LARGE-SCALE SHOCK-IONIZED AND PHOTOIONIZED GAS IN M83: THE IMPACT OF STAR FORMATION

Our WFC3 data are part of the WFC3 Science Oversight Committee (SOC) Early Release Science (ERS) program (program ID11360, PI: Robert O'Connell). The observed field, centered at R.A. = 13:37:04.42, decl. = −29:51:28.0 (J2000), covers the nuclear starburst region and the inner part of the northeast spiral arm of M83. Three or four (depending on the filter) spatially dithered exposures were used to remove cosmic rays through the MultiDrizzle software (Fruchter et al. 2009). We adopt the PHOTFLAM values, available at http://www.stsci.edu/hst/wfc3/phot_zp_lbn, to convert instrumental data number (DN) to physical flux. We use the flux calibration value of F658N for F657N, for which a calibration is not available, since their values for line emissions are similar within a few percent. The detailed information about our data set is summarized in Table 1. Before we derive line ratio maps, we rebin the images by 5 × 5 pixels to reduce registration errors. The binned pixel size is 02 or 4.3 pc in physical scale, i.e., smaller than the typical size of an H ii region, but comparable to the physical size of star clusters (Maiz-Apellaniz 2001).

The F487N and F502N narrowband filters each contain one line emission per filter (Hβ and [O iii](5007 Å), respectively, redshifted to the recession velocity of M83, 513 km s⁻¹). F657N and F673N contain multiple lines. In the case of F673N, the lines are both [S ii], from the 6716 Å and 6731 Å doublet, so we will simply consider the sum of the two. In the F657N filter, the [N ii] doublet at rest frame 6548 Å and 6584 Å is included in the filter bandpass in addition to Hα. Hence, we have simpler filter throughput equations to obtain Hβ and [O iii](5007 Å) fluxes than Hα and [S ii](6716 Å+6731 Å). As a trade-off, however, the stellar continuum contained in the F487N and F502N filters is more affected by variations in the stellar population mix and the local dust extinction than the redder lines, which means their stellar-continuum estimates have worse intrinsic accuracy than F657N and F673N. Furthermore, the F555W filter, which we use as the broadband continuum filter to estimate the stellar contribution to F487N and F502N, is self-contaminated by Hβ and [O iii](5007 Å); we assume that [O iii](4959 Å) is negligible compared to the two other lines. Therefore, we have to correct our filter fluxes for the following: (1) contamination of Hβ and [O iii](5007 Å) in the F555W filter and (2) [N ii] contamination in F657N.

To subtract the Hβ and [O iii](5007 Å) lines from the F555W image, we apply an iterative method which can be schematically described as

$$\begin{eqnarray*} \rm Cont_{0} &\leftarrow & {\rm F555W} \nonumber \\ \rm H\beta _{i} &\leftarrow & {\rm F487N} - \rm Cont_{i} \nonumber \\ \big [\rm O\,{\mathsc {iii}}\big ]_{i} &\leftarrow & {\rm F502N} - \rm Cont_{i} \nonumber \\ \rm Cont_{i+1} &\leftarrow & {\rm F555W} - \rm H\beta _{i} - [\rm O\,{\mathsc {iii}}]_{i}, \nonumber \end{eqnarray*}$$

where each term represents the flux calibrated image for the denoted line emission and filter. In this method, the starting value for the stellar continuum is the uncorrected F555W, Cont₀. With it, we obtain the first guesses to the Hβ and [O iii](5007 Å) emission line images by subtracting the stellar continuum from the respective narrowband filters. Then, by subtracting those first-guess line emissions from F555W, we can derive the first-order corrected continuum, Cont₁. We can iterate the procedure until the image converges. This procedure is similar in concept to the iterative procedure applied in Mackenty et al. (2000) for NGC 4214.

To quantify the improvement of the iterative method, we compare the corrected F555W continuum after each iteration with the F547M image available in the HST archive for the central region of M83, since F547M is a line-emission-free filter. We produce a residual image, $\frac{ {\rm F547M} - \mu {\rm F555W} }{{\rm F547M}}$, for each iteration step to investigate the effect of each iteration on the F555W image. The parameter, μ, is chosen to minimize the difference between the images in the two filters and is related to the scaling factor for the stellar-continuum subtraction from narrowband images.

Figure 1 shows the pixel histogram of residual image for each iteration. The uncorrected, 0th iterated, residual image shows a negative mean which indicates excess flux from Hβ and [O iii](5007 Å) in F555W. After the first iteration, the residual images show a more symmetric pixel histogram than the uncorrected one showing that the iterations remove the excess of line emission in F555W. The difference between the uncorrected and the first corrected is appreciable especially in localized regions, where flux changes up to 100% have been measured. Further iterations do not change the F555W image appreciably. To quantify the difference for each iteration step, we show the mean (top) and the standard deviation (bottom) of the residual images (left) and the corrected F555W (right) in Figure 2. We can observe that one, at most two, iterations are sufficient to reach convergence. The converged residual histogram in Figure 1 can be considered as an intrinsic difference between the two filters. We take as final Hβ and [O iii](5007 Å) emission line images those resulting from the second-iterated F555W stellar-continuum image.

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The optimal scale factor to be applied to the broadband images for continuum subtraction in the narrowband filters is found with the skewness transition method (S. Hong et al. 2011, in preparation). The skewness is defined as

$$\begin{equation*} {\rm skewness} = \frac{1}{N-1} \sum _{i=1}^{N} \bigg (\frac{x_i - m}{\sigma } \bigg)^3 \nonumber, \end{equation*}$$

where m is the mean, σ is the standard deviation, and N is the number of pixels in a sample image. The skewness is generally used to measure asymmetry of a statistical distribution. For symmetric functions, the value of the skewness is zero. If a distribution has a long "right" tail, the skewness of the distribution is positive, i.e., positive-skewed. For a distribution with a long "left" tail, the skewness is negative, i.e., negative-skewed. For an image of blank sky, the pixel histogram is generally Gaussian (or Poissonian). So, the skewness is zero (or a small positive number). Additional astronomical sources in a blank field, therefore, are weighing on the right-hand side of pixel distribution which makes the distribution "positive-skewed." Since the continuum subtraction process removes stellar flux from the narrowband image, increasing the subtraction weight decreases the skewness value. In a perfectly subtracted narrowband image, the skewness of the image pixels that do not contain line emission is zero for a Gaussian background. Our method attempts to recover the optimal stellar-continuum subtraction value by exploiting this property of the skewness. Our simulations (S. Hong et al. 2011, in preparation) show that the skewness function shows a "transition" in correspondence of the optimal scaling factor for the stellar continuum. So, by locating where this transition occurs in our HST images, we have derived the optimal scaling factor for each narrowband filter.

It should be noted that the use of a single scaling factor across each image assumes that large color gradients (due to either changes in the stellar population mix or in the dust extinction) are not present across the broadband filters. For F657N and F673N, this assumption is mitigated by interpolating the two broadband filters, F814W and the corrected F555W, to derive stellar-continuum images at the appropriate wavelength. Furthermore, except for a few regions in the nucleus of M83, colors do not change dramatically across the F555W or F814W filter bandpasses. We use a single continuum image interpolated at the intermediate wavelength 660 nm for both of F657N and F673N. Since the widths of the broadband images are larger than 100 nm, the interpolated image at 660 nm can be used as continuum for nearby emission lines located within a couple of 10 nm.

We produce two subtracted versions (optimized subtraction for the central region and the spiral arm each) for [O iii](5007 Å) and Hβ, since the bluer continuum F555W suffers from more local deviation from color differences of background stellar population than the redder filters. We take a single optimized subtraction for Hα and [S ii](6716 Å+6731 Å). We consider potential changes in color within the broadband filters as a source of error in our photometry.

We assume that [S ii](6716/6731) ≈1.2, since the ratios are between 1.0 and 1.4 in the ISM of M83 (Bresolin & Kennicutt 2002, hereafter BK02). For the [N ii] correction to Hα, we adopt the spectroscopic flux ratios, [N ii]/Hα = 0.42 for the spiral arm and 0.54 for the center from BK02. We, thus, generate two "Hα" only maps; one with the [N ii] subtraction optimized for the central region and one optimized for the spiral areas. (Note that Hβ and [O iii](5007 Å) have two optimized versions due to different continuum subtraction, while for Hα due to different [N ii] correction.) The [N ii]/Hα ratios range from 0.40 to 0.47 in the spiral arm and from 0.53 to 0.56 in the center. The difference of the corrected Hα fluxes within each of these ranges is less than 10%, which is small enough to be negligible in our analysis. C04 used the relation [N ii] ≈2× [S ii] too as an alternative method for [N ii] correction. The ratio [N ii]/[S ii] has been observed to be relatively constant, since the ratio has less dependences on abundance and extreme variations in UV radiation (Rand 1998; Kewley & Dopita 2002). C04 discuss the [N ii] correction in more details. Our adopted method produces results similar to those of C04. A summary of the images or combination of images used for the stellar-continuum subtraction of each narrowband image is given in Table 1.

Figure 6 shows the overall distribution of the ionized gas in M83 on the diagnostic diagram. The gray lines are photoionization models from K01 and the black lines are shock-ionization models from Allen et al. (2008, hereafter A08), which will be described later in the section. The photoionized grids adopted from K01 are based on the stellar population synthesis model STARBURST99 and the gas ionization code MAPPINGS III (Leitherer et al. 1999; Binette et al. 1985; Sutherland & Dopita 1993). The spectral energy distributions (SEDs) generated from STARBURST99 provide the photoionization source, and the MAPPINGS III code calculates the ionization states and the line emission fluxes. From those, we can derive the theoretical line ratios for photoionization. The plotted photoionization grids in Figure 6 are calculated assuming a constant star formation history, Geneva stellar evolution tracks (Schaller et al. 1992) and Lejeune stellar atmosphere models (Lejeune et al. 1997); see K01 for more details. While the assumption of constant star formation may not strictly apply to the spiral area H ii regions, it is a good representation of star formation in the starburst nucleus of M83 (C04). The case of instantaneous burst models will be discussed later in this section.

The selected ISM densities are 10 and 350 cm⁻³ which we take as representative of the ISM conditions in M83, and the metallicities are chosen to be 1.0 Z_☉ and 2.0 Z_☉, the range observed in the galaxy (BK02). The dimensionless ionization parameter, q, defined as the ratio of mean photon density to mean atom density, ranges from 5.0 × 10⁶ to 3.0 × 10⁸ for each model. The line called "Photoionization Limit" in the legend of Figure 6 is the conservative track termed "Maximum Starburst Line" in K01. Above and to the right of this track, line ratios cannot be explained by photoionization. Since the outputs of STARBURST99 depend on a variety of inputs, such as stellar evolution tracks, stellar atmosphere models, and star formation history, we can use our theoretical grids primarily for qualitative comparisons rather than a quantitative analysis.

One of the interesting results from the photoionized zone in Figure 6 is that the observed [O iii]/Hβ ratios at low [S ii]/Hα values span the range covered by the photoionization models for different values of the metallicity; higher [O iii](5007 Å)/Hβ ratios correspond to lower metallicity in the models. Generally, [O iii](5007 Å)/Hβ ratios are not enough to determine the metallicity of a region (Kewley & Dopita 2002), except in the range between solar abundance to super-solar abundance. The red "P" box in Figure 6 is a photoionized region, where the [O iii](5007 Å)/Hβ line ratio is sensitive to metallicity. We re-project the pixels of the P box on the line emission images and select small sub-regions, labeled as PA1, PA2, PA31, PA32, and PA4, as shown in Figure 4, to investigate the relation between the observed [O iii](5007 Å)/Hβ ratio and metallicity. Those regions are bright in each emission line and geometrically clustered in compact regions. The sizes of the regions are close to the size of the spectroscopic aperture used in BK02. In addition, PA1 and PA4 correspond to the regions, "A" and "9" in BK02, respectively.

In the P box, we can also observe a weak rank ordering of the [O iii]/Hβ ratios according to the regions they belong to: A1>A2>A3 ≈ A4. Interestingly, that is the exact order of distance from the center. This relation between the [O iii]/Hβ ratios and the distance from the center appears consistent with the metallicity gradient from the center to the spiral arms in M83.

To verify this, we present the observed relation between oxygen abundance and [O iii]/Hβ ratios in Figure 7. The black (named "MG") and the gray (named "E") points are borrowed from the spectroscopic results of BK02. The names "MG" and "E" indicate the different oxygen abundance calibrations from McGaugh (1991) and Edmunds (1989). The figure shows the direct correlation between [O iii]/Hβ ratio and oxygen abundance. To compare our data with those from BK02, we convert the distance of each region to the oxygen abundance using the relation between distance and oxygen abundance in BK02 and overplot them in Figure 7. The horizontal error bar is due to the physical size of each region and the vertical error bar represents the standard deviation of the line ratio distribution among the pixels within each region. Since our resolution is much higher than the spectroscopic aperture, 02 for each pixel, the line ratios are distributed in a broad range for the A1, ..., A4 regions as well as the PA1, ..., PA4 regions. The overall trend is consistent with the same metallicity trend as BK02. So, the metallicity gradient from the center to spiral arm appears to cause the spread in [O iii]/Hβ values in the "photoionized" area of the diagnostic diagram of Figure 6 at low [S ii]/Hα values.

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To investigate in detail the physical properties of the photoionized gas in M83, we present additional photoionization models in Figure 8. The two top panels show two different star formation history models; constant star formation (left) and instantaneous burst (right) from K01. The constant star formation model assumes durations larger than 8 Myr, when the dynamical balance between the stellar births and deaths is set up for UV radiation. The instantaneous burst model is the case for zero-age stellar population, which is the extreme end in star formation history. Thus, these two models bracket a range of star formation histories for our regions. Both show similar metallicity dependence; lower [O iii]/Hβ ratio for higher metallicity. The constant star formation model with 2.0 Z_☉ marks the lower envelope to the photoionized data, thus fully including all pixels in A1.

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Dopita et al. (2006, hereafter DP06) introduced models for time-evolving H ii region. While K01 treat the ionization parameter as an independent parameter, DP06 calculate the ionization parameter as a function of age of the stellar cluster. The DP06 models are based on a one-dimensional spherical geometry for the evolving H ii region. The radius and pressure evolution are derived from the works of Castor et al. (1975) and Oey & Clarke (1997, 1998):

$$\begin{eqnarray*} R &=& \left(\frac{250}{308\pi }\right)^{1/5} L_{{\rm mech}}^{1/5} \rho _{0}^{-1/5}t^{3/5} \nonumber \\ P &=& \frac{7}{(3850\pi)^{2/5}} L_{{\rm mech}}^{2/5} \rho _{0}^{3/5}t^{-4/5}, \nonumber \end{eqnarray*}$$

where L_mech is the instantaneous mechanical luminosity from the cluster, ρ₀ is the ambient ISM density, and t is the time. DP06 found that the ionization parameter in their models depends on the mass of the stellar cluster and the pressure of the surrounding ISM, and it scales as q ∝ M^1/5_clP^−1/5₀, where M_cl is the initial mass of the stellar cluster and P₀ is the initial ISM pressure surrounding the stellar cluster. Hence, the ratio, R = log₁₀[(M_cl/M_☉)/(P₀/k)], where P₀/k is measured in cgs units (cm⁻³ K), uniquely determines the time-evolving track of the ionization parameter as an initial condition (see DP06 for more details). The middle panels in Figure 8 show the DP06 models for two different metallicities, 1.0 Z_☉ (left) and 2.0 Z_☉ (right). We also compare these models with re-binned data (see bottom panels of Figure 8) to investigate the impact of the binning size on our results. In all cases analyzed, we find that an evolving H ii region scenario at constant metallicity does not fully reproduce the observed trend in the data, although each covers a portion of the locus occupied by the data points. The full range of the data can be covered by varying the metal abundance by more than a factor 10, which we consider unlikely given the relative small size of our regions (≈970 pc). At this stage, the best model to fit the photoionized gas appears to be the continuous starburst scenario.

The instantaneous models assume zero-aged stellar population and DP06 models track the age effect on such instantaneous models using the evolution dynamics described by the above equations. These two models are hard to reconcile with observations if the stellar population contains a mix of stellar clusters with various ages or if the ionization parameter cannot be derived from the equations above. Those equations are exact only in the case of an isolated H ii region. For a starburst region, the photoionized gas is diffuse and distributed on a large scale plus the region itself is the complex superposition of many H ii regions. For this case, the ionization parameter is better treated as an independent parameter rather than derived from an isotropically expanding sphere. The age distribution of stellar clusters in M83 approximately follows a power-law distribution (Chandar et al. 2010): there are many clusters formed within 10⁷ years, and the power law extends by a few million years. Therefore, the combination of multiple stellar population ages and the complex geometry of the photoionized gas can be the reasons why the continuous models fit the observation more closely.

The adopted separation criteria for the shock- and photoionized gas need to be discussed in this kind of study, because there is no objective separation between the two phases in the diagnostic diagram. The maximum starburst line, or "Photoionization Limit" in Figure 6, is a conservative limit (see K01 and Kauffmann et al. 2003), above and to the right of which line ratios cannot be produced by photoionization. This provides a lower limit to the amount of shock-ionized gas; in Table 2, we list, for this discriminant (called M1), the Hα luminosity, fraction of the total luminosity, and fraction of the total area occupied by shocks. A second discriminant can be provided by photoionization models matched to the solar-to-super-solar metallicity of M83. If we choose, conservatively, the N350Z1.0 model of Figure 6, the fraction of Hα luminosity and area occupied by shocks increases dramatically (M2 in Table 2). In this case, even the H ii regions located along the spiral arm outside the central region show evidence for a shock component, albeit at the level of ≈1%. Conversely, in the central starburst, about 15% of the total Hα luminosity is due to shocks. A third discriminant (called M3) can be provided by shock-ionization models. Data points will be considered shocks if they lie within the region covered by shock+precursor models. The M3 criterion is the most generous, among the three discussed so far, in including pixels from each region among the "shocks," it will provide a robust upper limit to our shock estimates. The shock Hα luminosity in the spiral arm regions is now 4% (A3) or less of the total Hα luminosity, still not a significant amount. A much larger fraction, about 33% of the total, is derived for the central starburst, the most generous estimate among all criteria.

Finally, as the low surface brightness of [O iii](5007 Å) is the major limiting factor for our diagnostics, we attempt to use the single line ratio criterion, [S ii]/Hα > − 0.5, to overcome this limitation (M4 in Table 2). This is another generous criterion for discriminating shocks from photoionization, like the M3 criterion, although it provides a less accurate separation than the diagnostic diagram involving the [O iii] line; however, it does not suffer from the limitations produced by faint or undetected [O iii](5007 Å). Figure 9 shows the theoretical relation between normalized Hα flux and [S ii]/Hα ratio from the continuous starburst model of K01 and the shock+precursor model of A08. In this figure, we define three regions: (1) the shock zone, log ([S ii]/Hα)> − 0.5, (2) the mixing zone, −1 < log ([S ii]/Hα) < −0.5, and (3) the photoionization zone, log ([S ii]/Hα) < −1. Our single-ratio diagnostics, log ([S ii]/Hα)> − 0.5, thus contains contributions from photoionized gas at low surface brightness. We consider this "contamination" acceptable, in view of the fact that we recover all signal from shocks. Figure 10 shows the observed relation between the dust-extinction-corrected Hα flux and the [S ii]/Hα ratios for A1, A2, A3, and A4. The comparison of Figures 9 and 10 suggests that shocks are present in all four regions analyzed.

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In Table 2, the SFR is calculated from the photoionized gas only (total Hα luminosity−shock Hα luminosity), i.e., corrected for the effects of extinction using the WFC3 Pβ(λ1.282 μm) image (G. Liu et al. 2011, in preparation). The SFR density is calculated by dividing the SFR by the area of the photoionized pixels. Figure 11 shows the spatial distribution of the ionized gas from Table 2 according to each shock separation criterion, M1, M2, M3, and M4; the Hα images (4σ cut) covering the regions, A1, A2, A3, and A4, are shown in the first column together with the locations of photoionized gas (red) and shock-ionized gas (blue) with the shock criteria of M1 (the second column), M2 (the third column), M3 (the fourth column), and M4 (the fifth column).

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In the spiral arm (regions A2, A3, A4), the shock gas from the "Maximum Starburst Line" criterion (M1) is negligible. In the other criteria (M2, M3, and M4), the luminosity ratios and the area ratios are 4% or less. Figure 10 also shows that most of the log ([S ii]/H_α) values in A2, A3, and A4 are less than −1, so located in the photoionization zone. Therefore, feedback from star formation is very low in the spiral arm of M83 perhaps owing to the youth of the H ii regions we detect. Shocks remain a small or negligible component in the outer H ii regions.

For the central starburst, the SFR is 2.7 times larger than the previous study of C04 due to a better Hα filter coverage in the present study (the WFPC2 narrowband filter used in the C04 study placed the redshifted Hα on the red shoulder of the filter). In addition, the Pβ/Hα extinction map we use probes larger dust extinction values than the Hα/Hβ extinction map (G. Liu et al. 2011, in preparation). The SFR density of A1 is three times larger than the values of A2, A3, and A4. For the conservative shock estimate (M1), the luminosity ratio and the area ratio of A1 are consistent with the previous study of C04 when we consider the range of values for different [N ii] corrections of the Hα filter. In this conservative criterion, a few percent of the Hα luminosity come from shock gas. The area occupied by the shock gas is larger than the luminosity contribution, consistent with the fact that the shock gas has lower Hα brightness but is distributed more diffusely than the photoionized gas. For the other criteria (M2, M3, and M4), the shock Hα luminosities can reach 15%–33% of the total luminosity. The covering areas of shocks are also larger totaling 28%–53% of the total area. The M3 and M4 criteria are generous and may misclassify as shocks some regions that could actually contain mostly photoionized gas; we thus expect the shock luminosity, and area can be overestimated for M3 and M4. We conclude that the acceptable values are 15% for the Hα luminosity and 30% for the areal coverage of shocks in the center of M83. When comparing our 15% fraction of shocked gas in the central starburst of M83 with expectations for the mechanical energy output from the starburst itself (4%–9%, Columns 4 and 8 of Table 6 in C04), we conclude that virtually all of the available mechanical energy from massive star winds and supernovae is radiated. This is in agreement with the findings of Martin (2006), who concludes that only a few percent of the mechanical energy from star formation is available as kinetic energy to drive the ISM.

In this section, we compare our data with shock-ionization models and investigate the properties of the shock-ionized gas. The shock-ionization model of A08 uses the ionizing radiation field from hot radiative shock layers dominated by free–free emission and the MAPPINGS III code to calculate the gas ionization state and the intensity of the emission lines. The emission from shocks consists of two components; the shock layer (post-shock component) and the precursor (pre-shock component). The shock layer is the cooling zone of the radiative shock, and the precursor is the region ionized by the upstreaming photons from the cooling zone. Since free–free emission is dominant in shock layers, the ionizing radiation field from shocks is mainly determined by the shock velocity and the pre-shock gas density (see A08 for more details). So, for a given metallicity and pre-shock gas density, the shock velocity is the main parameter determining the line ratios in the diagnostics. The main branch of the shock grids labeled with "B = 1.0E-4" in Figure 6 shows the line ratios for shock velocities from 100 km s⁻¹ to 900 km s⁻¹, with a fixed ISM magnetic field of 10⁻⁴ μG. The magnetic field in the ISM plays an important role in determining the post-shock gas density: higher ISM magnetic fields correspond to lower post-shock densities, with major effects on the ionization parameter of the post-shock gas component. Hence, the magnetic field is the second main parameter in shock models. The side branches from the selected shock velocities, 100, 150, ..., 500 km s⁻¹, show the effect of changing the magnetic fields from 10⁻⁴ μG to 10 μG. The metallicity of the model is 2 Z_☉ and the pre-shock gas density is 1 cm⁻³.

Two peculiar features can be identified in Figure 6, in the region dominated by shock excitation. One is a series of pixels in a roughly horizontal sequence, around log  ([O iii]/Hβ) ∼0, which seem to be consistent with the horizontal feature of the shock+precursor model from A08. This horizontal distribution of shock-ionized gas is a unique feature when compared with other solar and sub-solar abundant galaxies such as NGC 3077, NGC 4214, and NGC 5253 in C04, which have the shock-ionized gas near or outside of the "Maximum Starburst Line." A part of the feature is marked by a box labeled "S2" in the figure, where it is outside of the photoionization locus. So, the "S2" region can be considered as a shock-ionized region with high shock velocities (>300 km s⁻¹) according to the shock models. The other peculiar feature is a vertical plume located at log  ([O iii]/Hβ) >0.2 and −1 < log  ([S ii]/Hα) <−0.5, where some low-velocity shocks are likely to be present based on the shock models. This region, also marked by a box in Figure 6, is labeled as "S1." Both regions belong to the nuclear region A1, where the most active star formation in the galaxy is taking place.

The horizontal feature around S2 in the diagnostic diagram is highlighted in Figure 12, where the data are compared with the shock+precursor models from A08 (top left panel) and the precursor and the shock shown as separate curves, also from A08 (top right panel). To assess again the impact of spatial sampling on our data, we reproduce the top panel with the data rebinned in boxes of 35 × 35 pixels, or 14 × 14 (bottom panels). The models clearly indicate somewhat different natures for the horizontal feature. The A08 models suggest that the feature could be due to shocks-only or shock+precursor (but not precursor-only model), with velocities in the range 250–350 km s⁻¹. The pixels corresponding to the S2 data points in the diagnostic diagram of Figure 13 are re-projected onto a spatial reproduction of A1 in the left panel of Figure 13. Those points are mostly located at the edges of the region of photoionization, where we would expect to find shock-ionized gas. In addition, many S2 points are located inside the largest of the regions in A1, in correspondence to the "bubble" created by one or more of the young stellar clusters in the starburst (Harris et al. 2001); this is also an area where we do expect shocks to be present.

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Region S1 in Figure 6 is enlarged in the right panel of Figure 13, and its pixels spatially projected in the left panel of the same figure. A number of those data points from the diagnostic diagram, especially those with the highest log  ([O iii]/Hβ), distribute randomly on the spatial projection, indicating that they are the result of noisy pixels combined with our generous 4σ cut in the line emission images. However, a number of pixels in the S1 region appear correlated, and, like most of the pixels from S2, crowded in regions at the edges of the A1 line emission area. We name those regions S1a (magenta), S1b (cyan), and S1c (gray), indicated with open circles in the left panel, and identify those regions in the diagnostic diagram in the right panel of Figure 13. Those data points, marked with circles in the right panel of the figure, are consistent with low-velocity shocks+precursor models by A08, with velocity in the range 100–150 km s⁻¹. These areas (also marked with open circles in the left panel of Figure 13) are located close to identified supernova remnants (SNRs) from Dopita et al. (2010) as shown in the bottom panel of Figure 13. Using the naming convention from that paper, we find SNRs, N3, N4, and N7 close to our region S1a, N2 to S1b, and N14, N15, N17, and N18 to S1c. S1a and S2b seem to correspond to the SNRs, N3 and N2, respectively. There is no corresponding SNR for S1c. It is interesting that S1c is surrounded by the four SNRs, N14, N15, N17, and N18. However, four SNRs, N14, N15, N17, and N18 are located in correspondence to features both in S1 and S2 (top left with bottom panel of Figure 13). Thus, it is likely that the identified low-velocity shocks are closely related to the identified SNRs.

Two of the S1 sub-regions (S1a and S1b) are located adjacent to the dust lane that crosses the center of M83. Although the diagnostic diagram tends to be fairly unaffected by dust extinction, the large dust column densities found in dust lanes may have an impact on the line ratios. We cannot eliminate this possibility with the data in hand. Finally, dynamical interactions may play a role in the creation of low-velocity shocks. S1a and S1c are located at the junction points of the spiral arms to the central outer ring, while S1b is in-between the spiral arm and the outer ring. The interaction between those morphological features could be at the basis of the observed shocks.

The width of the precursor of a shock front is generally larger than our binned pixel size (∼4.3 pc), while photoionization equilibrium can be achieved well within the size. For the shock model of A08 with solar abundance, 1 cm⁻³ pre-shock gas density, 200 km s⁻¹ shock velocity, and 3.2 μG magnetic field, the length of pre-shock-ionized zone is 40 pc, while the length of post-shock cooling zone is less than 4 pc. Even though the post-shock zone (shock layer) can be small enough to fit in our bin size, the pre-shock component is much larger than our bin scale. This means that, unlike the photoionization model, the shock-ionization model needs to be applied carefully when we compare it with the data. For instance, if a pixel line of sight passes through both precursor and shock front, the pixel line ratio is meaningful when compared with the shock+precursor grids. If a pixel only covers a part of the precursor region or shock front, the comparison has to be made with shock-only or precursor-only models. When we consider the complicated geometry through observed line of sights, it is hard to determine which light of sight is for shock-only, precursor-only, or shock+precursor. Therefore, we may need to make a geometrical block enough to cover both of shock and precursor, but excluding photoionized gas, and sum up the whole line flux in the block in order to compare it with the shock+precursor model. So, basically shock-ionization models may need, in principle, to be compared on a large-scale basis than what done so far. However, as shown in the bottom panels of both Figures 8 and 12, rebinned to pixel sizes of 14 (∼30 pc), the quantitative distribution of the data points on the diagnostic diagram does not change, implying that our smaller pixel scale is adequate to average out effects of spatial variations in shocks.