SPATIALLY RESOLVED CHEMISTRY IN NEARBY GALAXIES. II. THE NUCLEAR BAR IN MAFFEI 2

The Sb galaxy Maffei 2 is one of the nearest and brightest extragalactic molecular line sources, at a distance of only 3.3 Mpc (1'' ∼ 15 pc; Fingerhut et al. 2007; see discussion in MTH08). A strongly barred and somewhat asymmetric galaxy, Maffei 2 has undergone a recent interaction with a small companion that has driven a large quantity of gas into the nucleus, building up a compact central bulge seen in the NIR (Hurt et al. 1993, 1996). This bar-like compact bulge has further driven the molecular gas into a central molecular zone of radius R ∼ 300 pc that is barred and highly inclined (Ishiguro et al. 1989; Hurt & Turner 1991). This nuclear bar, containing M(H₂) ∼2 × 10⁷ M_☉ of gas (MTH08), is structurally reminiscent of a miniature version of large-scale gaseous bars (Athanassoula 1992; Figure 1). Using 2 cm and 3 mm radio/millimeter continuum to trace ionizing radiation, it is seen that the intersections of bar arms and central ring are sites of intense localized star formation (SFR ∼ 0.04 M_☉ yr⁻¹ per GMC or a total of L_OB ∼ 10⁸ L_☉; Turner & Ho 1994; Tsai et al. 2006; MTH08). Averaged over the inner ∼20'' radius, gas consumption timescales decrease below 100 Myr, making Maffei 2's nucleus a starburst.

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A central molecular ring of radius ∼7'' (110 pc) is clearly resolved in gas kinematics, although the ring is less apparent in integrated intensity images (MTH08). GMCs D, E, and F (cloud designations following MTH08 are shown in Figure 1) are located along the eastern side of the nuclear ring. Bar arms (including GMCs B and C in the north and G and H in the south) extend off the leading edges of the ring. The bright GMCs of the central ring, typically ∼60–80 pc in extent, and with masses of a few 10⁶ M_☉, delineate the sites where gas flowing in along the bar arms piles up at the inner ring. Dense gas traced by HCN preferentially picks out the arm–ring intersections. Gas not incorporated into the dense component at the starburst locations is tidally sheared into a moderate density, smoothly distributed ring (MTH08). Massive star formation is largely absent in the western side of the ring (MTH08). Based on HCN, the fraction of dense gas is significantly lower toward the bar ends. Densities derived from CO tend to be fairly constant ($n_{{\rm H_2}} \sim 10^{3}$) over the inner bar, with the clouds associated with young star formation slightly warmer (T_K ∼ 30–40 K) than the others (T_k ∼ 20 K). Gas clouds on the quiescent western side of the nuclear ring are slightly cooler yet (MTH08).

Column densities are determined assuming optically thin emission, and LTE:

$$\begin{equation} N_{{\rm mol}} = \left(\frac{3k Qe^{E_{u}/kT_{{\rm ex}}}}{8\pi ^{3}\nu S_{{\rm ul}}\mu _{0}^{2} g_{K_{u}}g_{I_{u}}} \right)I_{{\rm mol}}, \end{equation} \tag{ 1 }$$

where S_ul, g, and E_u are the line strength, degeneracy, and upper energy of each state, respectively, and T_ex is the excitation temperature associated with the transition. Given that we have mapped only one transition of each species, corrections for background radiation and opacity have been ignored. Column densities are sensitive to T_ex through the partition function, Q, and the energy of the upper state. The asymmetric tops (HNCO and CH₃OH) are more sensitive to temperature changes than are the linear rotors. Changes in gas density also affect excitation, particularly for molecules with high critical densities (HNC, N₂H⁺, and HC₃N). Densities have been at least partially constrained by observation in Maffei 2 (MTH08). We adopt a T_ex = 10 K for the molecular transitions here. This is similar to what is derived from the ¹³CO data (MTH08) and is the same as assumed for IC 342 (MT05), permitting easy comparison. However, T_ex = 10 K may slightly underestimate excitation at the massive star-forming regions. Measured line intensities, peak temperatures, line centroids, and line widths for the GMCs are reported in Table 3. Fractional abundances ($X({\rm mol})\equiv N_{{\rm mol}}/N_{{\rm H}_{2}}$) calculated from the intensities given the above assumptions are listed in Table 4, based on molecular parameters in Table 1.

Table 3. Measured Intensities, Line Widths, and Centroids

GMC	Transition	Imol	Tb	vo	Δv
αo,δo		(K km s−1)	(mK)	(km s−1)	(km s−1)
A	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:57.17)	SiO(1–0; v = 0)	<1.0	<23	⋅⋅⋅	⋅⋅⋅
(59:36:42.4)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	<3.3	<34	⋅⋅⋅	⋅⋅⋅
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	<3.3	<34	⋅⋅⋅	⋅⋅⋅
	HCO+(1–0)	16 ± 7	270 ± 38	−34 ± 5	21 ± 10
	HNC(1–0)	<2.9	45 ± 16	−100 ± 11	120 ± 25
	HC3N(10–9)	<1.0	<26	⋅⋅⋅	⋅⋅⋅
	N2H+(1–0)	<1.9	<30	⋅⋅⋅	⋅⋅⋅
	C34S(2–1)	<2.2	<28	⋅⋅⋅	⋅⋅⋅
	CH3OH(2k–1k)	<3.2	46 ± 19	−100 ± 6	45 ± 15
	HNCO(505–404)	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
B	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:55.75)	SiO(1–0; v = 0)	<1.0	35 ± 12	−67 ± 13	55 ± 30
(59:36:29.6)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	<3.3	<34	⋅⋅⋅	⋅⋅⋅
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	<3.3	<34	⋅⋅⋅	⋅⋅⋅
	HCO+(1–0)	61 ± 7	470 ± 38	−84 ± 3	68 ± 7
	HNC(1–0)	9.1 ± 1	150 ± 16	−134 ± 3	65 ± 7
	HC3N(10–9)	<1.0	<26	⋅⋅⋅	⋅⋅⋅
	N2H+(1–0)	5.1 ± 1	60 ± 15	−98 ± 6	50 ± 10
	CH3OH(2k–1k)	10 ± 2	53 ± 19	−87 ± 8	48 ± 20
	C34S(2–1)	<2.2	<28	⋅⋅⋅	⋅⋅⋅
	HNCO(505–404)	≲4.8	50 ± 29	−112 ± 20	110 ± 50
C	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:55.48)	SiO(1–0; v = 0)	<1.0	24 ± 12	−80 ± 20	83 ± 47
(59:36:24.8)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	11 ± 2	100 ± 17	−88 ± 6	93 ± 15
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	3.9 ± 2	48 ± 17	−76 ± 17	90 ± 40
	HCO+(1–0)	82 ± 7	520 ± 38	−78 ± 3	83 ± 6
	HNC(1–0)	24 ± 1	200 ± 16	−120 ± 4	120 ± 8
	HC3N(10–9)	2.8 ± 0.5	42 ± 13	−88 ± 7	65 ± 16
	N2H+(1–0)	9.6 ± 1	110 ± 15	−88 ± 5	77 ± 10
	CH3OH(2k–1k)	5.0 ± 2	100 ± 19	−99 ± 4	48 ± 8
	C34S(2–1)	<2.2	<28	⋅⋅⋅	⋅⋅⋅
	HNCO(505–404)	≲4.8	130 ± 29	−89 ± 5	42 ± 10
D	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:55.14)	SiO(1–0; v = 0)	2.5 ± 0.5	<23	⋅⋅⋅	⋅⋅⋅
(59:36:20.7)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	17 ± 2	110 ± 17	−82 ± 9	130 ± 22
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	11 ± 2	80 ± 17	−77 ± 17	120 ± 35
	HCO+(1–0)	180 ± 7	580 ± 38	−74 ± 3	110 ± 7
	HNC(1–0)	41 ± 1	250 ± 16	−109 ± 4	140 ± 8
	HC3N(10–9)	3.2 ± 0.5	50 ± 13	−80 ± 6	67 ± 15
	N2H+(1–0)	9.4 ± 1	110 ± 15	−87 ± 4	82 ± 8
	CH3OH(2k–1k)	5.5 ± 2	95 ± 19	−101 ± 5	57 ± 12
	C34S(2–1)	<2.2	<28	⋅⋅⋅	⋅⋅⋅
	HNCO(505–404)	≲4.8	86 ± 29	−90 ± 11	82 ± 15
E	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:55.08)	SiO(1–0; v = 0)	∼0.77	22 ± 12	−2.0 ± 26	220 ± 60
(59:36:18.4)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	19 ± 2	97 ± 17	−73 ± 12	160 ± 28
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	13 ± 2	77 ± 17	−72 ± 16	130 ± 38
	HCO+(1–0)	130 ± 7	520 ± 38	−73 ± 4	130 ± 8
	HNC(1–0)	44 ± 1	220 ± 16	−104 ± 4	150 ± 10
	HC3N(10–9)	2.1 ± 0.5	39 ± 13	−80 ± 8	67 ± 18
	N2H+(1–0)	6.6 ± 1	85 ± 15	−83 ± 5	92 ± 12
	CH3OH(2k–1k)	6.7 ± 2	70 ± 19	−94 ± 8	75 ± 18
	C34S(2–1)	<2.2	<28	⋅⋅⋅	⋅⋅⋅
	HNCO(505–404)	<4.8	<58	⋅⋅⋅	⋅⋅⋅
F	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:54.86)	SiO(1–0; v = 0)	<1.0	35 ± 12	17 ± 8	50 ± 18
(59:36:09.6)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	9.4 ± 2	63 ± 17	10 ± 12	130 ± 50
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	<3.3	∼46	⋅⋅⋅	⋅⋅⋅
	HCO+(1–0)	85 ± 7	450 ± 38	−6.9 ± 4	83 ± 8
	HNC(1–0)	36 ± 1	250 ± 16	−0.9 ± 3	67 ± 17
	HC3N(10–9)	4.1 ± 0.5	31 ± 13	0.1 ± 13	130 ± 30
	N2H+(1–0)	15 ± 1	150 ± 15	5.4 ± 6	70 ± 10
	CH3OH(2k–1k)	15 ± 2	190 ± 19	−43 ± 3	68 ± 5
	C34S(2–1)	5.0 ± 1	∼30	−46 ± 26	180 ± 62
	HNCO(505–404)	22 ± 2	190 ± 29	−1.6 ± 3	40 ± 7
G	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:54.12)	SiO(1–0; v = 0)	1.2 ± 0.5	52 ± 17	28 ± 4	32 ± 13
(59:35:59.6)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	6.1 ± 2	110 ± 17	12 ± 4	55 ± 10
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	4.1 ± 2	51 ± 17	27 ± 12	72 ± 28
	HCO+(1–0)	∼15 ± 7	200 ± 38	15 ± 7	62 ± 15
	HNC(1–0)	17 ± 1	200 ± 16	20 ± 2	55 ± 5
	HC3N(10–9)	<1.5	<26	⋅⋅⋅	⋅⋅⋅
	N2H+(1–0)	10 ± 1	140 ± 15	23 ± 3	57 ± 7
	CH3OH(2k–1k)	25 ± 2	300 ± 19	−27 ± 2	55 ± 3
	C34S(2–1)	3.3 ± 2	47 ± 19	40 ± 6	50 ± 15
	HNCO(505–404)	33 ± 2	320 ± 29	21 ± 2	43 ± 3
H	SiO(1–0; v = 1)	<19	<88	⋅⋅⋅	⋅⋅⋅
(02:41:53.76)	SiO(1–0; v = 0)	<1.0	<23	⋅⋅⋅	⋅⋅⋅
(59:36:04.7)	C2H($\frac{3}{2}$–$\frac{1}{2}$)	<3.3	60 ± 17	5.8 ± 9	78 ± 22
	C2H($\frac{1}{2}$–$\frac{1}{2}$)	<3.3	<34	⋅⋅⋅	⋅⋅⋅
	HCO+(1–0)	<15	150 ± 38	6.2 ± 6	35 ± 13
	HNC(1–0)	7.8 ± 1	130 ± 16	10 ± 5	58 ± 17
	HC3N(10–9)	<1.0	<26	⋅⋅⋅	⋅⋅⋅
	N2H+(1–0)	<1.9	73 ± 15	20 ± 6	57 ± 10
	CH3OH(2k–1k)	8.4 ± 2	200 ± 19	−32 ± 2	60 ± 5
	C34S(2–1)	<2.2	<28	⋅⋅⋅	⋅⋅⋅
	HNCO(505–404)	≲4.8	110 ± 29	11 ± 4	32 ± 10

Notes. T_b is the main-beam brightness temperature based on a 8'' aperture. I_mol is the peak integrated intensity in units of K km s⁻¹ for the resolution given in Table 2. Uncertainties are based on the rms noise for the temperatures and intensities, and 1σ from the least-squared Gaussian fits for the velocity information. Upper limits represent 2σ values.

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Fractional abundances also require an H₂ column density, N(H₂). N(H₂) is most easily obtained from the CO(1–0) brightness and an empirical Galactic conversion factor, X_CO. However, X_CO overpredicts N(H₂) in nearby galaxy centers, including Maffei 2, by factors of a few (MTH08). An alternative measure of N(H₂) can be obtained from the CO isotopologues, which tend to be optically thin. We use the ¹³CO(1–0) integrated intensity and [H₂/¹³CO] = 7.0 × 10⁵ ([¹²CO/¹³O] = 60 and [CO/H₂] = 8.5 × 10⁻⁵) when calculating the H₂ column densities (see MTH08 for a detailed discussion of N(H₂) and its uncertainties in Maffei 2).

Fractional abundances for the species below are estimated to be uncertain to at least a factor of three, although the relative column densities—that is, the relative spatial distributions within the nucleus of the different molecules—should be more reliable. MT05 have a detailed discussion of the uncertainties associated with the abundance estimates. For reference, Table 1 records the change in derived column densities if T_ex is changed from 10 K to 50 K, more typical of the large beam gas kinetic temperatures.

We now discuss the morphologies of each species. Spectra taken at selected locations across the nucleus with 8'' apertures are shown for each transition in Figure 2. Figure 3 displays maps of the transitions detected with OVRO and Figure 4 displays those detected with BIMA. In the subsequent analysis, we also include 3 mm continuum emission and CO isotopologues from MTH08. The millimeter continuum in Maffei 2 is dominated by free–free emission rather than dust emission (MTH08).

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SiO—silicon monoxide. The J = 2–1 rotational line of both the v = 0 and 1 vibrational states were observed. The v = 1, J = 2–1 transition is a maser in the Galaxy (Snyder & Buhl 1975), but we do not detect it in Maffei 2. The thermal v = 0 transition of SiO is tentatively detected toward GMCs B, F, and G with peak temperatures over the 8'' aperture of 35 mK (Figure 4). The integrated intensity map is noisy but consistent in morphology to HNCO and CH₃OH, extended along the southern arm. Implied SiO abundances reach ∼1 × 10⁻¹⁰. This abundance is lower than estimated for IC 342 and the nearby starburst nuclei, NGC 253 and M82 (García-Burillo et al. 2000, 2001; Usero et al. 2006), but typical of diffuse Galactic clouds (Greaves et al. 1996; Turner 1998b) away from molecular outflows (Martín-Pintado et al. 1992); it is much larger than what is found for Galactic dark clouds (e.g., Ziurys et al. 1989).

C₂H—ethynyl. We detect both the J = (3/2)–(1/2) and (1/2)–(1/2) fine structure components of the N = 1–0 line. C₂H is brightest toward the northern star-forming ring (GMC D+E), peaking at 0.11 K, and weakens significantly along the bar arms (Figure 4). Toward GMCs F and G, C₂H avoids the column density peaks traced in ¹³CO(1–0). Line widths are significantly broader than those seen in the other weaker lines, so the hyperfine structure of each fine structure component is being marginally resolved here. Evidence for the most blueshifted N = 1–0, J = (1/2)–(1/2), and F = 1–0 hyperfine component is seen toward the brightest GMCs (see Figure 2). There is a plume of emission along the minor axis in the (3/2)–(1/2) line. From the relative intensities of the fine structure lines, we can determine the C₂H opacity. The ratio of the brightness temperature of the two fine structure transitions, I((3/2)–(1/2))/I((1/2)–(1/2)) ranges from 1.2 to ∼2.8, with lowest values toward the regions with the brighter emission. For optically thin, LTE excitation a this ratio should be 2.0. Therefore, C₂H opacities are significant along the central ring, with implied values for the (3/2)–(1/2) transition of τ_CCH ≃ 1.5. Along the arms τ_CCH <1 except at regions around GMC G away from the ¹³CO(1–0) column density peaks where τ_CCH ∼ 3. Hence, despite its lower signal to noise, the (1/2)–(1/2) transition probably represents a closer picture of the true C₂H abundance distribution. Fractional abundances, assuming C₂H is optically thin, peak at ∼2.5 × 10⁻⁸. If we account for opacity, the abundance rises to ∼4.8 × 10⁻⁸. These are similar to those seen toward the PDR site in IC 342 (MT05) and at the high end of the range seen in Galactic cores (Wootten et al. 1980; Huggins et al. 1984; Watt 1983; Turner et al. 1999; Lucas & Liszt 2000).

HCO⁺—formyl ion. HCO⁺(1–0) is the brightest line of this sample, and is imaged at high resolution (∼2''). The emission is dominated by GMCs D+E and F, with line peaks of 2.0 K (0.58 K over the 8'' aperture; Figure 3). Like HCN(1–0) (MTH08), HCO⁺(1–0) is primarily confined to the central ring region. There is a second blueshifted velocity component at ∼ −135 km s⁻¹ (LSR) along the northern portion of the bar. HCO⁺(1–0) abundances in Maffei 2 are between 2 and 8× 10⁻⁹, but these (along with those of HCN and HNC) should be considered lower limits since these very bright transitions may have significant optical depths (see Section 4.1.1). These agree well with the HCO⁺ abundances in most Galactic dense clouds (e.g., Pirogov et al. 1995; Lucas & Liszt 1996; Turner 1995a) and single-dish extragalactic measurements (Nguyen-Q-Rieu et al. 1992).

HNC—hydrogen isocyanide. The J = 1–0 line of the linear molecule HNC is bright over the whole nuclear bar, with peak temperatures ∼0.25 K (Figure 4). At this resolution, the morphology closely matches both ¹³CO(1–0) and HCN(1–0), being dominated by the bright clouds, D+E and F, but HNC emission is seen from every cloud including the non-nuclear bar GMC, A. Toward the northern side of the bar HNC emission is especially bright at higher blueshifted velocities, similar to the component seen in HCO⁺(1–0). HNC abundances are (1–2) × 10⁻⁹, in agreement with IC 342 (MT05). These abundances are intermediate between typical massive star-forming cores and Galactic dark clouds (Wootten et al. 1978; Blake et al. 1987; Hirota et al. 1998; Nummelin et al. 2000).

HC₃N—cyanoacetylene. We mapped the J = 10–9 rotational line of HC₃N. This molecule has the largest electric dipole moment and the highest upper energy state of the (thermal) sample (Table 1). It is thus not surprising that we observe HC₃N to be faint and spatially confined (Figure 4). To improve signal-to-noise ratio (S/N), the HC₃N map was smoothed to a slightly larger beam size, but even then peaks at only ∼50 mK toward two unresolved locations at the intersection of the ring and bar arms (C and F). Abundances are ∼10⁻⁹, similar to those in IC 342 (MT05; Meier et al. 2011), somewhat higher than in cold Galactic clouds but much lower than the localized Galactic hot core values (>10⁻⁷; e.g., Morris et al. 1976; Vanden Bout et al. 1983; Chung et al. 1991; de Vicente et al. 2000).

N₂H⁺—diazenylium. In the Galaxy, N₂H⁺ is regarded as a tracer of quiescent gas. We observed the J = 1–0 rotational state of this linear ion, which has hyperfine splitting much smaller than the observed line widths. As is the case in IC 342, N₂H⁺ is bright and extended across the nucleus (Figure 4). Emission peaks toward GMC F with a peak brightness temperature reaching ∼0.15 K. GMCs D and E, the closest clouds to the northern star formation region, show weak emission in N₂H⁺: X(N₂H⁺) reaches ∼7 × 10⁻¹⁰ at GMC F and drops by nearly a factor of three toward the 3 mm continuum peak. The highest abundances are similar to what is seen in IC 342 and dense, quiescent cores in the Galactic disk (Womack et al. 1992; Benson et al. 1998).

C³⁴S—carbon monosulfide. This is an isotopologue of the dense gas tracer CS. The J = 2–1 rotational transition of C³⁴S is tentatively detected only toward GMCs A, C, and F, at <30 mK (Figure 4). The tentative detections imply X(C³⁴S) abundances of at most a few × 10⁻¹⁰, typical of Galactic dense cores and diffuse/translucent clouds (for a C³²S/C³⁴S isotopic abundance of 23; e.g., Nyman 1984; Drdla et al. 1989; Wang et al. 1993; Chin et al. 1996; Morata et al. 1997; Lapinov et al. 1998; Lucas & Liszt 2002). In the GMCs near the northern star-forming region, abundances are an order of magnitude lower. Evidently, C³⁴S(2–1) is not strongly enhanced anywhere across the nucleus, and especially not at the massive star formation sites. Limits on the CS/C³⁴S isotopologue ratio assuming optically thin CS ranges from 4 to >14 based on the CS(2–1) line of Kuno et al. (2008). The tentative detection of CS/C³⁴S ∼ 4 suggest opacities significantly greater than unity in CS(2–1).

CH₃OH—methanol. We observed the low energy, blended set of 2₁–1₁E, 2₀–1₀E, 2₀–1₀A+, and 2₋₁–1₋₁E thermal transitions of CH₃OH (hereafter labeled the 2_k–1_k transition). We cannot resolve these transitions in this group, given the source line widths. The 2_k–1_k transition of CH₃OH is very bright across the nucleus, with peak temperatures reaching 0.28 K (Figure 4). Of the species observed in this paper, only HCO⁺(1–0) is brighter. Remarkably, though, the morphology of CH₃OH is completely different from what is seen in most of the other lines, including ¹³CO(1–0) and HCN(1–0). CH₃OH peaks strongly toward the southern nuclear bar end (G and H) and the southern nuclear bar arm/ring intersection region (F). By contrast, emission is barely detected near GMC D+E. The emission favors the right side of the southern arm, which is the trailing, upstream side. At the bar ends, methanol abundances peak at ∼1.5 × 10⁻⁸. Toward GMC D abundances drop by a factor of five. The peak arm abundances are a factor of two higher than those of IC 342 (MT05). Galactic methanol abundances can reach these levels in small localized hot core regions (e.g., Kalenskii & Sobolev 1994; Kalenskii et al. 1997; Bachiller & Perez Gutierrez 1997; Turner 1998a; Nummelin et al. 2000; Minier & Booth 2002). CH₃OH velocities appear to be consistently blueshifted with respect to most of the other transitions. In the north, the velocity shift is ∼ −10 km s⁻¹, growing to ∼ −40 km s⁻¹ along the southern bar end. The shift toward the northern cloud is not significant; however, the shift seen toward GMCs F and G appears to be real. This may result from an increased population in the higher excitation blueshifted lines that make up the quadruplet or somewhat different kinematics due to the presence of shocks (see Section 4.4.1).

HNCO—isocyanic acid. We observed the K₋₁ = 0 transition of the J = 5–4 rotational state (5₀₅–4₀₄) of this prolate, slightly asymmetric top. In the higher resolution OVRO maps, HNCO peaks at GMCs F and G, with faint emission along the bar connecting the two clouds (Figure 3). When smoothed to match the resolution of the BIMA data, HNCO has a very similar morphology to CH₃OH. Over the 8'' aperture used for the spectra in Figure 2, HNCO has a peak brightness of 0.25 K, whereas over the 40 pc resolution achieved in the OVRO data peak brightnesses reach 1.0 K. No emission is detected toward GMC D in the high-resolution map. HNCO abundances reach X(HNCO) ≃ 9 × 10⁻⁹ along the southern nuclear bar. These abundances are typical of those observed on one to two orders of magnitude smaller scales in Galactic massive dense cores (Zinchenko et al. 2000) and are even a factor of three larger than the HNCO enhanced shock regions in IC 342 (MT05). CH₃OH and HNCO in Maffei 2 have some of the most pronounced morphological differences from CO yet seen in extragalactic sources. These two species illustrate the importance of high spatial resolution interferometric observations of chemical species.

Other transitions. Table 5 presents the limits (2σ) for other potentially detectable transitions within the observed bandwidth. These include the ¹³C substituted isotopologues of HNC(1–0) and HC₃N(10–9) and two transitions of the radical HCO. None of these transitions are detected. In the case of the ¹³C isotopologues, only the HN¹³C(1–0) limits are at all constraining (Table 8). Toward the central ring and southern bar end 1σ HNC(1–0)/HN¹³C(1–0) line ratio lower limits are >10–16, which, in these locations, are consistent with or slightly above the corresponding CO isotopic line ratios (MTH08). Therefore, the HNC(1–0) opacities are lower than ¹²CO(1–0) opacities.

Table 5. Other Observed Transitions

Molecule	Transition	ν	Tmb	GMCs
		(GHz)	(mJy beam−1)
HCO	10, 1–00, 0; $\frac{1/2}{1/2}$; 1–1	86.777	<20	⋅⋅⋅
HCO	10, 1–00, 0; $\frac{1/2}{1/2}$; 0–1	86.806	<20	⋅⋅⋅
HN13C	1–0	87.091	<22	⋅⋅⋅
HCC13CN/HC13C2N	10–9	90.593/90.602	<22	⋅⋅⋅
⋅⋅⋅
⋅⋅⋅	⋅⋅⋅	89.222(5)	70 ± 15	C
⋅⋅⋅	⋅⋅⋅	90.912(5)	10 ± 6	F

Note. Upper limits are 2σ.

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To facilitate the exposition, we omit the transitions for each species where possible in the remainder of the text. We discuss transition-dependent effects specifically where important.

The maps give a picture of the molecular cloud astrochemistry in the nuclear region of Maffei 2. To interpret these maps, we need to establish similarities and differences between the molecules. The correlations reveal trends in the chemistry, which, in turn, can suggest the physical driving forces responsible for these characteristics and how they change across the nucleus.

As in MT05, we quantify morphological correlations amongst the images via a PCA. PCA is a common technique (e.g., Murtage & Heck 1987; Krzanowski 1988; Everitt & Dunn 2001; Wall & Jenkins 2003) used to reduce the dimensionality of a data set. The PCA simplifies the picture of molecular distribution, reducing a large amount of information to a few images, providing an excellent framework within which to study the complex variations in molecular properties in Maffei 2. For a general description of PCA applied to multi-transition molecular maps, see Heyer & Schloerb (1997) or for specific applications to extragalactic molecular maps, see MT05. The PCA is dependent on the particular set of data given to it; here, we are analyzing the correlations of 3 mm lines of heavy molecules, so the results we obtain pertain to the cool and relatively dense cloud population in Maffei 2.

To calculate the principal components (PCs) for Maffei 2, the line maps were remade to the same geometry and beam size (that of HNC; Table 2), normalized and mean-centered. Thirteen maps, including ¹³CO(1–0), HCN(1–0), and 3 mm continuum from MTH08, plus the ten transitions of the nine species discussed in Section 3.3, were sampled at 1'' intervals over the central 38'' × 56'', making up a 27,664 element data space. The algorithm used to calculate the PCs is that of Murtage & Heck (1987).

The results of the PCA are tabulated in Tables 6 and 7. Table 6 shows the matrix of pairwise correlation coefficients among all of the 13 maps. Table 7 records the projection of each map onto the seven modeled PCs. Figure 5 displays the maps of the first three (most important) PCs. These three PCs account for 80% of the variation present in the data set. The projections of each map onto the first three PCs are shown vectorially in Figure 6.

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Table 6. PCA Correlation Matrix

Maps	13CO	3MM	C2H($\frac{3}{2}$)	HCN	HCO+	HNC	CH3OH	HNCO	N2H+	HC3N	C34S	SiO	C2H($\frac{1}{2}$)
13CO	1.00
3MM	0.88	1.00
C2H($\frac{3}{2}$)	0.85	0.77	1.00
HCN	0.93	0.92	0.84	1.00
HCO+	0.89	0.88	0.81	0.98	1.00
HNC	0.95	0.87	0.84	0.97	0.94	1.00
CH3OH	0.68	0.47	0.49	0.43	0.34	0.51	1.00
HNCO	0.52	0.27	0.32	0.21	0.12	0.33	0.86	1.00
N2H+	0.86	0.71	0.67	0.77	0.72	0.82	0.71	0.58	1.00
HC3N	0.54	0.53	0.41	0.62	0.60	0.62	0.32	0.16	0.63	1.00
C34S	0.20	0.24	0.17	0.18	0.20	0.19	0.14	0.095	0.20	0.15	1.00
SiO	0.38	0.23	0.34	0.34	0.30	0.38	0.35	0.30	0.35	0.31	−0.023	1.00
C2H($\frac{1}{2}$)	0.64	0.60	0.70	0.66	0.63	0.63	0.27	0.18	0.45	0.24	0.008	0.32	1.00

Note. ^aData from MTH08.

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Table 7. PCA Eigenvectors

PCA Comp.	1	2	3	4	5	6	7
13CO	0.35	−0.045	−0.0043	0.11	−0.042	0.15	−0.064
3MM	0.32	0.15	−0.10	0.12	−0.086	0.19	−0.50
C2H($\frac{3}{2}$)	0.31	0.097	0.086	0.24	0.12	0.020	0.81
HCN	0.34	0.21	0.00	−0.012	−0.057	0.16	−0.086
HCO+	0.33	0.28	−0.029	−0.024	−0.055	0.21	−0.038
HNC	0.35	0.11	0.0015	−0.031	−0.054	0.16	0.038
CH3OH	0.23	−0.55	−0.03	0.10	−0.091	0.0061	−0.031
HNCO	0.17	−0.65	−0.01	0.17	−0.050	−0.10	−0.061
N2H+	0.32	−0.19	−0.089	−0.12	−0.20	−0.061	0.070
HC3N	0.23	0.067	−0.13	−0.68	−0.29	−0.52	0.086
C34S	0.080	−0.0027	−0.81	0.0092	0.56	−0.11	−0.0031
SiO	0.16	−0.19	0.43	−0.51	0.66	0.23	−0.074
C2H($\frac{1}{2}$)	0.24	0.19	0.33	0.37	0.29	−0.70	−0.23
Egnv. %	59	13	8.3	6.6	5.6	2.7	1.5

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Inspection of Figure 6 reveals that PC 1 is most strongly correlated with all maps. It represents a mix of the ¹³CO and HCN maps, implying that PC 1 is a good density-weighted column density map of the low excitation molecules in Maffei 2. This was also found in IC 342; however, here ¹³CO projects along PC 1 more closely than HCN, hence PC 1 is nearer to a pure column density map than its analogue in IC 342. All maps except the low S/N ratio C³⁴S show significant correlation with PC 1.

PC 2 characterizes the dominant variation seen once the distribution of column density has been accounted for. PC 2 distinguishes two major distinct groups of molecules, those peaking toward the northern star-forming region and those peaking toward the southern nuclear bar end. Species with large positive projections on PC 2 (star formation peakers) include HCO⁺, HCN, HNC, C₂H, and of course 3 mm continuum, which traces star formation directly. Species with large negative projections (southern bar peakers) include HNCO, CH₃OH and, to a lesser extent, N₂H⁺ and SiO. PC 3 has a quadrupolar morphology dominated by SiO and C³⁴S. PC 4 and beyond are at best marginally significant so we do not discuss them in detail.

The correlation matrix resulting from the PCA (Table 6) shows in more detail the correlations among various species. The following trends are noted.

• 1.  
  HCN, HNC, HCO⁺, and 3 mm continuum are all extremely tightly correlated, indicating a close association with massive star formation. At the resolution of the PCA HCO⁺, and HCN are effectively perfectly correlated. At three times higher spatial resolution, subtle differences become apparent (Figure 7). HCN is the map most tightly correlated with the 3 mm continuum. Therefore, the (massive) star formation rate (SFR) versus HCN line luminosity relation seen in single-dish surveys (e.g., Gao & Solomon 2004) persists to at least 100 pc scales in Maffei 2, as noted in (MTH08). However, the correlation between HC₃N(10–9) and 3 mm continuum is weaker than found for IC 342.
• 2.  
  CH₃OH and HNCO are very well correlated with each other and are strongly anticorrelated with the massive star formation. This leaves little doubt that on these GMC spatial scales the chemistries of these two species are either directly coupled or are mutually coupled to a specific chemical mechanism. Moreover, these species show little correlation with 3 mm continuum and hence star formation is not relevant to establishing the morphologies of these species. Nor are these species correlated with the standard dense gas tracers, HCN, HCO⁺, and HC₃N. Figure 8 displays the position–velocity diagrams of ¹³CO, C₂H, and HNCO. The strong differences between the starburst tracers and CH₃OH or HNCO carry over to the kinematics. The "parallelogram" originating from the central ring is nearly absent in CH₃OH and HNCO but remains pronounced in C₂H.
• 3.  
  SiO and especially C³⁴S are less tightly correlated with the other species. This may in part be due to their low S/N ratio and that some of the structure that appears in these maps are noise. However, C³⁴S was also anomalous in IC 342 (MT05).

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The CO/HCN ratio is widely used to study the relative fraction of dense gas in galaxies. MTH08 used the CO/HCN ratio to identify the sites of high dense gas fraction and concluded that the x₁–x₂ orbital intersections and the eastern (star forming) portion of the central ring are the locations of the high dense gas fraction. The fraction of dense gas drops toward the western ring and moving out along the bar arms.

To study the nature of the dense component directly, line ratios among dense gas tracers are required, since CO does not trace dense gas. Line ratios among bright, high critical density species, such as HCN, HCO⁺, HNC, HC₃N, and CS are useful diagnostics of the physical and chemical properties of the dense component of the interstellar medium. Much observational and theoretical effort has been dedicated to understanding these diagnostic species in nearby starbursts (e.g., Henkel et al. 1991; Nguyen-Q-Rieu et al. 1992; Solomon et al. 1992; Helfer & Blitz 1993; Kohno et al. 2001; Aalto et al. 2002; Gao & Solomon 2004; Imanishi et al. 2007; Baan et al. 2008; Graciá-Carpio et al. 2008; Juneau et al. 2009; Bayet et al. 2009; Lindberg et al. 2011; Aladro et al. 2011b). Unfortunately, interpreting these results can be difficult since most of these studies have been done at low spatial resolution, either with single-dish telescopes or in distant sources. These ratios mix many interstellar environments into one beam.

Now that we have access to an inventory of dense gas tracers at 30–100 pc resolution, we investigate changes in the HCN/HCO⁺, HCN/HNC, HCO⁺/N₂H⁺, HNC/HCO⁺, and HCN/CS line ratios on GMC scales across the nucleus of Maffei 2. Figure 7 displays four of these line ratios. Line ratios are tabulated in Table 8. Organized variations in all ratios are observed on these scales and are discussed in terms of the CO/HCN ratio.

Table 8. Selected Intensity Ratios

Location	$\frac{{\rm HCN}(1\hbox{--}0)}{{\rm HNC}(1\hbox{--}0)}$	$\frac{{\rm CCH}(3/2\hbox{--}1/2)}{{\rm CCH}(1/2\hbox{--}1/2)}$	$\frac{{\rm HCN}(1\hbox{--}0)}{{\rm HCO}^{+}(1\hbox{--}0)}$	$\frac{{\rm HNC}(1\hbox{--}0)}{{\rm HN}^{13}C(1\hbox{--}0)}$	$\frac{{\rm CS}(2\hbox{--}1)}{{\rm C^{34}S}(2\hbox{--}1)}$	$\frac{{\rm HCN}(1\hbox{--}0)}{{\rm CS}(2\hbox{--}1)}$
A	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	>0.79	>1.4	≲1.6
B	2.4 ± 0.4	⋅⋅⋅	0.63 ± 0.1	>4.5	>1.4	4.9 ± 1.5
C	1.6 ± 0.2	2.8 ± 1.5	0.90 ± 0.1	>6.6	>6.0	2.5 ± 0.8
D	1.3 ± 0.2	1.5 ± 0.3	1.1 ± 0.2	>10	>14	2.1 ± 0.6
E	1.3 ± 0.2	1.5 ± 0.3	1.3 ± 0.2	>9.4	>13	2.2 ± 0.7
F	1.1 ± 0.2	2.8 ± 1.8	1.7 ± 0.2	>16	∼4.1	2.4 ± 0.7
G	0.9 ± 0.1	1.5 ± 0.7	∼2.2	>11	∼3.8	1.1 ± 0.4
H	1.0 ± 0.1	⋅⋅⋅	⋅⋅⋅	>4.4	>1.0	<2.4

Notes. The resolution of the measurements is set by the lowest resolution input maps. The HCN(1–0) is from MTH08 and the CS(2–1) from Kuno et al. (2008). In determining the CS/C³⁴S ratio it is assumed that CS is spatially completely resolved by the Kuno et al. (2008) map. If this assumption is incorrect true ratios will be slightly lower than those quoted. Uncertainties reflect absolute flux calibration except for the C₂H ratios which are based on signal to noise. Upper limits are 1σ.

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4.1.1. HCN/HCO⁺: Tracer of Intermediate Gas Densities

4.1.2. HCN/HNC: Proposed Tracer of Warm Gas

4.1.3. HCO⁺/N₂H⁺: Tracing the Dense Gas

Both HCN and HCO⁺ (and to a lesser degree HC₃N) are observed to maintain large abundances in PDRs, shocks, and other energetic regions. By contrast, in the Galaxy N₂H⁺ is observed to avoid PDR regions, maintaining high abundances only in dense, quiescent, dark cloud-like conditions (Womack et al. 1992). In dense, quiescent gas both N₂H⁺ and HCO⁺ form from proton transfer reactions of H⁺₃ with N₂ and CO, respectively:

$$\begin{equation} {\rm H_{3}^{+} + N_{2} \rightarrow N_{2}H^{+} + H_{2}}, \end{equation} \tag{ 2 }$$

$$\begin{equation} {\rm H_{3}^{+} + CO \rightarrow HCO^{+} + H_{2}}. \end{equation} \tag{ 3 }$$

Given the reasonable assumption that the rate coefficients for these two reactions, k₂ and k₃, are approximately equal (Woodall et al. 2007), then X(N₂H₊)/X(HCO⁺) ≃ X(N₂)/X(CO). However, only HCO⁺ maintains a relatively rapid formation route in diffuse or PDR gas (C⁺ + OH → CO⁺ + H followed by H₂ + CO⁺ → HCO⁺ + H). No corresponding route exists for N₂H⁺ in PDRs (Turner 1995b). This explains the observed behavior of the HCO⁺/N₂H⁺ line ratio (Figure 7 and Table 8). Toward the PDR regions associated with the active star formation sites, HCO⁺ can maintain appreciable abundances while N₂H⁺ is readily destroyed. The fact that this ratio, which reflects dense gas properties, is modified by the starburst PDRs implies that toward this region (GMC E and the eastern ring) PDRs penetrate the dense gas. The strong correlation between high HCO⁺/N₂H⁺ ratios and PDR tracers like C₂H, suggests that this ratio may be a powerful new probe of dense PDRs in external galaxies.

Along the arms, X(N₂H⁺)/X(HCO⁺) abundances are typically ∼0.1–0.15, with values reaching up to ∼0.33 toward the southern bar end. If a standard CO abundance of X(CO) ≃ 10⁻⁴ is adopted, X(N₂) abundances of (1–3) × 10⁻⁵ are implied. If metallicities are solar (e.g., Anders & Grevesse 1989) and all N is in the form of N₂, then X(N₂) ≃ 4 × 10⁻⁵. Evidently, in the more quiescent dense clouds of the nucleus of Maffei 2, at least a quarter of all nitrogen is in molecular form. Using the above X(N₂) estimation together with Table 4 gives X(N₂)/X(N₂H⁺) ≃ 2 × 10⁴ for these regions.

Following the analysis of MT05, X(N₂)/X(N₂H⁺) provides indirect constraints on the cosmic-ray ionization rate, ζ. Adopting X(N₂)/X(N₂H⁺) ∼2 × 10⁴ and the extremely conservative lower limit, X(e⁻) = X(ion) ⩾X(N₂H⁺) + X(HCO⁺) ⩾(6–9) × 10⁻⁹, Figure 9 of MT05 indicates $\zeta /n_{{\rm H}_{2}} > 10^{-21}$ s⁻¹ cm³. Less conservatively, for X(e⁻) ≃ 10⁻⁷ typical of Galactic star-forming regions (e.g., Caselli et al. 1998), $\zeta /n_{{\rm H}_{2}} > 10^{-20.5}$ s⁻¹ cm³. Therefore, ζ is at least the Galactic value if the density of the gas that the N₂H⁺ and HCO⁺ emission originates in is $n_{{\rm H}_{2}} > 10^{4}$ cm⁻³. These constraints are comparable to though somewhat stronger than observed for IC 342.

4.1.4. The CS(2–1)/HCN(1–0) and CS(2–1)/C³⁴S(2–1) Ratios

4.1.5. HC₃N(10–9)

Ionizing radiation from massive stars impinging on nearby molecular clouds changes their chemical composition. Large abundances of ionized carbon in PDRs drive a rich hydrocarbon chemistry on cloud surfaces. One of the simplest species from such regions is C₂H. C₂H is formed from rapid dissociative recombination of C₂H⁺₂ coming from reactions between C⁺+CH₃ (Wootten et al. 1980; Sternberg & Dalgarno 1995). C₂H chemistry is particularly closely tied to ionized carbon and is an excellent probe of these PDRs. Its usefulness as an extragalactic PDR tracer was demonstrated in MT05.

After accounting for opacity effects (see Section 3.3 for C₂H(1–0; (1/2)–(1/2)) for an optically thin C₂H transition) C₂H pervades much of the molecular clouds in the northern star-forming region. Lower level C₂H emission extends over the rest of the nucleus but avoids the cloud cores, instead favoring the side of the dense cloud facing star formation (traced here by 2 cm radio continuum; see Figure 9). This is particularly clearly seen west of GMC F and northeast of GMC G.

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As discussed in Section 4.1.3, the dramatic increase in the HCO⁺/N₂H⁺ line ratio across the central ring shows not only that PDRs are prevalent near the young, star-forming region but that the PDRs penetrate much of the dense gas there. Given the distinct region of altered chemistry, constraints can be placed on the range of influence of the current burst of star formation. For the northern star-forming region, the region of elevated HCO⁺/N₂H⁺ ratio is 80 pc diameter in extent. We assume that the volume of the region emitting strong PDR emission reflects the volume of molecular gas engulfed within H ii regions that have expanded into the ambient medium due to overpressure. This should be reasonable on GMC scales. For an ionized gas sound speed of 10 km s⁻¹, N_Lyc = 5 × 10⁵¹ s⁻¹ and a uniform density of $n_{{\rm H}_{2}}\simeq 10^{2.75}$ cm⁻³ typical of the central ring (MTH08), a standard expanding H ii region would reach a radius of 40 pc in ∼7 Myr. While this analysis is sensitive to the exact density distribution, it is interesting that this timescale for dynamical evolution of GMCs due to pressure is an order of magnitude longer than characteristic chemical timescales and consistent with the timescale of massive star evolution.

C₂H emission appears to trace a molecular outflow along the minor axis (Figure 9). The northwest extension of this bipolar flow is redshifted by ∼15 km s⁻¹ and the southeast blob blueshifted by ∼ −15 km s⁻¹ with respect to the velocity of the corresponding in-plane material. These velocity shifts have the correct sign for outflow given Maffei 2's geometry (northern arm being nearer to us, and the arms trailing). There is tentative evidence for the flow in HNC and SiO (and possibly CO(1–0); MTH08) but the molecular outflow is not obvious in any of the other species. This is understandable given the strength of C₂H in the outflow reflects its relatively low critical density and its ability to maintain high abundances in the presence of ionizing radiation.

The molecular outflow in Maffei 2 does not appear to follow the distribution of ionized gas traced by 2 cm. This is different from what is seen in the much more pronounced outflow in M82 (Walter et al. 2002). The 2 cm radio continuum emission appears to trace the walls of Maffei 2's outflow (Figure 9; Turner & Ho 1994). The C₂H emission must trace entrained molecular material being driven out directly. The explanation for the 2 cm emission along the edges remains unclear but may be due to a path length effect of a cone of ionized gas surrounding the molecular flow. Since evidence is seen for a small minor axis outflow, it is possible to obtain a second estimate of the characteristic age by assuming that the gas traced in C₂H is free to flow ballistically along the minor axis. The extent of the outflow is ±200 pc. For an inclination angle of 67° and the measured line-of-sight velocity, the time of flight corresponds to 6 Myr. This is a very young outflow. The agreement with the characteristic in-plane timescale is excellent, suggesting that the current starburst may have an age of τ ∼ 6–7 Myr.

Elevated gas-phase abundances of species whose formation is sensitive to the grain processing, such as CH₃OH, HNCO, or SiO, are important probes of hot core gas and shocks. As noted in MT05, and illustrated even more clearly here, these species do not trace hot cores. Typical Galactic hot cores, even significant collections of them cannot produce the required emission necessary to explain the intensities on these large scales. Moreover, we detect no spatial connection between CH₃OH and HNCO, and star formation, if anything, we see an anticorrelation. We can, therefore, safely conclude that the above three species are not tracing hot core emission or outflows from young stellar objects but must originate in large-scale shocks. Inter-comparisons can be used to identify the responsible shock source (MT05; Requena-Torres et al. 2006; Rodriguez-Fernandez et al. 2006; Martín et al. 2008) and place constraints on shock properties such as shock strength, type of shock, and liberated grain/mantle composition (Usero et al. 2006).

In this data set, three shock tracers, CH₃OH, HNCO, and SiO, are mapped. Each is sensitive to somewhat different shock properties. It is expected that elevated gas-phase SiO results from the release of Si from destruction of silicate grain cores (e.g., Martín-Pintado et al. 1992). That the grain core must be disrupted requires "strong" shocks capable of sputtering grain cores. High observed abundances of gas-phase CH₃OH likely come from direct liberation of CH₃OH that has formed on grain surfaces by complete hydrogenation of CO (e.g., Millar et al. 1991; Bachiller et al. 1995). Liberation of mantles does not require shocks as strong as those that effect the grain core. Thus, the relative enhancement of SiO versus CH₃OH will depend on the strength of the shock. Grain core destruction requires shock velocities of ≳25 km s⁻¹, whereas shock velocities of only ≳10–15 km s⁻¹ are required for significantly elevated gas-phase CH₃OH abundances (e.g., Caselli et al. 1997; Bergin et al. 1998). It is reasonably well established that HNCO is a mantle species along with CH₃OH (MT05; Rodríguez-Fernández et al. 2010). But its formation mechanism remains unclear. The most commonly proposed mechanism is partial hydrogenation of OCN on grain surfaces followed by direct liberation (e.g., Hasegawa & Herbst 1993). Other suggested mechanisms include acid–base reactions between CO and NH₃ and UV photolysis (Schutte & Greenberg 1997; Keane et al. 2001). Thus, if HNCO forms on grain mantles and is liberated directly then its unsaturated nature implies that it originates in grain mantles with different chemical composition from CH₃OH (however, see Tideswell et al. (2010) for a possible formation mechanism in more saturated ices). Unsaturated ices are favored when gas accretes in atomic hydrogen-poor environment, whereas saturated ices favor atomic hydrogen-rich accretion (e.g., Charnley et al. 1997; Watanabe & Kouchi 2002). Hydrogen-poor conditions reflect accretion at high densities when almost all hydrogen is in molecular form. If it is assumed that the shock simply injects molecules into the gas phase, the HNCO/CH₃OH abundance ratio is then sensitive to gas physical conditions during ice mantle formation.

Chemistry is not the only effect that influences the relative abundance of these three species. Excitation is also important. The excitation requirements of SiO(2–1), CH₃OH(2_k–1_k), and HNCO(5₀₅–4₀₄) transitions differ (see Table 1). The critical density of the HNCO transition is an order of magnitude higher than SiO and CH₃OH. Furthermore, the energy of the upper state in HNCO(5₀₅–4₀₄) is more than twice that of SiO and higher than two of the three main transitions that make up the CH₃OH line. Therefore, CH₃OH and SiO lines will be favored over HNCO in lower density gas. Also in the presence of ionizing radiation each species dissociates at different rates. HNCO is photodissociated at a rate twice that of CH₃OH and ∼30 times that of SiO (Roberge et al. 1991; Sternberg & Dalgarno 1995).

Thus, considering the distribution of CH₃OH, HNCO, and SiO can give insights into both the chemical and physical conditions present in the shocked gas and potentially tell us about nature of the shocks themselves. Below we discuss the overall structure of the shock tracers in the context of nuclear bar models, and then we analyze the subtle differences between each shock tracer to further constrain shock properties.

4.4.1. Overall Shock Tracer Morphology and Bar Structure

4.4.2. Relative Shock Tracer Morphologies and Bar Properties

What about changes in shock properties across the nuclear bar? Figure 10 displays the HNCO/CH₃OH, SiO/CH₃OH, and SiO/HNCO peak temperature ratios smoothed to 8'' and sampled at the GMCs. Given the significant difference in the native resolution of the three data sets and the fact that they were obtained with two different interferometers, only the clearest trends are discussed.

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As demonstrated by the PCA, the morphologies of the three species are strongly correlated, implying that we have a robust measure of the locations of shocked gas. So similar are the maps that only very subtle differences between HNCO, CH₃OH, and SiO appear, suggesting that shock conditions are uniform across the nucleus. With the possible exception of the uncertain SiO ratios toward GMC B, the arm clouds (C, D, F, and G) have effectively constant HNCO/CH₃OH (∼1.1 ± 0.2), SiO/CH₃OH (∼0.20 ± 0.02), and SiO/HNCO (∼0.19 ± 0.03) ratios. Only toward GMC E and the off arm spray regions (GMC H and just south of the western ring) are different ratios observed. Toward GMC E (the northern star-forming region), HNCO/CH₃OH is lower and the SiO ratios are higher relative to the rest of the arm. In the off arm regions, HNCO/CH₃OH ratios are depressed while the SiO/CH₃OH ratio is elevated and SiO/HNCO are elevated (spray region) or flat (GMC H).

From these ratios, three main points are concluded.

• 1.  
  While GMC G (the bar end) is the brightest source in the nuclear bar, indicating that the largest fraction of gas along this line of sight is shocked, evidently shock strengths are not enhanced here. SiO to mantle species have the same basic ratio at the bar end as it has over the rest of the bar.
• 2.  
  Toward GMC E, the decreased intensity of HNCO relative to CH₃OH and SiO is consistent with what is expected from photodissociation. From Section 4.2, we know that the dense gas here is permeated by UV photons for the young star formation. The shock tracer ratios further confirm this. Because of this, the absence (or faintness) of shock tracers toward the central ring and in particular the northern x₁–x₂ orbit intersection cannot be taken as evidence of absence of shocks here.
• 3.  
  The spray regions upstream (counterclockwise) from the main bar favor CH₃OH and to a lesser degree SiO relative to HNCO. It is possible that because gas is more diffuse in this region grain mantles are H-richer than in the denser arm. However, we favor a simpler explanation associated with changing excitation. The spray regions have lower density, hence the higher critical density HNCO transition is expected to be weaker relative to the lower critical density, CH₃OH, and SiO transitions. That the 5₀₅–4₀₄ transition of HNCO preferentially favors the dense clouds relative to more extended CH₃OH explains why larger beam single-dish multi-line observations derive an excitation temperature for HNCO that is nearly a factor of ∼2 larger than derived for the CH₃OH transitions in Maffei 2 (Hüttemeister et al. 1997; Martín et al. 2009). Note that the excitation temperature of both species is quite low (T_ex < 15 K), implying that the shock regions remain cool or the densities are low enough for these transitions to be sub-thermal.

In summary, we conclude that there is little evidence for strongly varying grain chemistry across the shocked regions on 8'' scales. The small level of variation seen is consistent with changing physical conditions (radiation field and gas density).

The overall nuclear structures of Maffei 2 and IC 342 are similar. Both have extended bar-like arms that terminate on a central ring that is actively forming stars. The molecular gas morphology of IC 342 is consistent with that of a gaseous bar (Turner & Hurt 1992). However, because of the very small central ring and ambiguous kinematics, other conclusions including unbarred spiral arms coupled with massive star feedback remain feasible (Schinnerer et al. 2008). On the other hand, Maffei 2 is clearly a nuclear bar based on both its morphology and kinematics (e.g., MTH08; Kuno et al. 2008). Given the potential dynamical similarities of the two nuclei a comparison of the chemistry of the two can provide important insights on the generalizability of the overall chemical picture developed in MT05.

The statistically robust PCA demonstrates that the chemistry of the two nuclei is remarkably consistent. Maffei 2 can be defined chemically as a highly inclined copy of IC 342 (Figure 11). In both systems, the first PC characterizes the density-weighted column density, and peaks along the inner arms and central ring. The second PC separates the main chemical forces responsible for controlling observed abundances, namely, shocks versus PDRs. PDR species dominate close to the young star-forming region while the shock tracers peak along the arm, with preference for the cuspy bar ends. As a result, the bar-driven star formation/chemical scenario outlined in MT05 must apply also to Maffei 2's nuclear bar.

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However, the chemical picture is not precisely identical, and these differences give added insight into the relative differences in evolutionary phase of the two nuclei. The main difference between the two galaxies is in the distribution of N₂H⁺. In IC 342, the PDR tracers are confined, appearing to be primarily cloud surface features, lining the inner ring. Significant N₂H⁺ (and HNCO) seen near the young star-forming region in IC 342 implies that its main star-forming region influences the dense gas only locally, on scales of 50 pc or less. Whereas in Maffei 2, the N₂H⁺/HCO⁺ ratio and photodissociation of HNCO clearly demonstrate that the star formation has begun to dramatically alter the chemical state of the dense molecular clouds in its immediate environment, not just the surfaces.

Evidently, the central molecular ring in Maffei 2 is structurally different (lower clump density) and that toward GMC E star formation is somewhat more evolved than the main burst in IC 342. This is consistent with the steeper radio spectrum toward GMC E (Turner & Ho 1994; Tsai et al. 2006). The crude estimate of timescale required to alter the chemistry of the dense component is ∼7 Myr. This is a reasonable timescale compared to stellar evolution of the burst in Maffei 2 and the kinematics of the outflow. However, this timescale is still very short; short enough that even this "evolved" part of the burst is in its early stages. The star formation extending to the north and south of GMC E is likely as young as the embedded star formation in IC 342.

In IC 342, the peak temperature ratios between SiO, CH₃OH, and HNCO, are similar to those seen in Maffei 2. The PDR GMC in IC 342 has slightly lower HNCO/CH₃OH and elevated SiO/HNCO ratios. This is exactly the behavior exhibited by the PDR-modified GMC E in Maffei 2, lending strong support for the influence of photodissociation on shock tracer brightness. The shock chemistry dominated cloud in IC 342 has slightly elevated HNCO relative to the other species, making its set of ratios a match within the uncertainties of GMC G. This agreement suggests that both the grain composition and shock properties are the same for these structurally similar locales. However, since brightnesses are sensitive to radiative transfer effects, one must be careful overinterpreting ratios if gas excitation is changing rapidly. Maffei 2 and IC 342 do have rather similar CO excitation conditions (Meier et al. 2000; Meier & Turner 2001; MTH08).

In summary, we find that when the dynamical environments are similar, as they are in IC 342 and Maffei 2, a consistent chemical picture begins to emerge. Gas chemistry is confirmed as a powerful method for isolating the physical mechanisms that influence gas conditions in spiral nuclei. In future papers in this series, we will broaden the range of galactic environments studied to assess how far chemistry can be pushed as a diagnostic of sub-beam physics.