The SAMI Galaxy Survey: impact of star formation and AGN feedback processes on the ionized gas velocity dispersion

We generate aperture spectra integrated within an elliptical 1 $R_{\rm e}$ aperture using the data cubes from the SAMI DR3 for a reliable fit of narrow and broad line components. However, simple integration inevitably broadens emission lines by summing spectra with different radial velocities. Moreover, aperture spectra sometimes show strong substructures in their emission lines according to the distribution of the radial velocity fields within the aperture. The velocity structures embedded in the integrated emission lines obstruct an accurate estimate of narrow and broad line components. We therefore eliminate the velocity differences between spaxels before we integrate the spectra to prevent line broadening caused by velocity fields while maintaining a high S/N (Rosales-Ortega et al. 2012; Swinbank et al. 2019; Avery et al. 2021).

We used ionized gas rotation velocities published in the SAMI DR3 as a reference point to eliminate the relative velocity differences between individual spectra. The SAMI team measured the rotation velocity of ionized gas for individual spaxels using the emission line fitting code lzifu (Ho et al. 2016), after subtracting the continuum that is estimated using the Penalized Pixel-Fitting method (pPXF; Cappellari & Emsellem 2004; Cappellari 2017). Owers et al. (2019) provide more details on the measurement of the continuum. We shifted spectra from each spaxel to remove the relative differences in their rotation velocities and then integrated the shifted spectra within 1 $R_{\rm e}$. In Figure 1, we present example H$\alpha$ and [NII] emission lines to show the difference between aperture spectra with and without aligning the velocity fields. Integrated emission lines without removing rotation show complex structures that are difficult to describe as sums of narrow and broad line components. Moreover, there is a high chance of artificially introducing a broad component with such complex emission line structures. In contrast, emission lines integrated after removing the velocity differences do not show such complex structures.

We use the peak amplitude-to-noise (A/N) ratio of the H$\alpha$ emission line flux to assess the influence of the velocity correction on the emission line within the aperture spectra, given that the S/N derived from the continuum is less informative about the strength of emission lines. We note that the noise was locally estimated over the wavelength range of 6300–6900 Å. In Figure 2, we present the comparison of the H$\alpha$ A/N between two aperture spectra: one with the velocity correction applied and the other without the correction. The aperture spectra that underwent the velocity correction consistently show an improved H$\alpha$ A/N compared to the ones without the correction. The clean distribution and the higher A/N of emission lines from the velocity-corrected aperture spectra justify correcting the velocity differences between individual spectra within 1$R_{\rm e}$.

We generated velocity-field-corrected aperture spectra for 2955 galaxies, excluding nine galaxies from the initial 2964 primary target sample of the SAMI survey due to the absence of MGE $R_{\rm e}$ measurements. We applied a stellar mass cut of $10^{9}\,{\rm M_{\odot}}$ for a reliable measure of gas kinematics, given the spectral resolution limit of SAMI ($\sim$29.9 km/s in red arm; van de Sande et al. 2017) and low signal-to-noise (S/N) in the low mass galaxies, resulting in a sample size of 2517. We then select 1285 emission galaxies whose H$\alpha$, H$\beta$, [N II], and [O III] A/N ratios are greater than 5.

We utilized the pPXF method with the MILES simple stellar population (SSP) library (Vazdekis et al. 2010) and younger SSP templates from González Delgado et al. (2005) to estimate the continuum and subtracted it from the integrated spectra, as described in Owers et al. (2019). Subsequently, we employed lzifu to perform a simultaneous fit of strong emission lines, including [OII] $\lambda$3727+3729, H$\beta$, [OIII] $\lambda$5007, H$\alpha$, [NII] $\lambda$6583, [SII] $\lambda$6716, and [SII] $\lambda$6731. We performed spectral fitting twice using lzifu, employing both single and double Gaussian components. Zovaro et al. (2024) introduced a third extra-broad emission component to the emission line fitting and reported that galaxies with such components are rare. Therefore, we decided not to include the third components in our analysis. The mean velocities and velocity dispersions were constrained to be the same for all the emission lines, while the relative strengths of the emission lines were allowed to vary. Additionally, we computed the reduced $\chi^{2}$ values for both the single- and double-component fits ($\rm\overline{\chi}^{2}_{S}$ and $\rm\overline{\chi}^{2}_{D}$) to assess the goodness of fit. Figure 3 presents example of the emission line fitting performed using lzifu with single and double Gaussian components.

When conducting the double component fitting, we assigned the label ‘narrow’ to the results from the component exhibiting the lower velocity dispersion, while the other component was designated the ‘broad’ component. We employed several initial guesses for the kinematics of the narrow and broad models. We assign the initial velocity for the narrow component as the systemic velocity derived from the redshift listed in the SAMI input catalogue (Bryant et al. 2015; Owers et al. 2017). Following this, we specify initial velocities for the broad component to be -50, 0, and +50 km/s relative to the initial velocity of the narrow component. We explored the following input guesses of the velocity dispersions for the narrow and broad components ($\rm\sigma_{N}$ and $\rm\sigma_{B}$): $\rm\sigma_{N}$= 30, 50, 80, $\rm\sigma_{S}$, and $\rm\sigma_{B}$=80, 150, 250, 2$\times$$\rm\sigma_{S}$, 3$\times$$\rm\sigma_{S}$, where $\rm\sigma_{S}$ is the velocity dispersion measured from the single-component fit.

We then categorized the sample of emission-line galaxies into three groups based on the presence and reliability of the broad component. We calculate the fraction, $f_{\rm B}$, of the total line flux attributed to the broad component as:

where $F_{\rm H\alpha,N}$ and $F_{\rm H\alpha,B}$ are the H$\alpha$ emission line fluxes of the narrow and broad components, respectively, obtained through the double-component fit. We identified single-component galaxies when either the $\overline{\chi}^{2}_{\text{S}}$ value was lower than the $\overline{\chi}^{2}_{\text{D}}$ value or the fraction of the broad component was less than 10% ($f_{\rm B}$ $<0.1$). Note that the identification of most single-component galaxies relied on the $f_{\rm B}$ $<0.1$ criterion, as they tend to display a slightly better fit with double components, despite having insignificant flux in their second component.

Double-component galaxies were identified based on several criteria. Firstly, their $\overline{\chi}^{2}_{\text{D}}$ value had to be lower than the $\overline{\chi}^{2}_{\text{S}}$ value, indicating a better fit for the double-component model. Additionally, the fraction of the broad component had to be between 10% to 90% ($0.1\leq f_{\text{B}}\leq 0.9$), indicating a significant contribution from both components. Although the 10% fraction cut is arbitrary, the results throughout the paper remain stable even when this fraction cut is slightly varied (e.g., $0.2\leq f_{\text{B}}\leq 0.8$). Furthermore, for reliable measurements, all four optical emission lines used for diagnostics (H$\beta$, [OIII], H$\alpha$, and [NII]) had to exhibit A/N$>$3 for each individual component. Lastly, the velocity dispersion of the broad component ($\sigma_{\rm B}$) had to exceed the velocity dispersion of the narrow component ($\sigma_{\rm N}$) by at least its uncertainty ($\sigma_{\rm B,error}$). By applying these criteria, we confidently identified double-component galaxies, allowing us to investigate the properties and characteristics of the broad and narrow components within these systems. Galaxies not meeting the criteria for either a single- or double-component galaxy were classified as ‘uncertain’. Applying these criteria, the sample consists of 386 single-component galaxies, 356 double-component galaxies, and 543 uncertain galaxies. In Appendix A, we explore classification using the Bayesian Information Criterion (BIC); we conclude that using the BIC does not change the main results of this study.

Uncertain galaxies show significantly lower A/N in their emission lines compared to those from single- and double-component galaxies. For instance, the median A/N ratios of the H$\alpha$ line are 332$\pm$58, 453$\pm$84, and 184$\pm$39 for single-component, double-component, and uncertain galaxies, respectively. Consequently, among the 543 uncertain galaxies, 299 exhibit A/N$<$3 for at least one of the four lines in their broad component, with 82% of them associated with the low A/N of the H$\beta$ line. Additionally, 448 uncertain galaxies do not satisfy the condition of $\sigma_{\rm B}-\sigma_{\rm B,error}>\sigma_{\rm N}$, and 69% of them show $\sigma_{\rm B,error}$ higher than $\sigma_{\rm B}$. Therefore, we infer that uncertain galaxies in this study do exhibit a preference for double components in describing their emission lines. However, their measured line fluxes and kinematics, especially for the broad components, lack the accuracy required for this study. For further analysis, we focussed solely on comparing single- and double-component galaxies to maintain simplicity and avoid uncertainty regarding the reality of the narrow and broad components.

We present the characteristics of single- and double-component galaxies in this section. Most of the parameters presented in this section have been obtained from the SAMI DR3 catalogue. For each parameter, we provide a concise description along with the primary reference source. The bulge-to-total (B/T) ratio has been obtained from the catalogue published by Barsanti et al. (2021) and Casura et al. (2022). These studies employed ProFit, a Bayesian two-dimensional galaxy profile modelling routine developed by Robotham et al. (2017), to derive the B/T ratio. The stellar $\rm(V/\sigma)_{R_{e}}$ ratio was determined by calculating the flux-weighted mean within 1$R_{\rm e}$, using the 2-dimensional velocity and velocity dispersion maps (van de Sande et al. 2017), following the approach outlined by Cappellari et al. (2007). The inclination was derived using the axial ratio ($b/a$) and intrinsic flatness ($q_{0}$) of 0.2 following the conversion:

The fifth-nearest neighbour surface density $\Sigma_{5}$ is determined using galaxies with absolute $r$-band magnitudes $\rm M_{r}<-18.6$ (Brough et al. 2017). The $\rm C_{AGN}$ parameter serves as a quantitative measure of the relative contribution of power sources to the ionized gas using optical emission-line diagnostics, the so-called BPT diagnostics (Baldwin, Phillips & Terlevich 1981; Veilleux & Osterbrock 1987). We adopted the definition of $\rm C_{AGN}$ as described by Oh et al. (2022): the shortest orthogonal departure, on a logarithmic scale, from the empirical demarcation line established by Kauffmann et al. (2003) in the BPT diagram (as demonstrated in Section 4.2). We use $\rm C_{AGN,S}$, derived using emission line ratios measured from the single-component fit in this section, and later use that for individual components.

The star formation rate (SFR) surface density within 1$R_{\rm e}$ ($\rm\Sigma_{SFR}$) was derived by using the dust-corrected H$\alpha$ emission flux. The derivation assumes an intrinsic Balmer decrement of $\rm H\alpha/H\beta=2.86$ along with the Cardelli extinction law (Cardelli et al. 1989) and incorporates empirical calibrations based on Kennicutt et al. (1994) with adjustments for the Chabrier (2003) initial mass function, as detailed in Medling et al. (2018). We specifically use $\rm\Sigma_{SFR,N}$ as a proxy for star-forming activities, derived from the H$\alpha$ emission flux measured from the narrow component, to avoid potential contamination in total H$\alpha$ emission in non-star-forming galaxies. We also explored $\rm\Sigma_{SFR}$ using the spectral energy distribution (SED) fitting method described in Ristea et al. (2022), which is less susceptible to AGN contamination. Although there are some systematic changes in the range of two $\rm\Sigma_{SFR}$  these alterations lead to only minimal changes in the results, particularly when discussing the connection between $\rm\Sigma_{SFR}$ and gas kinematics. Therefore, although $\rm\Sigma_{SFR,N}$ may provide upper limits for the true $\rm\Sigma_{SFR}$ for AGN, the results with $\rm\Sigma_{SFR,N}$ in this study are less likely artificially originated by the contamination of H$\alpha$ flux by AGN activities. We decided to use $\rm\Sigma_{SFR}$ based on the H$\alpha$ flux because we lack SFR measurements from SED fitting for 45 galaxies in the sample, and estimating $\rm\Sigma_{SFR}$ for individual emission components is not feasible.

The distributions of various galaxy parameters in single- and double-component galaxies are shown in Figure 4. The median values highlight the statistically distinct distributions observed in $\rm M_{*}$, redshift, inclination, $\rm\Sigma_{SFR,N}$, and $\rm C_{AGN,S}$ between the two groups. We specifically examined whether the 95% confidence intervals of the medians in the two groups overlap. Single-component galaxies are predominantly composed of low-mass galaxies, while double-component galaxies exhibit higher mass distributions. There might be a bias in identifying low-mass galaxies with double components due to the challenges in resolving their emission components, especially in blue wavelengths at the SAMI resolution limit. Single-component galaxies are more populated at lower redshifts, likely because SAMI employed multiple volume-limited samples, which introduces selection effects, leading to a higher frequency of low-mass galaxies at lower redshifts. Double-component galaxies are more frequently found in galaxies with lower inclinations, possibly because the outflow component is less detectable in edge-on galaxies. Additionally, double-component galaxies demonstrate higher values of $\rm\Sigma_{SFR,N}$ and $\rm C_{AGN,S}$, suggesting a connection between the presence of a broad component and the ionization source of the emission lines. Our results confirm the distinct distributions between single- and double-component galaxies in stellar mass, inclination, and star-formation rate surface density, as reported by Zovaro et al. (2024) for the star-forming sample. They also discussed possible observational biases on multi-component emission line fits.

On the other hand, double-component galaxies share similarities with single-component galaxies in terms of both photometrically-defined (B/T) and kinematically-defined ($\rm(V/\sigma)_{R_{e}}$) galaxy types. Additionally, they exhibit similar values for local density $\Sigma_{5}$, pointing to internal processes as the primary physical mechanisms driving the formation of the broad component. We emphasize that double-component galaxies are not specifically associated with galaxies exhibiting high A/N ratios of H$\alpha$ emission. This result implies that the presence of double-component galaxies is not strongly influenced by, or a selection effect related to, the quality of spectra. The majority of the integrated spectra, after the velocity correction, exhibit an (A/N)_Hα higher than 100 for both single- and double-component galaxies. Moreover, low A/N galaxies are predominantly classified as uncertain galaxies and are subsequently excluded from the final sample. Consequently, the classification of galaxies as single- or double-component is not strongly dependent on the quality of the spectra, at least in this study.

We employ emission-line diagnostics based on the emission-line flux ratios derived from single-component fitting (Figure 5). The emission-line diagnostics diagram highlights the differences in emission line ratios between single- and double-component galaxies. The vast majority (93%) of single-component galaxies are found among star-forming galaxies below the dashed demarcation line ($\rm C_{AGN,S}$<0). The remaining single-component galaxies are primarily situated within the region associated with composite galaxies, lying between the two demarcation lines established by Kewley et al. (2001) and Kauffmann et al. (2003). We rarely observe AGN-like emission from single-component galaxies positioned above the solid demarcation line defined by Kewley et al. (2001). In contrast, double-component galaxies exhibit a more diverse distribution: 23% and 13% of them are associated with composite and AGN classifications, respectively.

From another perspective, non-star-forming galaxies ($\rm C_{AGN,S}$>0) often exhibit a broad component. Out of the 155 galaxies with $\rm C_{AGN,S}$>0, a substantial majority, 129 (83%), are classified as double-component galaxies. These double-component non-star-forming galaxies in our sample display low $\rm\Sigma_{SFR,N}$ values, as indicated in panel (d). The median log $\rm\Sigma_{SFR,N}$ values for double-component galaxies among the non-star-forming ($\rm C_{AGN,S}$>0) and star-forming ($\rm C_{AGN,S}$<0) groups are $-$2.30 and $-$1.67, respectively, with a standard deviation of 0.51 dex. This result independently supports the notion that the mechanisms contributing to the broad component in the $\rm C_{AGN,S}$>0 sample are less likely associated with star-forming activities.

On the other hand, the 590 star-forming galaxies ($\rm C_{AGN,S}$<0) in our sample are distributed between single-component (61%) and double-component (39%) galaxies. Star-forming galaxies with double components tend to exhibit higher $\rm\Sigma_{SFR,N}$ values compared to those with a single component. Specifically, the median log $\rm\Sigma_{SFR,N}$ values for star-forming galaxies with a single component and those with double components are -2.21 and -1.67, respectively, with a standard deviation of 0.47 dex. This result suggests that a broad component is more commonly observed in star-forming galaxies with higher $\rm\Sigma_{SFR,N}$ values. For additional insights, refer to the study by Zovaro et al. (2024), which also presents distinct distributions of $\rm\Sigma_{SFR}$ in single and double-component galaxies based on a spatially resolved classification.

In conclusion, galaxies tend to exhibit a broad component when their $\rm\Sigma_{SFR,N}$ is high or when they display AGN-like emissions ($\rm C_{AGN,S}$>0), suggesting multiple contributors for generating the broad component. However, as illustrated in Figure 4, the stellar mass emerges as the most decisive factor, having the most significant differences in the distributions between single- and double-component galaxies. In the next section, we further explore the impact of $\rm C_{AGN,S}$ and $\rm\Sigma_{SFR,N}$ on the structures and kinematics of ionized gas emission beyond stellar mass.

In Figure 6, we present the relations between the stellar mass and the ionized gas velocity dispersions measured for single ($\rm\sigma_{S}$), narrow ($\rm\sigma_{N}$), and broad component ($\rm\sigma_{B}$). We display data points for both single-component galaxies (open circles) and double-component galaxies (filled circles) when examining $\rm\sigma_{S}$ in panels (a), (d) and (g). For panels involving either $\rm\sigma_{N}$ or $\rm\sigma_{B}$, we only consider double-component galaxies. We determine the best-fit line in each panel by fitting velocity dispersions to the stellar mass, aiming to analyze any deviations from the velocity dispersion predictions offered by the stellar mass. The insets in each panel provide the residual trends in velocity dispersion with respect to $f_{\rm B}$, $\rm C_{AGN,S}$ and $\rm\Sigma_{SFR,N}$. The Spearman coefficient ($\rho$) is displayed in each inset panel to quantify the significance of the residual. There are no discernible residual trends with metallicity and the other parameters presented in the previous section; thus, they were not included in the analysis.

Figure 6(a) shows there is a significant residual trend in $\rm\sigma_{S}$ with $f_{\rm B}$. This result suggests that galaxies with a more pronounced presence of the broad emission-line component tend to exhibit higher $\rm\sigma_{S}$ than is predicted by their mass alone. The residual trend with $f_{\rm B}$ is not clearly evident in $\rm\sigma_{N}$ and $\rm\sigma_{B}$ (panels b and c), implying that the influence of $f_{\rm B}$ on the kinematics of the narrow and broad components is relatively limited. Hence, the residual trend observed in $\rm\sigma_{S}$ with $f_{\rm B}$ does not originate from the individual components in isolation but rather emerges from their cumulative effect. The influence of $f_{\rm B}$ on $\rm\sigma_{S}$ becomes more pronounced due to the significantly higher value of $\rm\sigma_{B}$ compared to $\rm\sigma_{N}$. Panel (d) introduces another substantial residual trend in $\rm\sigma_{S}$ relating to $\rm C_{AGN,S}$. It is noteworthy that the observed residual trend with $\rm C_{AGN,S}$ extends its influence to $\rm\sigma_{N}$ and $\rm\sigma_{B}$ as well (panels e and f). This result suggests that, unlike $f_{\rm B}$, $\rm C_{AGN,S}$ is connected to the kinematics of both the broad and narrow components. The presence of a residual trend in $\rm\sigma_{S}$, $\rm\sigma_{N}$ and $\rm\sigma_{B}$ when examining $\rm C_{AGN,S}$ indicates that power sources have a significant role in regulating the dynamics of the entire emission-line system within galaxies. We do not observe any residual trend in gas velocity dispersions with $\rm\Sigma_{SFR,N}$ (panels g–i).

In Figure 7, we present the relationships between the stellar mass and the gas velocity dispersion within subsamples categorized by their dominant power sources. Panels (a)–(f) display star-forming galaxies with $\rm C_{AGN,S}$<0, while panels (g)–(l) present non-star-forming galaxies exhibiting AGN-like emissions ($\rm C_{AGN,S}$>0). Our results confirm a well-established observational connection between the ionization sources and stellar mass (e.g. Juneau et al. 2011): non-star-forming galaxies are predominantly found among massive galaxies (log ($\rm M_{*}/M_{\odot}$)>10), while star-forming galaxies are distributed more evenly across the entire mass range. Substantial and persistent residual trends in gas velocity dispersions with $\rm C_{AGN,S}$ are evident among non-star-forming galaxies (panels g–i). We do not notice any correlations between residual velocity dispersions and $\rm\Sigma_{SFR,N}$ in panels (j)–(l), confirming that the kinematics of non-star-forming galaxies defined by $\rm C_{AGN,S}$>0 are, indeed, independent of star-forming activities.

Even among star-forming galaxies with $\rm C_{AGN,S}$<0, we continue to observe positive residual trends in gas velocity dispersions associated with $\rm C_{AGN,S}$ (panels a–c), though less pronounced compared to the whole sample. This attenuation may result from the limited variation in $\rm C_{AGN,S}$ for star-forming galaxies. The connection between the residual in $\rm\sigma_{S}$ and $\rm\Sigma_{SFR,N}$ only becomes evident when the sample is restricted to the star-forming galaxies (panel d). This residual trend observed in $\rm\sigma_{S}$ appears to primarily originate from the narrow component rather than the broad component. Specifically, the narrow components exhibit a notable residual trend with $\rm\Sigma_{SFR,N}$ (panel e), while the broad component does not display such a trend (panel f). However, when non-star-forming galaxies are included, the residual trend with $\rm\Sigma_{SFR,N}$ becomes diluted, resulting in the absence of residual trends in Figure 6(g)–(i).

As shown in Figures 6 and 7, significant correlations between stellar mass and gas velocity dispersions are detected, particularly in star-forming galaxies. Therefore, in the previous section, we examined the impact of $\rm C_{AGN}$ and $\rm\Sigma_{SFR}$ as proxies for the power of star formation and AGN-driven feedback, excluding the influence of stellar mass on gas velocity dispersions. In this section, we discuss the reasons behind the significant correlation between stellar mass and ionized gas velocity dispersions.

The stellar mass is expected to be proportional to the global potential of a galaxy. In this context, one may anticipate a correlation between the stellar mass and gas kinematics, given that ionized gas is also a part of a galaxy influenced by the gravitational potential. Recent studies employing IFS have indeed reported positive correlations between stellar mass and the gas velocity dispersion (or emission line width) (Cortese et al. 2014; Barat et al. 2019, 2020; Rodríguez del Pino et al. 2019; Swinbank et al. 2019; Varidel et al. 2020; Oh et al. 2022). However, the connection between gas kinematics and the global potential is expected to be less prominent, owing to their sensitivity to local physics, including turbulences in the interstellar medium (e.g. Federrath & Klessen 2012), star-formation feedback (e.g. Lehnert et al. 2009; Green et al. 2010), AGN feedback (e.g. Guillard et al. 2015); gas accretion (e.g. Klessen & Hennebelle 2010), gravitational instability (e.g. Krumholz & Burkert 2010); and thermal contamination of H ii region (e.g. Krumholz et al. 2018).

SAMI data, in general, are limited by seeing effects, with beam smearing playing a significant role in the observed correlation between gas velocity dispersions and stellar mass. Beam smearing spatially smooths line-of-sight radial velocity distributions from the IFS data, resulting in artificially elevated velocity dispersions and decreased velocity gradients. Varidel et al. (2020) estimated intrinsic gas kinematics for 383 star-forming galaxies correcting for the impact of beam smearing using a 3D forward-modelling technique. Figure 3 of Varidel et al. (2020) highlights that corrected gas velocity dispersions are significantly lower than the observed velocity dispersion. Nevertheless, a positive correlation still exists between the corrected gas velocity dispersions and stellar mass. However, their M_∗– gas $\sigma$ correlation is less pronounced, with a Spearman coefficient of 0.31, compared to the correlation shown in this study (see Figure 7(a) with a Spearman coefficient of 0.65) for star-forming galaxies. We therefore suspect that beam smearing artificially amplifies the M_∗– gas $\sigma$ correlation, by convolving rotational velocity (a proxy for mass) into the velocity dispersion.

The magnitude of beam smearing increases primarily when either the size of the seeing relative to the galaxy size or the velocity gradient is high. The former condition implies a greater impact on small galaxies, given the small variations in seeing in the SAMI data. We estimated the local gas velocity gradient $\nabla V$ at each x, y coordinate using the line-of-sight velocity values of neighbouring spaxels (V), following the approach outlined in Varidel et al. (2016):

where $W_{\rm pix}$ is the size of the SAMI spaxel (0.5 arcsecs). We find a strong positive correlation between stellar mass and $\nabla V$, with Spearman coefficient of 0.61, thereby confirming the influence of beam smearing on the M_∗–gas $\sigma$ relation presented in this study (see also Zhou et al. 2017).

We investigated whether the influence of beam smearing extends to the roles of $\rm\Sigma_{SFR}$ and $\rm C_{AGN}$, as illustrated in Figure 7. In Appendix B, we present a result similar to Figure 7, replacing stellar mass with $\nabla V$ and considering $\nabla V$ as a proxy for the impact of beam smearing. We observed that, even after accounting for the $\nabla V$–$\rm\sigma_{N}$ relation in Figure 11(e), there is still a robust residual correlation between $\rm\Sigma_{SFR,N}$ and $\rm\sigma_{N}$. Furthermore, we detected residual correlations between gas $\sigma$ and $\rm C_{AGN}$ beyond the $\nabla V$–$\rm\sigma_{N}$ relation (Figure 11g-i). Additionally, there were no significant changes in the results throughout this study when replacing stellar mass with $\nabla V$. Therefore, we conclude that star-formation and AGN-driven outflows associated with $\rm\Sigma_{SFR}$ and $\rm C_{AGN}$ are contributing to the inflation of gas velocity dispersions even after accounting for the impact of beam smearing. See also Lehnert et al. (2013) reporting a positive connection between $\rm\Sigma_{SFR}$ and gas $\sigma$ after correcting for the impact of beam smearing.

Our analysis involving $\nabla V$ is not intended to suggest that the M_∗–gas $\sigma$ relation originates entirely from beam smearing. Although we use $\nabla V$ as an indicator for the magnitude of beam smearing, it is a conservative approach because $\nabla V$ is also a physically motivated quantity and is not determined solely by observational limitations. For instance, galaxies with compact H$\alpha$ emissions or outflows may exhibit steep velocity gradients. Furthermore, previous studies have confirmed a positive correlation between stellar mass and gas $\sigma$, even after correcting for beam smearing. Therefore, we interpret the M_∗–gas $\sigma$ relation as being partially driven by the dependence of gas kinematics on the global potential, but the relation has been artificially strengthened by beam smearing. In the following sections discussing the narrow and broad component kinematics, we continue to use stellar mass to account for the impact of both global potential and beam smearing on gas kinematics.

Figures 6 and 7 suggest that, along with stellar mass, both $\rm C_{AGN}$ and $\rm\Sigma_{SFR}$ contribute to gas kinematics in certain cases. In this section, we further examine the correlations between the velocity dispersion of the narrow component and the key parameters (Figure 8). We utilise $\rm C_{AGN,N}$ and $\rm\Sigma_{SFR,N}$ measured from the line fluxes of the narrow component, but the results remain consistent even when we employ $\rm C_{AGN,S}$ and $\rm\Sigma_{SFR,S}$ instead. In Figure 8, panels (a) and (b) indicate that both stellar mass and $\rm C_{AGN,N}$ display strong positive correlations with $\rm\sigma_{N}$, as evidenced by their Spearman coefficients (0.54 and 0.57, respectively). In contrast, panel (c) reveals no discernible correlation between $\rm\Sigma_{SFR,N}$ and $\rm\sigma_{N}$. However, when considering all sample galaxies, these findings do not provide a clear explanation for the influence of key parameters on gas kinematics, particularly with regard to $\rm\Sigma_{SFR,N}$. To address this, we further divided the sample into star-forming galaxies (panels d-f) and non-star-forming galaxies (panels h-j).

Star-forming galaxies still exhibit a strong positive correlation between stellar mass and $\rm\sigma_{N}$ (Figure 8d). The insets in panels (d) and (e) suggest that stellar mass describes $\rm\sigma_{N}$ better than $\rm C_{AGN,N}$ for star-forming galaxies. Panel (f) clearly shows a positive correlation between $\rm\sigma_{N}$ and $\rm\Sigma_{SFR,N}$, which was not detected in panel (c) when considering all sample galaxies. The inset in panel (f) also reveals a residual trend with respect to stellar mass. By integrating the results from panels (d)–(f) in Figure 8 with panel (e) in Figure 7, we conclude that both stellar mass and $\rm\Sigma_{SFR,N}$ independently contribute to the narrow-component kinematics of star-forming galaxies. The results suggest an association between the narrow component in star-forming galaxies and the gravitational potential, establishing a correlation between stellar mass and the velocity dispersion of ionized gas. However, it is important to consider that the connection with the gravitational potential may be significantly lower than indicated by the M_∗–$\rm\sigma_{N}$ relation, given the impact of beam smearing discussed in the previous section. Additionally, the influence of $\rm\Sigma_{SFR,N}$ indicates that star-formation-driven outflows perturb the motion of ionized gas within the narrow component. This result supports previous studies reporting positive correlations between the gas $\sigma$ and $\rm\Sigma_{SFR}$ (e.g. Lehnert et al. 2009, 2013; Green et al. 2010; Varidel et al. 2020).

Among our sample, non-star-forming galaxies are predominantly massive galaxies (log($\rm M_{*}/M_{\odot}$)>10), as shown in Figure 8(g). For these galaxies, narrow-component kinematics are primarily dependent on $\rm C_{AGN,N}$ (panel h). The inset in panel (h) confirms that there is no residual trend with respect to stellar mass beyond the correlation between $\rm C_{AGN,N}$ and $\rm\sigma_{N}$, indicating that stellar mass does not effectively describe $\rm\sigma_{N}$ in non-star-forming galaxies, probably due to their limited mass range. The dependence of $\rm\sigma_{N}$ on $\rm C_{AGN,N}$ for non-star-forming galaxies may provide evidence for the impact of AGN-induced turbulence (e.g.  Guillard et al. 2015; Carniani et al. 2017; Wittor & Gaspari 2020). Additionally, non-star-forming galaxies do not exhibit any dependency of $\rm\sigma_{N}$ on $\rm\Sigma_{SFR,N}$ (panel i). The influence of $\rm\Sigma_{SFR,N}$ is only observed in the narrow-component kinematics of star-forming galaxies, while non-star-forming galaxies obscure the connection between star formation and gas kinematics.

We further examine the narrow component of non-star-forming galaxies by considering the equivalent widths of the H$\alpha$ emission line measured from the single-component fit ($\rm EW(H\alpha)_{S}$), which is often used to identify retired galaxies that have ceased star formation (e.g. Cid Fernandes et al. 2010, 2011). We find that all star-forming galaxies show $\rm EW(H\alpha)_{S}$ values above 5 Å. On the other hand, 59% of non-star-forming galaxies with $\rm EW(H\alpha)_{S}$>3 Å are expected to be associated with AGN, and their narrow component may be associated with the ‘narrow line regions’ (NLR) in AGN. The remaining 41% of non-star-forming galaxies have $\rm EW(H\alpha)_{S}$ values below 3 Å, indicating that they can be classified as retired galaxies. Consequently, the narrow component in the retired galaxies does not appear to be associated with star formation or young stars; instead, it is powered by old stars.

Figure 8(g)-(i) highlights that retired galaxies typically exhibit high stellar masses (log($\rm M_{*}/M_{\odot}$) $\gtrsim 10.5$), low $\rm\Sigma_{SFR,N}$ values (log$\rm\Sigma_{SFR,N}$ $\lesssim-2.5$) and $\rm C_{AGN,N}$ values broadly distributed above 0. The retired galaxies show a positive correlation between $\rm C_{AGN,N}$ and $\rm\sigma_{N}$ (Figure 8h), similar to AGN with $\rm EW(H\alpha)_{S}>3$ Å, suggesting that old stellar populations also contribute to the narrow component kinematics. This contribution is possibly due to hot old post-AGB (post-asymptotic giant branch) stars (Singh et al. 2013). However, it is less likely to be from extraplanar diffuse ionized gas (Belfiore 2016), as the majority of retired galaxies in this study are massive early-type galaxies. However, it is important to note that selecting retired galaxies using the $\rm EW(H\alpha)_{S}$ measured within 1 $R_{\rm e}$ may introduce a bias. AGN emissions are often highly centrally concentrated, and using integrated spectra with a large aperture (e.g., 1 $R_{\rm e}$) can obscure the AGN contribution, leading to an overidentification of retired galaxies.

In this section, we further investigate the correlation between the velocity dispersion of the broad component and key parameters. In Figure 9, panel (b) clearly demonstrates a strong correlation between $\rm\sigma_{B}$ and $\rm C_{AGN,B}$, underlining $\rm C_{AGN,B}$ as the primary driver of broad-component kinematics. Importantly, the inset of panel (b) reveals no residual correlation between $\Delta$(log $\rm\sigma_{B}$) and stellar mass. Thus, the observed correlation between stellar mass and $\rm\sigma_{B}$ in panel (a) is secondary, stemming from the strong link between stellar mass and $\rm C_{AGN,B}$ (for further observational evidence, see Juneau et al. 2011 and Vitale et al. 2013). Furthermore, simulations indicate a positive correlation between instantaneous AGN power and stellar mass, as illustrated in Figure 7 of Beckmann et al. (2017). This correlation may stem from the positive relationship between stellar and black hole masses and/or high accretion rates (e.g. Silk & Norman, 2009). The result provides compelling evidence that broad components are disconnected from the gravitational potential but are significantly influenced by non-gravitational feedback processes, such as galactic outflows. Note that even after excluding retired galaxies with $\rm EW(H\alpha)<3$, the results remain consistent, with a Spearman coefficient of 0.79 for the correlation between $\rm\sigma_{B}$ and $\rm C_{AGN,B}$.

There is no positive correlation between $\rm\sigma_{B}$ and $\rm\Sigma_{SFR,B}$, indicating that the kinematics of the broad component remain largely unaffected by the level of star formation (panel c). In contrast to narrow-component kinematics, differentiating between star-forming and non-star-forming galaxies when analyzing $\rm\Sigma_{SFR,B}$ does not reveal hidden relationships. For non-star-forming galaxies, we do not anticipate any correlations between $\rm\sigma_{B}$ and $\rm\Sigma_{SFR,B}$ since their broad component is not associated with star formation processes. However, even in star-forming galaxies, no significant correlation between $\rm\sigma_{B}$ and $\rm\Sigma_{SFR,B}$ is visible. We also conducted the same analysis using $\rm\Sigma_{SFR,N}$ instead of $\rm\Sigma_{SFR,B}$, considering its significance as an indicator of star formation activity, as broad components may not appear to be closely tied to star-forming processes, particularly in galaxies influenced by AGN or dominated by old stars. We obtained consistent results when using $\rm\Sigma_{SFR,N}$, not finding any correlations between $\rm\sigma_{B}$ and $\rm\Sigma_{SFR,N}$ even for star-forming galaxies ($\rho=-0.08$).

It is important to emphasize that the absence of the direct correlation between $\rm\sigma_{B}$ and $\rm\Sigma_{SFR,N}$ does not necessarily indicate that the broad components in star-forming galaxies are entirely disconnected from star-forming activities. In fact, we do observe broad components in star-forming galaxies, particularly when their $\rm\Sigma_{SFR,N}$ is elevated. Furthermore, the emission line ratios of the broad components closely resemble those of star-forming (i.e. $\rm C_{AGN,B}$<0) or composite galaxies in the BPT diagnostic diagram. Therefore, we can rule out AGN and old stars as the primary sources of the broad component in star-forming galaxies. One plausible scenario is that active star formation triggers gas outflows, leading to the formation of a broad emission-line component. However, even more intense star-forming activities may only increase the magnitude of the outflows (or $f_{\rm B}$), but may not increase the velocity of the outflow, which therefore does not exert a significant additional influence on the gas kinematics (Hopkins et al. 2018).