The Cold and Dusty Circumstellar Matter around Fast-expanding Type Ia Supernovae
Xiaofeng Wang, Jia Chen, Lifan Wang, Maokai Hu, Gaobo Xi, Yi Yang, Xulin Zhao, Wenxiong Li
aa r X i v : . [ a s t r o - ph . H E ] J un Draft version June 17, 2019
Preprint typeset using L A TEX style emulateapj v. 12/16/11
THE COLD AND DUSTY CIRCUMSTELLAR MATTER AROUNDFAST-EXPANDING TYPE IA SUPERNOVAE
Xiaofeng Wang , Jia Chen , Lifan Wang , Maokai Hu , Gaobo Xi , Yi Yang , Xulin Zhao , Wenxiong Li , Draft version June 17, 2019
ABSTRACTType Ia supernovae (SNe Ia) play key roles in revealing the accelerating expansion of the universe,but our knowledge about their progenitors is still very limited. Here we report the discovery of a rigiddichotomy in circumstellar (CS) environments around two subclasses of type Ia supernovae (SNe Ia)as defined by their distinct photospheric velocities. For the SNe Ia with high photospheric velocities(HV), we found a significant excess flux in blue light during 60-100 days past maximum, while thisphenomenon is absent for SNe with normal photospheric velocity (Normal). This blue excess canbe attributed to light echoes by circumstellar dust located at a distance of about 1-3 × cm fromthe HV subclass. Moreover, we also found that the HV SNe Ia show systematically evolving Na I absorption line by performing a systematic search of variable Na I absorption lines in spectra of allSNe Ia, whereas this evolution is rarely seen in Normal ones. The evolving Na I absorption canbe modeled in terms of photoionization model, with the location of the gas clouds at a distance ofabout 2 × cm, in striking agreement with the location of CS dust inferred from B-band lightcurve excess. These observations show clearly that the progenitors of HV and Normal subclasses aresystematically different, suggesting that they are likely from single and double degenerate progenitorsystems, respectively. Subject headings: supernovae: general—supernovae: progenitors — supernovae: distance scale INTRODUCTION
It is conventionally accepted that type Ia super-novae (SNe Ia) result from thermonuclear explosion ofa carbon-oxygen (CO) white dwarf (Nomoto et al. 1997,Hillebrandt et al. 2000, Maoz 2014). Two popularscenarios are: merger-induced explosion of two whitedwarfs (the so-called double degenerate (DD) scenario)and accretion-induced explosion of a massive WD witha non-degenerate companion (the so-called single degen-erate (SD) scenario). Many progenitor classes have beenproposed (Gilfanov et al. 2010, Wang & Han 2012,Maoz 2014), but observational evidences have not yetreached definitive conclusions on particular progenitorsystems. The SD scenario is favored by the possible de-tections of circumstellar materials (CSM) around someSNe Ia through detections of strong ejecta-CSM interac-tion (Hamuy et al. 2003, Wang et al. 2004, Alderinget al. 2006, Taddia et al. 2012, Silverman et al. 2013,Bochenek et al. 2018) or evolving narrow absorptionlines possibly due to CSM (Patat et al. 2007, Blondinet al. 2009, Sternberg et al. 2011, Dilday et al. 2012),while there are also observational findings suggesting nocompanion signatures for some SNe Ia (Li et al. 2011a,Gonzalez et al. 2012, Schaefer et al. 2012, Olling etal. 2015). This may suggest that SNe Ia have multiple Physics Department and Tsinghua Center for As-trophysics, Tsinghua University, Beijing 100084, China;wang [email protected] Mitchell Institute for Fundamental Physics and Astronomy,Texas A&M University, College Station, TX 77843, USA Purple Mountain Observatory, Nanjing, 201008, Jiangsu,China Department of Particle Physics and Astrophysics, Weiz-mann Institute of Science, Rehovot 76100, Israel Department of Physics, Tianjin University of Technology,Tianjin 300384, China progenitor systems, as favored by the discovery that SNeIa with different ejecta velocities originate from distinctbirthplace environments (Wang et al. 2013).Observationally, spectroscopically normal SNe Ia con-sists of ∼
70% of all SNe Ia (Branch et al. 1993, Li et al.2011b) and can be categorized into high-velocity (HV)and normal-velocity (NV) subclasses based on ejecta ve-locities inferred from the blueshifted Si II 6355 ˚A line,i.e., 12,000 km s − (Wang et al. 2009). Compared toNV ones, HV SNe Ia have systematically redder B − V colors at maximum light and prefer abnormally low to-tal to selective absorption R V ratios (Wang et al. 2009).It is thus important to examine whether this differencearises from the intrinsic difference of the SN ejecta orfrom systematic difference in circumstellar (CS) and/orinterstellar environments of the two groups. These is-sues may shed light on the elusive progenitor systems ofSNe Ia.The presence of CS dust can be tested by examiningthe behaviors of narrow interstellar absorption features.The interstellar sodium Na I doublet (D I absorption in low-resolution spectra of SNeIa as well as an overall analysis of the behavior of theirlate-time light curves, with an attempt to constrain thedust environments around SNe Ia and hence the prop-erties of their progenitors. This paper is organized asfollows: in Section 2, we describe the dataset of SNe Iaused in our analysis. The results from interstellar Naabsorptions and late-time light curves are presented inSection 3. Discussions and conclusions are given in Sec-tion 4. DATASET
The spectral sample used to measure the Na absorp-tion features in SNe Ia are primarily from the Centerfor Astrophysics (CfA) Supernova Program (Riess et al.1996), the Carnegie Supernova Project (CSP; Hamuy etal. 1996). The former sample contains 2603 spectra of462 nearby SNe Ia (Blondin et al. 2012), and most (94%)of which were obtained with the FAST spectrograph onthe 1.5 m telescope at the Fred Lawrence Whipple Obser-vatory (FLWO). The latter dataset contains 604 spectraof 93 SNe Ia (Folatelli et al. 2013), which were mainlyobtained with the 2.5 m du Pont Telescope at Las Cam-panas Observatory. All of the spectra were reduced in aconsistent way and have a typical FWHM (full-width athalf maximum) resolution of 6-7 ˚A, providing the largesthomogeneous spectroscopic dataset of SNe Ia. We alsoused the spectra from the Berkeley Supernova Program(BSP, Silverman et al. 2012), consisting of 1298 spectrafor 582 SNe Ia, to get further classifications of our SN Iasample and measure the Na absorptions whenever nec-essary. The spectral phases were obtained with respectto the B -band maximum light, based on the publishedlight curves of CfA (Riess et al. 1999, Jha et al. 2006,Hicken et al. 2009, Hicken et al. 2012), Lick ObservatorySupernova Survey (LOSS, Ganeshalingam et al. 2010),and Carnegie Supernova Project (Contreras et al. 2010,Stritzinger et al. 2011, Krisciunas et al. 2017). Thelight-curve parameters, including the peak magnitudes,the B max − V max colors at the maximum light, and thepost-maximum decline rates ∆ m (B) (Phillips 1993) areestimated by applying polynomial fits and/or the SALT2fit (Guy et al. 2007) to the observed data. A weightedaverage is adopted when the estimations from the abovetwo methods are both reasonable. The measurement re-sults and relevant photometric parameters for each SNsample are listed in Table 1.To eliminate the effects from noise spikes on thecontinuum determination of Na I absorption doublet,we smoothed the observed spectra in the range of5850 ∼ ∼ I Dabsorption of some SNe Ia is found to show temporalevolution within one week from the maximum light (seealso Figure 2), the EW of each SN is taken as a weightedmean of the results obtained at t ∼ m (B), the B-bandmagnitude decline rate in 15 days from the maximum ;Column (5), B max − V max color at the maximum light,corrected for the Galactic reddening; Column (6), theweighted mean value of the equivalent width (EW) ofNa I absorption over the period 0 . t .
30 days when-ever possible; Column (7), the B -band magnitude declinein the first 60 days after the B-band maximum; Column(8), the V -band magnitude decline in the first 60 daysafter the B-band maximum; Column (9), References. RESULTS
Narrow Na I Absorption Features
Figure 1 shows the B − V colors at the maximumlight versus the EWs of the Na I D absorption due tothe host galaxies. Foreground Galactic reddening correc-tions have been removed from the observed colors. The B max − V max color has been usually used as an indica-tor of reddening (Phillips et al. 1999, Wang et al. 2009,Folatelli et al. 2010, and Burns et al. 2014), though thesubclasses of 91T-like and 91bg-like SNe Ia tend to havepeculiar colors and they are thus not shown in Fig.1.As can be readily seen, the correlation between B max − V max color and strength of Na absorption is apparentfor the HV and NV subclasses, with stronger Na I Dabsorptions corresponding to redder colors (and hencelarger reddening). However, these two subclasses ofSNe Ia show noticeable differences in the distributionof their B max − V max colors and the Na I D EWs. Atwo-dimensional Kolmogoroff-Smirnoff (KS) test gives aprobability of 0.01% that they have statistically identicalNa I D EW and color distribution. Examining the EW ofNa I absorption and the B max − V max color separatelyold Dust Around Fast-expanding SNe Ia 3 -0.20.00.20.40.60.81.01.21.41.6 N u m b e r EW (A) NV Number o HV B m a x V m a x ( m a g ) NV (N=107) B m a x V m a x ( m a g ) HV (N=48)
06X 99cl
10 20 30 40
NV HV -0.20.00.20.40.60.81.01.21.41.6
Fig. 1.—
Relation between absorption strength (expressed asequivalent width) of interstellar sodium lines in spectra of SNe Iaand the corresponding values of their B max − V max colors. The”HV” subgroup (red squares) represents the SNe Ia with larger Si IIvelocity at B -band maximum light, i.e., v Si II ≥ − ,while the ”NV” subgroup (blue circles) denotes those with v Si II < − . The red and blue lines represent the best-fitlinear relationship to the HV and NV SNe Ia, respectively, whilethe dashed, black line shows the relationship inferred from the Naabsorption and reddening due to the Milky Way. SN 2006X wasnot included in the fit due to the saturation of the Na I lines (Patatet al. 2007), and SN 2006et appears to be an outlier and was notincluded in the fit, either. The plot is then projected onto the twoside panels where a histogram is displayed for each SN Ia subclassin each of the dimensions. yields a respective probability of 1.4% and 0.0002% thatthe two subclasses have the same parent distribution.The mean B max − V max colors estimated for these twosubclasses are 0.26 mag (HV) and 0.08 mag (NV), re-spectively, while the mean Na I D EWs are 1.1 ˚A (HV)and 0.7 ˚A (NV), respectively. In general, the HV sub-class have redder colors and stronger Na I D absorptionlines, and the fraction found with EWs & EW − ( B max − V max ) rela-tion for the HV and NV SNe Ia separately, we found thatthe former subclass have a larger slope of 0.239 ± ± I D absorption in HV SNe Ia. If the SN ex-ploded near a dusty shell/slab, we may expect variableNa I absorptions in SN spectra due to photoionizationeffect (Chugai et al. 2008, Patat et al. 2011). Thestrength of the absorption may then be correlated withthe rise and fall of the supernova luminosity. The trendthat the Na I D absorptions become stronger after max-imum light has already been reported for a few SNe Iasuch as SN 2006X (Patat et al. 2007), SN 2007le (Simon et al. 2009), SN 1999cl (Blondin et al. 2009), but thedecrease in strength of Na I absorption expected shortlyafter explosion was never observed in SNe Ia.To investigate the EW variations, we consider all ob-jects having at least three-epochs of spectroscopic datawithin ∼ σ detection cut and a minimum EW variation of 0.5 ˚Ato the CfA and CSP data, we get a sample of 16 SNe Iashowing prominent Na I D variations. Table 2 lists therelevant parameters of this sample showing variable Naabsorptions. Of this 16 SNe Ia, there are 11 HV and 2NV SNe Ia, with a fraction of 68.8% and 12.5%, respec-tively. This sample increases to 23 when applying a 2- σ cut, which contains 13 HV SNe Ia (56.5%) and 6 NV SNeIa (26.0%). The above analysis indicates that the vary-ing of Na I D absorptions are statistically associated withthe HV subclass. The probability of a chance coincidenceis less than 0.1%. Variable sodium features have alreadybeen detected in the high-resolution spectra of SN 2006Xand SN 2007le, and low-resolution spectra of SN 1999cl.It is gratifying to note that the evolutions of their Na I Dline are nicely recovered in these low resolution data.Note that SN 2006dd was also proposed as an SN Iashowing significant changes in the Na I D absorptions(Stritzinger et al. 2010) and is thus listed in Table 2.Its EW of Na I D absorption seems to decrease from ∼ ∼−
12 and t ∼ +86 days to ∼ ∼ +137days and then increase to ∼ ∼ +194.4 day spectrum. Sucha large change may indicate improper wavelength cal-ibration, or the identified ”Na I” absorption might beactually caused by other unknown features given thatthis SN has relatively blue B − V color.The Na I D absorption of some representative SNe Iawith significant time evolution is shown in Figure 2. Theplot suggests that the Na I D line of these objects gen-erally follow a qualitatively similar evolutionary trend.At early times the strength of the Na I D absorptionwas found to decrease with time, as is clearly seen inSN 2002bo, SN 2002dj, SN 2006X, and perhaps in SN2002cd. Such an evolution can be attributed to photoion-ization of neutral Na by the UV photons of supernovae(Borkowski et al. 2009). After the declining phase, theNa absorption strength undergoes a rising stage lastingfor about 10 days and remains at constant level afterthat. The overall evolution looks like a ”square-root”sign, which can be well explained with a model of Na I Dphotoionization and recombination in CS dust (see solidcurves in Figure 2) as discussed in § Late-time Light Curves
The presence of CS dust can be also tested by examin-ing the behaviors of late-time light curves of SNe Ia. Thisis because some of the SN photons will be scattered bysurrounding dust and arrive at the observer with a timedelay (Wang et al. 1996, Wang et al. 2005, Patat et al.2006). The delayed photons can be seen as a light echo(LE) and may contribute to the observed light curves Xiaofeng Wang et al. -20 -10 0 10 20 30 40 50 600.00.51.01.52.02.53.03.5 E W ( N a I D )( A ) Days Since B-band Maximum
SN 2002bo o SN 2002cd SN 2002dj SN 2001N SN 1999cl SN 2006X
SN 2006dd
SN 2002cd o SN 2002bo
Rest-frame Wavelength[A]
SN 2006X N o r m a li ze d F l ux +5.4 d +10.6d +33.5d SN 2001N
SN 2002dj
Fig. 3.—
Temporal evolution of the equivalent width of Na Idoublet for type Ia supernovae (SNe Ia). Top panels: Variable Naabsorptions detected in some well-observed objects such as SNe1999cl, 2001N, 2002bo, 2002cd, 2002dj, and 2006X. Note that allof the 6 SNe Ia shown in the plot belong to the ”HV” subclass.Overplotted are the curves derived with a model of Na I photoion-ization and recombination in CS dust. Bottom: the continuum-normalized Na I D profile shown at several epochs for some well-observed HV SNe Ia. The black and red lines represent the earlierand near-maximum-light phase spectra, respectively, while the blueones show the profile in the recombination phase. in the early nebular phase, especially in blue bands. Toexamine the difference of the late-time light curves forour sample of SNe Ia, we measured the magnitude de-cline within 60 days from the B - and V -band maximumlight, as defined by ∆m (B) and ∆m (V), respectively.These two quantities are obtained by applying a linearfit to the observed data spanning the phase from t ∼ +40days to t ∼
100 days, as listed in Table 1.Figure 3 shows the BV -band light curves and the B − V color curves for some well-observed SNe Ia. Althoughthese SNe Ia have similar light curves in early phases,they show remarkable scatter in the B -band from t ∼ B -bandmagnitude measured at t ∼
60 days from the peak candiffer by over 0.5 mag in the B band (see Fig 3(a)). Sucha late-time discrepancy is much smaller in the V band(see Fig 3(b)), which leads to an apparently bluer B − V color for the HV SNe Ia relative to the NV objects, asshown in the right panel of Figure 3. forAs more luminous SNe Ia tend to have brighter tailswith slower decay rates, it is thus necessary to examine whether the excess emission seen in the tail light curvesof HV SNe Ia is partially due to that they have intrin-sically high luminosity. We plot the measured values of∆m as a function of the corresponding ∆m (B) forour sample in Figure 4, where one can see that the tailbrightness does show a significant correlation with thedecline rate in both B and V bands for the NV sampleof SNe Ia. While this correlation shows large scatter inthe B band for the HV subsample, with the measured∆m (B) being systematically smaller than that of theNV ones at a given ∆m (B). This comparison furtherconfirms that the excess emission in the blue band is notintrinsic to the HV SNe Ia. Instead, we found that the∆m (B) shows a strong positive correlation with theSi II 6355 velocity measured around the maximum light,as shown in Fig 4(c). This indicates that the origin ofthe larger expanding velocity might be closely related tothe formation of dusty environments around SNe Ia. Modeling of the Observed Results
In this subsection, we will explore the presence of CSdust and constrain its distance from the SNe by compar-ing the modeling results with both the variations of NaI D absorption observed in the spectra and the excessemission detected in the late-time light curves.
Photonionization Model
To study the effect of photonionizations on the ob-served Na I absorptions in SN Ia spectra, we considera simple model with a spherical CS dust shell. Sim-ilar models have been employed in previous studies(Borkowski et al. 2009, Patat et al. 2007) to studythe variations in Na absorption lines, while only the re-combination process was emphasized. The Na ionizationstate is actually determined by the balance between ion-izations and recombinations. In our calculations, both ofthese two stages are explored based on the change of theionization and recombination rates with the ultravioletflux emitted by the SNe Ia at different phases. Assumingthat the pre-explosion number of Na I in the CS shell is N (Na I)(t ) well before the SN explosion, and the changeof this number over a time span dt can be written as: dN ( N a I )( t ) /dt = dN ( N a I ) ion ( t ) + dN ( N a I ) rec ( t ) dt = − N ( N a I )( t ) · R ion ( t )+[ N ( N a I ) − N ( N a I )( t )] · R rec ( t ) . (1)Where R ion (t) and R rec (t) represent the ionization rateof Na I and recombination rate of Na II, respectively.Defining the fraction of Na I as Frac(Na I(t))= N ( Na I )( t ) N ( Na I )( t ) and inserting it into the above equation, we can derive adifferential equation as: dF rac ( N a I )( t ) dt +[ R ion ( t )+ R rec ( t )] · F rac ( N aI )( t ) − R rec ( t ) = 0 , (2)Which has the following solution: F rac ( N aI )( t ) = exp { Z tt exp − [ R ion ( t ′ ) + R rec ( t ′ )] dt ′ }×{ Z tt exp e R t ′ texp [ R ion ( t ′′ )+ R rec ( t ′′ )] dt ′′ · R rec ( t ′ ) dt ′ + 1 } (3)old Dust Around Fast-expanding SNe Ia 5 V ( m a g ) Days after B maximum B ( m a g ) Days after B maximum B V ( m a g ) Days after B maximum
Loci of
Lira-Phillips relation
Fig. 3.—
The B -(left panel), V -band light (middle panel) and B − V color (right panel) curves of some well-observed SNe Ia (see Table1 for the references of the data), with the curves being all normalized to the corresponding values at around the maximum light. Thefilled and semi-filled symbols the HV SNe Ia, and the open symbols denote the NV ones. SNe Ia of these two subclasses exhibit largedifferences in B band and B − V colors 40 days after the maximum brightness. The black solid lines indicate the mean light curves ofNV subsample. The extra emission by scattering of SN light on CS materials of a spherical shell, asymmetric shell, and a disk structure,at a distance of ∼ × cm, are shown with the gray dash-dot-dotted line, red dash-dotted, and blue dashed line, respectively. Theresultant light curves by including contributions of CS scattering are indicated by the same symbols. The black solid line shows the best-fitto the B − V color curves of NV SNe Ia using the updated Lira − P hillips relation (Burns et al. 2014), with the non-reddening loci beingshifted redwards by 0.2 mag. During 40 days < t <
100 days, the color curves of most HV SNe Ia are apparently bluer than those ofnormal SNe Ia, following a slope much steeper than the
Lira − P hillips relation. m ( V ) ( m a g ) m (B) (mag) (b) m ( B ) ( m a g ) m (B) (mag) HV SNe Ia Normal SNe Ia 91bg-like SNe Ia 91T-like SNe Ia01bf (a) m ( B ) v si (10 km s -1 ) (c) Fig. 4.— a,b , Tail brightness of SNe Ia, measured as magnitude decline at t ∼ +60 days from the peaks of B - and V -band light curves,versus the luminosity indicator of SNe Ia ∆ m (B) that is measured as the magnitude decline within the first 15 days after the B -bandmaximum (Phillips et al. 1993). c , A plot of the B -band tail brightness as a function of Si II velocity obtained around B -band maximumlight. The subclasses of HV, NV, spectroscopically peculiar ones like SN 1991T and SN 1991bg SNe are shown by blue open squares, reddots, gray stars, and orange triangles, respectively. The blue dashed line in each panel represents the best linear fit for the NV subsample. According to the photoionization theory, the ionizationrate and recombination rate can be expressed as: R ion ( t ) = σ · I ( t ); R rec ( t ) = α ( T e ( t )) · n e ( t ) (4)Here, σ is the photoionization cross-section of Na I;and I(t) is the photon count rate per unit area. Thephotoionization cross-section depends on the energy ofthe incoming photons, and only the photons with energyhigher than 5.139 eV can remove the electrons from the ground state for Na I (Verner 1996a). In other words,the photons responsible for Na ionizations should havea wavelength shorter than 2412 ˚A. Here we adopted thespectral template of SNe Ia (Nugent et al. 2002, Hsiaoet al. 2007) to generate the UV photons needed to ionizeNa I. The UV flux has been scaled to the peak luminosityof SNe Ia with Cepheid distances (Riess et al. 2016) andis then converted into photon count rate. Meanwhile, thesecond equation of Eq.(4) shows that the recombinationrate of Na II is related to the recombination coefficient Xiaofeng Wang et al. α (T e (t))(which can change with the temperature T ) andelectron density within the CS shell n e (t). We simplyassume a constant temperature and electron density inour model by adopting them as the mean values of thesetwo parameters. Then the recombination rate can be ex-pressed as R rec = α (T e ) · n e . According to the studies ofsome literatures (i.e., Kamp et al. 2001, Douvion et al.2001, Johansson et al. 2013), we adopt a typical tem-perature of 100 K for the CS dust. And the relationshipbetween α and T e is determined by (Verner et al. 1996b).Some model curves from our calculations, adjusted forthe observed data of some SNe Ia in our sample, areshown in Fig. 2. One can see that the overall evolutionof Na I D absorption seen in some HV SNe Ia is simi-lar to that predicted by a simple CS shell model (seethe solid curves in Fig.2). By comparing with the modelcurves, typical values of R S ∼ × cm) andn e ∼ × cm − can be found for the subsample show-ing evolving Na I D absorptions. Of the sample listedin Table 2, the reddening towards SN 2001N may bedominated by the CS dust as Na seems to be nearlycompletely ionized around the peak luminosity; and thedust shell may be located at a distance with R S < &
30 days) suggeststhat the density of the CS material is quite low, e.g., n e ( . cm − ). Note that estimates of the above parame-ters may suffer large uncertainties from the difficulties indistinguishing the CS component from the component ofNa I D absorption in these low-resolution spectra. More-over, it is also difficult to determine accurately the totalamount of neutral Na due to line saturation. Neverthe-less, the above analysis indicates that the excess redden-ing of HV SNe Ia is related to the CS dust.
Dust Scattering Model
Dust scattering process can be dealt with an elasticscattering (including Rayleigh scattering and Mie scat-tering). Light scattering in circumstellar environment ofSNe Ia was first studied by Wang (2005) who found thatinclusion of the scattered light tends to reduce the to-tal extinction and hence the ratio of extinction to colorexcess, i.e. R V = A V /E(B − V). This provides an al-ternative explanation for the unusually low R V observedin some SNe Ia. Later on, Goobar (2008) conducted asimilar study by considering the effects of both scatter-ing and absorption (due to a CS shell) on the SN light.Multiple scattering process will predominately attenuatephotons with shorter wavelengths, thus steepening theeffective extinction law. Moreover, such a light scatter-ing can be observed as a light echo phenomenon at latetime when the SN light becomes faint enough. As bluephotons usually scatter more for dust grains with smallersize, the resulting echo would thus appear blue. How-ever, after multiple scattering, the blue photons could befinally absorbed or directed off the line of sight for somespecific optical depth, while the red photons suffer lessscattering and absorption. And this contrast will lead tothe production of a red echo.The extra light seen in the B -band light curves of theHV SNe Ia shown in Fig. 3 could be due to the scatteringof SN light by the nearby CS dust, which can be quanti-tatively modeled for any given geometric configurations.In our models of dust scattering, we adopt Mie scatter- ing and consider three structures of CS dust: a sphericalshell, an asymmetric shell (AsyShell), and a disk configu-ration, as shown in Figure 5. There are more complicatedconfigurations such as torus or blobs, and these discus-sions will be presented in a forthcoming paper (Hu et al.2019 in prep.).For the spherical shell and disk structures, the numberdensity of dust grains along the radial direction ( N ( R ))is assumed to decrease inversely with radius squared, i.e., A/R , where R is the distance to the SN and A relates tothe optical depth. Thus three parameters, R inner (innerradius of the shell), R outer (outer radius of the shell),and τ (optical depth) can be used to define the geometricproperty of the shell structure. For the asymmetric shell,however, we consider additional dependence of the dustdensity on the angle from the symmetry axis θ , with N ( R, θ ) =
A/R × (1 + (sin n θ − s ), where n and s describe degrees of asymmetry relative to the sphericalshell and their best-fit values are 2.0 and 0.6, respectively.This modified relation can be regarded as an extendedform of number density given in Chevalier et al. (1986).For the disk structure, an opening angle parameter θ disk is needed to address the thickness of the disk. Moreover,an observing angle θ obs needs to be assumed for both thedisk and AsyShell structures.In our calculations of the dust scattering, all the val-ues of albedo (= σ s /( σ s + σ a )), absorption cross-section( σ abs ), scattering cross-section ( σ sca ), and phase functionrelated to scattering process are taken from Draine et al.(2003). The size distribution of dust grains is adoptedas, f ( r ) = r − a exp {− b (log rr ) . } (5)where a and b is adopted as 4 . .
5, respec-tively, to be consistent with the results derived in Nozawaet al.(2015).The modeled light/color curves, obtained by taking themean light curves of NV SNe Ia as input of light scatter-ing, are overplotted in Figure 3. To match the observed B - and V -band light curves of our HV sample, the CSdust is required to have an inner radius of R inner ∼ × cm and an outer radius of R outer ∼ × cm formost of our HV sample, with the optical depth τ be-ing about 0.12, 0.15, and 0.7 for the CS dust of spheri-cal shell, asymmetric shell, and disk structures, respec-tively. The best-fit opening angle for the disk structureis θ disk ∼ ◦ . For the CS dust of asymmetric shell anddisk structures, the symmetry axes are tilted at an angle θ obs ∼ ◦ with respect to the observer. Note that the re-sults listed for the above parameters represent their aver-age values because there are many sets of parameter val-ues that can give reasonable fit to the light curves. Thecorresponding mass-loss rate of the stellar wind ˙ M w is es-timated as ∼ × − M ⊙ yr − , ∼ × − M ⊙ yr − , and ∼ × − M ⊙ yr − for the CS dust of shell, AsyShell, anddisk structures, respectively. The calculation of ˙ M w isbased on the equation of N = A/R = ˙ M w / (4 πv w R m ),where m is the average mass of each dust grain.It is remarkable that the model light curves of dif-ferent geometric configurations agree with the observedlight/color scatter seen at 40-100 days after optical max-imum. Note that the color measurements at these datescorrespond to those used in the Lira-Phillips relationold Dust Around Fast-expanding SNe Ia 7 Fig. 5.—
An illustration of the vertical planes of three differentstructures of CS dust, spherical shell (top left), asymmetric (topright), and the disk (bottom). The vertical dashed lines show thesymmetry axes of the dust distribution. θ obs shows the directionto the observer. The structures are rotationally symmetric withrespect to the vertical dashed lines. The boundaries of the CSMare identified by the inner radius ( R inner ) and the outer radius( R outer ). The gray scale indicates the number density of the dustgrains. The dust density decreases inversely with radius squared inboth cases. For (a), the azimuth density dependence follows sin θ ,with θ being the angle to the symmetry axis. (Lira et al. 1998) for color excess estimates of SNe Ia.This agreement is encouraging and suggestive of the va-lidity of these models, favoring for the presence of CSdust around SNe Ia. Moreover, the distance of the CSdust inferred from modeling of the late-time light curveis in strikingly consistent with that derived from the pho-toionization calculations presented in § B − V color evo-lution. They simulated the propagation of Monte Carlophotons through a dust region and constrained the dustdistances to their SN Ia sample at 4 × -10 cm, whichis on average larger than our estimates. This difference islikely related to the dust properties adopted in the analy-sis. In Bulla et al. analysis they chose the Mikyway-typedust and adopt a thin disk without an extended struc-ture, while we adopt three different structures of CS dustwith an average dust size of 0.5 µ m. A smaller dust grainis also favored for those SNe Ia with unusually low R V (Wang et al. 2008b, Goobar 2008). In addition, the de-rived color excess E( B − V ) from the B − V color maysuffer relatively large uncertainties due to larger photo-metric errors and that some SNe Ia may have peculiarcolor evolution. DISCUSSIONS AND CONCLUSIONS
The formation of nearby CSM around an SN progen-itor is a direct consequence of its progenitor evolution.The CSM can be ejected continuously similar to stel-lar winds, or episodically similar to nova shell ejections. −20 0 20 40 60 80 100 120 140
Days after B Maximum d e g r ee o f p o l a r i z a t i o n p ( % ) B (Disk)V (Disk)B (Asyshell)V (Asyshell)
Fig. 6.—
The predicted time-evolution of the polarization in the B - (solid line) and V -band (dot-dashed line) at a viewing angleof 30 degrees for the asymmetric shell. The blue curves show thepolarization inferred from the asymmetric shell, while the red onesrepresent case for the disk structure. Typical blueshift in the Na I lines of SNe Ia is ∼ − according to a statistical study using high- andintermediate-resolution spectra of a large sample of SNeIa (Sternberg et al. 2011; Maguire et al. 2013). Thevelocity and distance of the CS dust inferred here forHV SNe Ia suggest that they may have symbiotic novaprogenitors, similar to RS Ophiuchi (Patat et al. 2011).Theoretical expectations for the fraction of SNe Ia fromthe symbiotic progenitor channel are ∼ − ) ejected from recurrent nova outbursts willbe slowed down by the slow-moving stellar wind blownfrom the companion star, i.e., a red giant. Such an inter-action process can create a large evacuated region aroundthe SN progenitor and form a CS shell with a velocityof ∼
100 km s − at a distance ranging from 10 cm to10 cm , consistent with the estimates for the HV sam-ple. The extension and distance of the CS dust from theprogenitor are likely related to the accretion rate, periodof recurrent nova, and the time lag between the explosionand mass loss before explosion.The distribution of the CS dust derived for the HV SNeIa is typically around 10 cm according to the aboveanalysis, which is too compact to be spatially resolvableat extragalactic distances. The progenitors of SNe Ia in-volve binaries with one or two degenerate stars, the dustejected from such systems may be naturally asymmet-ric. Polarimetry study of such compact light echoes isable to map the geometric structures of the CSM and setobservational constraints on the progenitor systems. Weremark that the asymmetric dust distribution naturallyleads to polarized radiation at late times when the scat-tered light is the strongest, corresponding to about 60-90days after optical maximum, as shown in Figure 6. Theabsolute level of the degree of polarization is sensitiveto the assumed geometric structure. Although only theSNe with highly asymmetric CS dust shells close to beingedge-on are expected to produce strong polarization, thedetection of such polarized signal and its evolution can Xiaofeng Wang et al.be a prime evidence for the presence of the CS matteraround the SNe (Wang et al. 1996). Unfortunately, ex-isting polarimetry data are mostly taken around opticalmaximum (Wang & Wheeler 2008). Indeed, recent deepHST imaging polarimetry of SN 2014J taken on day 277after maximum reveals an abnormal polarization signalthat can be identified with a light echo from a dust lumpof at least 2 × − M ⊙ , located at a distance of 5 × cm (Yang et al. 2018). More polarimetry at late epochscoupled with photometric monitoring holds the key tounlock the mystery concerning the CSM around SN Iaprogenitors.Our studies demonstrate that the HV SNe Ia are as-sociated with the CS dust, which is in accordance withthe detection of systematically blueshifted velocity struc-ture (or outflow) in the Na I lines of SNe Ia having highSi II velocity (Sternberg et al. 2011). There are severaladditional evidences favoring that the HV subclass mayoriginate from single degenerate progenitor system. Forexample, a significant ultraviolet excess is possibly de-tected in SN 2004dt and SN 2009gi (Wang et al. 2012,Foley et al. 2013), which is expected from the collisionbetween ejecta and a larger companion such as a massiveMS star or a red giant star (Kasen 2010). Moreover, thereis a tendency that unburned carbon (i.e., C II 6580˚A) isdetected in the earlier spectra of NV SNe Ia (Parrent etal. 2011, Blondin et al. 2012, Silverman et al. 2012)but not in the HV SNe Ia. Recent studies also indicatethat these two subclasses of SNe Ia also show significantdifferences in the velocity distribution of outer-layer oxy-gen and silicon (Zhao et al. 2016). These results are inline with the idea that SNe Ia with different ejecta veloc-ities have different progenitor systems and/or explosionmechanisms. Combining with the results from the evolv-ing narrow interstellar Na I absorptions and the late-time light curves presented in this report, we suggestthat SNe Ia with fast expanding ejecta likely arise from progenitor systems with a red giant companion.Nevertheless, some secular merger models may produceblueshifted absorbing materials, i.e., through interactionof tidal disrupted ejecta with interstellar medium (Raski& Kasen 2013) or wind blown from the accretion disk(Dragulin & Hoflich 2016). However, the former one canonly produce an absorbing shell with a blueshifted veloc-ity of about 100 km s − , after the ejection of tidal tailfor about 10 years when the absorbing materials movedto a distance of about 10 cm. While the fast wind fromthe accretion-disk (with a velocity of ∼ − ) tendto produce a low-density void region several light yearsacross, surrounded by a dense shell at a distance & cm (Dragulin & Hoeflich 2016). Thus, neither of thesetwo merger models could produce the CSM consistentwith our result. Moreover, the core-degenerate (CD) sce-nario, an explosion of a WD and the core of an AGB star,has also been proposed as an alternative way to explainthe presence of CSM around some SNe Ia (i.e., Tsebrenko& Soker 2015, Soker 2015), but it is not obvious whetherthe observed properties of a CD SN Ia would resemblethat of a typical SN Ia. ACKNOWLEDGMENTS
We thank the anonymous referee for his/her sug-gestive comments to help improve the manuscript.This work is supported by the National Natural Sci-ence Foundation of China (NSFC grants 11325313,11633002, and 11761141001), and the National Programon Key Research and Development Project (grant no.2016YFA0400803). The work of L.W. is supported byNSF grant AST-1817099. This research has made useof the CfA Supernova Archive, which is funded in partby the National Science Foundation through grant AST0907903. This research has also made use of the super-nova archives from the Carnegie Supernova Project andthe Berkeley Supernova Program, which are also fundedin part by the US National Science Foundation.
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TABLE 1Summary of Classification, Spectroscopic and PhotometricProperties of the SN Ia Sample
SN name SN type v Si II ∆m (B) B max − V max EW ∆m (B) ∆m (V) Ref. ∗ ( × km s − ) (mag) (mag) (˚A) (mag) (mag)Branch normalSN 1984A HV 1.47(04) 1.22(10) 0.16(09) ... 3.10(10) 2.59(05) 1SN 1989B NV 1.05(03) 1.35(05) 0.32(09) 3.17(19) 3.41(06) ... 2SN 1994M HV 1.24(02) 1.47(06) 0.10(04) 0.22(21) ... ... 3,4,5SN 1994ae NV 1.11(03) 0.89(05) − − > − − − − − − − − − old Dust Around Fast-expanding SNe Ia 11 TABLE 1 — Continued
SN name SN type v Si II ∆m (B) B max − V max EW ∆m (B) ∆m (V) Ref. ∗ ( × km s − ) (mag) (mag) (˚A) (mag) (mag)SN 2003du NV 1.04(03) 1.00(02) − − − − − − − − − − − − − − − − − − − − − − − − TABLE 1 — Continued
SN name SN type v Si II ∆m (B) B max − V max EW ∆m (B) ∆m (V) Ref. ∗ ( × km s − ) (mag) (mag) (˚A) (mag) (mag)SN 2007ux NV 1.07(03) 1.53(08) 0.11(03) 0(15) 3.63(05) 2.95(04) 3,4,18SN 2008C NV 1.06(03) 1.19(03) 0.15(03) 1.22(08) ... 2.69(04) 4,16,18,23SN 2008Z NV 1.12(03) 0.88(03) 0.10(03) 0.93(21) 3.30(05) 2.60(04) 3,4,23SN 2008ar NV 1.02(02) 1.09(03) − − − − − − − − − − − − − old Dust Around Fast-expanding SNe Ia 13 TABLE 1 — Continued
SN name SN type v Si II ∆m (B) B max − V max EW ∆m (B) ∆m (V) Ref. ∗ ( × km s − ) (mag) (mag) (˚A) (mag) (mag) Note: The uncertainties shown in the brackets are 1 σ , in units of 0.01 mag for ∆m (B), B max − V max , ∆m (B), and ∆m (V), and in unitsof 0.01 ˚A for EW of Na I D absorption. ∗
1= Barbon et al. 1989; 2 = Wells et al. 1994; 3 = Silverman et al. 2012; 4 = Blondin et al. 2012; 5 = Riess et al. 1999; 6 = Riess et al. 2005;7 = Jha et al. 2006; 8 = Matheson et al. 2008; 9 = Jha et al. 1999; 10 = Ganeshelingam et al. 2010; 11 = Hicken et al. 2009; 12 = Kotak et al.2005; 13 = Stanishev et al. 2007; 14 = Krisciunas et al. 2007; 15 = Altavilla et al. 2007; 16 = Contreras et al. 2010, Krisciunas et al. 2017; 17 =Pastorello et al. 2007; 18 = Folatelli et al. 2013; 19 = Wang et al. 2009; 20 = Wang et al. 2008a; 21 = Stritzinger et al. 2011, Krisciunas et al.2017; 22 = Zhang et al. 2010; 23 = Hicken et al. 2012; 24 = Yuan et al. 2008; 25 = Zhang et al. 2016; 26 = Brown et al. 2015; 27 = Zhang etal. 2018; 28= Filippenko 1992; 29 = Lira et al. 1998; 30 = Filippenko et al. 1992; 31 = Taubenberger et al. 2008.
TABLE 2Candidates of type Ia supernovae with variable Na I D absorptionfeatures
SN name ∆EW(˚A) a ∆EW/ σ b Number c Phase of the Spectra (days) d TypeSN 1997bp 0.66 3.5 13 -1.6,2.3,+20.3, +33.2,+51.2 HVSN 1997bq 0.96 4.7 8 -10.6, -4.5, +12.4, +20.4 HVSN 1999cl 1.07 5.0 11 -6.7,-2.6, +9.3, +39.3 HVSN 1999dq 0.73 3.8 21 -9.5, -3.5, 30.3, +59.3,+90.3 91TSN 2001br 1.27 4.4 4 -1.1,+1.9, +26.9,+53.8 HVSN 2001N 1.64 6.9 6 +3.6,+10.6,+12,7, +33.5 HVSN 2002bf 1.38 4.7 4 +3.8,+6.8,+8.8,+12.8 HVSN 2002bo 0.85 3.4 31 -12.0,-5.9,-1.1,+11.0,+22.0 HVSN 2002cd 2.19 12.5 9 -8.7,-4.7,+0.3,+15.2, HVSN 2002dj 1.89 10.0 6 -10.0,-5.9,+10.1,+17.1 HVSN 2003ep 2.23 10.6 3 a few weeks later · · ·
SN 2005hf 1.10 3.9 6 +3.0,+7.0,+13.1 PecSN 2006N 1.02 4.1 7 +2.2,+5.2,+8.2,+28.2 NVSN 2006X 0.93 8.2 21 -6.6,+3.0,+8.0,+15.0,+34.0 HVSN 2006dd 2.53 3.7 5 -12.0, +86.4, +137.0, +194.4 · · ·