Physical Properties of the Southwest Outflow Streamer in the Starburst Galaxy NGC 253 with ALCHEMI

Fig. 1 shows the integrated intensity maps of CO, ¹³CO, HCN, H¹³CN, and N₂H⁺ in the J = 1-0 transition and CH₃OH (methanol) in the J_k = 2_k-1_k transition series. We extract spectral channels covering $1000\,\rm km\,s^{-1}$ velocity range around each transition from the continuum-subtracted cubes, where the rest-frame frequencies are 115.271, 110.201, 88.632, 86.340, 93.174, and $\sim$96.741 GHz, respectively. The black solid line in Fig. 1(a) marks the galactic major axis (hereafter major axis) with a position angle of 55^∘, and is defined following Krieger et al. (2019). The strong CO(1-0) emission in Fig. 1(a), which is marked by the blue contour at 4300 K km s^-1, concentrates in the galactic center and distributes along the major axis. Similar structures also exist in other panels of Fig. 1. Das et al. (2001) found that a bar structure along the major axis is necessary for modeling the ionized gas velocity field in the central $\sim$100 pc region of NGC 253. A bar structure is also applicable in the CO map in the central $\sim$300 pc region of NGC 253 (Paglione et al., 2004). A stellar bar, which is known as an efficient mechanism for gas accretion, can trigger strong molecular emission along the major axis as is seen in Fig. 1. One different point in Fig. 1(f) from the other panels in Fig. 1 is that the strongest CH₃OH(2_k-1_k) emission exists on the outskirts of the gas disk, suggesting quasi-thermal emission in agreement with Humire et al. (2022).

The CO(1-0) contours (especially the white one at 180 K km s^-1) in Fig. 1(a) are extended towards the SW streamer defined by Walter et al. (2017), which is indicated by a white arrow. Similar extent can be found in the HCN(1-0) contours (Fig. 1c), while the ¹³CO(1-0) contours are not so extended (Fig. 1b). Based on the ratios between the main and rarer isotopologues, Meier et al. (2015) found that CO(1-0) and HCN(1-0) emission is on average optically thick in the central kpc-scale region of NGC 253. As ¹³C-bearing molecular species, ¹³CO(1-0) emission should be moderately optically thin (Martín et al., 2019). The different extents towards the SW streamer of CO(1-0) and HCN(1-0) emission from the ¹³CO(1-0) emission imply that the optical depths of CO(1-0) and HCN(1-0) emission in the SW streamer region may be lower than that in the gas disk. Moreover, the fainter emission of H¹³CN(1-0), N₂H⁺(1-0) and CH₃OH(2_k-1_k) in Figs. 1(d), 1(e) and 1(f) share similar extents towards the SW streamer with ¹³CO(1-0).

Fig. 2 shows the intensities of five molecular lines from Fig. 1 and SiO in the J = 2-1 transition ($\sim$86.847 GHz, see Huang et al. 2023 for its integrated intensity map) in the PVDs along the major axis with systemic velocity reserved and distance referenced from the phase center. The CO(1-0) PVD in Fig. 2(a) mainly follows a rotating pattern, which is consistent with Figure 5 from Krieger et al. (2019). Another common point is that the CO(1-0) PVD shows non-disk features towards both redshifted and blueshifted sides. The strong CO(1-0) emission that is marked by blue contours at [20, 30] K is located in the region within a galactocentric distance range of [-10, 10] arcsec and follows a rotating pattern. The white arrow in Fig. 2(a) points to the SW streamer, and the strongest CO(1-0) emission is located near the base of this streamer.

The ¹³CO(1-0) PVD in Fig. 2(b) is less extended than the CO(1-0) and HCN(1-0) PVDs, but all have similar strong emission patterns. The H¹³CN(1-0), SiO(2-1), and CH₃OH(2_k-1_k) PVDs in the second row of Fig. 2 are the least extended. For H¹³CN(1-0) and SiO(2-1) PVDs in Figs. 2(d) and 2(e), the strong emission marked by the blue contours at 0.62 K is distributed in a few clumpy regions, among which the strongest two clumps are located near the base of the SW streamer (indicated by the white arrow). For the CH₃OH(2_k-1_k) PVD in Fig. 2(f), the strongest emission originates from the outskirts of the gas disk, which agrees with the integrated intensity map in Fig. 1(f).

Fig. 3 shows the intensities in the PVDs along a slice across the SW streamer (SW slice, black dashed line in Fig. 1a) with systemic velocity reserved and distance taken zero in the slice center. The slice center is the same as Figure 1 from Walter et al. (2017), and the position angle of the slice equals 150^∘. In Fig. 3(a), the CO(1-0) emission in the PVD is dominated by the disk component, and is extended towards the SW streamer in the region with D$\sim$[-15, 0] arcsec and V$\sim$200 km s^-1. Such extension outlined by the white dashed profiles, is consistent with Figure 2 from Walter et al. (2017). The ¹³CO(1-0) and HCN(1-0) PVDs in Figs. 3(b) and 3(c) are less extended, but have similar patterns as the CO(1-0) PVD. The H¹³CN(1-0), SiO(2-1) and CH₃OH(2_k-1_k) PVDs in the second row of Fig. 3 are least extended, where the molecular emission only extends at the base of the SW streamer with D$\sim$[-5, 0] arcsec and V$\sim$200 km s^-1. The intensities of N₂H⁺(1-0) in the PVDs along the major axis and along the SW slice are also checked, which show similar patterns to the H¹³CN(1-0) PVDs.

The CO(1-0) line is generally the best tracer of total molecular gas content thanks to its high abundance and low critical density for excitation. Fig. 4 shows the kinematics of the molecular gas in NGC 253 traced with CO(1-0). There are two interesting kinematic features in Figs. 4(a) and 4(b): (1) the velocity field showing gradients along both major and minor axes; (2) the blueshifted velocity and high velocity dispersion in the SW streamer region.

The white contours showing the velocity gradient in the center within a radius of $\sim$100 pc in Fig. 4(a) have the same pattern as the CO velocity field from Das et al. (2001) and Krieger et al. (2019). Their studies showed that the molecular bar shares the same direction as the stellar bar in the near-infrared band, and tilts $\sim$18^∘ with respect to the major axis (Peng et al., 1996; Iodice et al., 2014). The direction of molecular and stellar bars is shown as a white solid line in Fig. 4(a). There is a velocity gradient (white contours) in Fig. 4(a) along the direction of the molecular bar (white solid line). Yet the ionized bar traced with the H92$\alpha$ recombination lines is almost parallel to the major axis (Cohen et al., 2020). Das et al. (2001) explained this phenomenon as different velocities for the gas moving in different bar orbits and suggested that the perturbation in the gas velocity field in NGC 253 is due to an accretion event occurred $\sim$10 Myr ago.

The gas velocity in the SW streamer region (pointed out by the black arrow) is blueshifted ($\sim\rm 200\,km\,s^{-1}$) as shown in Fig. 4(a), which means the outflowing gas is on the approaching side of NGC 253. The blueshifted outflow is visibly distinguishable from the redshifted ($\sim\rm 380\,km\,s^{-1}$) disk rotation. Meanwhile, the other outflow streamers are indistinguishable in Fig. 4(a), because they are fainter than SW streamer and/or locate behind the galactic disk (Bolatto et al., 2013). In Fig 4(b), the gas in the SW streamer region presents high velocity dispersion, which can be contributed by blueshifted outflow and redshifted rotation.

To compare the kinematics between the outflow and disk, we decompose two components from the CO(1-0) spectra in the SW streamer region. From a circular region in the SW streamer region having the same area as the beam size (the black empty circle in Fig. 4b), we extract the averaged CO(1-0) spectrum, which is displayed by the black solid profile in Fig. 4(c). The averaged CO(1-0) spectrum shows a double-peak structure, where we take the velocity $\sim$300 km s^-1 as a reference velocity for the emission near the base of the SW streamer. Combining the velocity field of CO(1-0) in Fig. 4(a), the blueshifted component relative to the reference velocity is emitted by the SW streamer, and the redshifted component is emitted by the gas disk. We also extract the averaged CO(1-0) spectrum from a region with high-velocity-dispersion (high-$\sigma$) in the SW streamer region (the black empty ellipse in Fig. 4b), which is displayed by the black solid profile in Fig. 4(d) also showing a double peak structure. Using Python-based tool curve_fit, we fit the CO(1-0) spectra in Figs. 4(c) and 4(d) with double Gaussian function. The blue dashed profiles show the blueshifted Gaussian components, the red dashed profiles show the redshifted Gaussian components and the green solid profiles show the superpositions. The velocity and full width at half maximum (FWHM) in the velocity space of each Gaussian component are listed in Table 1.

We find that the blueshifted and redshifted components of the averaged CO(1-0) spectrum from the beam-size region (the black empty circle in Fig. 4b) have similar FWHMs in the velocity space (line widths). The redshifted component of the averaged CO(1-0) spectrum from the high-$\sigma$ region (the black empty ellipse in Fig. 4b) has similar FWHM to the components from the beam-size region, while the blueshifted component is $\sim$50% wider than the redshifted component. Moreover, there is a gradual velocity shift along the SW streamer in the CO(1-0) PVD outlined by white dashed profiles in Fig. 3(a). The velocity gradient inside the SW streamer can be evidence for an inside-out acceleration on the gas velocity, i.e., the gas inside the SW streamer is accelerated as it outflows. It can also be attributed to the ability for the fast ejecta to reach farther away than the slow ejecta. Those two possibilities were also discussed in Walter et al. (2017). If we take the velocity center of the blueshifted component from the high-$\sigma$ region ($\sim$219.7 km s^-1) as the averaged velocity for the SW streamer, then the projected local velocity of the SW streamer equals $\sim$80 km s^-1. Considering the inclination angle of the gas disk ($\sim$78.5^∘) and the outflow being perpendicular to the disk, the deprojected local velocity of the SW streamer approaches $\sim$400 km s ^-1, which is comparable with the outflow velocity in the ionized gas phase (Westmoquette et al., 2011).

Figs. 1(a) and 1(b) show the contours of CO(1-0) emission being more extended towards the SW streamer region than ¹³CO(1-0) emission, which can be a result of the different optical depths. Fig. 5(a) shows the integrated intensity ratio map of CO/¹³CO(1-0) based on self-calibration, where we masked the regions with ratio S/N being less than $3\sigma$. The CO/¹³CO(1-0) ratio increases in the SW, southeastern (SE) and northwestern (NW) directions (named after Bolatto et al. 2013), which are pointed out by the black/grey arrows and are perpendicular to the gas disk (Fig. 5). The black contour with CO/¹³CO(1-0) ratio of 15 defines the boundary between the outflow streamers and the disk. The CO/¹³CO(1-0) ratio further increases in part of the outflow region and is outlined by the blue contour at 21, where the CO/¹³CO(1-0) ratio is highest in the SW streamer region. CO is generally optically thick, while its isotopologue ¹³CO is optically thinner. The molecular gas in the CMZ of NGC 253 shows high kinetic temperature in the previous studies (Paglione et al., 2004; Sakamoto et al., 2011), which weakens the fractionation effects on C-bearing species (Colzi et al., 2020). Moreover, ¹³C preferentially forms in the center, while the C and ¹³C can be well mixed in the outflow region. The CO/¹³CO(1-0) ratio is expected to be similar to the C/¹³C isotope ratio in the optically thin limit, and decreases as the optical depth increases.

Martín et al. (2019) estimated a value of the isotopic ratio C/¹³C$\sim$21$\pm$6 via the integrated intensity ratio between C¹⁸O(1-0) and ¹³C¹⁸O(1-0). In Fig. 5(a), the observed CO/¹³CO(1-0) ratio in the gas disk is lower than the C/¹³C ratio, which can be contributed by the optically thick CO emission in the disk. The CO/¹³CO(1-0) ratio in the SW, SE and NW outflow regions approaches or exceeds the C/¹³C ratio, where the fluctuation in isotopic abundance is weak. Part of the outflow region (outlined by the blue contour at 21), including the SW streamer region, shows the CO/¹³CO(1-0) ratio consistent with the C/¹³C ratio. Except for NGC 253, Weiß et al. (2005) found the integrated intensity ratio CO/¹³CO(1-0) of the prominent molecular streamers being comparable to that of the starburst disk in M82, which is different from the increasing CO/¹³CO(1-0) ratio towards the directions of outflow in NGC 253.

To decompose different velocity components, we plot in Figs. 6(a) and 6(b) the intensity ratio of CO/¹³CO(1-0) in the PVDs along the major axis and the SW slice, which are marked by the black solid and dashed lines in Fig. 1(a). In Fig. 6(a), the CO/¹³CO(1-0) ratio increases in the non-disk components and is highest on the blueshifted side, which implies the decrease in the optical depth of CO emission in the molecular gas on the approaching side of NGC 253. This phenomenon is more obvious in the PVD along the SW slice in Fig. 6(b), where the CO/¹³CO(1-0) ratio is low along the gas disk and increases inside the SW streamer with D$\sim$[-15, 0] arcsec and V$\sim$200 km s^-1 outlined by the two black dashed profiles. Combining Figs. 5(a), 6(a), and 6(b), we infer that the decrease in the optical depth of CO emission happens inside the molecular outflow including the SW streamer, which can be attributed to the gas velocity gradient inside the outflow.

Measuring the molecular mass outflow rate is important because it may indicate the rate at which the fuel for star formation is expelled, which may significantly suppress star formation activity. The optical depth of CO emission is a key factor in estimating the molecular mass outflow rate. Zschaechner et al. (2018) derived the optical depth with the integrated intensity ratio of CO(2-1)/CO(1-0), and suggested that the majority of the CO emission is optically thick in the outflow region of NGC 253. However, the ¹³C-bearing molecular species being optically thinner than the ¹²C-bearing ones implies that the CO/¹³CO(1-0) ratio is a more reliable indicator of CO optical depth. Hence, the agreement between the CO/¹³CO(1-0) ratio (Fig. 5a) and the C/¹³C ratio (Martín et al., 2019) suggests that the CO emission in a considerable portion of the outflow region is optically thin in NGC 253. Such phenomenon supports the estimation from Bolatto et al. (2013) on the total molecular mass outflow rate $\sim 9\ M_{\odot}\ yr^{-1}$, which is three times the star formation rate $\sim 3\ M_{\odot}\ yr^{-1}$ (Ott et al., 2005) in NGC 253.

HCN is one of the most abundant high dipole-moment molecules that trace dense gas. The permanent electric dipole-moment of HCN ($\mu_{e}\sim$ 2.99 D) is much higher than CO ($\mu_{e}\sim$ 0.11 D) (Ebenstein & Muenter, 1984; Goorvitch, 1994), which makes the critical density of HCN three orders of magnitude higher than that of CO. Fig. 5(b) shows the integrated intensity ratio map of HCN/¹³CO(1-0). The HCN/¹³CO(1-0) ratio is lowest in the gas disk, increases towards the outflow directions, and becomes the highest in parts of the outflow region (outlined by the blue contour at a ratio of 2) including the SW streamer region. Such a trend reminds us of the increasing CO/¹³CO(1-0) ratio in the outflow region with an increasing distance from the major axis in Fig. 5(a). Given that HCN(1-0) emission is optically thick in the central $\sim$kpc region of NGC 253 (Meier et al., 2015), the increased line width attributed to gas velocity gradient in the SW streamer region not only can decrease the optical depth of CO(1-0) emission tracing molecular gas, but also can decrease the optical depth of HCN(1-0) emission tracing dense gas.

The HCN/CO(1-0) ratio is widely used as an indicator of the fraction of dense gas, which is immediately responsible for the star formation inside galaxies (Gao & Solomon, 2004a, b; Lada et al., 2012). Tanaka et al. (2024) presented non-LTE analyses with ALCHEMI data for the CMZ of NGC 253, and compared the dense gas fraction in this region with the center of the Milky Way. The difference turned out to be consistent with that in the HCN/CO(1-0) ratio between the CMZ of NGC 253 and the Galactic center, which confirms the HCN/CO(1-0) ratio as a good measurement of the mass fraction of the dense gas to the entire molecular gas.

Fig. 5(c) shows the integrated intensity ratio map of HCN/CO(1-0). The HCN/CO(1-0) ratio is the highest in three clumpy regions along the major axis (black solid line), which are marked by the blue contour at a ratio of 0.15. The physical sizes of the three regions in Fig. 5(c) are $\lesssim$100 pc, which fit the scales of giant molecular clouds (GMCs), and can be further resolved into star-forming clumps ($\sim$10 pc) (Ando et al., 2017). The positions of those GMCs are consistent with the observation in Leroy et al. (2015), which were numbered 3, 6, and 7. The bar of NGC 253 traced with ionized gas is also along the major axis (Das et al., 2001). The inflowing gas along the bar interacting with the gas in the disk can trigger star formation inside those GMCs. The existence of supernova remnants and Hii region in the inner 200 pc of NGC 253 has been revealed about thirty years ago (Ulvestad & Antonucci, 1997). The forming super star clusters and the winds from young clusters were detected in high spatial resolution (Leroy et al., 2018; Levy et al., 2021, 2022). The GMCs 3, 6, and 7 in Fig. 5(c) are located at the base of outflow streamers outlined by the white contour, and the black contour at 0.09 is extended towards the directions of outflow streamers. Given that the dynamical age of the SW streamer equaling $\sim$1 Myr is short (Walter et al., 2017), the star formation inside the GMCs can be the engine for the outflow streamers (Krieger et al., 2019).

Walter et al. (2017) measured the ratio of peak intensities between HCN(1-0) and CO(1-0), which equals $\sim$1/10 both in the SW streamer region and the starburst center of NGC 253. The orange, purple, and yellow stars in Fig. 5(c) mark the corresponding positions at -1.5^′′, -4^′′ and -6.5^′′ offsets from the slice center along the SW slice following Walter et al. (2017). Based on the spatially resolved map, we can estimate the integrated intensity ratios at the three stars to be $\sim$0.19, 0.13, and 0.08. It is understandable that the dense gas fraction is the highest inside the GMC, and monotonously decreases away from the GMC.

Figs. 7(a) and 7(d) show the intensity ratio of HCN/CO(1-0) in the PVDs along the major axis and the SW slice. In Fig. 7(a), the HCN/CO(1-0) intensity ratio increases at the bottom of the PVD where the blueshifted non-disk component is located. In Fig. 7(d), the HCN/CO(1-0) ratio is highest in the SW streamer region with D$\sim$[-5, 0] arcsec and V$\sim$200 km s ^-1. Figs. 4(c) and 4(d) show that the averaged projected velocity of the outflowing gas in the SW streamer region is around 200 km s ^-1. Hence, the HCN/CO(1-0) ratio increases in the gas at the base of the SW streamer that shares the same velocity with the molecular outflow. The HCN/CO(1-0) ratio in the extended streamer region with D$\sim$[-15, -5] is moderate as in the gas disk (Fig. 7d), which agrees with the tendency at -6.5^′′ offset in Figure 7 from Walter et al. (2017).

It is possible to detect strong molecular emission at densities below the critical density. The effective excitation density is defined as the density at which the integrated intensity of a molecular line equals 1 K km s^-1 with reasonable assumptions about the column density and kinetic temperature. Shirley (2015) calculated the optically thin critical densities and effective excitation densities at assumed column density and kinetic temperature for the common dense gas tracers. The kinetic temperatures are assumed to be $\sim$100 K (Mangum et al., 2019) in the following comparisons on the effective excitation densities between different tracers. Shirley (2015) calculated the critical density and effective excitation density of HCN(1-0) at a column density of 10¹⁴ cm^-2, to be $1.1\times 10^{5}$ cm^-3 and $1.7\times 10^{3}$ cm^-3, respectively.

To confirm the distribution of the dense gas in the CMZ of NGC 253, we turn to tracers of dense gas with lower opacity. The critical density and effective excitation density of H¹³CN(1-0) at a column density of 10^12.3 cm^-2, equal $9.7\times 10^{4}$ cm^-3 and $6.5\times 10^{4}$ cm^-3. Even though the higher effective excitation density originates from a lower reference column density compared with that of HCN (Shirley, 2015), H¹³CN(1-0) as an isotopologue can trace the dense gas with less limitation of optical depth. Fig. 7(b) shows the intensity ratio of H¹³CN/¹³CO(1-0) in the PVD along the major axis, where the ratio also increases in the blueshifted non-disk component. Although the H¹³CN/¹³CO(1-0) ratio in the PVD along the SW slice in Fig. 7(e) is not as extended as HCN/CO(1-0), we still observe high ratios in two regions. One is the ellipse named region A with D$\sim$0 arcsec and V$\sim$300 km s ^-1 (reference velocity) that represents the gas inside GMC 3. The other is the ellipse named region B with D$\sim$[-5, 0] arcsec and V$\sim$200 km s^-1 (outflow velocity) that represents the gas at the base of the SW streamer.

The critical density and effective excitation density at a column density of 10¹³ cm^-2 of another dense gas tracer N₂H⁺(1-0) equal $2\times 10^{4}$ cm^-3 and $2.6\times 10^{3}$ cm^-3. Even though the critical density of N₂H⁺(1-0) is lower than HCN(1-0) and H¹³CN(1-0), Galactic parsec-scale observations show that the N₂H⁺(1-0) emission is exclusively associated with rather dense gas (Kauffmann et al., 2017; Tafalla et al., 2021). The intensity ratio of N₂H⁺/¹³CO(1-0) in the PVD along the major axis (Fig. 7c) has an accordant pattern with H¹³CN/¹³CO(1-0) PVD (Fig. 7b). In the PVD along the SW slice (Fig. 7f), the N₂H⁺/¹³CO(1-0) ratio increases at the base of the SW streamer (region B). On one hand, the increased patterns in Figs. 7(d) and 7(f) are highly consistent. Given that N₂H⁺(1-0) is not safely optically thin and the optical depths of HCN(1-0) and CO(1-0) can be different in the central region, the N₂H⁺/¹³CO(1-0) and HCN/CO(1-0) ratios inside GMC 3 may be affected by optical depths. On the other hand, all three ratios in Figs. 7(d), 7(e) and 7(f) are higher in region B, which implies a negligible influence of optical depths at the base of the SW streamer, not to mention in the extended streamer region (Fig. 6b).

In summary, we find that the dense gas fraction is high inside GMC 3 (with reference velocity, region A) and at the base of the SW streamer (with outflow velocity, region B). The dense gas fraction in the extended streamer region (outlined by the black dashed profiles) is moderate in Fig. 7(d) and doesn’t show visible signs of accumulation of dense gas traced with HCN/CO(1-0). Combining the low optical depths of CO(1-0) and HCN(1-0) emission in the extended streamer region (Figs. 5a and 5b), we suggest the existence of gas velocity gradient prevents the gas from accumulation inside the SW streamer of NGC 253.

Si-bearing material and solid-phase methanol are located in different parts of the dust grains. Silicon tends to reside in the core of grains and can be sputtered to the gas phase by fast shocks (v${}_{\rm shock}\gtrsim$ 15-20 km s^-1, Kelly et al. 2017). Gas-phase silicon reacts with molecular oxygen or a hydroxyl radical and forms SiO (Schilke et al., 1997). On the other hand, solid-phase methanol is in the icy mantle of grains. Slow shocks (v${}_{\rm shock}\lesssim$ 15-20 km s^-1, Nesterenok 2022) are able to impact the icy mantle and inject gas-phase methanol into the ISM without destroying the grain core nor the methanol molecule (Millar et al., 1991; Charnley et al., 1995). Huang et al. (2023) studied the shock tracers SiO and HNCO with the ALCHEMI data, and revealed a picture that most of the GMCs are subjected to shocks. They declared that HNCO may not be a unique tracer of slow shocks, while a high abundance of silicon in the gas phase can only be explained by fast shocks. In this section, we will explore the methanol emission to verify the state of slow shocks, and inspect the relation between fast shocks traced by SiO emission and outflow streamers.

Fig. 8(a) shows the integrated intensity ratio map of SiO(2-1)/CO(1-0). The three dense GMCs (labeled by ‘3’, ‘6’, ‘7’ following Fig. 5c) also show increased SiO(2-1)/CO(1-0) ratio that is marked by the blue contour at 0.01. Moreover, two SiO(2-1)/CO(1-0) ratio peaks appear around GMC 3 in Fig. 8(a), with the second one consistent with the position of GMC 4 in Leroy et al. (2015). To examine the influence of optical depth, we also plot the integrated intensity ratio map of SiO(2-1)/¹³CO(1-0) in Fig. 8(b). The increased SiO(2-1)/¹³CO(1-0) ratio exists in the four GMCs (marked by blue contour at 0.1). The increased ratios in the GMCs imply the enhanced fast shocks there. The grey contour in Fig. 8(b) outlines the outflow streamers that originate from the four GMCs. Both the distributions of SiO(2-1)/CO(1-0) (marked by black contour at 0.003) and SiO(2-1)/¹³CO(1-0) (marked by black contour at 0.04) are extended towards the outflow streamers, which connect the fast shocks with the formation of the molecular outflow.

Fig. 8(c) shows the integrated intensity ratio map of CH₃OH(2_k-1_k)/¹³CO(1-0). The increased CH₃OH(2_k-1_k)/¹³CO(1-0) ratio that is marked by black contour at 0.15 located on the outskirts of the gas disk. Locations with high CH₃OH(2_k-1_k)/¹³CO(1-0) ratio are similar to those with high CH₃OH(2_k-1_k) integrated intensity shown in Fig. 1(f). Such a tendency is in agreement with HNCO 4_0,4-3_0,3 emission in Huang et al. (2023) that shows high integrated intensity in the outermost CMZ of NGC 253. The strong methanol emission on the outskirts, with positions in consistent with the methanol masers found by Gorski et al. (2017), implies the frequent occurrence of slow shocks. Meanwhile, the weak methanol emission in the center could be a result of the infrequent slow shocks, or the depletion of methanol molecules (Hartquist et al., 1995; Ellingsen et al., 2017) by fast shocks or photo-dissociation due to intense star formation (Humire et al., 2022). The non-cospatial distributions of fast and slow shocks were also found in another nearby galaxy NGC 1068 (Kelly et al., 2017) and imply that fast shocks do not necessarily occur with slow shocks. To obtain the relative strength between the fast and slow shocks, we plot the integrated intensity ratio map of SiO(2-1)/CH₃OH(2_k-1_k) in Fig. 8(d), where the central region turns out to be dominated by the fast shocks.

Fig. 9 shows intensity ratios of the shock tracers in PVDs, where the top panels show the PVDs along the major axis and the bottom panels show the PVDs along the SW slice. The asymmetric and increased pattern (including regions A and B) of SiO(2-1)/¹³CO(1-0) ratio in PVDs (Figs. 9a and 9d) are highly similar to the H¹³CN/¹³CO(1-0) ratio in PVDs (Figs. 7b and 7e). We will study in detail the correlation between the dense gas fraction and the strength of fast shocks in the next section. The increased intensity ratio of CH₃OH(2_k-1_k)/¹³CO(1-0) on the outskirts of the gas disk in Fig. 9(b) is coherent with the distribution of the increased integrated intensity ratio in Fig. 8(c). It is worth noting that a few red pixels located in region B of Fig. 9(e) indicate an enhancement of the slow shocks at the base of the SW streamer. In Figs. 9(c) and 9(f), we plot the SiO(2-1)/CH₃OH(2_k-1_k) ratio in PVDs. The region A in Fig. 9(f) is dominated by the fast shocks, while the SiO(2-1)/CH₃OH(2_k-1_k) ratio in region B is not so high as region A. We infer that the fast shocks are triggered by the star formation inside GMC, which supports the second scenario for the origin of shocks in Huang et al. (2023). Meanwhile, the fast and slow shocks co-exist in the SW streamer, and can further be related to the formation of the molecular outflow.

Fig. 11(a) shows the integrated intensity ratio map of H¹³CN/¹³CO(1-0), where the GMCs have the highest ratios marked by the blue contour at 0.12, and the black contour at 0.06 is extended towards the outflow streamers. Such increased patterns are similar to that of SiO(2-1)/¹³CO(1-0) in Fig. 8(b). Moreover, the increased H¹³CN/¹³CO(1-0) and SiO(2-1)/¹³CO(1-0) ratios in PVDs in Figs. 7 and 9 also share similar patterns. The consistency in the enhanced emissions of H¹³CN(1-0) and SiO(2-1) implies a positive correlation between the dense gas fraction and the strength of fast shocks in NGC 253. We regrid the H¹³CN(1-0), SiO(2-1) and ¹³CO(1-0) data cubes to a 1.6^′′ beam-size to avoid oversampling, then statistically quantify the linear relationship between H¹³CN/¹³CO(1-0) and SiO(2-1)/¹³CO(1-0).

The blue points in Fig. 11(b) show the H¹³CN/¹³CO(1-0) and SiO(2-1)/¹³CO(1-0) ratios in each beam size region from Figs 8(b) and 11(a). To check the linear relationship between two ratios, which is visibly tight, we calculate the Pearson correlation coefficient using the Python-based package pearsonr. The correlation coefficient ($r$) equals 0.85, which reveals a tight positive correlation between H¹³CN/¹³CO(1-0) and SiO(2-1)/¹³CO(1-0) ratios. We perform a linear fit for the data set, which is shown by the grey solid line in Fig. 11(b). We also calculate the Pearson correlation coefficient between H¹³CN(1-0) and SiO(2-1) integrated intensities, which approaches 0.96 and reveals a tight correlation between the intensities of two lines. Therefore, the correlation between H¹³CN/¹³CO(1-0) and SiO(2-1)/¹³CO(1-0) ratios is real, it is not a result from the common denominator. Meanwhile, we keep in mind that the high critical densities of H¹³CN(1-0) and SiO(2-1) may contribute to the tight positive correlation between two ratios. Theoretically, the star formation that happens in the region with a high dense gas fraction can trigger fast shocks. Combining the similar extensions of the SiO(2-1) and H¹³CN(1-0) emissions towards the outflow in Figs 8(b) and 11(a), the star formation inside the GMCs can trigger fast shocks and contribute to the formation of the molecular outflow in NGC 253.

The difference between the tracers of dense gas and shocks presents when we further analyse the molecular spectra in Fig. 10(b). Given that all the lines show double peak structures, we can distinguish the contributions of steamer and disk via the double Gaussian fits. In the last column of Table 2, we list the streamer-to-disk peak intensity ratios (streamer-to-disk ratios for short) together with errors for different molecular lines. Each ratio is calculated by dividing the peak intensity of the streamer component by that of the disk component.

The streamer-to-disk ratio of CO(1-0) is higher than its isotopologue ¹³CO(1-0), which can be explained by the lower opacity environment inside the SW streamer than in the gas disk for CO emission as discussed in Section 3.3. It is interesting to find that all the dense gas tracers (marked by the star symbols in the first column of Table 2) have higher streamer-to-disk ratios than the others. The optical depth decreasing inside the SW streamer for HCN emission can explain the highest streamer-to-disk ratio of HCN(1-0) among the dense gas tracers. In addition, the SiO(2-1) and methanol, as the tracers of fast and slow shocks, respectively, have similar streamer-to-disk ratios to ¹³CO(1-0). It seems that the enhancement of dense gas fraction is stronger in the SW streamer than in the gas disk, while the shock strength is equivalently enhanced in the SW streamer and the gas disk. More detailed clues are needed to explain such a difference.

We suggest the physical pictures that are related to the SW streamer in NGC 253 as follows: (i) The GMCs (Fig. 5c) in the direction of the major axis are related to the gas accretion along the bar structure that further provides material for the star formation. Meanwhile, the star formation inside the GMCs that are located at the base of the outflow streamers contributes to driving the molecular outflow, which is in agreement with the model presented by Levy et al. (2022). (ii) There can be intense star formation inside the GMCs also presenting as higher dense gas fraction, and results in enhanced shock strength at the base of the outflow (Figs. 7 and 9) including the SW streamer. (iii) The optical depths of CO and HCN emission decrease in the SW streamer (Figs. 5a and 5b), and the dense gas is diluted in the extended SW streamer region (Fig. 7d), which can be attributed to the gas velocity gradient inside the molecular outflow.