Circumnuclear star formation in Mrk 42 mapped with Gemini Near-infrared Integral Field Spectrograph
Moire G. Hennig Rogemar A. Riffel O. L. Dors Rogerio Riffel Thaisa Storchi-Bergmann Luis Colina


firstpage–lastpage
The X-ray Ribs Within the Cocoon Shock of Cygnus A
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    December 30, 2023
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We present Gemini Near-infrared Integral Field Spectrograph (NIFS) observations of the inner 1.5×1.5 kpc^2 of the narrow-line Seyfert 1 galaxy Mrk 42 at a spatial resolution of 60 pc and spectral resolution of 40 . 
The emission-line flux and equivalent width maps clearly show a ring of circumnuclear star formation regions (CNSFRs) surrounding the nucleus with radius of ∼ 500 pc. The spectra of some of these regions show molecular absorption features which are probably of CN, TiO or VO, indicating the presence of massive evolved stars in the thermally pulsing asymptotic giant branch (TP-AGB) phase. The gas kinematics of the ring is dominated by rotation in the plane of the galaxy, following the large scale disk geometry, while at the nucleus an additional outflowing component is detected blueshifted by 300-500 , relative to the systemic velocity of the galaxy.
 Based on the equivalent width of   we find evidences of gradients in the age of H ii regions along the ring of Mrk 42, favoring the pearls on a string scenario of star formation. The broad component of  emission line presents a Full Width at Half Maximum (FWHM) of ∼ 1480 , implying in a mass of ∼ 2.5×10^6 M_⊙ for the central supermassive black hole. Based on emission-line ratios we conclude that besides the active galactic nucleus, Mrk 42 presents nuclear Starburst activity.







galaxies: individual (Mrk 42) – galaxies: active – galaxies: ISM – infrared: galaxies
 






§ INTRODUCTION






Since the early studies by <cit.> and <cit.> – see also <cit.> – that showed that there are many spiral galaxies hosting circumnuclear star formation regions (CNSFRs), much progress has been done in our knowledge about how are these regions originated.
 Inflows of gas from hundred of parsec scales towards the center of galaxies are now commonly observed <cit.>. These inflows, besides possibly feeding the central supermassive black hole (SMBH) can also trigger (circum-)nuclear star formation, such as it has been observed in some active galaxies.  This relation between nuclear activity and star formation is commonly called as the Active Galactic Nuclei-Starburst  (AGN-Starburst) connection <cit.>. 

Studies on AGN-Starburst  connections are  of fundamental importance to explain the possible co-evolution of SMBH and its host galaxy, as the star formation in the central region leads to the growth of the bulge mass, while gas accreted by the SMBH leads to the its growth  <cit.>. 


In barred galaxies the material probably flows through the large scale bars to reach the circum-nuclear region <cit.>, where it can be accumulated and forming a gas reservoir favoring the star formation in circum-nuclear rings with radius of a few hundreds of parsecs <cit.>. Inflows of ionized and molecular gas within the inner kiloparsec of nearby active galaxies have also been observed in association to dust spirals using optical <cit.> and near-infrared <cit.> Integral Field Spectroscopy (IFS). 
Rings of circumnuclear star-formation regions (CNSFRs) are commonly observed in spiral galaxies, being associated to the inner and outer Lindblad resonances  and can be produced by bar or oval distortion perturbations <cit.>. Such rings are more frequently found in AGN hosts in comparison to normal galaxies or starbursts <cit.>. In addition, Low-Ionization Nuclear Emission-line Regions (LINERs) hosts show higher fractions of inner rings, while for Seyfert galaxies outer rings are more often observed, with ring fractions being several times larger than in normal galaxies <cit.>. Regarding the presence of bars, <cit.> found that  active and non-active galaxies show similar incidence of them, thus the distinct fraction of rings seems to be the only morphological difference between active and non-active galaxies.
   

Several recent studies were aimed in constraining the physical properties of CNSFRs in active and non-active galaxies <cit.>. 
 CNSFRs show star-formation rates of 10^-3–10^-1 M_⊙ yr^-1 and have ionized gas masses ranging from 10^4 to 10^5 M_⊙ <cit.>. 
The scenario that leads to the formation of CNFRs is still an open issue and the way the material settles in the circum-nuclear region may represent different processes for the star formation.  For example, <cit.> considers a distinction between CNSFRs and nuclear star formation regions: in the former, the material that arrives in the central region forms a circum-nuclear ring with ∼ 2 kpc radius, while in the latter the material settles in more internal regions (within a few hundred parsecs).
 Two main scenarios have been proposed for the origin of CNSFRs: the popcorn and pearls on a string scenarios <cit.>. In the first scenario, after an increase in the gas density due to accumulation of material in the ring, the stellar clusters are formed at random positions. In this scenario, there are no age sequence for the star clusters along the ring. In the second scenario, the gas flows to the central region along bars and is accumulated at two locations (at the tips of the bar), originating over-dense regions - ODR, in which the stars are formed. Due to the differential rotation of the bar and the disk of the galaxy, the star formation “moves" along the ring, leading to a sequence of ages for young stellar clusters. 

Until now, studies on star formation in CNSFRs seem to have not produced yet conclusive results about the star formation scenario. In fact, <cit.>, who used photometric  data of 22 CNSFRs, found that about half of the rings contain azimuthal age gradients, while <cit.> and <cit.>  did not found any sequence of age in CNSFRs located in three galaxies, using optical and near-IR IFS.

With the goal to improve the knowledge of star formation in CNSFRs, increasing the sample of objects, we have used near-IR IFS to study the circumnuclear star formation and nuclear activity in the nearby active galaxy Mrk 42. This object is classified as an SBa galaxy harboring a Narrow-Line Seyfert 1 nucleus <cit.>, being located at a redshift z=0.024634 <cit.>, 
corresponding to a distance of 102.6 Mpc by assuming a Hubble constant H_0=  72  km  s^-1  Mpc^-1. At this distance, 1^'' corresponds to 497 pc at the galaxy.
 It harbors a SMBH of mass (0.7-18)×10^6 as derived from scaling relations and  based on the X-ray excess variance <cit.>. 

<cit.> present an atlas of the central regions of 75 Seyfert galaxies imaged in the near-UV with the Hubble Space telescope (HST), including Mrk 42 in their sample. They found that Mrk 42 has a very bright compact nucleus with a ring of star formation ≈ 300 pc of radius, with many stellar clusters individually resolved. Indeed, the observed spiral arm seen in Mrk 42 is very coiled, being described by  <cit.> as  clear ring of star-formation surrounding the nucleus. The size of the ring of CNSFRs observed in Mrk 42 is similar to that derived for the rings in other galaxies, such as NGC 1068 and NGC 7469, resulting from a gas ring formed through bar-forcing at  the inner Lindblad resonance <cit.>.   
 A broad band HST image of Mrk 42 obtained with the Wide Field Planetary Camera 2 (WFPC2) through the filter F606W shows grand-design nuclear spiral arms, originating from a bar with an extent of 15^'' oriented along position angle PA=-20/160^∘, and  the CNSFRs ring is clearly observed <cit.>. The nuclear region of Mrk 42 presents strong 6.2 μm PAH emission as revealed by Spitzer mid-infrared spectroscopy, with a luminosity of 2×10^41 erg s^-1, providing strong evidence for intense ongoing star formation in the circumnuclear region <cit.>. 
 

We use J, H and K-band IFS of the inner 3^''×3^'' (1.5×1.5 kpc^2) of Mrk 42 to map, for the first time, its near-IR emission-line flux distributions and kinematics. This paper is organized as follows. In section <ref>, we describe the observations and data reduction procedures. In section <ref> we present maps for the fluxes, flux ratios, line-of-sight velocities and velocity dispersions of the molecular and ionized gas emission lines. These maps are discussed in section <ref> and our conclusions are presented in section <ref>.






















§ OBSERVATIONS AND DATA REDUCTION



The observations of Mrk 42 were done using the Gemini Near-infrared Integral Field Spectrograph <cit.> operating with the ALTAIR adaptive optics module on the Gemini North telescope in May 2014 under the programme GN-2014A-Q-28. The J, H and K-band observations were obtained following the standard Object-Sky-Object dithering sequence, with individual exposures of 520 sec each. We obtained eight on-source exposures for each band, and thus the total integration time is ∼ 1.2 hours per band. The NIFS has a square field of view of 3^''× 3^'', which was centred at the nucleus of the galaxy during the observations.


For the J-band, we used the filter J_G5603, resulting in a spectral range from 1.15μm to 1.35μm and a spectral resolution of ≈ 1.7Å, as obtained from the Full Width at Half Maximum (FWHM) of typical Ar calibration lamp lines. The H-band observations were centred at 1.65μm, covering a spectral range between 1.48μm and 1.80μm at a spectral resolution of ≈ 2.5Å using H_G5604 filter. 
In K-band the resulted spectral range is 2.01–2.42μm, centred at 2.20μm  and the observations were performed using the K_G5605 filter. The resulting spectral resolution for the K-band is ≈ 3.2Å, as obtained from FWHM of typical ArXe wavelength calibration lamp emission lines.

The data reduction followed the standard procedure of near-IR spectroscopic data treatment and was accomplished using tasks contained in the gemini.nifs IRAF[IRAF is distributed by National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation] package as well as generic IRAF tasks.  
The data reduction procedure included trimming of the images, flat-field correction, sky subtraction, wavelength calibration and s-distortion correction. The telluric absorptions were removed by dividing the spectra of the galaxy by the normalized spectrum of a telluric standard star of A spectral type, observed just before or after the observations of the galaxy. These standards have also been used to flux calibrate the spectra by interpolating a blackbody function to fit the spectrum of each standard star.
 
Finally, individual datacubes for each exposure were created with a spaxel size of 005×005, which were then combined to a single datacube for each band using the gemcombine task of the GEMINI IRAF package. The final datacube for each band contains about 3600 spectra and covers the inner 3^''× 3^'' of the galaxy. The angular resolution is about 012 for all bands, as obtained from the FWHM of the flux distribution of the telluric standard stars, corresponding to ≈60 pc at the galaxy. Similar FWHM values are obtained from the flux distributions of the ,  and O iλ1.129 μm  broad components.



In order to eliminate high frequency noise from the data, but with no loss in the image quality and preserving the flux, we used the IDL script bandpass_-filter.pro to apply a filter of order 3 and a cutoff frequency of 0.35 Ny on all bands. The filter was chosen by comparing the filtered and original continuum image, making sure that there was no removal of intrinsic emission from the galaxy.

 Similar procedures were already applied to NGC 4303 SINFONI datacubes by our group <cit.> and Butterworth filtering has extensively been used in the treatment of optical IFS of nearby galaxies <cit.>.





§ RESULTS


In the left panel of Figure <ref>, we present an optical image of the inner 40^''×40^'' of Mrk 42 obtained with the HST WFPC2 through the filter F606W <cit.>. The central cross marks the position of the nucleus indicated by `+' and the central square indicates the field of view (FOV) of the NIFS observations of 3^''×3^''. The nuclear grand-design spiral arms and bar are clearly seen in this image, as discussed in <cit.>. The right panel of this figure shows the continuum image of the nuclear region obtained from the NIFS data cube by averaging the fluxes between 2.26 and 2.28 μm, a region with no strong emission/absorption lines. Although the continuum is more elongated in the direction of the bar, the presence of the bar in the inner 3^''×3^'' region is not evident. In addition, the K-band continuum image does not show any enhancement at the locations where the CNSFRs were detected in UV continuum images <cit.>, which is an expected result, since young SP are enhanced in the UV spectral region while in the near-IR just a very small fraction of their light is detected <cit.>.

The locations of the CNSFRs are identified from the  Equivalent Width map shown in the bottom-left panel of Fig.<ref>.



In Fig. <ref> we show the J (left panel), H (center panel) and K-band (right panel) spectra for the nucleus and for the CNSFRs. These spectra were extracted within a circular aperture of 025 radius, centred at the nucleus and location of each CNSFR, identified as the locations of peak in the Equivalent Width (EqW) map for the  emission line, shown in the bottom-left panel of Fig. <ref>.  The nucleus is labeled as `N' and the CNSFRs from `A' to `H' in Fig. <ref>. The size of the aperture was chosen to include most of the emission form each CNSFR and for region `A', a larger aperture with 04 radius was used. The spectra show several emission lines, as , , ,  and , as well as absorption features, as the CO band heads at the K and H bands. These spectral features can be used to investigate the origin and kinematics of the emitting gas, as well as physical properties of the stellar populations.


We fitted the profiles of the strongest emission lines by Gaussian curves in order to map their flux distributions and the gas kinematics. The fitting was done using the PROFIT (line-PROfile FITting) routine <cit.>.  At most locations the emission line profiles of   , ,  and  are well reproduced by a single Gaussian function, but for the inner 045 radius the recombination lines were fitted with a narrow and a broad component, corresponding to an origin in the Narrow-Line Region (NLR) and Broad-Line Region (BLR), respectively. As the BLR is unresolved, the central wavelength and the width of the broad component were kept fixed at the values obtained by fitting the nuclear profiles shown in Fig. <ref>, while the amplitude of the Gaussian was allowed to vary. The line-of-sight velocity (V_ LOS) of the broad component is blueshifted by 190  relative to the systemic velocity of the galaxy (as derived in section <ref>) and its FWHM is 1480 , which is larger than the values reported for  of 670–865  by <cit.> and <cit.>. Examples of fits for the  and  profiles are shown in Fig. <ref> for the nuclear position (top) and for the position of the CNSFR labeled as `A' in Fig. <ref>. We used the resulting measurements for the emission-line fluxes, V_ LOS and velocity dispersion (σ) to construct the two-dimensional maps that are presented in the following sections. 












 §.§ Emission-line flux distributions and Equivalent Width maps










In the top panels of Fig. <ref> we present maps for the  (left),  (center) and  (right) emission line flux distributions. We do not show maps for  and  as they are very similar to those of  and , respectively, but noisier. The gray regions in the flux maps represent masked locations where the uncertainties in flux measurements are larger than 40% or due to the non detection of the emission line.  The blue circle overlaid to the  flux map delineates the region where two-gaussian components were fitted to the  line profile at the nuclear region. All maps clearly show the presence of the ring of CNSFRs with radius of 06 (∼ 300 pc), co-spatial with the ring seen in the UV HST image <cit.>, but some differences are seen among the maps. While strongest extra-nuclear  emission is observed for region `A' at the north-east of the nucleus, the  and  emission show stronger emission from regions located at the north-west of the nucleus. In addition,  show strong nuclear emission, while a weaker nuclear emission is observed in  and  is not detected at the nucleus of Mrk 42.  In Table <ref> we present flux measurements for the , , ,  and  emission lines for the nucleus and the CNSFRs integrated within a circular aperture of 025 radius, except for region `A', for which an aperture of 04 was used.



The bottom panels of Fig. <ref> show the Equivalent Width (EqW) maps for the  (left),  (center) and  (rigth), which can be used to better identify the CNSFRs, as the EqW measures the flux relative to the continuum emission and thus is 'a pure' line emission diagnostic. The white circles overlaid to the  map (that clearly delineates the CNSFRs ring) marks the locations of the CNSFRs labeled from `A' to `H', as well as the position of the nucleus (`N'). The size of the aperture was chosen to be larger than our spatial resolution bin and includes most of the line emission from the CNSFRs. The gray continuous line represents the orientation of the bar seen in the optical HST image, shown in Fig. <ref>.  The  and  show EqW values ranging from nearly zero to ∼ 5, while  shows higher values of up to 14. The highest values of  EqW  are seen for regions `A' and `B' to the north-east of the nucleus, while the other lines show the highest values both to the north-east and north-west of the nucleus. In addition, the smallest values of EqW for the  are seen at the nucleus, which may be due to an increase of the continuum emission due to hot dust, as suggested by the nuclear spectrum (see Fig. <ref>), which is redder than the extra-nuclear spectra. 

 It should be noticed that the EqW values observed for all emission lines are small and a possible explanation for this is that the continuum contains an important contribution from bulge stars, that dominates the near-IR continuum emission at the central region of galaxies. In order to evaluate the contribution of the stellar bulge continuum, we followed the methodology of <cit.> and performed aperture photometry on the continuum images  to measure the continuum emission at the locations of the CNSFRs and in the surrounding regions. We concluded that the bulge contributes with about 80, 85 and 90 % of the total flux in the K, H and J bands respectively. This translates to an increase in EqW values – after subtracting the contribution from the continuum – by a factor of 4 for  and  lines, a factor 6.7 for the  and a factor of 10 for the  and  lines. The EqW values of  and  emission lines can be even larger if stars formed in previous episodes of star
formation in the ring are present, but evaluating the contribution of these stars requires  high signal-to-noise spectra to allow a proper spectral synthesis and this is beyond the scope of this paper. 

 
 




 §.§ Emission-line ratios










The excitation mechanisms of the  and  emission lines can be investigated using the / and / line ratios, respectively <cit.>. We show maps of these line ratios for Mrk 42 in Fig. <ref>. The left panel shows the / ratio map, while the / map is shown in the middle panel.  Gray regions represent masked locations where the signal-to-noise ratio of one or both lines was not high enough to allow good fits. In addition, we do not show the values for the inner 045, for which no  emission is detected (see Fig. <ref>) and the  and  are marginally detected and thus the uncertainty in the / is high. In addition, the origin of the nuclear emission will be discussed in section <ref>.  



Both / and / flux ratio maps show values smaller than 0.6 at most locations, suggesting that the  and  lines are excited by the star-forming regions <cit.>. However, some differences are found between these maps. While / shows low values along the whole ring of CNSFRs, the / shows higher values (of up to 0.7) for the CNSFRs located to the north-west of the nucleus.

 In Table <ref> we present the / and / line ratio values for the CNSFRs of Mrk 42, obtained by measuring the fluxes of the emission line from the integrated spectra shown in Fig. <ref>, and identified in Fig. <ref>. Small values of / (<0.5) and / (<1.0) are observed for all CNSFRs.





The / flux ratio can be used to map the gas extinction. The reddening (E(B-V)) can be obtained by


    E(B-V)=4.74 log(5.86/F_ Paβ/F_ Brγ),


where F_ Paβ and F_ Brγ are the fluxes of Paβ and Brγ emission lines, respectively. We adopted the intrinsic ratio F_ Paβ/F_ Brγ=5.86 corresponding to case B recombination for an electron temperature T_e=10^4 K and electron density N_e=100  cm^-3 <cit.> and used the extinction 
law of <cit.>. The resulting E(B-V) map is shown in the right panel of Fig. <ref>, where values ranging from 0 to 1.2 are derived. The last column of Tab. <ref> shows the resulting E(B-V) for the nucleus and for each CNSFR.  The reddening derived for the CNSFRs of Mrk 42 are consistent with those obtained for star forming regions in other galaxies and H ii galaxies <cit.>. 














 §.§ Gas velocity fields and velocity dispersion maps



Gas velocity fields (top panels) and velocity dispersion (bottom panels) maps are shown in Fig. <ref>. Gray regions in the maps correspond to masked locations, using the same criteria as for the emission-line flux maps (see sect. <ref>). The velocity fields for   (top-left panel),  (top-center panel) and  (top-right panel) are presented after the subtraction of the systemic velocity of the galaxy (V_s = 7390 ), as derived by the modeling of the  velocity field by a rotating disk (see Sec. <ref>). At the inner 045, where the  profile was fitted by two Gaussian curves, we use the results for the narrow component. The velocity fields for all lines are similar and suggest gas rotation in the plane of the galaxy with the line of nodes oriented approximately along the north-south direction and a line-of-sight velocity (V_ LOS) amplitude of 150 .  Besides ordered rotation, in the inner 045 an additional velocity component is observed as indicated by the larger redshifts seen in  and  V_LOS maps, possibly due to outflows from the nucleus.
  

The bottom panels of Fig. <ref> show the velocity dispersion maps for the  (left panel),  (center panel) and  (right panel)  emitting gas. These maps were corrected for the instrumental broadening, as σ=√(σ_obs^2 - σ_ins^2), where σ_obs is the observed velocity dispersion and σ_ins is the instrumental velocity dispersion given by σ_inst= FWHM/2.355 with the FWHM measured from typical lines present on the wavelength calibration lamp (as presented in Sec. <ref>).  Small values of σ (< 50 ) are observed along the ring of CNSFRs for all emission lines, while higher values are seen within the inner 045 for the  emission with σ values of up to 200 . For illustration purpose,  the σ map for  shows only values smaller than 80 , which allows the comparison with the  and  σ maps.  The high σ values seen at the nuclear region for  support the interpretation that an outflow is present within the inner 05. 

Some higher σ values are also seen for the  at the nucleus, reaching values of up to 80 . 

In Table <ref> we present the velocity dispersion values obtained for each CNSFR by fitting the line profiles seen in the integrated spectra of Fig. <ref>, which suggest that the  profile is usually narrower than the  and  profiles. In Figure <ref> we over-plot the ,  and  line profiles from each CNSFR, which suggests that indeed the  and  profiles are broader than that of  for most regions, although it should be noticed that the  is only marginally resolved in our spectra.
















 




§ DISCUSSION





 §.§ Origin of the H_2 and [Fe ii] emission from the ring of CNSFRs




The [Fe ii]λ 1.25μm/Paβ line ratio can be used to investigate the excitation mechanism of the [Fe ii] emission. Some studies indicate that the [Fe ii] emission in active galaxies can be produced by shocks due to the interaction of radio jets with the interstellar medium <cit.>,  while other studies indicate that photo-ionization can produce most of the observed [Fe ii] emission <cit.>. A way to disentangle what are the main excitation mechanisms of the  emission is based on the use of [Fe ii]λ 1.25μm/Paβ flux ratio <cit.>. Typical values for Seyfert nuclei are 0.6<[FeII]1.2570μm/Paβ<2.0, while smaller values than 0.6 are observed for Starburst galaxies and H ii regions and values higher than 2.0 may be associated to shocks, e.g. due to radio jets or supernovae explosions <cit.>. As observed in the left panel of Fig. <ref>, the [FeII]1.2570μm/Paβ flux ratio map presents values smaller than 2.0 at all locations of the ring of CNSFRs, indicating that the origin of the  line emission is photo-ionization by young stars.


The origin of the H_2 emission in active galaxies has been addressed by several studies <cit.>. In summary, 
the H_2 lines can be originated by two mechanisms: (i) fluorescent
excitation through absorption of soft-UV photons, e.g. from H ii regions or AGNs <cit.> and (ii) collisional excitation due to heating of the gas 
by shocks <cit.> or by X-rays from the AGN  <cit.>. The H_2 λ 2.12μm/Brγ line ratio can be used to investigate the H_2 main excitation mechanism: values smaller than 0.6 are commonly observed in H ii regions and Starburst galaxies, where the H_2 lines are originated by fluorescence, while larger values are observed for AGNs and supernova remnants, where heating of the gas by X-rays and shocks may dominate <cit.>. For Mrk 42, the H_2 λ 2.12μm/Brγ  flux ratio map (middle panel of Fig. <ref>) show values smaller than 0.6 at all locations of the CNSFRs ring, indicating that the observed H_2 emission is produced by fluorescent excitation due to absorptions of UV photons emitted by young stars.



 §.§ A nuclear Starburst in Mrk 42


Using the flux values presented in Table <ref> for the nucleus of Mrk 42 we obtain very low  H_2 λ 2.12μm/Brγ and [Fe ii]λ 1.25μm/Paβ values. Both ratios show values smaller than ∼0.1, which are not consistent with those usually observed for Seyfert nuclei <cit.>. 


 By fitting the SDSS <cit.> spectrum of Mrk  42, we obtain [N ii]λ6583/Hα≈ 0.2 and [O iii]λ5007/Hβ≈3, which put the nucleus of Mrk 42 in the Starburst region of the BPT diagram <cit.>, consistent near-IR line ratios, although it should be noticed that the SDSS spectrum is obtained for an aperture of 3^'' diameter, which includes the CNSFRs ring. However, it is well know that this galaxy presents an type 1 AGN, as broad recombination lines are detected. The low-emission line ratios detected at optical and near-IR can be explained if, besides the central AGN, Mrk 42 presents also strong nuclear Starburst activity, which dominates the gas excitation. Similar nuclear Starbursts are seen in other galaxies with CNSFRs rings, as for NGC 4303 <cit.>.















  





































 §.§ Gas kinematics


The velocity fields presented in Fig. <ref> clearly show a rotation component. In order to obtain the kinematical and geometrical parameters, we have fitted the observed  velocities by a rotating disk model, assuming circular orbits in the plane of the galaxy, using the following equation <cit.>:


    V_r(R,Ψ) = V_s +  
    A R  cos(Ψ-Ψ_0) sin(i) cos^ pθ/R^2[ sin^2(Ψ-Ψ_0) +  cos^2(i) cos^2(Ψ-Ψ_0)] + c_0^2 cos^2(i)^ p/2,

where V_r  is the circular velocity and R and Ψ are the coordinates of each pixel in the plane of the sky, V_s is the systemic velocity, A is the amplitude of the rotation curve in the plane of the galaxy, Ψ_0 is the position angle of the line of nodes, c_0 is a concentration parameter, defined as the radius where the rotation curve reaches 70 % of the velocity amplitude, i is the disc inclination relative to the plane of the sky and p is a model fitting parameter. The parameter p measures the slope of the rotation curve where it flattens, in the outer region of the galaxy
and it is limited between 1 ≤ p ≤ 3/2. For p = 1 the rotation curve at large radii is asymptotically flat
while for p = 3/2 the system has a finite mass.

We fitted the  velocity field by the equation above using the MPFITFUN routine <cit.> to perform a non-linear least-squares fit, where initial guesses are given for each parameter and the routine returns their values for the best fitted model. The  velocity field was chosen because the  emission line presents the highest signal-to-noise ratio among the observed emission lines. During the fit, we excluded regions at r<045 from the nucleus, where an additional kinematic component is observed.  During the fit, the position of the kinematical center was kept fixed at the nucleus, defined as the location of the peak of the continuum emission.


The resulting kinematical model is shown in the middle panel of Fig. <ref>, while the observed  velocity field is shown in the left panel. Gray locations represent masked positions, where we were not able to obtain good velocity measurements (distances larger than 1 from the nucleus) and the nuclear region, where outflows from the central AGN seem to co-exist with a disk component. The residual map, obtained as the difference between the observed velocities and the model is presented in the right panel. The residual map presents values very close to zero at all locations (smaller than 10 ), showing that the velocity field is well represented by the model and thus, dominated by regular rotation. 


The resulting parameters for the best fit model are: i = 20.2^∘±2.0^∘, V_s = 7391±11 km s^-1, corrected to the heliocentric reference frame, A = 259±24 km s^-1, 
Ψ_0 =8^∘±1^∘, c_0 = 0.56 ± 0.05 arcsec and p = 1.5, which was limited between 1 and 1.5. The disk inclination is slightly larger than that of the large scale disk, obtained assuming i= acosb/a, where a and b are the semi-major and semi-minor axis of the galaxy and the value of the systemic velocity (V_s=7385 ) is in a good agreement with that of <cit.>. The orientation of the line of nodes is similar to that of the large scale disk, quoted in the Hyperleda database <cit.>. 


  





Within the inner  r<045 radius, the  emission line seems to present two narrow kinematic components: the blueshifted component is seen with velocity of V_ blue≈-300 , relative to the systemic velocity, while the redshifted component is seen with velocities very close to the nuclear velocity. The blueshifted component is only marginally detected and thus, we were not able to properly fit it. A possible interpretation of these two components is that the blueshifted one is originated from outflowing gas from the nucleus excited by the central AGN, while the redshifted one may be originated from the nuclear Starburst located at the disk of the galaxy. 




 §.§ Stellar populations and CNSFRs



We used the integrated emission-line fluxes of Table <ref> to calculate the following properties: the mass of ionized M_ H II gas; rate of ionizing photons Q[H^+]; the star formation rate (SFR) and the mass of hot molecular M_ H2.

The mass of ionized gas can be estimated by <cit.>
 

    (M_ H II/M_⊙) = 3 × 10^19(F_ Brγ/ erg cm^-2 s^-1) (D/ Mpc)^2(N_e/ cm^-3)^-1,

 where F_Brγ is the Brγ flux, D is the distance to the galaxy and N_e is the electron density, under the assumption of case B recombination at an electron temperature of  10^4K <cit.>. The mass of hot molecular gas can be estimated by <cit.>



    (M_ H_2/M_⊙) = 5.0776 × 10^13(F_ H_2λ 2.1218/ erg cm^-2 s^-1) (D/ Mpc)^2,

where F_H_ 2λ 2.1218 is the flux of the H_2 λ 2.1218 emission line and we assume local thermal equilibrium and an excitation temperature of 2000 K for the H_ 2.
 


The emission rate of ionizing photons is obtained following <cit.>:


    (Q [H^+]/ s^-1) = 7.47 × 10^13(L_ Brγ/ erg s^-1),

where L_ Brγ is the Brγ luminosity and the star formation rate is obtained by:


    (SFR/M_⊙ yr^-1) = 8.2 × 10^-40(L_ Brγ/ erg s^-1),

following <cit.>. The equations above for SFR and  Q[ H^+] are derived under the assumption of continuous star formation, and should be considered just proxies of these parameters.


In order to estimate the mass of ionized gas and the resulting physical properties of each CNSFR of Mrk 42 that are shown in Table <ref>, we have assumed the electron density value of N_e=300  cm^-3, which is the mean value of the electron density for a sample of CNSFRs derived from the [S ii]λ 6717/λ 6731 intensity ratio by <cit.> and <cit.>. 





The derived physical parameters for the CNSFRs of Mrk 42 can be compared with previously published values. <cit.> used optical IFS to study the CNSFRs of the Seyfert 2 galaxies NGC 1097 and NGC 6951 and found SFR in the range 0.002–0.14 M_⊙ yr^-1 for the eight star-forming regions studied. <cit.> used the observations from the Sloan Digital Sky Survey (SDSS) to study a sample of 385 objects classified as star-forming galaxies and found an average value for the SFR of 0.14 M_⊙ yr^-1. <cit.> used SINFONI data to study the star formation in the inner 700 pc of the active  spiral galaxy NGC 613 and obtained SFR∼ 10^-2-10^-1 M_⊙ yr^-1 for eight CNSFRs. <cit.> found SFR  of (0.4-2.0)× 10^-2 M_⊙ yr^-1 for the CNSFRs of NGC 4303 derived from SINFONI observations.  Thus, the values of SFR derived for the ring of Mrk 42 (0.07–0.2 M_⊙ yr^-1) are within the range of values observed for other galaxies with similar nuclear rings.


The emission rates of ionizing photons for the CNSFRs of Mrk 42 are in the range log(Q)=51.8-52.3 photons s^-1, in agreement with values already obtained for CNSFRs in other galaxies <cit.>. Such rates correspond to more than hundred O3 stars in each CNSFR <cit.>, but these values should be considered only as a proxy as a continuous star formation regime was assumed and the most probable scenario may be that of instantaneous star formation.

Finally, the masses of ionized and hot molecular gas observed for Mrk 42 are similar to that observed for other CNSFRs <cit.>. The average ratio between the ionized and hot molecular gas masses is <M_ H II/M_ H_2>∼ 3312, being similar to that observed for the CNSFRs of NGC 4303 <cit.>, and also in the range of of values obtained for the inner kiloparsec of nearby Seyfert galaxies, of  200–8000 <cit.>.

 The total mass of ionized gas in the ring (derived by measuring the fluxes of  and  from an integrated spectrum comprising distances between 045 and 13 from the nucleus is 1.9 times larger than the sum of M_ H II of all CNSFRs. The total mass of hot molecular gas in the ring is 2.8 times larger than that of the CNSFRs, indicating that a large amount of gas is observed outside the CNSFRs.        













 




We can also use the spectra shown in Fig. <ref> to better investigate the stellar content of the CNSFRs.  These spectra show strong absorption features at 1.17-1.20 μm, which may be molecular absorptions from stars in the thermally pulsing asymptotic giant branch (TP-AGB) phase, as suggested by simple stellar populations models <cit.> and detected in the nuclear spectra of nearby AGNs <cit.>. In addition, these features are clearly present in the spectra of stars in the TP-AGB phase <cit.>. By comparing the spectra of the CNSFRs `E', `F' and `G', with the stellar spectra shown by <cit.>, one can see that similar features are also seen in  the spectra of oxygen (e.g. from TiO and VO) and carbon (e.g. CN features) rich stars in the upper AGB phase. 
<cit.> also reported the detection of signatures of stellar
population dominated by the TP-AGB (as CN, TiO and ZrO absorptions) in near-IR spectra of H ii galaxies, which show a similar absorption features at ∼1.19 μm as seen in the CNSFRs of Mrk 42. However, stellar population synthesis performed for star-forming galaxies by  <cit.> do not find a clear correlation between the near-IR (e.g. CN) indexes and the presence of intermediate-age stellar populations, but this is attributed by these authors as due to observational limitations. Thus, the detection of these molecular features in the CNSFRs `E', `F' and `G' suggests that these regions are older than the other CNSFRs of Mrk 42 and already present some evolved stars. 








 §.§ How does the star formation proceed in the CNSFRs ring?
 


Gas inflows towards the central region of galaxies provide a gas reservoir, which can trigger (circum-)nuclear star formation and a central AGN.  
The way the material flows towards the central region may be through bars, spiral arms or interactions with neighbor galaxies. Inflows of gas associated to nuclear dust spirals and bars have been observed for nearby active galaxies at scales of a few hundred parsecs, mostly using optical and near-IR IFS <cit.>, but the presence of nuclear dust structures is not a sufficient condition to produce gas streaming <cit.>. 


Two possible scenarios have been proposed for the origin of the CNSFRs at scales of few hundred parsecs: the popcorn and pearls on a string scenarios <cit.> that show distinct distributions in age of the stellar clusters.   In the popcorn scenario, the gas is accumulated in the circumnuclear region resulting in a ring of higher density material, which allows a simultaneous star formation in the whole ring or in individual hotsposts, collapsing at different times within the ring. Thus, for this scenario there is no relation between the age of the recent formed stellar clusters and their locations within the ring.    

In the pearls on a string scenario, a short-lived, quasi-instantaneous burst of star formation is induced and located in a certain region of the ring. The locations of these  over-density regions (ODR, where the gas density is high enough to trigger the star formation) depends on details of the gravitational potential, but they are frequently found at locations where the gas reaches the central region, as for example, at the tips of bars. Stellar clusters are formed in these ODRs, which follow orbits within the ring, resulting in several stellar clusters  with a sequence of ages, and are called “pearls on a string". Thus, in this scenario, two segments of stellar clusters, on opposite sides of the ring, are expected in which the youngest clusters have their locations near the ODRs, becoming older when approaching the opposite ODR, i.e. there is a correlation between the stellar cluster age and the ring localization. 


In order to distinguish between the popcorn and pearls on a string scenarios for the origin of the ring of CNSFRs in Mrk 42, we constructed Fig. <ref> that shows the sequence of EqW values for  (open blue circles) and  (filled red circles) emission lines for the regions labeled from 'A' to `H'. The EqW values were measured from the integrated spectra of Fig. <ref> and are shown in Table <ref>. The EqW values of H recombination lines can be used to determine the age of the star formation regions, with higher values observed for younger regions and lower values for older regions, under the assumption that all regions are intrinsically equal in stellar mass and the mass in the burst is the same  <cit.>.

By comparing  EqW values observed for the CNSFRs of Mrk 42 with the predicted values by evolutionary photo-ionization models <cit.>, we conclude that all regions have ages between 5 and 6 Myr, considering the correction due to the contribution to the bulge stars to the underlying continuum in the derived EqW values, as discussed  in Sec. <ref>. The highest EqW values are observed for region `A', decreasing to a minimum value for region `D'. A second gradient is seen from region `F' to `H'. As the EqW of the H recombination lines can be associated with the age of the stars, these gradients can be interpreted as a signature of two age sequences, one from region `A' to `D' and another from region `F' to `H', favoring thus the pearls on a string scenario if the gas reaches the center along the major axis of the galaxy (close to the orientation of the bar - see Fig. <ref>). On the other hand, the spectra for the regions `E', `F' and `G' clearly show the presence of the molecular absorption bands at 1.17–1.20 μm. These absorptions (TiO, CN or VO) are originated in more evolved stars that are in the TP-AGB phase <cit.>, indicating that these regions are older than the remaining and suggests no clear sequence in age for these CNSFRs and thus not supporting the above sequence of ages for these CNSFRs.  








 §.§ Mass of the SMBH
 














The mass of the SMBH can be obtained directly from the  width and luminosity using the following equation <cit.>: 

    M_BH/M_⊙ = 10^7.04±0.02(L_ Paβ/10^42 erg s^-1)^0.48 ±0.03 ( FWHM_ Paβ/10^3 km s^-1)^2,

where L_ Paβ is the luminosity  and  FWHM_ Paβ corresponds to width of the broad Paβ  component. Assuming L_ Paβ=(9.0± 0.3)× 10^39 erg s^-1 and FWHM_ Paβ=1480±40 , measured from the  profile within a circular aperture of 025 radius,  we obtain M_ BH = 2.5^+0.7_-0.6×10^6 M_⊙.

The mass of the SMBH of Mrk 42 derived here is in good agreement with values obtained using scaling relations based on optical observations and  based on the X-ray excess variance, which are in the range (0.7-18)×10^6  M_⊙ <cit.>.


We notice that the width of the  broad emission line is larger by a factor of 1.7–2.2 than those quoted in the literature for the Hβ broad component <cit.>. However, it should be noted that the values of FWHM for Hβ available in the literature are based on more than 20 years old low resolution spectra. Using the Sloan Digital Sky Survey <cit.> spectrum of Mrk  42, we note that the broad Hβ component is just marginally detected, but its width is consistent with our measurement for . The Hα broad component of Mrk 42 is clearly detected in the SDSS spectrum and has a FWHM≈1400 , being similar to that derived for . 










§ CONCLUSIONS


We used J, H and K bands Gemini NIFS observations to map the flux distributions and kinematics in the near-IR emission lines of the inner 1.5×1.5 kpc^2 of Mrk 42 at a spatial resolution of 60 pc and velocity resolution of ∼40 . The main conclusions of this work are: 








  * The emission-line flux distributions and EqW maps clearly show the ring of CNSFRs, previously detected in HST image at ∼300 pc from the nucleus. 
We detected 8 CNSFRs (labeled from `A' to `H') in the ring and by comparing the observed EqW values of the Brγ emission line with those predicted by photo-ionization models, we conclude that their age is between 5 and 6 Myr. 
These regions present star formation rates in the range 0.06–0.21 M_⊙ yr^-1, ionizing photons rate of log(Q)=51.8-52.3 photons s^-1, masses of ionized gas in the range (6.5–22)×10^4 M_⊙ and masses of hot molecular gas between 18 and 43 M_⊙. These masses represent ≈ 53% and 36% of the total masses in the ring, respectively. 


  * In addition to a central AGN, line-intensity ratios indicate that Mrk 42 harbors a nuclear Starburst. 


  * The spectra of the regions `E', `F' and `G'  show molecular absorption bands at at 1.17-1.20 μm, possibly originated from evolved stars at the TP-AGB phase.


  * The near-IR emission lines of  and  from the star forming regions  have as main ionizing source young stars with 5–6 Myr of age. 


  * The gas velocities at locations beyond the inner 045 (∼ 220 pc) are dominated by rotation, being well reproduced by a disk model assuming circular orbits in the plane of the galaxy. At the nucleus, the gas kinematics suggests  two components: one due to the disk of the galaxy, with V_ LOS similar to the systemic velocity of the galaxy (7391±11 km s^-1) and another blueshifted by 300-500 , attributed to a nuclear outflow.




  * The EqW values of the  emission line suggest two age sequences, one from region `A' to `D' and another from region `F' to `G'. These age sequences favor the `pearls on a string' scenario for the origin of the CNSFRs in Mrk 42, although the presence of signatures of TP-AGB stars in some of the regions undermines this interpretation. 


  * The FWHM of the broad component of  emission line is ∼ 1480 , being larger than the values previously observed for Hβ. Using this value we obtain a mass of M_BH = 2.5^+0.7_-0.6×10^6 M_⊙ for the central supermassive black hole.














§ ACKNOWLEDGEMENTS

We thank the anonymous referee for valuable suggestions which helped to improve the paper.
This work is based on observations obtained at the Gemini Observatory, 
which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the 
NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology 
Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research 
Council (Australia), Ministério da Ciência e Tecnologia (Brazil) and south-eastCYT (Argentina). 
This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).
The authors acknowledge support from CNPq and  FAPERGS. 

O.L.D. is grateful to FAPESP (2016/04728-7) and CNPQ (306744/2014-7).






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