MNRAS 452, 3281–3292 (2015)

doi:10.1093/mnras/stv1498

Constraining the amount of circumstellar matter and dust around Type Ia
supernovae through near-infrared echoes
Keiichi Maeda,1,2‹ Takaya Nozawa,3 Takashi Nagao1 and Kentaro Motohara4
1 Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
2 Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
3 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
4 Institute of Astronomy, Graduate School of Science, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan

ABSTRACTThe circumstellar (CS) environment is key to understanding progenitors of Type Ia supernovae(SNe Ia), as well as the origin of a peculiar extinction property towards SNe Ia for cosmologicalapplication. It has been suggested that multiple scatterings of SN photons by CS dust may
explain the non-standard reddening law. In this paper, we examine the effect of re-emission of
SN photons by CS dust in the infrared (IR) wavelength regime. This effect allows the observed
IR light curves to be used as a constraint on the position/size and the amount of CS dust.
The method was applied to observed near-infrared (NIR) SN Ia samples; meaningful upper
limits on the CS dust mass were derived even under conservative assumptions. We thereby
clarify a difficulty associated with the CS dust-scattering model as a general explanation for thepeculiar reddening law, while it may still apply to a sub-sample of highly reddened SNe Ia. For
SNe Ia in general, the environment at the interstellar scale appears to be responsible for the nonstandard extinction law. Furthermore, deeper limits can be obtained using the standard natureof SN Ia NIR light curves. In this application, an upper limit of Ṁ  10−8 −10−7 M yr−1(for the wind velocity of ∼10 km s−1 ) is obtained for a mass-loss rate from a progenitor up to∼0.01 pc, and Ṁ  10−7 −10−6 M yr−1 up to ∼0.1 pc.
Key words: Circumstellar matter – stars: mass-loss – supernovae: general – dust, extinction.

1 I N T RO D U C T I O NType Ia supernovae (SNe Ia) are mature standardized candles. Intrinsic dispersion of the peak absolute magnitude can be minimized
to the level of ∼0.15 mag or even smaller, and can be accurately
used as a cosmological distance indicator (Phillips et al. 1999).
However, this standardization generally requires a non-standard extinction law, i.e. RV ≡ AV /E(B − V)  2, as opposed to the typical
Galactic value of RV ∼ 3.1 (e.g. Folatelli et al. 2010). This indicatesthat the properties of dust in SN Ia host galaxies may be systematically different from those in our Galaxy (e.g. Phillips et al. 2013).
Alternatively, it has been suggested that multiple scatterings of
SN photons on circumstellar (CS) dust may explain the non-standard
nature of the reddening law (Wang 2005; Goobar 2008). Despite
the implications that have been discussed (e.g. Folatelli et al. 2010),
researchers have yet to find a smoking gun to test this hypothesis,
apart from the various model predictions for optical wavelengths(Amanullah & Goobar 2011). This interpretation is also associ- E-mail: keiichi.maeda@kusastro.kyoto-u.ac.jp

ated with as yet unclarified progenitor evolution, through the dense
circumstellar medium (CSM) and high mass-loss rate that would
be required. Qualitatively, the scenario favours a so-called singledegenerate model (i.e. a pair consisting of a C+O white dwarf and anon-degenerate star; Whelan & Iben 1973; Nomoto 1982; Hachisu,
Kato & Nomoto 1999), which should create a relatively dense (or‘dirty’) CS environment.
In this paper, we examine the effects of re-emission of SN photons for infrared (IR) wavelengths. While the ‘scattering’ must be
accompanied by ‘absorption and re-emission’ (a CS dust echo), thisprocess has not been examined with respect to the CS environment
around SNe Ia (with the exception of recent work that focused on
the mid- and far-IR; Johansson, Amanullah & Goobar 2013). The
remainder of this paper is organized as follows. In Section 2, wedevelop a simple echo model for CS dust heated by SN photons. In
Section 3, we apply the method to observed NIR SN Ia samples. We
place both conservative and deeper limits for the amount of CS dust
under different assumptions. In Section 4, we discuss the effects ofdifferent types of CS dust species, as well as future observational
strategies for a better constraint on the amount of CS dust and theenvironment. The paper is closed in Section 5 with conclusions.

C 2015 The Authors
Published by Oxford University Press on behalf of the Royal Astronomical Society

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Accepted 2015 July 6. Received 2015 July 6; in original form 2014 September 20

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2 MODELS

2.1 Shell model
Let us first consider a situation in which we observe a dust shellwith temperature T(θ ) and mass Md , where θ is the angle between
the observer’s line of sight and a direction vector pointing from theshell centre (i.e. the explosion centre) to the position of the volume
element within the shell under consideration. Then, the luminosityof the thermal emission from dust is given as follows:
4πκa,ν Bν (T (θ ))ρ dV
Lecho,ν =V= 2πMd κa,ν

 πsin θ Bν (T (θ )) dθ.

(1)0Here, κ a,ν is the absorbing opacity of the dust at frequency ν. It
is specified by the dust properties, which are assumed to be uniform within the shell. Furthermore, the shell is assumed to have
uniform density (ρ). The above expression can be converted into
time-dependent luminosity by introducing t (the time since the explosion, measured in the observer’s frame) and t (observer-frame
time when the light was emitted from a given volume element at θas observed at time t). The relationship between t and t is given by
the following:R(1 − cos θ).
(2)cCombining equations (1) and (2), we obtain the following expression for the echo luminosity at time t: tc
Lecho,ν (t) = 2π Md κa,νBν (T (t  )) dt  .
(3)Rmax(t− 2Rc ,0)t = t −The temperature evolution of the CS dust at time t, under radiativeequilibrium with an incoming SN flux, LSN, ν (t), is given by ∞ ∞LSN,ν (t)κdν=
4πκa,ν Bν (T (t)) dν.
(4)
a,ν
4πR 2
0
0
MNRAS 452, 3281–3292 (2015)

2.2 Ring/torus model
The CSM around an SN Ia may be confined within the equatorial plane (e.g. Dilday et al. 2012), therefore we also consider atorus/ring-like structure, again under the infinitely thin assumption
in the radial direction. We denote θ 0 as the opening angle of thering, as measured from the equatorial direction. While it is possible to derive general expressions for an arbitrary viewing direction,
hereafter, we focus on two extreme cases: pole-on and edge-on
viewing.
For an observer sitting at the pole-on position, the echo luminosity
is expressed as follows: t− R (1−sin θ0 )
c
c Md
κa,ν
Bν (T (t  )) dt  .
(5)Lecho (t) = 2π
R sin θ0max(t− Rc (1+sin θ0 ),0)If t − Rc (1 + sin θ0 ) < 0, then the integral is set to zero.

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In this section, we present our model of CS dust echoes. We restrict
the model to absorption and re-emission processes, not including
scattering. This is justified because, (1) given that the spectral peakof the SN light lies at optical wavelengths, the contribution of thescattered SN light at NIR–IR wavelengths is very small, compared tothat of thermal emission from CS dust, and (2) in the distribution of
CS dust of interest in this paper, further scattering of the re-emitted
NIR/IR photons is negligible. While computational methods for anecho from spherically distributed CS dust (e.g. Dwek 1983, 1985)
and further from aspherically distributed CS dust (especially formodelling the light echo from SN 1987A; Dwek & Felten 1989;
Felten & Dwek 1989) have been developed, we assume for thesake of simplicity that the distribution of CS dust is represented
by an infinitely thin shell located at radius R from the centre ofan explosion. The thin-shell approximation further simplifies thecomputation as shown below. Furthermore, in providing an upper
limit for the amount of CS dust as a function of R, the thin-shell
approximation basically provides the most conservative limit, as any
spherically symmetric distribution can be described as a convolutionof different shells. Namely, if one adds another shell at R , that isdifferent from R for which the constraint is considered, then thisadditional shell will increase the predicted flux without contributing
to the CS dust mass at R; therefore, the upper limit on this CS
dust mass should be reduced (i.e. the predicted flux must be below
observations).

This equation provides T(t) once the SN flux evolution is specified.
Under the condition considered in this paper, the photon–dust collision time-scale is shorter than the cooling time-scale of the dustby thermal radiation. Therefore, stochastic heating is negligible,
and we can assume that virtually all of the dust particles have atemperature determined by radiative equilibrium.
We first compute T(t) for a given R using the above equation.
For the SN flux, we use the Hsiao template spectra as an input(Hsiao et al. 2007). For the dust opacity, we use the LMC-like dust
properties as our fiducial model; specifically, we adopt the opacityfrom U to Ks from Goobar (2008) so as to be consistent with theproposed CS scattering model. We extend the opacity towards theblue (beyond U) and red (beyond K), assuming slopes of −1.5 and−1, respectively. Then the evolution of T(t) is used as an input inthe computations of echo luminosity and multiband light curves.
Because the incoming SN light peaks in optical wavelengths, andbecause the dust temperature under the situation examined in thispaper is determined by the opacity in the NIR wavelength, the treatment of the opacity below the U band and above the Ks band does
not substantially affect our results. To check this, we performed two
additional test calculations: one having a slope of −2.0 below the
U band and the other having a slope of −0.5 above the K band for ourreference LMC dust model; these models are unrealistically steep
and flat, respectively, and thus provide a conservative measure of
the uncertainty for the treatment of different slopes. The difference
between the reference model and the one using the different slopes(dJ, dH, dKs ) is larger for a model with a larger R. For the typicalmaximum distance for which a meaningful constraint is placed at
different bands (see Section 3), the difference in the echo magnitudeis given by dJ = −0.12 mag (for 0.03 pc), dH = −0.30 mag (for0.3 pc) and dKs = −0.31 mag (1 pc) for the different slope below
the U band. For the different slope above the Ks band, dJ = 0.2 mag(for 0.03 pc), dH = 1.4 mag (for 0.3 pc) and dKs = 1.9 mag (for1 pc). Therefore, in the worst-case scenario, our echo luminosity
constraint (and, thus, the dust mass) could have an uncertainty factorof 5; however, in most cases the uncertainty would be much smaller
than this. A further discussion of the dust properties is given in
Section 4.1.
The resulting echo luminosity, as computed above, is for unobscured luminosity. We now consider the optical depth within theshell. The average optical depth is computed as τ ν = κ a, ν ρR;
then the NIR echo luminosity is dimmed by this amount of absorption. The same procedure is adopted for the model with a different
geometry (see below).

CS dust around SNe Ia
To be an explanation for the non-standard extinction law requires
R  ctpeak ∼ 5 × 1016 cm, to introduce the effect of scattered photons
around the maximum light. An observer in the equatorial direction
does not have this constraint. We note that both situations should
be considered simultaneously, because there should be roughly anequal number of edge-on and pole-on counterparts (depending onθ 0 ), if we adopt the ring-like geometry. Finally, the echo luminosity
arising from the same configuration, but viewed edge-on, is given
as follows:  t− R (1+cos θ0 )
c
c Md
κa,ν
Bν (T (t  )) dt Lecho,ν (t) = 2π
R sin θ0
,0)
max(t− 2Rc t− R (1−cos θ0 )c

t− Rc (1−cos θ0 )sin θ0
sin θ



dt 

(6)

2.3 Bipolar blob model
Another interesting possibility for the CS dust distribution is abipolar morphology, i.e. a pair of blobs/jets, as inferred for somenovae (e.g. Chesneau et al. 2012). Therefore, we also consider apair of bipolar blobs for the distribution of the CS dust, again under
the infinitely thin assumption in the radial direction. We denote θ 0
as the opening angle subtended by each blob, as measured from thepolar direction.
For an observer sitting at the pole-on position, the echo luminosity
is expressed as follows:  t− R (1+cos θ0 )
c
Md
c
κa,ν
Bν (T (t  )) dt Lecho,ν (t) = 2π
R 1 − cos θ0max(t− 2R
c ,0)

 t
+
Bν (T (t  )) dt  .
(7)
t− Rc (1−cos θ0 )The echo luminosity arising from the same configuration, butviewed edge-on, is given as
 t− R (1−sin θ0 )
c
Md
c
κa,ν
(8)
Lecho,ν (t) = 2π
R 1 − cos θ0t− Rc (1+sin θ0 )×2Bν (T (t  )) cos−1π

cos θ0sin θ

dt  .

(9)

Similar to the case of the pole-on observer for the ring-like CS dust
distribution, a constraint is placed on the CS dust radius if the multiple scattering model is to account for the non-standard extinction
law. For the edge-on observer of the bipolar blob geometry, the CS
dust radius must satisfy R  ctpeak ∼ 5 × 1016 cm to introduce thescattered photon effect around the maximum light. This constraint
does not apply to the pole-on observer; however, both situations(pole-on and edge-on) should be considered simultaneously, following the same argument given for the ring-like geometry.
3 R E S U LT S
Fig. 1 shows the evolution of T and the predicted NIR (J, H, Ks )light curves for different values of R and for a fixed value of Md(10−5 M ); for the light curves, only the shell model is shown. The
evolution of T closely follows the optical light curve of SN Ia. For
R  0.01 pc, the peak temperature exceeds ∼2000 K; therefore, thedust may well have evaporated, depending on the nature of the CS
dust. In such a case, essentially there should be neither scattering nor
thermal emission from the CS dust. Therefore, no constraint can beobtained regarding the amount of pre-existing CS dust, and the CS
dust cannot be an origin of the non-standard extinction law towards
SNe Ia. The effects of different geometries are demonstrated inFig. 2; light curves are shown for the shell CSM, pole-on and edgeon views for a ring-like CSM with θ 0 = 10◦ , and pole-on and edgeon views for bipolar blobs with θ 0 = 10◦ . Throughout this paper, weconsider these geometry types for the CS dust distribution, while
adopting the shell model as our fiducial model.
The light-curve evolution is similar in various NIR bands; its
time-scale is basically determined by the travelling time of light,
and thus the CS dust at larger R results in a longer lived, fainter
NIR echo. For small R, the travelling time of light is shorter than
the time-scale of the SN light-curve evolution; thus in this case, thelight curve reflects the SN light-curve evolution, and the echo lightcurve evolution traces the decreasing temperature of the CS dust
as a function of time. On the other hand, for large R, the travelling
time of light far exceeds the SN light-curve evolution time-scale;therefore, the temperature evolution has little influence on the shapeof the light curve. Emission at longer wavelengths is stronger forlarger R, which stems from smaller T for larger R. As such, the peakwavelength in the thermal emission is shorter than the J band forsmaller R, while it is even longer than the Ks band pass for larger R.
Fig. 3 shows examples of the constraint on the amount of CS
dust using the shell model. Without the dust echo, NIR luminosities
of SNe are powered by radioactive decay of 56 Co and subsequent
thermalization; the NIR spectral energy distribution (SED) roughly
follows a blackbody of ∼5000–10 000 K in the early photosphericphase (100 d), while the SED reflects the forbidden lines of Fepeak elements in late nebular phases (100 d). In any case, a conservative upper limit on the CS dust mass is obtained by the condition
that the resulting echo luminosity cannot exceed the observation at
any epochs. As the echo luminosity is proportional to Md in the
optically thin regime, for a given R, one can derive a maximallyallowed value for Md . Note that this is not a fit to the observed
light curve – the echo light-curve model for small R resembles theobserved light curve to some extent, but this is because the echo
evolution follows the SN evolution for small R (see above).
The left-hand panel of Fig. 3 shows how an early-phase light
curve (up to ∼100 d since the B-band maximum) can be used toconstrain the amount of CS dust. Generally, the early-phase data
provide a strong constraint on Md for small R, but lose diagnostic
power for CS dust at large R. The model prediction for small R is
similar for different bands; typically the J band provides the deepest
limit, thanks to its extensive coverage within the NIR. We notethat the I band, which typically has much better coverage than the
J band, is not so useful for this purpose, as the wavelength of thethermal emission peak is longer than that of the I band.
The right-hand panel of Fig. 3 shows the other extreme within
the NIR wavelengths, namely a constraint obtained through latetime photometry in the Ks band. Such an observation can provide aconstraint on the CS dust at large R, up to ∼1 pc.
By applying different models (i.e. with a different R and geometry) to the available, observed multiband light curves, a constraint
can be obtained for Md as a function of R for each SN. The light
curves for different bands provide mutually independent upper limits; we adopted the strongest limit among J, H and Ks . The resultis shown in Fig. 4, where the method was applied to a ‘typical NIR
observation’ using the CSP sample, SN 2006X, as an example ofvery intensively observed early-phase light curves, including the
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2Bν (T (t  )) sin−1
t− Rc (1+cos θ0 ) π t+Bν (T (t  )) dt  .
+

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Figure 2. Effect of different geometries on the echo light curves. For demonstration purposes, the distance to the CS dust is fixed at R = 0.1 pc. The reference
shell model is shown in cyan (solid). The echo light curve from a ring-like CS dust distribution is shown by red (dotted) curves for an edge-on observer (thin)
and a pole-on observer (thick). The same is shown for a blob-like CS dust distribution by blue (dashed) curves for an edge-on observer (thin) and for a pole-on
observer (thick).

Ks band and extending to a relatively late epoch; also shown are
SNe 1998bu, 2000cx, 2001el, 2003du and 2003hv, for which NIR
late-phase (∼1 yr) magnitudes are available. It is seen that generally the strongest constraints are obtained through the J- or H-band

MNRAS 452, 3281–3292 (2015)

data for the CS dust at R  0.1 pc, and through the Ks band at
R  0.1 pc.
Fig. 4 also contains lines indicating various physical situations.
The thick solid lines indicate the absorptive optical depth in the

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Figure 1. NIR light echo models. (a) Temperature of the CS dust (T) as a function of the rest-frame days, in which the B-band maximum is shown for various
distances to the CS dust (R = 3.24 × 10−3 , 1.02 × 10−2 , 3.24 × 10−2 , 1.02 × 10−1 , 3.2 × 10−1 , 1.02 and 3.24 pc from top to bottom). In all of the models, theCS dust mass is set to 10−5 M . (b)–(d) The echo model light curves for J (b), H (c) and Ks -bands (d) as a function of the observed days for the shell model.
The colour coordinate denotes the model for different distances to the CS dust (red for R = 3.24 × 10−3 pc, green for 1.02 × 10−2 pc, blue for 3.24 × 10−2 pc,
cyan for 1.02 × 10−1 pc and magenta for 3.24 × 10−1 pc).

CS dust around SNe Ia

3285

B band, which gives indication of the likelihood that the CS dust is
the origin of the non-standard extinction law (i.e. an optical depth ofan order unity is required). The thin solid lines show the equivalentmass-loss rates of the progenitor systems; we adopted the dust-togas ratio of 0.01 (i.e. Ṁ/vw = 100Md /R, where v w is the velocity ofthe mass-loss outflow). Vertical dashed lines show the temperatureof the CS dust as a function of R.
Fig. 4 shows that the upper limits for Md , as obtained in the argument using the NIR echo (with the shell model), are Md  10−5 Mfor the CS dust at R  0.01 pc, Md  10−4 M at R ∼ 0.03 pc andMd  10−2 M at R ∼ 0.1 pc. Beyond this radius, the results areespecially sensitive to the quality of the observational data, as essentially one needs still-rare late-time photometry for the Ks band.
The strongest constraints for R  0.1 pc are obtained for SNe
2000cx, 2001el and 2003hv, which are only three examples to datehaving the late-time Ks -band photometry at ∼1 yr. For these SNe,
Md  0.01 M is derived for R ∼ 0.4 pc. At R  1 pc, even the
NIR bands are too blue; thus, we can only provide a very loose constraint on the CS dust mass as Md  1 M , even for the best-casescenario (SN 2003hv). To probe the CS dust beyond R ∼ 1 pc, midor far-IR observations should be more effective (Johansson et al.
2013, 2014).
The derived upper limits are sufficiently tight to constrain theorigin of the non-standard extinction as a scattered echo, as proposedby Wang (2005) and Goobar (2008). The resulting upper limit forthe optical depth in the B band is generally 0.1 for the CS dust at
R  0.1 pc. At R  0.1 pc, the constraint is weaker, but for a few
SNe, we place the constraint as τ a (B)  0.01 at R ∼ 0.4 pc. AboveR ∼ 1 pc, the upper limit is consistent with τ a (B) ∼ 1. These values
should be compared to the requirement that the optical depth mustbe at an order of unity for the scattered echo to have a substantial
effect on the extinction law. From this analysis, we conclude that
it is difficult for the scattered echo to be a general origin of thenon-standard extinction law towards SNe, as long as the CS dust isplaced at R  0.1 pc. A possibility that the CS dust at R  1 pc
creates the non-standard extinction law is not rejected, althoughcategorizing it as ‘CS’ dust is questionable (see below). A dust
shell at R ∼ 0.1–1 pc is rejected for some SNe Ia when the late-timeKs -band data are available, but not generally constrained due to alack of such data.
The above constraints are for the shell model. One might guessthat the constraint would be weakened if the CS dust is confined ina specific direction, e.g. in an equatorial ring or in bipolar blobs, as
the CS dust mass required to create τ a (B) ∼ 1 should be reduced.
While this is true, several additional effects must be considered.
First, the shell model does indeed provide the most conservative
upper limit on the CS dust mass. If one confines the same amountof CS dust in a specific direction, then the local density increases.
This generally results in larger luminosity at a specific epoch thanin the corresponding shell model, and thus a tighter limit on Md isobtained using the observational data at the corresponding epoch(Fig. 2). For example, the edge-on ring model predicts a larger
luminosity than the shell model with the same CS dust mass at the
beginning and the end of the NIR echo. In contrast, the same model
viewed pole-on has a shorter duration and a larger luminosity. Thislarge luminosity in the ring model is achieved when the emission
at the ring-edge reaches the observer. A similar argument applies tothe blob model.
As for the required CS dust mass within the scattering echo modelfor the extinction law, it is true that the required mass is reduced
for an edge-on observer to the ring-like CS dust structure (Fig. 4).
However, for the pole-on case, this effect is compensated for by
an increase in the predicted luminosity (Fig. 2). Thus, the resulting
upper limit for τ a (B) in the pole-on ring model is similar to thatof the shell model (Fig. 4). Statistically, there must be edge-on andpole-on counterparts; the NIR echo constraint in this paper, using a

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Figure 3. Examples of the light-curve constraints on the CS dust mass, applied to the J-band light curve of SN 2006X (left; Wood-Vasey et al. 2008) (alsoshown is the Hsiao template, represented by a black solid line) and the Ks -band light curves of SN 2003hv (right; Motohara et al. 2006; Leloudas et al.
2009). For SN 2006X, two observational light curves are shown – one being the original light curve (crosses) and the other constructed from the residual after
subtracting the template light curve (open circles; see main text). The shell CS dust echo modelled with the maximally allowed CS dust mass are shown for
select values of R (red/solid for 3.24 × 10−3 pc, green/dashed for 1.02 × 10−2 pc, blue/dot–dashed for 3.24 × 10−2 pc, cyan/dotted for 1.02 × 10−1 pc andmagenta/dot–dashed for 3.24 × 10−1 pc). For SN 2006X, two models are shown for each R – one using the original light curve (thick, ‘C’ in the labels) andthe other using the residual light curve (thin, ‘D’ in the labels). These examples highlight the importance of good early-phase light curves to constraint the
CS dust mass at small R especially coupled with the template light curves, as well as deep late-time photometric points preferably at longer wavelengths toconstrain the CS dust mass at large R.

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number of SNe, is sufficiently strong to reject this possibility. If one
introduces a more confined configuration, then this increases thelikelihood that it will not be viewed from that direction. In addition,
for a pole-on observer to have a substantial scattering effect, thetime required for light to travel to the CS dust must be shorter than
the rising time of SNe Ia (i.e. ∼15–20 d), and therefore the CS
dust beyond R ∼ 0.02 pc never affects the extinction law if viewed
pole-on.
The above argument should be slightly modified for a very confined case, such as when considering the bipolar blob geometry.
Similar to the ring-like geometry, the upper limits on the CS dust
mass for a bipolar blob are comparable to or deeper than the corresponding shell model, depending on the viewing direction. If this isconverted into the optical depth, the derived upper limits are indeed
not extremely strong to readily reject the multiple scattering modelfor the extinction law, i.e. τ a (B) ∼ 1 (Fig. 4). However, in this case,the amount of scattered photons should already be limited, due toa small opening angle subtended by the distribution of CS dust.
In summary, introducing the confined CS geometry does not help
interpret the non-standard extinction law as generally having comeMNRAS 452, 3281–3292 (2015)

from CS scattered light. SNe suffering a substantial ‘CS’ scattering
echo effect must be limited to at most only a fraction of SN Ia
samples.
For the CS dust to have originated from the mass-loss of a progenitor, the CS gas mass should be  a few M , i.e. Md  a
few × 10−2 M . This amount of CS dust can create a substantial
scattering effect, only if R  0.2 pc, even if we use the conservativerequirement τ a (B) ∼ 0.1 (or ∼0.05 pc if we adopt τ a (B) ∼ 1). We
generally reject such a large amount of CS dust at R  0.2 pc (seeabove). Therefore, if the echo scenario is to be a general originof the non-standard extinction law, then the dust must indeed beinterstellar medium (ISM) in origin, located at R  0.2 pc.
One may question what implications this mass-loss rate may
have for the progenitor scenario. Indeed, the CS scattering model
requires a much larger amount of CSM, compared to that predictedby typical progenitor scenarios. Our limit is Ṁ  10−6 M yr−1
for the mass-loss wind velocity of ∼10 km s−1 below 0.01 pc, or,in the final ∼400 yr before the explosion. This is not as strong as
the constraint from radio and X-rays (e.g. Ṁ  10−9 M yr−1 forthe same velocity, for SN 2011fe; Chomiuk et al. 2012; Margutti

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Figure 4. Conservative upper limit on the amount of CS dust as a function of R (distance to the CS dust), for the shell CSM (a), the ring-like CSM as viewed
from the equator (b) and from the polar direction (c), and the bipolar blob-like CSM as viewed from the equator (d) and from the polar direction (e). The
symbols indicate the observational sample for which the constraints are derived: CSP sample (filled square; Folatelli et al. 2010), SN 2006X (open square;
Wood-Vasey et al. 2008), SN 1998bu (filled circle; Hernandez et al. 2000; Spyromilio et al. 2004), SN 2000cx (open circle; Candia et al. 2003; Sollerman
et al. 2004), SN 2001el (filled triangle; Krisciunas et al. 2003; Stritzinger & Sollerman 2007), SN 2003du (open triangles; Motohara et al. 2006; Stanishev
et al. 2007) and SN 2003hv (filled star; Motohara et al. 2006; Leloudas et al. 2009). For each radius and given SN, the symbol is coloured according to thephotometric band that gives the tightest constraint: J (blue), H (green) and Ks (red). The thick solid lines indicate Md corresponding to τ a (B) = 1, 0.1 and 0.01.
If the origin of the dust is ‘CS’, Md would not exceed a few 0.01 M , corresponding to a few M in the CSM mass (dotted horizontal line for Md = 0.03 M ).
For the CS dust to be the origin of the peculiar extinction law, τ a (B) should exceed at least 0.1 (conservatively) – the corresponding radius is indicated by thevertical dotted line, left of which is considered to be CSM and right as ISM. The dashed vertical lines indicate the radius at which the equilibrium temperatureof the CS dust is 3000, 2000 or 1000 K. Assuming a gas-to-dust ratio of 100, the equivalent steady-state mass-loss rate is shown by the thin solid lines (in unitof M /10 km s−1 ).

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et al. 2012). However, we emphasize that radio and X-rays probe thematerials inside R ∼ 3 × 10−3 pc; our proposed method using the
NIR echo can extend the constraint by an order of magnitude in thespatial dimension (or to the past before the explosion), making ourlimit independent and unique. From the present analysis (see below
for possible improvement), the only scenario that can be marginallyrejected, for normal SNe examined in this paper, is a symbiotic
system. However, we do note that SNe Ia resulting from this path
may appear as an atypical SN Ia (Dilday et al. 2012).
Thus far, our limit has been rather conservative, and is based on
the condition that the echo luminosity cannot exceed the observed
one. However, most of the light should have originated from aradioactive decay chain and subsequent thermalization, as demonstrated by NIR spectroscopy (Gerardy et al. 2007; Marion et al.
2009; Hsiao et al. 2013). Given this observational fact, we can refine our limit as follows. First, attribute the template light curvesin each band to the SN light without any contribution of the possible NIR echo; subtract the templates from the light curves fromindividual SNe; and then use the residual light curve (here we takethe absolute value if the subtraction results in a negative value)
to place an upper limit on the CS dust mass. Namely, we assume
that the echo luminosity does not exceed the variation in the NIR
light curves, seen in different SNe. As a demonstration, in Fig. 3(left-hand panel) we show the case of SN 2006X, for which a goodlight curve is available. The figure shows that the magnitude of thisresidual light curve is 1–5 less than that of the original, highlighting
the standard nature of the NIR light curves.
Using this argument, much tighter constraints can be obtained(as shown by the thin solid lines in Fig. 3). Fig. 5 shows the resultsfor SN 2006X. Because J- and H-band data are of the best quality,
following the template closely, the upper limit for the CS dust
mass, especially at R  0.1 pc, improved significantly. For smallR, the upper limit was reduced by two orders of magnitude, whichreflects a residual light curve that was fainter than the originalby ∼5 mag. With this method, all of the models with different
geometric types result in τ a (B)  0.1 (τ a  0.01 for most situations),robustly rejecting the CS scattering model for the extinction law
for this particular SN. The upper limit for the mass-loss rate is
now Ṁ  10−7 M yr−1 for R  0.01 pc, much deeper than theconservative limit, as described earlier in this section.
4 DISCUSSION
4.1 Dust properties
In this paper, our analysis has been based on a particular dust model,
i.e. the LMC-type dust opacity. In this section, we examine theeffects of different types of CS dust. Fig. 6 shows the ‘conservative’
limits on the CS dust mass derived for (a) astronomical silicate and(b) amorphous carbon or graphite, both for the shell model. Fig. 7
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Figure 5. Deeper upper limit on the amount of CS dust as a function of R (distance to the CS dust), for the shell CSM (a), the ring-like CSM viewed from theequator (b) and from the polar direction (c), and the bipolar blob-like CSM as viewed from the equator (d) and from the polar direction (e). Here, an upper
limit is placed on the requirement that the resulting echo flux must be below the difference between the observed magnitude and the template magnitude. The
deeper limit is shown by the open squares (blue, green and red constrained in J, H and Ks , respectively); the conservative limit is shown as filled grey squares
to show the potential for improvement in the constraint.

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Figure 7. Same as Fig. 5, but (a) for astronomical silicate dust and (b) for amorphous carbon/graphite.

shows the same but for the ‘deeper limit’ for SN 2006X (i.e. Fig. 5
but for astronomical silicate or carbon). The opacities are calculatedusing optical constants by Draine (2003) and Zubko et al. (1996).
To the first approximation, the behaviour can be understood by thedifference in a typical opacity for different dust models, e.g. theopacity in the B band. The opacity is roughly a factor of 2 lower
for silicate than the reference LMC-like dust model; thus, the upper
limit for the CS dust mass is weakened by the same factor. The
opacity is roughly an order of magnitude higher for carbon than the
LMC-like dust model, and therefore the upper limit on the CS dust
mass is deeper for the carbon dust model by an order of magnitude
than our fiducial model.
However, these different constraints on the CS dust mass would
not substantially alter the constraints on the ability of the CS dust
to create the non-standard extinction law. The optical depth itself
is scaled by the same factor; therefore, the upper limits on τ a (B)would not change substantially.
4.2 Implications for some specific cases
Our results should be compared to SNe, in which a large amountof dust is inferred either by the detection of an optical (scattered)echo or other probes (e.g. narrow absorption systems). For example,
we have obtained a tight limit for the amount of CS dust for SN
2006X (Fig. 5), while this SN was detected in a scattered echo
(Wang et al. 2008); its optical spectrum at ∼1 yr after the explosion
showed a blue echo component, indicating τ a (B) ∼ 1. In contrast,
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we obtained the constraint that τ a (B) < 1, as long as the echo source
is at R  0.4 pc (or even τ a  0.01 at R  0.1 pc). Taken together, thedetected echo in SN 2006X must be created by ISM, as suggested
by Crotts & Yourdon (2008) using Hubble Space Telescope (HST)
data. To date, even for cases where an (optical) echo is detected,
evidence of a CS echo remains weak.
Another example is highly extinct SN Ia 2014J in M82. No variability has been found in the narrow absorption lines (e.g. Goobar
et al. 2014). Foley et al. (2014) have claimed temporal evolution in
RV , while no apparent variability has been detected in polarization
measurements (Kawabata et al. 2014). While a consistent interpretation for all of these features has yet to be reached, it seems thattogether they suggest that the CS scattering scenario is unlikely, but
perhaps a combination of multiple scattering and true absorption at
the ISM scale could provide a consistent solution. Indeed, detectionof an echo has been reported for SN 2014J through high-resolution
HST images at ∼230 d after the explosion (Crotts 2015). This has
been interpreted as echoes originating at the interstellar scale. At
this epoch, the SN still dominates the light in the vicinity of the
SN and no strong signature of the echo from the CS dust has beenobtained (see also Johansson et al. 2014).
In Fig. 8, we show the results of simulated Ks -band images ofan echo from the CS dust located at R = 1 pc for different geometries, for an SN at 3.8 Mpc. For the ring and blob geometries, wehave adopted θ 0 = 30◦ and the viewing direction of 45◦ for the
purpose of demonstration. The model images are convolved witha Gaussian kernel of 0.1 arcsec to roughly simulate observations

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Figure 6. Same as Fig. 4, but (a) for astronomical silicate dust and (b) for amorphous carbon/graphite.

CS dust around SNe Ia

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Figure 9. Simulated images of a CS echo in the Ks band, for an SN at a distance of 3.8 Mpc as observed with a spatial resolution of 0.01 arcsec (i.e. TMT,
E-ELT, GMT). The distance to the CS dust is set as R = 0.3 pc. The images are created by smoothing the echo model by a Gaussian kernel with 0.01 arcsec(shown by a green circle). The time evolution is shown from the left to the right, and different geometric models are shown from top to bottom. An SN at thisdistance is represented by SN 2014J.

by HST; the narrow field channel of HST/NICMOS has a spatial
resolution of ∼0.14 arcsec at ∼1.6 μm. Thus our simulation could
overestimate the spatial resolution up to ∼50 per cent, but it could
anyway be compensated by increasing the assumed physical scaleof the CS dust by the same factor. Note that these images are for a‘pure’ echo component – if the projected echo size is smaller thanor comparable to the instrument’s spatial resolution, then the SN
must fade away below the level of the echo luminosity to examine
the geometry of the echo signal. Note that there is a better chance toapply this exercise to later epochs. Fig. 8 shows the expected evolution covering ∼5 yr, to investigate the possibility of distinguishingdifferent CS dust geometries if a CS dust echo is detected. Even for
nearby SN 2014J and using HST, probing the CS dust echo using
spatially resolved imagery can be difficult.
For a ring-like structure, an elongated structure is visible whent ∼ R/c. For this particular bipolar blob model, the echo ‘disappears’
when t ∼ R/c. For both models, there is a (non-monotonic) shift
in the centre of the echo light. The size of this shift for theseparticular models is about half of the spatial resolution, and could be
detectable with precision astrometry techniques. These diagnostics
could apply to SN 2014J if the CS dust echo is detected in the

future following the SN luminosity decrease. Continuous HST highresolution observations are strongly encouraged.
4.3 Future possibility of high-resolution imaging observations
While investigation of the CS echo through direct imaging observations is currently limited by the spatial resolution of ∼0.1 arcsec at
NIR wavelengths even with HST (Section 4.2), the situation is expected to improve dramatically in the coming decade. The planned
James Webb Space Telescope (JWST) will reach to a spatial resolution by a factor of ∼2.5 better than HST. Furthermore, with theavailability of NIR adaptive optics (AO) attached to 30-m classtelescopes such as the Thirty Meter Telescope (TMT), European
Extremely Large Telescope (E-ELT) and Giant Magellan Telescope(GMT), spatial resolutions of ∼0.01 arcsec are expected. Figs 9
and 10 show synthesized images at different epochs for an SN at
a distance of 3.8 Mpc, surrounded by CS dust shell/ring/blobs, asviewed with a spatial resolution of 0.01 arcsec (for the viewing
direction of 45◦ as a specific example). With this resolution, one
can distinguish different CS dust geometries, even for the CS dust
located at R = 0.3 pc. For a spherically symmetric distribution,
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Figure 8. Simulated images of a CS echo in the Ks band, for an SN at a distance of 3.8 Mpc, observed with a spatial resolution of 0.1 arcsec. The distance to
the CS dust is set as R = 1 pc. The images are created by smoothing the echo model by a Gaussian kernel with 0.1 arcsec (shown by a green circle). The time
evolution is shown from the left to the right, and different geometric models are shown from top to bottom. An SN at this distance is represented by SN 2014J.
The adopted resolution slightly overestimates the HST resolution in the K band (∼0.15 arcsec), but here it is adopted for the purpose of demonstration; since theangular size scales linearly with the physical scale, this relative-flux map applies to the case with R = 1.5 pc if the angular resolution is worse by 50 per cent.

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Figure 11. Same as Fig. 9, but for an SN at a distance of 15 Mpc. On average, one SN per year has been discovered within 15 Mpc.

Figure 12. Same as Fig. 11, except that R = 1.0 pc.

investigation of the radial distribution is within reach, as seen by
the hole for the shell model. The ring and blob models show asymmetric image profiles that are clearly different from the shell model(but depend on the viewing direction). The shift of the centre inthese models should be easily resolved beyond the spatial resolution – for example, using this shift, the blob model is distinguishable
from any spherically symmetric distribution.
An SN at a distance of 3.8 Mpc is a rare event, at an observed
rate of one per decade or two. Figs 11 and 12 show the same images, but for an SN at a distance of 15 Mpc. At this distance, we
expect an event rate of roughly one per year; thus, such observations are, in principle, annual occurrences. For CS dust located at
R = 0.3 pc around an SN at a distance of 15 Mpc, as observed

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by TMT/E-ELT/GMT (Fig. 11), the situation is similar to the caseshown in Fig. 8. An elongated profile of the ring distribution could
be marginally resolved, and the shift in images for asymmetrically
distributed CS dust (e.g. ring or blobs) could be detectable by a
sub-spatial resolution astrometry. For the CS dust at R = 1 pc,
observations with a spatial resolution of 0.01 arcsec can distinguish various CS dust geometries, given that such echo signals aredetected.
Thus, we conclude that the proposed future high-resolution NIR
AO can open up a new window to examine the CS environment
around nearby SNe. We note that a target does not have to be one
discovered after the new instruments become available. For example, SN 2014J can already be a target – assuming an observation at

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Figure 10. Same as Fig. 9, except that R = 1 pc.

CS dust around SNe Ia
year 2024, CS dust located at 2 pc can still be investigated. Pilot
work on this measurement may already be possible with 8-m classtelescopes approaching the diffraction limit (∼0.05 arcsec).
5 CONCLUSIONS
We investigated the effects of re-emission of SN photons by CS dust
for IR wavelengths. We have shown that this effect allows observed
IR light curves to be used to place constraints on the position/sizeand the amount of CS dust. We applied the method to observed NIR
SN Ia samples, and found that meaningful upper limits on the CS
dust mass can be derived, even under conservative assumptions.
Our results are summarized as follows.

From these results, we conclude the following regarding the possibility of the dust-scattering scenario for the non-standard extinction
law towards SNe Ia:(i) The ‘CS’ dust (at R  1 pc) echo cannot be a general explanation of the non-standard extinction law with regard to SNe Ia. The
scenario would work for at most a fraction of SNe Ia, presumably
at most, the highly reddened ones.
(ii) If the echo scenario is responsible for the extinction law ingeneral, then the dust must be located at R  1 pc. The required
mass is, however, 100 M ; therefore, this must be attributed to
ISM rather than CSM.
We have also demonstrated an approach that allows deeper limits
to be applied. This involves first using the standard nature of the
NIR light curves. We demonstrated this for SN 2006X, showingthat the upper limit can be deepened by two orders of magnitude
from the conservative limit, as given above. We suggest that further
improvement is possible by refining the analysis method along thisline via standardization of the NIR light curves for a given sample
and minimization of the dispersion as a function of time. This would
allow a deeper limit to be placed on the mass-loss rate, potentiallyto the level to limit various models other than the particular symbiotic scenario. Again, one of the main advantages of the proposed
method, compared to radio and X-ray constraints (which are indeed
complementary to the proposed method here), is the following: thelimit to the amount of dust placed by the NIR echo extends an orderof magnitude larger in the spatial dimension (or an order of magnitude to the past in the time dimension), reflecting the fact that thelight speed (for the echo) is by an order of magnitude faster than
the shock velocity (for radio and X-rays).
As we have shown in this paper, late-time photometry, evensparse, especially in the Ks band, is essential to constrain dust (andgas) mass in the environment at R  0.1 pc. Our method underlines

the importance and usefulness of such data. Our analysis is also
highlighted by the possibilities of (1) constraining the origin of thenon-standard extinction law, and (2) constraining the CSM mass up
to ∼1 pc, namely the regimes that the other methods like radio and
X-ray diagnostics cannot probe. Because the data are still rare, we
propose increasing the sample of NIR/mid-IR SNe with continuous
observational efforts. Of course, if one wants to go further towards
the ISM regime, mid- and far-IR data are important (Johansson et al.
2013, 2014), and a combination of the early radio/X, early and latetime NIR, and late-time mid-/far-IR, perhaps complemented by theabsorption system study (e.g. Phillips et al. 2013), will hopefully
provide a complete view of these issues.
We also investigated the possibility of studying the CS dust distribution through high spatial resolution observations. Our results
are summarized below.
(i) CS dust around SN 2014J could potentially be resolved by
future HST observations, given that dense CS dust shell/ring/blobs
exist at R  1 pc from the SN site.
(ii) Future NIR AO instruments attached to 30-m class telescopes
are capable of distinguishing various distributions of CS dust, thus
providing a powerful means for investigating the CS environment
around SNe Ia.
(iii) Such observations will be possible for nearby SNe at a rateof roughly once a year.

AC K N OW L E D G E M E N T S
The authors thank Ariel Goobar for fruitful discussion. KM acknowledges financial support by Grant-in-Aid for Scientific Research (no. 23740141 and 26800100) from the Japanese Ministryof Education, Culture, Sports, Science and Technology (MEXT).
The work by KM is partly supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.
The authors also thank the anonymous referee for her/his many
constructive comments.

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Downloaded from http://mnras.oxfordjournals.org/ at National Astronomical Observatory of Japan on August 10, 2015(i) Md  10−5 M for the CS dust at R  0.01 pc, Md  10−4 M
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