Extended high-ionization [MgIV] emission tracing widespread shocks in starbursts seen by JWST /NIRSpec
Miguel Pereira-Santaella Ismael García-Bernete Eduardo González-Alfonso Almudena Alonso-Herrero Luis Colina Santiago García-Burillo Dimitra Rigopoulou Santiago Arribas Michele Perna










Instituto de Física Fundamental, CSIC, Calle Serrano 123, 28006 Madrid, Spain 

miguel.pereira@iff.csic.es
Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
Universidad de Alcalá, Departamento de Física y Matemáticas, Campus Universitario, 28871 Alcalá de Henares, Madrid, Spain
Centro de Astrobiología (CAB), CSIC-INTA, Camino Bajo del Castillo s/n, E-28692 Villanueva de la Cañada, Madrid, Spain
Centro de Astrobiología (CAB), CSIC-INTA, Ctra de Torrejón a Ajalvir, km 4, 28850, Torrejón de Ardoz, Madrid, Spain
Observatorio Astronómico Nacional (OAN-IGN)-Observatorio de Madrid, Alfonso XII, 3, 28014, Madrid, Spain
School of Sciences, European University Cyprus, Diogenes street, Engomi, 1516 Nicosia, Cyprus









We report the detection of extended (>0.5–1 kpc) high-ionization  4.487 (80 eV) emission in four local luminous infrared galaxies observed with NIRSpec. Excluding the nucleus and outflow of the Type 1 active galactic nucleus (AGN) in the sample, we find that the  luminosity is well correlated with that of H recombination lines, which mainly trace star forming clumps in these objects, and that the  4.530 (75 eV), usually seen in AGN, is undetected. On 100–400 pc scales, the  line profiles are broader (σ()=90± 25 km s^-1) and shifted (Δ v up to ±50 km s^-1) compared to those of the H recombination lines and lower ionization transitions (e.g., σ(Hu-12)=57± 15 km s^-1).

The  kinematics follow the large scale rotating velocity field of these galaxies and the broad  profiles are compatible with the broad wings detected in the H recombination lines.
Based on these observational results, extended highly ionized gas more turbulent than the ambient interstellar medium, possibly as a result of ionizing shocks associated with star-formation, is the most likely origin of the  emission.
We also computed new grids of photoionization and shock models to investigate where the  line originates. Shocks with velocities of 100–130 km s^-1 reproduce the observed line ratios and the  luminosity agrees with that expected from the mechanical energy released by supernove (SNe) in these regions. Therefore, these models support shocks induced by SNe as the origin of the  line.
Future studies on the stellar feedback from SNe will benefit from the  line that is little affected by obscuration and, in absence of an AGN, can only be produced by shocks due to its high ionization potential.







Extended high-ionization [Mgiv] emission tracing widespread shocks in starbursts seen by NIRSpec
    Miguel Pereira-Santaella<ref>
Ismael García-Bernete<ref>
Eduardo González-Alfonso<ref>
Almudena Alonso-Herrero<ref>
Luis Colina<ref>
Santiago García-Burillo<ref>
Dimitra Rigopoulou<ref>,<ref>
Santiago Arribas<ref>
Michele Perna<ref>

    April 29, 2024
=============================================================================================================================================================================================================================================






§ INTRODUCTION


Feedback from active galactic nuclei (AGN) is an important element for the evolution of galaxies (e.g., ).
However, detecting deeply buried AGN is still difficult due to dust obscuration. 
This is particularly challenging in local luminous and ultra-luminous infrared (IR) galaxies (ULIRGs; L_ IR>10^11 L_⊙). Local ULIRGs are mostly interactingmerging systems, so they represent a key phase in the evolution of galaxies (e.g., ), and their activity (AGN and star-formation) occurs in extremely dust-embedded environments.


Activity diagnostics in the optical fail in many ULIRGs since they host the most obscured nuclei in the local Universe (N_ H>10^25 cm^-2; e.g., ).
Indirect methods using mid-IR spectroscopy pointed out the presence of AGN in a large fraction, ∼70%, of ULIRGs (e.g., ). These mid-IR methods suggested a modest AGN contribution to the total luminosity. However, radio and sub-mm observations, which are insensitive to dust extinction, revealed compact nuclei exceeding the surface brightness density of a maximal starburst, hence likely AGN, dominating the bolometric luminosity of the majority of ULIRGs <cit.>.
Therefore, the direct detection of these AGN remains elusive and its exact contribution to the total luminosity is still debated.


The reduced dust extinction in the near- and mid-IR spectral ranges, along with the superb sensitivity and angular resolution of the James Webb Space Telescope (), for the first time allows the search for high-ionization emission lines, which may eventually provide direct evidence of these elusive AGN in ULIRGs.
Specifically, the  4.487 line, with a high ionization potential (IP; 80 eV), is not expected in gas photoionized by young stars since they do not emit significant quantities of photons with the energies beyond 54 eV (He^+ ionization energy). Therefore, the detection of the  line, which lies close to the minimum of the dust opacity (e.g., ), has been proposed as an excellent tracer of deeply embedded AGN (e.g., ). However, fast ionizing shocks (>80 km s^-1; ) can also produce highly ionized gas that can emit high-ionization lines. For instance, the  25.9 line (IP 55 eV), which is well correlated with the AGN power (e.g., ), is also associated with shocks in starbursts (e.g., ). 





In this Letter, we investigate the origin (AGN, star-formation, or shocks) of the extended  emission detected in a sample of four local LIRGs observed with the Near Infrared Spectrograph (NIRSpec; ).
We first analyze the spatial distribution of the  emission and compare the  line profiles with those of other low-ionization and H recombination lines. Then, we use new grids of photoionization and shock models to determine the physical and dynamical conditions of the gas producing this line.






§ SAMPLE AND DATA REDUCTION


Four local (39 < D_ LMpc < 161) LIRGs, with L_ IR=10^11.6-11.9, were observed with NIRSpec using the high spectral resolution grating G395H (R∼1900–3600; 2.87–5.27) and the integral field unit (IFU) mode <cit.>, and with Mid-Infrared Instrument (MIRI) using all the bands of the Medium Resolution Spectrograph (MRS; ).

These observations were part of the Director's Discretionary Early Release Science (DD-ERS) Program #1328 (PI: L. Armus and A. Evans).
These four objects cover a wide range of properties: from pre-mergers to late merger stages and from heavily obscured AGN to Type 1 AGN (see Table <ref>).



For the data reduction, we used the  calibration pipeline (version 1.12.4; ) and the context 1197. We followed the standard reduction recipe complemented by a number of custom steps to reduce the effect of bad pixels and cosmic rays. Further details on the data reduction of the NIRSpec and MIRIMRS data observations be found in <cit.> and <cit.>.



§ ANALYSIS AND RESULTS




 §.§ Spatially extended  emission




Fig. <ref> shows the rest-frame 4.31–4.57 spectra from 23 regions selected in the four systems. To extract these spectra we used apertures with a diameter of 054 (100–400 pc depending on the target). We did not apply any aperture correction as the emission appears spatially resolved.
Nevertheless, in a worst-case scenario of a point source, the error in the line ratios discussed below (Sect. <ref>) would be small, <5%.


The regions were selected to cover the extended  emission detected in the line maps (see Figs. <ref> and <ref>-<ref>).
For simplicity, in this Letter we excluded regions with strong CO v=1–0 band, since the  transition is almost coincident with the CO v=1–0 R(24) 4.489 line (Fig. <ref>). We note, however, that after modeling the band, it is possible to detect  emission also in these regions (see ).

The spectra show clear  detections, two H_2 lines, the Humphreys-12 4.376 (Hu-12) recombination line, and, in some cases, weak absorptions from the R-branch of the CO v=1–0 band. The  4.530 transition, with an IP of 75 eV slightly lower than , is only detected in the nucleus and outflow of the Type 1 AGN NGC 7469 with both lines having comparable intensities (see also ).
The latter is consistent with the Infrared Space Observatory (ISO) detections of the  and  line pair in two AGN (Circinus and NGC 1068), where the  line is ∼2 times brighter <cit.>. Based on these previous results for AGN, the absence of the  transition in the remaining regions is surprising and suggests that distinct physical conditions, maybe not related to an AGN, can lead to this  emission.



To determine the origin of the  line, we created 2D emission maps of tracers of the ionized gas phase (Hu-12 and Pf-γ 3.741), the warm molecular gas phase (H_2 0–0 S(8) 5.053), and fast shocks ( 5.340).
Warm molecular gas excited by shocks has been identified in interacting systems and ULIRGs (e.g., ) but the shock velocities are typically lower than that of the ionizing shocks traced by .
We extracted the spectra using a running 2x2 spaxels box and fitted a local linear continuum level and a Gaussian profile to determine the flux and velocity at each position (Figs. <ref> and <ref>-<ref>). The  morphology is spatially extended, from few hundreds pc to ∼1 kpc, and its spatial distribution is more similar to that of the ionized and shocked gas (Hu-12 and ) than to the warm molecular H_2 emission. Actually, for the regions selected before, there is a very good linear correlation between the Hu-12 and the  luminosities (excluding the nucleus and outflow of NGC 7469) which spans almost 2 dex and has a Spearman correlation coefficient of 0.94 (Fig. <ref> top). This correlation also holds when we consider the individual spaxels (Fig. <ref> bottom). The correlation between the shock tracer  and  is also good (Fig. <ref> bottom panel).
For the warm H_2, the correlation coefficient is lower, 0.72, and the correlation, if real, would not be linear (Fig. <ref> top panel).







 §.§ Broad  line profiles









We compared the kinematics of the gas emitting the  line with that of the ionized gas traced by other transitions by modeling their profiles.
In particular, we analyzed the following lines in the spectra of the selected regions: the Hu-12 line that is close in wavelength to  and the effects of differential extinction are minimized;
Pf-γ, which can be more affected by extinction in these dusty galaxies (A_ Pf-γ A_= 1.14; ), but is intrinsically brighter than Hu-12 (Pf-γHu-12 = 5.53 at 10 000 K; );
 5.340, which is a good tracer of shocks <cit.>; and  6.985, which also traces ionized gas, but has significantly higher signal to noise ratios (SNR).

The observed line profiles and best-fit models are presented in Figs. <ref> and <ref>. A single Gaussian component reproduces well the  and Hu-12 profiles. We find that the  profile is systematically broader than the Hu-12 profile (top panel of Fig. <ref>). The average widths, corrected for the instrumental resolution, are: σ_ corr()=90± 25 km s^-1 and σ_ corr( Hu-12)=57± 15 km s^-1. In addition, the  emission presents velocity shifts, up to ±50 km s^-1, with respect to Pf-γ (the NIRSpec absolute wavelength accuracy for the G395H grating is ∼12 km s^-1; priv. comm.).
In the higher SNR profiles of Pf-γ, a second broader component is clearly detected through higher velocity wings in all the profiles. Wings are also detected in the  and  lines (Fig. <ref>, two right most panels). Broad profiles (>200 km s^-1) have been detected in the mid-IR lines of local ULIRGs typically associated with the narrow line region (NLR) of AGN and ionized outflows <cit.>. However, we note that the regions selected here are widespread over the entire extent of these objects and not specifically selected to encompass outflows or the NLR of AGN.

We show the best-fit two Gaussian model for these lines in the third, fourth, and fifth columns of Figs. <ref> and <ref>. We find a remarkable similarity between the widths and velocity shifts of the  and the broad Pf-γ profiles. The
σ^ broad_ corr(Pf-γ) =105± 15 km s^-1 is comparable to σ_ corr() and the great majority (85%) of the velocity shifts have the same sign (i.e., lie in the blue- or red- shaded areas in the bottom panel of Fig. <ref>).



In most of the cases (∼75%) the  line is blue-shifted relative to the narrow component in Pf-γ.
Although extinction is greatly reduced at ∼4.5, it might affect the receding side of the  emission and explain this uneven distribution of the sign of the shifts. A detailed study of the extinction is beyond the scope of this Letter. We also note that the sign of the shifts of the broad component of  and  follow the same trend (Fig. <ref>) and the widths are also comparable to that of the  line, σ^ broad_ corr()=112± 27 km s^-1 and σ^ broad_ corr()=102± 20 km s^-1.








§ ORIGIN OF THE  EMISSION: STAR-FORMATION, AGN, AND SHOCK MODELS


Despite its high IP, the results described in Sect. <ref> are not fully consistent with an AGN origin of the  emission because: (1) it is extended and correlated with the Hu-12 emission, a H recombination line tracing star forming regions based on its morphology; (2) the  line, with a slightly lower IP and typically found in other AGN, is undetected, except in the outflow and nucleus of the Type 1 AGN; and (3) the  profile is broader and shifted compared to the other transitions.


Therefore, we created three grids of models (star-formation, AGN, and shocks) to investigate the origin of the  emission.
We briefly describe the models in this section and provide further details in Appendix <ref>.



We modeled the emission from gas photoionized by AGN or star-formation using the spectral synthesis code Cloudy <cit.>. We mostly followed <cit.> to create these grids but updated the spectral energy distributions (SEDs) of the incident radiation field. For the star-formation grids, we used the Binary Population and Spectral Synthesis (BPASS) library <cit.>, which includes stripped-envelope stars that have harder ionizing spectra (e.g., ) and could contribute to the  emission.
For the AGN models, we used the three SEDs for low, medium, and high Eddington ratios derived by <cit.>, which provide a more realistic approximation to the intrinsic SED of AGN than a power-law.

Based on these grids, we can reject that the  line originates in gas photoionized by stars since the observed Hu-12 ratio (∼0.5; Fig. <ref>) is >2.3 dex larger than the predicted ratio (Fig. <ref>).

The AGN photoionization predictions for the Hu-12 and  ratios are shown in the left panel of Fig. <ref>. The outflow and nucleus of the Sy1 NGC 7469 lie close to the grid with ionization parameters, log U, between -2.00 and -2.25 in the range of Seyfert AGN (e.g., ). For the remaining regions, the lower Hu-12 ratio and the non-detection of  would imply log U<-3.25, which is low but is also found in some AGN and low-ionization nuclear emission regions (LINERs; e.g., ).



Finally, we created a grid of shock models using MAPPINGS V following <cit.>, which includes several improvements compared to the models in <cit.> (see Appendix <ref>). The Hu-12_ broad ratio and the  3σ upper limit are compatible with the emission produced by shocks with shock velocities v_ s=100-130 km s^-1 (Fig. <ref> right). The v_ s is not directly equivalent to σ_ corr (e.g., ), however, the fact that they are similar, σ_ corr()=90± 25 km s^-1 (Sect. <ref>), supports that shocks are a possible origin of the  emission.




In summary, while we cannot completely reject the AGN origin in a very low log U environment based on these line ratios, the morphology and kinematic properties of the  emission (broader profile and velocity shifts) favor the shock origin.
Under this assumption, the good correlation between the extended  emission and the recombination line Hu-12, which traces star forming clumps, is naturally explained if the shocks producing the  emissions are powered by supernove (SNe).
To estimate if the energy released by SNe can produce the observed  luminosity relative to the star-formation rate (i.e., Hu-12 ratio), we combined stellar population evolution models and the shock models. 
Shock models predict efficient  emission at v_ s∼110–160 km s^-1, so observing  emission at these velocities is also favored (Fig. <ref>). Using these relations (see Appendix <ref>), the predicted log Hu-12 ratio from a star forming region with shocks produced by SNe is between -1.4 and -0.5.
The observed log Hu-12 ratio, -0.29± 0.18, lies at the upper end of the range but is consistent with it considering the relatively large uncertainties of both the shock models (e.g., v_ s, Mg abundance) and the star-formation models (e.g., initial mass function, energy per SN, electron temperature). Therefore, it is plausible that SNe can provide enough mechanical energy to generate the observed  emission.




§ SUMMARY AND CONCLUSIONS


Using NIRSpec integral field spectroscopy, we investigated the extended high-ionization  4.487 (IP 80 eV) emission in a sample of four local LIRGs, only one of them hosting a Seyfert-like AGN.
Excluding the nucleus and outflow of this AGN, we find that shocks related to star formation are the most likely origin of the extended  emission since: (1) the  luminosity is well correlated with the recombination line Hu-12 4.376, which traces star forming clumps in these objects; and the  4.530 line (IP 75 eV), which is common in the spectra of AGN, remains undetected; and (2) the  profile is broader (σ_ corr()=90± 25 km s^-1) and shifted up to ±50 km s^-1 relative to the recombination lines (σ_ corr(Hu-12)=57± 15 km s^-1). The  line kinematics actually track the faint wings of the lower ionization lines (Pf-γ 3.741,  5.340, and  6.985) and resembles the large scale rotating velocity field of the galaxies.



Supporting this interpretation, shock models with v_ s∼100–130 km s^-1 (i.e., similar to the σ of  and the broad component in other species) are consistent with the observed Hu-12 ratio and the  upper limit. Also, the  luminosity is comparable to that expected from shocks associated with the mechanical energy released by SNe in these regions.
Based on these results, the detection of  emission is expected in pure star-forming galaxies, at least in objects with high gas and star-formation surface densities similar to those of local LIRGs (e.g., ).


Due to its high IP,  offers a unique view of the shocked gas by tracing the highly ionized phase, contrasting with classic shock tracers such as the  transitions, which have a lower IP of 7.9 eV and are more easily ionized.
Compared to the  25.9 line (IP 55 eV), the higher sensitivity and angular and spectral resolutions of  at the shorter wavelength of the  line will be beneficial for future studies of stellar feedback caused by these widespread shocks in strong starbursts.



We thank the referee for their useful comments and suggestions.

The authors acknowledge the GOALS ERS team for developing their observing program.
MPS acknowledges support from grant RYC2021-033094-I funded by MICIU/AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRTR.
IGB and DR acknowledge support from STFC through grants ST/S000488/1 and ST/W000903/1.
AAH acknowledges support from grant PID2021-124665NB-I00 funded by the Spanish
Ministry of Science and Innovation and the State Agency of Research
MCIN/AEI/10.13039/501100011033  and ERDF A way of making Europe.

This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST; and from the European JWST archive (eJWST) operated by the ESAC Science Data Centre (ESDC) of the European Space Agency. These observations are associated with program #1328.




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§ EMISSION LINE MAPS


Figs. <ref>-<ref> show the emission maps for the complete sample.
























§ EMISSION LINE PROFILES


Fig. <ref> shows the emission line profiles for all the selected regions.











§ RELATION BETWEEN THE LUMINOSITY AND KINEMATICS OF  AND H_2 S(8), , AND 








Fig. <ref> shows the relation between the  and the H_2 S(8) and   5.34 luminosities. We scaled the MRS spectra to match the NIRSpec continuum at ∼5. The scaling factors are between 0.7 and 1.3. We did not correct for the differential extinction affecting these lines.
Fig. <ref> presents the comparison between the  line kinematics observed with JWSTNIRSpec and the longer wavelength lines ( and ) observed with JWSTMRS.




§ STAR-FORMATION, AGN, AND SHOCK MODELS






In this section, we present a more detailed description of the grids of models used in Sect. <ref>. For the star-formation and AGN photoionization models, we used Cloudy version 23.01 <cit.> and mostly followed <cit.> to create the grids. The main differences are the updated SEDs used for the incident radiation field (see below). For the shock models, we used the MAPPINGS V code version 5.2.0 following <cit.>.



 §.§ Star-formation models


We used a constant density slab model. The indicent radiation field is obtained from the BPASS library (version 2.2; ). This library includes the effect of stripped-envelope stars in binary systems, which increase the hardness of the spectrum.
We assumed an instantaneous burst of star-formation with ages between 10^6 to 10^8 with 0.1 dex steps. We considered three stellar metallicities (0.4 , , and 2 ), and two initial mass functions (IMFs), both with an upper stellar mass limit of 300 : a standard <cit.> IMF and a top-heavy IMF with a power-law exponent of -2 between 0.5 and 300 .
The initial gas phase abundance was matched to the stellar metallicity and the metals depleted using the “ISM_CloudyClassic.dpl” table. The gas-to-dust mass ratio were adjusted similar to <cit.>.
We varied the gas volume density, n_ H, between 10^2 and 10^4 cm^-3 in 1 dex steps and the ionization parameters between log U=-6.75 and -1.0 in 0.25 dex steps. The models are stopped when the temperature drops below 1000 K or the
H^+ abundance is below 0.1%.

In order to trace the temporal evolution of the line ratios, we need to define how log U varies with the age of the stellar population. log U is proportional to the rate of ionizing photons, Q( H). Thus, 
similar to <cit.>, we defined, for every combination of IMF and stellar metallicity, log U_0 as the ionization parameter when Q( H) is maximum (Q( H)_ 0; typically at ages of ∼1–2 Myr), and scaled log U_ age relative to log U_0 using the ratio Q( H)(age)/Q( H)_ 0.
Then, the line emission at each stellar age is interpolated from the grid using log U_ age.

Figure <ref> shows the Hu-12 ratio as function of the stellar age for log U_0 between -1.0 and -3.0. Only the n_ H=10^2 cm^-3 ratios are presented since the variation of this ratio in the explored n_ H range (10^2–10^4 cm^-3) is small, <30 %.






 §.§ AGN photoionization models


Similar to the star-formation models (Sect. <ref>), we assumed a constant density slab. For the incident radiation, we used the three SEDs derived by <cit.> for low, medium, and high Eddington ratios. These SEDs represent a more realistic characterization of the SED of AGN than a power-law (e.g., ).
We considered three gas phase abundances (0.4 , , and 2 ) which were depleted using the “ISM_CloudyClassic.dpl” table and their gas-to-dust mass ratio were adjusted (see Sect. <ref>).
We varied n_ H between 10^2 and 10^5 cm^-3 in 0.5 dex steps and log U between -4.0 and -1.75 in 0.25 dex steps.
Line ratios derived from these grids are shown in the left panel of Fig. <ref>.

















 §.§ Shock models


We used MAPPINGS V code version 5.2.0 to create a grid of shock models <cit.>.
This grid includes several improvements compared to the models presented by <cit.>.
For instance, the fully time-dependent solution for the photoionized precursor is computed for the first time (see  for details).

The effect of dust is not taken into account by the MAPPINGS V shock code. This is justified for the high-temperature post-shock gas where dust grains can be effectively destroyed (see ). However, dust will be present in the photoionized precursor. This is particularly important since Mg is known to condense on silicate grains (e.g., ). As a first order correction, we reduced the gas phase abundances of metals in the precursor using the default cloudy depletion factors (0.2 for Mg).
We also updated the atomic parameters relevant for the emission lines of interest (e.g.,  and ) to match those used in Cloudy version 23.01. We used atomic data from the CHIANTI database version 10 <cit.> and the Stout database from Cloudy <cit.>.

We followed <cit.> to create the grids varying four input parameters: the gas metallicity, Z_ gas; the shock velocity, v_ s; the ram pressure parameter, R=(n_ H 1  cm^-3) ×(v_ s km s^-1)^2; and the magnetic to ram pressure ratio, η_ M=B^2 (4πρ v_ s^2), where B is the magnetic field and ρ the density.
For Z_ gas, we used 0.5Z_⊙, Z_⊙, and 2Z_⊙ and for v_ s we used a logarithmic grid between 80 and 500 km s^-1 with ∼0.04 dex steps. We used three pressures, R=10^4, 10^6, and 10^8, which are equivalent to densities of n_ H=1, 100, and 10^4 cm^-3 at 100 km s^-1. For the magnetic field, we used η_ M=10^-4, 10^-2, and 10^-1, which correspond to the “standard”, “moderate”, and “strong” magnetic cases identified in <cit.> and are equivalent to B=5.4, 54, and 170 μG for R=10^6. The standard magnetic case is presented in the right panel of Fig. <ref> and the moderate and strong in Fig. <ref>. The main effect of the magnetic field on the Hu-12 ratios is that
that a higher v_ s is needed to obtain the same ratio because more energy is needed to compress the gas when the magnetic field is stronger.




 §.§  luminosity from SNe


We estimated the expected  luminosity produced by SNe shocks for a constant star-formation rate, traced by H recombination lines, by combining the shock models and the stellar population evolution models from the BPASS library.

Assuming Case B conditions, the H recombination lines can be used to measure Q( H). For temperatures between 5 000 and 10 000 K, the HαHu-12 ratio is 1250–1820 <cit.> and Q( H)(s^-1)= (0.85-1.41)×10^15 L(Hu-12)(erg s^-1).

According to the BPASS stellar population models, for metallicities between 0.4  and 2, and assuming a constant star-formation rate, log (Q(H)(s^-1)Ė_ SN(erg s^-1))=11.72–12.10, where Ė_ SN is the power released by SNe.
This ratio is sensitive to the assumed energy released per SN event (10^51 erg), and also to the IMF (e.g., ). For this calculation, we used the <cit.> IMF and a top-heavy IMF (see Sect. <ref>).

For these metallicities, shock models (Sect. <ref>) predict that  is emitted more efficiently at v_ s∼110–160 km s^-1. These v_ s are also comparable to the observed dispersion of the  line profiles. Therefore, in this v_ s range, log L()Ė_ shock, where Ė_ shock=0.5ρ v_ s^3 is the rate of mechanical energy flux across the shock, is between –4.25 and –4.05 (Fig. <ref>). We note that this fraction is very small compared to the ∼0.2% shock energy that is released by some  transitions (e.g., ). 

Combining these three relations, matching the abundances of the stellar population and the shock models, and taking into account the Hu-12 emission from the shock (right panel of Fig.<ref>), the predicted log L()L(Hu-12) ratio in a region with constant star-formation rate and shocks produced by SNe would be –1.4 and –0.5.




















































































