<figure><img src="image_16.png" /><figcaption>**Fig. B.1.** Results of the Gaussian fitting of the BLR to recover the observed point spread function. On the top, the BLR observed flux maps, the best-fit model, and residual from left to right. On the bottom, the corner plot reports the best-fit results and uncertainties. The amplitude is a normalization constant, $x_0$ and $y_0$ are the displacement in arcsec of the centroid from the galaxy center coordinates, $\sigma_x$ and $\sigma_y$ are the minor and major axis standard deviations in arcsec, $\theta$ is the rotation angle in radians measured counterclockwise from the positive y-axis. Above each histogram, we show the best value for each parameter and the $2\sigma$ interval.</figcaption></figure>
# Appendix C: Morphological and kinematic fitting

In this Section, we present the outputs and corner plot for the morphological and kinematic fitting discussed in Sections 3.3 and 7 and we also present an alternative kinematic fitting including only an exponential disk to show that the nonparametric approach is the best model to reproduce this galaxy kinematics.

## C.1. Posterior distributions

In figure C.1 we present the corner plot distribution for the fitting of the flux map where we model the emitted flux as a sum of a 2D Sèrsic profile to take into account the extended emission from the galaxy and a 2D Gaussian to reproduce the emission from the marginally resolved and unresolved source of emission (BLR, outflow, bulge) which parameters are marked as “AGN” as it is the dominant contribution source. In Figure C.2 and C.3 we present the posterior distribution for the kinematic fitting parameters presented in Section 7.

## C.2. Alternative kinematic fitting

To understand if the velocity and velocity dispersion map fitting really require a nonparametric model to reproduce the observed galaxy kinematic, we also tried a more conservative approach adopting a parametric modeling of the velocity and velocity dispersion curves.

To model the velocity curve we assume that velocity contribution was only due to the exponential disk component that can be described as a function of radius:

$$V_d^2(r) = 2y^2 \frac{GM_D(R_0) \frac{\mathcal{I}_0(y)\mathcal{K}_0(y) - \mathcal{I}_1(y)\mathcal{K}_1(y)}{r_D} \frac{1 - \exp(-R_0/r_D)(1 + R_0/r_D)}{1 + \exp(-R_0/r_D)(1 + R_0/r_D)}, \quad (C.1)$$

where $y \equiv r/(2r_D)$, while $\mathcal{I}_0$, $\mathcal{I}_1$, $\mathcal{K}_0$, and $\mathcal{K}_1$ are modified Bessel functions. We fixed the value of $r_D$ as the value of the exponential disk scale radius found in the morphological fitting, and we left the disk mass $M_D$ computed within a radius $R_0 = 5$ kpc, which corresponds to ~2-3 disk scale lengths: $M_d = M_d(R_0) = M_d(r = 5\text{kpc})$ free to vary.

The velocity dispersion curve was instead modeled as Gaussian:

$$\sigma(r) = \sigma_0 \times \exp(-r^2/r_\sigma^2) \quad (C.2)$$

where $\sigma_0$ is the velocity dispersion in the center of the galaxy and $r_\sigma$ is a measure of how quickly the velocity dispersion of the galaxy decreases with radius.

We fixed the inclination at the value of 22 deg, and we left the PA, disk mass, systemic velocity, $\sigma_0$, and $r_\sigma$ free to vary. The best-fit model and residuals are shown in Figure C.4, and the best-fit values and the posterior distribution are reported in Figure C.5.

In Figure C.4 the model velocity map is not able to reproduce the blue-shifted side. As the velocity in that side of the galaxy increases faster with radius than the red one, the exponential disk is not able to reproduce that fast growth, indicating the presence of an extra component in the central region of the galaxy to reproduce that fast rise in the velocity. The BIC test for the velocity map extremely favors the nonparametric modeling ($\Delta\text{BIC} > 100$).

The Gaussian decreasing velocity dispersion model is also disfavored by the BIC test in comparison to the nonparametric modeling ($\Delta\text{BIC} \sim 20$), as it is not able to reproduce the very high central velocity dispersions and the sharp decrease around 1.5 kpc.
# Appendix C: Morphological and kinematic fitting

In this Section, we present the outputs and corner plot for the morphological and kinematic fitting discussed in Sections 3.3 and 7 and we also present an alternative kinematic fitting including only an exponential disk to show that the nonparametric approach is the best model to reproduce this galaxy kinematics.

## C.1. Posterior distributions

In figure C.1 we present the corner plot distribution for the fitting of the flux map where we model the emitted flux as a sum of a 2D Sèrsic profile to take into account the extended emission from the galaxy and a 2D Gaussian to reproduce the emission from the marginally resolved and unresolved source of emission (BLR, outflow, bulge) which parameters are marked as “AGN” as it is the dominant contribution source. In Figure C.2 and C.3 we present the posterior distribution for the kinematic fitting parameters presented in Section 7.

## C.2. Alternative kinematic fitting

To understand if the velocity and velocity dispersion map fitting really require a nonparametric model to reproduce the observed galaxy kinematic, we also tried a more conservative approach adopting a parametric modeling of the velocity and velocity dispersion curves.

To model the velocity curve we assume that velocity contribution was only due to the exponential disk component that can be described as a function of radius:

$$V_d^2(r) = 2y^2 \frac{GM_D(R_0) \frac{\mathcal{I}_0(y)\mathcal{K}_0(y) - \mathcal{I}_1(y)\mathcal{K}_1(y)}{r_D} \frac{1 - \exp(-R_0/r_D)(1 + R_0/r_D)}{1 + \exp(-R_0/r_D)(1 + R_0/r_D)}, \quad (C.1)$$

where $y \equiv r/(2r_D)$, while $\mathcal{I}_0$, $\mathcal{I}_1$, $\mathcal{K}_0$, and $\mathcal{K}_1$ are modified Bessel functions. We fixed the value of $r_D$ as the value of the exponential disk scale radius found in the morphological fitting, and we left the disk mass $M_D$ computed within a radius $R_0 = 5$ kpc, which corresponds to ~2-3 disk scale lengths: $M_d = M_d(R_0) = M_d(r = 5\,\text{kpc})$ free to vary.

The velocity dispersion curve was instead modeled as Gaussian:

$$\sigma(r) = \sigma_0 \times \exp(-r^2/r_\sigma^2) \quad (C.2)$$

where $\sigma_0$ is the velocity dispersion in the center of the galaxy and $r_\sigma$ is a measure of how quickly the velocity dispersion of the galaxy decreases with radius.

We fixed the inclination at the value of 22 deg, and we left the PA, disk mass, systemic velocity, $\sigma_0$, and $r_\sigma$ free to vary. The best-fit model and residuals are shown in Figure C.4, and the best-fit values and the posterior distribution are reported in Figure C.5.

In Figure C.4 the model velocity map is not able to reproduce the blue-shifted side. As the velocity in that side of the galaxy increases faster with radius than the red one, the exponential disk is not able to reproduce that fast growth, indicating the presence of an extra component in the central region of the galaxy to reproduce that fast rise in the velocity. The BIC test for the velocity map extremely favors the nonparametric modeling ($\Delta\text{BIC} > 100$).

The Gaussian decreasing velocity dispersion model is also disfavored by the BIC test in comparison to the nonparametric modeling ($\Delta\text{BIC} \sim 20$), as it is not able to reproduce the very high central velocity dispersions and the sharp decrease around 1.5 kpc.
<figure><img src="image_17.png" /><figcaption>**Fig. C.1.** Posterior distribution for the free parameters in the fitting of the flux map. The dashed lines represent the 16th, 50th and 84th percentile. The galaxy is modeled as a 2D Sérsic profile, while the AGN is modeled as a two-dimensional Gaussian. The coordinates of the centers are expressed in arcseconds where the position (0,0) corresponds to the coordinates of RA = 03:32:29.3, Dec = -27:56:19.6. The radius of the galaxy and the standard deviation of the Gaussian component $\sigma_x$ and $\sigma_y$ are measured in arcseconds and $\theta_{gal}$ is the angle measured in radians between the y-axis and the semi-major axis of the galaxy.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Fig. C.1.** Posterior distribution for the free parameters in the fitting of the flux map. The dashed lines represent the 16th, 50th and 84th percentile. The galaxy is modeled as a 2D Sérsic profile, while the AGN is modeled as a two-dimensional Gaussian. The coordinates of the centers are expressed in arcseconds where the position (0,0) corresponds to the coordinates of RA = 03:32:29.3, Dec = -27:56:19.6. The radius of the galaxy and the standard deviation of the Gaussian component $\sigma_x$ and $\sigma_y$ are measured in arcseconds and $\theta_{gal}$ is the angle measured in radians between the y-axis and the semi-major axis of the galaxy.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. C.2.** Posterior distribution for the free parameters in the velocity map fitting. The dashed lines represent the 16th, 50th and 84th percentile. The units of the velocities are km s⁻¹, the PA is measured in degrees.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. C.2.** Posterior distribution for the free parameters in the velocity map fitting. The dashed lines represent the 16th, 50th and 84th percentile. The units of the velocities are km s⁻¹, the PA is measured in degrees.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Fig. C.3.** Posterior distribution for the free parameters in the velocity dispersion map fitting. The dashed lines represent the 16th, 50th and 84th percentile. The units of the velocities are km s⁻¹.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Fig. C.3.** Posterior distribution for the free parameters in the velocity dispersion map fitting. The dashed lines represent the 16th, 50th and 84th percentile. The units of the velocities are km s⁻¹.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. C.4.** Parametric best-fit results for the modeling of the Hα velocity and velocity dispersion maps. From left to right on the top the observed velocity map, the best-fit model map, and the residuals. From left to right on the bottom the observed velocity dispersion map, the best fitting model dispersion map, and the residuals. The colorbars of the residual range between −3σ and +3σ, and the black lines indicate ±1σ.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. C.5.** Posterior distribution for the free parameters in the parametric fitting of the moment maps. The dashed lines represent the 16th, 50th, and 84th percentile. The PA is measured in degrees, the mass is measured in solar mass units, the systemic velocity and $σ_0$ in km s⁻¹, and $r_σ$ is measured in arcseconds.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. C.4.** Parametric best-fit results for the modeling of the Hα velocity and velocity dispersion maps. From left to right on the top the observed velocity map, the best-fit model map, and the residuals. From left to right on the bottom the observed velocity dispersion map, the best fitting model dispersion map, and the residuals. The colorbars of the residual range between −3σ and +3σ, and the black lines indicate ±1σ.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. C.5.** Posterior distribution for the free parameters in the parametric fitting of the moment maps. The dashed lines represent the 16th, 50th, and 84th percentile. The PA is measured in degrees, the mass is measured in solar mass units, the systemic velocity and $σ_0$ in km s⁻¹, and $r_σ$ is measured in arcseconds.</figcaption></figure>