M31 circum-nuclear region: a molecular survey with the IRAM-interferometer

TL;DR

This study presents a detailed molecular survey of the circum-nuclear region of Andromeda using IRAM interferometry, revealing quiescent, low-density molecular clumps with no current star formation, consistent with a passive galaxy core.

Contribution

First high-resolution molecular survey of Andromeda's center, characterizing molecular clumps, their physical state, and star formation activity, highlighting their transient nature and quiescent conditions.

Findings

12 molecular clumps detected with total mass ~8.4 x 10^4 M_sun

Clumps are non-virialized and likely transient structures

Region shows no current star formation and is consistent with passive galaxy core

Abstract

We analyse molecular observations performed at IRAM interferometer in CO(1-0) of the circum-nuclear region (within 250 pc) of Andromeda, with 2.9 arcsec = 11 pc resolution. We detect 12 molecular clumps in this region, corresponding to a total molecular mass of (8.4 +- 0.4) x 10**4 Msol. They follow the Larson's mass-size relation, but lie well above the velocity-size relation. We discuss that these clumps are probably not virialised, but transient agglomerations of smaller entities that might be virialised. Three of these clumps have been detected in CO(2-1) in a previous work, and we find temperature line ratio below 0.5. With a RADEX analysis, we show that this gas is in non local thermal equilibrium with a low excitation temperature (Tex = 5-9 K). We find a surface beam filling factor of order 5 percent and a gas density in the range 60-650 cm**{-3}, well below the critical density. With a gas-to-stellar mass fraction of 4 x 10**{-4} and dust-to-gas ratio of 0.01, this quiescent region has exhausted his gas budget. Its spectral energy distribution is compatible with passive templates assembled from elliptical galaxies. While weak dust emission is present in the region, we show that no star formation is present and support the previous results that the dust is heated by the old and intermediate stellar population. We study that this region lies formally in the low-density part of the Kennicutt-Schmidt law, in a regime where the SFR estimators are not completely reliable. We confirm the quiescence of the inner part of this galaxy known to lie on the green valley.

Figures

Tables

Table 1. Table 1: Positions of the 4 fields observed at IRAM-PdB in 2012. The phase centre of the observation was 00 h 42 m 44.99 s ,  + + 41 ∘ 15 ′ ′ \arcmin 57.8 ″ ″ \arcsec . Beside the J2000.0 equatorial coordinates of the centre of each field, we also provide the number of visibilities acquired per field, and the corresponding beam and pixel size (square). The sampling of the 4th field is worse than for the other ones, which explains a larger level of noise.

Field	RA	DEC	Visibilities	Beam	Pixels
1	00h42m44.39s	$+$41∘16′08.3′′	4473	3.37${}_{}{}^{\prime \prime }\times$2.45′′	0.61${}_{}{}^{\prime \prime }\times$0.61′′
2	00h42m46.78s	$+$41∘16′12.3′′	4432	3.37${}_{}{}^{\prime \prime }\times$2.45′′	0.61${}_{}{}^{\prime \prime }\times$0.61′′
3	00h42m45.27s	$+$41∘15′54.3′′	4743	4.53${}_{}{}^{\prime \prime }\times$2.76′′	0.74${}_{}{}^{\prime \prime }\times$0.74′′
4	00h42m43.50s	$+$41∘15′36.3′′	3131	4.53${}_{}{}^{\prime \prime }\times$2.76′′	0.74${}_{}{}^{\prime \prime }\times$0.74′′

Table 2. Table 2: Summary of the identification of cores process. We select spectra with at least 2 consecutive channels deviating from 3 σ 𝜎 \sigma from the continuum level. We keep positive and negative signals at each stage, in order to have an estimate of the noise level. We provide the number of pixels and the number of core clumps derived. Only core clumps with at least 3 adjacent pixels are kept for subsequent analysis. The approximated mean flux is the mean value of the sums of detected pixels fluxes of all core clumps.

	Number of pixels			Core clumps			Mean Surface (pixels)		Approx. mean flux (mJy/beam)
	Total	Positive	Negative	Total	Positive	Negative	Positive	Negative	Positive	Negative
2 pixels	142	65	77	102	47	55
$>$ 2 pixels	903	598	305	101	54	47	11.1	5.6	766	-313

Table 3. Table 3: Properties of the 12 selected molecular clumps extracted from our datacube. The offsets are calculated according to the optical centre of M31 at coordinates at J2000 coordinates 00 ​ h ​  42 m ​  44.37 s 00 ℎ superscript 42 𝑚 superscript 44.37 𝑠 00h\,42^{m}\,44.37^{s} and + 41 ∘ ​  16 ​ ′ ​  8.34 ​ ″ superscript 41 16 ′ 8.34 ″ +41^{\circ}\,16\arcmin\,8.34\arcsec (Crane et al. 1992 ) . V 0 subscript 𝑉 0 V_{0} is the velocity at the peak flux Φ max subscript Φ max \Phi_{\text{max}} and the noise of the associated spectrum is σ noise subscript 𝜎 noise \sigma_{\text{noise}} . The S/N ratio S ​ N ​ R peak 𝑆 𝑁 subscript 𝑅 peak SNR_{\text{peak}} is derived from these. σ v subscript 𝜎 v \sigma_{\text{v}} , R eq subscript 𝑅 eq R_{\text{eq}} and F CO subscript 𝐹 CO F_{\text{CO}} are the extrapolations found through the methodology in Sect.  2.3 . S ​ N ​ R tot 𝑆 𝑁 subscript 𝑅 tot SNR_{\text{tot}} is found with F CO subscript 𝐹 CO F_{\text{CO}} and the noise of the integrated spectrum associated.

						Extrapolations
ID	Offsets	$V_0$	${\Phi }_{\text{max}}$	${\sigma }_{\text{noise}}$	$SN{R}_{\text{peak}}$	${\sigma }_{\text{maj}}$	${\sigma }_{\text{min}}$	${\sigma }_{\text{v}}$	$F_{\text{CO}}$	$SN{R}_{\text{tot}}$
	$\left(arcsec\right)$	$\left(km{s}^{-1}\right)$	$\left(\frac{mJy}{beam}\right)$	$\left(\frac{mJy}{beam}\right)$		$\left(pc\right)$	$\left(pc\right)$	$\left(km{s}^{-1}\right)$	$\left(Jykm{s}^{-1}\right)$
1	$-5.2,-32.5$	45.1$\pm$0.7	55.8	5.4	10.3	6.6$\pm$0.4	5.7$\pm$0.3	8.8$\pm$0.3	2.23 $\pm$ 0.09	64.4
2	$30.8,2.3$	145.5$\pm$0.4	58.4	4.5	12.9	6.0$\pm$0.4	5.8$\pm$0.4	6.0$\pm$0.3	1.48 $\pm$ 0.09	56.9
3	$34.4,-3.8$	110.9$\pm$1.5	26.8	5.6	4.8	9.7$\pm$0.5	7.6$\pm$0.4	7.8$\pm$0.2	1.42 $\pm$ 0.05	49.4
4	$29.0,10.8$	76.6$\pm$0.7	34.8	3.7	9.4	8.1$\pm$0.4	5.9$\pm$0.3	6.0$\pm$0.2	1.10 $\pm$ 0.06	46.4
5	$13.1,-22.7$	112.9$\pm$1.2	29.9	5.1	5.9	8.7$\pm$0.5	5.5$\pm$0.3	6.7$\pm$0.2	1.15 $\pm$ 0.05	39.6
6	$0.9,-45.9$	-35.8$\pm$0.9	48.1	7.7	6.3	5.4$\pm$0.3	5.4$\pm$0.3	6.5$\pm$0.2	1.98 $\pm$ 0.07	36.0
7	$19.8,5.9$	65.8$\pm$1.4	20.5	4.1	5.0	9.2$\pm$0.7	4.3$\pm$0.3	10.7$\pm$0.3	0.73 $\pm$ 0.03	31.1
8	$35.7,0.4$	171.5$\pm$1.5	27.7	5.0	5.5	7.3$\pm$0.4	7.3$\pm$0.4	8.7$\pm$0.3	0.75 $\pm$ 0.04	23.8
9	$2.1,-9.9$	4.3$\pm$1.5	15.5	3.2	4.8	11.4$\pm$0.5	7.9$\pm$0.3	4.4$\pm$0.2	0.44 $\pm$ 0.02	22.8
10	$7.6,-24.0$	95.8$\pm$1.0	21.4	5.1	4.2	10.7$\pm$0.6	10.6$\pm$0.5	6.2$\pm$0.2	0.65 $\pm$ 0.03	19.0
11	$-22.3,-33.7$	-167.6$\pm$1.4	24.0	5.7	4.2	9.9$\pm$0.4	9.5$\pm$0.3	3.4$\pm$0.2	0.57 $\pm$ 0.03	15.4
12	$1.5,1.7$	-176.5$\pm$1.1	19.1	3.5	5.4	10.8$\pm$0.7	7.8$\pm$0.5	6.1$\pm$0.2	0.39 $\pm$ 0.02	15.2

Table 4. Table 4: Characteristics of the 12 selected molecular clumps. The descriptive properties are shown in Table  3 . The offsets are calculated according to the optical centre of M31 at J2000 coordinates 00 h ​  42 m ​  44.37 s superscript 00 ℎ superscript 42 𝑚 superscript 44.37 𝑠 00^{h}\,42^{m}\,44.37^{s} and + 41 ∘ ​  16 ​ ′ ​  8.34 ​ ″ superscript 41 16 ′ 8.34 ″ +41^{\circ}\,16\arcmin\,8.34\arcsec . The calculation of R eq eq {}_{\textrm{eq}} is explained in Sect.  2.3 . The CO luminosity L CO ′ superscript subscript 𝐿 CO ′ L_{\text{CO}}^{\prime} , the luminous mass M H 2 subscript 𝑀 subscript H 2 M_{\text{H}_{2}} , the surface density Σ H 2 subscript Σ subscript H 2 \Sigma_{\text{H}_{2}} , the virial parameter α vir subscript 𝛼 vir \alpha_{\text{vir}} and the H 2 column density N H 2 subscript H 2 {}_{\text{H}_{2}} calculations are detailed in Sect.  3 .

ID	Offsets	R${}_{\text{eq}}$	$L_{\text{CO}}^{\prime }$	$M_{{\text{H}}_2}$	${\Sigma }_{{\text{H}}_2}$	${\alpha }_{\text{vir}}$	N${}_{{\text{H}}_2}$
	$\left(arcsec\right)$	pc	$Kkm{s}^{-1}p{c}^2$	${10}^3{M}_{\odot }$	$M_{\odot }{\text{pc}}^{-2}$		${10}^{20}c{m}^{-2}$
1	$-5.2,-32.5$	11.0 $\pm$ 0.7	3321 $\pm$ 138	14.5 $\pm$ 0.6	36.4 $\pm$ 6.3	68 $\pm$ 11	20.2 $\pm$ 3.5
2	$30.8,2.3$	10.3 $\pm$ 0.9	2202 $\pm$ 137	9.6 $\pm$ 0.6	27.8 $\pm$ 6.5	44 $\pm$ 10	15.4 $\pm$ 3.6
3	$34.4,-3.8$	15.8 $\pm$ 0.7	2119 $\pm$ 77	9.2 $\pm$ 0.3	11.3 $\pm$ 1.4	121 $\pm$ 15	6.2 $\pm$ 0.8
4	$28.9,10.8$	12.4 $\pm$ 0.6	1644 $\pm$ 84	7.2 $\pm$ 0.4	14.3 $\pm$ 2.1	71 $\pm$ 13	7.9 $\pm$ 1.2
5	$13.1,-22.7$	12.4 $\pm$ 0.5	1709 $\pm$ 70	7.5 $\pm$ 0.3	14.9 $\pm$ 1.9	87 $\pm$ 12	8.3 $\pm$ 1.1
6	$0.9,-45.9$	9.2 $\pm$ 0.7	2940 $\pm$ 107	12.8 $\pm$ 0.5	46.6 $\pm$ 8.4	35 $\pm$ 6	25.9 $\pm$ 4.7
7	$19.8,5.9$	11.1 $\pm$ 0.5	1087 $\pm$ 49	4.7 $\pm$ 0.2	11.8 $\pm$ 1.7	311 $\pm$ 45	6.6 $\pm$ 0.9
8	$35.7,0.4$	13.1 $\pm$ 0.8	1112 $\pm$ 65	4.8 $\pm$ 0.3	8.6 $\pm$ 1.6	236 $\pm$ 47	4.7 $\pm$ 0.9
9	$2.1,-9.9$	17.5 $\pm$ 0.6	650 $\pm$ 30	2.8 $\pm$ 0.1	2.8 $\pm$ 0.3	142 $\pm$ 23	1.5 $\pm$ 0.2
10	$7.6,-24.0$	19.8 $\pm$ 1.1	968 $\pm$ 41	4.2 $\pm$ 0.2	3.3 $\pm$ 0.5	209 $\pm$ 30	1.8 $\pm$ 0.3
11	$-22.3,-33.7$	18.0 $\pm$ 0.7	852 $\pm$ 40	3.7 $\pm$ 0.2	3.5 $\pm$ 0.4	66 $\pm$ 12	1.9 $\pm$ 0.2
12	$1.5,1.7$	17.0 $\pm$ 0.9	579 $\pm$ 37	2.5 $\pm$ 0.2	2.7 $\pm$ 0.4	294 $\pm$ 56	1.5 $\pm$ 0.2

Table 5. Table 5: Characteristics of the CO(2-1) and CO(1-0) lines integrated in a 12 ′′ FWHM beam at 3 positions. The MC13 corresponds to the identification proposed in Melchior & Combes ( 2013 ) , the offsets of each position are computed with respect to the optical centre. As the parameters, namely integrated flux F C ​ O = S C ​ O ​ Δ ​ v subscript 𝐹 𝐶 𝑂 subscript 𝑆 𝐶 𝑂 Δ 𝑣 F_{CO}=S_{CO}\Delta v , the central velocity V 0 subscript 𝑉 0 V_{0} , the linewidth Δ ​ V Δ 𝑉 \Delta V , the peak value S peak , the rms level of noise computed on the baseline, and the line ratios computed in Jy and in K, are derived from a Gaussian fit in CLASS in the GILDAS environment.

MC13 : Offsets	$S_{CO}\Delta v$		$V_0$		$\Delta V$		Speak		rms		(2-1)/(1-0)
ID : arcsec	Jy km s-1		km s-1		km s-1		mJy		mJy		Flux	Temp.
	(2-1)	(1-0)	(2-1)	(1-0)	(2-1)	(1-0)	(2-1)	(1-0)	(2-1)	(1-0)	ratio	ratio
15 :  -9.0,-32.3	3.0$\pm$0.4	1.5$\pm$0.3	-248$\pm$2	-248.	24$\pm$4	17$\pm$3	115	81	16	22	1.41	0.35$\pm 0.08$
28 : +15.,-20.3	1.8$\pm$0.4	1.6$\pm 0.3$	-190$\pm$1	-178	14$\pm$3	23$\pm$6	130	64	19	16	2.03	0.51$\pm 0.15$
36 : +27.,+3.7	4.7$\pm$0.8	0.91$\pm$0.2	-153$\pm$5	-150.	53$\pm$11	13$\pm$3	84	68.	20.5	17	1.23	0.31$\pm 0.09$

Table 6. Table 6: Characteristics derived by Viaene et al. ( 2014 ) and Draine et al. ( 2014 ) from infrared data at the position of the CO(2-1) and CO(1-0) detections in 36 ′′ × 36 ′′ superscript 36 ′′ superscript 36 ′′ 36^{\prime\prime}\times 36^{\prime\prime} and 18 ′′ × 18 ′′ superscript 18 ′′ superscript 18 ′′ 18^{\prime\prime}\times 18^{\prime\prime} pixels. As described in Sect. 4.1 and in Melchior & Combes ( 2016 ) , η b ​ f subscript 𝜂 𝑏 𝑓 \eta_{bf} provides the beam filling factor computed for a brightness temperature of 5 K relying on the RADEX results presented in Sect 4.1 and 30 K assuming it is thermalised with the dust. T C subscript 𝑇 𝐶 T_{C} and T W subscript 𝑇 𝑊 T_{W} correspond to the cold and warm dust components, M d ​ u ​ s ​ t subscript 𝑀 𝑑 𝑢 𝑠 𝑡 M_{dust} and M s ​ t ​ a ​ r subscript 𝑀 𝑠 𝑡 𝑎 𝑟 M_{star} are the dust and stellar masses scaled to the prorata of the 12 ′′ superscript 12 ′′ 12^{\prime\prime} CO FWHM beam. τ V d ​ u ​ s ​ t subscript superscript 𝜏 𝑑 𝑢 𝑠 𝑡 𝑉 \tau^{dust}_{V} and τ V D ​ i ​ f ​ f subscript superscript 𝜏 𝐷 𝑖 𝑓 𝑓 𝑉 \tau^{Diff}_{V} are the dust and diffuse dust optical depths, given for the order of magnitude as they are the poorest constrained parameters according to Viaene et al. ( 2014 ) . SFR is the star formation rate scaled to the prorata of the 12 ′′ superscript 12 ′′ 12^{\prime\prime} CO FWHM beam. The last column provides the SFR estimate of Ford et al. ( 2013 ) integrated on the 12 ′′ beam.

MC13	${\eta }_{bf}^{5K}$	${\eta }_{bf}^{30K}$	$T_C$	$T_W$	$M_{dust}$	$M_{star}$	${\tau }_V^{dust}$	${\tau }_V^{Diff}$	SFR	$U_{mean}$	$U_{min}$	$T_{mean}$	$T_{min}$	SFR
ID	${10}^{-2}$	${10}^{-2}$	K	K	$M_{\odot }$	${10}^7{M}_{\odot }$			$M_{\odot }$/Myr			K	K	$M_{\odot }$/Myr
			(Viaene et al. 2014)							(Draine et al. 2014)				(F13)
15	4.8	4.0	29.8	63.7	33	1.8	0.152	0.022	0.22	18.6	15.0	29.3	28.3	8
28	3.1	2.7	29.8	63.7	33	1.8	0.152	0.022	0.22	32.3	22.0	32.1	30.13	77
36	7.8	6.6	29.8	63.7	38	2.0	0.162	0.027	3.25	27.1	25.	31.2	30.7	133

Equations

$${\sigma }_{\text{maj}}\left({\Phi }_{\text{iso}}\right)=\sqrt{\frac{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}[x_{\text{i}}-\overline{x}\left({\Phi }_{\text{iso}}\right){]}^2}{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}}},$$

$${\sigma }_{\text{min}}\left({\Phi }_{\text{iso}}\right)=\sqrt{\frac{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}[y_{\text{i}}-\overline{y}\left({\Phi }_{\text{iso}}\right){]}^2}{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}}},$$

$$\overline{x}\left({\Phi }_{\text{iso}}\right)=\frac{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}{x}_{\text{i}}}{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}},\overline{y}\left({\Phi }_{\text{iso}}\right)=\frac{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}{y}_{\text{i}}}{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}}.$$

$${\sigma }_{\text{v}}\left({\Phi }_{\text{iso}}\right)=\sqrt{\frac{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}[v_{\text{k}}-\overline{v}\left({\Phi }_{\text{iso}}\right){]}^2}{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}}},$$

$$\overline{v}\left({\Phi }_{\text{iso}}\right)=\frac{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}{v}_{\text{k}}}{{\sum }_k^{iso}{\sum }_i^{iso}{\Phi }_{\text{i,k}}}$$

$$F_{\text{CO}}\left({\Phi }_{\text{iso}}\right)=\sum _k^{iso}\sum _i^{iso}{\Phi }_{\text{i,k}}\delta x\delta y\delta v,$$

$${\sigma }_{\text{r}}={\left(\sqrt{{\sigma }_{\text{maj}}^2\left({\Phi }_0\right)-{\sigma }_{\text{beam,maj}}^2}\sqrt{{\sigma }_{\text{min}}^2\left({\Phi }_0\right)-{\sigma }_{\text{beam,min}}^2}\right)}^{1/2},$$

$$\begin{array}{rl}PC1& =0.23\widetilde{R_{\text{eq}}}+0.57\widetilde{SN{R}_{\text{peak}}}+0.67\widetilde{SN{R}_{\text{tot}}}+0.41\widetilde{{\sigma }_{\text{v}}}\\ PC2& =0.92\widetilde{R_{\text{eq}}}-0.38\widetilde{SN{R}_{\text{peak}}}+0.01\widetilde{SN{R}_{\text{tot}}}+0.001\widetilde{{\sigma }_{\text{v}}}\end{array}$$

$$1.15\widetilde{R_{\text{eq}}}+0.68\widetilde{SN{R}_{\text{tot}}}+0.41\widetilde{{\sigma }_{\text{v}}}+0.19\widetilde{SN{R}_{\text{peak}}}\ge 0.55$$

$$\frac{L_{\text{CO}}^{\prime }}{Kkm{s}^{-1}p{c}^2}=\frac{3.25\times 10^7}{{\left(1+z\right)}^3}\frac{F_{\text{CO}}}{Jy.km.s^{-1}}{\left(\frac{D_{\text{L}}}{Mpc}\right)}^2{\left(\frac{{\nu }_{\text{rest}}}{GHz}\right)}^{-2},$$

$$\frac{M_{{\text{H}}_2}}{M_{\odot }}=4.4\frac{L_{\text{CO}}^{\prime }}{Kkm{s}^{-1}p{c}^2}\frac{X_{\text{CO}}}{2\times 10^{20}c{m}^{-2}{\left(Kkm{s}^{-1}\right)}^{-1}},$$

$$N_{{\text{H}}_2}=\frac{{\Sigma }_{{\text{H}}_2}}{M_{\odot }p{c}^2}\frac{M_{\odot }}{kg}{\left(\frac{2.3m_p}{kg}\right)}^{-1}{\left(\frac{pc}{cm}\right)}^{-2},$$

$${\alpha }_{\text{vir}}=5{\sigma }_{\text{v}}^2\frac{R_{\text{eq}}}{G{M}_{{\text{H}}_2}}.$$

Full text

1 Introduction

The evolution of the gas content and star formation activity in the central kiloparsec of galaxies is key to understand the coupling of the black hole evolution with the rest of the galaxy. Beside the activity of the central engine probably powered by mass accretion (e.g. Lynden-Bell 1969; Urry & Padovani 1995), the properties of the host galaxy are directly impacted by this so-called AGN feedback (Fabian 2012, and references therein). The scaling relations, between the supermassive black hole mass and the bulge mass and velocity dispersion of the host (e.g. Ferrarese & Merritt 2000; Tremaine et al. 2002; Marconi & Hunt 2003; Gültekin et al. 2009; Kormendy & Ho 2013; McConnell & Ma 2013), suggest a close connection between supermassive black holes and their hosts (e.g. Silk & Rees 1998; Di Matteo et al. 2005; King & Pounds 2015). The growth of supermassive black holes over cosmic time is probably dominated by external gas accretion (e.g. Soltan 1982; Croton et al. 2006). Indeed, galaxy mergers (e.g. Barnes & Hernquist 1991; Springel et al. 2005; Hopkins et al. 2006) or galactic bars (e.g Pfenniger & Norman 1990; Begelman et al. 2006; Hopkins & Quataert 2010) may efficiently transport gas towards the galactic nucleus through gravitational torques (e.g García-Burillo et al. 2005) over a few dynamical times.

While the total AGN activity is correlated with the global star formation rate (SFR) as a function of cosmic time (e.g. Heckman et al. 2004; Heckman & Best 2014), SFR has been mostly quenched in the local Universe (e.g. Belfiore et al. 2016) while the activity of central black holes has been much reduced (e.g. Sijacki et al. 2015). The mechanisms responsible for this quenching are currently investigated. Relying on simulations, Bower et al. (2017) show these red and blue sequences of galaxies result from a competition between star formation-driven outflows and gas accretion on to the supermassive black hole at the galaxy’s centre. Belfiore et al. (2016) argue that the quenching occurred inside out, and that the star formation stopped first in the central region. However, these inside-out mechanisms are probably not universal as in dense environments, like groups or clusters of galaxies, the quenching could also occur outside-in. Peng et al. (2015) argue that the strangulation mechanism in which the supply of cold gas to the galaxy is halted is the main mechanism responsible for quenching star formation in local galaxies with $M_{*}<10^{11}M_{\odot}$. In the GASP (GAs Stripping Phenomena in galaxies with MUSE) survey, Poggianti et al. (2017) are exploring in the optical more than hundred galaxies in different environments, with the idea to get better constraints on both types of scenarios. Gullieuszik et al. (2017) have shown that gas is stripped out in JO204 a jellyfish galaxy in A957 and the star formation activity is reduced in the outer part. With a study based on local galaxies, Fluetsch et al. (2018) argue that AGN-driven outflows are likely capable of clearing and quenching the central region of galaxies.

With a stellar mass of $5\times 10^{10}\,M_{\odot}$(Viaene et al. 2014), Andromeda belongs to the transition regime between the active blue-sequence galaxies and passive red-sequence galaxies (e.g. Bower et al. 2017; Baldry et al. 2006) which happens around the stellar mass of 3 $\times$ 1010 M⊙ (e.g. Kauffmann et al. 2003). It is a prototype galaxy from the Local Group where the star formation has been quenched in the central part. It hosts both very little gas and very little star formation, while the black hole is basically quiet, with some murmurs (Li et al. 2011). In a previous study about M31 nucleus, Melchior & Combes (2017) show that there is no gas within the sphere of influence of the black hole. Indeed, the gas has been exhausted. Most scenarios of the past of evolution of Andromeda reproduce the large scale distribution, and show evidence of a rich collision past activity (Ibata et al. 2001; Thilker et al. 2004; Gordon et al. 2006; McConnachie et al. 2009; Ibata et al. 2014; Miki et al. 2016; Hammer et al. 2018). However, the exact mechanism quenching the activity in the central kilo-parsec is still unknown (Tenjes et al. 2017). Block et al. (2006) proposed a frontal collision with M32, which could account for the 2 ring structures, observed in the dust distribution. Melchior & Combes (2011) and (2016) show the presence of gas along the minor axis and support the scenario of the superimposition of an inner 1-kpc ring with an inner disc. Melchior & Combes (2013) estimated a minimum total mass of $4.2\times 10^{4}M_{\odot}$ of molecular gas within a (projected) distance to the black hole of 100 pc. This is several orders of magnitude smaller than the molecular gas present in the Central Molecular Zone of the Milky Way (Pierce-Price et al. 2000; Molinari et al. 2011). In the Galaxy, while large amounts of dense gas are present in the central region, Kruijssen et al. (2014) discuss the different processes that combine to inhibit the star formation, observed a factor 10 times weaker than expected (e.g. Leroy et al. 2008).

In this article, we analyse new molecular gas observations obtained with IRAM Plateau-de-Bure interferometer achieving a 11 pc resolution. This resolution well below the typical size where a tight correlation is observed between star formation rate and gas density (K-S law). We study the properties of this gas and how it relates with the star formation activity in this region.

In Sect. 2, we present the analysis of the data cube, enabling an automatic selection of 12 molecular clouds. In Sect. 3, we discuss the properties of these clumps. In Sect. 4, we discuss how this detection of molecular clouds in the equivalent of the Central Molecular Zone correlates with the information available on the star formation activity.

2 Data analysis

We here describe the identification of molecular clumps in the IRAM-PdB data cube. In Sect. 2.1, we describe the IRAM-PdB observations and data reduction. In Sect. 2.2, we select the core of significant clumps above a given threshold and discuss their significance. In Sect. 2.3, we compute the 3D size, velocity dispersion and total flux of these core clumps following the method proposed by Rosolowsky & Leroy (2006). In Sect. 2.4, we discuss the velocity distribution of the detections and proceed to clean side lobes. In Section 2.5, we apply the principal component analysis statistical method to discriminate reliable candidates using the descriptive parameters of the previous subsections. A final check is performed with a visual inspection of each selected clump. Last, in Sect. 2.6, we sum up our procedure and present our final selection.

2.1 Observations and data reduction

We present here an analysis of an IRAM-PdB interferometer mosaic of 4 fields covering the centre of Andromeda and a field of view of about 2 arcmin off-centred to the South-East. As described in Melchior & Combes (2017), the initial motivation of these observations was to search for molecular gas next to the black hole, and the region corresponding to the sphere of influence of M31’s black hole, i.e. $R_{SOI}\sim 14$ pc, has been explored. A 2 mJy signal with a line-width of 1000 km s*-1* was expected by Chang et al. (2007), but were excluded at a 9 $\sigma$ level. Only a small 2000 $M_{\odot}$ clump, lying most probably outside the sphere of influence of the black hole, has been detected, and is seen in projection. In this article, we extend this first exploration to the whole data cube that covers the equivalent of the Central Molecular Zone for the Milky Way (Morris & Serabyn 1996; Oka et al. 1996). The observations have been performed in 2012 with the 5-antenna configuration with the WideX correlator. It covers a wide velocity band $[-3000,6000]$ km s*-1*, with a velocity resolution of $\delta v=5.07$ km s*-1* and a pixel size of 0.61$\arcsec$. Four fields have been observed at the positions provided in Table 1 and integrated for about 4 hours. A standard reduction has been performed with the GILDAS software and these fields have been combined. We perform our analysis on the mosaic assembled with a beam of 3.37$\arcsec\,\times\,$2.45$\arcsec$ (PA $=70^{\circ}$) and a pixel size of 0.61$\arcsec$. We focus our work on the $[-600,0]$ km s*-1* velocity band, binned in 119 channels.

A quick view of the data cube confirms the absence of large amount of gas in this region. However, there are numerous clumps of molecular gas with a low velocity dispersion. In Figure 1, we observe a non-Gaussian flux distribution typical of a data cube with signal. We optimise a selection procedure to disentangle genuine clumps from noise. Given this configuration, we perform a 1-iteration CLEAN procedure to correct for the primary beam. We do not have single dish observations in CO(1-0) of this region. So we cannot correct from short spacing. In addition, as the signals are not extended and relatively weak, it is not possible to analyse the data cube with standard algorithms, e.g. the signal characteristics do not match the criteria stated in Rosolowsky & Leroy (2006). Hence, we perform a basic signal detection in the data cube in an automatic way, and check our results with careful visual inspections and classical methods (e.g. GILDAS).

2.2 Detection of 3$\sigma$ peaks

We rely on the first and second moments of each spectra with a $3\sigma$ clip to get a best estimate of the mean flux $\langle\Phi\rangle{(x,y)}$ and rms noise level $\sigma_{\text{noise}}\left(x,y\right)$, where $(x,y)$ refers to the pixel position. We will refer to these parameters simply as $\langle\Phi\rangle$ and $\sigma_{\text{noise}}$ hereafter. The noise level, which map is displayed in Melchior & Combes (2017), is at its lowest close to the black hole about 3.2 $mJy/beam$ at the velocity resolution (5.07 km/s), and increases towards the edges of the field of view (up to 13 $mJy/beam$). In Sect. A, we derive 3$\sigma$ upper limit on the continuum level: about 15 $\mu$Jy within 15$\arcsec$ estimated on the whole bandwidth $[-3000,6000]$ km s*-1*.

We select pixels which spectrum exhibits more than 2 consecutive spectral channels with a flux excess or deficit of 3 $\sigma_{\text{noise}}$. At this stage, we keep the negative signals in order to access the coherence of the detections with respect to noise. As detailed in Table 2, we detect 1045 pixels: 663 (resp. 382) with a positive (resp. negative) signal. As isolated pixels or aggregates of two pixels are most likely noise, we define clump candidates as groups of at least 3 adjacent pixels exhibiting more than 2 consecutive channels at 3 $\sigma_{\textrm{noise}}$ from the mean level. In principle, this criteria selects the core of possible clumps, i.e. the central 3 $\sigma$ pixels with high S/N ratio. 142 pixels (65 positive and 77 negative) with less than 3 adjacent pixels are excluded. We thus keep 598 (resp. 305) pixels gathered in 54 positive (resp. 47 negative) 3-$\sigma$ clumps. 33.8% of the detected signals are negative. Positive (resp. negative) 3-$\sigma$ clumps have a mean flux of 766 mJy/beam (resp. -313 mJy/beam). Their average surface is of 11.1 pixels (to be compared to 6.5 for the negative 3-$\sigma$ clumps). The number of pixels at half-power beam width (HPBW) is about 25 pixels, hence we only see the inner parts of the clumps. Given the relatively small number of pixels in the 3-$\sigma$ clumps compared to 25, we expect that the detections are close to the spatial resolution. Figure 24 displays the mean velocity map of positive (left panel) and negative (right panel) 3-$\sigma$ peak detections above 3$\sigma_{\textrm{noise}}$.

We estimate the peak S/N ratio (SNR${}_{\textrm{peak}}$) associated to detected 3-$\sigma$ clumps as the ratio of the peak flux $\Phi_{\textrm{peak}}$ of the 3-$\sigma$ clump to the noise estimated for its spectra. We show this S/N distribution in Figure 2. The average SNR${}_{\textrm{peak}}$ for the positive (resp. negative) 3-$\sigma$ clumps is 4.4 (resp. -3.7) with 28 positive (resp. 16 negative) 3-$\sigma$ clumps showing a peak signal higher than 4 $\sigma_{\textrm{noise}}$ (resp. lower than -4 $\sigma_{\textrm{noise}}$), and 3 positive 3-$\sigma$ clumps with peak S/N larger than 8. The clumps we detect are thus significantly brighter than the level of noise, estimated with the negative clumps. Although the two sets behave differently, more investigations are required to select with confidence genuine molecular clouds. In the three next subsections, we calculate global properties, exclude side lobes and apply principal component analysis to make our final selection.

2.3 Physical quantities derived from moment measurements

In order to further characterise the detection of molecular clouds, we estimate the clump sizes, velocity dispersions and total fluxes. Rosolowsky & Leroy (2006) note a strong correlation between the resolution and the measured size of clumps for those with a size close to the spatial resolution. This is probably the case here: most detected clumps are unresolved or close to the detection limit. We expect them to have an elliptical shape similar to the beam. Hence, we adapt the CPROPS (Cloud PROPertieS) method proposed by Rosolowsky & Leroy (2006) in order to optimise these measurements. We can note that Rosolowsky & Leroy (2006) have shown that this extrapolating method is optimum for a peak S/N larger than 10, while our data host only 2 clumps as strong as this. However, these authors have shown that the properties derived from interferometric data are underestimated with respect to single dish data, with a lost of order of 50% in the integrated luminosity as already discussed by Sheth et al. (2000).

We calculate the second moments of the major x-axis and minor y-axis (defined for each clump). A principal component analysis, also performed with similar intent in Koda et al. (2006), is used to define these axes: x and y refer to the major and minor axes respectively hereafter. For each clump, we define an elliptical box with major and minor axes twice as big as the beam centred on the pixel with peak flux $\Phi_{\text{max}}$. This intends to exclude surrounding regions with potential noise. We define a variable $\Phi_{\text{iso}}$, which corresponds to the equal-intensity isophotes. We, then, study the evolution of the size, the velocity dispersion, and total flux as a function of the intensity values corresponding to each isophote, varying from $\Phi_{\text{max}}$ to 2$\sigma_{\text{noise}}$. Up to 100 isophotes are thus used for each clump. We choose 100 isophotes since our box size may contain up to 60 pixels with 3 to 6 channels. Each value of $\Phi_{\textrm{iso}}$ delimits a region over which we sum the following moments over all pixels $i$ and channels $k$, with the major (resp. minor) axis size $\sigma_{\text{maj}}$ (resp. $\sigma_{\text{min}}$):

[TABLE]

[TABLE]

where $\Phi_{\text{i,k}}$ is the flux in $Jy\,beam^{-1}$ over all channel $k$ and pixel $i$ respectively. $x_{i}$ and $y_{i}$ refer to the offset positions along the major and minor axis respectively. $\overline{x}$ and $\overline{y}$ are the coordinate of barycentre of each isophote:

[TABLE]

Similarly, the velocity dispersion can be defined as:

[TABLE]

where :

[TABLE]

and $v_{\text{k}}$ is the velocity at channel $k$. Last, the total integrated flux in $Jy\,km\,s^{-1}$ can be computed as:

[TABLE]

where $\delta x$ and $\delta y$ are the size of the spatial pixels in arcsec and $\delta v$ is the spectral resolution in $km\,s^{-1}$. In order to find the values of the size, velocity dispersion and flux of the clumps, we use a weighted (by the number of pixels in each isophote) linear least-square regression to extrapolate the moments at $\Phi_{\text{iso}}=\Phi_{0}=0$ Jy/beam. Figure 3 (resp. Figure 26) displays the principle of this procedure applied to the determination of the parameters of the strongest cloud (resp. the cloud analysed in Melchior & Combes (2017)), we obtain the values of $\sigma_{\text{maj}}\left(\Phi_{0}\right)$, $\sigma_{\text{min}}\left(\Phi_{0}\right)$, $\sigma_{\text{v}}\left(\Phi_{0}\right)$ and F${}_{\text{CO}}\left(\Phi_{0}\right)$. For comparison purposes, we also include values of the velocity dispersion and flux measured through Gaussian fit within the CLASS method in the software GILDAS. We do observe a good agreement between the two methods. In order to get consistent measurements we will subsequently use the extrapolated $\sigma_{\text{v}}$. Gratier et al. (2012) and Corbelli et al. (2017) adopt the Class/Gildas measurements for the velocity dispersions and integrated fluxes as they provide lower uncertainties. As further explained below, we do compute errors on the extrapolated values the same way as Rosolowsky & Leroy (2006), with the bootstrap method and we do find uncertainties compatible with the Class measurements based on a Gaussian fit on the integrated spectra.

The uncertainty over the extrapolated parameters is found through the bootstrapping method, which is a robust technique to estimate the error when it is difficult to formally determine the contribution of each source of noise. We proceed as follows: each isophote contains a number N of pixels, we choose randomly N pixels with replacement and so on for each isophote. A new extrapolation is made from this bootstrapped clump. This process is repeated 500 times and the standard deviation of the distribution of extrapolated values multiplied by the square root of the number of pixels in a beam, the oversampling rate (in order to account for pixels being correlated), is used as the uncertainty. The resulting uncertainties can be seen in Figure 3 and in Table 3 which lists our final sample.

The root-mean-squared spatial size $\sigma_{\text{r}}$ of each clump is then calculated by deconvolving the spatial beam from second moments of the extrapolated clump size, assuming the clumps have the shape of a 2D Gaussian, and substracting the RMS beam sizes $\sigma_{\text{beam,maj}}$ and $\sigma_{\text{beam,min}}$:

[TABLE]

where $\sigma_{\text{maj}}\left(\Phi_{0}\right)>\sigma_{\text{beam,maj}}$ and $\sigma_{\text{min}}\left(\Phi_{0}\right)>\sigma_{\text{beam,min}}$, a condition met for all our sample, including negative clumps. Note that we compare the moments of major and minor size extrapolated at $\Phi_{0}$ to the RMS size of the beam, not to the projection at $\Phi_{0}$ of the beam size. This is a robust approach to take into account the resolution bias when clumps are barely resolved. This method shows high performances on marginal resolution, low S/N molecular clouds (Rosolowsky & Leroy 2006). While the beam has a position angle of 70*∘, the mean inclination of the major axis of our clumps is (82$\pm$25)∘* indicating that some clumps are resolved and exhibit structures, most structures are unresolved. This will influence $\sigma_{\text{r}}$ calculation, hence we assume the clumps to be spherical which might lead to a slight underestimation of the spatial size.

The equivalent radius R${}_{\text{eq}}$ of the assumed spherical clump is chosen following the definition from Solomon et al. (1987) : $R_{eq}\approx 1.91\sigma_{r}$. It was derived from the assumption that clumps behave as spherical clouds with a density profile $\rho\propto r^{-\beta}$ where $\sigma_{r}^{2}\left(\beta\right)=\frac{3-\beta}{3(5-\beta)}R^{2}$ and $\sigma_{r}^{2}\left(\beta=1\right)=\sqrt{6}R^{2}\sim 2.45R^{2}$ . The slightly different value found empirically by Solomon et al. (1987) can be explained by the behaviour of the 12CO which displays a shallower density profile than the used model. As it is also used in Rosolowsky & Leroy (2006), it provides an adequate approximation that permits comparison. From now on, we will refer to $\sigma_{\text{maj}}\left(\Phi_{0}\right)$, $\sigma_{\text{min}}\left(\Phi_{0}\right)$, $\sigma_{\text{v}}\left(\Phi_{0}\right)$ and F${}_{\text{CO}}\left(\Phi_{0}\right)$, as $\sigma_{\text{maj}}$, $\sigma_{\text{min}}$, $\sigma_{\text{v}}$ and F${}_{\text{CO}}$ since only the extrapolated values hold any relevance in this work.

From these properties, we can compute the S/N ratio $SNR_{\text{tot}}$ based on the total flux $F_{\text{CO}}$ and the noise of the spectrum integrated within the box containing each clump.

2.4 Velocity coherence and side lobes

It is unlikely that two genuine clumps would have identical velocities, and we expect a velocity gradient up to 600 km s*-1* in this region. Hence, it is highly probable that two clumps with the exact same velocity but different intensities correspond to one genuine clump and a side lobe which should be rejected from our selection. As seen in Figure 24, which shows the maps of positive and negative signals as well as the corresponding velocity distributions, a noticeable amount of clumps display similar or identical velocities. The cleaning of side lobes is done through the Mapping method in the software Gildas. A Clean algorithm (Gueth et al. 1995) is run over each channel where more than one clump is detected, with a support centred on the strongest clump. To assess the robustness of signals, we keep negative clumps and side lobes in a first step in order to explore their behaviour statistically, as described below.

2.5 Principal Component Analysis

We apply PCA to the full sample of molecular cloud candidates (both negative and positive clumps), using the following parameters: $SNR_{\text{peak}}$, $SNR_{\text{tot}}$, $R_{\text{eq}}$ and $\sigma_{\text{v}}$. These four parameters are first standardized as follow: $\widetilde{T}=(T-\langle T\rangle)/\sigma_{T}$, where T is the studied parameter, $\langle T\rangle$ its mean value and $\sigma_{T}$ its standard deviation. Second, with the Python ScikitLearn library, we extract two principal components, corresponding to the eigenvectors with the highest eigenvalues. They are a linear combination of these four standardized parameters:

[TABLE]

Figure 4 maps the sample on two axes defined as the two main principal components accounting for 50 $\%$ and 25 $\%$ of the behaviour of the sample. The top panel maps the clumps kept by the cleaning procedure, while the bottom panel displays the identified side lobes and negative clumps. After visual inspection and cross-check with the negative signals, we eliminate the red dots in the top panel of Figure 4 below the blue dashed line. Hence, on the top panel, we keep blue dots with:

[TABLE]

The bottom panel displays candidates rejected as side lobes and/or exhibiting a negative signal. This shows the limitation of this analysis. Amplitude of side lobes can be important and 4 positive side lobes with relatively high significance with respect to the selected signals (in the top panel) are rejected.

We thus keep 12 clumps whose parameters are displayed in Table 3. They have SNR${}_{\mathrm{peak}}\geq 4.2$ and SNR${}_{\mathrm{tot}}\geq 15.2$ as displayed in Figure 5. The maps and corresponding spectra are displayed in Figure 7.

2.6 Final sample selected

We show the maps and integrated spectrum for all 12 selected clumps in Figure 7, by order of decreasing $SNR_{\text{tot}}$. As said in Section 2.3, the position angle of several clumps differs significantly from the position angle of the beam. It tends to happen for extended clumps which display structures.

Our selection went through a 5-step procedure:

In Sect. 2.2, the 3-$\sigma$ peak detection allowed us to find 54 positive candidates within the data-cube, including faint signals which needed further investigation. At this stage, 47 negative clumps were kept in order to perform a statistical analysis: those negative (false) detection with similar characteristics compared to our sample of positive candidates provide statistical information on the noise affecting the data. The SNR${}_{\textrm{peak}}$ of each core was calculated. 2. 2.

In Sect. 2.3, we extrapolated the values of $\sigma_{\textrm{maj}}$, $\sigma_{\textrm{min}}$, $\sigma_{\textrm{v}}$ and F${}_{\textrm{CO}}$ for both positive and negative clumps. This allowed us to find the values for R${}_{\textrm{eq}}$ and SNR${}_{\textrm{tot}}$. 3. 3.

In Sect. 2.4, with the use of Gildas Clean algorithm, we check clumps with identical velocities for side lobes. Positive and negative clumps, some with a significant SNR${}_{\textrm{tot}}$ were found to be side lobes of three positive 3-$\sigma$ clumps. 4. 4.

In Sect 2.5, we apply a statistical analysis on our sample of clumps.

Hence, we complete the selection procedure. The final map is presented in Figure 8, with the clump mean velocity in colour. Although the CO emission is patchy, it follows the general velocity field found in H$\alpha$ (Boulesteix et al. 1987). The CO emission globally corresponds well to the star formation map of Ford et al. (2013). 12 clumps are kept with $SNR_{\text{tot}}$ showed in Figure 5. Their properties are summed up in Table 3. The distribution of $\sigma_{\text{maj}}$, $\sigma_{\text{min}}$, $\sigma_{\text{v}}$ and F${}_{\text{CO}}$ for selected clumps is displayed in Figure 9.

3 Cloud properties

In this Section, our goal is to determine the physical properties of the identified molecular clouds in the centre of M31, size, velocity dispersion, mass and Virial ratio, to compare them to nearby galaxy clouds, and to their scaling relations.

3.1 Velocity dispersion

The average velocity dispersion of our selected sample, computed as in Equation (4) is $6.8\pm 1.3\,km\,s^{-1}$. The corresponding histogram is shown in Figure 9. Caldù-Primo & Schruba (2016) detected molecular clouds, mostly located in the 10 kpc ring of M31, found a median velocity dispersion of $3.1\pm 1.1\,km\,s^{-1}$ with interferometric data.

We do find here a median velocity dispersion of $6.35\,km\,s^{-1}$. However, the relation velocity dispersion and radius do not follow the expected Larson’s relation (cf Figure 11), contrary to the mass-radius relation, as discussed below. While averaging over the whole extent of the clouds, it is possible to find a dispersion as low as 3 km/s in one clump (note that the corresponding FWHM would be $\sim$ 7 km/s), the present spectral resolution (and sampling) (FWHM of 5.07 km/s) is a strong limitation in our determinations.

3.2 Mass estimates

The luminous mass $M_{\text{H}_{2}}$ of the clumps can be derived from the total integrated flux. First we calculate the CO luminosity L${}_{\text{CO}}^{\prime}$, which is defined as (Solomon et al. 1997):

[TABLE]

where $D_{\text{L}}=780\,kpc$ is the distance to M31, $\nu_{\text{rest}}=115.271$ GHz is the observed frequency and $z=0$. This leads to the luminous mass:

[TABLE]

where X${}_{\textrm{CO}}$ is the $CO$-to-$H_{2}$ conversion factor (Bolatto et al. 2013). The mass is then given by $M_{\textrm{H}_{2}}=\alpha_{\textrm{CO}}\,L_{\textrm{CO}}^{\prime}$, with $\alpha_{\textrm{CO}}=4.36\,M_{\odot}\,\left(K\,km\,s^{-1}\,pc^{2}\right)^{-1}$, based on the conversion factor of the Milky Way $3.2\,M_{\odot}\,\left(K\,km\,s^{-1}\,pc^{2}\right)^{-1}$ corrected by a factor 1.36 to account for interstellar helium (Tacconi et al. 2010). We find a total H2 mass of $\left(8.4\pm 0.4\right)\times 10^{4}\,M_{\odot}$ which is coherent with Melchior & Combes (2013) estimation of a minimum total mass of $4.2\times 10^{4}\,M_{\odot}$. We have a mean $M_{\text{H}_{2}}$ of $\left(7.0\pm 0.3\right)\times 10^{3}\,M_{\odot}$ for the detected clouds. We find our values for the mass and size of clumps to be consistent with Larson’s mass – size relation found in Salomé et al. (2017), Gratier et al. (2012) and Rosolowsky (2007), cf Figure 10. It is not the case for the velocity – size and velocity – mass relations though. This might be explained in part by the fact that our minimal value of $\sigma_{\text{v}}$ is biased high by our spectral resolution and selection process (we ask for a minimum of two consecutive channels). Hence, our velocity dispersions are somewhat over-estimated. Although, for signals with SNR${}_{peak}<10$, Rosolowsky & Leroy (2006) has shown that measurements based on interferometric data tend to underestimate size and velocity dispersion.

The surface density $\Sigma_{\text{H}_{2}}$ is found by dividing the molecular mass of the clump by its area in squared parsecs. The area is calculated for an elliptic shape with the major and minor axis deconvolved from the beam. We find an average surface density of $15.3\pm 2.6\,M_{\odot}\,pc^{2}$. This is three times less than in NGC 5128, about two times less than in the Milky Way but close to the value found in the LMC, $21\pm 9\,M_{\odot}\,pc^{2}$ (Salomé et al. 2017; Miville-Deschênes et al. 2017; Hughes et al. 2013).

The molecular column density is calculated as follows :

[TABLE]

where we multiply the proton mass $m_{p}$ by $2.3$ to take into account the helium mass. The average column density is $\left(8.5\pm 1.5\right)\times 10^{20}\,cm^{-2}$

In order to estimate the impact of the magnetic, kinetic and gravitational energy of the clumps, we finally calculate the Virial parameter (Bertoldi & McKee 1992; McKee & Zweibel 1992):

[TABLE]

A value of $\alpha_{\text{vir}}\leq 1$ indicates a gravitationally bound core with a possible support of magnetic fields while if $\alpha_{\text{vir}}\leq 2$, it means the core is gravitationally bound without magnetic support. In our case, clumps have $\alpha_{\text{vir}}\gg 2$, their kinetic energy appears dominant and they are not virialized. Compared to the virial parameter in Salomé et al. (2017); Miville-Deschênes et al. (2017) and Hughes et al. (2013) for giant molecular clouds, our mean value is $140\pm 72$ which is one to two orders of magnitude higher than these since our clumps are smaller and less massive.

Figure 11 reveals that the velocity dispersions of our measured clumps lie well above the relation for Milky Way clouds. Certainly our spectral resolution prevents us to detect velocity dispersions below the relation. However, even after deconvolution from the spectral resolution, the majority of clumps have a broad dispersion. We conclude that the virial factors $\alpha_{vir}$ are in a large majority much larger than 1, and the clumps are not virialized. Certainly, they are transient agglomerations of smaller entities, which might be virialized.

4 Discussion

In the following, we discuss how this new molecular gas detection compares with other measurements. In Section 4.1, we discuss the line ratios of some clumps based on CO(2-1) detection from Melchior & Combes (2013) and CO(3-2) from Li et al. (2018). In Sect. 4.2, we study the spectral energy distribution of this region and discuss the star formation tracers available in this region. We show the absence of correlation between dust, most probably heated by the interstellar radiation field, and the FUV due to the old bulge stellar population plus the 200 Myr inner disc discussed by Lauer et al. (2012). Last, relying on the SFR estimate of this region, we discuss, in Sect. 4.3, the extreme position of our measurement on the Kennicutt-Schmidt law.

4.1 CO(2-1)-to-CO(1-0) line ratio

4.1.1 Data

In Melchior & Combes (2013), we analysed IRAM-30m CO(2-1) data obtained with the HERA instrument. These data overlap the IRAM-PdB CO(1$-$0) mosaic studied here. We do not find a priori a one-to-one correspondence with the signals detected in Melchior & Combes (2013). The CO(2-1) signal is detected in more regions than CO(1-0). However, many detections were below 4$\sigma$ and were not recovered by the IRAM-PdB data presented here. While this is not surprising given the low S/N ratio, the signal could be affected by interferometric filtering if the gas is extended. Indeed, Rosolowsky & Leroy (2006) studied that for a given mass, a significant fraction of the flux can ben lost when the peak S/N is lower than 10. 3 spectra (labelled 15, 28 and 36 in Melchior & Combes (2013)), actually detected above 4$\sigma$ in CO(2-1), have a counter-part in the CO(1-0) interferometric data cube. Each CO(2$-1$) pointing corresponds to a 12-arcsec HPBW. These CO(1-0) maps of these 3 simultaneous CO(1-0) and CO(2-1) detections are displayed in Figure 12 and correspond to the clumps No1, 2 and 5 in Table 3. As displayed in this figure, the CO(2-1) detections are not centred on the CO(1-0) peak of emission, and the CO(1-0) clumps do not fill the single dish beam. In order to study the line ratio, we integrate interferometric data within 12” diameter circles at these 3 positions. We obtained the spectra displayed in Figure 13. We use the usual conversion factors 5 Jy/K for the CO(2-1) single dish data and 24 Jy/K for the CO(1-0) interferometric data. The results of this analysis is presented in Table 5.

In Table 6, we provide the dust characteristics of the positions, where CO(1-0) and CO(2-1) are detected, derived from the maps of Viaene et al. (2014), Draine et al. (2014) and Ford et al. (2013). There is a strong interstellar radiation field $U\sim 20-30$ due to the bulge stellar population, while the cold dust temperature is around 30 K.

Following Eq. 10 and 11, we estimate a mean luminous mass along the line of sight, and within the 12 arcsec $=$ 40 pc beams, for these 3 offsets of 8700 M⊙. The fraction of gas with respect to the stellar mass along these lines of sight is very small: $4.\times 10^{-4}$, while the dust-to-gas ratio is about 0.01. This is a sign of high SFR recycling and high metallicity. The Andromeda circum-nuclear region lies well below the dust scaling relation presented by Galliano et al. (2018), as this is observed for early-type galaxies.

4.1.2 Evidences of local non-thermal equilibrium conditions

The R${}_{21}=$ CO(2-1)-to-CO(1-0) line ratio (in temperature) has been computed for each three detection and is provided in the last column of Table 5. This ratio lies in the range 0.3-0.5, well below 1. Hence, we expect this gas to be sub-thermally excited. This is also a strong evidence that this gas is optically thick. Furthermore, this quite low ratio supports the fact that we have not lost significant flux in the interferometric measurements in these regions detected both in CO(1-0) and CO(2-1). We expect that the detected gas is not extended but rather clumpy. One should note that the FWHM velocity width of these lines are in overall good agreement for CO(1-0) et CO(2-1), but for MC13-36. In addition, this clump has a velocity mismatch in Li et al. (2018), so it should be considered with caution.

In parallel, there are clouds detected only in CO(2-1), that fall below our CO(1-0) sensitivity. There are 7 such clouds. 6 of them have a weak signal-to-noise ratio between 3 $\sigma$ and 4 $\sigma$. There is one cloud detected at 6 $\sigma$ in CO(2-1) that is not seen in CO(1-0) at the offset (-9.0*′′,-8.3′′). Li et al. (2018) has detected CO(3-2) molecular gas at this position and estimate a line ratio $R_{32}=0.33\pm 0.11$. Given the CO(1-0) $3\sigma$ upper limit (S${}_{CO}^{1-0}<1.14$ Jy  km  s-1*), we estimate a temperature ratio R${}_{{2-1}/{1-0}}\geq 0.83\,(3\sigma)$, which is not very likely according to our modelling, and the CO(1-0) molecular gas might have been missed due to interferometric spatial filtering. Relying on the CO(2-1) and CO(3-2) single-dish detections, it is probable that this clump has properties similar to the three other clumps analysed below.

The molecular gas is not in thermal equilibrium with the dust. We considered a kinetic temperature in the range $7-15$ K and assumed an excitation temperature $T_{ex}=5$ K. First, assuming this gas is optically thick, we derive a beam filling factor $\eta_{bf}=T_{obs}/(T_{ex}-T_{bf})\times\Delta V/\delta v$, where $T_{obs}$ is the peak main beam temperature, Tbg is the cosmic microwave background, $\Delta V$ is the FWHM width of the line and $\delta V$ the velocity resolution. We consider CO(2-1) measurements as they are not affected by beam filtering. We thus estimate a mean $\eta_{bf}^{5K}$ value of 5.2 $\%$. We check that we find a similar value if we consider an excitation temperature of 30K (4.4 $\%$). This would correspond to clumps with an effective size $d=\sqrt{\eta}_{bf}D_{Beam}\simeq 10$ pc. This value is compatible with the measurements performed in Table 4 and the maps displayed in Figure 12. Second, we derive the mean column density of molecular hydrogen for the 3 positions studied in this section and found $\langle N_{H}\rangle=3\times 10^{20}$ cm*-2*, within the range found for the whole sample. We assumed a standard CO abundance $N_{CO}=10^{-4}\times N_{H}$. We consider as input for the RADEX simulations (van der Tak et al. 2007) a CO column density of $N^{{}^{\prime}}_{CO}/{\Delta V}=N_{CO}/\eta^{5K}_{bf}/{\Delta V}=1.9\times 10^{16}$ cm*-2* km*-1* s*+1* considering a mean ${\Delta V}=30\,km/s^{-1}$.

We display in Figure 14 the line ratios as function of the hydrogen density. We run RADEX simulations (van der Tak et al. 2007) for three different kinetic temperatures. The densities corresponding to the measured line ratios are weak and imply low excitation temperatures in the range 4-9 K. We find densities that are in the range 60-650 cm*-3* (resp. 250-1600 cm*-3*) for T${}_{K}=$ 15 K (resp. 7.5 K). We can further check the consistency of these density estimates. Considering one single effective clump with a mean mass of 8700 M⊙ and a molecular hydrogen density in the range 60-650 cm*-3*, we expect a typical size in the range 8-16 pc. Alternatively, if we consider 5 clumps in the beam, the clumps will have a typical size of 5-10 pc.

In Figure 15, we check that the ratio R21 points towards low density values lower than critical for T${}_{K}=15$ K. We then derive the R31 ratio relying on the CO(3-2) measurements of Li et al. (2018). Given the uncertainties, the R31 ratios are compatible within $2\sigma$.

In summary, we detect gas in non-local thermal equilibrium, with a low excitation temperature ($T_{ex}\sim 5-9$ K). The kinetic temperature around 15 K (and possibly smaller) is significantly weaker that the dust temperature estimated in the infrared around 30 K. The volume density of molecular gas is well below the critical density.

4.2 Tracing star formation

While the central region of Andromeda does not reveal any obvious star forming region, global star formation estimates usually display a non-zero star formation rate (SFR) in this region known to host ionised gas and dust. However, depending on the star formation tracers, quite different values have been estimated, even though this does not affect global SFR estimates (Viaene et al. 2014; Ford et al. 2013), while the bulge is also often avoided (e.g. Lewis et al. 2015, 2017).

In distant galaxies, it is customary to estimate the amount of obscured star formation observed in FUV by correcting the observed emission from young stars with the observed 24 $\mu$m Spitzer flux. This has been studied statistically by Leroy et al. (2008) and on sub-kpc scale by Bigiel et al. (2008), and applied to Andromeda by Ford et al. (2013). The FUV maps are expected to trace mainly the O and early B stars. It can be severely obscured by dust, while the UV emission from young stars is expected to heat and re-radiate in the mid-IR. The idea is hence to remove the contribution from the stellar emission and to perform a linear combination of the FUV and 24 $\mu$m fluxes calibrated as proposed originally by Salim et al. (2007) and further tested by Leroy et al. (2008).

The region studied here is about 1/10th of the region studied as the bulge in Ford et al. (2013). It is dominated by the stellar light with a very strong gradient. In this section, we reinvestigate this estimation of the SFR in the region where we observed molecular gas. In Sect. 4.2.1, we gather and reproject a series of publicly available FUV-to-24$\mu$m images to study the spectral energy distribution of this region. In Sect. 4.2.2, we compare the SED with various templates. On this basis, we show that an estimate of the SFR based on FUV and 24$\mu$m emissions corrected from stellar emission detect features at the noise level.

4.2.1 Spectral energy distribution

We gather photometric maps obtained in the past ten years on the Andromeda galaxy. While we are interested in the central kilo-parsec field, it reveals important to get a full mosaic of the galaxy as the background determination is challenging and residuals prevent any photometric use of the maps. In the UV, we used the FUV and NUV GALEX Atlas of Nearby Galaxies (Gil de Paz et al. 2007). We retrieve 1 square degree ugriz SDSS mosaic from Image Mosaic Service (Montage) at IPAC. We get the JHK 2MASS Large Galaxy Atlas (Jarrett et al. 2003). We retrieve IRAC 3.6$\mu$m and 4.5$\mu$m and MIPS 24$\mu$m maps from Spitzer Heritage Archives. IRAC 5.8$\mu$m and 7.9$\mu$m maps suffer from bad background estimates in the central kilo-parsec and we were not able to use them111We also have to remove a constant background of 2.5 MJy sr*-1* in order to get results consistent with Ford et al. (2013).. Last, we used the WISE image services to get the 3.4$\mu$m and 4.6$\mu$m maps found in excellent agreement with the IRAC Spitzer maps obtained at similar wavelengths.

In order to study the spectral energy distribution on a pixel basis, we first convolve each map to a 7 arcsec FWHM Gaussian relying on the convolution technique based on kernels proposed by Aniano et al. (2011). Second, we reproject all the maps on a 2.4 arcsec grid corresponding to 24$\mu$m Spitzer maps with Kapteyn Package. We can then plot the spectral energy distribution for each pixel and/or in an integrated area. To compute the spectral energy distribution displayed in Figures 16 and 17, we reproject the maps on the nuclear region observed by Hemachandra et al. (2015) with Spitzer/Infrared Spectrograph (IRS). The nucleus was observed with the IRS short-low (SL1, SL2 and SL3) and long-low (LL2) modules which allows observations over the 5.2–20.75 $\mu$m band. The maps sizes were obtained by 18 overlapping observations for SL (32${}^{\prime\prime}\times$57*′′) and 11 overlapping observations for LL (58${}^{\prime\prime}\times$168′′*), both regions overlapping in the central area (see Figure 18). The spectrum was integrated over the central region from which we cropped the sides since they contained clear border effects, including strong negative signals. SL2 (5.2–7.6 $\mu$m) and SL1 (7.5–14.5 $\mu$m) were connected using the overlapping SL3 (7.33–8.66 $\mu$m) mean flux. SL3 showed no offset with SL2, so the offset was added to SL1. SL1 was connected to LL2 (14.5–20.75 $\mu$m) with an offset to LL2 in order to obtain a coherent continuity with Spitzer IRAC (4.5 $\mu$m) and MIPS (24 $\mu$m) measurements.

Figure 16 corresponds to the field of view observed with IRAM-PdB, but excluding the FUV bright region (with a FUV flux non-corrected for Galactic extinction smaller than 0.15 MJy sr*-1* kpc*-2*). We find a good agreement with an 8 Gyr stellar templates from Bressan et al. (1998) and a small contribution from a 200 Myr stellar population (PEGASE.2, Fioc & Rocca-Volmerange (1999)). The crosses included a correction of foreground extinction (Fitzpatrick 1999) assuming $E(B-V)=0.05$ following Dalcanton et al. (e.g. 2012) and $R_{V}=3.1$. This is in general agreement with the current belief that this region is dominated by old stellar population (e.g. Rosenfield et al. 2012). In the near infrared, we observe an excellent agreement with all stellar templates below 5 $\mu$m. We do find an excellent agreement of the near infrared measurements with the Hemachandra et al. (2015) IRS Spitzer spectra, with a significant silicate ’bump’ around 10 $\mu$m . It is also very close to the passive galaxy template displayed in Figure 2 of Panuzzo et al. (2011). This is typical of early-type galaxies (ETG) as discussed by Panuzzo et al. (2011) and Rampazzo et al. (2013) and more generally old stellar populations. While Saglia et al. (2010) observe a metallicity gradient with slit spectroscopy but with a large uncertainty, metal-rich $Z=0.05$, $\leq$ 10-Gyr templates from Bressan et al. (1998) exhibit an infrared excess incompatible with the 24$\mu$m Spitzer data. Solar metallicity SSP templates of 8 Gyr and 200Myr adjust correctly the data. Large metallicity templates improve the match with the data in the optical part but not in the UV nor IR (for an age smaller or equal to 10 Gyr). One can note the presence of weak fine-structure emission lines discussed in Hemachandra et al. (2015), which confirms the presence some interstellar ionised gas. One can point to relatively large [NeIII] emission line, often correlated to the 24 $\mu$m dust emission (e.g. Inami et al. 2013).

Figure 17 restricts to the FUV bright region excluded in Figure 16. This region is known to host an UV bright 200 Myr stellar cluster as studied by Lauer et al. (2012). It is more difficult to match the data with a single template, suggesting a mixture of stellar population from different origins. The contribution of the 200 Myr is more important, and it is also necessary to add a large metallicity template to reproduce the UV and optical part of the spectral energy distribution. Here, the stellar background is stronger and the fine-structure emission lines are relatively weaker. Again, the FUV emission can be accounted for by stellar templates. There is no sign of star formation, while some atomic ionised gas and weak dust emission (see below) are tracing the interstellar medium of this region, probably heated by the stellar population (Groves et al. 2012).

4.2.2 Dust emission and star formation estimate

Leroy et al. (2013) used a SFR estimate based on FUV and 24 $\mu$m. This method has been used by Ford et al. (2013) who seem to overestimate the SFR in the circum-nuclear region with respect to Viaene et al. (e.g. 2014). In Figure 19, we compute the correlation between the FUV and 24 $\mu$m with 3.6 $\mu$m as computed by Ford et al. (2013), with a colour-coding corresponding to the projected distance to the centre. These authors used the 3.6 $\mu$m as an estimate of the stellar contribution to the 24 $\mu$m and FUV for a 3.6 $\mu$m flux smaller than 100 MJy sr*-1*. We can note that there is a non-linear increase for a 3.6 $\mu$m flux above 100 MJy sr*-1* observed both in FUV and at 24 $\mu$m. According to the spectral energy distribution of the region displayed in Figure 17, this can be accounted for by a mixture of stellar populations.

Figure 20 displays the 24 $\mu$m and FUV emissions after the subtraction of the emission from the stellar population performed with the adjustments displayed in Figure 19. We do detect in the 24 $\mu$m map dust emission in the East side of the IRAM-PdB observations corresponding to three high SNR${}_{\textrm{tot}}$ ($>45$) CO clumps, as displayed in Figure 8, and corresponding to the MC13 $\#$28 and $\#$36 positions, CO(2-1) has been detected. We can note that weak 11.2 $\mu$m is detected in this region observed at the edge of the IRS/Spitzer field (Hemachandra et al. 2015). In addition, a 24 $\mu$m clump is observed 15*′′* North of the nucleus, where weak 11.2 $\mu$m and 17 $\mu$m PAH features are detected. No molecular gas has been detected there. In these positions, no 6-9$\mu$m PAH features escape detection even though (Hemachandra et al. 2015) discuss the importance of template subtractions. However, such 6-9 $\mu$m to 11.2$\mu$m PAH contrast is often observed in elliptical galaxies (Kaneda et al. 2005; Vega et al. 2010). Beside a very weak feature next to the nucleus, the other 24 $\mu$m features are at the level of noise. In FUV, there is a bright spot next to the centre, which most probably corresponds to the subtraction of the FUV stellar cluster, while there might be some extinction on the North-West side of the field, corresponding to the inclination of the main disc. These features correspond to about 10 $\%$ of the stellar continuum in this region and their amplitude is very sensitive to the linear correction adopted (see Figure 19). When we combined these 2 maps following Leroy et al. (2008), we find the SFR map on the left hand side of Figure 21. It seems dominated by the dust emission discussed above, that is most probably heated by the interstellar radiation field (Groves et al. 2012). While this map averages to zero with a standard deviation of 0.004 M⊙ yr*-1*, the correlation between the FUV and 24 $\mu$m maps displayed in Figure 20 is shown in the right panel of Figure 21. Leroy et al. (2008) discussed that in case of star formation, a correlation is expected between the 24 $\mu$m dust emission and the FUV extinction. We can observe here that we do observe a correlation in the North-West side, corresponding to the PAH dust emission discussed above, which supports the presence of dust with no molecular gas detection. There is also a correlation in the middle of the field, but it corresponds to a FUV-excess and negative dust feature. It is possibly an artefact at the limit (0.09MJy/sr in FUV flux) used to correct the stellar contribution, and does not correspond to an effect of star forming region. The regions where we detect molecular gas do not exhibit a correlation coefficient close to $-1$, as can be seen with a comparison of Figure 8 with the right panel of Figure 21. This supports the view that there is residual gas in this region that is not forming star, and some dust is heated by the intermediate and old stellar population.

4.3 Kennicutt-Schmidt law

M31 quiescence in its central region is made strikingly clear in our measurements. We estimate in the previous section an upper limit on the surface density SFR $\Sigma_{\mathrm{SFR}}<0.0012(3\sigma)$ M⊙ yr*-1* kpc*-2*. In Table 4, we estimate a mean molecular gas surface density of the detected clumps $\Sigma_{\mathrm{H_{2}}}=15$  M⊙ pc*-2*, but when averaged on the region (of equivalent radius of 165 pc), this density reduces to $\Sigma_{\mathrm{H_{2}}}=0.9$ M⊙ pc*-2*. This is a lower limit as smaller clumps have escaped detection. Last, we rely on Braun et al. (2009) to estimate a neutral hydrogen surface density of the region of $\Sigma_{\mathrm{HI}}=2\pm 0.5$ M⊙ pc*-2*. In Figure 22, we compare to the Kennicutt-Schmidt law (N = 1.4) with data from Williams et al. (2018); Ford et al. (2013); Bigiel et al. (2010) and Leroy et al. (2008). Our upper limit is compatible with surface density SFR derived from Ford et al. (2013), Viaene et al. (2014).

The circumnuclear region of Andromeda is typically not forming stars and we reach the limits as discussed by Calzetti et al. (2012). One can argue that the region considered is small but we nevertheless integrate along the line of sight given the inclination of the disc.

Following Leroy et al. (2008), we define Star Formation Efficiency (SFE) as the SFR surface density per unit H2, SFE(H2) = $\Sigma_{\textrm{SFR}}/\Sigma_{\textrm{H}_{2}}$. Hence, we find a star formation efficiency of H2 smaller than 1.3$\times$ 10*-9* yr*-1* (3$\sigma$), which is within the uncertainties of Leroy et al. (2008) who finds SFE(H2) = 5.25 $\pm$ 2.5 $\times$ 10*-10* yr*-1* at scales of 800 $pc$. A constant SFE(H2) is expected if the GMC properties are universal and the conditions within the GMC constitute the driving factor (Krumholz & McKee 2005).

5 Conclusion

We have analysed molecular observations made with the IRAM-Plateau de Bure interferometer, towards the central 250 pc of M31. The CO(1-0) mosaic was compared with previous CO(2-1) single dish mapping with the IRAM-30m HERA instrument. The spectral energy distribution of the region and tracers of star formation have been studied. The main results can be summarized as follow :

We first identified molecular clumps from high S/N peaks in the map, and selected genuine clouds using both robust data analysis and statistical methods. Our modified approach to the CPROPS algorithm allowed us to extract a catalogue of 12 CO(1-0) clumps with a total S/N ratio larger than 15 in a region of low CO density. 2. 2.

We derived the size, velocity dispersion, H2 mass, surface density and virial parameter for each cloud. The clouds follow the Larson’s mass-size scaling relation, but lie above the velocity-size relation. We discuss that they are not virialised, but might be the superimposition of smaller entities. 3. 3.

We measured a gas-to-stellar mass ratio of $4\times 10^{-4}$ in this region. 4. 4.

We discussed the CO(2-1)-to-CO(1-0) line ratio from the single dish observations from Melchior & Combes (2013) when the CO(1-0) map is smoothed to the 12 arcsec resolution. We have been able to compute the CO(2-1)-to-CO(1-0) line ratio for 3 positions. This ratio is below 0.5, supporting non LTE conditions. Relying on RADEX simulations, we discuss that this optically thick gas has a low gas density in the range $60-650$ cm*-3* with sub-thermal excitation ($T_{ex}=5-9$ K. We find a filling factor of order 5 $\%$. 5. 5.

We study the spectral energy distribution of the region, and show that it is compatible with a quiescent elliptical galaxy template, with weak MIR atomic fine-structure emission lines. These lines correlates with the 24$\mu$m dust emission detected in the region. 6. 6.

A correlation between the FUV extinction and 24$\mu$m dust emission is observed in a position at 15 arcsec North of the nucleus, where Hemachandra et al. (2015) have detected 11.2 and 17. $\mu$m PAH. No molecular gas is detected in this position. In the region located East of the nucleus, where several molecular clouds have been detected, there is 24$\mu$m dust emission as well as 11.2 $\mu$m PAH emission (Hemachandra et al. 2015). 7. 7.

We subtracted the stellar contribution in order to use 24 $\mu$m and FUV as tracers of star formation. This region averages to zero star formation, deriving an upper limit compatible with previous works. This low density region (both in gas and SFR) lies formally on the Kennicutt-Schmidt law.

The circum-nuclear region of M31 appears depleted in gas, both HI and H2. This depletion is compatible with the absence of star formation. The gas and dust observed in this region are heated in the centre by the radiation of intermediate and old stellar populations. The galaxy then appears to be quenched from inside out, since star formation continues to occur in the outer ring. The presence of diffuse ionized gas in the centre, together with low abundance of neutral gas (atomic and molecular) and lack of young stars in the centre is quite similar to the LIER galaxies described by Belfiore et al. (2016).

In the case of M31, many scenarios have been proposed. Dong et al. (2018) observations suggest that there was a strong peak in SFR less than 500 Myr ago, which could contribute to the gas depletion. This is in line with the conclusions of Block et al. (2006) which point at a collision with M32 as a reason for the low molecular gas density in the centre of Andromeda, also explaining the atypical two-rings architecture of M31. D’Souza & Bell (2018) claim that M32 was in the past a much bigger galaxy, able to produce a major interaction with M31 2 Gyr ago. This allows also the remaining M32-core to re-enter the M31 disk almost head-on towards the centre and produce more recently the two rings in the disk. Observations of higher-J CO emission, and also shock-tracing molecules will be helpful to disentangle the various scenarios.

Acknowledgements.

Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). We acknowledge the IRAM Plateau de Bure team for the observations. We thank Sabine König for her support for the data reduction. We warmly thank Eric Rosolowsky, our referee, for his very helpful and constructive comments. We are grateful to Pauline Barmby for providing us with reduced Spitzer data in the nucleus region. ALM has benefited from the support of Action Fédératrice Structuration de l’Univers et Cosmologie from Paris Observatory. This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research made use of Montage, funded by the National Aeronautics and Space Administration’s Earth Science Technology Office, Computational Technnologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. The code is maintained by the NASA/IPAC Infrared Science Archive. This research makes use of GALEX, SDSS, 2MASS, Spitzer and WISE archive data of Andromeda.

Appendix A Upper limit on the continuum level

We estimate an upper limit on the continuum level with an average on the whole bandwidth $[-3000,6000]$ km s*-1*.

In Figure 23, we display the mean flux and associated (rms) noise in $\mu$Jy achieved in integrating the whole spectra in circular regions of given radius R. We significantly improve the first 3$\sigma$ upper limit measured at 1 mm by Melchior $\&$ Combes (2013) of 0.65 mJy with single dish observations. We estimate a 3 $\sigma$ upper limit at 3 mm of about 15$\mu$Jy within a radius of 20 arcsec.

This excludes the value (60 $\mu$Jy) at 12 $\sigma$ expected with a simple extrapolation of the synchrotron emission detected at 6 cm (5 GHz) of about 0.2 mJy by Giessubel $\&$ Beck (2014) with a measured spectral index of $-0.4\pm 0.03$. As the primary beam has a HBPW of 45 arcsec, we do not expect to significantly smooth large scale signals. We thus expect a steeper slope.

We can also exclude large quantities of hidden cold dust. However, it is already well-known that this region hosts very little dust (e.g. Melchior et al. 2000), and our upper limit does not provide more constraints than the infrared dust emission presented in the Figure 3 of Groves et al. (2012), as dust emission at 3 mm is expected at the level of 10*-6*$\mu$Jy. If a weak 3mm continuum exists in this region, it is probably due to synchrotron emission.

Appendix B Selection procedure

With a 2-D Gaussian model using the transfer function of a point-like signal we show that isolated pixels showing an excess are impossible to distinguish between signal and noise. We see that a minimum of 3 adjacent spatial pixels is required. We define as a cloud an area of at least 3 adjacent spatial pixels with signals with velocities $V_{0}$ varying within a range of $10\,km\,s^{-1}$ maximum. We find 54 molecular clouds (displayed in Figure 24) with peak flux ranging from $\Phi_{max}=11.8\,mJy/beam$ to $\Phi_{max}=60.1\,mJy/beam$. $3-\sigma$ clumps with negative flux are also found, we display 47 negative clumps in Figure 25. These negative signals are expected to be noise or side lobes: we keep them to test our selection procedure. The velocity distribution histograms for positive and negative clumps show that negative clumps with numerous pixels lie in the same regions as positive core clumps with high S/N ratio.