²CO line emission above J_up = 20 while Mrk 231 shows a ¹²CO SLED shape that is relatively flat for the higher-J transitions. In both cases, Mashian et al. (2015) and van der Werf et al. (2010) claim that the results are consistent with the presence of a central X-ray source illuminating the circumnuclear region. Hailey-Dunsheath et al. (2012) also found that in NGC 1068 the gas can be excited by X-rays or shocks although they were not able to differentiate between the two. For representative SB galaxies, we selected M 82 and NGC 253. Panuzzo et al. (2010) found that the ¹²CO emission in M 82 peaks at J_up = 7, quickly declining towards higher J. These latter authors argued that turbulence from stellar winds and supernovae may be the dominant heating mechanism in this galaxy. Rosenberg et al. (2014a), studying NGC 253, concluded that mechanical heating plays an important role in gas excitation, although heating by UV photons is still the dominant heating source. The results from Pérez-Beaupuits et al. (2018) are also in agreement with those presented by Rosenberg et al. (2014a). We then selected the AGN–SB composite galaxy NGC 6240 for our analyses. Its ¹²CO SLED shows a similar shape to that of Mrk 231 but this is characterized by clear evidence of both shocks and mechanical heating (Meijerink et al. 2013). The ¹²CO SLED of one high-z dusty starburst sub-millimeter galaxy (SMG) analyzed by Cañameras et al. (2018) has been also considered.

We then derived the ¹²CO SLED for our AGN–SB composite galaxy NGC 4945 (Fig. 15). Comparing the different ¹²CO SLEDs normalized to the ¹²CO(1–0) flux of each individual galaxy, NGC 4945 seems to show a similar behavior to that found in Mrk 231 (AGN-dominated object) and M82 (SB galaxy) up to J_up ∼ 8; it then resembles Mrk 231 at 8 <  J_up <  13, before finally showing a trend in between those shown by Mrk 231 and NGC 6240 (AGN-SB galaxy) in the range 14 <  J_up <  20. The similarity of the ¹²CO SLED shape at higher J transitions to those characterizing Mrk 231 and NGC 6240 provides clues as to the presence of X-ray or shock mechanisms dominating at higher frequencies.

6.1.1. The dominant heating in NGC 4945

In order to quantify the contribution of the different heating mechanisms in NGC 4945 we applied the Kazandjian et al. (2015) models to investigate the effects of mechanical heating on molecular lines. According to their models, these latter authors found that the emission of low-J transitions alone is not good enough to constrain the mechanical heating (hereafter, Γ_mech) while the emission of ratios involving high-J (and also low-J) transitions is more sensitive to Γ_mech. The strength of Γ_mech is parametrized using the parameter α, which identifies the ratio between the mechanical heating, Γ_mech, and the total heating rate at the surface of a pure PDR (no mechanical heating applied), Γ_surf. This ratio can take values between 0 and 1. In particular, α = 0 corresponds to the situation in which no mechanical heating is present in the PDR, while α = 1 represents the model where the mechanical heating is equivalent to the heating at its surface (see Rosenberg et al. 2014a; Kazandjian et al. 2015). In their models, Kazandjian et al. (2015) assume that mechanical feedback processes like young stellar object (YSO) outflows and supernova (SN) events are able to heat the dense molecular gas. The former inject mechanical energy into individual clouds, while the latter inject mechanical energy into the star-forming region amongst the PDR clouds by turbulent dissipation. The mechanical energy liberated by these events is then deposited locally in shock fronts (see Loenen et al. 2008; Kazandjian et al. 2015).

For NGC 4945 we considered the observed ¹²CO fluxes up to J_up = 16 (PACS data). In order to properly constrain the ¹²CO SLED, we complement our SPIRE and PACS data with ground-based data obtained by Hitschfeld et al. (2008) at lower J transitions (J ≤ 4) using NANTEN2. The angular resolutions used in their work for the ¹²CO transitions from J_up = 1 to 4 vary from 45″ to 38″ (see Table 2 in their work). We scaled all these data using the largest angular resolution of 35″ as derived from the Herschel data.

The model which better reproduces our data has been identified by the use of the minimum reduced chi-square²¹ value (${\chi }_{\text{red}}^2~0.8$). The results are shown in Fig. 15 (right panel). According to the best-fit result we find that NGC 4945 is characterized by medium to high gas density (log n_gas = 3.0–5.0 cm⁻³) and FUV incident flux, G₀ ²², ranging from 10 up to 10⁶. We properly fit the observed ¹²CO emission using three PDR functions (mPDRI, mPDRII, mPDRIII), all of them requiring additional mechanical heating. Two of them (mPDRI, mPDRII) have α = 0.1 while the third model (mPDRIII) has α = 1.0 (or 0.75 according to the second-best fit value). For mPDRI, the α value translates into Γ_mech ∼ 4 × 10⁻²⁴ erg s⁻¹ cm⁻² while mPDRII is characterized by Γ_mech ∼ 3 × 10⁻²⁰ erg s⁻¹ cm⁻². For mPDRIII, the highest mechanical heating is achieved, Γ_mech ∼ 5 × 10⁻¹⁹ erg s⁻¹ cm⁻². According to these results, it is apparent that mechanical heating is needed to reproduce the observed data. Indeed, in contrast to the results derived for the SB galaxies NGC 253 (Rosenberg et al. 2014a; Pérez-Beaupuits et al. 2018) and Arp 299 (Rosenberg et al. 2014b), the shape of the ¹²CO ladder of NGC 4945 is flatter at higher J transitions (PACS; left panel in Fig. 15). In our case, the contribution of shock (or turbulent) heating is the main source of excitation for ¹²CO emission at J_up > 9–10. On the other hand, photoelectric heating seems to be the main source of heating at low- and mid-J transitions (J_up <  10).

These results confirm that at a resolution of 35″, physical processes like turbulent motions or shocks are able to excite the gas mechanically in the central region of NGC 4945. In the following section, we propose a plausible interpretation of the mechanical heating able to explain the emission of the high-J¹²CO lines detected with PACS.

Cañameras et al. (2018) analyzed a sample of sub-mm galaxies at high-z, deriving the G₀ and n_gas parameters. For their sample, they derived a typical gas density and a FUV radiation field in the range log n_gas ∼ 4–5.1 cm⁻³ and log G₀ ∼ 2.2–4.5 (in Habing units), comparing their values with those derived by Malhotra et al. 2001 for normal star-forming galaxies, namely log n_gas = 2–4 cm⁻³ and log G₀ ∼ 2.5–5 (in Habing units), and with those derived by Davies et al. 2003 for local ultra luminous infrared galaxies (ULIRGs): log n_gas = 4–5 cm⁻³ and log G₀ ∼ 3–5 (in Habing units). The values shown in Fig. 9 in their work can be used to compare our results with those obtained for these samples. For instance, in the case of the SB galaxy NGC 253 (Rosenberg et al. 2014a), a (mean) density of log n_gas ∼ 5.1 cm⁻³ and FUV radiation field of log G₀ ∼ 5.0 can be derived. For NGC 4945, we obtained (mean) values of log n_gas ∼ 4.6 cm⁻³ and log G₀ ∼ 5.5. Our results place NGC 4945 in the region covered by local SB galaxies (as NGC 253) and ULIRGs with similar density but characterized by higher FUV radiation.

From the results presented by Hollenbach et al. (1991) we are also able to derive a first-order estimate of the incident FUV flux radiation, G₀, assuming FUV heating from the dust properties derived in Sect. 3.2 following the equation:

$$\begin{array}{c}\hfill G_0=3.7\times {10}^{-3}{\tau }_{100\mu \mathrm{m}}{T}_{\mathrm{dust}}^5.\end{array}$$(8)

We used the opacity τ computed at 100 μm (τ_100 μm ∼ 1.2) estimated from the SED fitting assuming that the dust temperature is similar to the equilibrium dust temperature at the surface of the emitting region. Based on the SED fitting results (Sect. 3.2), we obtain two dust temperature components from which we derive log G₀ ∼ 5.8, similar (slightly higher) to that found for the cold component in NGC 253 (i.e., log G₀ ∼ 5.5; see Pérez-Beaupuits et al. 2018) and consistent with that found from the models (∼5.5).

On the other hand, the n_H2 densities derived from the LTE and LVG models applied to the ¹²CO molecule using HIFI and APEX data are in the range of n_H2 ≲ 10⁴–10⁵ cm⁻³. These values are in good agreement with the densities derived with the PDR model (n_H2 ∼ 10³–10⁵ cm⁻³).

6.1.2. Mechanical heating: the bar potential

According to the results derived in the 2D thermal structure analysis performed at different spatial scales (from ≲200 pc to 2 kpc) and focusing on the emission of the ¹²CO molecule from the J = 4–3 to 20–19 transitions we can make the following conclusions for the four regions:

• 700 pc–2 kpc: The ¹²CO/IR ratio of the low-J lines (J_up <  10) is larger by a factor of ≲2 in the inner 700 pc than in the surrounding region (2 kpc). However, for mid-J lines (J_up = 11–13), the ¹²CO/IR values are similar in both regions.

• Inner 700 pc: The LTE analysis of the inner 700 pc, which includes the whole range of ¹²CO lines (from J_up = 4 to 20), shows that the ¹²CO emission can be explained by a two-component model with temperatures of 80 K and 330 K and source sizes of about 20″ (400 pc) and 7″ (∼150 pc), respectively.

• 360 pc–1 kpc: The ¹²CO/IR ratios peak at the mid-J (J_up = 9, 10) lines in the central and northwest spaxels: this is in very good agreement with the distribution of the X-ray outflow (i.e., perpendicular to the disk of the galaxy, in the northwest direction). Normalizing for this contribution, we derive increased ¹²CO/IR ratios for the highest mid-J lines (J_up = 11 and 12) in the ring structure, in particular along the galaxy plane and toward the west. This result lets us argue that shocks probably dominate at these frequencies.

• Inner 200 pc–360 pc: The LTE analysis of the high-J¹²CO lines confirms the trend found at larger scales. The highest temperatures (∼560 K) are found around the nucleus (T ∼ 360 K, after correcting for the nuclear extinction), in the north–south direction along the galaxy disk.

We thus find a clear trend in the distribution of the excitation temperatures and the ¹²CO/IR ratios. At large scales (>700 pc), the highest temperatures are found toward the nucleus and the north, with moderate temperatures in the south. The high temperatures in the north might be related to the large-scale X-ray outflow. It is remarkable that, at almost all scales < 700 pc, the highest temperatures are not found toward the nucleus but toward the disk. As found at large scales, at intermediate scales (360 pc–1 kpc) we also see high temperatures in the direction of the X-ray outflow. At the smallest scales (∼200 pc), we clearly see that even if the largest column density is found in the nucleus, the highest temperatures are found in the disk.

This result is an agreement with that derived by Lin et al. (2011). In their work these latter authors analyzed the ¹²CO(2–1) emission of the central region (20″ × 20″) of this galaxy in detail using SubMillimeter Array (SMA) data, mainly focusing on its circumnuclear molecular gas emission. They showed that the S-shaped structure of the isovelocity contours can be well reproduced by the bending generated by a shock along the spiral density waves, which are excited by a fast rotating bar. As a result, their simulated density map reveals a pair of tightly wound spirals in the center which pass through most of the ring-like (claimed to be a circumnuclear SB ring by other authors) high-intensity region and also intersect several Paα emission line knots located outside the ring-like region (Fig. 16). According to their scenario, the inner region of NGC 4945 is characterized by high column density surrounded by lower values in the nearby spaxels. As shown in Fig. 16, high-density regions correspond to low temperatures, and vice versa, in very good agreement with our PACS results.

Fig. 16. Comparison between the results obtained at small scales using PACS (left) with those derived in Lin et al. (2011) (right). Left: excitation temperature (Tex; red colors) and column density (log NCO; blue colors) values derived using PACS data for the inner spaxels. The highest temperatures are found in correspondence of the two spaxels closed to the nucleus, in the northern and southern directions, while the peak in the column density is found in the central spaxel. Right (back): simulated spiral density waves overplotted to the velocity structure (Lin et al. 2011) in a FoV of 20″ × 20″. High density values are in red while lower values are in blue. Right (front): corresponding PACS spaxels overplotted onto the same FoV to show the respective excitation temperature distribution derived from PACS data. Higher values of the simulated density map reveal a pair of tightly wound spirals in the center which correspond to the highest NCO and lower Tex in PACS data. On the other hand, lower values in the surface density correspond to higher Tex and lower NCO according to PACS. North is at the top and East to the left.

Our data do not have the high angular resolution required to reveal the distribution of the thermal structure of this region. However, Henkel et al. (2018), using ALMA data, find their results to be in good agreement with the simulated results presented by Lin et al. (2011). As mentioned in Sect. 1, Henkel et al. (2018) find the presence of a dense and dusty nuclear disk (10″ × 2″) which encloses an unresolved molecular core with a radius of ≲2″ (of the same size as the X-ray source observed with Chandra). At scales larger than those shown by Lin et al. (2011), Henkel et al. (2018) also observed the presence of two bending spiral-like arms (one in the west turning toward the northeast and one in the east turning toward the southwest) at a radius of ∼300 pc (∼15″) from the center. The arms are connected through a bar-like structure with a total length of ≲ 20″ along the east–west direction. These latter authors also propose the presence of an inflow of gas from 300 pc down to 100 pc through the bar (see Fig. 26 in their work).

At the spatial scales sampled by our data, we find good agreement between the presence of a bar-like structure and tightly wound spiral arms (see Ott et al. 2001; Chou et al. 2007; Lin et al. 2011; Henkel et al. 2018 and our results). Accordingly, the mechanical heating produced by shocks, and possibly also driven by the outflow and by the bar potential, dominates in NGC 4945 at scales ≲20″ (≲360 pc).

6.2. Dust heating

Understanding the nature of the source that heats the dust in the nuclear regions of NGC 4945 is a topic under discussion. Many works suggest that the circumnuclear starburst, rather than the AGN activity, is the primary heating agent of the dust.

From the work by Brock et al. (1988), we know that ≲80% of the total infrared emission of this object is enclosed in a region no larger than < 12″ × 9″. This size is comparable to the continuum source we derived from the multi-wavelength SED fitting analysis (20″ × 10″) and for which we find two dust temperatures of 28 and 50 K. Within this area we find a total mass of dust of ≲10⁷ M_⊙, in agreement with previous works (Weiß et al. 2008; Chou et al. 2007). The dust temperature we obtain is lower than the excitation temperature of the mid-J¹²CO, characterized by energies from 55 K to 500 K above the ground state, as expected from mechanical heating.

Similar continuum source sizes at millimeter wavelengths have been derived by Chou et al. (2007) and Bendo et al. (2016). Chou et al. (2007) derived a deconvolved continuum source size of 9.8″ × 5.0″ at 1.3 mm and slightly smaller (∼7.6″ × 2.0″) at 3.3 mm. These emissions are not aligned with either the starburst ring or the larger galactic disk observed in Paα by Marconi et al. (2000).

The size of the continuum source derived by Chou et al. (2007) at centimeter wavelengths is much smaller (i.e., 7.4″ × 3.4″ at 21 cm) than that measured at 1.3 mm. Furthermore, the centimeter continuum source size and inclination are comparable with those of the starburst ring (i.e., ∼5″ or 100 pc-scale and position angle ∼45 degrees). Chou et al. (2007) proposed that at cm wavelengths the star formation activity (as SN events) in the SB ring can produce the nonthermal (synchrotron) emission which dominates at these wavelengths. They conclude that the dust emission dominates at 1.3 mm (and at 3.3 mm, with a radius of 4.9″), mainly heated by the star formation activity. The different origin of the dust emission at mm and cm wavelengths helps us to understand the different continuum source sizes obtained.

On the other hand, Bendo et al. (2016) analyzed the continuum emission at 85.69 GHz and the H42α emission line deriving a comparable size (∼7″ × 1.7″) to those measured by previous works at similar frequencies and emission lines (Ott et al. 2001; Cunningham & Whiteoak 2005; Roy et al. 2010). Bendo et al. (2016) support the hypothesis that if the gas around the nucleus were photoionized by the AGN then they would expect to see a central peak excess in their exponential disk model (with scale length of 2.1″). Indeed, the spatial extent of the emission derived in their work, and the absence of the peak excess and of any broad line emission, suggest that both (continuum and line) emissions originate from the gas photoionized from the circumnuclear SB, and not from the AGN.

Our results suggest that star formation (in the circumnuclear SB) is the main driving activity able to heat the dust. Unfortunately our data do not have the high angular resolution required to reveal the distribution of the thermal structure of the inner region. Continuum observations at higher angular resolutions, such as those feasible with the Stratospheric Observatory For Infrared Astronomy (SOFIA; Young et al. 2012) airborne observatory, are required to obtain photometric measurements of the dust continuum in the FIR in order to disentangle and characterize the contributions from the SB and the central AGN.

7. Summary and conclusions

We used data from the HIFI, SPIRE, and PACS instruments onboard the Herschel satellite and APEX to study the properties of the molecular ISM in the nearby galaxy NGC 4945, a remarkable prototype AGN–SB composite galaxy. The spectroscopy data presented in this paper include a combination of low- and high-density molecular gas tracers such as ¹²CO, ¹³CO, HCN, HNC, CS, [CI], HCO⁺ and CH. The main focus of the paper is to study the spatial distribution of ¹²CO emission over a large frequency range covering transitions from J = 3–2 to 20–19 by combining all data available from the instruments mentioned above. We also preset the SED of the dust continuum emission from 20 μm to 1.3 mm.

Under the assumption of LTE (analysis using MADCUBA) excitation, we derived the excitation temperature T_ex and the molecular column density N_mol for ¹²CO, ¹³CO, HCN, HNC, CS, [CI], HCO⁺ and CH by combining HIFI and, when available, APEX data. The highest column densities are found for ¹²CO, ¹³CO, and [CI], ranging between log N_mol ∼ 16.5–17.5 cm⁻². For the remaining molecules, we derived a column density in the range log N_mol = 13–14 cm⁻² and T_ex between 20 and 30 K. According to the NLTE approach (using RADEX) we derived moderate volume gas densities, with n(H₂) in the range 10³–10⁶ cm⁻³. Lower values are derived for ¹²CO, ¹³CO, and [CI], while higher values are obtained for the high-density gas tracers such as HCN, HNC, HCO⁺ and CS. From the low and high-density tracers in NGC 4945 we derived gas volume densities (10³–10⁶ cm⁻³) similar to those found in other galaxies with different types of activity.

We used the SPIRE and PACS spectroscopic data applying the LTE (multi-line transitions) analysis to derive the thermal and column density structures of the molecular gas ¹²CO for scales raging from < 200 pc up to 2 kpc. We also analyzed the ¹²CO SLED applying the Kazandjian et al. (2015) models. Our main results can be summarized as follows:

• At large scales (700 pc–2 kpc), as obtained from SLW SPIRE, we find that high temperatures are mainly found in the northern part of the galaxy as well as in the disk plane. This suggests that the presence of the outflow might affect the temperature observed in the northwest direction. Column densities are higher in the center and towards the south direction.

• At intermediate scales (360 pc–1 kpc), such as those obtained from the SSW SPIRE data, the heating is distributed along the disk plane and in the south direction as well. The column density follows a similar trend to that shown at larger scales, and is characterized by high values in the center and towards the south.

• When moving to smaller scales (∼200 pc), using PACS data, we find a peak in the column density in the central spaxel surrounded by lower column density but higher excitation temperatures. This result is an agreement with that derived by Lin et al. (2011), who proposed the presence of tightly wound spirals in order to explain the distribution of the surface density and the related velocity field in a 20″ × 20″ region.

• The thermal structure derived from the ¹²CO multi-transition analysis suggests that shocks seem to dominate the heating of the ISM in the nucleus of NGC 4945 located beyond 100 pc from the center of the galaxy. This result is confirmed by the mechanical heating models, which suggest the existence of PDRs but mainly dominated by mechanical heating (i.e., feedback from SNe) in the inner regions of NGC 4945. We propose that shocks are likely produced by the barred potential and the outflow observed in the optical and X-ray bands. The high temperatures in the north and northwest directions found at larger scales might be related to the outflow.

• The SED in NGC 4945 was obtained by combining photometric data from FIR (MSX, PACS and SPIRE) and sub-mm (LABOCA) and mm (SMA) data. From the SED fitting analysis we find that the source is resolved at these wavelengths. We find a good fit when two modified black-body functions are considered, characterized by a cold (T ∼ 28 K) and a warmer temperature component of 50 K and a source size of Ω_s = 20″ × 10″. Assuming a gas-to-dust ratio of between 100 and 150, for NGC 4945 we derive a total gas mass in the range ∼8–11 × 10⁸ M_⊙ in a region of 40″ × 40″. This result is consistent with the gas mass estimations derived in previous works (Weiß et al. 2008);

• The hydrogen column density derived from the SED fitting is in good agreement with that derived by Wang et al. (2004) using ¹²CO(1–0) and ¹²CO(2–1) transitions. NGC 4945 is characterized by N(H₂) ∼ 5 × 10²³ cm⁻²: this value is larger than those obtained for local SB galaxies (e.g., NGC 253) and similar to those obtained for Compton-thick Seyfert 2 galaxies.

The results obtained in this work seem to confirm that the presence of the AGN in NGC 4945 has little impact on the thermal properties of its nuclear SB. Infrared observations at higher spatial resolution are required to characterize both the dust and molecular line emissions. Spectroscopic and photometric observations, such as those that could be achieved by the instruments onboard SOFIA (e.g., HAWC+, CASIMIR and/or GREAT), are needed in order to characterize the physical conditions of the emission itself in the very inner regions of NGC 4945, such as the temperature, density, and structure.

Acknowledgments

We thank the anonymous referee for useful comments and suggestions which helped us to improve the quality and presentation of the manuscript. E. B. acknowledges the support from Comunidad de Madrid through the Atracción de Talento grant 2017-T1/TIC-5213. J.M.P. acknowledges partial support by the MINECO and FEDER funding under grant ESP2017-86582-C4-1-R and PID2019-105552RB-C41. M.A.R.T. acknowledges support by the APEX project M-081.F-0034-2008. S.G.B. acknowledges support from the research projects PGC2018-094671-B-I00 (MCIU/AEI/FEDER, UE) and PID2019-106027GA-C44 from the Spanish Ministerio de Ciencia e Innovación. This work is based on observations acquired with the Herschel Satellite, obtained from the ESA Herschel Science Archive, and with the APEX antenna, obtained from the project M-081.F-0034-2008. This research has made use of: (1) the ESA Herschel Science Archive; (2) the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

References

Appendix A: Deriving the flux density values for the SED fitting analysis

In this Appendix we explain how the flux densities used in the SED fitting in Sect. 3.2 are computed for the different wavelengths. The additional data are given in different units. We then summarize the several conversion factors applied to transform the flux densities into Janskys as well as the formula applied for the conversion. In Table A.1 we show the computed flux density values (with their associated errors), the conversion factors, and the pixel sizes for each band.

• For the MSX catalog we used the following formula:

  $$\begin{array}{c}\hfill F({40}^{″})=F_{\mathrm{OBS}}·\mathrm{CF}·{\left(\frac{\mathrm{pixel}}{3600}\frac{2\pi }{360}\right)}^2.\end{array}$$(A.1)

  The conversion factors (CFs) are used to transform the [W m⁻² sr⁻²] into [Jy sr⁻¹] and they have been taken from the website²³.

• Taking into account the LABOCA data from Weiß et al. (2008) we considered the flux density of 15.8 (±1.6) Jy computed in a beam of 80″ × 80″. From their work we also know that in a beam of 19″ × 15″ (average beam 17″) the flux density is 7.2 (±0.8) Jy. If we assume uniform emission outside the beam of 17″ (<80″) we are able to compute the flux density in an annular beam with a size in between 17″ and 40″:

  $$\begin{array}{c}\hfill \frac{(15.8-7.2)[\mathrm{Jy}]}{({80}^2-{17}^2)[\mathrm{arcsec}]}·({40}^2-{17}^2)[\mathrm{arcsec}]=1.85[\mathrm{Jy}].\end{array}$$(A.2)

  This can be considered a reasonable assumption according to the LABOCA data from which we derived that half of the total flux density emission is enclosed in a beam ≲20″, while the remaining emission is diluted in the annular beam between ∼20″ and 80″.

  Finally, to derive the flux density in a beam of 40″, we added the flux density value obtained in the annular beam to the flux density obtained in a beam of 17″. This gives a total flux density (in a beam of 40″) of 7.2 Jy + 1.85 Jy = 9.05 (1.3) Jy.

All Tables

All Figures

Fig. 1. Left: combined image of X-ray emission from Chandra (low energy: magenta, high energy: blue) overlaid on an optical image from ESO. Credits from NASA/CXC/Univ degli Studi Roma Tre/Marinucci et al. (2012), Optical: ESO/VLT & NASA/STScI. Right: cartoon of the central region (<1 kpc) of NGC 4945. The optical image shown in the left panel is used as the background. The size (diameter) of the different components observed in the (soft and hard) X-ray, NIR, and radio bands are highlighted: the limb-brightening “plume” in soft X-rays as well as the nuclear hard X-ray emission region (Marinucci et al. 2012), the starburst ring in Paα (Marconi et al. 2000), and the nuclear molecular disk along with the unresolved molecular core (Henkel et al. 2018).

In the text

	Fig. 2. SLW (upper panel) and SSW SPIRE (lower panel) spectra corresponding to the peak emission in the same FoV in the rest-frame frequency. 12CO lines are shown in blue while fine structure lines, such as [CI] and [NII], are indicated in red. Other molecular species observed in emission and/or absorption are shown in green.
In the text

Fig. 3. Photometric images of NGC 4945 at the PACS (70, 100 and 160 μm; top) and SPIRE (250, 350 and 500 μm; bottom) wavelengths. The flux units have been converted to Jansky for both the PACS and SPIRE data (see text for details). The black circle in each panel identifies a beam of 40″ × 40″. From PACS 70 μm to SPIRE 500 μm wavelengths, an aperture of 40″ corresponds to 25, 25, 12.5, 6.7, 4, and 3 pixels, respectively. The black cross represents the peak emission in each band.

In the text

Fig. 4. SED-fitting results for NGC 4945. The best-fit solution (red solid line) is obtained when two dust components with temperatures of 28 K (blue MBB) and 50 K (green MBB) are needed, assuming a source size of 20″ × 10″. The total dust mass obtained from the fit is ≲107 M⊙. The SPIRE and PACS data are shown using red and violet squares, respectively. Additional data used in the fit are shown in filled black squares. In particular, at shorter frequencies the SMA (Chou et al. 2007) and LABOCA (Weiß et al. 2008) data were added (see text for details) obtaining a β parameter of 2.0. At higher frequencies the MSX data point is considered in the fit while two IRAC data points are only shown for completeness (in gray).

In the text

Fig. 5. High resolution molecular spectra from APEX and HIFI for all molecules analyzed in this work. The observed spectra and LTE fit obtained using MADCUBA are shown in black and red, respectively. For the 12CO molecule, we highlight a cold (blue) and a hot (green) component because two temperature components were needed to properly fit the emission. For each APEX (Jup ≤ 4) and HIFI (Jup≥ 5–9) spectrum, the J transitions are identified. Other detected molecular species like CH, 13CH and 12CO (in the image band) are shown in green. For each molecule the range in temperature is the same for all J (APEX and HIFI) transitions with the exception of 12CO and HCN, which show different ranges to better appreciate the fainter emission of the HIFI data. The emission is shown in main beam temperature (TMB) in kelvin.

In the text

	Fig. 6. LTE results derived with MADCUBA for each individual molecular species. From left to right: excitation temperature, Tex, in kelvin, along with the molecular column density, Nmol, in units of cm−2.
In the text

Fig. 7. From left to right: schematic view of the different FoVs involved in the analysis of SLW, SSW SPIRE, and PACS data. Left: in the SLW SPIRE map the green square highlights the FoV considered in the analysis (∼100″). These data are characterized by a beam of 35″ identified by the yellow small square. Middle: in the SSW SPIRE map the yellow square represents the 3 × 3 spaxels area involved in the analysis. The map is characterized by a beam of 19″ (small black square). Right: in the PACS map the black square identifies a FoV of ∼19″ (i.e., one SSW SPIRE spaxel) while the yellow square identifies a FoV of ∼35″. The star symbols represent those spaxels where the 12CO emission is observed: in particular, white stars highlight the spaxels characterized by stronger 12CO emission than that observed in the remaining spaxels marked using yellow stars. PACS data are characterized by a beam of 9.4″.

In the text

Fig. 8. Left:12CO(8–7) emission map showing a FoV of 3 × 3 spaxels (35″ each; light green square) considered when combining the SSW and SLW SPIRE data at the same resolution (i.e., 35″, large spatial scale). The peak emission (in red) and a ring of one spaxel width around that maximum (green area) are identified. Middle: excitation temperatures (Tex) and the (logarithmic) column densities (NCO) are derived for each spaxel using the rotational diagrams. The yellow boxes represent the spectra characterized by high Tex and NCO values. Right:12CO/IR flux ratios computed for the different J transitions in the SPIRE domain. In red are shown the values derived at the position of the flux density peak (spaxel #5 in the left panel) while in green the ratios derived integrating the emission in the ring. The ratio between the maximum peak and the ring for each transition is also shown (i.e., “peak-to-ring ratio”, in blue) divided by 100 (a factor of 100 has to be applied to obtain the real values). The dashed gray lines identify the lower and upper limit values of the peak-to-ring ratios computed within the errors. Higher 12CO/IR values are derived for high J (Jup ≥ 11–10) in the ring structure, implying lower (≲1) peak-to-ring ratios.

In the text

Fig. 9. Top: averaged SLW, SSW SPIRE (Jup = 4 up to 13), and PACS12CO spectra (Jup = 15 up to 20) of the central region combined together at the same resolution (35″). The original spectra are shown in black while the total simulated 12CO emission obtained from the LTE approach is shown in blue. Other molecular species like [CI] and OH are identified in emission (green). Bottom: table from MADCUBA showing the output parameter values (i.e., column density NCO, excitation temperature Tex, vLSR, FWHM of the line as well as the source size) deriving different source sizes for the cold and hot components.

In the text

Fig. 10. Bottom left:SPIRE SSW12CO emission maps showing the nine spaxels involved in the analysis. Top left: hard (green) and soft (red) X-ray emission from Chandra from Marinucci et al. (2012) of the outflow observed in the central region (∼1′ × 1′) in NGC 4945. Middle:12CO/IR results obtained using SSW SPIRE data (19″ beam) numbered following the scheme shown in the bottom-left panel. Right:12CO/IR results normalized to the emission of the central spaxel (red square).

In the text

Fig. 11. LTE results derived combining SSW SPIRE and PACS spectra. Top: distribution of the excitation temperature (Tex, top left) and column density (NCO, top right) derived applying MADCUBA to the combined SSW SPIRE and PACS spectra. The FoV covered by 3 × 3 spaxels (∼1′ × 1′) is the same as that shown in Fig. 10. Bottom: observed (black) and simulated (blue) 12CO emission spectra from combining SSW SPIRE and PACS. The spaxels are identified using the same number used in the top panel. For spaxels #3 and #6 only SPIRE data are available while for spaxels #1, #5 (central), and #8 SSW SPIRE and PACS data are combined together. The 12CO emission is found in the inner region (3 × 3 spaxels) and mainly located in the disk, with some contribution in the perpendicular direction.

In the text

	Fig. 12. Left: observed 12CO PACS spectra (black) along with the simulated Gaussian fit results (blue). The respective rotational transition (J + 1 → J) is shown for each spectrum. The flux emission is shown in main beam temperature (TMB). The OH emission lines close to the 12CO(16–15) transition are also observed (see Fig. 9).
In the text

	Fig. 13. Rotational diagrams derived for PACS data. The excitation temperatures (Tex) and the (logarithmic) column densities (NCO) with their respective uncertainties are derived for each spaxel.
In the text

	Fig. 14. Excitation temperature and (logarithmic) column density distributions at different spatial scales as derived using SPIRE (SLW, SSW) and PACS data. The yellow squares identify the spaxels with high values for each parameter.
In the text

Fig. 15. Left: comparison of 12CO SLEDs (normalized to the 12CO(1–0) flux of each specific source) obtained from different sources. Starburst, AGN, and AGN–SB sources have been considered. A 12CO SLED of a SMG at high-z analyzed by Cañameras et al. (2018) is also shown. Different colors identify the galaxies while different symbols indicate the types of objects. In each group, the following galaxies have been selected: M82 and NGC 253 as SB, NGC 6240 and NGC 4945 as AGN–SB composite galaxies, and NGC 1068 and Mrk 231 as AGN-dominated galaxies. The galaxy G244.8+54.9 has been chosen as representative of SMG at high-z, for which the authors derived log ngas ∼ 5.1 cm−3 and log G0 ∼ 3.7 (Habing units). Right: results of the 12CO SLED of NGC 4945 from J = 1–0 through 20–19 applying the Kazandjian et al. (2015) mechanical heating models. The black points are the observed 12CO fluxes obtained from ground-based observations (Hitschfeld et al. 2008) while in green are the data from this work. The fit was constrained to three PDR models, all of them with some contribution of mechanical heating (mPDR), displayed in green, magenta, and blue. Dashed gray lines show the other best-fit results for the three PDRs. The dashed blue line is also shown to represent a model with the same ngas and G0 parameters as those characterizing the PDRIII model but with no mechanical heating contribution (α = 0). The red line represents the best fit with the minimum ${\chi }_{\text{red}}^2$ (∼0.8) while the light red area shows the combination of other best fits with slightly higher χ2 (<1.4). The H2 density (i.e., ngas in log cm−3), G0 (log Habing flux), and percentage of mechanical heating α values are shown in the legend for the three best-fit components.

In the text

Fig. 16. Comparison between the results obtained at small scales using PACS (left) with those derived in Lin et al. (2011) (right). Left: excitation temperature (Tex; red colors) and column density (log NCO; blue colors) values derived using PACS data for the inner spaxels. The highest temperatures are found in correspondence of the two spaxels closed to the nucleus, in the northern and southern directions, while the peak in the column density is found in the central spaxel. Right (back): simulated spiral density waves overplotted to the velocity structure (Lin et al. 2011) in a FoV of 20″ × 20″. High density values are in red while lower values are in blue. Right (front): corresponding PACS spaxels overplotted onto the same FoV to show the respective excitation temperature distribution derived from PACS data. Higher values of the simulated density map reveal a pair of tightly wound spirals in the center which correspond to the highest NCO and lower Tex in PACS data. On the other hand, lower values in the surface density correspond to higher Tex and lower NCO according to PACS. North is at the top and East to the left.

In the text