Constraining the Sub-Galactic Relationship Between Star Formation and the Hot Interstellar Medium in NGC 4254

Abstract

We investigate the relationship between star formation and X-ray emission from the hot interstellar medium (ISM) on $\sim$kpc scales in NGC 4254 (M99) by combining spatially resolved star formation histories (SFHs) and Bayesian X-ray spectral fitting. We measure sub-galactic star formation rates (SFR) by modeling spectrophotometric UV-IR data with flexible SFHs, and we produce point-source-subtracted maps of the diffuse X-ray emission using Chandra data. We extract and fit the spectra of 5 regions selected by their SFR density $Σ_{\rm SFR}$, deriving hot gas luminosities and plasma temperatures. We examine the sub-galactic $kT-Σ_{\rm SFR}$ and $L^{\rm gas}_X-Σ_{\rm SFR}$ scaling relations in NGC 4254, and compare to predictions from simple models of the feedback into the ISM from core collapse supernovae (CCSNe). The hot gas emission from NGC 4254 is consistent with thermalization of $\approx 40-50\%$ of the energy from CCSNe in the ISM, and mass-loading of the CCSNe ejecta which decreases as $Σ_{\rm SFR}^{-1/3}$. Our optimized model implies a temperature and X-ray production efficiency that scale as $kT = (0.72^{+0.26}_{-0.18}~{\rm keV}) Σ_{\rm SFR}^{0.34\pm0.10}$ and $η= (0.03^{+0.02}_{-0.01}) Σ_{\rm SFR}^{0.34\pm0.18}$, respectively, for $Σ_{\rm SFR} = 0.01-0.13~{\rm M_{\odot}~yr^{-1}~kpc^{-2}}$. We also compare the properties of the hot ISM to other ISM phases using data from the PHANGS program. The diffuse X-ray emission of a given region is on average 200 times fainter than the H$α$ emission, and we see evidence that the hot ISM is over-pressurized compared to the large-scale dynamical equilibrium pressure of the galaxy, consistent with expansion of the hot ISM into the ambient medium.

Figures (18)

• Figure 1: Three phases of the ISM, imaged by Chandra, MUSE, and ALMA. Top Row: From left to right, the adaptively smoothed soft band Chandra image created in \ref{['sec:data:xray']}, the extinction-corrected MUSE $\rm H\alpha$ map, and the ALMA CO(2-1) moment 0 (integrated line flux) map using the "broad" masking leroy2021b. Each image is displayed with an asinh stretch on a 99% scale. The white circle in the lower left corner of the Chandra image represents the FWHM of the smoothing kernel near the center of the image; in the MUSE and ALMA images, the (nearly invisible) white circles represent the FWHM of the homogenized PSF and synthesized beam, respectively. Bottom: Three-color composite of the images in the top row. Several qualitative, kpc-scale trends are visible in this composite, though we caution that we have not performed an absolute astrometric reprojection of the Chandra image to the PHANGS frame and an $\approx 0\farcs24$ offset is expected (see \ref{['sec:data:xray']}) In the spiral arms, the hot gas appears to fill large gaps near bright CO knots in the ALMA map in at least on region around R.A.$=$12:18:52.2, Dec.$=+$14:25:10.0, while associating with $\rm H\alpha$ emission on scales $\sim 1$ kpc. In both upper and lower panels, Chandra contours are plotted at arbitrary levels to guide the eye.
• Figure 2: Schematic of the pixel-by-pixel UV-to-IR SED-fitting procedure. Top left: SDSS $gri$ composite of NGC 4254 with $0\farcs5$ pixels. NGC 4254 is a grand design spiral with prominent Northern and Southern arms and a faint third arm in the Northeast (all images are displayed with North up and East to the left). Bottom left: A three-color composite extracted from the PSF-matched multiwavelength data cube, with red = Spitzer MIPS $24~\rm \mu m$, green = SDSS $g-$band, and blue = AstroSat F154W with two example pixels marked by color-coded diamonds. The SED fits and SFHs for these same example pixels are shown in the upper-right panel. The pixel size in this panel is $10"$, 20 times larger than the SDSS image. Upper right: We show the full UV-optical-IR SED fits and the corresponding piecewise SFH for the two pixels marked in the bottom left panel; the border colors of the plots correspond to the color of the two diamond markers in that panel. Note the different axis scales for both SED and SFH plots. The pixel in the inner Northern arm (magenta border; magenta diamond in the lower left panel) has significant ongoing star formation and is both significantly brighter and more attenuated; the pixel in an inter-arm region in the outer disk (orange border; orange marker in lower left panel) is fainter and last experienced significant star formation $\gtrsim30$ Myr ago. Bottom right: The $0-30$ Myr average SFR ($\rm SFR_{30}$) map derived from the full set of pixel-by-pixel SED fits. In the bottom left and bottom right panels, the green circle shows the $25"$ FWHM of the homogenized PSF.
• Figure 3: Bayesian X-ray spectral fits for two $\Sigma_{\rm SFR}$ bins: the top panel shows the fit to the two hexagonal tiles in the $0.09 \leq \Sigma_{\rm SFR} / ({\rm M_{\odot}~yr^{-1}}) < 0.13$ bin, while the lower panels show the fit to the 31 hexagonal tiles in the $0.01 \leq \Sigma_{\rm SFR} / ({\rm M_{\odot}~yr^{-1}}) < 0.03$ bin. The colored bands show the 16th-84th percentile range in each model component, with the total model shown as a blank band. The central lines in each band show the median. The best-fitting background model is shown as a dashed gray line. To compactly display the fits, which were performed jointly to all five ObsIDs, we have combined the spectra and responses of all five observations and folded the fitted spectral models through the combined responses. The source spectra are displayed grouped with 10 counts per spectral bin; the background spectra are grouped with 300 counts per spectral bin. Spectra and models have been normalized by the total area over which the spectra were extracted to emphasize differences in intensity between different $\Sigma_{\rm SFR}$ bins. We show the normalized data$-$model $/ \sigma$ residuals for the best fitting model in each case, though we caution that this is a contrived method of showing the fit quality when the data are grouped for plotting, as we performed the fits to the ungrouped data with cstat. The remaining spectral fits are shown in \ref{['sec:specfits']}.
• Figure 4: X-ray properties from spectral fits to tiles in each of the six $\Sigma_{\rm SFR}$ bins, displayed as a function of the central $\Sigma_{\rm SFR}$ of the bin. In the second panel, the orange line shows the Galactic column density along the line of sight. The X-ray luminosities have been normalized as surface densities $\Sigma = L_X / A$ for fair comparison of the luminosities of the different stacks and the full galaxy. The properties measured within the X-ray extent of the galaxy are shown with a pink star marker at the average $\Sigma_{\rm SFR}$ of the galaxy. In the third panel we show the mineo2012 relation for the 0.5-2 keV hot gas luminosity (without absorption correction; their Equation 2) as a blue line with shaded band representing their measured 0.34 dex scatter. We have adjusted the mineo2012 relation upward (i.e., decreasing the SFR) by a factor of 1.45, accounting for the difference in IMF eldridge2018.
• Figure 5: Radial variation of X-ray model-independent quantities extracted in the unbinned hexagonal tiling for tiles within the measured extent of the X-ray emitting plasma (see \ref{['sec:galint']}): net counts per area, net counts per $\rm SFR_{30}$ (as a proxy for X-ray production efficiency), and soft-band $(S2 - S1) / (S2 + S1)$ hardness ratio (as a proxy for temperature and obscuration; see text for definition). The radial coordinate $r$ is the distance from the center of the galaxy to the centroid of the hexagonal tile. The annotation for each panel gives the median and 16th-84th percentile of the fitted linear parameters ($y = a_0 + a_1 x$) with the corresponding Pearson (P) and Spearman (S) statistics and $p-$values for the correlation between the shown parameters and $r$ within the measured extent of the X-ray emitting plasma. The green line and shaded region show the pointwise median and 16th-84th percentile range of the fitted line. We also calculated the same quantities in an aperture defined by the X-ray extent of the galaxy, and we show their 1$\sigma$ equivalent confidence intervals as a horizontal pink-shaded band.