Dense gas tracing the collisional past of AndromedaBased on observations carried out with the IRAM 30m radio telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).

# Dense gas tracing the collisional past of Andromeda1

An atypical inner region?
###### Key Words.:
galaxies: abundances; galaxies: individual: M31; galaxies: kinematics and dynamics; submillimeter: ISM; molecular data

The central kiloparsec region of the Andromeda galaxy is relatively gas poor, while the interstellar medium appears to be concentrated in a ring-like structure at about 10 kpc radius. The central gas depletion has been attributed to a possible head-on collision 200 Myr ago, supported by the existence of an offset inner ring of warm dust. We present new IRAM 30 m radio telescope observations of the molecular gas in the central region, and the detection of CO and its isotopes CO and CO(21), together with the dense gas tracers, HCN(10) and HCO+(10). A systematic study of the observed peak temperatures with non-LTE equilibrium simulations shows that the detected lines trace dense regions with n in the range  cm, while the gas is very clumpy with a beam filling factor of . This is compatible with the dust mass derived from the far-infrared emission, assuming a dust-to-gas mass ratio of 0.01 with a typical clump size of 2 pc. We also show that the gas is optically thin in all lines except for CO(1-0) and CO(2-1), CO lines are close to their thermal equilibrium condition at 17-20 K, the molecular hydrogen density is larger than critical, and HCN and HCO+ lines have a subthermal excitation temperature of 9 K with a density smaller than critical. The average CO/CO line ratio is high ( 21), and close to the CO/CO ratio () that was measured in the north-western region and estimated in the south-east stacking. The fact that the optically thin CO and CO lines have comparable intensities means that the secondary element C is depleted with respect to the primary C, as is expected just after a recent star formation. This suggests that there has been a recent starburst in the central region, supporting the head-on collision scenario.

## 1 Introduction

While the outer parts of the Andromeda galaxy exhibit numerous relics of past interactions (McConnachie et al. 2009), the main disc exhibits an enhanced star formation activity in a ring at 10 kpc (Ford et al. 2013) and the central part is atypical. The M31 galaxy hosts a very massive black hole with a mass of (Bacon et al. 2001; Bender et al. 2005) that is one of the most under-luminous supermassive black holes (Garcia et al. 2010), which is surrounded by very little gas (Melchior & Combes 2013). Infrared data and optical ionised gas display a 0.7 kpc off-centred inner ring, and Block et al. (2006) have proposed a frontal collision with M32 to explain this double ring structure. This collision would have occurred 200 Myr ago. In this paper, we present observations of millimetre molecular lines probing dense gas regions along the minor axis in the inner ring. In Sect. 2, we present the data used in this paper. In Sect. 3, we describe the data reduction. In Sect. 4, we describe our results and which physical information we can extract. In Sect. 5, we argue that our results support a 200 Myr old starburst triggered by the frontal collision with M32. For consistency with our previous analysis, we consider a distance of M31 of 780 kpc and a pixel size 1 arcsec 3.8 pc.

## 2 The data

### 2.1 Millimetre observations

We observed five positions listed in Table 1, which also gives the offsets and integration time. We computed the offsets with respect to the position of the optical centre ((J2000) 41) provided by Crane et al. (1992) and used in previous papers (Melchior et al. 2000; Melchior & Combes 2011, 2013). The observed positions lie in the inner 1 kpc ring along the minor axis (of the main disc inclined at 77 ). The total integration time for each position is provided in the last column. In Figure 1, these positions are superimposed on the Herschel 100 m map provided by Viaene et al. (2014) and A extinction contours computed in Melchior et al. (2000). In the 100 m and A maps, we can see the 0.7 kpc off-centred inner ring.

The observations have been performed with the IRAM 30 m radio telescope equipped with the EMIR receiver in the period 20-23 December 2011. They were performed in dual polarisation and the E0/E2 band combination were tuned in order to cover the following frequency bandwidths:

1. 87.4-91.4 GHz and 83.8-87.8 GHz (optimised for HCO+(1-0) and HCN(1-0))

2. 218.65-222.65 GHz and 214.95-218.95 GHz (optimised for CO(2-1) and CO(2-1)).

Two backends were connected to two main receivers: FTS with a spectral resolution of 0.19MHz and WILMA autocorrelator with a spectral resolution of 2MHz. WILMA was non-operational in some observations, and have mainly been used to check the quality of the observations. We smoothed the FTS data to the optimised resolution of 2.1 km s up to 34 km s. Observations were performed in non-symmetric wobbler mode to avoid sky subtraction from Andromeda’s main disc. The azimuthal radius of the wobbler was set to 240 arcsec or set manually, relying on the extinction map of the area (Melchior et al. 2000). As discussed by Greve et al. (1996), large wobbler throws reduce the sensitivity to point sources. However, this is restored to a large extent with an active near-focus correction. It is also possible that some emission is subtracted by the OFF signal. In principle, this would occur at a velocity different from the signal velocity, even though this cannot be excluded given the complex velocity pattern. One can also argue, on the basis of the detections discussed in the next section, that the emitted signal is weak, so the probability of chopping a strong source is small. As shown in the figures discussed below, there is no obvious sign of emission in the OFF measurements, so this is in the worst case a second order effect. In addition, these effects are expected to affect CO(2-1) and CO(2-1) similarly, as well as HCO+(1-0) and HCN(1-0). They could nevertheless affect the normalisation with respect to CO(2-1) and CO(1-0) obtained independently.

We retrieved CO(2-1) and CO(1-0) data from previous IRAM observations described in Melchior & Combes (2011, 2013) (and in prep.). CO(1-0) detection is only available for M31I.

### 2.2 Infrared data

The five positions observed at IRAM 30 m were observed by Herschel/SPIRE instrument. The 1-kpc ring hosts cold temperature gas, while inside the ring the gas is hotter and not detected at large wavelengths. We extracted different parameters relevant for our study from the work of Viaene et al. (2014) and Draine et al. (2014). These parameters are summarised in Table 2.

Draine et al. (2014) adjusted a physical dust model on Herschel and Spitzer observations to estimate the mean intensities of starlight heating the dust. These authors computed these mean intensities for the SPIRE 350/Herschel and MIPS 160/Spitzer resolutions of and , respectively. Viaene et al. (2014) account for two more photometric channels. The mean starlight recovered for both resolutions are provided in the second and third columns of Table 2. These differences have an amplitude comparable to the discrepancy between the inferred heating rate and the value predicted by a simple model of bulge starlight discussed by Draine et al. (2014). This provides an idea of the real uncertainty of these estimates, which smooth the substructures, while the corresponding resolutions (24.″9 and 39″) are comparable and larger than those of our millimeter observations (11″, 21″, and 28″; see Table 3). We then provide the cold dust temperatures computed according to the Draine & Li (2007) model as . In the studied area, Draine et al. (2014) find that the starlight heating intensity is compatible with the stars in the bulge, as found by Groves et al. (2012). Relying on Herschel data, as well as GALEX, SDSS, WISE, and Spitzer, Viaene et al. (2014) model the spectral energy distribution to extract physical quantities. They estimate cold dust temperatures, which are similar to those derived from Draine et al. (2014), as shown in Table 2. The differences could be accounted for by the different datasets used as well as different modelling, Viaene et al. (2014) directly fit the spectral energy distribution, while Draine et al. (2014) relies on a physical model. Viaene et al. (2014) have also provided a warm dust temperature (labelled ”birth cloud” in their paper) larger than in the surrounding regions. This suggests that there are substructures linked to recent star formation, corresponding to (weak) star-forming activity (3-15MMyr). We can expect the kinetic temperatures to be equal at most to the dust temperature, depending on the molecular hydrogen density. In the following, we consider a kinetic temperature of 20 K, which corresponds to the cold gas temperature.

## 3 Data reduction

We used the CLASS4 package for the data reduction. We inspected individual spectra. Various interference lines are present far from the expected astronomical signals. These interference lines affect the determination of the baselines, and they have been carefully removed on each spectra. The M31I position has suffered an interference next to the strongest peak of the CO(1-0) line. This interference only affects the data acquired on 20 December 2011 (18/30). We thus set to zero the corresponding channels on data taken with the FTS backend with the best spectral resolution (0.26 km s).

The observations averaged in the two main bandwidths are presented in the Figs. 2 and 3. We used default weighting with exposure time and system temperature. These spectra reveal multicomponent signals corresponding to the Andromeda velocity range (given its systemic velocity of -300 km s).

Characteristics of the main astronomical molecular lines (Schöier et al. 2005) present in the observed bandwidths are provided in Table 3 as follows: half power beam width (HPBW), beam efficiency, rest-frame frequency, and velocity bin corresponding to 14 MHz. We also provide the following characteristics of these molecules: energy level, Einstein coefficient A, collisional de-excitation rate C, and critical density n computed at 20 K. If we consider a collisional temperature of 50 K, the critical densities of HCN and HCO+ increase by 56 and 21, respectively, but by 7.4 for CO. As indicated in Figs. 2 and 3, there are obvious detections of HCO+(1-0), HCN(1-0), and CO(2-1) in the summed spectra and a weak signal in CO(2-1). There is no obvious contamination from the Milky Way, which could be possible as M31 is 20  below the Galactic plane. The spectra obtained in the lower outer bands are presented in Fig. 15 but do not exhibit any signal. They are used to derived upper limits. For each position, the detections are adjusted with a Gaussian function. Up to three different CO lines are detected at different central velocity at each position. As discussed in Melchior & Combes (2011), this is due to several intervening molecular components along the line of sight.

All of the measurements are summarised in Table 4. The columns on the right side provide the CO line measurements. We provide, for each CO line, the central LSR velocity, the FWHM velocity dispersion v, the peak (main-beam) temperature T, and the integral I of the line. In the last two columns, the CO/CO(2-1) and CO/CO(2-1) line ratios and lower limits are shown. We also provide (in the bottom of this table) our CO(1-0) measurements described in Melchior & Combes (2011) for M31-I with a beam resolution of 21 arcsec, similar to the resolution achieved for HCN(1-0) and HCO+(1-0), and the N column density derived as discussed below but directly computed from CO(1-0). These column density estimates differ by up to a factor of 3 with respect to CO(2-1)-based estimates, due to the difference in resolution and corresponding dilution effects.

The columns on the left side of Table 4 list HCN(1-0) and HCO+(1-0) measurements and 3 upper limits (for v32 km s) for some of the lines presented in Table 3. The central table provides the remaining upper limits, as well as column densities (and upper limits) of the species with some detections, namely CO, CO, HCN, and HCO+, assuming local thermal equilibrium (LTE) and optically thin conditions. The column densities have been corrected for the beam filling factor, as further discussed in the next section. Given the velocity dispersion of the observed HCN lines (25 km s), the HCN hyperfine line structure ( 10 km s) will not be detected. We also provide the N column densities of molecular hydrogen relying on X and CO(2-1)/(1-0) line ratio values. We assume a Galactic ratio Xcm(K km s) following Strong et al. (1988) and Dame et al. (2001), which is compatible with the findings of Smith et al. (2012) for Andromeda and Mauersberger et al. (2003) for local galaxies. As further discussed in Sect. 4.3, we take . We assume a CO(2-1)/(1-0) line ratio of 0.8, as measured by Melchior & Combes (2011) in a clump located within 10 ″of M31I (and named M31G), to compute column densities.

## 4 Results

In this section, we describe our results. In Sect. 4.1, we describe the detections of five different molecular emission lines in the two observed positions along the minor axis. In Sect 4.2, we compute the line ratios relying on previous detections and compare them with previous results achieved in other galaxies, in particular, Galactic giant clouds and in M31’s disc. In Sect. 4.3, we discuss the basic properties we can derive from the detections, including excitation temperatures, optical depths, beam filling factors, and column densities, and the uncertainties and limitations of this type of analysis. In Sect. 4.4, we discuss the parameters estimated under LTE conditions and compare them with Galactic values. In Sect. 4.5, we run RADEX (van der Tak et al. 2007) simulations to relax the LTE conditions and test the validity of our previous assumptions. While CO emission lines correspond to gas in thermal equilibrium, gas traced by HCN and HCO+ emission lines is under subthermal excitation conditions.

### 4.1 Description of the detections

The CO lines detected in the north-west (south-east) region are shown in Fig. 4 (Fig. 5). The HCN(1-0) and HCO+(1-0) lines detected on the north-west side are shown in Fig. 6.

As shown in Table 4, we detected up to five different molecular lines (two to four per position and per velocity component). For some positions (M31I, M31I-B, M31-2d-a), there are clearly several well-identified peaks with different velocities, while for other positions the signal is very wide and best fitted with several components. The most striking cases are M31-2c-a, and the low-velocity component of M31-2d-b. The 4 CO(2-1) signal measured for M31-2c-a is affected by a small integration time and the detection integrates several CO components. Hence, this signal is not used for subsequent stacking. Apart from the CO and some CO lines, the detections are weak with peak temperatures at the mK level. We detected HCO+(1-0) (HCN(1-0)) at the 6 and 9 (4 and 5) levels, while most CO(2-1) detections are above 4 with a strong one at 11; but three weak CO detections in the south-east region are kept at the 3.3 level. Knowing the low intensities of these lines, we can infer that it is extremely challenging to perform multi-transition observations of these molecules.

While CO and CO are detected on both regions, CO, HCN(1-0) and HCO+(1-0) are only detected on the north-west side. If the dust-to-gas mass ratio is similar on both sides, according to Viaene et al. (2014) we expect a gas mass a factor of 3 larger on this side (see Table 2). Similarly, when one averages the observed column densities of molecular hydrogen provided in Table 4 along the two lines of sight, the north-west positions have a column density a factor of 2 higher than the south-east positions. Also, the radiation field (U) is larger on the south-east side than in the north-west side: this may be related to larger CO column densities and to the fact that dense gas (CO, HCN, HCO+) is not directly detected in the south-east positions.

The CO detection corresponds to the component at the systemic velocity, while the HCN and HCO+ detections are in the blueshifted components. However, as shown in Fig. 7, stacking of the  km s CO detections (excluding the M31-I(3) detection) also reveals a redshifted component in CO with an amplitude comparable with CO. The characteristics of this stacking detection is presented in Table 5. We thus have at least two different CO components in two different velocity ranges.

Figure 16 denotes the stacking of v km/s and v km/s of HCN(1-0) and HCO+(1-0) spectra. The detected signals are summarised in Table 5. The south-east spectra have been shifted to the CO velocities and averaged with standard weights (). For HCN, there is 3.7 detection in the blue stacking while there is a possible 2.6 detection in the red stacking. In contrast to the direct observations, the stacked HCN signal is stronger than the HCO+ signal, with a HCO+/HCN line ratio of in the red stacking and in the blue stacking.

The difficulty of the interpretation of these dense gas detections is due to a complicated configuration. We integrate the signal over a relatively large beam (42-106 pc in projection), and the velocity dispersions are significantly larger than those (2 km/s) detected in M31’s main disc (Schruba et al., in prep) with  km s for most of our detections. This is because of the strong velocity gradient present in this region and to the superposition of several clouds. This also points towards inner elongated orbits observed with a large radial velocity range (in contrast to the outer orbits observed in the main disc where small velocity dispersions ( 2 km s) are expected and observed). M31-I(1) has a smaller velocity dispersion, which is still four times larger than disc clouds. The other components of M31-I are very large and could correspond to an underlying (possibly continuous) component with a 150 km s width with non-circular orbits. This could be a relic of a spiral arm or dissolved bar.

### 4.2 Observed line ratios

In this section, we analyse the observed line ratios, which are directly derived from the observations.

When one computes line ratios based on velocity-integrated intensities as shown in Table 6, dilution effects due to the unknown beam filling factors should be removed at least at first order. Empirical comparisons with similar targets can be performed.

Figure 8 shows that our measured CO/CO(2-1) line ratios lie below the (1-0) measurements of Liu et al. (2014) in infrared Galactic dark clouds (average 4.41.3; see their Fig. 2), but corresponds to the lower end of the Tan et al. (2011) starburst sample distribution based on CO/CO(1-0) line ratio. Our measured line ratios are also significantly lower than the M51’s spiral arms gas detected by Schinnerer et al. (2010) (their average CO/CO line ratio: 3.5).

It is remarkable that the CO detection is at a level comparable to the CO detection, in contrast to what is observed in the Galaxy (e.g. Nishimura et al. 2015; Shimajiri et al. 2014), where the CO is usually 10 to 150 times weaker than CO. CO/CO line ratios close to one are expected if CO is optically thick or if C is depleted with respect to C, such as after a starburst.

In Fig. 9, we compare our CO/CO(2-1) line ratios with values measured previously in other galaxies. We consider the following catalogues:

• the (2-1) line ratio compilations for different morphological types from Krips et al. (2010) (We provide the different morphological types under the form of hatched histogram);

• the (1-0) line ratio measured by Li et al. (2015) in nearby galaxies;

• the (1-0) line ratio measured by Matsushita et al. (2010) in starburst and post-starburst galaxies; and

• the (1-0) line ratio measured by Tan et al. (2011) in nearby infrared-bright galaxies and starbursts.

The (1-0) line ratios have been corrected with the average CO/CO(1-0)/(2-1) ratio (1.33) from Krips et al. (2010). These authors found that the CO/CO(2-1) ratios of three SAURON galaxies are somewhat higher than those in galaxies of different Hubble types. The hatched histogram of Fig. 9 shows the different morphological types when available, and indicates that there is no trend with morphology. As discussed by Li et al. (2015), the isotopologue ratio does not depend on the morphological type of the galaxy. Our measurements (with an average CO/CO), shown with a thick line hatched histogram, lie below the standard isotopic ratio () (Wilson & Rood 1994) but fall in the same range as the other measurements. This is consistent with the fact that CO is optically thick. As a result of very different cloud geometries, it is difficult to compare our CO/CO(2-1) line ratio measurements in M31 with studies performed in Galactic regions. For instance, Orion regions observed by Nishimura et al. (2015) or Planck cold dust clumps (Wu et al. 2012) exhibits relatively low CO/CO line ratio () because the dense clouds fill the beam and CO is very optically thick.

Figure 10 shows the HCN/HCO+(1-0) and CO/CO(2-1) ratios we measured in the components approaching us in the north-western positions and the south-east stacking detection, which is redshifted. We compare these line ratios with previous observations from the literature. By superposing our measurements on the wide range of galaxy types observed by Krips et al. (2010), we find that our detections seem to lie in the peculiar/merger region, rather than in the star-forming (M33) and starburst part of the diagram. The HCN/HCO+ line ratio is compatible with the average ratio computed for M31’s disc by Brouillet et al. (2005). Again, the Galactic clouds of Nishimura et al. (2015) lie on the right hand side of this figure and are difficult to compare with M31 measurements. Our measurements are not compatible with Seyfert galaxies, which makes sense because there is no sign of active galactic nuclei (AGN) in M31 (Li et al. 2011). Interestingly, on the one hand, the HCN/HCO+ line ratio detected here is compatible with the value (1.5) measured by Liu et al. (2013) in infrared dark clouds. The red stacking ratio has a larger value but it is affected by a large error bar. On the other hand, HCN/HNC(1-0) line ratio is systematically larger than that measured in dark clouds by these authors. The HCN(1-0) line detections enable us to estimate lower limits on the HCN/HNC(1-0) line ratio towards the positions in the north-western area (M31I and M31I-B), which are 0.9 and 2.9, respectively. Figure 17 compares the HCO+/CO(1-0) and HCN/CO(1-0) line ratios detected on the north-western side of the inner ring with other positions in M31’s main disc (Brouillet et al. 2005) and with other galaxies. Our detections are compatible with the Brouillet et al. (2005) measurements performed in M31’s disc, but lie in the lower end of the overall distribution of Krips et al. (2010). Figure 18 shows the detections and the upper limits of our observed CO line ratios.

Our detections differ from measurements performed in M33’s giant molecular clouds (Buchbender et al. 2013). They are compatible with line ratios available for clouds in M31’s disc studied by Brouillet et al. (2005), but there is no information on the CO isotopic ratio in the disc. The main trends regard the CO/CO line ratio, which is depleted, while the HCN/HCO+(1-0) line ratio is very typical of what is observed in other local galaxies.Liu et al. (2013) have studied infrared dark clouds and argue that the abundance ratio of HCN and HCO+ may be unaffected by the environment. Even though the 100m and A maps shown in Figure 1 do not exhibit strong features, we argue in Sect. 4.3 that our detections correspond to dense cores. These ratios depend non-linearly on physical parameters, such as optical depth, excitation temperature, density, and some lines are probably optically thick and not necessarily in thermal equilibrium. This is explored further in Sects. 4.3, 4.4, and 4.5.

### 4.3 Estimate of the beam filling factors

The temperatures we have detected for CO(2-1) are well below the cosmological background, even though the molecular lines are detected in emission. This is due to the low surface filling factor of the gas detected in the beam. In this section, we try to derive estimates of the beam filling factors affecting our observations. These estimates affect all absolute parameters (temperature, density, abundance, column density, etc.) that could be determined later, and thus the possible interpretation of the state of the detected gas.

As the average CO/CO line ratio (20) is well below the standard Galactic C/C abundance ratio (53) of Wilson & Rood (1994) and the CO line intensity comparable to the CO intensity, we consider that the CO line is optically thick. As the gas is detected in emission, we can then derive a minimal excitation temperature of about 3 K from the intrinsic brightness temperature , with the usual formula

 TB=(f(Tex)−f(Tbg))×(1−e−τ) (1)

where

 f(T)=hνkexp(hνkT)−1 (2)

Relying on the modelling of infrared measurements, Viaene et al. (2014) and Draine et al. (2014) estimated a cold dust temperature of the order of 20 K (see Table 2). Since we measured the line ratio CO(2-1)/CO(1-0)0.8 (Melchior & Combes 2011), which is relatively high, we assume that the line is thermalised and that we can define a single excitation temperature. This makes sense for cold gas in the central part of a large galaxy. Most importantly, one has to take into account the beam filling factor , which is linked to the intrinsic brightness temperature as follows:

 TB=Tpeak/ηbf (3)

where is the peak temperature measured for our detections, i.e. the observed diluted main beam temperature. Given our assumptions about the excitation temperature and the CO optical depth, we can derive from our CO(2-1) detections as

 ηbf=Tpeak/[f(Tex)−f(Tbg)] (4)

If the molecular lines are close to thermal equilibrium around 20 K, the beam filling factor is below one percent. This order of magnitude is consistent with several different qualitative arguments, as follows: (1) The beam size is 44 pc for CO(2-1), while typical interstellar filaments have a size of 0.1 pc (André et al. 2014). (2) We are detecting gas complexes, which are probably extended and patchy according to the optical image. (3) The large velocity dispersions also suggest that we are integrating gas along a large depth. (4) Last, if one considers a standard gas-to-dust relation N cm (Bohlin et al. 1978), we estimate A and for M31-I(2) and M31-IB(1) (with no beam-filling factor corrections), while lower limits on extinction estimated on the optical images are of the order of A (Melchior & Combes 2011). This order of magnitude of the beam filling factor is also compatible with values previously discussed in the literature, for example Carlstrom (1988) estimated a volume filling factor smaller than in M82, while Berkhuijsen & Fletcher (2015) estimate a filling factor of approximately 4 in M31 and M51.

In the following, we consider that CO(2-1) is optically thick to determine the beam filling factors at thermal equilibrium, as provided in Table 7. The values we estimate for are consistent with Ginsburg et al. (2011), who discuss that giant molecular clouds consist of very low volume-filling factor () high-density (n(H) cm) clumps, as well as typical starburst galaxies (with ).

For a given excitation temperature, we can derive the optical depth corresponding to each optically thin line:

 τmol=−ln(1−Tpeakηbf1f(Tex)−f(Tbg)) (5)

We can then compute the column density associated to each molecular line assuming an excitation temperature :

 Nmol=8πkhc3Q(T)geEup/Texτmol1−e−τmolν2ICOηbf (6)

where is the level degeneracy for CO(2-1) molecules and for HCN(1-0) and HCO+(1-0), is the rotational partition function and is the energy level provided in Table 3. We also consider the beam filling factors defined in Table 7. The factor enables to account for non-optically thin conditions (e.g. Mangum & Shirley 2015). However, in practice, we have to assume an unknown abundance ratio to determine if it is optically thick, which limits the use of corrected column density in this analysis.

The optical depths thus computed and provided in Table 7 show that our hypotheses are consistent: CO is optically thin. In Sect. 4.4, we discuss abundances estimated assuming LTE conditions. In Sect. 4.5, we explore how to derive molecular hydrogen densities for lower excitation temperatures with RADEX simulations (van der Tak et al. 2007).

### 4.4 Local thermal equilibrium conditions

We consider here that the different detected lines correspond to some gas in LTE with an excitation temperature of 20 K. This enables us to derive physical parameters from the observations with an analytical formula and to give an initial idea of the physical configurations of the observed complexes.

#### Optical depths and column densities

With these assumptions, we derived optical depths for CO(2-1), CO(2-1), HCO+(1-0) and HCN(1-0) with the filling factor , computed in Sect. 4.3. These lines are optically thin, as shown in Table 7.

If we consider standard CO/CO line ratios from Wilson & Rood (1994) of for the molecular ring ( for the Galactic centre) and the CO optical depths provided in Table 7, we estimate an average optical depth for CO of (). The CO transition is indeed optically thick. These different optical depths discussed above are provided for each line of sight in Table 7.

In the middle panel of Table 4, we provide column densities of our main detections (CO, CO, HCN, HCO+), some upper limits for optically thin gas () in LTE, and the column density of molecular hydrogen derived empirically from the CO line intensity with a X factor as discussed in Sect. 3. All column densities account for the beam filling factor .

#### Abundance ratios

In Table 8, we tentatively compute the abundances (i.e. the ratio of the column density of the molecule with respect to the column density of molecular hydrogen) for the direct and stacking detections. In order to calculate the ratio of lines measured with similar HPBW resolutions, we use CO(2-1) to derive the molecular hydrogen column density for the CO(2-1) and C0(2-1) measurements and CO(1-0) (available for M31-I) for HCN(1-0) and HCO+(1-0) abundances. We thus study M31I(3) and M31I(2). We also include the red stacking detections for which we adopt an ad-hoc estimate of N based on the averaging of the measured I and I measurements performed with the spectra used for the stacking: a scaling factor is derived from these averaged measurements and applied to the stacked CO(2-1) measurement to estimate (2-1). It is then scaled to CO(1-0) with the 0.8 factor, as discussed in Sect. 3. For the sake of discussion, we also provide (in italics) M31I-B(1) and the stacking measurements for which we have HCN(1-0) and HCO+(1-0) measurements to no direct CO(1-0) measurements. As shown in Table 8, the molecular hydrogen column density exhibits variations up to a factor 3 owing to different resolutions (11 and 21).

We use the column densities presented in Table 4 and described in Sect. 3. We also provide for comparison the abundance values for the Galaxy computed in the molecular ring (MR) at 4 kpc from the Galactic centre and in the Galactic centre (GC) by Bergin et al. (1995) and Wilson & Rood (1994).

The abundances are affected by the uncertainties in the molecular hydrogen column densities computed empirically with the X factor and by the uncertainties in the excitation temperatures. For the CO transitions, we can expect that variations of the excitation temperatures are a secondary effect, and we can thus rely on abundance ratios for optically thin transitions.

The detected CO/CO abundance ratios are very different from the Galactic values. There is a discrepancy of a factor with the molecular ring (MR), and a factor with respect to the Galactic centre (GC) where gas has been processed regularly. Obviously, the gas is not in the same state as these obvious regions in the Galaxy. Considering the CO abundances in M31-I(3), it is relatively close to the molecular region value, while the discrepancy affects the CO. For the stacking, the CO abundance is a bit smaller and intermediate between GC and MR values, even though it is compatible with the M31I(3) abundance within 1 . While the CO abundance lies in the same range as the Galactic value, the CO abundance is deficient.

The HCN and HCO+ abundances differ from the Galactic values, and the abundance ratio. These discrepancies could be due to different excitation temperatures. However, our different measurements are globally compatible within 3. Liu et al. (2013) measured an HCN/HCO+(1-0) abundance ratio of in infrared dark clouds (IRDC) and discuss that this ratio may be unaffected by the environment. In parallel, they measured an average HNC/HCN abundance ratio of 1.470.50 in IRDC, while the upper limit we derived on the HNC/HCN abundance ratio for M31I-B(1) and M31I(2) is 1.01 and 1.14. As these authors discuss, we can argue that our detections are different from the IRDC. Our upper limits allow us to put some constraints on the kinetic temperature (e.g. Schilke et al. 1992; Hirota et al. 1998). This corresponds to kinetic temperatures in the range 38-100 K and 14-50 K, and is compatible with the results of Viaene et al. (2014) based on the analysis of infrared data. Similarly, we get HCO+/HOC+ abundance ratios larger than 1.7 and 4.9, but this is not restrictive enough as previous detections are in the range 50-12500 (Savage & Ziurys 2004).

In the next section, we explore with non-LTE simulations how different excitation temperatures could affect the different parameters and help to get a coherent set of parameters.

In order to check the consistency of our parameters, we ran some simulations with the radiative transfer code RADEX (van der Tak et al. 2007) for several molecules. The idea is to relax the LTE conditions to scan a range of excitation temperatures and of molecular hydrogen densities. Knowing the column densities of each emission line, we can estimate the excitation temperature and the density. As indicated in the figures discussed below, the standard abundances correspond to optically thick conditions and can be excluded.

In Fig. 11, we show the results of the simulations run for HCN and superimpose the various parameters discussed in the previous section, namely, the optical depth and the molecule column densities per unit velocity derived from our observations and from standard abundances. These results support the view that this gas is subthermally excited at 9 K with a density smaller than the critical density, which is provided in Table 3. This critical density plotted here (and in Figs. 19 and 12) does not match confirming the arguments of Shirley (2015) that this quantity is an oversimplified and incorrect interpretation of the excitation density of a transition. The results of the constraints of RADEX simulations with our observations are also consistent with the HCN(1-0) transition being optically thin. We detected two dense clumps with a molecular hydrogen density  cm on the north-west side of the inner ring. Our abundances are more than a factor of 10 lower than the column densities derived from the standard abundances estimated by Bergin et al. (1995) in the molecular ring (MR), and the discrepancy would be even larger if one considers the Galactic centre conditions.

We performed similar computations for HCO(1-0), as shown in Figure 19. We also find subthermal conditions with a molecular hydrogen density smaller than the critical density and an excitation temperature of 9 K. The abundances are also smaller (factor 5-6) than the column densities derived from the standard MR abundances (Bergin et al. 1995). The gas associated with the HCO+(1-0) detection has a density of  cm.

We applied the same procedure to M31-I(3) where CO and CO have been detected, as shown in Fig. 12. On the one hand, the best excitation temperature is consistent with 17 K but we cannot exclude 20 K given the error bars. On the other hand, the simulations support a molecular hydrogen density larger than the critical density. These lines are close to LTE conditions and trace clumps with a density larger than 2.24 cm. The CO measured abundance is smaller than the standard abundances by a factor 5, while the CO measured abundance is compatible within the error bars of the standard abundances estimated in the molecular ring.

The abundances we have derived are systematically smaller than the standard abundances (Bergin et al. 1995) for the molecular ring, but for CO. This is consistent with our previous discussion that CO is optically thick and CO depleted, with LTE and optically thin conditions for CO and CO. HCN and HCO+ abundances are consistent with subthermal excitation conditions with excitation temperatures of 9 K and are smaller than the standard abundances. As shown in Figs 17 and 10, the HCO+/HCN line ratio measured in the clouds studied here is similar to that measured in M31’s disc by Brouillet et al. (2005).

## 5 Discussion

In this section, we discuss our dense gas detection, how it can improve our knowledge of this inner region, and whether the properties of this gas are consistent with our understanding of previous observations. In Sect. 5.1, we discuss the geometrical configuration of the gas: the information derived from dust extinction affecting point sources, and the properties of various gas components observed at different wavelengths. In Sect. 5.2, we discuss our knowledge of the heating sources and the properties of the interstellar medium in this region. In Sect. 5.3, we discuss the kinematical information obtained with our millimeter observations.

### 5.1 Geometrical configuration of the gas

M31 has been targeted by different surveys. In Sect. 5.1.1, we study the distribution of point sources from different catalogues in search of possible signs of extinction that trace the gas. In Sect. 5.1.2, we summarise the arguments we can derive from the diffuse components.

#### Point sources and extinction

In Fig. 13, we considered four catalogues: X-ray sources from Stiele et al. (2011), deeper X-ray sources from Hofmann et al. (2013), planetary nebulae from Ciardullo et al. (1989), and UV sources from Rosenfield et al. (2012). The UV sources studied by Rosenfield et al. (2012) trace the old stellar population, and they have the same radial distribution as low-mass X-ray binaries, which correspond to the majority of the X-ray sources in Hofmann et al. (2013). The stellar kinematics has been studied by Saglia et al. (2010) with long slits: bulge stars exhibit a rotation with a maximum velocity of 100 km s along the major axis (considered at PA) and a zero (systemic) velocity along the minor axis). These velocities clearly do not correspond to the gas component we detected.

For each catalogue, we plotted the azimuthal distribution of point sources within a radius of 300, 200, and 140, depending on the area covered. These populations all belong to the same ellipsoid of PA as first discussed by Kaaret (2002). The maxima of the sinusoids correspond to the major axis, while the minima (where our dense gas has been detected) correspond to the minor axis.

The number of sources is significantly larger for Hofmann et al. (2013) than for Stiele et al. (2011); the former work is more sensitive as the data are stacked over a longer period. The work of Rosenfield et al. (2012) based on HST data contains an unprecedented number of sources thanks to deep integration and a gain in spatial resolution. We can observe that in these deep observations the two minima of the sinusoid are about at the same level, while the previous observations exhibit an asymmetry. This asymmetry is not really significant when compared to the Poisson error bars shown in the Fig. 13. While in radio we do not expect much extinction, the UV sources in Rosenfield et al. (2012) should be very sensitive to extinction. However, we do not detect any strong asymmetry: if we compute the ratio of the numbers of sources from the near and far sides, we find 0.9676 (0.9662) if we consider 52 deg (77 deg). These ratios are significant as they have a Poisson noise of 0.012. If this asymmetry is due to extinction, it affects 4 of the studied area. This order of magnitude is consistent with the gas beam filling factors computed in Sect. 4.3. However, we do not have the sensitivity to derive whether this patchy dust component belongs to the large scale disc (PA=) or the more face-on component detected in the stellar bulge population (PA). We can exclude the possibility that young stellar clusters from the disc component could create this inhomogeneity, as no HII region is detected in this area (Azimlu et al. 2011) beside the cluster close to the centre (Lauer et al. 2012). The (young) stellar UV cluster (Kang et al. 2012) closest to our detection has an age of 1 Gyr and is at the offset (,) from the centre and at a closest separation of 71 arcsec (271 pc in projection) to our north-western dense gas complex. Dong et al. (2015) detected an intermediate age (300 Myr to 1 Gyr old) stellar population at solar metallicity associated with the bulge, which could contribute up to 50 of the V intensity. However, they only studied the radial dependency, while we expect a smooth spatial distribution as the stars have performed numerous galactic rotations since their birth.

Assuming a uniform distribution in the stellar ellipsoid, one can estimate the ellipticity as done by Kaaret (2002). For the Rosenfield et al. (2012) (Hofmann et al. 2013) sample studied here within 140 (300), we estimate (). This is consistent with the measurements of the radial variation of the ellipticity and position angle performed on J-2MASS photometry by Melchior & Combes (see Figure A.1 2013). This supports our previous finding that there is very little extinction.

While these populations trace the bulge, there is an unexpected X-ray source alignment in the Hofmann et al. (figure 14, 2013) catalogue very close to the centre. Similar to that observed in the outskirts of M31 (e.g. McConnachie et al. 2009), these X-ray sources could be part of a tidal stream whose stellar population could be hidden by the crowding at other wavelengths. The facts that it corresponds to an old stellar population and that it is aligned are strong arguments to argue that they are far from the centre and seen in projection. However, it is not aligned with our positions nor any diffuse components discussed below.

#### Gas components

While the stellar population mainly belongs to the bulge, the diffuse components, apart from the UV to near-IR stellar continuum, are gaseous.

Radio component The analysis of the radio emission (Gießübel & Beck 2014) reveals complementary information. There is a significant continuum flux at 3.6 cm and 6.2 cm, and a weak polarised component (10). There is a relatively flat spectral index (), while the contribution from the black hole is very weak and localised (Li et al. 2011). This flat spectral index cannot be accounted for by an inverted synchrotron emission due to a present AGN, but we cannot exclude relic emission from past AGN activity (e.g. Ishibashi & Fabian 2015). The flat spectral index could be due to the combination of synchrotron and free-free emissions. In the Block et al. (2006) scenario, the inner ring forms and expands to its actual position in 150 Myr. The corresponding past starburst activities (150-200 Myr old) could account for the continuum emission stronger close to the centre. The polarisation map of Gießübel & Beck (2014) is illustrated as contours in Fig. 14. The polarisation is blurred by the Faraday rotation of the electrons. On the north side, no polarisation is detected, while it is detected on the south side. This polarisation pattern corresponds to a good approximation to the simple modelling proposed in Melchior & Combes (see Fig. 16 and Tab. 7, 2011) of the inner ring with a PA of -35  and an inclination of 40 , together with the two discs components strongly depolarising the north-western side. In addition in the south side, we clearly see some inhomogeneities in the polarised emission detected: there is a gap that corresponds to the H() emission. This confirms the parameters of the inner ring’s location on the near side, i.e. in the south-east direction. This supports some previous tentative interpretations (Ciardullo et al. 1988) that we are observing structures more face-on than the 77  main disc with the near side on the north side and a more edge-on structure on the south side.

Supporting the post-starburst scenario, the central field exhibits a remmant tidal swirl observed in radio at 3.6 cm and 6.2 cm (Gießübel & Beck 2014) and in ionised gas (Ciardullo et al. 1988). These radio emissions could trace relic activities of stellar populations younger than 200 Myr (Condon 1992) i.e. following the impact and expansion of the inner ring. This remnant tidal swirl could be dominated by shocks, e.g. from supernovae as [NII] is larger than H (Rubin et al. 1972), while the inner ring is possibly stronger in H tracing a 200 Myr old starburst (Block et al. 2006).

Ionised gas While we know that the observed extinction is weak and the overall amount of gas is small, Melchior et al. (2000) has estimated a lower limit on A assuming all the gas is in front of the bulge. Even in locations where the extinction detected is small (i.e. probably underestimated by the previous assumption), it corresponds well with features detected in the infrared (e.g. at 100 m as indicated in Figure 1). As discussed by Ford et al. (2013), the central gas is hotter than the inner ring. The 100 m map exhibits hot dust and cold dust, while the 500 m map mainly shows cold dust in the inner ring (close to our observed positions). This central hot component corresponds to the ionised gas (Ciardullo et al. 1988). The ionsed gas is very inhomegeneous and its distribution does not exhibit any clear sign of extinction. This is compatible with the fact that the gas is very clumpy with a filling factor smaller than 1 and that the near/far-side asymmetry, possibly due to extinction, is at the level of 4 .

Molecular gas Our dense gas detections discussed here exhibit a surprising velocity pattern. This is the wavelength range where the best velocity resolution is achieved (few km/s), and we observe in two positions along the minor axis where the systemic velocity is expected atvelocities between -530 and -140 km s. This kinematical information demonstrates the presence of several molecular gas components along these lines of sight. In contrast to HI measurements (Braun et al. 2009; Chemin et al. 2009), we do not have a priori the sensitivity to detect molecular gas in the warp or the external parts of the galaxy.

### 5.2 Heating sources

We investigate here the possible heating sources, which could explain why the signal is stronger on one side and what heats the gas in general. Following Bogdán & Gilfanov (2008), we know that the diffuse X-ray gas detected in this area within 150-200″  from the centre is weak. The detected 0.5-1.2keV flux lies in the range 1.6 - 9erg scmarcsec, considering a molecular cloud of 1 pc with a distance of M31 of 780 kpc, we can estimate a rough X-ray incident radiation intensity of 6-34  erg scm. This is at least five orders of magnitude weaker than the radiation field considered by Meijerink et al. (2007) for XDR modelling. There is only one ROSAT (Second ROSAT PSPC catalogue) source within 12″(22″) from M31I (M31I-B) with a 14 arcsec positional error, with a flux of 10 erg scmarcsec.

There is an ultra-luminous X-ray source (Kaur et al. 2012) located 22″  from M31-2c-a, which has exhibited an outburst that lasted three months. ULX are correlated with star formation (Mapelli et al. 2009). As in the Cartwheel, this ULX is detected next to the inner ring. The presence of ULX in the ring supports the starburst scenario, as several ULX are detected in ring galaxies suspected of frontal collision (Prestwich et al. 2012). ULX are expected in low-metallicity environments (Prestwich et al. 2013), which could explain why only one has been detected. Barnard et al. (2012) measured an outburst flux of 50erg s, which could contribute at the level of  erg s cm.

In this inner region, the contribution of the central black hole could be significant. However, Li et al. (2011) measured a burst of activity in January 2006 with Chandra X-Ray Observatory at a level of 4.3 erg s and a quiescent level of 4.8 erg s. At the distance of M31I and M31I-B (supposed in the sky plane), this would contribute to the X-ray incident radiation intensity at a level of 6.9 and 5.5erg s cm (6.2 and 5.0erg s cm) in the quiescent state (during the outburst). This is four to five orders of magnitude weaker than the possible contribution of the ULX discussed above.

The X-ray sources shown in Fig. 14 are strongly concentrated towards the centre. The catalogue Hofmann et al. (2013) based on Chandra HRC is more sensitive than other catalogues (Stiele et al. 2011; Barnard et al. 2014). The surface density varies as (R/1 kpc). The contribution of the central part is thus more important than the black hole activity.

We can thus exclude that the excitation mechanism of the gas is due to X-ray radiation from the gas accreted by the black hole. The line emissions detected by Saglia et al. (2010) and M. Sarzi (private communication) can be accounted for by planetary nebulae and no LINER activity is necessary.

The heating is mainly due to the old stellar population as discussed by Draine et al. (2014) and Viaene et al. (2014). Transient X-ray sources, such as ULX, could contribute inhomogeneously to the heating. The heating rate U, based on Mathis et al. (1983) and computed by Draine et al. (2014), are provided in Table 1. The area around M31I and M31I-B have , while the other three positions have U in the range 1.8-2.7. This corresponds to an average dust temperature of 20 K, according to Draine et al. (2014).

### 5.3 Different velocity components

The kinematics of this area is complex with up to three different velocity components. The probability that the warp component, coming from radii larger than 15-20 kpc, is seen in CO emission towards the centre is negligible. This is the case because of the weak metallicity of this gas, which makes it undetectable in CO. As discussed in Melchior & Combes (2011), if we consider that the probability of chance alignment of gas is low and that the gas is inside the main galaxy, this means that we are in the presence of several structures. Indeed, an explanation in terms of non-circular motions in a possible barred potential has already been ruled out given the velocity disposition and the fact that the gas distribution is not aligned with any elongated structure, but in an off-centred ring (Melchior & Combes 2011). The component at the systemic velocity is compatible with gas along the minor axis of the main disc, while the two counter-rotating components could be orbiting in two planes with different inclinations and orientations. They could correspond to an inclined disc and to the inner 1-kpc ring. However, in presence of observations in two positions, it is difficult to fully constrain such a configuration. Apart from the inner ring detected in infrared (see Fig. 1 and Block et al. (2006)) and the H() structure detected inside (Ciardullo et al. 1988), we do not have kinematic observations covering these positions. Boulesteix et al. (1987) got the velocity field within a field and Nieten et al. (2006) did not integrate deep enough in the central part to detect CO. Opitsch et al. (2015) has detected two rotating components in , but their two components rotate in the same direction, which adds complexity to the problem. Interestingly, the polarisation map of Gießübel & Beck (2014) corresponds to the parameters proposed by Melchior & Combes (2011) for the three-component modelling.

Finally, the amplitudes between our different velocity components are different and larger than the simulated modulation proposed by Dierickx et al. (2014).

The alternative interpretation is that we are observing gas superimposed on the central part of M31, i.e. gas in the outskirts of the disc (Koch et al. 2015; Lehner et al. 2015; Wolfe et al. 2013; Lockman et al. 2012) is ruled out. No high velocity clouds have been detected in CO (Combes & Charmandaris 2000; Miville-Deschênes et al. 2005), while Galactic gas should be around  km s.

### 5.4 13 C depletion and evidence for a post-starburst scenario

In Sect. 4.1, we discussed that it is remarkable that the CO detection is at a level comparable to the CO detection, in contrast to what is observed in the Galaxy (e.g. Nishimura et al. 2015; Shimajiri et al. 2014), where the CO is usually 10 to 150 times weaker than CO. In Table 7, we have shown that CO and CO are optically thin, so we can claim that the CO is under-abundant with respect to CO. In Sect. 4.5, we have shown that these two CO components are close to thermal equilibrium. Hence, we can rely on the abundance ratios computed in Table 8; the deficit is five to ten times weaker than with the Galactic abundances. This deficit could be accounted for by a post-starburst scenario. This kind of CO deficit was first observed by Casoli et al. (1991) in post-merger. Davis (2014) also find an anti-correlation of CO and star formation and gas surface densities in local galaxies.

This could be the signature of a 200 Myr old starburst triggered by a collision with a galaxy like M32, as proposed by Block et al. (2006). This scenario accounts for the two off-centred ring structures of M31, with most star formation in the 10 kpc ring (Ford et al. 2013) and a smaller ring, where we have detected CO and dense gas.

## 6 Conclusion

We have detected CO(2-1) and CO(2-1) lines with multiple velocity components along the minor axis of M31 on both sides of the inner 1-kpc ring. We detected dense gas traced by CO(2-1), HCN(1-0), and HCO+(1-0) on the north-west side at the systemic velocity for CO(2-1) and in the blue-shifted component for HCN(1-0) and HCO+(1-0). We also detected a redshifted component for the three molecules by stacking at the CO velocity on both sides.

Draine et al. (2014) and Viaene et al. (2014) found lower measurements for the stellar heating in this area on the north-west side, which could explain why dense gas has only been detected directly on this side. A careful analysis has shown that CO is optically thick while the other CO lines are optically thin and close to LTE at an excitation temperature of 17.5-20 K. The gas is very clumpy and the averaged beam filling factor is 0.8. The average column density of molecular hydrogen is 16 10 cm. The derived abundances are all smaller than the standard abundances, but for CO. The comparison of the derived abundances with RADEX simulations shows that the HCN and HCO+ gas correspond to dense clumps with molecular hydrogen density of the range  cm and an excitation temperature of 9 K. The HCO+/HCN line ratio is comparable with that measured for clouds detected in M31’s disc (Brouillet et al. 2005), while the derived abundances are smaller than the Galactic abundances (Bergin et al. 1995), with a larger discrepancy for HCN(1-0). Only one transient ULX object has been identified as a possible secondary source of heating, while the bulge stellar population is sufficient to heat the gas and reproduce the infrared maps.

Our isotopic CO lines and HCN/HCO+ lines detections are all weak and close to the detection limits. We detected CO in a single point at the systemic velocity. Stacking of all