Spitzer SNe

# A Comprehensive Analysis of Spitzer Supernovae

Tamás Szalai Department of Optics and Quantum Electronics, University of Szeged, H-6720 Szeged, Dóm tér 9., Hungary Szanna Zsíros Department of Optics and Quantum Electronics, University of Szeged, H-6720 Szeged, Dóm tér 9., Hungary Ori D. Fox Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA Ondřej Pejcha Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic Lyman Spitzer Jr. Fellow, Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540, USA Tomás Müller Millennium Institute of Astrophysics, Santiago, Chile Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 782-0436 Macul, Santiago, Chile Department of Physics and Astronomy, University of Southampton, Southampton, Hampshire, SO17 1BJ, UK LSSTC Data Science Fellow
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###### Abstract

The mid-infrared (mid-IR) range offers an obvious and advantageous choice in following the late-time evolution of supernovae (SNe). First, the peaks of their spectral energy distributions (SED) shift toward the IR after the photospheric phase; second, mid-IR observations are practically free of interstellar extinction. Moreover, special astrophysical processes can be traced with mid-IR observations including dust formation, as well as interaction between the SN ejecta and the circumstellar matter (CSM). Recently, the Spitzer Space Telescope has been the most essential tool to detect mid-IR radiation of SNe and to follow the years-long evolution of these objects. Within the framework of targeted surveys, more than 200 SNe have been followed with Spitzer to date; however, there are even more SNe that have been captured during non SN-targeted surveys. Here we present the results of a comprehensive study based on archive Spitzer/IRAC images of more than 1100 SN sites; from this sample, 121 SNe of various Types have been found to appear as point sources at the images, including 48 objects with previously unpublished detection in mid-IR. These results include statistical analysis of the mid-IR evolution of different types of SNe, the highlighting of objects showing peculiar behavior in this wavelength-range, as well as the modelling of SEDs, which gives insight into whether the source of mid-IR radiation is newly-formed or pre-existing dust, and whether the dust is heated collisionally or radiatively.

editorials, notices — miscellaneous — catalogs — surveys
supernovae: general – infrared: stars – circumstellar matter
journal: ApJ\correspondingauthor

Tamás Szalai

## 1 Introduction

Following the evolution of supernovae (SNe) in different wavelength-ranges from the first hours up to years (maybe decades) after explosion is an essential, but hardly accomplishable aim of researchers. While the current ground-based transient surveys ensure the optical follow-up of hundreds of SNe per year (at least, in the photospheric phase), more specific observations (e.g. late-time optical spectra or non-optical measurements) require to use large telescopes or space devices; thus, detailed studies can be carried out only in a small fraction of these objects within the current facility constraints.

In the mid-infrared (mid-IR) range, thanks to the NASA’s Spitzer Space Telescope (hereafter Spitzer), there are available datasets for following the mid-IR evolution of a number of nearby SNe during several years. Within the framework of targeted observations and surveys, more than 200 SNe has been followed with Spitzer to date. Between 2003 and 2009, in the cryogenic (or Cold Mission) phase, when all the detectors – the 3.6, 4.5, 5.8, and 8.0 m imaging channels of the Infrared Array Camera (IRAC); the 24, 70, and 160 m imaging channels of the Multiband Imaging Spectrometer (MIPS); and the spectroscopic and peak-up imaging arrays of Infrared Spectrograph (IRS) covering the 5.238.0 m and 13.526.0 m ranges, respectively – worked with full capacity, only a moderate number (50) of nearby SNe were directly observed with Spitzer. Since 2009, called post-cryogenic or Warm Mission phase, only the two shortest-wavelength channel (CH1 and CH2) of the IRAC detector have been available for observations; however, these data can be also per se important in studying stellar explosions. Two SN-targeted surveys, carried out in the Warm Mission phase, should be mentioned anyhow here: a program aimed to observe all known Type IIn SNe (68 observed SN sites, 10 detected targets, see Fox et al., 2011, 2013), and SPitzer InfraRed Intensive Transients Survey (SPIRITS), a systematic mid-IR study of nearby galaxies, which has resulted in the detection of 44 objects of various types of SNe (observing 141 sites, Tinyanont et al., 2016) to date, as well as in the discovery of two obscured SNe missed by previous optical surveys (Jencson et al., 2017), and of a large number of other variables and transients including ones with unusual infrared behaviour (Kasliwal et al., 2017).

Mid-IR data could play an essential role in following the late-time evolution of distant, continually fading objects like SNe. Because of the cooling of the expanding ejecta, the peak of the spectral energy distribution (SED) of these objects shifts toward the IR after the photospheric phase; additionally, mid-IR observations are practically free of interstellar extinction. Above all, traceability of special astrophysical processes could make these data even more valuable. We mention first dust formation in the expanding ejecta, which process has a relevance not just in studying SNe but also in revealing the primary sources of cosmic dust, and which topic is an object of a long-term debate in the literature (see below). On the other hand, a similarly important goal is to observe any kind of interaction between the SN ejecta and the circumstellar matter (CSM) that may originate from the pre-explosion mass-loss of the progenitor and/or its companion star (see e.g. Gall et al., 2011, for a review). In the latter case, detected mid-IR emission may arise from newly-condensed dust in a cool dense shell (CDS) produced by the interaction of the ejecta forward shock with a dense shell of CSM (see e.g Mattila et al., 2008; Smith et al., 2009), or by an IR echo from pre-existing circumstellar dust grains (see e.g. Bode & Evans, 1980; Sugerman, 2003; Kotak et al., 2009). Moreover, the shocked gas cools through atomic and molecular emission lines mostly occur in the mid-IR range (see e.g. Reach et al., 2006).

Since Type II-P explosions, based on theoretical expectations (see e.g. Kozasa et al., 2009; Gall et al., 2011), have seemed to be the best candidates for dust formation among SNe, some of these objects were targets of Spitzer observations in the first years of the mission. The published mid-IR data of these objects, usually completed with optical and near-IR observations, have allowed to study the timeline of dust formation processes 1-3 yr after explosion, as well as to estimate the amount and some physical parameters of newly-formed dust. Beside several detailed studies of single objects (e.g. Meikle et al., 2006, 2007, 2011; Sugerman et al., 2006; Kotak et al., 2009; Andrews et al., 2010; Fabbri et al., 2011; Szalai et al., 2011), Szalai & Vinkó (2013) presented an analysis of twelve type II-P SNe (detecting nine of them on the Spitzer images). An important general conclusion of these papers is that mid-IR data do not support the prediction of intense (0.01 ) dust production in SNe, based on theoretically calculated dust formation rates, as well as on the large observable amount of dust in some old SN remnants and in high-redshift galaxies. This controversy has been tried to be resolved in different ways, e.g. imperfections of grain condensation models, the probability of clumping dust formation, or significant grain growth in the interstellar matter (ISM), see Gall et al. (2011) for a review, as well as Szalai & Vinkó (2013). According to a popular idea, the expectedly large amount of dust may be present in the form of very cold (50 K) grains in the ejecta, in a continuously growing amount from already some years after explosion forward; however, this assumption has been unambiguously proven only in the case of the very nearby, peculiar SN 1987A based on far-IR and sub-mm observations (Matsuura et al., 2011, 2015; Indebetouw et al., 2014; Wesson et al., 2015), and on line profile asymmetries (Bevan & Barlow, 2016).

In Type IIn SNe, the interaction of ejecta with the dense CSM in the close environment of the exploding star may lead to either heating of pre-existing circumstellar grains or dust condensation in the CDS generated between the forward and reverse shock. Papers on individual objects (e.g. Fox et al., 2010; Andrews et al., 2011a; Gall et al., 2014), together with the comprehensive Spitzer study of SNe IIn mentioned above (Fox et al., 2011, 2013) helped to make a step in revealing the background of these processes and their signs in mid-IR. In the special case of the very well observed SN 2010jl, a connection between the early (CSM-dominated) and late (ejecta-dominated) dust mass evolution has been revealed (Gall et al., 2014); however, several important questions remained still open, e.g. controversial results on dust masses and timescales of dust formation orginating from different types of analyses (see again e.g. Gall et al., 2014).

In contrast with the relatively large number of Type II-P and IIn SNe with published Spitzer data, there are many fewer objects with published mid-IR observations among thermonuclear explosions of C/O white dwarfs (Type Ia SNe) or stripped-envelope core-collapse (SE CC, including Type Ib/c, Ibn, and IIb) SNe; however, based on theoretical considerations, ejecta-CSM interaction could lead to late-time (1 yr) mid-IR excess, induced by either an IR echo or dust formation, also in these types of stellar explosions (see e.g. Nozawa et al., 2011; Gall et al., 2011). Observing the signs of such interactions would offer chances to find answers to some open questions regarding the final stages of stellar evolution. In the cases of SE CC SNe, both the transition to and the duration of the pre-explosion phases can be probed via revealing the mass-loss history of the progenitor. In SNe Ia, the key-question is the presence of any CSM, which could serve as an evidence in a long-term debate about which fraction of Ia progenitor systems contain a non-degenerate companion (known as single-degenerate scenario). Nevertheless, up to now, there is no detection of significant late-time mid-IR emission of “normal” SNe Ia, not even in the cases of the closest and most well-studied objects like SN 2011fe or SN 2014J (McClelland et al., 2013; Johansson et al., 2017). On the other hand, special objects called SNe Ia-CSM, which have dense, H-rich shells of CSM around (e.g. Silverman et al., 2013; Inserra et al., 2016), are very bright in mid-IR, even 3-4 years after explosion (Fox & Filippenko, 2013; Graham et al., 2017).

In the cases of SE CC SNe, different processes on different time-scales are expected to see in mid-IR. SNe Ib/c, thought to go through intense pre-explosion mass-loss processes, are expected to show mid-IR radiation from pre-existing dust heated by the optical/X-ray flux emerge during the ongoing CSM interaction, maybe within a few years after explosion. Even so, there are only a few of these objects with detected late-time mid-IR excess; however, these includes the bright and well-known interacting SN 2014C (Tinyanont et al., 2016). In SNe IIb, either a small amount of newly-formed ejecta dust or the effects of ejecta-CSM interaction could be the source of mid-IR excess; anyway, such signs have been detected only in SN 2013df (Szalai et al., 2016; Tinyanont et al., 2016), and, less clearly, in SN 2011dh (Helou et al., 2013). It is also worth to note that the well-known interacting SN 1993J is still visible in Spitzer/IRAC images more than two decades after explosion (Tinyanont et al., 2016). The special SNe Ibn, expected to explode in He-rich CSM, do not show late-time mid-IR excess; however, one of these objects, SN 2006jc, was bright in early-time Spitzer images (Mattila et al., 2008).

While the relatively high number of SNe with reported Spitzer observations calls out for comprehensive statistical studies, there is a deficiency of such papers in the literature. As we mentioned above, there has been an extensive study of Type IIn SNe with Spitzer carried out by Fox et al. (2011, 2013), while Szalai & Vinkó (2013) and Johansson et al. (2017) published comparative analyses on a moderate number of Type II-P and Type Ia SNe, respectively. The most comprehensive study to date has been published by Tinyanont et al. (2016), whose results are based on the observations of 140 SNe of different types; however, it has to be noted that their program contains galaxies only within 20 Mpc, and that their paper focuses on only core-collapse explosions.

The motivation of the current work was to review the mid-IR properties of different type of SNe based on a uniform analysis of Spitzer/IRAC data, including also objects observed during non-SN targeted galaxy surveys (which number can be comparable with, or, may exceed that of have been directly observed with Spitzer during targeted programs). Here we present a comprehensive study based on the mid-IR observations of more than 1100 SNe, from which 121 objects have been declared to be positive detections; this sample includes all previously published SN data as well as unpublished data of 48 objects mainly found on archive images captured during non-SN targeted galaxy surveys. In Section 2, we describe the steps of data collection and of the photometry of Spitzer/IRAC data. After that, we present our most important findings (Section 3); this part includes the statistical analysis of the mid-IR evolution of the different types of SNe, together with the highlighting of some objects show interesting behavior in this wavelength-range. We also fitted simple models to the SEDs calculated from the mid-IR data of SNe, combined them with optical data in some cases; here, we also discuss the limitations of this step of the analysis. Finally, the conclusions of our study are presented in Section 4.

## 2 Observations and data analysis

### 2.1 Collection of supernova data from the Spitzer Heritage Archive

Using he list of SNe on the website of Central Bureau for Astronomical Telegrams (CBAT), and the website of All-Sky Automated Survey for Supernovae (ASAS-SN)222http://www.astronomy.ohio-state.edu/assassin, we selected all SNe that were discovered before 2015 and have been spectroscopically classified (at least as Type I or Type II objects). We also selected nearby ( 0.05) SNe, none of them shown in the lists above, using the Open Supernova Catalog (Guillochon et al., 2017). This search gave 4500 objects, all of which positions have been checked in the Spitzer Heritage Archive (SHA) (using a 100 environment for the queries). We found 1134 SN sites that have been observed with Spitzer after explosion; for these objects, we downloaded the available IRAC data for further analysis (this group of objects includes SNe both with or without previously reported Spitzer observations). We note that although MIPS and IRS data can also give significant contribution to understand the mid-IR behaviour of SNe (see e.g. Kotak et al., 2006, 2009; Gerardy et al., 2007; Fabbri et al., 2011; Szalai et al., 2011; Szalai & Vinkó, 2013), there are only a few objects observed with these detectors, and only before 2009; thus, we focus on only IRAC data in this work.

### 2.2 Object identification and photometry on Spitzer/IRAC images

We collected and analyzed all available IRAC post-basic calibrated data (PBCD) on the selected SNe. The scale of these images are 0.6/pixel. Identifying a point source at the position of an SN explosion can be misleading, because, in such large distances, compact H ii regions or the host clusters of SNe may be also point-like sources on Spitzer/IRAC images. In the cases of objects where either pre-explosion or late-time exposures (on which there are no visible source at the position of the SN) are available, the presence of the transient source can be followed many times by eye; however, the usual way to get a direct evidence is measuring the flux changes between the epochs.

In some of these cases, because of the faintness of the target and/or of the presence of a complex background, clear identification of SN was not easy. In these cases, we applied HOTPANTS code (developed by A. Becker) to perform image subtraction technique, which have been also used in several studies to analyse Spitzer data of SNe (see e.g. Meikle et al., 2007; Kotak et al., 2009; Szalai & Vinkó, 2013; Tinyanont et al., 2016). We illustrate the effectiveness of this technique in Fig. 1. There were also some fields with single-epoch Spitzer images but with a mid-IR point-source at the position of the SN. In such a case, we accepted it as a positive detection if no compact source can be seen at the position of the SN on other images (2MASS, SDSS, DSS, …) of the region; in this part of the work, Simbad database (Wenger et al., 2000) was a helpful tool. Upper limits for nondetections (5 Jy and 15 Jy at 3.6 and 4.5 m, respectively) were set by the point-source sensitivity in Table 2.10 of the IRAC Instrument Handbook version 2.

For measuring fluxes, we carried out simple aperture photometry on the PBCD frames using the phot task of IRAF777IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. as a first step. We generally used an aperture radius of 2″and a background annulus from 2″to 6″(226 configuration), applied aperture corrections of 1.213, 1.234, 1.379, and 1.584 for the four IRAC channels (3.6, 4.5, 5.8, and 8.0 m, respectively) as given in IRAC Data Handbook; in the cases of close and bright sources, we also used the 337 configuration (aperture corrections: 1.124, 1.127, 1.143, and 1.234, respectively), and, in a very few cases, the 51220 configuration (aperture corrections: 1.049, 1.050, 1.058, and 1.068, respectively). In the cases where image subtraction was carried out, we repeated the aperture photometry on the background-subtracted images with the same configuration. We generally found good agreement between the two methods (10% difference in fluxes, which is within the approximated uncertainty of Spitzer/IRAC photometry); in the few cases where the difference was larger, we determined the mean values of the fluxes.

In the cases of objects with complex backgrounds where no pre-explosion or late-time exposures could be used for image subtraction, we applied the photometric method described by Fox et al. (2011) (called hereafter as “Fox+11 method”). During that, we used a set of single apertures with a fixed radius to estimate both the SN and average background flux. This technique allowed us to visually identify only local background associated with the SN, as opposed to the annuli regarding the aperture configurations mentioned above.

The detailed results of our statistical analysis are presented in Section 3. Basic data – which we collected using the Open Supernova Catalog, the NASA/IPAC extragalactic database (NED), and references therein – and the mid-IR fluxes of SNe with previously unreported Spitzer photometry are shown in Tables A1 and A2, respectively. We also checked all the previously published Spitzer/IRAC SN-photometry in the literature. In general, we found good agreements with the published values (10% difference in fluxes). In a few cases, the flux differences are larger, but all of these objects were captured in a very faint phase and/or with a complex sky background; thus, the uncertainties of their fluxes are implicitly large.

## 3 Results

### 3.1 Demography

We summarize the statistics of the processed Spitzer data of SNe in Table 1. The total number of the observed SN sites is over 1100. Since the majority of objects are nearby (z0.05) SNe, 40 of the objects (mostly Type Ia ones, originating from the CBAT list) are located in distant, anonymous galaxies. The reason why we did not filter out these SNe from our sample was to look at analogues of SNe Ia-CSM and other strongly interacting SNe (e.g. SN 2014C), which all were extremely bright in mid-IR, thus, the mid-IR radiation of similar objects could be detected even at a distance of several hundreds of Mpcs.

Nevertheless, we did not find any positive detection among these distant objects. Thus, and because of the lack of well estimable distances, we eliminated these objects (anonymous hosts, 0.05) from the final steps of the of analysis including the calculation of overall detection rates (Table 2), as well as creating Figs. 2 and 3, which shows the number of detected/undetected SNe belonging to different types, according to the distances and to the timescales after explosion.

Multiple detections are available in the cases of roughly half of the studied SNe, but only 12% of the SN sites were observed before explosion. While, as we mentioned above, positive detection of SNe in IRAC images is sometimes accomplishable during the measuring of flux changes (or, in the cases of single exposures, the comparison with images originating from other sources), this low ratio has probably affected the detection statistics quite negatively. Moreover, there are 60 SNe in the filtered list that are located very close to the center of their hosts; in these cases, because of the resolution limit of Spitzer and/or of the saturation of the concerned pixels, even image subtraction is a non-effective method to identify an SN as a possible mid-IR source. We have also excluded these objects from the detection statistics (Tables 2, Figs. 2 and 3).

In total, we have identified 121 SNe with positive mid-IR detection, including 48 objects that had no reported Spitzer detection before. As we mentioned above, Tables A1 and A2 shows the basic data of these SNe and the results of IRAC photometry, respectively. These Tables also include three additional objects (SNe 2012aw, 2012fh, and 2013ee), which have been published by Tinyanont et al. (2016) as positive Spitzer detections, but no photometric values have been reported regarding them.

Consequently, final detection statistics (Table 2, Figs. 2 and 3) includes all SN sites with multiple Spitzer/IRAC observations, and, additionally, all SNe classified as a positive detection based on single-epoch Spitzer images (see Section 2.2); at the same time, these rate do not include objects appeared in distant, anonymous galaxies, or are located too close to the center of their host galaxies. Based on the method presented by Tinyanont et al. (2016), we present the detection rates separated in three time bins after discovery: less than one year, one to three years, and more than three years. If an SN is observed with at least one detection in a bin, it is marked as detected, even though it might fade away later in the same bin.

In Table 3, we compare our detection rates with those are based only on the SPIRITS survey (Tinyanont et al., 2016). Since the numbers regarding to our larger sample are more or less similar to the published ones, we have to take some notes on that. First, since SPIRITS is a systematic, volume-limited study based on well-sampled and long-scale observations of SNe, it allows to draw way more trustable statistical conclusions than what our heterogeneous and poorly observed sample does (for this reason, we were not able to give statistical error ranges). We also note that Type IIb explosions are included in the rates of Type II SNe for being comparable with the results of Tinyanont et al. (2016).

{longrotatetable}

### 3.2 Mid-IR evolution: trends and outliers

We present the mid-IR evolution of all SNe with positive Spitzer detection in Fig. 4. While similar figures have been also published by Fox et al. (2016) and Tinyanont et al. (2016), the current plot is based on a 50% larger sample. All the calculated absolute Vega magnitudes, including the ones determined from previously published fluxes, distances and values, are also presented in Table A3. In this Section, we examine the trends according to the mid-IR evolution of certain Types of SNe, highlighting single explosions showing peculiar properties at 3.6 and/or 4.5 m wavelengths. Note that for seeing through Fig. 4 better, we excluded some objects with decade-long mid-IR datasets – e.g. Type II-pec SN 1987A (Dwek et al., 2010), Type II-L SN 1979C, or Type IIb SN 1993J (both from Tinyanont et al., 2016) – from the plot; at the same time, these objects are all involved in the demographic statistics discussed above.

#### 3.2.1 Thermonuclear SNe

Regarding thermonuclear SNe, our study more than doubles the number of objects with positive mid-IR detection (33 vs. 15). As we discussed in Section 1, and as Fig. 5 also shows, the mid-IR evolution of these explosions are quite heterogeneous. “Normal” Type Ia SNe show quite similar, continuously declining brightness in the first year after explosion, and only a small fraction of them are detectable at later epochs; this is in total agreement with the findings of Tinyanont et al. (2016) and of Johansson et al. (2017) based on a much smaller sample.

At the same time, objects belong to the group of Type Ia-CSM SNe are extremely bright at mid-IR wavelengths. Nevertheless, only about a dozen of objects have been classified to this type of SNe to date, and only five of them have been observed with Spitzer. As it can be seen in Fig. 5, brightnesses of SNe 2012ca and 2013dn, presented in this work, are quite similar to those of published before (SNe 2002ic and 2005gj: Fox & Filippenko (2013), PTF11kx: Graham et al. (2017)). Although this sample is quite small, and there are no more than 3-4 observed epochs per object, an interesting trend seems to emerge: the fluxes increase up to 500 days after explosion, and, after that, they show a continuous decrease. Because of the large distances of known SNe Ia-CSM, and of the small size of the sample, the long-term mid-IR evolution of these objects is ill-known: since PTF11kx (200 Mpc) has been still detectable at 1800 days, SN 2002ic (280 Mpc) has been faded at a similar age, and it is also non-detectable at the IRAC images obtained in 2014 (12 years after explosion). Additionally, there is another non-detection in the case of SN 2005gj from 2014 (9 years after explosion).

One of the main goal of our study was to find unidentified SNe Ia-CSM at non-SN targeted Spitzer/IRAC images, or, find “intermediate” cases that have mid-IR fluxes larger than usually seen in SNe Ia at a given epoch. As we described in Section 3.1, we examined the Spitzer images of hundreds of thermonuclear SN sites (most of them exploded in distant, anonymous galaxies), pictured on various timescales after explosion. The idea behind that is based on a wide-spreading concept (see e.g. Vinkó et al., 2017) that predicts that many of thermonuclear SNe may show detectable sign of circumstellar interaction. In these cases, CSM shells may be far away from the explosion site, thus, the interaction and the radiation that are produced by it would occur at later times (maybe 5-6 years, or decades after explosion), or, in the case of not-so-dense CSM, the signs of interaction would be (much) less luminuous events in the infrared.

Conclusively, we did not find any other objects producing amount of mid-IR radiation similar to those of known SNe Ia-CSM in the studied sample. This finding may show that dense CSM is indeed very rare in the environments of thermonuclear SNe (which may also hint that these explosions arise from different progenitor systems than the majority of SNe Ia), or, that CSM shells may be indeed far away from the explosion sites. Nevertheless, further large and more systematic surveys would be necessary for the thorough study of this problem.

At the same time, as it is marked in Fig. 5, we found some other thermonuclear explosions with interesting behaviour in mid-IR. SNe 2010B and 2010gp, caught in early phases, seem to be definitely brighter than what is suggested by the trend. Nevertheless, it has to be noted that there are no pre-explosion or late-time data regarding SN 2010B, and it has a complex galactic background; thus, it is questionable whether the observed fluxes really denote an extra mid-IR radiation originating from dust formation and/or from CSM interaction, or not. On the other hand, SN 2010gp, locates quite far (100 Mpc) is decidedly a good draw; its mid-IR excess can be verified also with subtraction of pre-explosion images. This object may be detected at the beginning of CSM interaction, but, unfortunately, this statement cannot be proved in the lack of further data. A similarly interesting finding is SN 2011iy; this is a relatively nearby (20 Mpc), neglected SN Ia with a clear detection at 4.5 m (after image subtraction, see Fig. 1) at 1030 days after explosion (note that the object is not detectable at 3.6 m).

SN 2014dt, classified as a Type Iax SN, should be also highlighted here: this object shows a clear and even growing mid-IR excess 1 yr after explosion, which has been explained with the presence of newly-formed or heated, pre-existing dust (Fox et al., 2016). Since SNe Iax are in the focus of current SN research (see e.g. Foley et al., 2013; McCully et al., 2014; Barna et al., 2017), it would be especially interesting to follow their mid-IR evolution, which could provide new insight into the origin and environment of these stellar explosions. Unfortunately, there are only a few SNe Iax observed with Spitzer (see Table 1), and most of them have been captured only several years after explosion. The only other SN Iax we identified as a mid-IR source on Spitzer images is SN 2005P; instead of SN 2014dt, this object does not have detectable mid-IR fluxes at 1 yr after explosion. At the same time, it seems to be slightly detectable at 8.0 m at 180 days after explosion; however, this finding cannot be compared with the case of SN 2014dt, since the latter one has been observed during the Warm Mission phase.

#### 3.2.2 Stripped-envelope CC SNe

From the point of view of dust formation and circumstellar interaction, as we described in Section 1, the general properties of SE CC SNe are somewhat similar to those of thermonuclear explosions: neither of these objects seem to be significant dust sources, and a very limited number of them have been captured showing signs of strong CSM interaction. Since the term of SE CC SNe includes various types of explosions (Types Ib/Ic, Ibn, IIb), their mid-IR evolution also show a kind of heterogeneity. As Fig. 6 shows, the mid-IR absolute magnitudes of different types of objects are quite similar in the early phases; however, only a small number of SE CC SNe have been captured by Spitzer at a 100d age. At later epochs, some differences seem to arise.

Unfortunately, Type Ibn explosions, which show signs of CSM interaction by definition, are especially undersampled in the Spitzer database: there are observations only of SN 2006jc (4 epochs, but only one from the first year, see Mattila et al., 2008) and PS1-12sk (1 epoch). These two events are bright in mid-IR during the early-time CSM interaction, but this brightness decline quite fast (at least in the case of SN 2006jc, where it can be followed).

A special case is SN 2014C, in which the transformation from a “normal” Type Ib into a strongly-interacting, Type IIn-like SN has been caught in action via multiwavelength observations (Milisavljevic et al., 2015; Margutti et al., 2017). SN 2014C, appeared in one of the target galaxies (NGC 7331) of the SPIRITS program, has been also intensively followed with Spitzer: as Tinyanont et al. (2016) presented, the object has a high, roughly constant IR-luminosity in the first 800 days, even showing a unique re-brightening at 250 days, in accordance with the beginning of intense CSM interaction detected at other wavelengths.

Another very interesting object is SN 2001em, a known strongly-interacting Type Ib/c object, which has been produced strong X-ray, radio and optical emission 3 years after explosion (see Stockdale et al., 2004; Pooley & Levin, 2004; Soderberg et al., 2004; Chugai & Chevalier, 2006). In this case, the transformational process could not have been followed from the beginning, thus, the overall comparison with SN 2014C is not feasible. Browsing in Spitzer data, there is only one epoch when SN 2001em was observed; however, this targeted measurement was obtained at the time of the detection of strong CSM interaction, and the data covers all the four IRAC channels. As Fig. 6 shows, SN 2001em seems to be even brighter in mid-IR than SN 2014C; however, it has to be noted, that instead of SN 2014C, there are no pre-explosion images for the correct background-subtraction. We present a more detailed analysis of SN 2001em in Section 3.3.

Beyond these two, well-known explosions, we would like to highlight another object, SN 2011ft: it is a distant ( 100 Mpc) SN Ib seems to be as bright as SN 2014C at 250 days after explosion. Since it is a promising result, we have to note that there are no other Spitzer data of this object, and that there has been only a 3.6 m image obtained at that single epoch.

Among Type IIb SNe, no objects showing large late-time mid-IR excess have been found. At the same time, the known moderately interacting SN 2013df (Kamble et al., 2016; Maeda et al., 2015; Szalai et al., 2016) produces a slowly-declining mid-IR light curve between 270-820 days (Tinyanont et al., 2016; Szalai et al., 2016); another object, SN 2001gd shows a similar brightness at 950 days. SN 2011dh, one of the best-sampled SN in mid-IR, has been also detectable up to almost two years after explosion; however, its brightness decline much faster than that of SN 2013df. Mid-IR evolution of “normal” Type Ib/Ic SNe seems to be even faster. The three SNe IIb mentioned before are located within 20 Mpc (16.5 Mpc for SNe 2001gd and 2013df, and 8 Mpc for SN 2011dh); if we examine the close Type Ib/Ic events sampled well enough, we found the ones within 10 Mpc – SNe 2005at (Kankare et al., 2014) and 2012fh – and between 1020 Mpc – SNe 2014L, 2014df (both from Tinyanont et al., 2016), and 2009em – being detectable up to 600-700 days and 400-500 days, respectively.

Adding that the very nearby ( 3.7 Mpc), strongly interacting Type IIb SN 1993J were followed up to almost 24 years in mid-IR (Tinyanont et al., 2016), while other Type IIb SN 2008ax ( 7.8 Mpc) were not detectable only 4 years after explosion, a plausible trend can be outlined: the length of mid-IR detectability seem to correlate with the assumed sizes of the progenitors of SE CC SNe. SNe 1993J, 2001gd and 2013df, can be followed longer time with Spitzer, have been classified as Type eIIb objects (Chevalier & Soderberg, 2010; Szalai et al., 2016), which denotes that these explosions originate from extended progenitors (yellow or red giants). SN 2008ax is known as a representative of Type cIIb objects, which are assumed to have more compact progenitors, similarly to Type Ib/Ic objects; while SN 2011dh seems to be an intermediate case in progenitor size ( a few tens of ) as well as in the length of mid-IR detectability. This picture per se could allow processes taking place either in the ejecta or in the shocked CSM as the background of the general mid-IR evolution of SE CC SNe. Nevertheless, there are some important circumstances can influence dust formation and/or CSM interaction in these SNe, e.g. dust production efficiency connecting to the metallicity of the progenitor (Gall et al., 2011), or the binarity of the progenitor system (Kochanek, 2017). Moreover, studied primarily in Type IIb SNe, there is a controversal picture regarding episodic vs. continuous dust formation, as well as the large dust content of some old SN remnants (e.g. Cas A) vs. the small dust masses can be observed in earlier phases of SNe (see e.g. Gall et al., 2011; Bevan et al., 2017); moreover, estimating of the survival rates of grains with different size-distribution and composition should be also an important step in such studies (see e.g. Kozasa et al., 2009; Gall et al., 2011). Conclusively, both improved theories, and multiwavelength, long-time observational follow-up of even more objects seem to be necessary to find answers to these open questions.

#### 3.2.3 Type II-P SNe

As we presented in Sections 1 and 3.1, Type II-P and IIn explosions constitute the main base of SN-targeted Spitzer observations. Focusing first on SNe II-P (Fig. 7), we can basically see a homogeneity in their mid-IR evolution. As we described in Section 1, theoretical expectations indicate that ejectae of most of Type II-P SNe may be the places of observable dust formation and that a strong evidence for that would be mid-IR re-brightening between 300-600 days. Although there are several SNe II-P observed at multiple epochs falling into this range, there are only a few objects showing this effect: SNe 2004dj (Szalai et al., 2011; Meikle et al., 2011), 2011ja (Andrews et al., 2016; Tinyanont et al., 2016), and 2014bi (Tinyanont et al., 2016) – however, it is necessary to note that this low rate can be influenced by the poor sampling of the other observed Type II-P SNe. As a complication, this effect seems to be not always observable at 4.5 m; both SNe 2004dj and 2014bi show a linear decline in this wavelength-range, while the re-brightening is clearly seen at 3.6 m (see Fig. 7), and, in the case of SN 2004dj, also at 5.8 and 8.0 m (see Szalai et al., 2011); as it is assumed, there could be an extra flux at 4.5 m caused by the 10 vibrational band of CO at 4.65 m (see Kotak et al., 2005) during the declining phase, but disappears at 500d (Szalai et al., 2011; Szalai & Vinkó, 2013).

Two other Type II-P SNe, 2004et (Kotak et al., 2009; Fabbri et al., 2011) and 2007oc (Szalai & Vinkó, 2013), as well as Type II-P/II-L SN 2013ej (Tinyanont et al., 2016; Mauerhan et al., 2017) also show mid-IR rebrightening, but it has occured later (between 700-1000 days) in these cases. The other difference is that this later rebrightening is evenly observable at both 3.6 and 4.5 m (at least in the cases of SNe 2004et and 2007oc; SN 2013ej becomes undetectable at 3.6 m after 800 days). As it is described in these cited papers, the reason behind this late-time mid-IR rebrightening is most probably the formation of new dust in the CDS behind the reverse shock. In Fig. 7, all SNe II-P showing any kind of re-brightening are highlighted with coloured symbols, while the ones without such kind of observational signs are marked with gray circles.

#### 3.2.4 Type IIn SNe

The review of mid-IR evolution of Type IIn SNe is presented in Figure 8. As it was revealed during the systematic studies of this kind of explosions (Fox et al., 2011, 2013), mid-IR excess comes in most cases from pre-existing dust, which is continuously heated by optical emission generated by ongoing interaction between the forward shock and CSM. This type of SNe typically show clear signs of ongoing CSM interaction (strong emission in H / X-ray / radio) even in the first months after explosion; however, unfortunately, there is a very limited number of such objects observed in this phase with Spitzer. SNe 2009ip (Fraser et al., 2015, and this work) and 2011A observed with Spitzer/IRAC in the first month appear as faint mid-IR sources; however, it has to be noted that both objects are special cases between low-luminosity Type IIn events and SN impostors, see the analyses of e.g. Pastorello et al. (2013), Fraser et al. (2013),Mauerhan et al. (2013), and Margutti et al. (2014), as well as of de Jaeger et al. (2015), respectively. An opposite case is the well-studied SN 2010jl, which is very bright in mid-IR in the first year (Andrews et al., 2011a; Fox et al., 2013), as well as during the whole observed period of almost 5 years (Fransson et al., 2014; Williams & Fox, 2015, and this work); the source of the detected early mid-IR flux is probably warm dust generated due to CSM interaction, transforming into an ejecta-dominated dust emission at later times (for the details, see Gall et al., 2014).

Revealing the early-time mid-IR properties of a larger sample of SNe IIn could be also an important step in understanding the long-term evolution of these SNe. As it can be seen in Figure 8 (and previously in Fox et al., 2013), most of SNe IIn showing large late-time mid-IR excess can be followed even up to 5-6 years after explosion; beyond the already mentioned case of SN 2010jl, several other objects (SNe 2005ip, 2006jd, 2007rt or 2013cj) show this effect. At the same time, other SNe IIn decline more fast at mid-IR wavelenghts; moreover, a significant part of this kind of explosions can not be detected in mid-IR at all (see Fig. 3 and Table 2, as well as Fox et al., 2011). The conclusion of Fox et al. (2011, 2013) suggests that, in the latter cases, the forward shock may have already overrun and have destroyed the dust shell; however, the details of this two-faced behaviour of Type IIn SNe will probably remain an object of further studies.

As Fig. 4 shows, Type II-P and Type IIn SNe are quite well distinguishable regarding their late-time mid-IR evolution (except one or two objects). We have found unidentified positive detections from both classes, as well as among unclassified Type II SNe (see Table 1). Using the disjunction of Type II-P and IIn SNe, there is also a possibility for a kind of late-time classification of Type II explosions without exact early-time classification. As Fig. 9 shows, most of these sources (in agreement with the general SN rates) may probably belong to the Type II-P class, except SNe 2005kd, 2008fq, and 2011dq, which may be rather the representatives of the Type IIn class.

### 3.3 SED fittings: limitations, methods, consequences

Mid-IR SEDs of SNe based on Spitzer measurements could be valuable by themselves for determining the main parameters of (warm) dust located in the environment of the explosions – especially those including data obtained with all the four IRAC channels as well as with MIPS and IRS (see e.g. Kotak et al., 2009; Szalai et al., 2011; Szalai & Vinkó, 2013). Nevertheless, as we discussed above (and as it can be also seen in Tables A2 and A3), only a minor part of SN observations belong to this group; most of the objects we studied have been captured in the Warm Mission phase, resulting fluxes only at 3.6 and/or 4.5 m. While SED fittings on two points have their own trivial limitations, there are other issues make the modelling processes difficult. During the first several months after explosion, a hot component, thought to be caused by an optically thick gas in the innermost part of the ejecta, may affect the continuum emission of the warm dust. This is particularly critical in the cases when only 3.6 and 4.5 m data are available in the mid-IR: 3.6 m data, and sometimes also 4.5 m ones, can be strongly affected by the hot component in the early stage. Moreover, the line emission by CO at 4.65 m (described in Section 3.2.3) could be also a significant contribution to 4.5 m fluxes; although this effect has been only shown in some Type II-P SNe (before 500 days after explosion) to date, it may also happen in other types of explosions. Thus, in most cases, presence of (nearly) contemporaneous optical and/or NIR data obtained would be necessary to properly determine the dust parameters in the early evolution phases (see e.g. Szalai & Vinkó, 2013).

Unfortunately, we have found a very limited amount of available additional data regarding the objects identified with previously unpublished Spitzer data; however, in these cases, we used these data to examine differences of the model curves we can fit to mid-IR and to combined optical-IR SEDs. Prior to fitting, all the mid-IR values and the available optical magnitudes have been transformed to values, which were dereddened using the galactic reddening law parametrized by Fitzpatrick & Massa (2007) assuming R = 3.1 and adopting values as listed in Table A1.

In order to illustrate the affection of the hot component, we first present the SED fittings of Type IIn SN 2011A and Type II-P SN 2014cx. Both of these objects have been captured with Spitzer within 3 months after explosion (at +86 and +53 days, respectively). In the case of SN 2011A, contemporaneous g’r’i’z’ data can be found in the paper of de Jaeger et al. (2015), while, in the case of SN 2014cx, BVRI and g’r’i’ data obtained at the epoch of Spitzer observations are also available (Huang et al., 2016). As it can be seen in Fig. 10, single black bodies (BBs) provide a good fit to the combined optical-IR SEDs of both SNe. If we do the similar fit to only the mid-IR SEDs, we get only slightly better match, but there is a large differences in radii and temperatures (see Table 4). Nevertheless, there is no sign of mid-IR excess can be caused by either dust formation in the ejecta or by CSM interaction, thus, these examples are only good to illustrate the strong limitation of model fitting to these kind of SEDs.

In the case of Type Ib SN 2009jf, it was also possible to create the combined optical-IR SED adopting BVRI measurements from Sahu et al. (2011b). Spitzer data were obtained at 100 days after explosion, while optical data are from +94 and +105 days; thus, we used the mean of the certain brightnesses during the calculation of the SED. As it can be seen Fig. 11, there is a clear excess at 4.5 m; however, since 3.6 m flux seems to arise mainly from the hot component and there are no other mid-IR data, it is not possible to extract trustible information about the amount and temperature of the assumable dust.

Additionally, it was possible to carry out a similar analysis in the case of Type II-P SN 2012aw. The earliest Spitzer data of this object is from +358d, for which epoch we could estimate V, R, and I brightnesses via interpolation of well-sampled data of Dall’Ora et al. (2014) extending to 330 days. At this late-time epoch, the hot component cannot be adequately modeled by a simple BB curve, since the optical depth of the continuously expanding ejecta is quite low at this time. Therefore, we applied the global light-curve model of Type II-P SNe (Pejcha & Prieto, 2015, called hereafter PP15 model) to estimate the contribution of the hot component to the mid-IR fluxes. In order to construct the PP15 model SED, we calculated its values at the wavelengths of BVRIJHK filters, while, at longer wavelengths, we used the the RayleighJeans approximation (F). The results of SED fittings are shown at the left panel of Fig. 12. As it can be seen, the (extrapolated) observational VRI data are matched perfectly with the values calculated from the PP15 model, although PP15 model fit is based on data that include Dall’Ora et al. (2014) among others (which seems to be an assurance for its applicability). The necessity of PP15 model here is clearly seen, since the simple BB curve fitted to the observed VRI fluxes is high above the 3.6 m flux measured by Spitzer. Similarly to the case of SN 2009jf, there is a clear excess at 4.5 m indicating the presence of warm dust, but it is difficult to estimate its real contribution to the SED (taking also into account the potential affection of the 4.5 m flux by line emission mentioned above, which can easily happen in a Type II-P SN at this epoch).

We also repeated this analysis for the known CSM-interacting Type II-P/II-L SN 2013ej. While the first (weak) signs of interaction – based on polarimetry, optical spectroscopy, and X-ray data – have been already pubished in several papers (Leonard et al., 2013; Bose et al., 2015; Kumar et al., 2016; Dhungana et al., 2016; Chakraborti et al., 2016), the detailed investigation of this topic has been carried out and presented by Mauerhan et al. (2017). Despite the amount of published data, the modelling of combined (UV)-optical-IR SEDs have not been presented in the literature. Although there are published measurements obtained at even later epochs in both ranges, we have found only one epoch (+236d) with nearly contemporaneous mid-IR and optical data (Tinyanont et al., 2016; Bose et al., 2015, respectively). Results of the SED fitting can be seen at the right panel of Fig. 12. Since the strong signs of interaction can be observed after 800 days (Mauerhan et al., 2017), the presence of the mid-IR excess is clearly visible even at that earlier epoch. While the presence of this excess could be identifiable even if we use only BB fitting, the contribution of the hot component can be highly more accurately estimated using the PP15 model SED with parameters from Müller et al. (2017). We note that in this case the fitting of the two-point mid-IR SED gives a very similar result for BB radius and temperature to the case when we use the PP15 model, see Table 5. We also note that the SED values calculated from the PP15 model agree well with the observed data also in this case, excluding the R filter, where the reason of the observed flux excess should come from the strong H-emission can be seen in the nebular spectra at 100-150 days (Bose et al., 2015; Huang et al., 2015; Dhungana et al., 2016) as well as after 400 days (Mauerhan et al., 2017).

Beyond all the mentioned limitations and difficulties, modelling of (even two-point) SEDs may play an important role in examining whether the source of mid-IR radiation can be newly-formed or pre-existing dust, and whether the dust is heated collisionally or radiatively. As another main goal of this study, we tried to carry out such an analysis to as many objects of this study (Table A2) as possible; however, based on the SED fitting cases presented above, it was necessary to define some criteria. Thus, we excluded from the analysis all objects observed only within the first three months after explosion without any additional optical/NIR data (because of the not exactly known influence of the hot component); additionally, there are also some objects that are detectable only at a single IRAC channel at a certain epoch (or, the field has been only captured using a single channel). Moreover, we also omitted the simple SED analysis of some further “normal” Type Ia SNe observed during the first year after explosion (some of them via all the four IRAC channels); the reason of that is that the interpretation of their SEDs probably require more complicated models than the ones we use here (see Nozawa et al., 2011); we intend to carry out a more detailed analysis of these objects in a separate paper (using also still unpublished MIPS and IRS data).

For the selected objects, following the method published in a number of papers (see e.g. Meikle et al., 2007; Fox et al., 2010, 2011, 2016; Fox & Filippenko, 2013; Szalai & Vinkó, 2013; Graham et al., 2017), we assumed a spherically symmetric, optically thin dust shell as a region of possible dust formation (or, the location of pre-existing dust). First, we calculated the minimum shell radii via fitting pure BBs () to the observed SEDs and, from the radii and the estimated ages, we also determined the corresponding velocities () assuming them being constant over time (see Table 6).

As a second step, we also fitted an analytic dust model, adopted originally from Meikle et al. (2007), assuming a homogeneous (constant-density) dust distribution:

 Lν=2π2R2Bν(T)[τ−2ν(2τ2ν−1+(2τν+1)exp(−2τν)], (1)

where is the radius of the dust sphere, is the Planck-function, is the temperature of the dust, and is the optical depth at a given frequency. To estimate the dust optical depth, we adopted the power-law grain-size distribution of Mathis, Rumpl & Nordsieck (1977), hereafter MRN, assuming = 3.5 for the power-law index and grain sizes between = 0.005 m and = 0.05 m. could be then calculated as

 τν=43πkρgrainκνR14−m[a4−mmax−a4−mmin], (2)

where is the density of dust grain material, is the grain number density scaling factor, and is the mass absorption coefficient. The dust is assumed to be distributed uniformly within a sphere. , , and were free parameters during the fitting. We used pure amorphous carbon (AC) grains in the model. Dust opacity values were taken from Colangeli et al. (1995), while density of dust grain material, = 1.85 g cm, was adopted from Rouleau & Martin (1991).

Parameters for the best-fit blackbodies and analytic amorphous carbon dust models to the mid-IR SEDs of the selected SNe are shown in Table 6. For modelling of four-point mid-IR SEDs (calculated from data obtained during the Cold Mission phase), we could present two cases (Figure 13). The first one is SN 2002bu, a Type IIn explosion observed 2 years after explosion, which SED can be well fitted with a single-component BB (or carbonaceous dust) model. The other object is the well-known interacting Type Ib/c SN 2001em. The mid-IR SED according to 1135 days after explosion (which is near contemporaneous with the observed, strong CS interaction detected at various wavelengths, see above) shows an interesting picture: it can be adequately described only with a two-component dust model. To fit such a model to only this four mid-IR fluxes is ambiguous because of the large number of free parameters. If we fit use blackbodies, we get the parameters shown in Figure 13. Comparing the assumed radii of the dust shells with the estimated size of the CS shell (r = ) determined by Chugai & Chevalier (2006), we get the same order of magnitude. Moreover, if we change the longer-wavelength BB to an amorphous carbon dust model, we get = 340K and = 0.03 , which are in a very good agreement with the theoretical expectations of Chugai & Chevalier (2006): their calculations resulted in 300K for dust temperature and 2-3 for the mass of the CS shell (which gives 0.02-0.03 dust mass assuming a 0.01 dust-to-gas mass ratio). As a conclusion, the modelling of this single mid-IR SED of SN 2001em seems to strengthen the earlier findings regarding the CSM interaction detected at various wavelenghts; additionally, the mid-IR data suggest the presence of a multiple pre-explosional dust shell.

All other SNe presented in Table 6 have only two-point mid-IR SEDs. While, as we discussed above, we have to be careful with the interpretation of these SEDs, some conclusions can be drawn from them. As a simplified, but useful parameter, can show whether the total estimated amount of dust can be newly-formed or not (again, connects to the minimum size of the assumed, optically thin dust-forming region). In cases where is quite low (several hundreds or a few thousands km s, only found in Type II explosions), it is possible that all the assumed dust formed in the ejecta; both the estimated temperatures and dust masses (10 are in agreement with this assumption and with the previously published values found in other Type II SNe (see e.g. Fox et al., 2011, 2013; Szalai & Vinkó, 2013; Tinyanont et al., 2016).

There is a group of studied SNe with moderately high values of (3000-10 000 km s); in these cases, there is still chance for the clear dust-formation, not necessarily in the ejecta, but (also) in the CDS behind the forward shock. We also note that, in the lack of pre-exposion or adequate late-time images, there was no possibility to carry out proper background-subtraction in the cases of all studied SNe; thus, it is possible that mid-IR fluxes of these objects originate only partly from the SNe themselves. Moreover, as the example of SN 2012aw shows, the affection of the hot component can be non-negligible even 2-300 days after explosion in Type II SNe.

Finally, in some cases we see very high values (over 10 000 km s); this means that even speed of the forward shock may be too low for generating such large dust forming regions. In these cases, the plausible explanation is the re-heating of pre-explosion grains. As it is discussed in detail e.g. in Fox et al. (2011) and in Fox & Filippenko (2013), this heating connects to ongoing CSM interaction, and can appear in the form of collisional (by hot electrons) or of radiative (by high-energy photons) processes; however, if we accept the large values of , they indicate the presence of the latter process. As we described above, this radiative heating process of pre-existing dust has been found as the most probable explanation in the cases of Type IIn SNe. In our sample, large values have been found in some unclassified Type II SNe (which can be SNe IIn), and in Type Ia-CSM 2012ca (which type seems to show IIn-like behaviour); the only odd one in this line is Type Ic SN 2013ff (note however, that it has been captured at a relatively early epoch). An alternative scenario, called IR echo (in which the dust shell is heated by the peak luminosity of the SN, see e.g. Bode & Evans, 1980; Dwek, 1983; Sugerman, 2003; Meikle et al., 2006), can be ruled out according to the objects studied by us: SN peak luminosities, implied by echo radii (, where is a lower limit determined by the epoch of the latest Spitzer observations and is the speed of light) and by the observed temperatures, should be orders of magnitude larger than expected (see details again in Fox et al., 2011).

Taking a look at SNe with combined optical-IR SEDs, we were able to estimate dust parameters only in the case of SN2013ej (see Table 5). Our results are comparable with those of Tinyanont et al. (2016) and Mauerhan et al. (2017); however, we note that they both used =0.1 m graphite grains in their dust models.

We also show the dust parameters (masses, temperatures, mid-IR luminosities) presented in Table 6, together with values found in the literature, in Figure 14. We underline again that most of the presented data are based on modelling two-point SEDs, which makes them quite uncertain; moreover, in estimation of dust masses, selection of the proper model is an essential but very difficult step. On the bottom left panel, we present the dust masses inferred assuming amorphous carbon dust and a MRN grain size distribution (0.005-0.05 microns), while values calculated from assuming larger grains and/or Si-containing dust are shown in the top left panel. As it can be seen in Table 6, as well as in the earlier publications, large (10) dust masses (observed mainly in Type IIn objects and other interacting SNe, and in a few II-P objects) are basically connected to large values that indicates the existence (at least, partly) of heated pre-explosion grains, or, that only a part of the observed mid-IR flux originates from the environment of the SN. We note that we only give dust masses inferred assuming Si-containing dust if there were any spectroscopic evidences for the presence of Si – e.g. SNe 2004et (Kotak et al., 2009; Fabbri et al., 2011) or 2005af (Szalai & Vinkó, 2013) –, or, if it was the only calculated model for the given SN, e.g. SNe 2007it (Andrews et al., 2011b) or 2007od (Andrews et al., 2010). Nevertheless, in the lack of spectroscopic information, the determined temperatures may give a base for the selection of the appropriate dust composition model: if 1000 K, using carbonaceous dust model seems to be the the plausible choice, since Si grains require lower temperatures for effective condensation. We also note that choosing non-spherical geometry for the dust-forming region, or, assuming clumpy dust formation (see e.g. Meikle et al., 2007; Ercolano et al., 2007; Andrews et al., 2016) can also result in orders of magnitude higher/lower calculated dust masses.

## 4 Conclusion

Here we presented a comprehensive study on far the largest mid-IR dataset of SNe ever studied. Our sample contains Spitzer/IRAC data of various types of stellar explosions (different kinds of thermonuclear, as well as stripped-envelope and other Type II core-collapse SNe), including high number of objects catched by non-SN targeted Spitzer surveys. In total, we achieved a 5 enlargement in the number of studied SN sites captured by Spitzer (from 200 to 1100), and an 1.7 enlargement in positive detections (70 to 120) (this rate is even larger, 2, regarding Type Ia and SE CC SNe).

We carried out a thorough photometric analysis of the complete studied SN sample, including re-checking of all previously published data. In general, we found good agreements with the published values (10% difference in fluxes), except in some objects that were captured in a very faint phase and/or with a complex sky background (however, for this reason, the uncertainties of their original fluxes are also implicitly large).

The results include the statistical analysis of the mid-IR evolution of the different types of SNe, together with the highlighting of some objects show interesting behavior in this wavelength-range. We also fitted black bodies and simple analytic dust models to the SEDs calculated from the mid-IR data of SNe, combined them with optical data in some cases. Modelling of SEDs (even in two-point cases) allow us to make a kind of disentangling between the possible scenarios of the mid-IR radiation (dust formation in the ejecta or in a cold dense shell between forward and reverse shocks, radiative/collisional heating of pre-existing dust, IR echo), and, in some cases, to determine the main physical parameters of the assumed dust.

Beyond the existing store of learning regarding the long-term evolution and mid-IR behaviour of different types of SNe, we could make some new statement, as well as strengthen some existing theories tested them on a larger sample than before. Regarding thermonuclear explosions, we found that i) SNe Ia showing obvious signs of strong CSM interaction (the so-called Type Ia-CSM objects) are rare, and ii) there can be only a very limited number of “intermediate” cases with moderately strong CSM interaction (or, they produce mid-IR excess only on a very short timescale, or, there is an effect that inhibit us from observing this excess).

In the heterogeneous group of stripped-envelope CC SNe, there are some similarities in the mid-IR evolution. Nevertheless, beyond the similarities, an interesting trend emerges from the analyzed data: the length of mid-IR detectability seem to correlate with the assumed size of the progenitor (the larger the progenitor was, the longer time can the SN be followed in the mid-IR). Similarly to SNe Ia, there could be also a low number of strongly interacting objects; however, there are some very interesting objects produced some unexpected changes within a few years after explosion. We highlight the case of the known interacting SN Ib/c 2001em, for which the analysis of a previously unpublished, single-epoch Spitzer/IRAC dataset obtained in 2004 (at the time of the strong CSM interaction) has given important new information: the two-component fit of the mid-IR SED not just strengthens the previous results on the observed interaction, but, additionally, indicate a multiple structure of the pre-explosion dust shell.

Although this study has significantly enlarged the number of both thermonuclear and SE CC SNe detected in mid-IR, it is an important note that the amount of data are still small (and, most of the objects are quite undersampled) for carrying out more sophisticated analyses. In the cases of Type II SNe, the situation is a bit better; however, the number of objects that are both spectrally and temporally well-sampled, is also not so high. This could lead to the picture we now have of Type II-P SNe: in some cases, we can see rebrightening effects in mid-IR (thought to be direct signs of dust formation) after some hundreds days (or, even a bit later) after explosion, but it cannot be detected in a number of other objects.

Type IIn SNe, showing clear signs of CSM interaction at various wavelengths, show also interesting behaviour in mid-IR: while some of them remain bright for several years after explosion, other members of the class fade more quickly, or, can not be detected in mid-IR at all. To reveal the background of this heterogeneity, it would be an important step to monitor as many SNe IIn as possible within 1 yr after explosion, in which phase these objects have been seriously undersampled either with Spitzer or with other (mid-)IR detectors.

Our study also show that every SN with known late-time (3 months) CSM interaction is bright in mid-IR. An obvious and known consequence is that the analysis of mid-IR SEDs (combined wit other data, as far as possible) can give new information about ongoing dust formation and/or CSM interaction. Moreover, it also suggests that Spitzer or other future mid-IR, large FoV detectors could be ideal ”tracers” for more specific devices (e.g. James Webb Space Telescope, JWST) in observing these processes. Future JWST observations of interacting (dust forming) SNe at some different epochs would allow to get essential and gap-filling datasets extending from optical to mid-IR wavelengths (up to 30 microns, including both photometric and spectroscopic information), simultaneously. Gathering such complex datasets of even a few SNe would be a great leap forward in revealing the composition, size and spatial distribution of dust grains, as well as the timescales and dynamics of CSM interactions via allowing the comparison of refined theoretical models with spectrally well-sampled, high-quality data. This new pieces of information would lead to even more essential results in studying the evolution of SNe and the interaction with their environments, as well as the late phases of stellar evolution and, in more general, the open questions of cosmic nucleosynthesis.

This work is part of the project “Transient Astrophysical Objects” GINOP-2-3-2-15-2016-00033 of the National Research, Development and Innovation Office (NKFIH), Hungary, funded by the European Union, and is also supported by the UNKP-17-4 New National Excellence Program of the Ministry of Human Capacities of Hungary. TS has received funding from the Hungarian NKFIH/OTKA PD-112325 Grant. OP is currently supported by award PRIMUS/SCI/17 from Charles University. TM was supported in part by the Ministry of Economy, Development, and Tourismâs Millennium Science Initiative through grant IC120009, awarded to the Millennium Institute of Astrophysics, MAS. TM thanks the LSSTC Data Science Fellowship Program, his time as a Fellow has benefited this work. This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration; the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration; and the SIMBAD database, operated at CDS, Strasbourg, France. We acknowledge the availability of NASA ADS services. \softwareIRAF, HOTPANTS

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## Appendix A Basic data and mid-IR photometry of the studied SNe

\startlongtable \startlongtable \startlongtable