THE FIRST REPORTED INFRARED EMISSION FROM THE SN 1006 REMNANT

The NW filament corresponds closely with the optical filament that appears only in the hydrogen Balmer lines (van den Bergh 1976; Winkler et al. 2003; Raymond et al. 2007), as shown in the deep continuum-subtracted image shown in the lower right panel of Figure 1. Such "non-radiative" filaments characterize fast shocks expanding into a low-density, partially neutral environment and that are generally associated with relatively young remnants from Type Ia SNe such as SN 1006. Balmer emission from these filaments has two components, both the result of neutral H atoms that cruise through the shock. In the hot post-shock environment, the neutrals can be excited and decay to produce narrow lines (with a width characteristic of the pre-shock temperature), or they can undergo charge exchange with hot protons to produce broad lines whose width is closely related to the post-shock proton temperature (e.g., Chevalier et al. 1980; Ghavamian et al. 2002; Heng 2010). Since the lifetime of neutral atoms in the hot post-shock environment is very short, the Balmer filaments can occur only immediately behind the shock and thus delineate the current position of the shock.

To investigate the post-shock characteristics of emission along the NW filament in various bands, we have compared 24 μm, Hα, and X-ray images. We have used a higher resolution Hα image, taken from the 0.9 m telescope at Cerro Tololo Inter-American Observatory on 2002 March 21, for which the stars were subtracted using a matched continuum image (for details, see Winkler et al. 2003), instead of the one shown in Figure 1(c). Likewise, in X-rays we have used the 0.5–2.0 keV data from a 90 ks observation taken 2001 April 26 and 27 with the Chandra ACIS-S (for details, see Long et al. 2003), rather than the mosaic of shorter ACIS-I exposures used in Figure 1(e). We first checked the alignment of all three images⁹ using four near point sources common to all, one bright star and three distant galaxies, and found their positions in all three bands to agree within 05. To simulate images in all three bands at a common epoch, we used the μ = 280 ± 8  mas yr^-1 proper-motion rate for the NW Balmer filaments, measured relative to the center of curvature at R.A.(2000.) = 15^h03^m162, decl.(2000.) = −42°00'30'' by Winkler et al. (2003), to extrapolate the Hα and X-ray images from their original epochs (2002.2 and 2001.3, respectively) to the 2007.5 mean epoch for the Spitzer MIPS scans (recent measurements from Chandra find X-ray proper motions along most of the NW rim of SN 1006 that agree with those measured for the optical filaments; Katsuda et al. 2013).

In Figure 2, we show a three-color combination that compares the 24 μm (red), Hα (green), and X-ray (blue) images of the NW filament, and in Figure 3 we plot radial profiles taken perpendicular to the filament, integrated over the four azimuthal regions outlined in Figure 2. It is clear that the 24 μm emission has a broader spatial profile that peaks 3''–5'' behind the Balmer filament, as best illustrated in region D of Figure 3, where the profiles are the cleanest. The filament is also noticeably broader in the IR than in Hα, with FWHM ≳15''. This is not simply a resolution effect. The resolution of the 24 μm mosaic image—measured from profiles of several isolated stars—is 6'' (FWHM), consistent with the diffraction limit, but small compared with the width of the filament.

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We attribute this IR emission to dust from the ISM that enters the shock, where it is heated through collisions with hot post-shock gas, produces IR emission, and is then destroyed. Somewhat further behind the shock, soft, primarily thermal, X-ray emission appears, rising to its peak about 10'' behind the shock, just as the 24 μm emission is decaying away. This indicates the longer timescale for producing the highly ionized species that radiate efficiently and dominate the X-ray emission (Long et al. 2003). We can estimate the timescales through simple kinematics: the primary shock is moving outward to the NW at μ = 280 ± 8  mas yr^-1, and if we assume the nominal compression ratio of 4 between the post-shock and pre-shock densities, the post-shock material is dropping behind the shock at speed v_s/4, or μ = 70  mas yr⁻¹ (relative to the shock). Therefore, the IR peak occurs some 60 years after that material was shocked, and the X-ray peak occurs ∼150 years after the shock. We shall discuss the emission profiles further in Section 5.1 of this paper.

In 2012 March, all-sky survey data from the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) were released.¹⁰ Examination of data from the SN 1006 region in all the WISE bands (3.4, 4.6, 12, and 22 μm) shows emission from SN 1006 only in the 22 μm band. Not surprisingly, the WISE 22 μm image is very similar to the Spitzer 24 μm one and clearly shows the NW filament. However, the WISE data have somewhat lower angular resolution and signal-to-noise ratio than that from Spitzer. The non-detection of emission in the shorter-wavelength WISE bands is consistent with the lack of short-wavelength emission in other Type Ia remnants (Borkowski et al. 2006). Close examination of the images from the Improved Reprocessing of the IRAS Survey (IRIS; Miville-Deschênes & Lagache 2005) also shows traces of the NW filament in the co-added 25 μm image; however, it is unlikely that this faint feature would ever have been independently discovered in these low-resolution (15) maps.

In addition to the narrow filaments along the NW rim of the shell, there is patchy, diffuse emission within much of the southern part of the SN 1006 shell, clearly visible in the 24 μm mosaic and less so in the 70 μm one. The morphology of this emission is similar at both 24 μm and 70 μm and is also similar to patchy emission extending well outside the SN 1006 shell, especially to the south and east. In the southern portion of SN 1006, there is also faint, diffuse emission in both Hα and X-rays (Figures 1(c) and (e)), but unlike along the NW rim, the morphology in the south is only vaguely similar to that seen in the IR. In the absence of further data, we cannot determine whether the faint IR emission is associated with SN 1006 itself or stems from cool foreground dust.

In X-rays, SN 1006 shows knots of emission interior to the shock that are thought to arise largely from SN ejecta, but there are no obvious small-scale IR features that correlate with these X-ray-emitting ejecta knots. Hence, we find no evidence for the formation of dust in SN 1006 ejecta. This is somewhat surprising in view of theoretical predictions for dust formation in SN Ia ejecta (Nozawa et al. 2011) but is consistent with observations of other Type Ia SNRs (Borkowski et al. 2006; Williams et al. 2012).

Infrared emission in typical SNR shocks is produced entirely by collisional heating of dust grains (Dwek & Arendt 1992), where energetic electrons and ions collide with the grains, heating them to temperatures of 50–100 K. Collisions with protons and heavier ions are also responsible for grain sputtering, reducing the size of large grains, and destroying many small grains entirely. We have developed models for such dust that self-consistently calculate both the heating and the destruction of grains in the post-shock gas as a function of the density of the hot plasma, n_p, the electron and ion temperatures, and the shock sputtering age τ = ∫^t₀n_pdt (Borkowski et al. 2006). For an arbitrary input grain-size distribution, we can use these models to calculate the IR spectrum and the post-shock profile that results as grains are heated and eventually destroyed.

The electron temperature, T_e, and the ionization timescale can be determined from a non-equilibrium ionization analysis of the X-ray spectra, as Long et al. (2003) did for the NW limb using Chandra data. We have revisited that analysis, taking into account hydrocarbon contamination of the ACIS detectors that was unrecognized at the time of the original analysis and using more reliable atomic data. We first redetermined the absorption column density N_H from the reprocessed synchrotron-dominated eastern limb data (region NE-1 of Long et al. 2003), fit using XSPEC (Arnaud 1996) with a pure synchrotron srcut model to obtain N_H = (8.2 ± 0.8) × 10²⁰ cm⁻². We fixed N_H at this value in fitting Long et al's region NW-1, which includes our IRS regions 1 and 2. We obtained reasonable fits using a solar-abundance plane-shock model (vnpshock) and obtained values of kT_e = 0.9 keV, ionization timescale n_et = 5.3 × 10⁹ cm^-3 s = 170 cm^-3 yr, and emission measure n_eM_g = 6.2 × 10⁻³ M_☉ cm⁻³. This is a somewhat higher electron temperature than the kT_e = 0.6 keV found by Long et al. (2003), but it is still far below the post-shock proton temperature of kT_p = 16 keV, inferred from the Balmer line profiles by Ghavamian et al. (2002; Vink et al. 2003 also measured a similar value for T_e at a different position along the NW rim). We then applied a Coulomb-heating model for collisions between electrons and protons behind the shock and found that, over the relatively small region we consider here, the mean proton and electron temperatures are 16 keV and 1.0 keV, respectively. We use these temperatures for the remainder of this work.

Our models also require as input a distribution of grain sizes in the ISM ahead of the shock. A commonly used distribution for the Galaxy is that of Weingartner & Draine (2001). Their models are appropriate for the diffuse ISM in the disk of the Galaxy, where the total-to-selective extinction ratio R_V ≡ A_V/E(B − V) = 3.1, and for dense clouds where R_V > 3.1. At the location of SN 1006 some 500 pc above the Galactic plane, however, the abundance of dust—both in total amount and in the distribution of grain sizes—is likely very different from that near the Galactic plane. There is significant evidence for much lower values for R_V at high Galactic latitudes (Larson & Whittet 2005). Mazzei & Barbaro (2011) have calculated grain-size distributions using the same formalism as Weingartner & Draine (2001) for over 70 lines of sight to stars with "anomalous extinction sightlines." Particularly relevant for our work, they extend these models down to low-density environments with R_V = 2.0. We use the model from Table 3 of Mazzei & Barbaro (2011), with R_V = 2.0 and 10⁵b_c = 5.0 (this is a parameterization in their models that corresponds to the number of small carbonaceous grains). The grain-size distributions corresponding to lower values of R_V are steeper than their "typical" Milky Way counterparts, i.e., they have an excess of small grains relative to large ones, resulting in a larger fraction of the total mass in grains being destroyed via sputtering for a given shock, as well as a different gas density required to produce the observed spectrum.

In our models, the spectrum from warm dust is most sensitive to the gas density in post-shock plasma, so we have used proton density n_p as the principal free parameter. Using the grain-size distribution described above, we have fit the IRS spectrum over the range 21–37 μm and obtain a best fit for a density of n_p = 1.4 ± 0.5 cm⁻³, shown in blue in Figure 5. The 21–37 μm range comprises all the data for which the signal-to-noise ratio is high enough to be useful. The uncertainty quoted is a formal 90% confidence limit based on statistical uncertainties only, determined from the rms deviations from an arbitrary smooth polynomial fit to the spectrum in this range. We have made no provision for systematic errors in the IRS spectra, which are difficult to quantify.

There is good reason to believe that the actual density is near the lower limit of the fitted range, near n_p = 1 cm⁻³. From an analysis of the thermal X-ray emission along the NW rim based on Chandra observations, Long et al. (2003) found a post-shock electron density n_e ∼ 1 cm⁻³. Analysis of X-ray data from XMM-Newton using a different modeling approach led Acero et al. (2007) to a pre-shock density value of n₀ ∼ 0.15 cm⁻³, equivalent to a post-shock density of n_p ∼ 0.6 cm⁻³ for a standard compression ratio of 4. And finally, an estimate based on the thickness of the Hα filaments in an image from the Hubble Space Telescope by Raymond et al. (2007), and subsequently corrected by Heng et al. (2007), gave n₀ = 0.15–0.3 and thus a post-shock density n_p ∼ 1 cm⁻³. In Figure 5 we also show, in red, a model with n_p = 1.0 cm⁻³, which gives an acceptable fit to the IRS data. Finally, we note that the predicted 70 μm surface brightness for any of our models is ≲0.25 MJy sr^-1, well below the upper limit reported in Section 2.

We have also calculated the spatial profile for the decay of IR emission as grains are destroyed through sputtering in the hot, post-shock environment, assuming that the shock has been advancing through an ambient medium of constant density. In comparing the model with the observed radial profiles, we find that the observed decay is far more rapid than the sputtering model predicts, as illustrated in Figure 6. Even if we assume a grain-size distribution heavily weighted toward small grains to give R_V = 2.0, for a density of n_H = 1 cm⁻³ the sputtering rate would need to be artificially enhanced by a factor of 6–8 to match the observed profiles.

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However, it is almost certain that the shock along the NW rim of SN 1006 has not been passing through a uniform-density environment. The ambient density to the NW is clearly higher than that around the remainder of the shell, as evidenced by the following facts: (1) the flattening of the shell to the NW; (2) the fact that the proper motion along most of the NW limb is only about 60% as high as that to the NE (Katsuda et al. 2013); (3) the density contrast around the shell required from X-ray observations (Long et al. 2003; Acero et al. 2007); and (4) the mere fact that there is significant IR emission along the NW limb, yet little or none elsewhere. Since the shell radius to the NW is only about 15% smaller than elsewhere, the shock must have encountered the denser region there relatively recently. As a result, the post-shock density profile, for both gas and dust, should drop as one moves inward from the shock. Therefore, the decrease in IR emission behind the shock is likely due in large part to the fact that farther inward the grain density has always been lower, representing an earlier epoch in the evolution of SN 1006. We suggest that this may account for the rapid drop in IR emission ∼20''–35'' behind the shock (Figure 6). For a density n_p = 1 cm⁻³ (equivalent to n_e = 1.2 cm⁻³), the shock age from X-ray spectroscopy is about 170/n_e = 140 years, suggesting that the shock was encountering considerably lower densities earlier. Detailed modeling of such a scenario is beyond the scope of the present paper.

Nevertheless, the fact that the observed post-shock drop in IR emission is so much sharper than predicted by the models, even close to the shock, probably indicates that current models significantly underestimate the actual dust sputtering rate. Effects that could be responsible include an even greater proportion of small grains, grains of high porosity, or a grain composition that leads to higher sputtering rates. Enhanced sputtering rates are not without precedent; Serra Díaz-Cano & Jones (2008) found that hydrogenated dust grains (perhaps the most common type of grains in the ISM, at least for carbonaceous materials) are sputtered at rates several times higher than their pure amorphous counterparts. The spectral data are insufficient to determine whether the carbonaceous grains in SN 1006 are hydrogenated or amorphous.

Almost independent of the models, we can determine the total amount of dust radiating in the NW filament, provided that the integrated IR luminosity is relatively well known. We have used the measured IR flux, F(24 μm) = 130 ± 30 mJy (Section 2), and assumed that the overall shape of the dust spectrum observed with IRS (shown in Figure 5) is applicable along the entire length of the filament to obtain L_IR = (1.7 ± 0.9) × 10³⁴ d²_2.2 erg s^-1, where we have scaled to a distance of 2.2 kpc: d_2.2 ≡ d/2.2 kpc. Our models assume optical constants from Draine & Lee (1984) for graphite and amorphous silicate grains in the ISM, with relative proportions and grain-size distributions from Mazzei & Barbaro (2011). As in Williams et al. (2008), we then calculate the dust mass in the NW filament as M_dust = (1.1 ± 0.6) × 10⁻⁵ d²_2.2 M_☉, where the uncertainty limits for both L_IR and M_dust include the overall 15% uncertainty in the Spitzer MIPS extended source flux calibration. Of course, this method of determining the total dust mass is insensitive to any cold dust—undetectable with Spitzer—but it is difficult to imagine how a significant fraction of interstellar dust (consisting almost entirely of small grains, a < 0.5 μm) could remain cold within the hot plasma behind such a fast shock. Our value for M_dust includes only the dust now radiating along the NW filament; the overall faintness of the rest of the SNR at 24 μm, combined with the lack of detection at 70 μm, precludes determination of a dust mass for the entire remnant.

In previous works (Borkowski et al. 2006; Sankrit et al. 2010; Williams et al. 2011a, 2011b), we have used the density determination from IR data, combined with the X-ray emission measure, to obtain a measure of the amount of shocked gas present within a given emitting volume. We have obtained the dust mass from the overall normalization to the dust spectrum, so dividing the two gives the dust-to-gas mass ratio. In the case of SN 1006, however, the IRS spectra do not strongly constrain the density. Thus, we employ an alternative approach.

Laming et al. (1996) examined the ultraviolet spectrum of a section of the NW filament obtained with the Hopkins Ultraviolet Telescope (HUT) and measured 0.02 He ii (1640 Å) photons cm⁻² s⁻¹. More recent work by P. Chayer (2012, private communication) has revised the reddening toward SN 1006 to be E(B − V) = 0.09, lowering the He ii flux to 0.017 photons cm⁻² s⁻¹. According to the Laming et al. models, 0.0067 He ii photons come out for each H atom crossing the shock. For the 200'' section of the filament observed (corresponding to a distance of 6.5 × 10¹⁸ cm at d = 2.2 kpc), the He ii flux measured at Earth would be

$$\begin{equation*} {F_{{\rm {He\, \scriptsize{II}}}}} = \left({0.0067\;\frac{{{\rm {photons}}}}{{{\rm {H\; atom}}}}} \right) ({6.5 \times {{10}^{18}}\,{\rm {cm}}}) \frac{{{n_0}{\upsilon _s}l}}{{4\pi {d^2}}}, \end{equation*}$$

where n₀ is the pre-shock H number density, v_s is the shock speed, and l is the line-of-sight depth through the emitting material, all of which are presumed (for this purpose) to be unknown. Taking F_He II = 0.017 photons cm⁻² s⁻¹, we can rearrange the above equation to give n₀v_sl = 2.26 × 10²⁶ cm⁻¹ s⁻¹. The length of the NW-1 region is 3', or 5.9 × 10¹⁸ cm at d = 2.2 kpc, so 1.3 × 10⁴⁵ H atoms per second enter the shock. If we assume a standard post-shock flow of 70  mas yr⁻¹, based on the proper-motion measurements of Winkler et al. (2003), then the width of the IR filament corresponds to a timescale of 150 years. During this time, the shock will have swept up 6.3 × 10⁵⁴ H atoms, or 7.6 × 10⁻³M_☉ of gas. The uncertainties in the HUT measurement of the He ii flux and in the reddening correction are about 15% each, while the uncertainty in proper motion is only 3% and the uncertainty in the relative atomic rates is probably about 30%, so we estimate an uncertainty in the gas mass of ∼40%. Using the dust mass determined above, this leads to a dust-to-gas mass ratio of ∼(1.5 ± 1.0) × 10⁻³. The expected dust-to-gas mass ratio for the Galaxy within the model of Mazzei & Barbaro (2011) is 5.3 × 10⁻³, a factor of ∼3 higher than what we measure.

The dust-to-gas mass ratio in the ambient medium surrounding SN 1006 appears to be lower than that expected from dust models for the Galaxy, including those at high Galactic latitudes. This has been the case for virtually all SNRs studied, both in the Galaxy (e.g., Blair et al. 2007; Arendt et al. 2010; Lee et al. 2009) and in the Magellanic Clouds (Borkowski et al. 2006; Williams et al. 2006, 2011b). The ultimate reason for this remains a mystery, but in the case of SN 1006 specifically, its location within the Galaxy may provide a clue. At some 500 pc above the Galactic plane, SN 1006 is located at the interface between the disk and halo (see Putman et al. 2012 for a review of gaseous galaxy halos and their interfaces to galactic disks). Accumulating evidence points to a lower dust content there than in the Galactic disk (Ben Bekhti et al. 2012), coupled with a higher proportion of smaller grains (Planck Collaboration et al. 2011). An expected increase in the sputtering rate for smaller grains might better match the rapid drop-off in the 24 μm profile behind the shock (Figure 6) than the current dust model, and it would also raise our inferred value of the pre-shock dust-to-gas mass ratio, bringing it even more in line with the Mazzei & Barbaro (2011) value. We further note that any dust that is too cold to be observed with Spitzer would increase the dust-to-gas mass ratio above our inferred value.

Our current determination of the dust-to-gas mass ratio is quite uncertain, as we do not know the grain-size distribution in the pre-shock gas. It is possible that models with a larger dust-to-gas ratio and a larger overabundance of small grains can be as viable as our current model with R_V = 2.0. This model degeneracy might be broken by future joint IR, X-ray, and UV studies focused on accurate determination of abundances of refractory elements in the post-shock gas.