arXiv:1701.05902v1 [astro-ph.SR] 20 Jan 2017 uut2018 August 6 o.Nt .Ato.Soc. Astron. R. Not. Mon. utFrainadteBnr opnoso Supernovae of Companions Binary the and Formation Dust n obedgnrt oes(e h eiwb aze al. et single Maoz the by distinguishing review the of (see means models a degenerate as double and SN Ia Type the on cused into mixed be to questions. survives open the remain which and medium SNe dust interstellar in easy that formed relatively dust of is of How- fraction amount evolve stars the 2014). AGB to both Cherchneff in measure, stars 2011, to formation al. for dust et time where Gall ever, little (e.g., AGB is the there in to with early where along particularly universe dust, stars, of the are (AGB) source branch SNe important giant an population. asymptotic be overall to and believed the companions their also well-characterize binary SNe, better for then survey much remnants cleanly to be their to would possible or role were progenitors, Their it a if 2012). et progenitors Eldridge understood al. their (e.g., et stars and Sana isolated SN 2008, of evolution ex- of the many on properties and invalidating based the 2016) likely for Stefano evolution, Di pectations stellar Kraus & Duchˆene & Moe modify 2012, 2014, can al. al. Bina- et et consequences. Sana Kobulnicky (e.g., their 2013, common prop- and are the (SNe) ries understanding supernovae for of peren- challenges the erties of and two are questions formation dust nial and binaries of role The INTRODUCTION 1 c 2 1 .S Kochanek S. C. etrfrCsooyadAtoatcePyis h hoSt Ohio The Physics, AstroParticle and Cosmology for Center eateto srnm,TeOi tt nvriy 4 Wes 140 University, State Ohio The Astronomy, of Department 00RAS 0000 erhsfrselrcmain oS aelreyfo- largely have SN to companions stellar for Searches 1 000 , 2 , 0–0 00)Pitd6Ags 08(NL (MN 2018 August 6 Printed (0000) 000–000 , jca hspoie en frcniigteTp I N a A, Cas SNe ( IIb dust Type of amount the significant reconciling a formed of condens and means lumin the companion a luminous and photo-ionizing provides rapidly hot This by sufficiently ejecta. formation ra However, dust com absorption explosion. suppress through the the can content mark after dust t unambiguously decades the of both for of obscuration will measurement variable expands the the mu (SNR) allow and companion remnant cloud binary SN dust any the expanding that an implies of This companion center dust. binary of a amounts have frequently significant both should (SNe) Supernovae ABSTRACT n ohv omdangiil muto ut( dust of amount lumin a negligible have to a appear formed which of have both to 2011dh, and and 1993J SNe IIb Type N21d,CsA N1987 SN A, Cas 2011dh, evide SN the why words: explain Key contradictory. to com so help luminous appears may a SNe companions in lack binary formation both of dependence as unrecognized properties An picture, the dust. this of amounts with significant consistent formed are 1987A SN tr:msie–sproa:gnrl–sproa:idvda:S individual: supernovae: – general supernovae: – massive stars: l. t nvriy 9 .WorffAeu,Clmu H43210 OH Columbus Avenue, Woodruff W. 191 University, ate 8hAeu,Clmu H43210 OH Columbus Avenue, 18th t n erhsfrrdoeiso steS hc passes shock (e.g., SN companion 2016). non-degenerate the al. a as et from Chomiuk emission wind 2013a), radio the al. et through for Shappee searches 2007, Leonard and for (e.g., from stripped searches companion material on 2010), the from lines companions Kasen emission (e.g., close hydrogen curves narrow of light effects In- SN the 2012). early-time Pagnotta include & searches (Schaefer direct 0509–67.5 1006 SNR SN and al. Gonz´alez 2007), Hern´andez2012) et al. 1980, al. et et Middleditch Ihara Kelly & 2004, (Schweizer Ty- 2011a, al. as et al. such (SNR) (Ruiz-Lapuente et remnants cho (Li supernova in 2011fe looking pre- and SN the 2014) for examining include data SNe fo Ia explosion searches Type Direct to stars con- existence. companion other companion’s the observing of indirect, sequences or companion, the observing 2013). al. et Kushnir Thompso 2011, (e.g., it companions since associated (tertiary) genuinely case non-degenerate be may with latter Ia’s the generate double complicates that doub po- means SN producing the Ia in a and Type oscillations be degenerate systems Kozai-Lidov never of triple should role of there tential prevalence companion model The a generate be double companion. always the should in si there the and in model simple: degenerate relatively was gle picture original The 2014). erhsfrcmain a ihrb iet simply direct, be either can companions for Searches A T E tl l v2.2) file style X M d ∼ < 10 − M 3 d M fds omto on formation dust of ∼ > ⊙ hrta emission than ther tdahadform and death at beseisi the in species ible .TeCa and Crab The ). 0 ecmainas companion he u companions ous . 1 u companion ous M hc ak a lacks which c o dust for nce ⊙ tlea the at lie st ainand panion ainand panion ,wt the with ), 1993J, N n- le n r 2 C. S. Kochanek
Far less observational attention has been given to the distinguishable due to being shock heated and hence over- binary companions to core collapse SN (ccSN), although luminous (e.g., Marietta et al. 2000, Shappee et al. 2013b, Kochanek (2009) estimated that 50-80% of ccSN are prob- Pan et al. 2014). Other signatures may be peculiar kine- ably members of a stellar binary at death. More generally, matics (Ruiz-Lapuente et al. 2004), chemical abundances most massive stars are in binaries and many ccSN progeni- (e.g., Ihara et al. 2007, Gonz´alez Hern´andez et al. 2009, tors should be the remnants of stellar mergers, have under- Kerzendorf et al. 2009, Kerzendorf et al. 2013) or fast ro- gone mass transfer or simply have a binary companion (e.g., tation rates (e.g., Kerzendorf et al. 2009, Pan et al. 2012, Sana et al. 2012, Kobulnicky et al. 2014, Moe & Di Stefano Kerzendorf et al. 2013, Pan et al. 2014). Finally, the su- 2016). For example, the numbers of stripped Type Ibc SNe pernova ejecta can produce broad absorption lines in the and the limits on their progenitor stars both suggest that spectra of stars either inside or behind the SNR (e.g., many are stripped through binary mass transfer rather Wu et al. (1993) for the star behind SN 1006 identified than simply wind (or other) mass loss (e.g., Eldridge et al. by Schweizer & Middleditch (1980) and the remnant of 2008, Smith et al. 2011, Eldridge et al. 2013). Most the- SN 1885 in M31 found by Fesen et al. (1989)). All these oretical studies (e.g., Yoon et al. 2010, Yoon et al. 2012, spectroscopic tests can also be applied to the companions Yoon et al. 2017, Claeys et al. 2011, Benvenuto et al. 2013, of ccSN even though they have been discussed almost ex- and Kim et al. 2015) have focused on the binary proper- clusively in the context of Type Ia SN. All spectroscopic ties of the stripped ccSN classes (Type IIb, Ib and Ic) as tests are, however, challenging to apply in an extragalactic cases where binary evolution is modifying the outcomes. As context because they require high resolution, high signal-to- with the Type Ia SN, companions can modify the early- noise spectra of the candidate star. Ideally, we need a time time light curves of the SN (e.g., Kasen 2010, Moriya et al. variable signature for a binary companion that can be car- 2015, Liu et al. 2015). Searching for narrow hydrogen emis- ried out with broad band photometry for decades after the sion lines in the nebular phase is less promising even for SN. Type Ib/c SNe because of the short stellar life times and Dust formation is predicted for most SN, with the to- the role of winds in stellar mass loss. Because luminosities tal amount produced diminishing with decreasing ejecta increase so rapidly with mass, the signatures of shock heated masses and increasing explosion energies because these lead companions to ccSNe will also be weaker than those for com- to higher velocities and more rapidly dropping densities panions to Type Ia SNe. (e.g., Dwek 1988, Kozasa et al. 1989 Todini & Ferrara 2001, There is no certain identification of a binary compan- Cherchneff & Dwek 2010, Nozawa et al. 2010, Nozawa et al. ion to a ccSNe. The Crab, Cas A, and SN 1987A lack 2011, Sarangi & Cherchneff 2015). Typical theoretical esti- luminous companions, with upper mass limits of order 1- mates are that ccSN produce Md ∼ 0.1-1M⊙ of dust while −3 2M⊙ (Kochanek 2017). Graves et al. (2005) found some- Type Ia produce Md ∼ 10 -0.1M⊙ of dust. These predic- what tighter limits for SN 1987A, but assumed far less dust tions appear to be consistent with late time observations of than is now known to be present (see below). The Crab SNR but such high dust masses are rarely seen shortly after was a low-energy Type II SN, possibly an electron capture a SN (see the reviews by Gall et al. (2011) or Cherchneff SN (e.g., Hester 2008, Smith 2013), Cas A was a Type IIb (2014)). Ignoring SN with strong circumstellar interactions, SN (Krause et al. 2008, Rest et al. 2008), and SN 1987A evidence for dust in SN is usually found roughly a year or was a (peculiar?) Type II SN (Arnett et al. 1989). The best two after the explosion as either a blue shift of the emission case for a detection is probably a hot, luminous companion lines or a mid-IR excess due to the presence of hot dust. Ex- 5 (T ∼ 20000 K, L ≃ 10 L⊙) to the Type IIb SN 1993J amples include SN 1987A (Wooden et al. 1993), SN 2003gd (Maund et al. 2004, Fox et al. 2014). The existence of a (Sugerman et al. 2006), and SN 2004et (Kotak et al. 2009). similar companion to the Type IIb SN 2011dh is debated, Observations of SNR at much later times (decades or with Folatelli et al. (2014) arguing for a detection and longer), particularly at longer wavelengths corresponding to Maund et al. (2015) arguing that the flux may be dominated emission by cooler dust, generally find dust masses more by late time emission from the SN. There is some evidence of compatible with theoretical predictions. Recent examples a blue companion for the Type IIb SNe 2001ig (Ryder et al. include SN 1987A (Matsuura et al. 2011, Indebetouw et al. 2006) and SN 2008ax (Crockett et al. (2008). There are lim- 2014, Matsuura et al. 2015), Cas A (Barlow et al. 2010, its on the existence companions to the Type Ic SNe 1994I De Looze et al. 2016) and the Crab (Temim & Dwek 2013, (Van Dyk et al. 2016) and SN 2002ap (Crockett et al. 2007) Owen & Barlow 2015). These higher dust masses may not −2 and the Type IIP SN 2005cs (Maund et al. 2005, Li et al. be universal, as Temim et al. (2010) find only a few 10 M⊙ 2006), and SN 2008bk (Mattila et al. 2008). All the claimed of dust in the pulsar wind-containing remnant G54.1+0.3. detections are blue, which is expected for most binary com- There is little evidence for cold dust in the Tycho or Ke- −2 panions (Kochanek 2009). However, in the presence of dust pler Type Ia remnants (Md < 10 M⊙, Gomez et al. 2012). formation, early-time limits on the existence of binary com- A fundamental problem for all these estimates is that they panions are problematic, as we discuss below. depend on identifying dust by emission. Observations dur- For either SN class, the challenge is to prove that any ing the SN are generally only sensitive to hot dust be- candidate is a real binary companion with the further com- cause they depend on observations at relatively short mid-IR plication of triples, particularly for the single versus dou- wavelengths (e.g., the Spitzer 3.6 and 4.5µm bands), while ble degenerate debate. Pre-supernova light curves can iden- searches for cold dust require observations at long wave- tify close binaries, but data of adequate depth and cadence lengths where the combination of luminosities and sensitiv- are only beginning to exist (e.g., Kochanek et al. 2012a, ities usually restrict the searches to the Local Group or just Kochanek et al. 2016) and any detections depend on rare, to the Galaxy and Magellanic Clouds. favorable geometries. Stars identified after the SN may be In theory, these two problems can solve themselves –
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Figure 1. Absorption (κa, solid) and scattering (κs, Figure 2. Expected visual optical depths (τ0, Equation 3) as a dashed) opacities for Draine & Lee (1984) graphitic (black) and function of time for ccSNe (solid) and Type Ia (dashed) SN. The Laor & Draine (1993) silicate (red) dust as a function of size a. rough expectations for the sources discussed in the text are indi- 4 2 We scale the results to κ = 10 κ4 cm /g. cated by squares and triangles for ccSNe and Type Ia SNe, respec- tively. The scalings assume a dust mass of Md = 0.1M⊙, an ex- plosion energy of E = 1051 erg, a visual opacity of κ = 104 cm2/g the time variable absorption from the dust produced by (see Figure 1) and ejecta masses of either 10M⊙ (ccSNe) or 1.4M⊙ a SN is a nearly unique signature of a binary companion, (Type Ia). and the absorption of light from the companion by the dust is a temperature-independent probe of the amount of dust formed. The observations are also feasible for decades af- els with E51 = 1 for our standard results. The break radius ter the SN, permitting relatively large surveys for both dust scale is and binary companions at the sites of SN limited only by the 17 r0 = v0t = 9.5t100 v3000 × 10 cm (2) luminosity of the companions. In §2 we introduce a simple model for the dust and discuss its implications for specific where t = 100t100 years and v = 3000v3000 km/s. The size SNe. There is, however, a caveat. As we discuss in §3, a suf- of the ejecta cloud grows sufficiently rapidly that we can ficiently hot and luminous binary companion can suppress simply view any binary companion as lying at the center of dust formation, which may explain the difference between the dust distribution. the Type IIb SNe Cas A (lots of dust and no luminous com- If the ejecta contains dust with a total mass of Md = panion) and SN 1993J (no dust and a luminous companion). 0.1Md0.1M⊙ which is uniformly mixed with the gas and has 4 2 In §4 we use the simple model for binary companions to SNe a constant opacity of κ = 10 κ4 cm /g, then the optical from Kochanek (2009) to illustrate the effects of dust on the depth scale is detectability of binary companions. We end in §5 with a 15κMd −2 −2 general discussion and potential observations. τ0 = 2 2 = 0.33κ4 Md0.1v3000t100. (3) 32πt v0 Alternatively, we can replace the ejecta velocity with the kinetic energy to find that 2 MODELS 15κMdMe −1 −2 τ0 = = 0.30κ4M 0 1M 10E51 t100. (4) We consider a simple self-similar (e.g., Chevalier 1982) 64πEt2 d . e model for the SN ejecta density distribution, For a fixed dust mass, Type Ia SN will have less optical depth −x 15Me r at any given time due to their significantly faster expansion. ρ(r, t)= 3 3 (1) 32πv0 t v0t The optical depth of the inner region from the center to radius r ≤ r0 is where x =0(x = 8) for v < v0 (v > v0) or, equivalently, r < v0t (r > v0t). The total kinetic energy of the debris of r v 2 τin = τ0 = τ0 (5) E = Mev0 /2 is determined by the ejecta mass Me and the r0 v0 velocity scale v0. By mass, 5/8 of the ejecta lies in the inte- and the optical depth from radius r0 = v0t outwards to rior region and 3/8 lies in the exterior region. For an energy 51 radius r ≥ r0 is scale of E = 10 E51 erg and a mass of 10M⊙ (1.4M⊙), the 7 7 characteristic velocity is v0 ≃ 3200 km/s (v0 ≃ 8500 km/s) τ0 r0 τ0 v0 τout = 1 − = 1 − . (6) for a Type IIP (Type Ia) SN. We adopt these simple mod- 7 r 7 v
c 0000 RAS, MNRAS 000, 000–000 4 C. S. Kochanek
If one puts all the material with v > vs > v0 into a thin (see Fesen et al. 1989, Fesen et al. 2015), Tycho, Kepler, and shell at radius vst, the optical depth of the shell is SN 1006. 7 The first point to note from Figure 2 is that SNR should τ0 v0 τshell = . (7) be optically thick to dust for their first 6 vs 1/2 1/2 1/2 −1/2 1 This shows that the detailed arrangement of the outer ma- tτ> = 55κ4 Md,0.1Me10 E51 years (9) terial has little effect on the optical depth. Other changes if the amount of dust formed in anyway corresponds to the- in the density profile will produce similar, modest changes oretical expectations. For the ccSNe, the theoretically pre- in the dimensionless prefactors of these expressions and are dicted dust mass can be ten times larger. For the Type Ia 1/2 1/2 unimportant compared to changes in the opacity, mass, en- 1 SNe, the time scale is tτ> ≃ 20κ4 Md,0.1 years, where the ergy, velocity or age of the ejecta. theoretically predicted dust mass might also be a ten to a The dust opacity is obviously a key quantity, with hundred times smaller. Overall, core collapse SNRs should 3 Q(a,λ) be optically thick for decades up to a century, and Type Ia κ(λ)= (8) SNRs should be optically thick for years up to a decade. 4ρg a The SN 1987A remnant should still be very op- −3 where ρg (≃ 2.2 and 3.5 g cm for graphitic and silicate tically thick given the recent Herschel and ALMA es- dusts) is the bulk density of a grain, a is the grain size, and timates that the cold dust mass is Md ≃ 0.5 Q(a,λ) is is the usual efficiency factor. Figure 1 shows the to 1.0M⊙ (Matsuura et al. 2011, Indebetouw et al. 2014 visual absorption and scattering opacities, κa and κs, for Matsuura et al. 2015). Graves et al. (2005), in their lim- standard graphitic and silicate dust as a function of grain its on any surviving binary companion, used much lower size (Draine & Lee 1984, Laor & Draine 1993). The total optical depth estimates based on dust masses estimated opacity is κt = κa + κs and the effective absorption opacity from the ratio of optical/UV to mid-IR emission found by 1/2 is (κaκt) due to the increase in path lengths created by Bouchet & Danziger (1993) 2172 days after the explosion. scattering. More or less independent of composition or grain Apparently, much of the dust must have formed at slightly 4 2 size, the scale of the V-band opacity is of order 10 cm /g, as later times (see, e.g., Wesson et al. 2015). Another impor- used in the optical depth scalings given above. We will treat tant point is that the bulk of the dust appears to have ex- the absorption as a foreground screen since the differences pansion velocities of v ∼< 1400 km/s, putting it well inside between a foreground screen and an unresolved dust shell the expanding shock between the ejecta and the surrounding are unimportant for our order of magnitude discussion (see medium. This might be expected because the outer layers of Kochanek et al. 2012a). the ejecta are the least likely to form dust both because they Figure 2 shows the V-band optical depth scale τ0 as a have the lowest metal fractions (i.e. Type IIP envelopes) function of time for a fiducial model with Md = 0.1M⊙ of and because they have the highest expansion velocities and 4 2 dust, an opacity of κ = 10 cm /g, an explosion energy of so the most rapidly dropping densities (e.g., Kozasa et al. 51 E = 10 erg, and either Me = 10M⊙ (v0 = 3200 km/s) or 1989). This means that the reverse shock does not start to 1.4M⊙ (v0 = 8500 km/s) to represent ccSNe and Type Ia destroy newly formed dust until late in the evolution of the SNe, respectively. The absolute normalization can be altered SNR. by changing the dust mass, the opacity, the debris velocity The best cases for the detection of binary compan- range over which dust forms or the structure of the self- ions to ccSNe are the Type IIb SN 1993J and SN 2011dh. similar model. Changes in the velocity range or the den- Maund et al. (2004) report the spectroscopic detection of sity structure should be relatively unimportant compared a early-B supergiant as the putative binary companion to to changes in the dust mass or opacity, which is why we SN 1993J 9.93 years after the explosion, and Fox et al. simply use the scale τ0. In particular, ccSNe likely produce (2014) argue that new HST observations taken in late 2011 more dust than Md = 0.1M⊙ and Type Ia SNe likely pro- and early 2014 (so ∼ 19 years post explosion) confirm the duce less. result. Both use an estimated extinction of AV ≃ 0.6 mag The simple τ ∝ t−2 power law dictated by expansion derived from photometry of nearby stars in Maund et al. will fail at early times (t ∼< 2 years) when the dust properties (2004). If we fit the F218W, F275W and F336W magni- are still evolving. It will also fail at late times as the reverse tudes from Fox et al. (2014) to the Solar metallicity PAR- shock begins to destroy dust (e.g., Bianchi & Schneider SEC models (Bressan et al. 2012), focusing only on tem- 2007, Nozawa et al. 2007), although this likely only matters perature and extinction, we find a slightly smaller estimate on longer time scales than we consider here. This model also AV ≃ 0.3 ± 0.1 mag, but there is unmodeled contamina- excludes any dust that might form in the contact discontinu- tion from SN emission that introduces additional system- ity (a “cold dense shell”) between the shocked ejecta and the atic uncertainties. With a Galactic extinction of roughly shocked CSM (e.g., Chevalier & Fransson 1994, Pozzo et al. AV ≃ 0.2 (Schlafly & Finkbeiner 2011), we can conserva- 2004). tively use a limit that AV ∼< 0.4 mag at both epochs corre- In Figure 2, we have also roughly marked where various sponding to τV ∼< 0.4. For an elapsed time of 10 or 19 years, −1 sources, many of which we introduced in §1, should lie given we would expect τV ≃ 30 and 8.2κ4Md0.1Me10E51 , respec- our fiducial parameter assumptions. For ccSNe, we show the tively, implying limits on the dust masses of Md ∼< 0.0013 −1 −1 Type IIb SNe 2011dh and 1993J, where there are arguments and 0.0049E51 κ4 Me10M⊙. The source also appears to have for the detection of a companion, along with the much older faded, presumably due to decaying emission by the SN, with- Type IIb remnant Cas A. We also show SN 1987A, the Crab out evidence that the contribution from the putative com- and G54.1+0.3. For Type Ia SNe, we show the very recent panion has increased as it should if veiled by dust formed in SN 2011fe (Nugent et al. 2011), along with the SN 1885 the SN.
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Figure 3. Fraction of all ccSNe with secondaries brighter than Figure 4. As in Figure 3 but with no dust formation if the black MV assuming no SN dust (heavy black solid, τV = 0). The dashed body flux of silicon ionizing photons (> 8.2 eV) exceeds Q∗ > black lines show the effect of including our standard absorption 1049 s−1, roughly matching the companion to SN 1993J. Many of model for times 20, 30, 50 and 100 years after the SN. The heavy the most luminous binary companions are now unobscured from red dotted line shows the integral magnitude distribution of the the start because dust formation is suppressed. The companion primaries when they explode for comparison. This model assumes to SN 1993J has MV ≃−5.9 mag. that all systems were binaries (F = 1), so the fraction with stellar companions at death is 70%. The time scale can be converted to other parameter choices following Equation 9. The upper scale shows the corresponding apparent magnitudes for a source at a Consider the Type IIb dust formation model of distance of 10 Mpc. Nozawa et al. (2010). When the star explodes, it is a 4.5M⊙ star which then ejects 2.94M⊙ of material. The inner regions of the ejecta will form grains based on Mg (0.11M⊙, A = 24, Because SN 2011dh is so much younger, the con- 7.6 eV), Al (0.01M⊙, A = 27, 6.0 eV), Si (0.11M⊙, A = 28, straints are correspondingly tighter. Folatelli et al. (2014) 8.2 eV), S (0.03M⊙, A = 32, 10.4 eV) and Fe (0.08M⊙, and Maund et al. (2015) analyze the same HST data taken A = 56, 7.9 eV), while the outer regions will form grains in August 2014, 3.2 years after the explosion. Folatelli et al. based on carbon (0.11M⊙, A = 12, 11.3 eV). The numbers (2014) adopt an extinction of A = 0.3 mag as found for V give the mass of the element in the ejecta, the atomic mass nearby stars by Murphy et al. (2011) and argue for the pres- of the most common isotope, and the first ionization en- ence of the blue, B star predicted in binary models for ergy. “Mixed” with the heavier elements is 1.6M⊙ of oxygen the production of SN 2011dh by Benvenuto et al. (2013). (A = 16, 13.6 eV), mixed with the carbon is roughly 1.5M⊙ Maund et al. (2015) agree with the photometry but argue of helium (24.6 eV) and there is roughly 0.08M⊙ of resid- that some or all of the observed flux could still be due ual hydrogen in the surface layers. While masses are not to the SN. The expected optical depth at this epoch is ∼ −1 −1 reported, nitrogen (14.5 eV) and neon (21.6 eV) will also 290κ4Md0.1Me10E51 , so a detection of the binary compan- −4 −1 −1 have significant abundances but are important only to the ion with A = 0.3 mag implies M < 10 E51κ M M⊙. V d ∼ 4 e10 extent that they absorb UV photons. Note that dust forma- This leaves a puzzle as to why some Type IIb SNe form dust tion can be blocked by photoionization without needing to (Cas A), while others apparently do not (SN 1993J and po- ionize the most abundant elements (H, He, O) or the other tentially, SN 2011dh). common, but “inert”, elements (N, Ne) because all these elements have higher ionization energies than the key dust forming elements. 3 THE EFFECTS OF A HOT BINARY We can approximate the structure by putting 0.34M⊙ COMPANION ON THE DEBRIS of silicon in the inner region (r c 0000 RAS, MNRAS 000, 000–000 6 C. S. Kochanek −17 2 where σp ∼ 10 σ17 cm is a typical photoionization cross of the photoionized region due to the injection of ionizing section near threshold, A = 28A28, and t = t1 years. This photons, the second term is the losses due to recombination, means that in the early phases we can assume that every and the third term is a Hubble expansion term from work- ionizing photon is absorbed. As the photosphere retreats, ing in terms ofr ˆ instead of r. The solution can be extended these metal atoms will initially be neutral, so a spectrum of beyond r0, but the expressions become more complicated. 5 any binary companion should show a strong absorption edge In practice, we considered a model with a L = 10 L⊙ and near 8 eV (1600A˚). That the UV spectra of the companion T = 20000 K black body source ionizing an inner region con- of SN 1993J from Fox et al. (2014) do not show such an taining 0.34M⊙ of silicon (A = 28, γ = 0.29) to be ionized, edge strongly suggests that the Mg, Si, etc., have all been and an outer region containing 0.11M⊙ of carbon (A = 12, photoionized. γ = 0.083). Using silicon is a reasonable proxy for the ac- Absent other sources of ionizing photons, the compan- tual mixture of Mg/Al/Si/S/Fe. We assume that the silicon ion will form a photoionized region at the center of the SNR. and carbon are either neutral or singly ionized and that all The ionizing flux needed to balance recombination interior other elements with their higher ionization potentials are to r0 is nearly neutral. In this model, the remnant is photoionized 2 2 3/2 in 530 days starting from neutral gas. The inner region is 75αMi 47 α13Mi0.1Me10 −1 Q0 = ≃ 2 × 10 s (11) photoionized in 200 days, while the photoionization of the 256πA2m2v3t3 2 3/2 3 p 0 A28E51 t1 outer region is slowed because of the higher ionization poten- −13 3 where α = 10 α13 cm /s is the recombination rate. This tial of carbon and the overestimation of the recombination rate created by putting all the carbon in the outer region. assumes that the elements included in Mi are either neutral or singly ionized and that any other elements in the inner With one-third the luminosity, it takes four years and with region are little ionized. This is likely true given the higher three times the luminosity it takes 240 days. ionization potentials of helium, nitrogen, oxygen and neon. The real evolution would be more complex since we Photoionizing the outer region (r>r0) requires 3/13 of this should follow the ionization of all the species. We have also flux. neglected the emission by the SN itself, which includes a A black body produces locally ionizing component because of the radioactive de- ∞ 15L hν 2 u −1 cays, the evolution of the photosphere, collisional ionization, ∗ − Q = 4 γ where γ(u)= duu (e 1) (12) and any ionizing radiation from the expanding shocks. Most π kT kT Zu of these effects should accelerate the photoionization of the photons with energies above hν. Since we are interested in ejecta by the secondary because it means the ejecta are ei- the photoionization of heavy elements with ionization po- ther starting from a partially ionized state or there are addi- tentials below that of hydrogen, the large deviations of stel- tional sources of ionization. Simply starting the process later lar spectra from black bodies beyond 13.6 eV are not of (e.g., at the end of the plateau phase) has almost no effect great importance. The overall scale is 15L/π4kT = 4.3 × 49 −1 −1 5 on the time at which photoionization is complete because 10 L4T5 s for a luminosity L = 10 L5L⊙ and tem- 4 the faster initial growth due to the lower densities compen- perature T = 10 T4 K. For a temperature of 20000 K, sates for the lost time at the start. For example, solutions γ(u) = 0.030, 0.083, 0.29, and 0.66 for H (13.6 eV), C to our simple photoionization model started 90 days after (11.3 eV), Si (8.2 eV), and Al (6.0 eV). Equating Equa- the start of the expansion simply merge onto the previous tions 11 and 12, the UV photons from the companion can solution. balance recombination over the full inner region after time 1/3 1/2 2/3 1/3 We chose these parameters because they roughly match 4 3 0 1 α13 Me10 Mi0.1T4 . ± . tr ≃ 0.34 years (13) the estimated properties of T ≃ 10 K and L ≃ 1/2 1/3 1/3 2/3 5.0±0.3 E51 γ0.1 L5 A28 10 L⊙ for the companion to SN 1993J(Maund et al. 2004). Fox et al. (2014) agree with this temperature esti- where γ(u) = 0.1γ0.1. For comparison, the time scale for the companion to produce ionizing photons equal in number to mate but provide no independent estimate of the luminos- the number of target atoms in the inner region is ity. Folatelli et al. (2014) do not directly estimate a tem- 3 perature and luminosity for their proposed companion to 4πr0 ρ 15Mi Mi0.1T4 SN 2011dh but compare to the models of Benvenuto et al. tp = = ≃ 0.060 years. (14) Q∗A 8AQ∗ A28γ0.1L5 (2013). In these models the secondary ranges from T ≃ 3.8 This means that if dust formation occurs on times scales 22000 K and L = 10 L⊙ if the accretion efficiency is low 4.8 of order a year, a sufficiently luminous, hot companion can to T∗ ≃ 39000 K and L = 10 L⊙ for high accretion effi- photoionize the condensible material before dust formation ciencies. Folatelli et al. (2014) favor the lower efficiency so- begins. lutions with the lower luminosity and temperature compan- We can model the growth of the ionized region us- ion. A star with the estimated proprieties of the companion ing the usual simple model for the growth of a Str¨omgren to SN 1993J or those of the hotter more luminous mod- sphere (Osterbrock 1989) modified for the expansion of the els for SN 2011dh would photoionize the most important medium. For example, the growth rate of the photoionized dust producing species on the time scales that Nozawa et al. zone in the inner (r c 0000 RAS, MNRAS 000, 000–000 Dust and Supernova Binary Companions 7 49.5 −1 50 −1 explain why the are no signs of strong absorption bluewards Q∗ > 10 s and is negligible for Q∗ > 10 s . Low- of ∼ 1600A˚. ering the threshold rapidly raises the fraction to 15% for 48.5 −1 48 −1 Q∗ > 10 s and 25% for Q∗ > 10 s . Not all of the visually luminous stars are unobscured, since there are 4 AN ILLUSTRATIVE MODEL some companions that are luminous but cool. The compan- ion to SN 1993J should have MV ≃−5.9 mag, and it lies in In Kochanek (2009) we considered a simple model for the the magnitude range of Figure 4 where the companions can expected properties of binary companions to ccSNe ignor- affect dust formation (as expected). ing binary interactions. Here we take one of these cases to illustrate the consequences of the evolving dust distri- bution. We assume that the distribution of primary masses −x 5 DISCUSSION 8M⊙ < Mp < 100M⊙ is Salpeter, dN/dMp ∝ Mp with x = 2.35 and that fraction F of the primaries have binary If SNe form dust as predicted in theoretical models and ob- companions distributed in mass Ms as f(q) with qmin < q = served in nearby SNRs, then the binary companions to SNe, Ms/Mp < qmax where dqf(q) ≡ 1. The joint distribution particularly ccSNe, should initially be heavily obscured. The of the primary and secondaryR stars in mass is decreasing optical depth depth due to expansion should lead to a steady brightening that should be a nearly unique sig- dN −x−1 = F Mp f(q) (16) nature of a binary companion. The inferred optical depths dMpdMs then provide an estimate of the amount of newly formed with a secondary mass distribution of dust that is independent of the dust temperature. Absorp- qmax tion by dust should be observable (optical depths > 0.01) dN −x x−1 ∼ = F fq Ms fq = q f(q)dq. (17) for decades to roughly a century after the explosion. The dMs Z qmin local SNR that might be probed through dust absorption An observed ccSN can be the collapse of a single star that are SN 1987A, Cas A and the Type Ia SN 1885 in M31. was never in a binary (fsingle = (1 − F )/(1 + F fq)), the The present day optical depth scale for SN 1987A is −1 primary of a binary (fp = F/(1+ F fq )), or the secondary of τ0 ∼ 3κ4 Md0.1 and current estimates are that Md ≃ a binary (fs = F fq/(1+F fq)). The fraction of ccSNe with a 0.5-1.0M⊙ (Matsuura et al. 2011, Indebetouw et al. 2014, stellar binary companion is just fp, since when the secondary Matsuura et al. 2015). Even for these high dust masses, of a binary explodes the primary is now a compact object SN 1987A is approaching the point where it is feasible (and the binary may have been disrupted). to search for either a surviving companion or a fortu- Here we will just consider the case with f(q) constant itously obscured background star in the near-IR. Many mod- over 0.02 c 0000 RAS, MNRAS 000, 000–000 8 C. S. Kochanek to measure the optical depth through the time variability are largely produced in a shell associated with the shock of the extinction of background stars. Over a decade, the region (e.g., Fransson et al. 2005). The companion is too −1 optical depth should drop by ∼ 0.002κ4 Md0.1 which is cool to contribute to producing these highly ionized states. well within the capabilities of difference imaging methods if Where a spherical shell produces exactly a top hat veloc- Md ≃ M⊙. This depends on the existence of a (non-variable) ity distribution, with dP/dv constant out to the expansion background star since Cas A seems to not have had a binary velocity of the shell, recombination lines produced by the companion (Kochanek 2017), but is an otherwise straight companion fully photoionizing the interior (r c 0000 RAS, MNRAS 000, 000–000 Dust and Supernova Binary Companions 9 nothing can be said about its properties because it may Eldridge, J. J., Fraser, M., Smartt, S. J., Maund, J. R., & simply be heavily obscured. If a secondary is detected, than Crockett, R. M. 2013, MNRAS, 436, 774 iPTF13bvn becomes another example of an SN making Eldridge, J. J., Fraser, M., Maund, J. R., & Smartt, S. J. −3 negligible amounts of dust (Md ∼< 10 M⊙) and the 2015, MNRAS, 446, 2689 companion should be at the maximum possible luminosities Eldridge, J. J., & Maund, J. R. 2016, MNRAS, 461, L117 predicted by Eldridge & Maund (2016). Fesen, R. A., Saken, J. M., & Hamilton, A. J. 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E., & Pagnotta, A. 2012, Nature, 481, 164 c 0000 RAS, MNRAS 000, 000–000 26 mag at 10 Mpc) sec- of τ0 ∼ 0.02κ4 Md0.1 is consistent with this comment and ondaries even though most SNe (70% for the F = 1 binary we make a quantitative estimate in Auchettl & Kochanek fraction used here) occur in systems with a stellar compan- (2017). ion. With the addition of dust, companions should almost The present day optical depth scale for Cas A should −1 never be observable until decades after the SN. However, this be similar to that of SN 1885, with τ0 ∼ 0.03κ4 Md0.1, leads to the interesting observational possibility of searching because the slower expansion of a ccSN compensates for for slowly reappearing stars at the sites of decades old SNe. Cas A’s greater age. With dust mass estimates approach- Now, suppose that dust formation is suppressed when- ing Md ∼ M⊙ (Barlow et al. 2010, De Looze et al. 2016), 49 −1 ever Q∗ > 10 s (Equation 12). This is roughly the flux of the optical depth of the SNR could be significant. This sug- silicon ionizing photons from the companion of SN 1993J. As gests trying the method of Trimble (1977), comparing the shown in Figure 4, many of the more luminous companions colors of stars superposed on the SNR to those of other are now easily observed because dust formation has been nearby stars. This method is probably infeasible because 49 −1 suppressed. For a threshold of Q∗ > 10 s , dust forma- of the limited numbers of stars and because even modest tion is suppressed in roughly 8% of the binary systems. If spatial inhomogeneities in the AV ∼ 5-6 mag of extinc- the threshold is even modestly higher, the mechanism does tion towards Cas A (Hurford & Fesen 1996) will confuse the not work, since the fraction drops to 3% for a threshold of measurements. With some patience, however, it is feasible