INFRARED CONTINUUM AND LINE EVOLUTION OF THE EQUATORIAL RING AROUND SN 1987A

Examination of the cryogenic data had indicated that the ratio of 24 μm IR to X-ray brightness (the IRX ratio) was approximately constant between days 6000 and 8000. However, continued observations at 3.6 and 4.5 μm have shown a trend that clearly diverges from the X-ray emission. Figure 2 depicts the observed light curves, as listed in Table 1.

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The soft 0.5–2 keV in-band X-ray flux is used throughout for comparison with the IR emission because it is more representative than the harder X-ray emission of the forward shock that propagates through the ER (Dwek et al. 1987). The X-ray data used here are those measured with the Chandra ACIS and published by Helder et al. (2013), to which we add three additional epochs of similarly observed and reduced Chandra observations. A more physically motivated comparison might use the integrated X-ray emission of the softer component of two-component fits to the total X-ray spectrum. The temperature of the soft component varies from 0.2 to 0.4 keV, and is sufficiently low that the fraction of emission at energies >2 keV is negligible. The soft component accounts for ∼33% of the flux in the 0.5–2 keV band at day 5000, rising to ∼41% at day 10,000. However, given uncertainties in the corrections of systematic effects in the X-ray data, and the relatively low signal-to-noise of the data at some epochs, both of which affect the spectral fitting, the light curve of the integrated soft X-ray component is much noisier than that of the simple 0.5–2 keV in-band flux.

A strong correlation between the evolution of the X-ray and IR luminosity would be an indication that the mid-IR emission of SN 1987A is from collisionally heated dust in the ER, as both the IR and X-ray emission should be proportional to the mass of shocked material. Figure 3 shows the evolution of flux density, S(λ), at each IR wavelength, λ, compared to scaled versions of the soft X-ray emission, S(X):

$$\begin{eqnarray}&&S(\lambda ,t)=a(\lambda )S(X,t).\end{eqnarray} \tag{ 1 }$$

The empirical fitting parameter a corresponds to a constant IRX ratio (Dwek et al. 1987; Dwek & Arendt 1992):

$$\begin{eqnarray}&&\mathrm{IRX}={n}_{\mathrm{dust}}{{\rm{\Lambda }}}_{\mathrm{dust}}({T}_{\mathrm{gas}})/{n}_{{\rm{H}}}{{\rm{\Lambda }}}_{\mathrm{gas}}({T}_{\mathrm{gas}}),\end{eqnarray} \tag{ 2 }$$

where T_gas is the gas temperature, Λ_dust(T_gas) and Λ_gas(T_gas) are the in-band cooling functions of the dust and gas, n_dust is the number density of dust grains, and n_H is the number density of hydrogen. This is for collisional heating of the dust. For radiative heating, the dust cooling function will depend on the radiation field rather than the gas temperature. The relative importance of radiative versus collisional heating of dust in supernova remnants has been discussed by Arendt et al. (1999), Andersen et al. (2011), and in more general circumstances by Bocchio et al. (2013). In all cases we only use data from days 6000 to 8000 to determine the parameter a. The fit is generally not very good, indicating that the simplest model, given by Equation (1), fails. However, the fit is significantly improved if the model allows a constant flux density offset, b:

$$\begin{eqnarray}&&S(\lambda ,t)=a(\lambda )S(X,t)+b(\lambda )\end{eqnarray} \tag{ 3 }$$

as shown in Figure 3. A non-zero value for the parameter b could indicate a systematic error in the measurement of the flux densities of SN 1987A, e.g., error in the subtraction of the contribution of nearby Stars 2 and 3. The parameter b would also account for a component of the SN's IR or X-ray emission that does not exhibit the same correlated temporal variation as the bulk of the emission.

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Using the 24 μm emission as the reference instead of the X-ray emission provides a check on whether the IR emission is evolving in a consistent manner across all wavelengths. This comparison is also shown in Figure 3. As with the X-ray emission, the shorter wavelengths are consistent with the 24 μm emission only if a constant emission component is present at each IR wavelength. The fit parameters (a, b) required here are consistent with those derived from the X-ray comparison given by Equation (3).

At 3.6 and 4.5 μm, the comparison to X-ray emission can be extended over for the longer time intervals from day 6000 to day 11,000. In these cases, the required constant term is increased such that it accounts for nearly all of the emission at day 6000, and the ratio of the evolving IR to X-ray emission drops correspondingly. Consistent results are obtained when the 3.6 μm flux density evolution is compared directly to that at 4.5 μm.

The empirical models described in the preceding subsection assume that the ratio of IR to X-ray emission should remain constant as the brightness evolves. However, a changing value of IRX could eliminate the need for a strong non-evolving IR emission component in the comparison of IR and X-ray emission. The IRX would be expected to change if the physical conditions (temperature, density, or dust-to-gas mass ratio) in the shocked gas change over time. The ratio of hard to soft X-ray emission has remained nearly constant since day ∼6000 (see Table 1 of Helder et al. 2013), therefore a decreasing IRX may indicate ongoing grain destruction and evolution of the dust to gas mass ratio n_dust/n_gas. Apart from the explicit dependence of the IRX on the dust to gas mass ratio and the gas temperature, see Equation (2), its numerical value will also depend on the dust grain size distribution, and on the abundances and ionization state of the gas.

A simple model that would allow divergent but related evolution of the IR and X-ray emission can be written as

$$\begin{eqnarray}&&S(\lambda ,t)=\alpha \ S(X,t){(t-{t}_{0})}^{\beta }\end{eqnarray} \tag{ 4 }$$

where t₀ represents the time at which the forward shock began interaction with the ER, α is the nominal IRX at that time, and β characterizes the evolution of IRX over time. If β = 0 we recover the constant IRX assumption of the model in Equation (1). Assuming t₀, we can solve for the free parameters α and β by performing a linear fit to:

$$\begin{eqnarray}&&\mathrm{log}[S(\lambda ,t)/S(X,t)]=\beta \mathrm{log}(t-{t}_{0})+\alpha .\end{eqnarray} \tag{ 5 }$$

For the choice of t₀ = 4600, we derive β = −1.0 for both 3.6 and 4.5 μm data. However, at this same t₀, β increases with wavelength, reaching −0.6 for the 24 μm data. Because there is a strong correlation between t₀ and β in this model, we can force β = −1.0 for each wavelength by making t₀(λ) a function of wavelength, e.g., t₀(24 μm) = 3270.

The value of β = −1 is of particular interest. If the volume of the X-ray emitting gas is accumulating as a power law function of $t-{t}_{0}$, integrated from t₀ to t₁, but the volume of the IR emitting region is restricted to a layer representing a finite duration behind the shock front, i.e., an integral from ${t}_{1}-{\rm{\Delta }}t$ to t₁, then the IRX should evolve as ${(t-{t}_{0})}^{-1}$ for ${\rm{\Delta }}t\ll (t-{t}_{0})$ (see Figure 7 of Dwek et al. 2010). The limited thickness of the IR-emitting region would arise if the dust destruction timescale is short compared to the cooling time of the gas.

Therefore if we make the assumption that β = −1, then we can derive t₀ and α via a linear fit to

$$\begin{eqnarray}&&S(X,t)/S(\lambda ,t)={\alpha }^{-1}(t-{t}_{0}).\end{eqnarray} \tag{ 6 }$$

Such fits are shown in Figure 4. If we use this prescription to transform the observed X-ray fluxes to IR flux densities, then the agreement is very good throughout the span of the IR observations (Figure 5). Extrapolation back to earlier times will fail if $t-{t}_{0}$ is less than the dust destruction timescale. The extrapolation of the 24 μm emission to later times may be verified in the future with the Stratospheric Observatory for Infrared Astronomy (SOFIA) (Young et al. 2012) or the James Webb Space Telescope (Gardner et al. 2006).

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Comparison of the IR and X-ray emission in the previous subsections indicates that the IRX does not remain constant. The changes may indicate that the decay timescale of the IR emission is much shorter than for the X-ray emission. Decreasing IR emission can occur if the dust cools or is destroyed.

The following models specifically examine whether the IRAC and MIPS data indicate evolution of dust mass, dust temperature, or both. These models use two dust compositions with independent temperatures to fit the IRAC and MIPS SED of SN 1987A at nine epochs between days 6000 and 8000, when observations at all wavelengths were obtained. Guided by the spectral models presented by Dwek et al. (2010), the warm dust component giving rise to the 8–35 μm emission is assumed to be silicate, with a temperature of ∼180 K, and the hot dust component giving rise to the 3–8 μm emission is assumed to be amorphous carbon, with a temperature of ∼460 K. The hot dust component could alternately be any other composition with a generally featureless spectrum (e.g., iron), and with temperatures that could be as much as ∼100 K lower (Dwek et al. 2010). These components are derived from fits to the Spitzer IRS low resolution spectra (5–30 μm) obtained between days 6000 and 8000. The warm dust is consistent with collisional heating by the X-ray emitting gas, and with even small dust grains residing at their equilibrium temperatures (Bouchet et al. 2006; Dwek et al. 2008). The hotter dust can also be collisionally heated, if the grain sizes are sufficiently small, dependent on the unknown dust composition (Dwek et al. 2010). Small carbon grains can reach these high temperatures under thermal equilibrium, but other compositions may require stochastic heating to reach sufficiently high temperatures (Dwek et al. 2010). However, if transiently heated grains are producing the hot component, then they should radiate more strongly at lower temperatures, producing more emission at λ > 10 μm which would dilute the relative strength of the 10 and 20 μm silicate features.

The fitting is constrained at different epochs by assuming that the temperature and dust mass evolve as functions of time:

$$\begin{eqnarray}&&S(\lambda ,t)=\displaystyle \sum _{i=1}^{2}\displaystyle \frac{4{\kappa }_{i}(\lambda )}{4\pi {d}^{2}}{M}_{i}(t)\pi {B}_{\nu }[{T}_{i}(t)]\end{eqnarray} \tag{ 7 }$$

where κ_i(λ) is the mass absorption coefficient of the dust, d is the distance to the SN, and ${B}_{\nu }(T)=2h{\nu }^{3}/{c}^{2}\ 1/({e}^{h\nu /{kT}}-1)$ is the Planck function. The mass absorption coefficient for silicate is taken from Draine & Lee (1984), and for amorphous carbon is from Rouleau & Martin (1991). We choose power law functions of time as a simple means of characterizing the evolution of the mass and temperature of separate warm (silicate) and hot (e.g., carbon) components:

$$\begin{eqnarray}&&{M}_{i}(t)={M}_{i,0}\ {(t-{t}_{1})}^{{\mu }_{i}}\end{eqnarray} \tag{ 8 }$$

and

$$\begin{eqnarray}&&{T}_{i}(t)={T}_{i,0}\ {(t-{t}_{1})}^{{\theta }_{i}}.\end{eqnarray} \tag{ 9 }$$

Dwek et al. (2010) illustrate how the mass power law index, μ, changes for idealized shocks expanding into one-, two-, or three-dimensional media, under the cases of free or Sedov expansion, and with or without rapid destruction of dust.

If the temporal evolution is measured with respect to the SN explosion (t₁ = 0) then $t-{t}_{1}$ only varies by a factor of 1.33 from day 6000 to 8000, which forces a large value of μ_i ∼ 4–5 to match the observed change in brightness. It is more realistic to choose t₁ as the start of the interaction between the blast wave and the ER. Assuming that t₁ = 5500 (Dwek et al. 2010), we find that ${\mu }_{1}=0.87$ (silicate) and μ₂ = 0.98 (carbon). The value of μ_i ≲ 1 could indicate free expansion into a one-dimensional medium without grain destruction or two-dimensional medium with grain destruction, or Sedov expansion into a two-dimensional medium (see Figure 7 of Dwek et al. 2010). For both dust components θ_i ∼ 0, indicating very little evolution of the temperature.

These results are shown in Figure 6, where the fitted dust temperatures are T_1,0 = 190 K for the warm silicate component, and T_2,0 = 525 K for the hot amorphous carbon component. These dust temperatures are warmer, though not significantly, than those derived by Dwek et al. (2010). Figure 7 compares the changes in the λ/24 μm colors of the data and the model. These changes are mostly driven by variation of the relative masses of the warm and hot components, not by changes in the dust temperatures. Figure 8 (top) shows the observed and modeled evolution of the flux densities. Over the fitted interval of days 6000–8000, the model is in fair agreement with the data. However, extrapolating the model to later times at 3.6 and 4.5 μm shows a clear deviation between the data and the model.

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Comparison between the model and observations is shown in Figure 8 (bottom). The ratio between the model and data is constant until about day 7500, after which the data fall linearly with respect to the model. Thus, we have constructed an altered model for the 3.6 and 4.5 μm data. Only the hot carbon dust component is used, because the warm silicate dust provides negligible emission at these wavelengths. The dust temperature is still a free parameter, but it is held constant because the previous models suggested very little evolution in temperature. Starting at day 7500, a linear decrease in the mass is applied. The slope of this decrease indicates a destruction timescale for the dust, ${t}_{{\rm{destr}}}^{-1}$, which is a free parameter to be derived from the data. The form of the model is thus:

$$\begin{eqnarray}S(\lambda ,t) & = & \displaystyle \frac{4\kappa (\lambda )}{4\pi {d}^{2}}{M}_{0}\ {(t-{t}_{0})}^{\mu }\ \pi {B}_{\nu }(T)\\ & & \ {\rm{for}}\ t\lt 7500\\ & = & \displaystyle \frac{4\kappa (\lambda )}{4\pi {d}^{2}}{M}_{0}\ {(t-{t}_{0})}^{\mu }[1-(t-7500)/{t}_{{\rm{destr}}}]\\ & & \times \pi {B}_{\nu }(T)\\ & & \ {\rm{for}}\ t\gt 7500.\end{eqnarray} \tag{ 10 }$$

The fits for this models are shown in Figure 8. The relative accuracy of this model is ∼3% at 3.6 μm and ∼2% at 4.5 μm (shown later in Figure 10).

Figure 9 shows the evolution of the IR emission measured by Spitzer compared to the optical emission in the B and R bands measured by HST (Fransson et al. 2015). The correlations are moderately good in both cases, but are better for the B band, which is dominated by the emission lines of Hγ, Hδ, and [S ii] 0.4069 μm (Fransson et al. 2015). Figure 10 (upper panels) illustrates that the application of Equation (1), but using the optical instead of the X-ray emission, provides a surprisingly effective model of the IR emission, especially when using the B band optical emission. However, the lower panels of the figure show that the IR emission is more closely matched by the previously discussed functions of the X-ray emission.

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These correlations between the optical and the IR emission may indicate the IR and optical emission originate in the same, or closely related, regions of the shocked ER. However, examination of the radiative luminosity of the SN at various wavelengths indicates that it is unlikely the dust heating can be predominantly radiative. Radiation from the ER is dominated by UV–X-ray emission with a total 0.01–8 keV luminosity of ∼1460 L_⊙ (France et al. 2015). The ER dust has an integrated IR luminosity of $\sim 1450\ {L}_{\odot }$. Radiative heating would require that half of the ER emission is absorbed by dust within the ring. The required optical depth is inconsistent with gas phase abundances indicating little depletion into dust (e.g., Mattila et al. 2010) and spectral analysis which requires only Galactic + LMC line of sight extinction corrections (e.g., Pun et al. 2002; Gröningsson et al. 2008b).

The atomic spectral lines seen in the mid-IR are usually the ground state fine-structure transitions of various ionized species. One or more higher-lying H recombination lines are seen, and one excited state transition of [Fe ii] is detected. Cutouts of the lines in the SH and LH data are shown in Figure 11, and lines in the SL and LL data are shown in Figure 12. Here we only discuss the lines, as the continuum in the SL and LL spectra has been analyzed by Bouchet et al. (2006) and (Dwek et al. 2008, 2010). The continuum in the SH and LH data adds no new information and is less reliably measured as the concatenation of many spectral orders.

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Nearly all of the observed emission lines can be attributed to the emission ring, as the widths of most lines seem to be unresolved at the R ∼ 600 resolution of the IRS SH and LH modules. However this spectral resolution is insufficient to distinguish between the ionized but unshocked component of the ring and the shocked component of the ring, which are clearly seen as narrow (FWHM ∼ 10 km s⁻¹) and intermediate (FWHM ∼ 300 km s⁻¹) width components in high resolution optical spectra (e.g., Gröningsson et al. 2008a).

One apparent exception is the [Si ii] line at 34.81 μm. At all epochs (barring the low signal to noise data of the initial observations at day 6109), this emission line seems to be flanked by a pair of lines at velocities of ±1700 km s⁻¹ with respect to the central component. The background spectra do not show any indication of the shifted lines. The velocities of the flanking lines are large compared to the velocities associated with shocked emission ring, but fairly small compared to the velocity of the SN ejecta. The distinctness of the flanking lines implies that they are not produced by an expanding spherical distribution (either a shell or a filled sphere) of material. Either a bi-polar or an expanding ring-shaped distribution could produce the flanking lines. The homunculus in the η Car nebula is an example of a bipolar structure in the circumstellar medium of a massive star. However its expansion velocity is lower, at ∼600–800 km s⁻¹ (e.g., Gehrz & Ney 1972; Meaburn et al. 1987). A ring-shaped distribution would also produce a plateau of emission between the flanking lines, but the presence of the central line makes it difficult to determine whether or not a plateau exists. Furthermore, the strength of the central component and any underlying plateau may be affected by imperfect subtraction of the background [Si ii] emission which is strong in the vicinity of SN 1987A. None of the other lines show this velocity structure, with the possible exception of the [Fe ii] 25.99 μm line.

The high resolution spectra show a complicated blend of lines at 26 μm. The strongest two components are [O iv] 25.89 μm and [Fe ii] 25.99 μm. Both of these identifications are confirmed by having velocity shifts in agreement with other unblended lines in the spectra. Additionally, there appear to be wings on both the red and blue sides of the [O iv] and [Fe ii] pair. The blue wing may be a separate line that is only marginally resolved from the [O iv] line. Bouchet et al. (2006) had pointed out that this feature could be [F iv] 25.83 μm (based on the line list used by SMART⁸ ). However, we now believe the [F iv] identification is unlikely because (a) other line lists⁹ cite a wavelength of 25.76–25.773 for this line, making the wavelength agreement worse, (b) no other fluorine lines are observed ([F i] 24.75, [F ii] 29.33, nor [F v] 13.40 μm) despite the fact that they lie in spectral regions with low noise, and (c) there are many other elements that are normally much more abundant than fluorine that are not seen in the spectrum. If not [F iv], then this blue wing is probably a velocity shifted component of [O iv] or [Fe ii]. If [O iv], it is a velocity structure not seen in any other lines. If [Fe ii], it may correspond to the flanking lines of [Si ii], however there is no corresponding feature on the red side. The red wing that is present on the 26 μm complex is much broader than the blue wing. We presume that it represents a higher velocity distribution of [Fe ii]. The 26 μm complex was fitted iteratively for [O iv], [Fe ii], [F iv] (or blue wing component), and the broad [Fe ii] component, subtracting each line before fitting the next.

The complex of [Si ii] and [Fe ii] lines at 35 μm was also fitted iteratively. The central [Si ii] line was fitted first. It usually has the largest width, which is possibly influenced by blending with the red and blueshifted components. In contrast, a simultaneous fit for all three [Si ii] lines often derives a much smaller width and a proportionally small flux for the central [Si ii] line. Thus the individual [Si ii] line fluxes may be uncertain by nearly a factor of 2 due to systematic effects, but the integrated flux of all three [Si ii] lines is consistent within 5%. The Gaussian fits to all lines in the SH and LH spectra at all epochs are listed in Table 2.

The IRS SL module provides coverage of the 5 < λ < 10 μm region which is inaccessible with the SH module. The strongest line seen here is [Ar ii] 6.99 μm which is clearly seen at all dates. The [Ni ii] 6.64 μm line (the single ground state fine structure transition of this species) is not so clear in the earliest data, but seems to be present in the later observations. Additional lines may be present near 7.48 and 7.65 μm. These features lie near the ends of the spectral orders of the IRS modules and are thus somewhat less reliable, but they do seem be present in multiple orders and at many or all epochs. The shorter wavelength feature may be a blend of the H i 6-5 and 8-6 transitions. This identification is supported by the weak detection of the H i 7-6 transition in the SH data. The 7.65 μm feature could be [Ne vi], which would make it the most highly ionized species that we observe.

Figure 13 illustrates the changes in the lines fluxes over a 5-year period for those lines seen in the SH and LH spectra. When present, the intensities of lines in the background are also plotted. This provides an indication of the potential systematic errors in measurements due to the different slit orientations and background fields at each epoch. The comparison with the background also shows that the SN 1987A line measurements are suspect or impossible when the background intensity is ∼2 or more times brighter then the SN (e.g., [S iv], [Ne iii], [S iii], and maybe [Si ii]). We have fitted these light curves with three models. The first model is that the line intensity is proportional to the continuum intensity: F_line = A F_{24 μm}, and is shown as a dotted line in each panel of the figure. The second model is that the line intensity is constant: ${F}_{\mathrm{line}}=B$, as indicated by the dashed lines. The third model uses two parameters to model the evolution as a linear function of time: ${F}_{\mathrm{line}}=\beta +\alpha \ t$ (dash-triple-dot line in the figure). Table 3 lists the derived parameters of the fits for each line and each model. The probabilities, P(<χ²), are the probability of finding a smaller value of χ² than the observed χ² under the assumption that the data are a random sampling of the model. Thus P(<χ²) ∼ 1 indicates the data are very unlikely to be related to the given model. Figure 14 and Table 4 provide the results for the comparable analysis of the low resolution spectral lines.

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Table 3.  High Resolution Line Evolution

		Fline = A F24 μm				Fline = B				${F}_{\mathrm{line}}=\beta +\alpha \ t$
Species	Ndata	A	χ2	P(<χ2)		B	χ2	P(<χ2)		β	α	χ2	P(<χ2)
[S iv]	5	5.326e-21	2.214	0.304		3.270e-22	3.418	0.510		−8.241e-22	1.557e-25	2.110	0.450
H i 7-6	6	4.888e-21	4.270	0.489		2.997e-22	12.553	0.972		−9.992e-22	1.751e-25	4.150	0.614
[Ne ii]	7	6.977e-20	468.208	1.000		4.351e-21	732.517	1.000		−4.534e-21	1.200e-24	196.869	1.000
[Ne v]	7	6.731e-21	41.675	1.000		4.367e-22	9.013	0.827		1.376e-21	−1.265e-25	2.653	0.247
[Ne iii]	7	2.164e-20	1256.515	1.000		1.286e-21	1123.777	1.000		1.703e-23	1.744e-25	1105.106	1.000
[Fe ii]	7	5.873e-21	19.530	0.997		3.847e-22	3.783	0.294		6.075e-22	−2.985e-26	3.410	0.363
[S iii]	3	1.123e-20	4.020	0.866		6.862e-22	0.774	0.321		2.720e-23	8.967e-26	0.047	0.172
[Ne v]	7	1.106e-20	19.626	0.997		6.718e-22	6.208	0.600		4.751e-22	2.701e-26	6.087	0.702
[F iv]?	7	1.083e-20	30.014	1.000		6.545e-22	8.623	0.804		1.909e-22	6.409e-26	7.182	0.793
[O iv]	7	4.425e-20	11.281	0.920		2.527e-21	5.414	0.508		−1.094e-21	5.074e-25	1.163	0.052
[Fe ii]	7	3.295e-20	11.028	0.912		1.785e-21	3.626	0.273		−5.983e-22	3.387e-25	0.760	0.020
[Fe ii] (broad)	7	1.512e-20	8.798	0.815		7.018e-22	55.182	1.000		−3.373e-21	5.859e-25	4.875	0.569
[S iii]	1	5.234e-20	⋯	⋯		1.387e-21	⋯	⋯		⋯	⋯	⋯	⋯
[Si ii] (blue)	6	3.135e-20	24.539	1.000		1.712e-21	48.649	1.000		−9.902e-21	1.612e-24	17.085	0.998
[Si ii]	7	8.463e-20	17.976	0.994		4.997e-21	7.062	0.685		−1.202e-21	8.615e-25	2.852	0.277
[Si ii] (red)	6	3.016e-20	17.694	0.997		1.661e-21	24.299	1.000		−5.840e-21	1.044e-24	16.277	0.997
[Fe ii]	6	1.992e-20	16.415	0.994		1.292e-21	17.693	0.997		−1.644e-21	3.909e-25	15.376	0.996

Note. A in (W m⁻²/Jy), B in (W m⁻²), α in (W m⁻²/day), β in (W m⁻²).

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Table 4.  Low Resolution Line Evolution

		Fline = A F24 μm				Fline = B				${F}_{\mathrm{line}}=\beta +\alpha \ t$
Species	Ndata	A	χ2	P(<χ2)		B	χ2	P(<χ2)		β	α	χ2	P(<χ2)
[Ni ii]	6	6.669e-21	4.896	0.571		4.619e-22	8.121	0.850		−4.041e-22	1.126e-25	4.060	0.602
[Ar ii]	6	2.635e-20	39.320	1.000		1.740e-21	109.060	1.000		−4.537e-21	8.266e-25	33.909	1.000
H i 6-5 and 8-6 ?	6	1.229e-20	3.427	0.366		7.400e-22	3.533	0.382		−6.394e-22	1.882e-25	2.722	0.395
[Ne vi] ?	5	8.163e-21	0.283	0.009		5.220e-22	0.818	0.064		−8.842e-22	1.880e-25	0.203	0.023
[Ne ii]	7	5.085e-20	79.567	1.000		3.060e-21	73.141	1.000		−1.700e-21	6.501e-25	35.054	1.000
[O iv]+[Fe ii]	6	6.886e-20	37.651	1.000		4.660e-21	11.664	0.960		3.246e-21	1.862e-25	11.360	0.977
[S iii]	4	1.587e-19	608.003	1.000		9.161e-21	472.367	1.000		3.072e-20	−2.996e-24	450.078	1.000
[Si ii]	6	2.137e-19	14.594	0.988		1.317e-20	52.898	1.000		−2.361e-20	4.970e-24	10.493	0.967

Note. A in (W m⁻²/Jy), B in (W m⁻²), α in (W m⁻²/day), β in (W m⁻²).

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The formal results of the fitting procedures indicate that the evolution of the line intensities are usually consistent with a constant value, although in several cases uncertainties are large enough that the intensities are also consistent with the models which increase over time. The only lines to exhibit significantly increasing intensities are the H i 7-6 and the broad [Fe ii] lines. The rising intensities correlated with the continuum may be associated from the increasing volume of the shocked portion of the ER. The line intensities that are flat (or possibly declining) may be dominated by emission for unshocked regions of the ER, corresponding to the narrow components seen in the optical emission lines (Gröningsson et al. 2008b).

The evolution of the IR emission lines has also been compared to the evolution of the Hα line components from the shocked and unshocked (pre-shock) portions of the ER (Fransson et al. 2015). Figure 15 shows the rising, then cresting, Hα intensity of the shocked material of the ER compared to scaled versions of the IR lines that appear to show similar trends. The other IR lines seems to show relatively little evolution and appear to be more consistent with the emission from the unshocked portion of the ER (Figure 16).

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The ratio of the [Ne v] lines is the only good density diagnostic these data provide since other useful line pairs ([S iii], [Ne iii], [Ar iii], [Ar v]) are either corrupted by the bright background or absent from the SN spectrum at this sensitivity. The ratio of the [Ne v] line intensities at the first epoch is ${R}_{(14.3/24.3)}=1.5\pm 0.6$, which implies an electron density of ∼3 × 10³ cm⁻³ (for T_e ∼ 10⁴ K) (see Figure 17). However, for all subsequent observations the ratio has a mean value of ${R}_{(14.3/24.3)}=0.63\pm 0.05$ which lies below the low density limit (n_e < 10³ cm⁻³) unless the gas temperature is ${T}_{e}\quad \lt$ 1300 K.

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Similarly low density and temperature are inferred from the ratio of Hα/H(7-6) ≈ 129, assuming case B recombination (Hummer & Storey 1987) (Figure 18). This observed ratio is the scale factor between the H(7-6) 12.37 μm light curve as measured at high resolution with the IRS, and the Hα light curve of the shocked gas measured with HST (Fransson et al. 2015). The possible blend of the H(6-5) and H(8-6) lines observed near 7.48 μm in the low resolution IRS spectrum suggests slightly higher densities and/or temperatures, but this measurement is less reliable.

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Dwek et al. (2008) had concluded that the collisionally heated dust must reside in gas with T_e ≈ 3.5 × 10⁶ K and n_e ≈ (0.3–1) × 10⁴ cm⁻³. This is denser, hotter, and at higher pressure than the line emitting regions, suggesting that the observed IR line emission does not arise for the same part of the ER as the dust continuum emission. To reach equilibrium temperatures of T ≈ 180 K for silicate grains, collisional heating at the low gas temperatures implied by the emission line ratios would require densities of n_e ≳ 10⁶ cm⁻³ (Bouchet et al. 2006; Dwek et al. 2008). Such high densities are ruled out by the observed line ratios (Figures 17 and 18).

With the long interval of observations now available, it has become clear that the SN emission at 3.6 and 4.5 μm has peaked and is now in decline. This suggests, that, as for the optical emission (Fransson et al. 2015), the SN blast wave has sent shocks through the bulk of the material in the ER, and the emission of any remaining swept up material is insufficient to make up for the fading of the ER material that has already been shocked. Despite the likelihood that the emitting dust is collisionally heated in the hot gas, it is also clear that 3.6 and 4.5 μm emission is not tracking the X-ray emission. If the X-ray emission is reaching a peak, it is >1000 days after the IR peak. The simplest explanation for this evolving IRX ratio is that the dust is being destroyed on timescales of a few years, ${\tau }_{{\rm{sput}}}\approx {10}^{6}a(\mu {\rm{m}})/{n}_{{\rm{H}}}({{\rm{cm}}}^{-3})$ year (Draine & Salpeter 1979) which is shorter than the cooling time for the X-ray emitting gas: ∼5–30 year (Dwek et al. 2010). The apparently short sputtering timescale and high dust temperature for the grains the produce the 3.6 and 4.5 μm emission are most easily achieved by relatively small grains compared to those that produce the 24 μm emission. However, the exact sizes depend on the unknown composition of the dust and on more precise estimates of the sputtering timescale (see Dwek et al. 2010). Bocchio et al. (2012) show that very small amorphous hydrocarbons and polycyclic aromatic hydrocarbons (PAHs) have even shorter lifetimes in a hot gas than classical sputtering calculations predict. Although the spectra of SN 1987A show no indications of the PAH emission features, the physical mechanisms they consider may also act to decrease the lifetimes of small grains of other compositions.

The 5–30 μm spectrum had been used to estimate the mass of warm dust in the ER as 1.2 × 10⁻⁶ M_⊙ at day 7554 (Dwek et al. 2010). Because there was little change in the dust temperature, this mass scales linearly with the evolving IR flux density. The spectral fits in Dwek et al. (2010, Figures 4 and 5) suggest that the dust responsible for the 3.6 and 4.5 μm emission is ∼2 times warmer and ∼100 times fainter (in the Rayleigh–Jeans tail). Therefore the mass of this hot dust is only ∼0.5% of the total dust in the ER, with a large uncertainty depending on the actual emissivity of these grains of uncertain composition. (If the hot dust component is stochastically heated rather than at equilibrium temperatures, then its total dust mass would be larger because only a small fraction of the dust would be contributing to the short wavelength emission.) The evident destruction of this hot dust component is not necessarily indicative of significant reduction in the total dust mass of the ER.

The IRX evolution model of Equation (6), as shown in Figure 4, indicates a correlation between wavelength and t₀. The parameter t₀ is the extrapolated time at which the IR emission began the trend of $S({IR},{t}^{\prime })\sim S(X,{t}^{\prime })/{t}^{\prime }$ where ${t}^{\prime }=t-{t}_{0}$. It is unclear if this trend really does extrapolate back to t₀, but if so, we can suggest two potential reasons for the correlation of wavelength and t₀.

The first possibility is that the UV flash from the SN has preferentially evaporated small dust grains, creating a gradient in the size distribution of dust grains as a function of radius as described by Fischera et al. (2002). In this case, the initial (near day 3200) IR emission from the interaction of the blast wave with the ER should be dominated by relatively large grains. These grains do not get heated to very high temperatures, and may thus produce strong 24 μm emission but little emission at <10 μm. As the blast wave expands further into the ring, near day 4500 it may begin encountering smaller grains that were sufficiently distant or shielded from the SN to have escaped evaporation. These smaller grains would be heated to higher temperatures capable of producing the observed emission and IRX trends at 3.6 and 4.5 μm. If this scenario is valid it would suggest that the small grains emitting at the shortest wavelengths are not carbonaceous. Fischera et al. (2002) show that the UV flash is significantly less effective at evaporating graphite grains than silicate or iron grains. Therefore, small carbonaceous grains would be encountered at earlier times than large (or any) silicate grains.

The second possibility is that grain–grain collisions in the post-shock gas are fragmenting larger grains into smaller ones. The result t₀ = 3251 at 24 μm would be interpreted as there having been sufficient time for all of the largest grains to be destroyed in the post-shock region. The result t₀ = 4523 at 3.6 μm would indicate that smaller grains are present for an additional ∼3.5 years after the destruction of the largest grains. However, grain–grain collisions are generally most effective in the cases of much slower shocks (e.g., 10 s of km s⁻¹) propagating into media at least as dense as the ER. In these higher velocity shocks, thermal and non-thermal sputtering would be the dominant destruction mechanism (Dwek et al. 2010), and small grains should be destroyed more rapidly than the larger grains.

The observed IR emission lines are mostly collisionally excited fine structure transitions in the ground state of various ions. The lines identified are typical of those seen in other supernova remnants (Arendt et al. 1999; Oliva et al. 1999; Temim et al. 2006; Neufeld et al. 2007; Smith et al. 2009; Andersen et al. 2011; Ghavamian et al. 2012; Sankrit et al. 2014). The accuracy of the measurement of the line strengths is limited by the modest S/N of some lines, and the presence of strong (sometimes dominant) and structured background emission from the ISM in some of the lines.

The evolution of the IR emission lines is puzzling. Many of the emission lines seem to show little evolution, consistent with the minimal evolution of optical emission lines from the unshocked portion of the ER (Figure 16). However, these lines include highly ionized species such as Ne v and O iv, which have much higher ionization potentials than other lines attributed to the unshocked portion of the ER.

Another puzzle is presented by the higher velocity components of the Fe ii and Si ii lines. These lines may originate in gas phase material, but they may also represent material that has been eroded from dust grains. The high velocities suggest shocked material, and indeed these lines do correlate with the rising intensity of the shocked Hα emission, as well as the increasing 24 μm (dust) flux density. The velocity structures of these two lines is somewhat mysterious. It is not clear why the Si ii should show distinct high and low velocity components, whereas the Fe ii line seems to show a simple broad component which would be expected for a spherical distribution of material. The lines may indicate the presence an expanding fossil remnant from the SN precursor as in η Carinae. The Fe lines may be from a more symmetrical fossil remnant than the Si lines. η Car has undergone multiple eruptions (at least 3 in the last ∼200 years), not all producing the same geometry (see Smith & Gehrz 1998, 2000). Alternatively, it may be that these lines originate in the SN ejecta, rather than the ER or other circumstellar structures, in which case, the velocity structures of the Si ii lines may reflect uneven distribution of Si in the ejecta. The presence of the redshifted component would indicate that the ejecta are not (uniformly) optically thick at ∼35 μm.

The final puzzle presented by the emission lines is that both the H recombination lines and the Ne v lines suggest low densities (n_e ≲ 10³ cm⁻³) and low temperatures (T_e ≲ 2500 K). The densities are much lower than estimated for the ER from pre-interaction observations (e.g., Plait et al. 1995) or analysis of the earliest hot spot (Michael et al. 2000; Pun et al. 2002). However, Gröningsson et al. (2008b) find indications of densities nearly this low for the narrow line emission of the unshocked material, and Mattila et al. (2010) invoke a 10² cm⁻³ component distributed over a wider area to account for the evolution of high-ionization lines at late times (days 5000–7500). So the densities suggest that the H and Ne emission lines may arise from the regional outside of the ER, perhaps associated with multiple ejections from the precursor. However implied the low gas temperature remains at odds with prior analyses, and seems unlikely since the recombination rate for Ne v is several times higher than the cooling rate (assuming solar abundances; Osterbrock 1989; Draine 2011).