Early Hard X-Rays from the Nearby Core-collapse Supernova SN 2023ixf

In both NuSTAR telescopes, a point source is clearly detected up to ≈30 keV in both epochs. This is the only source easily identified in M101 (Figure 1). The two coaligned telescopes detect the source and report offsets of 6'' and 3'' from the optical position of the supernova explosion (14:03:38.562, +54:18:41.94; Itagaki 2023). This is consistent with the SN location given the systematic errors in the NuSTAR absolute astrometry.

There is a strong evolution of the source between Epoch I and Epoch II, demonstrating that the NuSTAR emission is clearly dominated by the SN. We simultaneously fit the unbinned data from both telescopes using the W-statistic. Data are rebinned for plotting purposes below.

In Epoch I, the spectra for both telescopes show a clear turnover to low energies (e.g., a high absorption column) as well as a significant excess near the Fe line region around 6.4 keV. The width of the line in Epoch I is consistent with the energy resolution of the NuSTAR detectors, so we can only report an upper limit on the line width. In Epoch II, the overall source flux has increased below 10 keV, and the Fe line features have become slightly broader and shifted to higher energies (Figure 2). The change in the Fe line centroid and width may also be a blending of emission from various lines at higher ionization energies that are not resolved by NuSTAR.

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In both epochs we adopt a spectral model that consists of an underlying bremsstrahlung spectrum with neutral absorption along the line of sight. We include an additive line component to account for reprocessing of the high-energy emission in the absorbing material and/or the presence of ionized lines in the data. For all models we use the solar abundances of Anders & Grevesse (1989).

In XSPEC, our model is tbabs(nlapec+Gauss). Here the tbabs component accounts for both Galactic absorption along this line of sight and intrinsic absorption in the source. The Galactic component is low enough ⁵ (8 × 10²⁰ cm⁻²) that we neglect it in the discussion below. Below we adopt N_Hint to refer to the intrinsic absorbing material in the SN. The nlapec model is a "no-line," or continuum-only, emission from a collisionally ionized gas. We use this to approximate the bremsstrahlung continuum emission.

To estimate the uncertainties on the fit parameters we use the Markov Chain Monte Carlo (MCMC) method (emcee; Foreman-Mackey et al. 2013) as implemented in XSPEC to estimate 90% confidence intervals for all parameters. Table 2 provides the best-fit parameters and their confidence intervals.

Table 2. Spectral Fits for tbabs(nlapec+Gauss)

Epoch	NHint a	kT (keV)	Norm b	Line (keV)	Width (keV)	Norm c	Wstat/dof
Epoch I	26${}_{-7}^{+5}$	>25	1.06 ± 0.13	6.45 ± 0.08	<0.2	6.6 ± 2	888/843
Epoch II	5.6 ± 2.7	${34}_{-12}^{+22}$	1.3${}_{-0.1}^{+0.2}$	6.57 ± 0.17	0.45 ± 0.2	14 ± 5	892/842

Note. Uncertainties indicate the 90% confidence intervals based on the MCMC run.

^a 10²² atoms cm⁻². ^b nlapec normalization [10⁻³]. ^c 10⁻⁶ ph cm⁻² s⁻¹; frozen since the line is narrower than the energy resolution of the NuSTAR detectors.

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For the Swift data, while the supernova is not detected in the full 0.3–10 keV band in a stack of the first 25 observations that span 6 days with a total exposure time of 36.6 ks, it is detected in the 2–10 keV band with a count rate of ${7.7}_{-2.1}^{+2.4}\times {10}^{-4}$ counts s⁻¹. We fit the stacked spectrum with our fiducial model fixing all parameters to the NuSTAR Epoch I values, using a multiplicative constant to allow for flux variability. We find an observed 0.3–10 keV flux of ${6.6}_{-6.6}^{+10}\times {10}^{-14}$ erg cm⁻² s⁻¹, ≈9 × lower than measured by NuSTAR during Epoch I, implying some X-ray flux evolution. If we limit our analysis to the six observations that occurred during the NuSTAR Epoch I observation, the observed 0.3–10 keV flux is ${3.4}_{-2.5}^{+2.9}\,\times {10}^{-13}$ erg cm⁻² s⁻¹, which is consistent with the NuSTAR Epoch I flux extrapolated into this band. Unfortunately there were no Swift/X-ray Telescope (XRT) observations that took place during NuSTAR Epoch II so we cannot repeat our analysis for that observation.

No source is listed at the position of the supernova in the Chandra Source Catalog (CSC2; Evans et al. 2010), and the sensitivity of the Chandra observations at the position of the supernova is listed by CSC2 as 8 × 10⁻¹⁶ erg cm⁻² s⁻¹ in the 0.5–8 keV band and 1.2 × 10⁻¹⁵ erg cm⁻² s⁻¹ in the 2–8 keV band, well below the NuSTAR and Swift/XRT fluxes. We examined the deepest archival Chandra image of the region, observation 934 taken in 2000 for an exposure of 98 ks, and found the background flux within 20'' of the supernova location to be ∼1.5 × 10⁻¹⁴ erg cm⁻² s⁻¹ in the 0.3–10 keV energy range. We are therefore confident that the supernova emission dominates the Swift/XRT flux during these observations.

The early-time X-ray flux from SN 2023ixf is typical of other Type II supernovae. However, the large absorption column in Epoch I makes it difficult to compare with other supernovae that are relatively unabsorbed. To account for this, we compute an unabsorbed flux by changing the model definition to tbabs (cflux ∗ nlapec + Gauss). The cflux component measures the intrinsic flux in the underlying continuum. Table 3 provides the resulting flux in the 0.3–10 and 10–79 keV bands. For a distance of 6.9 Mpc, this results in a large intrinsic 0.3–79 keV luminosity of ∼10⁴⁰ erg s⁻¹ in both epochs.

Table 3. Computed Values

Epoch	EM	Flux 0.3–10 keV	Lum 0.3–10 keV	Flux 10–79 keV	Lum 10–79 keV
	(cm−3)	(erg cm−2 s−1)	(erg s−1)	(erg cm−2 s−1)	(erg s−1)
Epoch I	6.0 ± 0.7 × 1062	5.9 ± 0.3 × 10−13	0.34 ± 0.02 × 1040	3.4${}_{-1.3}^{+0.2}\times {10}^{-12}$	1.9${}_{-0.7}^{+0.1}\times {10}^{40}$
Epoch I a	⋯	1.7${}_{-0.1}^{+0.7}\times {10}^{-12}$	1.0${}_{-0.05}^{+0.34}\times {10}^{40}$	3.5${}_{-1}^{+0.3}\times {10}^{-12}$	2.0${}_{-0.7}^{+0.2}\times {10}^{40}$
Epoch II	7.5${}_{-0.5}^{+0.9}\times {10}^{62}$	1.44 ± 0.08 ×10−12	0.82 ± 0.05 × 1040	3.5 ± 0.9 × 10−12	2 ± 0.5 × 1040
Epoch II a	⋯	2.5 ± 0.3 × 10−12	1.4 ± 0.2 × 1040	3.5 ± 0.9 × 10−12	2 ± 0.5 × 1040

Notes. Uncertainties indicate the 90% confidence intervals based on the MCMC run. Distance is assumed to be 6.9 Mpc.

^a Deabsorbed values.

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The primary difference between the two NuSTAR epochs is the dramatic reduction in the absorbing column. The intrinsic spectrum does not appear to vary much between Epoch I and Epoch II, with the luminosity in the hard (10–79 keV) band staying effectively constant. The large uncertainties in the soft band luminosity due to the poorly constrained N_Hint are consistent with the X-ray source emerging from behind absorbing material.

We assume that the material producing the X-rays has been heated by the shock from the supernova explosion. The temperature of the emission can be used to infer the velocity of the shock. Using the formalism of Fransson et al. (1996) as in Brethauer et al. (2022),

$$\begin{eqnarray}&&T\approx 2.27\times {10}^{9}\mu {v}_{4}^{2}\,{\rm{K}},\end{eqnarray} \tag{ 1 }$$

where μ is the mean molecular weight of the shocked medium (here assumed to be 0.61 for solar-like, ionized material with equipartition between electrons and ions). For Epoch I, the NuSTAR spectra can only place a lower limit on the electron temperature due to the limited signal to noise at high energies. In Epoch II, the NuSTAR spectra can constrain the temperature to be ≈35 keV, which corresponds to a velocity of ∼5400 km s⁻¹. We take this as an order of magnitude estimate for the actual shock velocity, consistent with other supernova shocks.

However, we have explicitly assumed that the electrons and ions reach equipartition, which may not be correct. We measure the electron temperature T_e from the spectra. The timescale for energy transfer from ions to electrons is as follows (from Equation (26) of Chevalier & Fransson 2006):

$$\begin{eqnarray}\begin{array}{rcl}{t}_{e-i} & = & \displaystyle \frac{4.2\times {10}^{-22}}{\mathrm{ln}({\rm{\Lambda }})}\eta (Z)\displaystyle \frac{{T}_{e}^{3/2}}{\rho }\\ & \approx & 0.8\,{\rm{d}}{\left(\displaystyle \frac{{T}_{e}}{25\,\mathrm{keV}}\right)}^{3/2}\left(\displaystyle \frac{9.8\times {10}^{-16}}{{\rm{g}}\,{\mathrm{cm}}^{-3}}\right),\end{array}\end{eqnarray} \tag{ 2 }$$

where η = 1 for H and η = 4/Z for heavier elements of charge Z; $\mathrm{ln}({\rm{\Lambda }})\approx 30$ is the Coulomb logarithm, and we have normalized the equation to the values that apply to our first NuSTAR epoch.

Based on this result, complete electron–ion (e–i) equipartition is unlikely even at the time of our first NuSTAR epoch, as t_e−i is comparable to the time of our first NuSTAR epoch. For the second NuSTAR epoch at δ t ≈ 11 days the density is lower and we derive t_e−i ≈ 8 days: complete e–i equipartition is questionable. We can reverse this argument and calculate the minimum electron temperature at a particular time and density and compare this value to our constraint. Doing so we obtain a minimum electron temperature of ≈60 keV (35 keV) at the time of our first (second) NuSTAR epoch. Our high electron temperatures are therefore consistent with typical supernova shock velocities of ∼10⁴ km s⁻¹ (Fransson et al. 1996).

In the first epoch, the Fe line is consistent with neutral Fe Kα emission that is not broadened. This line therefore appears to be related to neutral (cold) Fe emission, rather than from shock-heated plasma. This is consistent with reprocessing of the X-ray emission in cold, circumstellar material responsible for the high absorption column. This is similar to the early neutral Fe lines observed in SN 2010jl (Chandra et al. 2012), which was associated with a clumpy circumstellar material.

To test this, we adopt a model with a power-law representation of the intrinsic spectrum absorbed by a neutral, spherically distributed medium. This model (Brightman & Nandra 2011) includes the reemission of the neutral lines self-consistently as well as the effects of Compton scattering in the surrounding medium. We find that the first epoch spectrum can be reasonably fit with the same N_Hint as in the baseline model.

We can use these measurements of the absorbing material to estimate the pre-supernova mass-loss rate for the star. Assuming a shock velocity of 15,000 km s⁻¹ places the forward shock at R₁ ∼ 5.7 × 10¹⁴ cm 4.4 days after the explosion and at R₂ ≈ 1.4 × 10¹⁵ cm at 11 days. The fast disappearance of the the flash ionization spectral features (Stritzinger et al. 2023; Yamanaka et al. 2023) supports a dense, but confined, CSM (e.g., Yaron et al. 2017). All of the absorbing material is assumed to be local to the SN environment, an assumption supported by the rapid decrease in N_Hint between the two NuSTAR epochs. If all of the material is local to the SN explosion, then the measured N_Hint at δt ≈ 4.4 days implies $\dot{M}\approx 2.5\times {10}^{-4}$ M_⊙ yr⁻¹ for an assumed v_w =50 km s⁻¹, hydrogen-dominated chemical composition, and a wind-like density profile with $\rho (r)=\dot{M}/4\pi {r}^{2}{v}_{w}$ and${N}_{\mathrm{Hint}}\,={\int }_{{R}_{1}}^{\infty }(\rho (r)/{m}_{p}{dr})=\dot{M}/4\pi {m}_{p}{v}_{w}{R}_{1}$.

An alternative estimate of the mass local to the SN environment comes from the observed decrease of neutral hydrogen absorption (ΔN_H) between the two NuSTAR epochs at 4.4 and 11.0 days. This assumes that the measured ΔN_H is largely a consequence of the shock plowing through the medium and emerging from the dense circumstellar material or that newly ionized material was mostly located between R₁ and R₂. The inferred mass-loss rate (for H-dominated composition and v_w = 50 km s)⁻¹ is $\dot{M}\approx 3.0\times {10}^{-4}$ M_⊙ yr⁻¹. For these parameters, the amount of circumstellar mass sampled by the shock during the first ∼11 d is M_CSM ≈ 1.7 × 10⁻³ M_⊙. The inferred particle density at R₁ is ∼6 × 10⁸ cm⁻³, decreasing to ∼3 × 10⁷ cm⁻³ at R₂.

We can also estimate of the density of the emitting region from the emission measure (EM) ≡ ∫n_e n_i dV, where the integral is over the X-ray emitting region, and the derived density is that of shock compressed material. For a strong shock applicable here we expect this density to be 4 times the unshocked CSM density (which is what we measured from the ΔN_H above). From our broadband X-ray modeling we infer EM (4.4 days) ≈ 5.7 × 10⁶² cm⁻³ and EM (11.0 days) ≈ 7.6 × 10⁶² cm⁻³. Assuming a hydrogen composition, complete ionization (consistent with the large T measured), constant particle density in the X-ray emitting region, spherical shell-like geometry with ΔR ≈ 0.1R, the inferred preshock particle density at R₁ is ∼4 × 10⁸ cm⁻³, decreasing to ∼10⁸ cm⁻³ at R₂. This density estimate is consistent with the inferences from the ΔN_H to within a factor of a few and thus supports the conclusion that the emitting region is the shocked CSM.

Kilpatrick et al. (2023) identified the stellar progenitor of SN 2023ixf as a red supergiant star (RSG) enshrouded in a dusty shell. Comparing the mass-loss rate of $\dot{M}\approx 3\,\times {10}^{-4}$ M_⊙ yr⁻¹ for an assumed v_w = 50 km s⁻¹ inferred above with those of RSGs in the Galaxy and in nearby galaxies we find that the RSG progenitor of SN 2023ixf lies in the upper end of the distribution (see, e.g., Massey et al. 2023, their Figure 1 with a compilation of data from Mauron & Josselin 2011; Beasor & Davies 2018; Beasor et al. 2020). A comparison to mass-loss rates inferred for other Type IIP SNe leads to a similar conclusion that the progenitor of SN 2023ixf experienced a large mass-loss rate in the final years before explosion (e.g., Smith 2014, their Table 1). We speculate that this might be related to the preexplosion progenitor variability reported by Kilpatrick et al. (2023). We end by noting that the inferred mass-loss rate implies an optical depth to electron scattering τ_es < 1 even at early times, which is not consistent with the presence of pronounced Lorentzian "wings" of the optical lines reported by Jacobson-Galan et al. (2023) if the physical origin of the wings is connected with repeated electron scattering events (e.g., Huang & Chevalier 2018; see Neustadt et al. 2023 for the alternative scenario of radiative acceleration applied to SN 2023ixf). A possible explanation for this disagreement is the deviation from spherical symmetry that can be tested with future observations of SN 2023ixf. Hints of the asymmetry in the CSM are already present in early optical spectroscopy (Smith et al. 2023).

By the time of the second epoch, the Fe emission no longer appears to be narrow and associated with neutral Fe. However, constraining the Fe line emission is difficult with NuSTAR alone as the continuum flux has increased (while the relative flux of the Fe line has not). The fact that the Fe line flux has dropped while the overall hard X-ray flux has remained constant is further evidence that the early narrow Fe emission is due to cold material local to the SNe explosion reprocessing the high-energy photons. At late times, the amount of material along the line of sight has decreased, resulting in a comparable decrease in the equivalent width of the Fe line.

We attempted to fit the spectrum with a standard apec model (which self-consistently includes the line emission), but still saw significant residuals near the Fe line. We conclude that this is likely due to contributions both from residual narrow Fe emission from whatever residual CSM material is still present external to the forward shock as well as from line emission from ionized species in the forward shock itself.

Radio nondetections of SN 2023ixf have been reported by Berger et al. (2023), Matthews et al. (2023), and Chandra et al. (2023). The flux limits reported are as follows: Submillimeter Array (SMA): F_ν < 1.5 mJy (3 rms), ν = 230 GHz, δ t ≈ 3 days (2023 May 21.17 UT; Berger et al. 2023). GMRT: F_ν < 75 μJy (3 rms), ν = 1.255 GHz, δ t ≈ 4 days (2023 May 22.74 UT; Chandra et al. 2023). Very Large Array (VLA): F_ν < 33 μJy (5 rms), ν = 10 GHz, δ t ≈ 4 days (2023 May 23 beginning on-source at 00:24:09 UT; Matthews et al. 2023).

If we assume the densities derived from the ΔN_H above, the (external) free–free optical depth ${\tau }_{230\,\mathrm{GHz}}(3\,\mathrm{days})\,\approx 200{\left(\tfrac{{{\rm{T}}}_{e}}{{10}^{4}\,{\rm{K}}}\right)}^{-1.35}$, decreasing to below 1 at ∼20 days; τ_{10 GHz}(4 days) ≈ 7 × 10⁴ decreasing to 1 at 150 days. Here the temperature T_e is the temperature of the electrons in the unshocked region (while the X-ray emitting electrons are in the shocked region and at a higher temperature). The 230 GHz SMA nondetection and the 10 GHz VLA nondetection are thus not surprising (e.g., Terreran et al. 2022) and consistent with the densities inferred from the X-ray modeling.