DISENTANGLING THE ORIGIN AND HEATING MECHANISM OF SUPERNOVA DUST: LATE-TIME SPITZER SPECTROSCOPY OF THE TYPE IIn SN 2005ip

As part of PID 50256, the Spitzer Infrared Spectrograph (IRS; Houck et al. 2004) obtained one mid-infrared spectrum on 2008 June 3 (936 days post-discovery) with the Short–Low module (R ∼ 60–120, 5.2–14 μm). The Spitzer Infrared Array Camera (IRAC; Fazio et al. 2004) followed the IRS observations with images of the supernova and host galaxy in all four bands on 2008 June 10. Table 1 lists the observational details.

2.1.1. IRAC

Spitzer collected 5 min IRAC exposures consisting of ten 30 s integrations. Pipeline-reduced and calibrated (BCD) images were taken from the Spitzer archive, and combined into single frames with enhanced pixel resolution of 075 pixel⁻¹ using the MOPEX software package provided by the Spitzer Science Center. Figure 1 shows a post-BCD 3.5 μm IRAC image with the IRS map overlay. Since the supernova lies near the center of NGC 2906, the rapidly varying background of the host galaxy complicates aperture photometry. Instead, a number of unsaturated, linear, and isolated (e.g., no other sources in the wings) stars were used to build an empirical point-spread function (PSF) for each channel, each of which was used to measure the brightness of the supernova. In each channel, the residuals from subtracting the best-fit PSF were small compared with the predicted uncertainty that the photometry task allstar provides, which factors in Poisson noise along with flat-field and profile-fitting errors as well as read noise. PSF-fit measurements of field stars in the frame were consistent with aperture photometry to within 5% in all channels.

Zoom In Zoom Out Reset image size

2.1.2. IRS

The Spitzer/IRS mapped the position of SN 2005ip, with 12 cycles of 5 exposures, stepped 27 perpendicular to the 37 wide slit. The target spectrum was extracted and calibrated from the central pointing observation using the SMART data analysis software (Higdon et al. 2004), with bad pixels identified by IRSCLEAN. Subtracting off-order observations removed sky and zodiacal background. All data collection events for a given order were then median combined and the spectra extracted using the advanced optimal extraction routine AdOpt (Lebouteiller et al. 2009). The AdOpt tool provides the powerful ability to simultaneously fit multiple sources using a super-sampled PSF plus a complex background at each row. This feature disentangles the supernova emission from that of the galaxy nucleus as well as removes background emission of the galaxy's spiral arms (Figure 2).

Zoom In Zoom Out Reset image size

Figure 3 shows the resulting IRS spectrum redshifted to account for the radial velocity of the galaxy (2140 km s⁻¹ + V_LSR), along with the IRAC photometry. Continuum emission peaking at around 3–4 μm tends to dominate the spectrum. Few, if any, emission lines are apparent.

Zoom In Zoom Out Reset image size

TripleSpec, a 0.9–2.5 μm, R = 3000 spectrograph operating at APO (Wilson et al. 2004; Herter et al. 2008), obtained a spectrum on day 862 post-discovery. Forty minutes of on-source integration consisted of eight independent 5 min exposures nodding between two different slit positions. We extract the spectra with a modified version of the IDL-based SpexTool (Cushing et al. 2004). The underlying galactic arm and sky are approximated in SpexTool by a polynomial fit and subtracted from the supernova. TripleSpec observations on day 1243 post-discovery suggest little evolution occurred between the two epochs. We therefore create a single spectrum from the near- and mid-infrared spectra (see Figure 3).

Assuming only thermal emission, the combined near- and mid-infrared spectra provide a strong constraint on the dust mass, temperature, and, thereby, the luminosity. The luminosity of a single spherical dust particle of radius, a, and temperature, T_d, is given as

$$\begin{equation} L_d (\lambda) = 4 \pi a^2 (\pi B_\nu (T_d) Q_\nu (a)), \end{equation} \tag{ 1 }$$

where B_ν(T_d) is the Planck blackbody function and Q_ν(a) is the emission efficiency. Fox et al. (2009) and Smith et al. (2009b) provide two pieces of evidence for optically thin dust: (1) $\tau \approx \frac{L_{\rm NIR}}{L_{\rm NIR} + L_{\rm OPT}} \approx 0.5$ and (2) the relatively high transmission of X-rays responsible for ionizing the unshocked circumstellar medium. For optically thin dust with mass, M_d, at a distance, d, from the observer, thermally emitting at a single equilibrium temperature, the total flux can be written as

$$\begin{equation} F_\nu = \frac{M_{d} B_\nu (T_d) \kappa _\nu (a)}{d^2}, \end{equation} \tag{ 2 }$$

where κ_ν(a), the dust mass absorption coefficient, is

$$\begin{equation} \kappa _\nu (a) = \Big (\frac{3}{4 \pi \rho a^3}\Big) (\pi a^2 Q_\nu (a)), \end{equation} \tag{ 3 }$$

for a dust bulk (volume) density ρ.

Given simple dust populations of a single size composed entirely of either silicate or graphite, Figure 4 plots the dust absorption coefficient and emission efficiency for several grain sizes of each composition, which is derived from Mie theory. For both the graphite and silicate models, Figure 5 shows the resulting best fits of Equation (2) to the observed spectrum (Figure 3) using IDL's MPFIT routine. The lack of an emission feature at ∼9 μm immediately rules out any silicate grain contribution. We therefore use only graphite models throughout the rest of this paper.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We fit a multi-component model to the combined spectrum, where each component assumes a single dust mass, M_d, at a single temperature, T_d, composed of graphite of a single grain size. The dust mass, temperature, and grain size of each component are all free parameters. Figure 5 shows the optimal fit, which consists of two dominant components: a "hot" (∼800 K), near-infrared (HNI) and a "warm" (∼400 K), mid-infrared (WMI) component.

Adding additional components to the fit tends to yield relatively small dust masses that do not improve χ² by more than a couple of percent. This result has two implications. First, two unique dust components exist, as opposed to a single dust component with a continuous temperature distribution. Second, a hotter (>1000 K) third component, if it exists, does not significantly contaminate the near-infrared fits at these late times. (At early times, a hot photospheric component is expected and is, in fact, observed to dominate the early J-band data in Fox et al. 2009.) We therefore only consider two-component fits throughout the rest of this article.

Table 2 lists the dust masses, temperatures, and luminosities associated with various grain size combinations but, overall, grain size has little consequence on either these parameter values or the resulting goodness of fit (χ²). The only size-dependent variable in Equation (2) is κ, but Figure 4 shows the dust opacity coefficient for graphite is independent of grain radius at infrared wavelengths (>1 μm) for grain sizes <1 μm, which is typical for most grains. Other methods (discussed in Sections 3.2 and 3.3), however, can constrain the grain size.

Figure 6 plots the luminosities of both the HNI and WMI components on day 936 for 0.1 μm grains, along with the time-series evolution of SN 2005ip at near-infrared (Fox et al. 2009) and visible luminosities (Smith et al. 2009b). Smith et al. (2009b) show that as the photospheric component drops off over the first ∼100 days, an optical luminosity plateau, L_plateau, appears and continues throughout the extent of the observations. This plateau arises from radiation generated by continuous shock interaction with the dense circumstellar medium, as opposed to an optical light echo powered by the peak supernova luminosity.

Zoom In Zoom Out Reset image size

Lacking mid-infrared observations, the data obtained prior to day 936 cannot distinguish between the multiple dust components. The HNI component in Figure 5, however, dominates the near-infrared observations (i.e., little contribution from the WMI component at near-infrared wavelengths), which plateau throughout the extent of the observations (see Figure 6). In fact, additional epochs of TripleSpec spectra obtained on days 862 and 895 show little evidence for spectral evolution at later times. Given these observations, we assume throughout this paper that all near-infrared results predominantly represent the HNI component evolution. For both the HNI and WMI components, the thermal emission arises from warm dust. Disentangling the composition, origin, and heating mechanism of these dust components, however, requires a detailed analysis of potential heating mechanisms.

For both shock heating and an infrared echo, the blackbody and shock radii respectively serve as useful reference points. The blackbody radius, given as $r_{{\rm bb}} = \big (\frac{L_{{\rm bb}}}{4 \pi \sigma T_{{\rm bb}}^4}\big)^\frac{1}{2}$ where σ is Stefan–Boltzmann's constant, defines the minimum shell size of an observed dust component. In the case of SN 2005ip, blackbody fits (Q = 1) of the combined spectrum on day 936 in Figure 5 yields blackbody radii of r_bb(WMI)≈ 4.8 × 10¹⁶ cm(0.048 lt-yr) and r_bb(HNI)≈ 7.7 × 10¹⁵ cm(0.0077 lt-yr).

The shock radius, given as r_s = v_st for a constant velocity, v_s, defines the maximum radius that the forward shock can travel in a time, t. The shock velocity can be derived from the optical emission line widths. For SN 2005ip, Smith et al. (2009b) observe broad emission lines corresponding to radial velocities of ∼15,000 km s⁻¹ (0.05c) through ∼900 days post-discovery, yielding a maximum shock radius on day 936 of r_s1 ≈ 1.25 × 10¹⁷ cm (0.125 lt-yr). At the same time, the intermediate-width lines correspond to slower shock velocities of ∼1000 km s⁻¹ (0.003c) through ∼900 days post-discovery. Chugai & Danziger (1994) propose that two unique shock velocities can coexist if the progenitor's wind is clumpy or asymmetric, as opposed to homogeneous and spherical. A relatively rarefied wind allows uninhibited shocks to maintain the observed high velocities, while a much slower shock propagates through the denser regions.

Since a shock will typically destroy any pre-existing dust, understanding the shock propagation is essential for modeling the evolution of any late-time infrared emission. If, for example, the denser regions are concentrated in a homogeneous equatorial disk, only the slower shocks need be considered as they propagate contiguously throughout the disk. Alternatively, if the denser regions are concentrated in clumps, the situation is more complicated. The fastest shocks will reach the clumps first, at which point the shock velocity drops. The average shock velocity is a function of the clump filling factor and distribution. Since the distribution of the dense regions is not well known, we consider a second shock radius for which we adopt a more modest shock velocity of v_s ∼ 5000 km s⁻¹, which is consistent with the intermediate component of many Type IIn supernovae (e.g., Salamanca et al. 2002; Smith et al. 2008a, 2010; Steele et al. 2008). This velocity yields an upper limit on a second shock radius on day 936 of r_s2 ≈ 4 × 10¹⁶ cm (0.04 lt-yr).

Both the HNI and WMI shells are optically thin, thereby confirming the assumptions presented in Section 2.3. The optical depth of each shell can be written as

$$\begin{equation} \tau = \frac{M_d}{4 \pi r^2} \kappa _{\rm avg}, \end{equation} \tag{ 4 }$$

where κ_avg = 435 cm² g⁻¹ is the absorption coefficient for graphite averaged over 1–15 μm. For 0.1 μm grains, Table 2 shows M_d(HNI) ≈ 5.2 × 10⁻⁴ M_☉ and M_d(WMI) ≈ 4.3 × 10⁻² M_☉. Given the minimum radii, r > r_bb(HNI)≈ 7.7 × 10¹⁵ cm(0.0077 lt-yr) and r > r_bb(WMI)≈ 4.8 × 10¹⁶ cm(0.048 lt-yr), Equation (4) yields τ< 0.6 and 1.3, respectively.

In the shock heating scenario, hot electrons in the post-shock environment collisionally heat pre-existing dust grains. Dwek (1987) and Dwek et al. (2008) provide a detailed description of this process for silicate dust grains and present post-shock equilibrium dust temperatures as a function of post-shock electron density, n_e, and temperature, T_e. Figure 7 presents a similar analysis for graphite grains.

Zoom In Zoom Out Reset image size

For shock heating to occur, the forward shock must have sufficient time to reach the pre-existing dust grains. As discussed in further detail in Section 3.3, the peak supernova luminosity of SN 2005ip (L_peak ≈ 10⁹ L_☉) vaporizes all dust grains out to a radius, r_evap ≈ 10¹⁶ cm (0.01 lt-yr). For the fastest observed shock velocities (v_s∼ 15,000 km s⁻¹), a shock would require ∼70 days to reach the evaporation radius, which is consistent with the earliest observations of the HNI component (see Figure 6). The earliest observation of the WMI component does not occur until the Spitzer observations on day 936, by which point even the slower shocks would have crossed the evaporation radius.

An independent calculation of the shocked dust mass provides a useful consistency check. Assuming the hot, post-shocked gas heats the dust shell, estimates of the total gas mass will determine the dust-to-gas mass ratio. The upper limit on the volume of the emitting shell is given as

$$\begin{equation} V_{\rm shell} = 4 \pi r_{\rm s}^2 \Delta r_{\rm s}, \end{equation} \tag{ 5 }$$

where r_s is the radius of the shock with velocity, v_s, at an age, t, and Δr_s is the shell thickness defined by the distance traveled by the shock over the grain sputtering lifetime, τ_sputt,

$$\begin{equation} \Delta r_{\rm s} = \frac{1}{4}v_{\rm s} \tau _{\rm sputt}, \end{equation} \tag{ 6 }$$

provided that τ_sputt < (t, τ_cool), where τ_cool is the radiative cooling timescale. The factor of $\frac{1}{4}$ comes from the shock jump conditions. For typical post-shock gas temperatures (>10⁶ K), Dwek & Arendt (1992) give the sputtering lifetime for a grain size, a, and gas density, n_g, as

$$\begin{equation} \tau _{\rm sputt}\, ({\rm yr}) \approx 10^6 \frac{a(\mbox{$\mu $m})}{n_g({\rm cm^{-3}})}. \end{equation} \tag{ 7 }$$

The total gas mass of the emitting dust shell is therefore

$$\begin{equation} M_{\rm g} = n_g m_{\rm H} V_{\rm shell}. \end{equation} \tag{ 8 }$$

Combining Equations (5)–(8) yields

$$\begin{equation} M_{\rm g} ({M_{\odot }}) \approx 8.3 \times 10^{-5} \bigg (\frac{v_{\rm s}}{{\rm 1000\; \hbox{km s$^{-1}$}}}\bigg)^3 \bigg (\frac{t}{{\rm yr}}\bigg)^2 \bigg (\frac{a}{{\rm \mbox{$\mu $m}}}\bigg), \end{equation} \tag{ 9 }$$

which reveals that the mass of the shocked gas is independent of the grain density.

Assuming a dust-to-gas mass ratio expected in the H-rich envelope of a massive star, $Z_d = \frac{M_d}{M_g} \approx 0.01$, gives the expected dust mass. For the maximum observed shock velocity, v_s< 15,000 km s⁻¹, and age, t = 936 days, Table 3 compares the predicted dust mass to the observed mass listed in Table 2. Assuming shock heating is also responsible for the HNI component at early times, Table 4 compares the predicted HNI dust mass at an age t = 70 days to the observed mass listed in Table 2. Although no measurement of the dust mass exists on day ∼70, the relatively constant HNI luminosity (see Figure 6) and temperature (see Fox et al. 2009) suggest a relatively constant HNI mass throughout the extent of the observations.

For both the WMI component on day 936 and the HNI component on day 70, only large grains (a > 0.3 μm) can reproduce the observed dust masses. These grain radii are large compared with typical grain sizes observed in supernova shocks (Dwek et al. 2008). Furthermore, upper limits were assumed for both the shock velocity (see Section 3.1) and dust-to-gas mass ratio (Williams et al. 2006). Lower values would require even larger grain sizes to reproduce the observed dust masses. These results likely rule out shock heating.

For an infrared echo scenario, the supernova luminosity heats a shell of dust at a radius, r, to a peak temperature, T_d. This outer shell may be pre-existing at the time of the supernova explosion or it may form when the peak supernova luminosity creates a vaporization cavity. In either case, light travel time effects cause the thermal radiation from the dust grains to reach the observer over an extended period of time, thereby forming an "IR echo" (Bode & Evans 1980; Dwek 1983). The infrared luminosity plateau occurs on year long timescales, corresponding to the light travel time across the inner edge of the dust shell. As dust cools from the peak temperature, it will contribute flux at longer wavelengths. As noted in Section 2.3, however, the SN 2005ip spectrum is best fitted by two components, as opposed to a continuous temperature distribution. Therefore, this analysis assumes a simple light echo model that is dominated by flux from only the warmest dust with a single temperature, T_d.

The equilibrium dust temperature is set by balancing the energy absorbed and emitted by the dust grains,

$$\begin{equation} L_{\rm abs} = L_{\rm rad}, \end{equation} \tag{ 10 }$$

where, for a single dust grain,

$$\begin{eqnarray} L_{\rm abs} & = & 4 \pi r_{\rm SN}^2 \frac{\pi a^2}{4 \pi r^2} \int {\pi B_\nu (T_{\rm SN}) Q_{\rm abs}(\nu) d\nu } \nonumber \\ & = & \frac{L_{\rm bol}}{\sigma T_{\rm SN}^4} \frac{\pi a^2}{4 r^2} \int {B_\nu (T_{\rm SN}) Q_{\rm abs}(\nu) d\nu } \end{eqnarray} \tag{ 11 }$$

and

$$\begin{eqnarray} L_{\rm rad} & = & 4 \pi a^2 \int {\pi B_\nu (T_d) Q_{\rm abs}(\nu) d\nu } \nonumber \\ & = & \frac{16}{3} \pi \rho a^3 \int {B_\nu (T_d) \kappa (\nu) d\nu }, \end{eqnarray} \tag{ 12 }$$

where r_SN is the effective supernova emitting radius, L_bol is the UV–optical luminosity, and T_SN is the effective supernova blackbody temperature. L_bol follows from Equations (10)–(12):

$$\begin{equation} L_{\rm bol} = \frac{64}{3} \rho a r^2 \sigma T_{\rm SN}^4 \frac{\int {B_\nu (T_d) \kappa (\nu) d\nu }}{\int {B_\nu (T_{\rm SN}) Q_{\rm abs}(\nu) d\nu }}. \end{equation} \tag{ 13 }$$

L_bol depends on the grain radius because although the dust opacity coefficient, κ, in Figure 4 is independent of grain radius for thermal emission at longer wavelengths, it does depend on grain radius for absorption at shorter wavelengths (e.g., UV and optical).

Using Equation (13), Figure 8 plots contours of the shell size, r, as a function of both luminosity, L_bol, and observed dust temperature, T_d. The luminosity is treated as a central point source, assuming the emitting region is internal to a spherically symmetric dust shell. Several grain sizes are considered for dust with a graphite composition. Although the calculation assumes T_SN≈ 10,000 K, the result is fairly insensitive to this choice. The vertical lines show the observed graphite dust temperatures listed in Table 2 and the approximate vaporization temperature of graphite dust, T_evap ≈ 2000 K. The horizontal lines show both the observed peak, L_peak, and late-time optical/infrared plateau, L_plateau, luminosities from Figure 6.

Zoom In Zoom Out Reset image size

The shaded regions highlight the dust shell radii allowed by the constraints. The shock radius sets the lower limit as any dust within this radius would be independently heated or destroyed by the forward shock (see Section 3.2 above). (For the WMI component, the blackbody radius, r_bb(WMI), actually sets the minimum radius, as described in Section 3.1.) Both the fast, r_s1, and slow, r_s2, shocks described in Section 3.1 are considered, distinguished by the hashed region. The near-infrared plateau timescale sets the upper limit. Figure 6 shows the plateau extends for at least ∼2.6 years and still shows little sign of declining. The current upper limit is therefore set by a "plateau radius," r_p, of 1.3 light years, although the final upper limit will only be determined once the light-curve plateau begins to decline. Should the plateau extend even longer than 2.6 years the larger implied radius only makes a light echo less likely.

Three possible light echo scenarios exist.

• 1.  
  In the first scenario, a sphere of dust completely encompasses the progenitor at the time of the explosion. The peak luminosity vaporizes all dust within a radius, r_evap, and warms the inside of the remaining dust shell to nearly the vaporization temperature (T_evap ≈ 2000 K). Figure 8(a) shows that the observed peak optical luminosity, L_peak, yields a vaporization radius of r_evap ∼ 0.013 lt-yr for a = 0.01 μm graphite grains and an even smaller radius for larger grains (see Figures 8(b) and (c)). These small evaporation radii, however, are inconsistent with the observations as a shell of this size cannot produce an infrared echo on three-year timescales. Furthermore, these evaporation radii are smaller than both shock radii. Even if the actual peak luminosity were a factor of 5 larger than observed (L_est ∼ 5 × 10⁹ L_☉), the vaporization radius would be insufficient to account for the observations. We therefore rule out this scenario for both the HNI and WMI components.
• 2.  
  The dust shell inner limit need not lie exactly at the vaporization radius. If the progenitor underwent an eruption many years before the supernova, the dust shell may lie at larger radii. In this second scenario, the peak luminosity, L_peak, heats the dust shell inner radius to only the observed temperature. The light echo duration therefore defines the minimum cavity radius (i.e., r_p = 1.3 lt-yr). Figure 8 shows that a minimum peak luminosity of L_bol > 5 × 10¹⁰ L_☉ is required to heat a dust shell of 1.3 light years in radius to the observed WMI temperature, while a minimum peak luminosity of L_bol > 5 × 10¹¹ L_☉ is required for the HNI component. A larger shell radius requires even larger peak luminosities.These required peak luminosities are significantly larger than the observed peak luminosity. The true peak luminosity of SN 2005ip, however, is not well constrained. The earliest R-band photometry was obtained 14 days post-discovery, and the discovery occurred a few weeks following the actual explosion so that the peak luminosity was likely several times larger than the observed early-time R-band luminosity (L_est ∼ 5 × 10⁹ L_☉). Still, while a significant amount of optical absorption might be expected by large amounts of pre-existing dust, significant reddening was not observed (Smith et al. 2009b) and a peak luminosity >10¹⁰ L_☉ is unlikely from this extrapolation.The shock breakout in the minutes to hours following the supernova explosion may reach peak luminosities >10¹¹ L_☉ (Soderberg et al. 2008; Rest et al. 2009), but no such breakout was observed for SN 2005ip. A peak luminosity >10¹¹ L_☉ would have made SN 2005ip one of the most luminous core-collapse events ever observed (Quimby et al. 2007; Rest et al. 2009), but Figure 11 of Rest et al. (2009) suggests SN 2005ip is nearly an order of magnitude fainter than SNe 2006gy, 2008es, 2005ap, and 2003ma, especially at early times. Furthermore, optical emission from the late-time circumstellar interaction successfully accounts for the observed dust temperatures (see below). These reasons rule out a light echo driven by the peak supernova luminosity for both the HNI and WMI components.
• 3.  
  A final scenario considers a pre-existing dust shell similar to scenario 2 above, but in this case the shell's inner radius is located at an intermediate radius between the shock and plateau radii (as defined on day 936). The late-time optical emission, L_plateau, continuously heats the dust shell to the observed temperature. This scenario is not so much a traditional infrared echo as it is a reprocessing of the optical emission by the dust. (Some authors refer to this as a circumstellar shock echo (Gerardy et al. 2002).) If the circumstellar interaction occurs on a timescale greater than the light travel time across the dust shell, the shell radius does not set the infrared plateau length. The observed flux therefore accounts for the entire shell.

Figures 8(a) and (b) show that for both a = 0.01 and 0.1 μm graphite grains, L_plateau can heat a dust shell of radius r ≈ 0.01 lt-yr to T_HNI and a shell of radius r ≈ 0.05 lt-yr to T_WMI. For a = 0.5 μm graphite grains, Figure 8(c) shows that L_plateau can only heat a dust shell of radius r < 0.005 lt-yr to T_HNI and a shell of radius r < 0.04 lt-yr to T_WMI. In this scenario, both the fast (r_s1 = 0.125 lt-yr) and slow (r_s2 = 0.042 lt-yr) shock radii are larger than the HNI shell radii by day 936, ruling out a light echo of this sort for the HNI component. The same is true for the WMI shell composed of larger grains (a > 0.5 μm). In the case of the WMI shell composed of smaller grains (a < 0.1 μm), however, the slower shock has not yet reached the shell radius (r ≈ 0.05 lt-yr). Not only is this scenario possible for the WMI component, but the radius is consistent with the WMI blackbody radius (r_bb (WMI) = 0.048 lt-yr). Furthermore, the grain sizes are typical of those observed in other supernova circumstellar environments (Dwek et al. 2008).

Predictions for the light-curve evolution can be made from this model. Dust that remains at radii beyond the slower shock radius, r_s2, will continue to radiate and contribute to the light echo plateau. Although the exact distribution of these dense, dusty regions is not well known, this scenario suggests they must be distributed in such a way that the fastest shocks do not interact with the dust. As described in Section 3.1, these dense regions may be concentrated in either an equatorial disk or clumps. The clumps must have a large filling factor if the fastest shocks are not to interact with a significant portion of the dust. As the slower shocks continue to expand, however, they will ultimately destroy the dust. Assuming the dust lies at a radius consistent with 0.1 μm grains (see parameters in Table 2), the WMI flux will begin to decrease at $t \approx \frac{r ({\rm WMI})}{v_s} \sim 2775$ days post-discovery and continue to decrease as a function of the emitting shock radius and the dust distribution. While this scenario is entirely consistent with the WMI observations at the current time, mid-infrared observations at later epochs can reveal the accuracy of this model's predictions.

The above HNI component analysis rules out the possibility of both pre-existing dust scenarios (i.e., shock heating or infrared echo). Only condensation models (i.e., in the ejecta or cool, dense shell) remain as viable scenarios for explaining the origin of the HNI component. Smith et al. (2009b) confirm new dust formation via extinction in the broad (∼15,000 km s⁻¹) Hα wings between days ∼60–170 and in the intermediate (∼2000 km s⁻¹) He i wings at days >413, but the location of this new dust remains ambiguous. The extinction in the broad and intermediate components suggests new dust in the fast ejecta at early times and post-shock cool, dense shell at later times, respectively.

To form dust at the high ejecta velocities, however, is difficult due to the lack of heavy metals traveling at these speeds. If the dust formed in the cool, dense shell at early times, as suggested in the case of SN 2006jc (Mattila et al. 2008), this would explain the attenuation of the broad Hα line observed by Smith et al. (2009b) without having to invoke dust formation at high velocities, but would fail to explain the lack of observed intermediate width He i lines produced by the circumstellar interaction. Smith et al. (2009b) propose one alternative scenario in which the dust may form in the post-shock gas of individual clumps, which then become incorporated into the expanding fast ejecta when a clump is eventually destroyed. This scenario, however, requires several assumptions, most of which rely on unknown clumping properties. While the available observations limit the ability to isolate the precise region of dust formation, the relatively flat near-infrared flux in Figure 6 suggests a majority of the dust contributing to the HNI flux must have formed at early epochs.

Newly formed dust cannot reproduce the observed HNI luminosity plateau solely by cooling from condensation to the observed temperature T_HNI ≈ 800 K. Given an average energy per particle = C_gΔT_d for the specific heat for graphite C_g (given by Draine & Li 2001) and ΔT ≈ 1200 K, an unsustainable mass condensation rate of $\dot{M} = L_{\rm HNI} / \epsilon \approx 100$ M_☉ day⁻¹ would be necessary to reproduce the observed flux (see a more detailed explanation of this argument for the case of SN 2006jc in Fox et al. 2009).

Instead, an alternative heating mechanism must power the thermal emission from this newly formed dust. Figure 6 shows that radioactive heating is insufficient to power the late-time near-infrared emission. While heating by the reverse shock is possible, a similar analysis as performed in Section 3.2 suggests this scenario is unlikely because only large grains (a > 0.5 μm) can reproduce the observed flux. More likely, the optical luminosity generated from the forward shock interaction continuously heats the newly condensed dust in the same way that it heats the WMI component discussed in Section 3.3. Unlike the infrared echo scenario, however, the newly formed dust exists interior to the forward shock radius and the shock emission cannot be treated as a central point source.

A multi-component dust model for SN 2005ip now begins to emerge, composed of both an inner, "hot" (∼800 K), near-infrared (HNI) and an outer, "warm" (∼400 K), mid-infrared (WMI) component. Newly formed dust in either the ejecta or cool, dense shell likely dominates the HNI component. The WMI temperature and blackbody radius, r_bb(WMI)≈ 4.8 × 10¹⁶ cm(0.048 lt-yr), are consistent with a pre-existing dust shell heated by the observed late-time optical luminosity generated by the forward shock interaction (Section 3.3). Figure 9 illustrates the locations of each component, as well as the likely origins and heating mechanisms.

Zoom In Zoom Out Reset image size

The large pre-existing dust mass that contributes to the WMI flux component suggests significant mass loss from the progenitor. Assuming a dust-to-gas ratio Z_d = 0.01, the observed WMI dust mass listed in Table 2 (M_d(WMI) ∼ 0.01–0.05 M_☉) yields a total gas mass of M_g(WMI)∼ 1–5 M_☉. This mass accounts for the entire WMI emission, as the entire shell contributes to the observed flux given the size of the shell (r_bb(WMI) ≈ 4.8 × 10¹⁶ cm(0.048 lt-yr)) is significantly less than the observational timescale (936 days). The associated mass loss rate is

$$\begin{eqnarray} \dot{M} &=& \frac{M_g {\rm (WMI)}}{\Delta r}\\ v_w &=& 7.5 \times 10^{-3} \Big (\frac{M_g ({\rm WMI})}{M_{\odot }}\Big) \Big(\frac{v_w}{120 \rm \;km \;s^{-1}}\Big)\nonumber\\ &&\times\Big (\frac{0.05\, \rm lt\hbox{-}yr}{r}\Big) \Big (\frac{r}{\Delta r}\Big)\; {(M_{\odot }\; {\rm yr}^{-1})}. \end{eqnarray} \tag{ 14 }$$

On day 413 post-discovery, Smith et al. (2009b) measured a progenitor wind velocity v_w = 120 km s⁻¹. Assuming a constant wind velocity and thin shell ($\frac{\Delta r}{r} = \frac{1}{10}$), the mass loss rate is $\dot{M}\approx 7.5 \times 10^{-2}\hbox{--}3.8 \times 10^{-1}$ M_☉ yr⁻¹, which is 2–3 orders of magnitude larger than calculated by Smith et al. (2009b) at inner radii. Furthermore, this mass loss rate is likely a lower limit. He i P Cygni profiles at 1.083 μm from the TripleSpec spectra show the progenitor wind velocity may have been closer to 200 km s⁻¹ at the WMI radius (Figure 10), assuming the P Cygni feature is generated by the cool, low-velocity circumstellar environment that coincides with the WMI shell.

Zoom In Zoom Out Reset image size

The larger mass loss rate (and possibly faster progenitor wind velocity) of the WMI shell suggests a denser progenitor wind (or "eruption") occurred at $t \lesssim \frac{r_{{\rm bb}} {\rm (WMI)}}{v_w} \approx \frac{4.8 \times 10^{11} {\rm km}}{120 {\rm \;km \;s^{-1}}} \approx 125$ years prior to the core collapse. Although Smith et al. (2009b) conclude that the SN 2005ip progenitor was likely a red supergiant, these stars typically only have wind speeds v_w ∼ 20–40 km s⁻¹ and mass loss rates up to $\dot{M} = 10^{-4}\hbox{--}10^{-3}$ M_☉ yr⁻¹ (Smith et al. 2009a). The observed characteristics associated with the WMI shell are more consistent with Luminous Blue Variable (LBV) stars (e.g., Davidson 1989; Humphreys & Davidson 1994), which can have wind speeds of order hundreds of km s⁻¹ (e.g., Leitherer 1997; Kotak & Vink 2006) and can have mass loss rates up to $\dot{M} = 10^{-1}$ M_☉ yr⁻¹ (Smith & Owocki 2006; Smith & Hartigan 2006; Smith et al. 2007).