Thermal X-ray Emission in the Western Half of the LMC Superbubble 30 Dor C

While 30 Dor C is a unique superbubble in the Large Magellanic Cloud for its luminous non-thermal X-ray emission, the thermal X-ray emission it emanates has not yet been thoroughly investigated and well constrained. Based on the separate ~1 Ms deep XMM-Newton and Chandra observations, we report the discovery of the thermally-emitting plasma in some portions of the western half of 30 Dor C. The thermal emission can be reproduced by a collisional-ionization-equilibrium plasma model with an average electron temperature of ~0.4 keV. We find a significant overabundance of the intermediate-mass elements such as O, Ne, Mg, and Si, which may be indicative of a recent supernova explosion in 30 Dor C. Dynamical properties in combination with the information of the OB association LH 90 suggest that the internal post-main-sequence stars dominate the power of the superbubble and blow it out in the past ~1 Myr.


INTRODUCTION
Superbubbles (SBs) are large shell-like structures of 10 2 -10 3 pc in diameter, composed of low-density, hot (∼ 10 6 K) shock-heated gas (Mac Low & McCray 1988).In SBs, both stellar winds from massive stars in OB associations and supernovae (SNe) may jointly play crucial physical roles.Energetic stellar winds of massive stars and intense shock waves of SNe sweep up the surrounding interstellar medium (ISM) and ejecta, resulting in a thin, dense, cold shell.As a result of the low density (∼ 0.01 cm −3 ) inside these bubbles, the shock wave needs to travel a long distance before it significantly decelerates, so effective particle acceleration occurs on a longer timescale than for single/isolated supernova remnants (SNRs, Lopez et al. 2020).At the same time, due to the contribution of both massive stars' winds and SNe to the total SB energy, the SB stores more energy than a single SNR and thus becomes a possible origin of high-energy cosmic rays.However, detailed studies of Galactic SBs are complex as they require observations with a large field of view.The interference of foreground or background objects along the line of sight and strong interstellar extinction at the Galactic plane also affect observations in several wavebands, including optical, ultraviolet, and X-ray.
The Large Magellanic Cloud (LMC) is an ideal laboratory for the study of various astrophysical objects and their physical mechanisms, with favorable conditions such as close proximity (at a distance ∼ 50 kpc, Feast 1999), low inclination (∼ 35°, almost face-on, van der ★ E-mail: ygchen@nju.edu.cn† E-mail: pingzhou@nju.edu.cnMarel & Cioni 2001), and low foreground absorption (  < 0.3 mag, Bessell 1991).In addition, the LMC harbors a large number of SBs, SNRs, pulsar wind nebulae (PWNe), and various other high-energy astrophysical objects that can be resolved by modern observational instruments.
30 Doradus C (30 Dor C for short) is one of the noticeable SBs in the LMC, located to the south-west of the star formation region 30 Doradus (30 Dor).It was discovered by Le Marne (1968) through radio continuum observation.Mills et al. (1984) figured out a shelllike structure ∼ 3 ′ or ∼ 40 pc in radius in the 843 MHz band.After that, it was detected in the X-ray band by Einstein for the first time (Long 1981) and was detected as a shell structure by ROSAT (Dunne et al. 2001).In 2000, XMM-Newton's first light observation was aimed at it, through which Dennerl et al. (2001) found a complete ring-like structure with ∼ 6 ′ in diameter in soft and hard X-rays.
X-ray emissions are widely observed from shocked gas and central OB associations in SBs, such as RCW 38 (Wolk et al. 2002) and Westerlund 1 (Muno et al. 2006) inside our Galaxy, N 11 (Maddox et al. 2009), N 51D (Cooper et al. 2004), and 30 Dor C (Bamba et al. 2004;Smith & Wang 2004;Yamaguchi et al. 2009;Kavanagh et al. 2015) in the LMC, and IC 131 (Tüllmann et al. 2009) in M 33.Among the SBs in the Local Group, only 30 Dor C has a non-thermal X-ray shell along with the brightest non-thermal X-ray and TeV emission (H.E. S. S. Collaboration et al. 2015), which has made it an ideal laboratory to study the mechanism of non-thermal emission of SBs.Non-thermal emission is distributed throughout the SB and it is brighter in the western shell than in the eastern shell.However, the sign of thermal X-rays emerges among the predominant sea of non-thermal photons.By Chandra and XMM-Newton observations,

Chandra
We retrieved Chandra data on SB 30 Dor C for spatially resolved spectroscopic analysis taking advantage of Chandra's high angular resolution.As there are only 5 observations (ObsIDs 17904, 19925, 20339, 21949, 22006) with a total exposure less than 170 ks specifically proposed for 30 Dor C, we used the find_chandra_obsid command in the Chandra Interactive Analysis of Observations (CIAO, Fruscione et al. 2006, version 4.14 and CALDB version 4.9.7)software to search for other observations in which the Advanced CCD Imaging Spectrometer (ACIS) also covers the SB.We selected 31 observations (shown in Table 1) with individual exposure ≳ 10 ks and a total exposure time ≳ 1.1 Ms.All the data were reprocessed with chandra_repro script.
In addition, the reproject_obs and flux_obs tasks were used to produce images, exposure maps, and point-spread function (PSF)  17904,19925,20339,21949,22006) were used for point-like source analysis.We employed the wavdetect script to search the merged images in the soft (0.5-1.2 keV), medium (1.2-2.0 keV), hard (2.0-7.0 keV), and broad (0.5-7.0 keV) bands, respectively.For point-like sources, only the sources in or close (at an angular distance from the shell < 0.5 ′ ) to the SB were retained.Moreover, they must be detected in both the broad-band and at least one of the three sub-bands at the same time.Fig. 1(b) shows the broad-band image with point-like sources marked in cyan.

XMM-Newton
XMM-Newton provides us with a larger effective area, especially in low energy bands as well as a slightly higher spectral resolution than Chandra, which is especially beneficial to the spectral analysis.We obtained all the available XMM-Newton observations that fully cover SB 30 Dor C with each individual exposure > 20 ks.The total flare-filtered exposure of all 16 observations spanning over 20 yr, as shown in Table 2, amounts nearly to 1 Ms.We processed and analyzed the data by employing the XMM-Newton Science Analysis System (SAS, version 19.1.0 Gabriel et al. 2004) along with the XMM-Newton Extended Source Analysis Software (XMM-ESAS, version 0.11.2) for background modeling (Snowden et al. 2004).All  the data files were reprocessed with scripts emchain and epchain and then filtered with mos-filter and pn-filter to remove the time intervals significantly contaminated by soft proton flares.
Taking advantage of a large effective area, we also employed imaging information of the XMM-Newton observations to study the energy characteristics of the diffuse emission.The images were produced with the SAS task evselect and the exposure maps were calculated with script eexpmap.To subtract the background of the instruments, we used script evqpb to simulate it.Then we made mosaic images of MOS2 and pn with the ESAS script merge_comb_xmm.The outof-time events of the bright source SN 1987A were also subtracted in this step.If necessary, the mosaic images were smoothed with the ESAS task adapt_merge.
For spectral analysis, we used commands mos-spectra and pnspectra to extract the spectra of different regions and generate related response files, while commands mos_back and pn_back are employed to estimate the quiescent particle background (QPB), which will then be subtracted from the source spectra.All the spectra are combined in accordance with the instruments (i.e., MOS1, MOS2, and pn).The HEAsoft (version 6.29) scripts ftmarfrmf and ftaddrmf were used to correctly weight the response matrices according to the effective areas and exposure times.The combined spectra were then binned by the task grppha for signal-to-noise ratio greater than 7. Xspec (Arnaud 1996, version 12.12.0)with AtomDB (version 3.0.9)was used for spectral analysis.

Point-like sources
There are 17 point-like sources detected and analyzed in our study with Chandra observations as listed in Table 3, among which sources 3, 10-11, and 14-17 are newly detected, while others were listed previously in Kavanagh et al. (2019).Source 3 is projected just outside the northern shell of the MCSNR J0536-6913.Sources 4-6 are in the center, sources 10, 16, and 17 are located outside, and other sources seem projected basically along the shell-like structure of the SB.As shown in the RGB image (Fig. 1(a)), these sources have different "colors", indicative of different stellar surface temperatures or different  The coordinates are given by the centroid of the ellipse regions produced with the script wavdetect.
The energy band is 0.5-1.2keV.Only 5 observations directly aiming at 30 Dor C were used here for the sake of a good PSF and effective area.The error is weighted assuming the counts are subject to Poisson distribution. The hardness ratio is defined as HR=(H-S)/(H+S), where H and S are the net fluxes in 1.5-7.0keV and 0.5-1.5 keV, respectively. The unabsorbed luminosity is estimated by assuming the effective energy in 1.5-7.0keV and 0.5-1.5 keV is 3.5 keV and 1.1 keV, respectively, with the LMC absorption  H ∼ 7 × 10 21 cm −2 .The distances to the sources are approximated as 50 kpc, the distance to the LMC; but for remote background AGNs, the distances are undoubtedly severely underestimated here.radiation mechanisms.Limited by the low count rates, we calculated their hardness ratio and roughly estimated their absorption-corrected luminosities.We also searched the SIMBAD astronomical database (Wenger et al. 2000) for potential optical counterparts within 1.5 ′′ , or 0.36 pc (at a distance 50 kpc), and gave their possible physical properties in Table 4.
All of the three point-like sources located in the center of 30 Dor C, sources 4, 5, and 6, correspond to post-main-sequence bluish stars (e.g.blue super giants and Wolf-Rayet (WR) stars) seen in the optical band and have the softest spectra among the sources.The fast stellar winds of the bluish stars can produce shocks to emit the X-ray emission.Noticeably, we found that source 6 seems to have a diffuse structure extending several arcseconds as shown in Fig. 2, exceeding the size of the PSF.Thus, source 6 is probably not a single point-like source but a group of sources jammed in a small space that cannot be resolved clearly.Actually, BAT99 80, the potential optical counterpart of source 6, is not only a binary candidate itself but also a member of the compact sub-association HD 269828 with nearly 20 massive stars including 3 WR stars within 10 ′′ (Testor et al. 1993).Unfortunately, the limit of angular resolution of the X-ray detectors and the low count rates make further spectral analysis difficult.Sources 12, 13, and 14 are the other three sources with potential optical counterparts within 1.5 ′′ .Source 12 was considered as the WR star Brey 58 (Bamba et al. 2004;Lopez et al. 2020).Here we come up with an alternative possibility that this source may be associated with one of the two other stars, the long-time variable OGLE LMC-LPV-72734 and the WR star Brey 58a, for smaller projected angular distances (1.03 ′′ and 1.17 ′′ , respectively, according to SIM-BAD (Wenger et al. 2000)) than Brey 58 (2.79 ′′ ).Like source 6, the emission of source 12 may also arise from stars and their interaction in a compact sub-association containing several post-main-sequence massive stars (Testor et al. 1993).Also, Fig. 2 shows that source 12 probably consists of more than one point-like source.Source 13 has a quite hard spectrum with little counts below 1.5 keV, suggesting it being fiercely absorbed, so we hold the same opinion as Bamba et al. ( 2004) and Lopez et al. (2020) that it is an AGN rather than an O-type star.Source 14 has never been detected and studied in previous studies and its relatively soft emission may be indicative of the X-ray counterpart of the WR star Brey 56.Among the point-like sources associated with bluish stars, sources 12 and 14 have significantly harder spectra than sources 4, 5, and 6 located in the SB center as indicated by the hardness ratios.The spectral difference in the foreground absorption (see Section 3.2.2),their environment due to distance to the bubble center (see Section 4.2), and radiation mechanisms (e.g.Zhekov & Palla 2007) may lead to this phenomenon.
Among the sources without optical counterparts, source 2 and source 9 are relatively soft in spectra, which may be indicative of low absorption or low temperature.It is not clear whether they are independent sources or knot structures on the shell of 30 Dor C. On the contrary, sources 1, 3, 7, 8, 10, 11, and 15-17 have hard spectra.Thus, we suppose that they are likely to be background AGNs.Stellar remnant is another possibility and Kavanagh et al. (2015) and Lopez et al. (2020) raised this notion when discussing the identity of source 1 and source 3.

Spatial distribution of hardness ratio
Fig. 1(a) shows differences in photon energies between the western and the eastern parts of SB 30 Dor C. To outline this difference, we constructed a "hardness ratio map" (Fig. 3) to map the flux ratio between the hard (2.0-5.0 keV) and soft (0.4-1.5 keV) bands (note the difference of the definition of the hardness ratio here for the diffuse emission from that for the point-like sources given in the caption of Table 3).Assuming the thermal emission to be dominant below 1.5 keV while the non-thermal emission is dominant above 2.0 keV (also see the spectra in Appendix A), the hardness ratio can reflect the relative intensity of the non-thermal emission to the thermal one.To guarantee the significance of the signals, we applied Weighted Voronoi Tessellation (Cappellari & Copin 2003;Diehl & Statler 2006), an adaptive binning method, to ensure an average signal-to-noise ratio of 10 per bin.The X-ray emission in the southeast of 30 Dor C is significantly softer than that in the west, where the hardness ratio gets lowest at the shell of the MCSNR J0536-6913.The emission is quite hard in the west and the hardness ratio looks uniform compared to the surface brightness among different structures.The high hardness ratio and its uniform distribution in the west indicate that the soft thermal emission is either intrinsically very weak or heavily absorbed by the foreground intervening gas.The latter possibility seems favored by the presence of molecular clouds (MCs) mostly in the west of the SB (Sano et al. 2017).Sasaki et al. (2022) claimed to discover a ∼ 0.6 keV thermal emission in 30 Dor C West with eROSITA data, and Lopez et al. (2020) reported detection of a ∼ 0.8 keV plasma in the south-western part of the bubble shell.However, both results are arguable for the lack of a local background taken into consideration so that the foreground and/or background emission may not be correctly subtracted.In fact, studies with more detailed spectral analysis based on the XMM-Newton data (e.g.Kavanagh et al. 2015;Babazaki et al. 2018) had never detected thermal emission in 30 Dor C West.With archival XMM-Newton data of long accumulation over up to 20 years, it is reasonable to review the spatially resolved spectroscopy with a higher signal-to-noise ratio to search for signatures of thermal emission and to constrain the physical parameters.

Spectroscopy
The selection of regions for spectral analysis is mainly based on the morphology of SB 30 Dor C, involving structures with high count rates to display line features in each spectrum in spite of domination by the non-thermal continuum.The regions we selected (as labeled in Fig. 4), similar to those in Kavanagh et al. (2015), are described in detail as follows.The south-western segment of the bubble shell is selected and denoted as region SW.For the north-western part of the shell, the bright segment is denoted as NW1, and a fainter segment to the south-west of NW1 is denoted as NW2.Kavanagh et al. (2015) noticed diffuse emission in the interior of the SB but failed to detect thermal signals.Here we divided it into three parts.
The diffuse structure just inside the western shell is labeled as region W, which is to the west of two bright point-like sources 12 and 13.On the other side of the two point-like sources, diffuse emission looks like an incomplete elliptical ring (CS+CN).
It is noticeable that the diffuse X-ray background of the SB differs between the eastern and the western regions (Fig. 3; also see Kavanagh et al. 2015), and the bright X-ray source SN 1987A is located to the south-west of the SB.Thus, we selected a region to the north-west of the SB as the background (see Fig. 4), similar to the selection in the previous studies (Kavanagh et al. 2015;Babazaki et al. 2018), for our spectral analysis of the western region.As shown in Fig. 3, the diffuse background in almost the whole western half of 30 Dor C shares a similar hardness ratio.It may thus be reasonable to assume that the true background has little spatial fluctuation and our selection of the background is feasible in this sense.
To avoid the influence of bright point-like sources, we excluded them before we selected the spectra-extracting regions.The influence of the PSF of SN 1987A and the stray light from LMC X-1 is weak enough to be neglected in our study.We analyzed the spectral data in 0.4-7.0keV for MOS and 0.5-7.0keV for pn to avoid the EPIC tail in soft energies and the line forest of pn above 7.0 keV.
We combined all of the available XMM-Newton spectra in terms of different instruments (i.e., pn, MOS1, and MOS2), instead of fitting them jointly.This helps intuitively outline the weak line features from 0.8 to 1.5 keV above the continuum, corresponding to the lines of O, Ne, and Mg (see the spectra treated in Appendix A).As the instrument background varies significantly in different positions of the XMM-Newton detector (Lumb et al. 2002;Kuntz & Snowden 2008), we used the QPB spectra and added extra Gaussian components representing Al (1.49 keV, for EMOS and EPN) and Si lines (1.75 keV for EMOS) to model the instrumental background.The astrophysical background is modeled, but not simply subtracted, to guarantee high signal-to-noise ratios in the soft band of the source spectra where thermal emission matters.For abundance, we applied the table of solar abundance according to Anders & Grevesse (1989) and assumed 0.5 solar abundance for the LMC (Russell & Dopita 1992).
The astrophysical background was characterized with a typical model comprising such components (Snowden et al. 2008;Kuntz & Snowden 2008) as the local hot bubble (represented by an apec model without absorption), the Galactic halo (represented by an apec model with an absorbing column  H = 6 × 10 20 cm −2 according to the Dickey & Lockman (1990) HI maps), and the ISM of the LMC plus the unresolved background AGNs (modeled by an vapec component plus a powerlaw component with a photon index Γ = 1.46 (Chen et al. 1997) and an absorption attributed to the Milky Way and the LMC).We grouped the spectra to achieve a signal-to-noise ratio ≥ 5 per bin.Since the background spectra show line features near 1.0 keV and 1.3 keV, we set the abundances of Ne and Mg free and added a Gaussian component near 0.9 keV as a mimic and finally the reduced chi-squared of the fitting is 1.21.This model was simply fixed and weighted according to the backscale, or rather the region's angular size, as a part of the model when fitting on-source spectra.
For the on-source spectrum of each selected region, two fitting models with different components are tested for the source spectra: a single powerlaw component or a powerlaw component plus a vapec thermal component with variable abundances, both with the absorption of the Milky Way and the LMC.A plasma component in a non-equilibrium ionization state has also been tested, but the fitted ionization parameter  =    exceeding 10 12 s cm −3 indicates a plasma component in a status of collision-ionization equilibrium (CIE).As SB 30 Dor C probably may have witnessed SN explosions Regions we selected for spectral analysis.The RGB image is an XMM-Newton pn and MOS2 mosaic in 0.4-1.2keV (red), 1.2-2.0keV (green), and 2.0-5.0 keV (blue).This image reflects the difference in the emission between the west and east as shown by Kavanagh et al. (2015).As all of the selected regions are located in the 30 Dor C west, we extracted a large area to the north-west of 30 Dor C as the background.
inside, we free the abundances of intermediate-mass elements including O, Ne, Mg, and Si.If a change of an abundance can reduce the chi-square statistics evidently, we keep its value and calculate the error range.Otherwise, the abundance is fixed to that of LMC.Since the added thermal components are very weak compared with the non-thermal components, we used the F-test to assess the difference between the two models, or in other words, the significance of the thermal components.Thus, we list the P-values or rather the possibility of a null hypothesis along with the chi-squared statistics and the degrees of freedom.In this way, we suppose that all the regions we select show evidence of thermal emission more or less.
The fitted spectra of the selected regions are presented in Appendix A and the spectral fitting results are listed in Table 5.In general, the significance of the thermal emission based on the P-value is anticorrelated with the foreground absorption and the intensity of the non-thermal component.
Spectral fittings for regions NW1 and NW2 located in the northwestern segment of the outer shell of 30 Dor C give the highest Pvalue (> 0.01) among all of the six regions.This low significance of the thermal emission is not unexpected as NW1 has the highest surface brightness and the foreground absorption in NW2 is the strongest.We let the abundances of Mg and Ne be free parameters, respectively, which indeed improves the fitting but the values cannot be well constrained.Both regions have higher gas temperatures than others; but since the significance of the thermal component is relatively low, we supposed that this arises from the degeneracy of the parameters.For these two regions, even if the properties of plasma could not be sufficiently reasonable, the emission lines of Mg and Ne are undoubtedly a signature of thermal emission.
Region W is located near the western edge of SB 30 Dor C, where the outer shell appears broken.In the hardness-ratio map (Fig. 3), this region shows the hardest emission along with region NW2.The high hardness of these two regions is consistent with the strongest foreground absorption with a column density of the highest order

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The upper and lower limits correspond to the 90% confidence intervals of the fit parameters.The solar abundance is based on Anders & Grevesse (1989). The model is phabs with LMC abundance. Unabsorbed flux at 1 keV in unit of counts keV −1 cm −2 s −1 .
, where D is the distance to LMC in this study, and   and   are the density of electron and proton, respectively. Probability of a null hypothesis given by F-test. These parameters improve fitting but cannot be well-constraint.
∼ 10 22 cm −2 among the selected regions.According to our fitting, a residual appears below 1 keV for a single power-law model, and the addition of a thermal ( < 0.1 keV) component may improve this with a P-value of ∼ 10 −3 .This result could reflect a scenario where a shock hits a cold dense cloud.
Different from NW1 and NW2, the south-western segment of the outer shell SW shows a relatively significant thermal emission (P-value ∼ 10 −7 ) with probable enrichments of intermediate-mass elements.The low absorption (∼ 5 × 10 21 cm −2 ) allows a spectrum with evident line features.The temperature here is relatively low compared to those in other regions, which will be discussed in detail in Section 4.2.Although this region is close to the bright source SN 1987A, we exclude the possibility of contamination from the filamentary pattern due to the PSF of the instrument.It is mainly because the ejecta of SN 1987A has not been shocked yet (Sun et al. 2021) and thus the metal enhancement can only account for the bubble itself.
CS and CN compose an elliptical structure in 30 Dor C West.We divided it into these two regions mainly based on the curvity of the structure and the count rate.The latter distinction can be well explained by the absorbing hydrogen column densities, where the CN emission is more heavily absorbed than the CS.With a weaker nonthermal emission, thermal signals are relatively strong here compared to those at the outer shell in the same position angle, i.e.NW1.With a much lighter foreground absorption, the P-value of CS is much lower than that of any other region we selected, and the high abundances compensate the residuals below 2 keV for the single power-law model.Although we cannot exclude the degeneracy between the normalization and the abundances, this result undoubtedly reflects line features from thermal emission.Despite different absorptions, these two regions share similar electron temperatures of 0.4-0.5 keV with elevated metal abundances.
Overall, we reveal signatures of thermal components and potential metal overabundance in the south-western regions (CS+SW) of SB 30 Dor C, where the foreground absorption is relatively low.The plasma is in a CIE state and cooler than that reported by Lopez et al. (2020) and Sasaki et al. (2022).The temperature and abundance are similar to that in the eastern half of the SB (Kavanagh et al. 2015).

Net flux maps
The spectral analysis above shows signatures of thermal emission in 30 Dor C West with enriched abundances of intermediate-mass elements (including O, Ne, Mg, and Si), which is consistent with the scenario that SB is filled with hot plasma shocked by stellar winds and SNRs and these metals gradually accumulate in the processes of stellar feedback.However, the emission is somewhere even weaker than the astrophysical background.To verify this result, we generated the narrow-band net flux map to show the spatial distribution of line emissions.With the available data, we focused on the O viii (∼0.6 keV), Ne ix (∼0.9 keV), Ne x(∼1.0 keV), and Mg xi (∼1.3 keV) lines.All of them are evident emission lines of the thermal component, as represented by the cyan dashed lines in the spectra shown in Appendix A. The Si xiii line is not used due to the severe contamination of the instrumental line of MOS near 1.75 keV.
As SB 30 Dor C is dominated by non-thermal emission, to exhibit the thermal signals, we apply linear interpolation to subtract the underlying continuum.For the emission lines, we selected the energy intervals according to Townsley et al. (2006), while for the  continua, we selected the energy intervals on both sides whose linear interpolation is adopted for the underlying continuum.The two-side continua of Ne ix and Ne x lines were selected far from the line center to avoid the Fe-L forest near 0.9 keV, and we only chose the low-energy shoulder of the Mg xi lines for extrapolation to eliminate the influence of the bright Al instrumental line near 1.5 keV.The energy intervals of the selected bands are listed in Table 6.To eliminate the contamination of the QPB noise, we modeled it through the FWC data and subtracted it from each narrow-band image.After the vignetting correction, each net flux map was rebinned to a pixel size of 2.5 ′′ × 2.5 ′′ and smoothed with a radius of 8 pixels in a tophat convolution method, which is comparable to the size of half-energywidth of XMM-Newton.The QPB and continuum subtracted net flux maps are shown in Fig. 5. Equivalent width (EW) maps, another tool widely used to assess the strength of the line emission through the ratio of the net flux to the underlying continuum in the integration of line width, are not produced in our work as the non-thermal emission dominates the continuum.In such a condition, the true equivalent width, or rather the emissivity, of emission lines would be significantly underestimated.Also, an EW map, as a ratio map, requires a higher signal-to-noise ratio than a simple net counts map, which makes it difficult to map the weak thermal emission in 30 Dor C. In  (10 −2 cm −3 )

Properties of thermal emission
Thermal emission is one of the keys to the physical nature of an SB, whose gas temperature and density reflect the evolution while the metal abundances can reveal the history of interior SN explosion.Different from temperature, the density cannot be directly measured by X-ray spectroscopy.Here, we assumed all the regions are oblate ellipsoids and roughly estimated the gas densities from the volume emission measures (VEMs) of the thermal components, which are listed in Table 7.
Generally, the density of thermal X-ray eminating gas in 30 Dor C West is ∼0.01-0.1 cm −2 , much more tenuous than typical ISM of ∼1 cm −3 , although the derived densities are of great uncertainty.This indicates stellar winds and SN shocks have swept away most mass in the SB.The uncertainty may come from some factors, such as limited counts, simplistic assumptions for the gas volume, and degeneracy among the parameters.For regions NW1, NW2, and W, we suggest that the gas temperature may degenerate with the VEM where the significance of the thermal component is relatively low in Section 3.2.2.Meanwhile, as the thermal signal is much weaker than the non-thermal component, we detect them from the residual of spectral fitting with a single power-law model, which is more sensitive to line features than the continuum from the bremsstrahlung.Thus there may be degeneracy between VEM and metal abundances.For instance, region CS shows a much more significant enhancement of intermediate-mass element abundances but its density is lower compared to that in region SW.Even so, the order of magnitude of the density is still worth a reference.
Metals in an SB contain information on previous interior SNe, as they mainly originate from the ejecta of SNe rather than the stellar winds (e.g.Sukhbold et al. 2016).However, it is currently difficult to make deep analysis.Firstly, the metal abundances are not constrained quite well and probably degenerate with the density as mentioned above.Secondarily, a considerable portion of the metals may be swept up into the cool dense shell of 30 Dor C and the Xrays cannot trace them (Weaver et al. 1977).Thus, the total mass of metals may be seriously underestimated.Moreover, the accurate number of SNe inside the bubble is not clear yet, making it difficult to deduce the progenitors.Nevertheless, the metal enhancement in regions SW and CS is exactly the feature of recent SN(e) in 30 Dor C. Noticeably, this is consistent with the case of some regions in the eastern half of 30 Dor C, for which Kavanagh et al. (2015) suggest that a recent SN may have exploded near the eastern shell, accounting for the metal enrichment and radio index.The coincidence of the metal abundances, including a higher abundance of Ne and Mg than O, probably suggests that the metals uncovered in different regions share the same origin.This is reasonable as the ejecta are hardly decelerated in a low-density space until they collide with the bubble shell.The OB subclusters and massive stars are mainly distributed in the western half of 30 Dor C (Testor et al. 1993;Yamane et al. 2021), where a recent SN explosion was more likely to have exploded.Also, the stellar winds from these stars may give rise to a flat radio spectrum in the west.As to the progenitors, as the age of the OB association is not more than 8 Myr (Testor et al. 1993), we suggest that the mass of the progenitor is ≳ 20  ⊙ , as for stars with lower mass, the main sequence stage is longer than the age of 30 Dor C (Tout et al. 1996;Chen et al. 2013).Meanwhile, Testor et al. (1993) pointed out that several stars in OB association LH 90 are ∼ 40  ⊙ in mass, indicative of possibly an even higher mass of the supernova progenitor.

A stellar-wind-dominant superbubble?
The thermal emission of SB 30 Dor C has been studied many times in the past two decades and the results differ in different studies.Without local X-ray background taken into account, Lopez et al. (2020) reported a relatively hot plasma (∼0.9 keV) in the south-west shell of 30 Dor C, and Sasaki et al. (2022) reported a ∼ 0.6 keV thermal component in the west of the bubble using the eROSITA data.Before that, no significant signal of thermal emission in the western part was detected (Bamba et al. 2004;Yamaguchi et al. 2009;Kavanagh et al. 2015;Babazaki et al. 2018).In our spatially resolved spectral analysis for the 30 Dor C West, most of the selected X-ray bright regions with a high significance of thermal emission have a gas temperature ∼ 0.4 keV or cooler, similar to that of the plasma in the east of 30 Dor C (Kavanagh et al. 2015).We here incorporate this temperature estimate and the stellar information of the OB association LH 90 to discuss the dynamical properties of the SB, and show that 30 Dor C is mainly powered by stellar winds from the internal post-main-sequence stars as well as a recent SN explosion.
We mainly apply the model given by McCray & Kafatos (1987) based on an adiabatic similarity solution (Weaver et al. 1977) to calculate the evolution of the SB.Adopting the radius of SB 30 Dor C  = 50 pc and applying the expansion velocity  ∼ 30 km s −1 inferred from the studies of the ambient molecular gas (Sano et al. 2017;Yamane et al. 2021), the age of the bubble is: where  50 and  30 are the bubble radius and expansion velocity in units of 50 pc and 30 km s −1 , respectively.Noticeably, this value is lower than the estimates of 4 Myr in the previous studies (e.g.Smith & Wang 2004) based on the age of the association (Testor et al. 1993), but is coincidentally similar to the lifespan of the WR stage, about ∼ 7 × 10 5 yr (Leitherer et al. 1997), which would probably be longer in the LMC with lower metal abundance.This probably indicates that strong stellar winds from WR stars and SN explosions may be the major energy sources of 30 Dor C, and we will show that the mechanical luminosity of stellar winds is dominated by WR stars below.Also, this timescale allows us to suppose that the power from stellar winds can be considered constant as post-main-sequence stars we now observe just left the main-sequence stage when the bubble formed.Testor et al. (1993) listed 8 WR stars and 25 O stars in the OB association LH 90 which outputs mechanical energy to the SB.The mechanical luminosity of the stellar wind from a single star is estimated from the mass loss rate and the terminal velocity of the wind.For the main sequence stars, we estimate the total power of 25 O stars at ∼ 5 × 10 37 erg s −1 (Puls et al. 1996;Kudritzki & Puls 2000, see Appendix B for details) but ignore that of B stars for they have much weaker wind and are not bright enough to be detected in the LMC.For the WR stars, we applied the mass loss rates of WN stars according to Hainich et al. (2014), while those of WC stars are estimated of  ∼ 10 −5 M ⊙ yr −1 .The terminal velocities of winds from WR stars are adopted from Niedzielski & Skorzynski (2002) and listed along with and the mass loss rates in Table 8.Thus we calculate the total mechanical luminosity of stellar winds   ∼ 1.6 × 10 38 erg s −1 , of which WR stars contribute ∼ 1.1 × 10 38 erg s −1 .
Although McCray & Kafatos (1987) supposed SNe would dominate the evolution of SBs after several explosions and thereafter the contribution of stellar winds is negligible, in the very early stage stellar winds are probably the main energy source.The power of stellar winds can be regarded as a minimum of the total mechanical luminosity since the overabundant intermediate-mass elements as we found in 30 Dor C should be enriched by the SN explosions in the interior of the SB.Here, with the age of the bubble and the mechanical luminosity of the stellar winds, the total energy input from the winds is: SB = (4.9× 10 51 erg) 50  −1 30 . (2) This indicates that the energy from stellar winds is commensurate with explosions of ∼5 canonical SNe.If the efficiency of transforming such energy to cosmic rays is comparable to that of SNRs (∼10%), it could satisfy the energy requirement of ∼ 5 × 10 50 erg to produce the TeV emission in 30 Dor C in a hadronic scenario (H.E. S. S. Collaboration et al. 2015).
For SNe, as their accurate number and explosion energy are still unknown to estimate the energy input, we introduce factor  as the ratio of the power from SNe to that from stellar winds, i.e., the total mechanical luminosity  = (1 + )   . is greater than 0, and later we will constrain factor  with observations.
The radius of an SB can be given by the mechanical luminosity and ambient density (McCray & Kafatos 1987): where  38 = /(10 38 erg s −1 ),  6 =  SB /(10 6 yr), and  0 is the density of the ambient ISM in units of cm −3 .For 30 Dor C, adopting the radius ∼50 pc and the age 9.8 × 10 5 yr calculated above, we can get the relation between the ambient gas density and the factor A: To verify the result above, we calculate and compare the mass of the bubble shell in two different ways.As pointed out by McCray & Kafatos (1987), 1/5 of total energy becomes kinetic energy of the shell, from which the mass of the shell can be estimated: On the other hand, the mass interior to the SB is chiefly comprised of the ambient material swept up into the shell by the shock driven by stellar winds and/or SNe.This mass would then be where   is the mass of a proton.The latter estimation is modelindependent, and the two estimates of mass are consistent quite well with one another.
Based on the age and mechanical luminosity of 30 Dor C calculated above, we then estimate the radial profile of temperature and density in the bubble based on Mac Low & McCray (1988): and where  = / is the dimensionless distance to the center of the SB.As the densities depend on the assumption of region shapes, they have much more uncertainties than temperatures which can be directly measured.Here we applied the gas temperatures of regions CN and CS, where thermal emission is the most significant and parameters are constrained relatively well.
We also adopted the study of Kavanagh et al. (2015) to expand the region sample.Regions B1 and I1 therein are supposed to have thermal emission as well.We here roughly supposed the projected distance from these regions to the bubble center as the approximate distance and plot the radial profile of temperature in Fig. 6.This plot excludes scenarios where the power of SNe is equal or superior to that from stellar winds (i.e.,  ≥ 1).On the other hand, the metal enhancement according to spectroscopy indicates the contribution of SNe.Thus, we suggest the energy source of 30 Dor C is dominated by stellar winds and at least one SN exploded recently.For instance,  = 0.2 corresponding to one conical SN fits the temperature radial profile quite well.Thus, the total mechanical luminosity  = (1 + )  would amount to 2 × 10 38 erg s −1 .

Particle acceleration in 30 Dor C
Superbubbles are candidates of powerful cosmic-ray accelerators, where turbulence, multiple shocks, and shock-wind interactions could accelerate particles effectively despite a high sound velocity inside (Bykov & Fleishman 1992;Parizot et al. 2004;Vink 2020;Vieu et al. 2022a).30 Dor C is a unique SB in the LMC for its luminous non-thermal X-ray emission up to 20 keV (Lopez et al. 2020).Also, it is the first SB detected in TeV band (H.E. S. S. Collaboration et al. 2015).These all suggest particle acceleration inside it.However, either non-thermal X-ray emissions or TeV -ray emissions have never been accurately robustly detected in other superbubbles in the LMC including N 11 (Maddox et al. 2009), N 51D (Cooper et al. 2004), N 158 (Sasaki et al. 2011), andN 206 (Kavanagh et al. 2012), and thus one must consider the origin of particle acceleration of 30 Dor C or what makes it stands out.
We suggest that the high energy input from stellar winds and exploded SNe probably account for a higher acceleration effect, which is dominated by WRs and supergiants.Compared to other SBs in the LMC as mentioned above, the number of WR stars in 30 Dor C, which dominate the power of stellar winds, is larger than that in any other bubble in the LMC except the famous star-forming region 30 Dor (Hung et al. 2021).The stellar winds can constantly inject energy into the bubble within ∼1 Myr, much longer than the average interval between two supernova explosions in an SB ∼ 3 × 10 5 yr (Mac Low & McCray 1988).Assuming the particle acceleration efficiency is ∼10%, which is typical for an SNR, the total power to accelerate particles is ∼ 2 × 10 37 erg s −1 injected by stellar winds along with an extra SN inside (see details in the subsection above).This coincides with the required energy injection of ∼ 2 × 10 37 erg s −1 in a time-dependent model to emit the TeV -ray emissions in a leptonic scenario (H.E. S. S. Collaboration et al. 2015).In 30 Dor C, the nonthermal X-rays, which trace the high-energy electrons, are enhanced in the north-west, coincident with the distribution of OB subclusters and massive stars (Yamane et al. 2021).This is quite similar to the case of Galactic Cygnus Superbubble with a mechanical luminosity of ∼ 2 × 10 38 erg s −1 (Aharonian et al. 2019) and evident -ray emissions from GeV to PeV (Ackermann et al. 2011;Bartoli et al. 2014;Abeysekara et al. 2021;LHAASO Collaboration 2023).
Another possible particle accelerator could be a recent SN in 30 Dor C as we pointed out above, although it may have a low possibility (Smith & Wang 2004).An SN of 10 4 yr ago, for instance, can raise the average mechanical luminosity of one order of magnitude larger than that of stellar winds in a short time (but in a long time scale, the energy of 30 Dor C is dominated by stellar winds as discussed above).Without constant energy input, an SNR can emit nonthermal keV X-ray emission in a short timescale in which the SNR shock propagates at a velocity not lower than ∼ 2 − 3 × 10 3 km s −1 (e.g.Vink 2012;Ge et al. 2021).Assuming a canonical SNR in the Sedov-Taylor phase (Sedov 1959;Taylor 1950), we estimate the timescale of emitting synchrotron X-rays as: where  SN is the explosion energy,  0 is the gas density in the SB, and   is the shock velocity.Compared to the time interval between two SNe of ∼ 3 × 10 5 yr (Mac Low & McCray 1988), it is quite short, indicative of a very low likelihood for the presence of non-thermal keV X-rays.
Even if an SN recently exploded, stellar winds can still play a key role in particle acceleration.Compared to other SBs lacking strong stellar winds, 30 Dor C allows multiple shocks (Bykov & Fleishman 1992;Parizot et al. 2004) or fierce turbulence arising from the interaction between the SNR shock and the strong winds (Vieu et al. 2022b) where the particles can be accelerated to higher energy up to ∼ 40 PeV (Bykov et al. 2015).These mechanisms may dominate the cosmic ray acceleration in the SB, whereas the high sound velocity in the hot medium leads to a low Mach number of explosive motion in it.Meanwhile, the stellar winds may provide power to reaccelerate these high-energy particles and thus allow the X-ray synchrotron to sustain for a much longer time.
In an SB, the most massive stars only exist in the first several million years due to their short lifespan.Later, the stellar winds are negligible compared to supernova explosions (Vieu et al. 2022a).Without strong stellar winds, particles would not be able to be accelerated to non-thermal X-ray emitting energies a couple of thousand years after an SN explosion, probably explaining the lack of X-ray synchrotron emissions in other SBs.At an age of ∼1 Myr, 30 Dor C is in a young stage when the stellar winds are strong enough and some of the most massive stars begin to explode, probably indicative of efficient and constant particle acceleration.The timescale of such a stage (∼ 1 Myr, Vieu et al. 2022a) is much shorter than the lifespan of SBs (≳ 10 7 yr, Mac Low & McCray 1988), corresponding to small samples of SBs emitting non-thermal X-rays like 30 Dor C.

SUMMARY
We employ deep Chandra and XMM-Newton observations to perform spatially resolved spectroscopic X-ray studies of the western half of SB 30 Dor C. We enlarge the sample of point-like sources in the SB interior and find large-scale signatures of diffuse thermal X-rays in the western half among the dominant non-thermal emissions.We summarize our results as follows.
1. We listed the basic information of 17 point-like sources, calculating their ratios and estimating their luminosity.We also searched for their potential optical counterparts and gave the likely associations of some of them according to hardness ratios and spectral properties.Several sources correspond to known WR stars or OB subclusters.
2. We applied spectral analysis and continuum-and-backgroundsubtracted narrow-band maps to search for thermal emission in the western half of SB 30 Dor C. Thermal signals are significant in the south-west of the bubble with a lower column density.For other regions, metal line emissions are also detected although some physical parameters cannot be constrained well.The electron temperature of the plasma is ∼ 0.3 − 0.4 keV, and abundances of intermediate-mass metals including O, Ne, Mg, and Si are elevated, which may come from a recent SN.
3. We calculated the mechanical luminosity of massive stars ∼ 1.6 × 10 38 erg s −1 , most of which is contributed by internal postmain-sequence stars, especially 8 WR stars and 3 supergiants.We suggest that SB 30 Dor C is dynamically dominated by stellar winds, although it may have witnessed an SN explosion event recently, and can be blown out within ∼ 1 Myr.The strong stellar winds, along with a recent SN, probably play a significant role in terms of its unique non-thermal X-ray emissions and TeV -ray emissions among the SBs in the LMC.

APPENDIX A: SPECTRAL FIT FIGURES
The spectra of different regions are presented here.Each region is fitted by a single powerlaw model (left) or added with a vapec model (right) as the thermal component.In each picture, we outline the different components of the model of MOS2 spectra with dash lines, including astrophysical background (yellow), instrumental Al and Si K- lines (grey), non-thermal emission (powerlaw, blue) and thermal emission (vapec, cyan).The reduced chi-squared is labeled on the upper right of each image.The spectra of regions NW1, NW2, W, SW, CN, and CS are plotted in Fig. A1, A2, A3, A4, A5, and A6, respectively.

APPENDIX B: WINDS OF THE O STARS
Apart from 8 WR stars, Testor et al. (1993) listed 25 O-type stars in the OB association LH 90 powering SB 30 Dor C. For lack of direct measurement of their mass loss rates and wind velocity, we apply a relationship between the stellar parameters and stellar winds (Kudritzki & Puls 2000).The mass loss rate  can be expressed as: where  mom is the modified wind momentum,   the wind velocity, and  * the star radius.Here, the subscript ⊙ represents the corresponding solar value, and the subscript * refers to quantities of stars.Adopting given by Kudritzki & Puls (2000), the mass loss rate can be rewritten as the function of the stellar luminosity  * and effective temperature  * : where the accurate value of  0 , , and   are adpoted from Kudritzki & Puls (2000)         in terms of supergiants.Testor et al. (1993) lists the LCs, effective temperatures, and bolometric magnitudes of 25 O-type stars in LH 90, which are shown in Table B1 along with the mass loss rates and mechanical luminosities.Stars without clear LCs are considered as main-sequence stars or giants here.Noticeably, three supergiants contribute over three-fourths of the total power from the O stars, of which 2-08 and 2-32 are in or near the sub-cluster associated with X-ray sources 12 and 6, respectively.The star 2-53, also named Sk -69 212, has the highest mechanical luminosity and spatially corresponds to the soft X-ray source 4. The power of a supergiant here is comparable to that of a WR star.
However, this result requires further correction due to the LMC's low metalicity.Puls et al. (1996) suggested a difference of 0.20 dex in the wind momentum between the Galaxy and the LMC, and the wind velocity in the LMC is slightly slower (Kudritzki & Puls 2000, Fig. 10 therein).Hence, we roughly estimate the total mechanism luminosity of O stars at ∼ 5 × 10 37 erg s −1 .

Figure 1 .
Figure 1.The left panel is the adaptively smoothed, vignetting corrected Chandra pseudo-color image in soft (0.5-1.2 keV), medium (1.2-2.0 keV), and hard (2.0-7.0 keV) bands.Non-thermal emission dominates the radiation in bluish 30 Dor C West while the western half is relatively dim in the soft band.The bright spot to the south-west of the SB is SN 1987A, and the shell-like MCSNR J0536-6913 is projected in the south-east of the SB.The right panel shows 30 Dor C in broad (0.5-7.0 keV) band with 17 point-like sources studied in this article circled in cyan.The image is smoothed in a scale of 3 pixels (∼ 1.5 ′′ ).

Figure 2 .
Figure 2. Chandra flux (unit: photon cm −2 s −1 ) image of source 6 (left) and 12 (right) in 0.5-7.0keV band.Both images are smoothed in a scale of 3 pixels (∼ 1.5 ′′ ), and green circles mark the size of 90 per cent enclosed count fraction.Some faint clumps appear to the west of source 6 and the south of source 12, and the diffuse morphology probably arises from more than one WR star in associated sub-clusters.

Figure 3 .
Figure 3.The hardness ratio map of 30 Dor C produced with the XMM-Newton MOS2 and pn observations with the QPB background subtracted.A hard band 2.0-5.0 keV and a soft band 0.4-1.5 keV are used to produce the ratio map.The map is binned for an average signal-to-noise ratio of 10 and the hardness is shown to increase from red to purple.The contours are made with the high-angular-resolution Chandra observations for positional reference.

Figure 4 .
Figure 4.Regions we selected for spectral analysis.The RGB image is an XMM-Newton pn and MOS2 mosaic in 0.4-1.2keV (red), 1.2-2.0keV (green), and 2.0-5.0 keV (blue).This image reflects the difference in the emission between the west and east as shown byKavanagh et al. (2015).As all of the selected regions are located in the 30 Dor C west, we extracted a large area to the north-west of 30 Dor C as the background.

Figure 5 .
Figure 5. Net flux maps of O, Ne, and Mg lines in the 30 Dor C West in a linear scale.The scale ranges are 0.05-0.35(O viii), 0.20-0.70(Ne ix), 0.10-0.40(Ne x), and 0.15-1.00(Mg xi) in a unit of counts s −1 deg −2 , respectively.The contours represent the 0.5-7.0keV intensities in the Chandra observations.
Fig. 5, different lines show different spatial distributions and are not simply in proportion to the broad-band X-ray intensity.In the south of 30 Dor C, especially in region SW, the south-western segment of the outer shell, almost all emission lines are, especially for O viii and Mg xi.The western edge of the SB (NW2+W) only shows weak emissions of Ne x and O viii, probably due to foreground absorption and/or resonant line scattering.Ne and Mg emissions are also shown in the northern part of 30 Dor C West.Generally, the net flux maps are roughly consistent with the spectral analysis in Section 3.2.2,although the emission line intensities are objective to various factors including the gas temperature, density, metal abundances, and degree of ionization.

Figure A1 .
Figure A1.The spectra and the folded models of region NW1.

Figure A2 .
Figure A2.The spectra and the folded models of region NW2.

Figure A3 .
Figure A3.The spectra and the folded models of region W.

Figure A4 .
Figure A4.The spectra and the folded models of region SW.

Figure A5 .
Figure A5.The spectra and the folded models of region CN.

Figure A6 .
Figure A6.The spectra and the folded models of region CS.

Table 1 .
Chandra observations maps for further point-like source detection.Fig. 1(a) shows a vignetting corrected deep RGB image of 30 Dor C. On account of a good PSF, only 5 on-axis observations (ObsIDs

Table 5 .
Results of spectral analysis

Table 6 .
Townsley et al. (2006)s used for the net flux maps, where the central energy intervals are consistent toTownsley et al. (2006).

Table 7 .
Estimation of gas density in 30 Dor C

Table B1 .
The mechanical luminosities of 25 O stars in LH 90