The Astrophysical Journal, 776:5 (16pp), 2013 October 10

doi:10.1088/0004-637X/776/1/5


C 2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

PROPERTIES OF NEWLY FORMED DUST GRAINS IN THE LUMINOUS TYPE IIn SUPERNOVA 2010jl∗
K. Maeda1 , T. Nozawa1 , D. K. Sahu2 , Y. Minowa3 , K. Motohara4 , I. Ueno5 , G. Folatelli1 ,T.-S. Pyo3 , Y. Kitagawa4 , K. S. Kawabata5 , G. C. Anupama2 , T. Kozasa6 ,T. J. Moriya1,7,8 , M. Yamanaka5,9,10 , K. Nomoto1 , M. Bersten1 , R. Quimby1 , and M. Iye11
1 Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study,

University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan; keiichi.maeda@ipmu.jp
2 Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India
3 Subaru Telescope, National Astronomical Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96720, USA
4 Institute of Astronomy, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan
5 Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
6 Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
7 Department of Astronomy, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyoku, Tokyo 113-0033, Japan
8 Research Center for the Early Universe, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyoku, Tokyo 113-0033, Japan
9 Department of Physical Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
10 Department of Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
11 National Astronomical Observatory, Mitaka, Tokyo, Japan
Received 2013 March 3; accepted 2013 July 30; published 2013 September 18

ABSTRACTSupernovae (SNe) have been proposed to be the main production sites of dust grains in the universe. However,
our knowledge of their importance to dust production is limited by observationally poor constraints on the nature
and amount of dust particles produced by individual SNe. In this paper, we present a spectrum covering opticalthrough near-Infrared (NIR) light of the luminous Type IIn supernova 2010jl around one and a half years after the
explosion. This unique data set reveals multiple signatures of newly formed dust particles. The NIR portion of thespectrum provides a rare example where thermal emission from newly formed hot dust grains is clearly detected.
We determine the main population of the dust species to be carbon grains at a temperature of ∼1350–1450 K at
this epoch. The mass of the dust grains is derived to be ∼(7.5–8.5) × 10−4 M . Hydrogen emission lines show
wavelength-dependent absorption, which provides a good estimate of the typical size of the newly formed dust
grains (0.1 μm, and most likely 0.01 μm). We believe the dust grains were formed in a dense cooling shell
as a result of a strong SN–circumstellar media (CSM) interaction. The dust grains occupy ∼10% of the emittingvolume, suggesting an inhomogeneous, clumpy structure. The average CSM density must be 3 × 107 cm−3 ,corresponding to a mass loss rate of 0.02 M yr−1 (for a mass loss wind velocity of ∼100 km s−1 ). This strongly
supports a scenario in which SN 2010jl and probably other luminous SNe IIn are powered by strong interactions
within very dense CSM, perhaps created by Luminous-Blue-Variable-like eruptions within the last century before
the explosion.
Key words: dust, extinction – infrared: stars – shock waves – supernovae: individual (SN 2010jl)
Online-only material: color figures

an additional power source for the SN emission besides theradioactive decay chain 56 Ni → 56 Co → 56 Fe (e.g., Chevalier& Fransson 1994; Chugai 2001; Chugai et al. 2004; Chevalier& Irwin 2011; Chatzopoulos et al. 2012; Moriya et al. 2013a,
2013b). These SNe show a range of luminosities (Taddia et al.
2013), perhaps due to a diversity in the strength of the interaction(i.e., in the ejecta properties and/or the CSM density). In an
extreme situation, either with a large kinetic energy of the
explosion and/or extremely high-density CSM, such a system
may also be responsible for (at least a part of) Super-Luminous
SNe (SLSNe; see Quimby et al. 2011; Gal-Yam 2012 andreferences therein).
In these strongly interacting SNe, the dense shell would
undergo strong radiative cooling, thus the temperature could
decrease to the dust condensation temperature while the density
is still high (Pozzo et al. 2004; Smith et al. 2008b). However,details of the process are yet to be clarified. One may expect that
this “cooling-shell” dust formation takes place more favorably
in an earlier phase than in other classes of CCSNe as reported ina few cases (e.g., Smith et al. 2008b), but constraining the dust
formation time is generally difficult since it requires an extensive
time-sequence from the optical through the IR to disentangle

1. INTRODUCTION
Core-collapse supernovae (CCSNe) are suggested to be oneof the major production sites of cosmic dust grains. This ishighlighted by their capability of producing dust in the early
universe due to the short time scale of massive star evolution
leading to core-collapse and explosion (e.g., Dwek et al. 2007).
Supernovae (SNe) eject metal-rich materials into space, whichcool rapidly and provide ideal conditions for dust condensation(Kozasa et al. 1989; Todini & Ferrara 2001; Nozawa et al. 2003).
Another dust production mechanism is also suggested fora class of SNe exploding within dense circumstellar materials(CSMs). Such SNe are classified as Type IIn due to their narrowhydrogen emission lines (Filippenko 1997), which probably
arise from unshocked CSM (Chevalier & Fransson 1994),
though some are also a rare class of SN Ib 2006jc-like objects(Type Ibn: Foley et al. 2007; Pastorello et al. 2008; Smithet al. 2008b; Tominaga et al. 2008; Anupama et al. 2009). The
strong interaction between the SN ejecta and CSM can provide∗ Based on data collected at the Subaru Telescope, operated by the National
Astronomical Observatory of Japan, and at the Himalayan Chandra Telescope,
operated by the Indian Institute of Astrophysics.

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Maeda et al.

other possibilities, such as an echo from pre-existing dust grainsin the CSM (see, e.g., Fox et al. 2011).
A main obstacle to understanding the importance of SNe in
the cosmic dust inventory is generally insufficient data (or lackof detailed analysis) to specify the macroscopic and microscopic
properties of newly formed dust grains in individual SNe. For
most SNe suggested to have experienced dust formation, thelink has been inferred by either a suppression of the red wingof spectral lines and/or a sudden drop in optical light curves(see Kozasa et al. 2009 for a review). Stronger cases have beenreported for some SNe showing an excess in IR wavelengths
that is attributed to thermal emission from newly formed dust
grains. For some SNe, the spectral energy distribution (SED)
was constructed from NIR and mid-IR photometry (e.g., Mattila
et al. 2008; Fox et al. 2009; Andrews et al. 2010; Fox et al.
2011). The best cases have been provided by detection of athermal component in their spectra, including SN II 1987A (inmid–far-IR; Moseley et al. 1989; Wooden et al. 1993), Type IIn
supernova (SN IIn) 1998S (in NIR; Gerardy et al. 2000; Pozzo
et al. 2004), SN IIp 2004et (mid-IR; Kotak et al. 2009), SN IIn
2005ip (NIR–mid-IR; Fox et al. 2010), and SN Ibn 2006jc (NIR;
Smith et al. 2008b; Sakon et al. 2009).
The most convincing case has been reported for SN 1987A,
where the dust is believed to have been formed deep in the
SN ejecta through the concurrent appearance of the following
events (e.g., Kozasa et al. 1989 for a review): (1) the blue shift
in emission lines in optical (and the NIR; Lucy et al. 1989;
Meikle et al. 1993), (2) the decline in the optical luminosity andincrease in the luminosities at longer wavelengths (Whitelock
et al. 1989; Suntzeff & Bouchet 1990), and (3) the thermal
continuum emission in mid–far IR (Moseley et al. 1989; Wooden
et al. 1993). It is, however, very rare that all these three signatures
are obtained for the same SN, given observational limitations.
Typically, the spectral peak in the dust thermal emission is outof the observed wavelength range, and the quality of the spectra
does not allow for a detailed investigation of line emissions at
IR wavelengths. To the authors’ knowledge, there has been no
NIR spectroscopic observation of dust-forming SNe that covers
a dust thermal emission peak and at the same time has a signalto-noise ratio (S/N) sufficiently high to allow for a detailed
study of line emissions.
SN IIn 2010jl offers a new, promising site to study dust
formation. This SN was discovered in an image taken on 2010
November 3.52 (UT; Newton & Puckett 2010) in nearby galaxy
UGC5189A (redshift of 0.010697 and luminosity distanceof 48.9 Mpc, according to the NASA/IPAC Extragalactic
Database12 , which we use throughout this paper). It is classified
as Type IIn (Benetti et al. 2010) and is intrinsically bright,
reaching an absolute magnitude of ∼−20 (Stoll et al. 2011;
Zhang et al. 2012). Throughout this paper, we assume that the
V-band maximum was reached at JD2455488 (Stoll et al. 2011),
and we express the SN phase relative to this V-band maximum
date. A pre-explosion image suggests that the progenitor of
SN 2010jl was likely a massive star with a main-sequence massof Mms  30 M (Smith et al. 2011). Host galaxy properties
imply that SN 2010jl exploded in a low metallicity environmentZ  0.3 Z (Stoll et al. 2011). SN IIn 2010jl was not only
bright but also showed a slow evolution similar to SN IIn
2006tf (Smith et al. 2008a). While the initial decay rate wasclose to that of 56 Co, later it flattened at around 100 days,
and this flat evolution continued until at least 200 days (Zhang
et al. 2012). If the initial decay phase is interpreted as being
powered by the decay of 56 Co, it requires an unusually large
amount of synthesized 56 Ni at the explosion, as large as 3.4 M
(Zhang et al. 2012). Alternatively, the initial phase could bedominated by the SN–CSM interaction (Moriya et al. 2013b).
In any case, there is no doubt that after ∼100 days (as is themain focus of this paper), the radioactive energy input cannot
be a major power source, and the SN–CSM interaction is themost likely power source. The total radiation energy output in
optical wavelengths up to ∼200 days, irrespective of the energy
source, reached ∼4 × 1050 erg (Zhang et al. 2012). The large
luminosity and radiation output place SN 2010jl close to SLSNe(Quimby et al. 2011; Gal-Yam 2012 and references therein), thus
understanding the properties of SN 2010jl could provide a hintin understanding yet unresolved origins of these SLSNe. Strong
SN–CSM interaction seems to provide a favorable site for thedust formation, perhaps through a dense cooling shell, as shownin some SNe IIn and the related SNe Ibn, including SN Ibn
2006jc, SNe IIn 1998S, 2005ip, and possibly SN IIn 2006tf andsome other SNe IIn (Gerardy et al. 2000; Pozzo et al. 2004;
Smith et al. 2008a, 2008b; Fox et al. 2010, 2011; Stritzinger
et al. 2012). This motivates our interest to study dust formationin luminous SN IIn 2010jl.
Dust formation in SN 2010jl, from relatively early phases
until ∼200 days after the discovery, is under debate. IR excess
peaking at ∼5 μm was reported by Andrews et al. (2011a) at∼77 days (relative to V-band maximum). Smith et al. (2012)
reported systematic blueshift in hydrogen emission lines atsimilar epochs. While Andrews et al. (2011a) attributed the
IR excess to an echo by pre-existing dust particles in the CSM,
Smith et al. (2012) speculated that these two features could
indicate new dust formation. Zhang et al. (2012) did not finda rapid decline in the optical light curve in the corresponding
epochs, which is expected from the obscuration by newly formed
dust particles, and suggested that the blueshifted emission lines
might be due to a gas-opacity effect rather than the dust opacity(see also Smith et al. 2012).
In this paper, we present spectroscopic and photometricobservations from the optical through the NIR of SN 2010jl
at a late phase, about 550 days after the V-band maximum. We
find strong evidence for newly formed dust particles in this latephase, and our data set allows detailed study on the propertiesof the dust. In Section 2, we describe our observations and data
reduction. Results are presented in Section 3, where we discuss
properties of both the dust grains and the SN ejecta and CSM.
Section 4 includes discussion and conclusions. Appendices A,
B, and C are given for the optical spectrum data reduction, theSN environment, and a constraint on a possible CSM echo in
the SN optical spectrum, respectively.
2. OBSERVATIONS AND DATA REDUCTION
2.1. NIR Observations
Our NIR observation was performed on 2012 April 24 (UT;JD2456041.35) at the 8.2 m Subaru Telescope using the Infrared
Camera and Spectrograph (IRCS; Kobayashi et al. 2000) and theSubaru 188 element Adaptive Optics system (AO188; Hayano
et al. 2008, 2010). The date corresponds to +553 days after the
V-band maximum (Stoll et al. 2011). For spectroscopy, we used
J, H, and K grism with a 52 mas pixel scale. The slit width
was 0. 225, resulting in a spectral resolution of ∼800 in each

12 The NASA/IPAC Extragalactic Database (NED:
http://ned.ipac.caltech.edu/) is operated by the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National
Aeronautics and Space Administration.

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band. Spectroscopy was performed in two different dithering
positions, A and B, with a total exposure time of 300, 600, and1200 s in J, H, and K, respectively. The air mass was ∼1 forall observations. The SN was observed in the Laser Guide Star
Adaptive Optics (LGS-AO) mode, where SN 2010jl itself wasused as a Tip-Tilt star. An A0V star, HIP104353, was observed
as a telluric standard star on the same night and in the samegrism and slit setups with the natural guide star (NGS) AO
mode. The acquisition images were checked to confirm that thetarget center was correctly placed on a slit, thus the effect of a
possible artificial spectral warping is minimal (Goto et al. 2003).
We used IRAF for the spectroscopic data reduction.13 We
followed a standard procedure for working on the difference
images between two dithering positions, with flat fielding, badpixel correction, and cosmic ray removal. The two-dimensional
images were created for the negative and positive images,
with the standard star spectrum being a reference for the
spectrum extraction. The wavelength was calibrated with acomparison Ar lamp, which was then further checked withstrong OH sky emissions. The one-dimensional spectra wereextracted for the positive and negative images with further sky
subtraction; here we optimized the aperture to provide the best
S/N without introducing an artificial change in the spectral
shape. The positive and negative one-dimensional spectra werethen combined to produce the final one-dimensional spectrum.
The telluric absorption was removed using the standard star
spectrum; the A star atmospheric absorption lines had been
removed before performing the telluric absorption correction.
The flux calibration was also done using the standard star
spectrum, assuming the blackbody temperature of 9500 K,
which we confirmed to be a good approximation in NIR for
the Kurucz template A0V star spectrum. The flux was thenfurther calibrated to match the photometry (see below).
The narrow field imaging observation was performed withthe same instruments, with LGS-AO for SN 2010jl and
NGS-AO for standard star FS143 (Hawarden et al. 2001). We
used a 20 mas pixel scale, resulting in a field of view of 21 ×21 .
Five-point dithering was performed with an exposure of 5 s ineach position. Given the narrow field of IRCS, we could not perform relative photometry with field stars. Thus, we performed
absolute photometry with standard star FS143. The sky condition was good, but we noted that a systematic error at thelevel of ∼0.1 mag in the absolute magnitude scale might beinvolved (while the color in different bands would not containsuch a large systematic error). The imaging data reduction was
performed using IRAF, following standard procedures. Every
image was checked at a different dithering position, and thosewith background fluctuations apparently different from the others were removed from the analysis (typically these occurred in
the first dithering position). Sky flat images were created withthe standard star images, which were then used for flat fielding and sky subtraction. Photometry was then performed on the
combined images from different dithering positions. We used
an aperture extraction of the flux, where we varied the size ofapertures to check the convergence. The FWHM without AO
core was typically 0. 6, and the typical size of the aperture weused was ∼(3–5)× FWHM. We confirmed that the zero-point
we derived for each band is consistent with the values reported
in the instrument web page and past observations using the same
instruments. We noted that standard star FS143 turns out to bea double star system spatially resolved in the AO-aided highresolution K  -band image, thus we adopted a large aperture so
as not to miss the total light from the system. Our photometry
results in J = 14.09 ± 0.1 mag, H = 12.89 ± 0.04 mag, andK  = 11.98 ± 0.02 mag (where the errors account for only thestatistical error).
2.2. Optical Observations
In the optical region, SN 2010jl was observed with the 2 m Himalayan Chandra Telescope (HCT) of the Indian Astronomical
Observatory, Hanle, India, on 2012 March 15 (JD 2456002.12)
and 2012 May 20 (JD 2456068.18), corresponding to +514
and +580 days since the V-band maximum, respectively. The
spectra were obtained using grisms Gr#7 (wavelength range
3500–7800 Å) and Gr#8 (wavelength range 5200–9200 Å) available through the Himalaya Faint Object Spectrograph Camera(HFOSC). Arc lamp spectra of FeAr and FeNe for wavelength
calibration and spectra of spectrophotometric standard, withbroader slits to correct for instrumental response and flux calibration, were also observed during the observing run. Data
reduction was carried out using various tasks available within
IRAF. The images were bias-corrected and flat-fielded, thenone-dimensional spectra were extracted from the cleaned image
using the optimal extraction algorithm (Horne 1986). The extracted arc lamp spectra were used for wavelength calibration.
The accuracy of the wavelength calibration was checked using
the night sky emission lines and, whenever required, a small
shift was applied to the observed spectrum. The wavelengthcalibrated spectra were corrected for the instrumental responseusing the spectrum of spectrophotometric standards observedon the same night, and the SN spectra were brought to a relativeflux scale. The flux-calibrated spectra in the two regions werecombined to a weighted mean to obtain the final spectrum on arelative flux scale.
Imaging observations of SN 2010jl were performed on 2012
March 27 (UT) and on 2012 May 21 (UT). These were obtainedin the Bessell BVRI bands with the HFOSC mounted on HCT.
With a plate scale of 0.296 arcsec pixel−1 , the central 2k ×
2k region of the SITe CCD chip used for imaging observations
covers 10 × 10 of the sky. The images were reduced in thestandard manner using IRAF. As the SN is embedded inside thegalaxy, we opted for the profile fitting photometry using daophot
available within IRAF. A set of secondary standard stars wascalibrated in the SN field over several nights under photometricsky conditions. Finally, the SN magnitudes were calibrated
with respect to the secondary standards. The photometry resultsin B = 16.96 ± 0.04 mag, V = 16.64 ± 0.03 mag, R =15.71 ± 0.05 mag, and I = 15.79 ± 0.02 mag on March
27; and B = 17.27 ± 0.04 mag, V = 17.02 ± 0.04 mag,
R = 16.00 ± 0.06 mag, and I = 16.16 ± 0.05 mag on May 21.
Note that the above photometry includes a possible contamination from an unresolved background region, thus it is likely
an overestimate of the SN magnitude. According to Zhang et al.
(2012), the host galaxy contamination is fainter than 18 magwithin the 3 diameter of the Sloan Digital Sky Survey. We
have roughly checked how much the contamination could be in
our photometry as follows: assuming that the brightest region
within the host galaxy is a hypothesized unresolved backgroundregion, we estimate that the upper limit of the background contamination would be 0.6–0.8 mag in B, V, and I and 0.2–0.3 mag
in R. More details on the light curve evolution and the estimateof the host galaxy contamination will be provided elsewhere(I. Ueno et al., in preparation).

13 IRAF is distributed by the National Optical Astronomy Observatory, which

is operated by the Association of Universities for Research in Astronomy, Inc.,
under cooperative agreement with the National Science Foundation.

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IRCS observation (+553 days). The spectrum is corrected
for the redshift of the host galaxy (z = 0.010697) and for
Galactic extinction from (E(B − V ) = 0.027 mag; Schlegel
et al. 1998). No correction has been made for host galaxy
reddening, following Smith et al. (2011). We adopted the optical
spectrum taken in March—the spectral evolution during thisphase was small, and for the purposes of this paper adopting
the spectrum taken in May does not change our conclusions.
For NIR spectrum, we have calibrated the flux scale with thephotometry taken in the same night. For the optical, we havefirst estimated the magnitudes at the same epoch by a linear
interpolation between the photometry in March and May, thenthe flux scale is matched to this estimate. The evolution in thelight curve is not large between these epochs (∼0.3 mag), andmoreover the colors in the optical bands have stayed almost
constant. As seen in Figure 1, the HCT spectrum matches thephotometry at different bands very well.
A striking feature in our spectrum is the clear detection ofa thermal continuum component in the NIR, which was absent
in the early phase (∼+100 days; Andrews et al. 2011a), as
seen by comparing our late-time NIR spectrum and the SED
at ∼+100 days (Figure 1). Unlike a few previous examples inwhich the continuum, increasing beyond the K-band, is detectedin the NIR spectra (see references in Section 1), the NIR
emission peak in SN 2010jl is within the H band, suggestingthat the temperature of the emitting materials (irrespective of
the nature of the material) is higher (i.e., ∼1000–2000 K) thanthe other examples.
Besides the continuum, the NIR spectrum shows Pβ andBrγ , but otherwise the spectrum is quite featureless. The optical spectrum exhibits Balmer series (H , Hδ , Hγ , Hα ) andHe i λ5876, which all have intermediate-width components
arising from the SN (see below). There are narrow emissions
like [O iii] λλ4959,5007, but they are probably from an unresolved background region (see Appendix A). All the resolved
strong lines with the intermediate-width component are hydrogen lines (plus He i λ5876), suggesting that the emitting
region is either the shocked hydrogen-rich envelope or thehydrogen-rich CSM.
Figure 2 shows line profiles of the hydrogen emission lines.
The line flux is expressed per velocity interval (i.e., ΔV ∝Δλ/λ0 , where λ0 is the rest wavelength of a line). The fluxes ofthe different lines are scaled according to the expected hydrogen
emission line strength ratios in the Case B recombination(Osterbrock 1989) for a temperature of ∼5000–10,000 K,
where the peak flux of Hα is taken to be about unity forthe normalization. Namely, if all the line strengths follow the
expected emission line ratios for the Case B recombination, then
all the lines should show the peak flux at about unity with thisnormalization.
In optical wavelengths, the lines exhibit two components,
a relatively narrow component at the rest wavelength (withthe line width 1000 km s−1 ) and a broader (intermediate)
component (FWHM ∼ 2000 km s−1 ). The narrow componentof Hα probably originates from the SN, as also seen in previous
works (Smith et al. 2012; Zhang et al. 2012), while the narrowcomponents in the other Balmer lines could be contaminatedby the unresolved host and/or SN site (see Appendix A). Dueto the limited spectral resolution in our observation, we areunable to distinguish these two possibilities from the kinematics(∼100 km s−1 or 28 km s−1 for the CSM case; Smith et al. 2011).
In NIR, no strong narrow emission lines from the backgroundare seen. Because of this possible contamination from the

Figure 1. Combined spectrum of SN 2010jl at +553 days since the V-band
maximum. The flux in each band converted from the photometry is shown by
open squares for day + 553 (see the main text). The early phase photometry is
shown by open triangles, taken from Zhang et al. (2012; day +87) and Andrews
et al. (2011a; day +95). In the lower panel, we show only the NIR portionof the spectrum, with a different scale in the vertical axis (for the sake ofdemonstration).

3. RESULTS
In this paper, we argue that dust grains were newly formedin SN 2010jl, probably around 1 yr after the V-band maximum.
The case for the dust formation is regarded to be solid when
the following three signatures are simultaneously detected (see,e.g., Kozasa et al. 2009 for a review): (1) thermal emission fromthe dust grains, which was absent before the dust formation, (2)blueshift of emission line profiles, especially with the degree ofthe shift depending on the wavelength, and (3) decrease in the
optical luminosity plus an increase in the luminosity at longer
wavelengths, corresponding to the thermal emission mentioned
above.
It is very rare that all these signatures are found for individual
SNe (except for SN 1987A and possibly 2006jc; see referencesin Section 1). In case only one or two signatures are found,
there is always a caveat that these features might be createdby mechanisms other than dust formation. This is the maindifficulty in investigating dust formation in SNe. Even withall these signatures detected, it is still possible to attribute
each feature to different mechanisms, though the new dust
formation is considered the most natural (and straightforward)
interpretation since the dust formation scenario explains allthese properties in a unified manner without fine-tuning. This is
our philosophy in this paper. Since we have detected all thesesignatures in SN 2010jl, as we show in the following sections, wesuggest that the case for dust formation is solid. We then analyze
properties of the newly formed dust grains under the assumptionthat these features are mostly attributed to the formation of thedust. Further, we check this assumption (the dominance of the
newly formed dust grains in causing these features) in view ofother possible alternative mechanisms and conclude that thisassumption is well justified.
3.1. Indications of the Newly Formed Dust Grains
Figure 1 shows a combination of the IRCS spectrum andthe HCT spectrum with the flux scaled to the date of the
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Maeda et al.

Figure 2. Comparison of the line profiles, shown for Brγ (blue), Pβ (green), Hα(red), Hβ (cyan), and Hγ (magenta). The line flux is shown per velocity interval(i.e., ΔV ∝ Δλ/λ0 ). The fluxes for the different lines are scaled according to the
expected hydrogen emission line strength ratios in the Case B recombination(Osterbrock 1989), where the peak flux of Hα is taken to be unity for thenormalization. Namely, if all the line strengths follow the Case B recombination,then all the lines should show the peak flux at about unity. To assist readers, therough positions of the central wavelength of the intermediate-width components
are marked by arrows (with the same color coordinates with the correspondinglines).
(A color version of this figure is available in the online journal.)

Figure 3. Optical light curves of SN 2010jl through the late phases. The
late-phase magnitudes obtained with the HCT telescope (large symbols) are
combined with the earlier phase magnitudes reported in Zhang et al. (2012).
The linear fits to the light curves in the phases between +100 and +200 days
are shown by the solid lines (Zhang et al. 2012). The late-phase magnitudes are
below the extrapolation from the earlier phase (see Section 3.4 for details). Notethat the unresolved background contamination has not been subtracted, which
could reduce the intrinsic SN latest-phase magnitude further by 0.6–0.8 mag
in B, V, and I, and by ∼0.2–0.3 mag in R (which correspond to the upper limit for
the host contamination), while this is negligible in the early phase. We suspectthat the last point reported in Zhang et al. (2012), which does not agree with
our photometry, would include a systematic error likely due to the backgroundcontamination; the difference may reflect the different size of the aperture in thephotometry.
(A color version of this figure is available in the online journal.)

background region to the narrow component in the optical lines,
we focus on the intermediate-width component hereafter.
From Figure 2, we see two clear features in the line profile:(1) the central wavelength of the intermediate-width component(see Figure 2) is blueshifted (especially evident in the opticallines). Note that the degree of the blueshift is smaller for lines at
a longer wavelength, with little or almost no blueshift for Brγ ;(2) a decrement in flux for lines at short wavelengths (especiallyevident in Hβ and Hγ ) with respect to those expected for CaseB recombination. Note that this decrement also persists if wenormalize the line flux by the blue wing (Section 3.3), whichmeans that at least a part of the decrement is independent ofeither the normalization or intrinsic fluxes of different lines.
It has been reported that the blueshift was already present
in the early phase, and it was about ∼550 km s−1 between
100–200 days (Smith et al. 2012; Zhang et al. 2012). We
emphasize that the degree of the blueshift was larger in the latephase (after 400 days), reaching to 700 km s−1 (Figure 2;
see also Zhang et al. 2012). Thus, it requires an additional
mechanism to create (increase) the shift in the late phase,irrespective of a cause of the blueshift seen in the earlier phase(this is still under debate; see Smith et al. 2012; Zhang et al.
2012). This additional mechanism is typically attributed to thedust formation when other signatures of the dust formation are
simultaneously detected. We also emphasize that our spectra
show a wavelength dependence in the degree of the blueshift, forwhich no mechanism has been suggested except for obscuration
by dust particles.
Figure 3 shows multi-band light curves of SN 2010jl, including our photometry points. Between 100 and 200 days,
SN 2010jl showed a flat light curve, which is interpreted as

being powered by the SN–CSM interaction within smoothly
distributed CSM materials (e.g., Zhang et al. 2012; Moriya et al.
2013b). The light curve shows that the optical luminosity decline accelerated around 1 yr after the V-band maximum, andthe luminosity at ∼550 days is about 1–2 mag (depending on theband and including uncertainty in the background contamination) below the extrapolation from the light curve at the earlier
phases.
As described above, we detected all three signatures of theformation of the dust grains in the late phase of SN 2010jl (seethe first paragraph of Section 3). In the following sections, wewill analyze the observational signatures and place constraints
on properties of the newly formed dust grains.
Our NIR spectrum is, to our knowledge, the first clear
spectroscopic detection of thermal emission covering the peakfrom newly formed hot dust from an SN in the NIR and one of
the strongest cases of dust formation in SNe to date; the NIR
thermal emission continuum from newly formed dust particles
have been (spectroscopically) seen in a few SNe (see referencesin Section 1), but in these examples the emission peaks were outof the observed wavelength range.
Since detecting the wavelength-dependent profile of hydrogen emission lines is not common due to observational limitations (see, e.g., Lucy et al. 1989; Smith et al. 2008b, 2012),
here we comment on this property. We note in particular that
it is not only the blueshift but also the decrement that depends on the wavelength (Figure 2; see above). We suggest the5The Astrophysical Journal, 776:5 (16pp), 2013 October 10

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Figure 4. Observed spectrum as compared to the dust emission models for (a) carbon, (b) astronomical silicate, (c) MgSiO3 , and (d) Mg2 SiO4 grains. The underlying
SN emission is assumed to be a blackbody with a temperature of 6500 K. Models with ad = 0.01 μm are identical to those with ad = 0.001 μm and thus are notshown here.
(A color version of this figure is available in the online journal.)

following interpretation for this behavior: for all the hydrogenlines, the intrinsic line profile of the intermediate-width component is at the rest wavelength, but as one moves to shorter
wavelengths, the intermediate-width component is blueshifted
and suppressed due to presence of dust. This scenario explains
the line profile change as a function of wavelength. The blueshift
and suppression of the intermediate-width component are in linewith the extinction by the newly formed dust particles, as we
see in the NIR continuum emission (see Sections 3.2 and 3.3 formore details). The emission contribution in the red wing of thelittle-obscured NIR lines (i.e., Pβ and Brγ ) suggests that there
is not a well-defined photosphere for the SN emission, and theSN emission is probably created as an optically thin emission
in the interacting region (not as a photospheric emission arising below the interacting region). Otherwise, electron scattering
would operate to suppress the emission from the receding side of
the SN, leading to the suppression of the red wing independentof the wavelength. This feature is difficult to reconcile with the
obscuration created by the SN photosphere, as was discussed
based on the early phase data (Smith et al. 2012; Zhang et al.
2012). The dust particles cannot be distributed deep in the SN
ejecta because in this case it would not produce the absorption at the rest wavelength (Smith et al. 2008b). Thus, the dust
particles should have a large overlap to the intermediate-widthcomponent emitting region in their distribution, supporting theformation of the dust particles in the cold-dense shell createdat the interaction (Smith et al. 2008b). We note that the narrow emission components in Hα and possibly in Pβ and Brγ do
not show the wavelength shift, and this is consistent with thedust formation: these narrow emission features (while possibly
contaminated by the background) are believed to arise from theunshocked CSM at a great distance, thus the newly formed dust
grains within the ejecta or interacting region would not obscuremuch of the narrow emission components.
We note that the suppression as compared to the expected line
ratios from the Case B recombination should not be taken to bequantitative, since it is not clear if the Case B recombination is agood approximation in SN 2010jl. Indeed, the suppression of Hγand Hβ seems too large to be explained only by extinction due
to the newly formed dust particles, given the mild wavelength
difference between these lines and Hα . We note that the CSM
density is probably very high in SN 2010jl (see Section 3.5),
and it is very likely that even the first excited level of the neutralhydrogen is overpopulated. In this case, we expect a cascadeof Hγ and Hβ to Hα and other low-energy hydrogen series (Xuet al. 1992) like what happens for the Lyman series in Case B(Osterbrock 1989). Thus, the intrinsic ratio of Hγ to Hα andthat of Hβ to Hα may well be much smaller than the CaseB recombination. This indeed supports the CSM interaction
scenario for a power source of SN IIn 2010jl. We discuss moredetails on this CSM density in Section 3.5.
3.2. Composition, Mass, and Temperature of the Dust Grains
The NIR spectrum of SN 2010jl shows a clear thermal
emission signature from newly formed dust particles. Figure 4
shows comparisons between the observed spectrum and thetheoretically expected emission for different dust species and
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In sum, either carbon or astronomical grains can reconcile
the NIR emission property, if the dust temperature is simply
taken as a free parameter. MgSiO3 is highly unlikely, given theextremely large dust mass required to fit to the NIR emission.
We exclude Mg2 SiO4 solely on the basis of the unacceptable fit
to the NIR emission spectrum. Additional information is given
in other wavelength ranges, and in Section 3.5 we will showthat the opacity behavior in mid-IR can also be used to reject
MgSiO3 and Mg2 SiO4 even without direct observations in sucha wavelength range.
The required temperature of the dust is too high for the
hypothesized astronomical silicate dust and higher than thecondensation temperature, which is typically ∼1000 K (Nozawa
et al. 2003). This indicates that the newly formed dust is mainly
carbon (either graphite or amorphous carbon). The condensation
temperature for carbon grains is ∼1900 K, fully consistent withthe lower temperature we have derived. As analyzed above, thederived properties of the carbon dust are not sensitive to theunknown size of typical dust particles as long as ad  0.1 μm,
where these are ∼1300–1350 K and ∼8.5 × 10−4 M , whilethese are ∼1800 K and ∼2.6 × 10−4 M if ad ∼ 1 μm.

sizes. We adopt the blackbody temperature of 6500 K for theunderlying SN emission (Zhang et al. 2012), which fits well theSN emission in the optical wavelength at 5000 Å. The blue
continuum is not well fit by a single blackbody temperature: it
may be contaminated by unresolved metal lines, e.g., Fe ii (Foley
et al. 2007) or by a scattered optical light echo (Miller et al.
2010; Andrews et al. 2011b). As we will discuss in Appendix C,
the bluest potion of our spectrum is consistent with (but not
exclusive to) the echo scenario, while the unresolved lines surely
exist as well. We estimate that the echo would contribute at most
∼50% of the total flux in our HCT optical spectrum.
The mass absorption coefficients of different dust species
are calculated using optical constants by Zubko et al. (1996)
for amorphous carbon, Draine (2003) for astronomical silicate,
Dorschner et al. (1995) for MgSiO3 , and Semenov et al. (2003)
for Mg2 SiO4 . Graphite has a mass absorption coefficient similar
to amorphous carbon in the wavelength range analyzed in thispaper, thus we frequently refer to the amorphous carbon andgraphite grains as simply carbon dust.
In this section, we assume that the dusty region is opticallythin to the NIR photons (see Section 3.4 for a detailed discussion). The total mass of the dust grains (Md ) and the temperatureof the dust (Td ) are connected byFν =Md Bν (Td )κν,
D2

3.3. Size of the Dust
Constraining the size of the dust particles is generally atough task for astronomical objects, one that requires deriving
the extinction curve across a broad wavelength range. Thisis an especially severe problem in studying newly formed
dust particles in SNe, as the intrinsic SED of SN emission is
not known a priori. For SN 2010jl, we propose an approachto tackle this problem by investigating the line profiles ofhydrogen emission lines from the optical through the NIR,
and by attributing the difference in the line profiles to different
optical depths at different wavelengths.
As shown in Figure 2, the intermediate-width componentof the hydrogen lines shows a blueshift especially evident in
the optical. This suggests that the line-emitting region and the
dusty region have a large overlap, and the receding part of theemitting region is (partly) hidden by the newly formed dust
particles (Section 3.1). The larger degree of the blueshift atshorter wavelengths also supports dust obscuration (Smith et al.
2008b).
Now, under a reasonable assumption that all the intermediatewidth component hydrogen lines are emitted from the same
region, we can obtain a rough constraint on how the dust opacity
depends on wavelength (i.e., the extinction curve). Under thisassumption, the intrinsic line profile is the same for all the lines,
and the photon path length within the dusty, obscuring region
is identical for all the lines. Specifically, we can connect theobserved profile (f (v)) and the intrinsic line profile (f0 (v)) as
follows, where v/c ≡ λ/λ0 − 1 (λ0 is the rest wavelength of thelines, and c is the speed of light):(1)

where Fν is the flux of the dust thermal emission, κν is the dust
mass absorption coefficient (which depends on the dust species
and size distribution), and D is the distance to the SN (48.9 Mpc).
Since the thermal emission was spectroscopically detected in our
NIR observation, we can obtain Md and Td without degeneracy
for the given dust species and size distribution. Our model fit isshown in Figure 4.
In principle, with the temperature of the dust being a freeparameter, the NIR thermal emission can be fit either by carbon,
astronomical silicate, or MgSiO3 grains. As long as the typicalsize of the dust (ad ) is smaller than ∼0.1 μm, the size is
not important in the NIR SED, and (Td , Md ) ∼ (1350 K,
8.5 × 10−4 M ) for carbon and (1450 K, 8.8 × 10−3 M ) for
astronomical silicate. If ad ∼ 0.1 μm, a slightly different set of(Td , Md ) is required to fit the NIR spectrum, but the result is notvery different from those where the dust is ad < 0.1 μm. Dust
particles as large as ad ∼ 1 μm have a flat opacity dependence
across the NIR wavelength range (as the dust size is similar to theelectromagnetic wavelength), and a large value of Td is requiredfor carbon. Regardless of the temperature, the astronomicalsilicate grains with ad  1 μm do not fit the NIR spectrum.
Since the absorption coefficients of astronomical silicates areabout an order of magnitude smaller than carbon, the dust mass
(Md ) required to fit the NIR spectrum for astronomical silicate isaccordingly larger than carbon by about an order of magnitude.
The fit by MgSiO3 grains provides qualitatively similar results
to those by astronomical silicate, while quantitatively there isa big difference. The wavelength dependence of the absorption
coefficients of MgSiO3 is even flatter than astronomical silicate
in the NIR wavelength range, and thus Td is larger for MgSiO3 .
Moreover, due to the small absorption coefficients of MgSiO3
in NIR, the dust mass has to be as large as a few M if the
newly formed dust is MgSiO3 . A similar situation is the case for
Mg2 SiO4 , where Md ∼ M is required to explain the flux levelof the NIR emission. Indeed, Mg2 SiO4 predicts a characteristic
bump in the H band, which does not fit to the observed smooththermal emission.

f (v) = f0 (v) exp(−τλ (v)) ,(2)
where τλ (v) = ρκλ ds ∝ κλ (ρ is the density of the dust
particles and ds is the path length, which are both independent
from the wavelength). The function τλ (v) describes the amountof absorption for a photon emitted from a given position.
While the optical depth (τλ (v)) depends both on the opacity(κλ ) and the column density, the latter is independent fromthe wavelength. Accordingly, the difference in the observed
profiles of different lines comes only from different values ofκλ under the assumptions described above. Although we do not
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The Astrophysical Journal, 776:5 (16pp), 2013 October 10

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Figure 5. Interpretation of the hydrogen line profiles by obscuration through the newly formed dust grains. The normalization for the line flux is taken at the blue
wing of the lines, i.e., assuming that the line profiles approach non-obscuration in the blue wing since this is the emission from the approaching side of the SN. (a) The
black line is the assumed intrinsic line profile, a Lorentzian with FWHM of 1800 km s−1 . Different lines show the obscured line profiles with different amounts ofabsorption characterized by τ0 , taken to be τ0 = 0.17 (Brγ ), 0.44 (Pβ ), 1.5 (Hα ), 2.5 (Hβ ), and 2.7 (Hγ ). (b) Same as (a) but this shows the flux scale normalized by
the assumed intrinsic line profile, shown for the blue wing. The figure shows the escaping fraction of light as a function of the wavelength (i.e., the emitting position,
which is closer to the observer along the line of sight for the light at shorter wavelength). The thick (smooth) curves are the same models as shown in (a). Note that our“obscured” model is intended to provide a reasonable fit only to the blue wing, and we are not aiming at fitting the red wing simultaneously (see Section 3.3). Also, the“narrow” component seen in the optical lines (Hα , Hβ , and Hγ ) is fully omitted from our analysis, so the discrepancy around the rest wavelength is totally an artifact.
(A color version of this figure is available in the online journal.)

know the intrinsic strengths of the hydrogen lines from different
transitions (which do not follow the Case B recombination; see
Section 3.1), we expect that the blue wing of the lines should
approach non-obscuration, and thus we scale the observed line
profiles of different lines (i.e., f (v)) at the blue wing.
The functional form of the absorbing fraction as a function of
the wavelength across the same line (i.e., dependence of τλ (v) onv) depends on the structure and kinematics of the emitting andabsorbing regions and is generally not expressed in an analytic
form. Still, we can test an approximated simple form for it, by
the requirement that the profiles of different lines can be at least
qualitatively explained by varying the single parameter τλ . We
have tested simple polynomial forms, and in Figure 5 we show
an example where we adopt τλ (v) = τ0 ((v/c + 0.01)/0.01)β(i.e., transparent for v/c < −0.01) and β = 5. This form
provides a reasonably good description of the blue portionsof different lines, with the intrinsic line profile described by a
Lorentzian (e.g., Stritzinger et al. 2012). The normalization of
the optical depth, τ0 (λ), is a parameter that is different for different lines and estimated by roughly fitting a position of thepeak flux in the absorbed line profiles. We adopt the following values for τ0 in Figure 5: τ0 = 0.17 (Brγ ), 0.44 (Pβ ), 1.5(Hα ), 2.5 (Hβ ), and 2.7 (Hγ ). The functional form we adopted
above creates too much absorption in the red, but we are mainly
concerned with the behavior in the blue to derive the relative optical depth for the different lines. We are not aiming
at fitting the detailed line profiles, since even without the absorption the interpretation of the intrinsic line profile in SNe
IIn has not yet been fully clarified (see, e.g., Chugai 2001;
Chugai et al. 2004). We emphasize that our procedure here isfocusing on deriving the optical depth difference at different
wavelengths—our treatment is quite general, and the results of
the optical depth differences would not be sensitively dependent
on the assumed functional form. This method allows the dependence of the opacity on the wavelength to be derived independently from the detailed kinematical properties of the emitting
region.

In the right panel of Figure 5, we normalize the line profiles
by the assumed intrinsic line profile, i.e., a Lorentzian with the
FWHM of 1800 km s−1 . This provides the escaping fraction of
the light as a function of the wavelength (i.e., the path length
within each line). The same analytic curves are shown in thisplot, which shows that the decreasing escaping fraction fromthe blue to the red is well described by our formalism.
With the estimate of the wavelength-dependent optical depth(which is only dependent on the opacity), we can extract a roughbehavior of the extinction of the newly formed dust as a functionof wavelength. In Figure 6, we compare the phenomenologicallyderived optical depth (for different hydrogen lines, as shown by
open squares) to the theoretical expectations for different dust
species and grain sizes (for carbon and astronomical silicate).
The dust model is the same as that used in Figure 4 for thethermal emission. Note that the observationally derived opticaldepth (κλ ∝ λ−1.6 ) follows roughly the expected behavior for
carbon dust (∼λ−1.4 ) when the dust size is smaller than the
wavelength of interest. Given the uncertainties involved in ourderivation, the behavior we have derived is surprisingly close to
the theoretical expectation. It again favors carbon over silicate,
independent from the argument of thermal emission, as thesilicate dust predicts a flatter opacity dependence (note thatMgSiO3 has even flatter distribution than astronomical silicate).
Also, we do not see clear saturation of the opacity at shorter
wavelengths, which constrains the dust size to ad  0.1 μm(more likely ad  0.01 μm from the derived opacity difference
within the optical wavelength).
3.4. Energy Balance and Effects of Internal Absorption
The above estimate on the optical depth at the line wavelengths suggests that there might be non-negligible extinction
operating on the intrinsic spectrum, and thus the dust properties estimated in Section 3.2 may need some modifications. In
Figure 7, we show the “intrinsic” NIR spectrum corrected fordust absorption. For the dust obscuration, we assumed that the
optical depth has the wavelength dependence of τλ ∝ λ−1.4 and
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Maeda et al.

Figure 7. Possible effects of the dust absorption. The observed (gray) andthe absorption-corrected (black) spectra are shown (assuming α = 1 in the
optical wavelength; τcont = ατline , where τline was derived independently). In
the optical, an intermediate case with α = 0.3 is also shown (blue). NIR thermal
emission models are shown for the observed (magenta) and absorption-corrected(green) spectra. The inset shows the expected magnitude decrease due to theinternal dust absorption, where α = 1 (black squares), 0.5 (red triangles), and
0.3 (blue circles).
(A color version of this figure is available in the online journal.)

Figure 6. Wavelength dependence of the optical depth estimated from theemission lines as compared with the theoretical expectations. The open squares
are the observationally derived optical depths for different hydrogen emission
lines. The dashed black line represents a power law behavior that fits to theoptical depths at different wavelengths we have derived. The other lines are
the theoretical expectations for carbon dust (thick solid lines) and astronomicalsilicate (thin dashed lines). The different size of the grains used are shownwith different colors (ad = 0.001 μm by gray, 0.01 μm by green, 0.1 μm byred, and 1 μm by blue). For the theoretical curves, the opacities are normalized
by 22,000 cm2 g−1 and 1000 cm2 g−1 for carbon and astronomical silicate,respectively.
(A color version of this figure is available in the online journal.)

The same exercise can be performed for the optical spectrum.
The observed luminosity in the optical wavelength is ∼1.4 ×
1042 erg s−1 (obtained by integrating the HCT spectrum in
Figure 1). Assuming the wavelength-dependent optical depth
as described above, we obtain the intrinsic optical luminosity as∼7.7 × 1042 erg s−1 . Namely, the luminosity absorbed by thedust particles (in the optical wavelength) is ∼6.4 × 1042 erg s−1 .
It is comparable to the NIR thermal emission luminosity.
However, there can be additional absorption occurring in the
UV range that is not considered here. This could therefore bean overestimate of the absorption in the optical, and given
the uncertainty in our treatment, we could allow a small
difference in the optical depth for the lines and continuum. Let us
now assume τcont (λ) = ατline (λ), where τcont is the optical depth
for the optical continuum emission while τline is the opticaldepth derived from the line profile argument. In Figure 7, weshow three examples, where we adopt α = 1, 0.5, and 0.3. The
case with α = 1 corresponds to the case described above. For
α = 0.5 and 0.3, we obtain an intrinsic optical luminosity of
3.1 and 2.2 × 1042 erg s−1 , respectively. The moderate case withα ∼ 0.5 is consistent with the NIR luminosity, with additional
absorption in the UV. We note that a value of α smaller than unity
would be consistent with a possible contribution of a CSM echo
at a greater distance (see Appendix C) since only a negligible
fraction of the echo light would be absorbed by the newly formed
dust grains.
The above argument additionally shows that the carbon dust
grains provide a consistent view here. Indeed, the balance
between the absorption in the optical and the emission in IR
provides an additional clue to distinguish different dust species.
Figure 8 shows the expected thermal emission from different
dust species in mid-IR, with the same model parameters (Td ,Md ) as in Figure 4 (which gives a good fit to the observed
NIR spectrum for astronomical silicate and MgSiO3 and arough fit to the NIR flux for Mg2 SiO4 ). Silicate dust, especiallythose without Fe, predicts a big bump at ∼10 μm. While nothat the normalization is taken at the optical depth derived at
the wavelength of Pβ . This relation represents very well the
carbon dust properties in the wavelength range of interest withthe typical size of ad  0.01 μm (see Figure 6). The dust thermal emission luminosity needed to fit the observed spectrum is∼5.1 × 1042 erg s−1 , and it increases to ∼6.6 × 1042 erg s−1 infitting the “intrinsic” spectrum.
To fit this “intrinsic” spectrum by thermal emission fromcarbon dust grains, as we did for the observed spectrum, wederive (Td , Md ) ∼ (1450 K, 7.5×10−4 M ). One would naively
expect that the required dust mass would go up if one includes
the dust absorption, but we find that it is indeed not necessarily
the case. Namely, it has been frequently mentioned that fitting
an observed spectrum with the dust emission under the “fully
optically thin” assumption provides a lower limit of the dust
mass, as there should be additional dust particles hidden in
the opaque region, but from our analysis we conclude that it
can operate in the opposite way. With absorption, the required
dust temperature and thus the specific intensity go up, andthis effect reduces the dust mass needed to explain a given
thermal emission flux. These two effects (color change andobscuration) almost negate one another for SN 2010jl, and theresulting dust mass is indeed not very different in the twosituations. Thus, we conclude that we can narrow down theproperties of the newly formed dust particles into a narrow range,
namely Td = 1350–1450 K and Md = (7.5–8.5) × 10−4 M . In
reality, the emission and absorption are coupled, and the transfer
effects could make for an inhomogeneous temperature structure.
Thus, radiation transfer simulations should be performed more
conclusively on these properties, but this is beyond the scope of
the present paper. Indeed, the optical depth we derived for the
NIR wavelengths is below unity, thus the transfer effect should
not be large anyway.
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Maeda et al.

in the magnitude due to the dust obscuration is ∼1.3 mag in B,∼1.2 mag in V, ∼1.4 mag in R, and ∼0.8 mag in I at +553 days,
as is shown in Figure 3. If we assume the maximum possible
contamination from the unresolved background (Section 2.2),
this could reach to ∼2 mag in B and V and ∼1.5 mag in
R and I. The difference is roughly consistent with the dust
obscuration with α in the range of 0.5 to 1. We also note that theestimated magnitude differences are generally greater for shorter
wavelengths, consistent with the dust extinction scenario. Given
our crude treatment, the value of α (∼0.5–1) indicates thatthe continuum and lines have experienced similar obscuration,suggesting that these two regions are roughly overlapping.
Note that the above argument is essentially identical to theheating balance frequently considered in studying the dust
properties (see, e.g., Nozawa et al. 2008). Since we haveconfirmed that the absorbed luminosity in optical is consistent
with the emission luminosity in the NIR adopting the dust
temperature and the dust absorption coefficient we estimatedindependently, we conclude that the dust temperature we derived
from the thermal emission is consistent with the expectationfrom the heating balance.
The argument presented in this section shows that the opticaldepth of the newly formed dust grains is largely consistent
with the observed light curve evolution without a significant
change in the behavior of the intrinsic light curve evolution—afrequently adopted assumption in discussing the dust formation.
Indeed, when the optical light curve shows accelerated fading,this is a widely accepted (though practically difficult) test to
distinguish whether the decrease is due to the intrinsic change inthe light curve evolution (i.e., strength of the CSM interaction,
which could arise from a change in the CSM distribution) or
mostly due to the absorption by the new source of absorption(i.e., newly formed dust grains). Generally, it is difficult todistinguish the two, but in this paper we are able to do thisdue to an independent measurement of the optical depth fromthe dust particles. Our analysis indicates that the absorption
effect is the main cause of the change in the optical luminosity
decline rate, while we do not reject a minor contribution from apossible change in the strength of the interaction.
The above point is highlighted in Figure 9, which shows a(roughly constructed) quasi-bolometric light curve of SN 2010jl,
with and without the NIR contribution. Without observations in
UV, we simply assume, following Zhang et al. (2012), that
the UV contributes 10% of the optical luminosity—this isvery likely an underestimate, given that the blue portion of
the spectrum shows an excess as compared to a blackbodyof ∼7000 K. Given this uncertainty, we adopt a conservative
error of ±30% for the bolometric luminosity. Figure 9 also
compares the observed light curve with a simple power law
behavior expected from the CSM interaction with smooth CSM
distribution. While the “optical” luminosity at >500 days iswell below the expectation from a smoothly evolving CSM
interaction, the “true” bolometric luminosity in this phase as asum of the optical and NIR emissions (mostly NIR) is largely
consistent with this expectation. Thus, we do not require asignificant change in the strength of the interaction (or CSM
distribution), and conclude that the obscuration by the newly
formed dust is mainly responsible for the optical light curve
evolution as well. There is a hint of a slight decrease in the totalluminosity as compared to the expectation, which might suggestthat the strength of the CSM interaction might have changedslightly (but not at the level of being the main reason for the
optical luminosity decrease). However, given our crude estimate

Figure 8. Expected dust thermal emission at IR wavelengths (up to 23 μm)
for carbon (red), astronomical silicate (blue), MgSiO3 (magenta), and Mg2 SiO4
(green). Those with ad = 0.001 μm (thick lines) and 1 μm (thin lines) are shown.
The macroscopic parameters, i.e., Td and Md , are the same as in Figure 4.
(A color version of this figure is available in the online journal.)

observations in such a wavelength range have been presented inthis paper, it should affect the thermal balance. The resulting dust
thermal emission luminosity is estimated to be 6.7×1042 erg s−1(astronomical silicate), 6.3 × 1044 erg s−1 (MgSiO3 ), and1.1 × 1044 erg s−1 (Mg2 SiO4 ). The astronomical silicate canstill be consistent with the thermal balance (although carbon
grains are preferred in other arguments), while MgSiO3 and
Mg2 SiO4 are again both rejected here as these dust particles
should emit mostly in mid–far IR (Figure 8); the expected
thermal emission would exceed the available energy budget if
these were responsible for the NIR emission.
The effect should be seen in the light curve as well. Here,adopting the properties of the dust grains obtained independently(Section 3.3), we estimate the effect of the newly formed dustin the optical light curve and compare the expected behavior
with the observed light curve. Figure 7 also shows how muchthe observed photometry changes due to dust absorption in
the B, V, R, and I bands (for carbon dust grains). SN 2010jl
shows a flat light curve in the early phase. The light curve ofSN 2010jl connecting the early (Zhang et al. 2012) and thelate phases is shown in Figure 3. The decline rate in each band
during ∼100–200 days is fairly linear, and the rate per 100 daysis ∼0.22 mag in B, ∼0.27 mag in V, ∼0.13 mag in R, and∼0.32 mag in I (Zhang et al. 2012). The magnitude at 388 days
after the V-band maximum was already below the extrapolationfrom this decline rate (Zhang et al. 2012), indicating that the dust
formation and the subsequent absorption had already started
at this epoch—inspection of data presented by Zhang et al.
(2012) indicates that the line profiles of Hα and Hβ showed achange (blueshift) around this epoch (Section 3.1), and the Hαluminosity evolution also changed its behavior around the sametime. Assuming that the “intrinsic” SN luminosity has evolved
following the linear behavior observed in the earlier phase before
the dust formation, we expect that the unobscured magnitudes
were likely B ∼ 15.8 mag, V ∼ 15.6 mag, R ∼ 14.5 mag, andI ∼ 15.2 mag at +553 days. Thus, we estimate that the change
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Inserting the opacity for carbon dust grains with 0.1 μm, we
obtain τλ ∼ 10 at 6563 Å (Hα ), 4 at 12,818 Å (Pβ ), and 2
at 21,661 Å (Brγ ). Namely, the opacity provided by the dustof Md ∼ 8 × 10−4 M obtained by the dust thermal emission(Section 3.2) is by a factor of ∼10 larger than that required toaccount for the dust absorption (Section 3.3).
In other words, the dust inferred by the thermal emission
will totally black out any SN emission if it were distributed
homogeneously in the SN emitting region. Thus, the dust
formation must have been localized within the ejecta, with the“filling factor” being ∼0.1, which suggests that the dust-forming
region is distributed as clumps within the ejecta.
The dominance of the hydrogen emission lines suggests thatthe dust formation region is either the shocked H-rich CSM or
shocked H-rich envelope of the SN ejecta. Assuming that all the
carbon atoms with the mass fraction of X(C) were condensed
into the dust particles within the swept-up region, then the dust
mass (Md ) and swept-up mass (Msw ) are connected as follows:
Md = Msw X(C). For the CSM case, taking the mass fractionof carbon atoms normalized by the solar abundance provides anestimate on the swept-up mass of Msw ∼ 0.27 M (Z/Z )−1 ,where Z is the metallicity of the SN site. Since the condensationof atoms into the dust may not be complete, this furnishes alower limit for Msw , namely Msw  0.27 M (Z/Z )−1 . The
environmental metallicity of SN 2012jl has been reported to be
low, Z  0.3 Z (Stoll et al. 2011; see also Appendix B). Thus,
we constrain the swept-up mass as Msw  0.9 M . If this wereejected by a steady mass loss, it corresponds to a mass loss rateof 0.02 M yr−1 , assuming that the mass loss velocity was∼100 km s−1 as was inferred from an emission component in ahigh resolution spectrum (or 6 × 10−3 M yr−1 with the windvelocity of 28 km s−1 as inferred from an absorption component;
Smith et al. 2011). The average CSM density up to ∼2×1016 cm
is nCSM  3 × 107 cm−3 , which is at least four or five ordersof magnitude greater than typical CSM density around SNe Ib/
c from a Wolf–Rayet progenitor (e.g., Chevalier & Fransson
2006; Maeda 2013) and at least two orders of magnitude larger
than SNe IIp from a red supergiant progenitor (e.g., Chevalier
et al. 2006). We note the above estimate should roughly apply
even if the dust formation site is the shocked H-rich SN ejecta,
since the amount of the SN ejecta swept up by the reverse
shock is comparable to the amount of the swept-up CSM by
the forward shock (Chevalier 1982) and the metal content in
the H-rich envelope should be similar to that in the CSM.
The high-density CSM derived here may indicate LuminousBlue-Variable-(LBV)-like eruptions, which are suggested totake place at the end of the evolution of a massive star withMms  30 M (Smith et al. 2011).
The above estimate assumes that the mass fraction of carbon
atoms in the dust-forming site is represented by the environmental (or progenitor) metallicity. However, this may well provide
merely a conservative lower limit for the swept-up mass, if one
considers possible effects of the stellar evolution on the carbon abundance in the progenitor surface and the CSM. If the
CSM was indeed created by LBV eruptions, then the carbon
abundance there is likely suppressed due to the CNO cycle,
as was observed in N-rich ejecta around Eta Carina (Davidson et al. 1986; Smith & Morse 2004). This will lead to anincrease in the estimate of Msw . On the other extreme, one may
consider the case where the C-rich materials processed by the
He-shell burning may have increased the carbon abundance inthe progenitor surface and the CSM. We judge this latter case ishighly unlikely since it would lead to abundant He content in the

Figure 9. Roughly constructed, quasi-bolometric light curve of SN 2010jl (seeSection 3.4 for details). The “optical” luminosity is shown by open circles (thesmaller of which are from Zhang et al. 2012). The bolometric luminosities
from our observations are shown by the large circles; open circles include only
the optical contribution and filled circles include both the optical and NIR.
The maximum possible contribution (i.e., the upper limit) of the contribution
from the 56 Co decay is shown by the dotted line, which is negligible at∼550 days. Power law behaviors expected from a smoothly distributed CSM
interaction are shown by the solid curves at different power law indexes (where
the power law index of −0.3 and −0.49 covers expectations from the CSM
distribution expressed by a steady mass loss with a range of the ejecta structure;see, e.g., Chevalier 1982; Moriya et al. 2013b). Given the rough treatment inconstructing the bolometric luminosity, the “true” bolometric light curve (theoptical plus the NIR) is fairly consistent with the simple “smooth” interaction
model.

of the bolometric luminosity, we regard this discrepancy as
only indicative. We also note that the energy input from thedecay of 56 Co can provide at most only a minor contribution
in the luminosity in the late phase (i.e., >100 days), with theupper limit defined by the requirement that the decay luminosity
cannot exceed the early phase luminosity (<100 days; note that
we do not insist that the early phase was powered by the decay,
but rather we simply place the upper limit).
3.5. Properties of the Ejecta and CSM
So far in this paper, the dust emission and absorption havebeen treated independently, and it is important to question
if these two are mutually consistent, or what implications
the combination of the two have. The emission line profiles
suggest that the emitting region is extended to the velocity ofV ∼ 4000 km s−1 , and it did not evolve much from the early tothe late phase (Zhang et al. 2012). The wavelength dependenceof the line profiles suggests that the line-emitting region andthe dusty region are largely overlapping (Sections 3.1 and 3.3).
Under the assumption that a dust mass of Md ∼ 8 × 10−4 M is
distributed in a shell whose inner radius is Rd , the optical depth
is estimated as follows:κ λ Mdκλ∼8
τλ ∼22,000 cm2 g−1
4π Rd2
−2
−2 

t
V
×
.
(3)
4000 km s−1
550 days
11

The Astrophysical Journal, 776:5 (16pp), 2013 October 10

Maeda et al.

interaction region, as was observed for SN Ibc 2006jc (e.g.,
Anupama et al. 2009), rather than the H-rich abundance inferredfrom the spectrum of SN IIn 2010jl.
We can place a conservative upper limit on the mass loss
as well (under the assumption that the carbon atom fraction isrepresented by Z). The “rarefied” region should be at a lower
density than the dusty clumps. Taking into account the filling
factor of about 0.1, then the mass loss properties cannot begreater than the above estimate by more than one order ofmagnitude. Thus, our constraints on the mass loss properties
are the following.
The swept-up mass:
0.9(Z/0.3 Z )−1 M  MSW  9(Z/0.3 Z )−1 M .
The mass loss rate (for a wind velocity of 100 km s−1 ):0.02(Z/0.3 Z )−1 M yr−1  Ṁ  0.2(Z/0.3 Z )−1M yr−1 .
The average density up to ∼2 × 1016 cm:
3 × 107 (Z/0.3 Z )−1 cm−3  nCSM  3 × 108 (Z/0.3 Z )−1
cm−3 .
The CSM density we estimated here can be further checkedwith the relative strengths of the hydrogen emission lines.
Assuming that the interaction region is largely ionized, we
expect that the electron number density is comparable to nCSM ,i.e., ne ∼ 108 cm−3 . At this electron density, the Hβ /Hα ratio canbe smaller than the Case B recombination if the Sobolev (gas)optical depth to Hα is large (τHα  10) (Xu et al. 1992). If we fit
the blue wing of Hβ to that of Hα (to estimate the Balmer line
ratios in the unobscured wavelength), the intrinsic Hβ /Hα ratioof ∼0.1 is derived, which is consistent with the expectation
based on the derived CSM density (nCSM ∼ 108 cm−3 ), ifτHα ∼ 10–100 (Drake & Ulrich 1980; Xu et al. 1992). The
electron density cannot be greater than ∼1012 cm−3 , since theHβ /Hα ratio will then increase above the Case B recombination
expectation (Drake & Ulrich 1980; Levesque et al. 2012). Thus,
we conclude that the CSM density we derived is consistent withthe hydrogen line strengths.
Now, with the properties of the CSM estimated above throughthe dust properties, we can check if the expected properties of
the SN arising from the SN–CSM interaction are consistent withthe observations. The energy budget (E) and energy generation
rate at the shock (L) due to the interaction are (see also Zhang
et al. 2012)
E ∼ 8 × 1050
L ∼ 2 × 10

43

Msw
5 M



V
4000 km s−1

Ṁ/0.1 M yr−1
vw /100 km s−1



4. DISCUSSION AND CONCLUSIONS
4.1. Summary
In this paper, we presented optical and NIR spectra of the luminous SN IIn 2010jl, at ∼+550 days since V-band maximum.
The NIR spectrum clearly shows a thermal continuum emission,
which was absent in the early phase. The hydrogen emission
lines show a wavelength-dependent line profile, where the optical lines show large blueshifts, Pβ shows a small blueshift,
and there is virtually no shift for Brγ . With these two spectroscopic features, we conclude that the dust grains were newly
formed in SN IIn 2010jl in the late phase. The flux in the optical bands at ∼+550 days is offset from an extrapolation of theflat evolution seen in the early phase up to ∼+200 days. Thisappears as additional evidence for dust formation in SN 2010jl,
namely the optical light is absorbed and re-emitted at longer
wavelengths. Thus, SN 2010jl in the late phase has all the expected properties of new dust formation. The dust we see in thelate phase (∼550 days) was most likely formed around 1 yr after
the V-band maximum.
We derived the mass and temperature of the newly formed
dust grains. Due to the spectroscopic detection, the propertiesof the dust grains are specified with little uncertainty.
The main species:
carbon grains, either amorphous carbon or graphite.
The typical size of the dust grains:ad  0.1 μm (most likely ad  0.01 μm).
The dust temperature:
Td ∼ 1350–1450 K.
The total mass of the dust grains:Md ∼ (7.5–8.5) × 10−4 M .
Note that the range of values of Td and Md takes into accountthe uncertainty in the optical depth of the dusty region to the
NIR photons. The argument for the carbon grains is not only
based on the NIR SED, but also on the opacity dependence withwavelength, as derived by the different line profiles of hydrogenlines at different wavelengths. We have checked the heatingbalance between the absorption in the optical and the emission
in the NIR, and we conclude that this is consistent with theproperties of the dust (e.g., temperature) that we have derived
by an independent method. Non-astronomical silicate grains
such as MgSiO3 or Mg2 SiO4 are clearly rejected by various
arguments.
With the properties of the dust grains, we estimated theproperties of CSM and SN ejecta as follows.
The swept-up mass:
0.9(Z/0.3 Z )−1 M  MSW  9(Z/0.3 Z )−1 M .
The mass loss rate (for the wind velocity of 100 km s−1 ):0.02(Z/0.3 Z )−1 M yr−1  Ṁ  0.2(Z/0.3 Z )−1M yr−1 .
The average density up to ∼2 × 1016 cm:
3 × 107 (Z/0.3 Z )−1 cm−3  nCSM  3 × 108 (Z/0.3 Z )−1
cm−3 .
The structure of the interacting region:
the dust grains are localized within ∼10% of the emittingvolume.
The CSM properties correspond to the mass loss history of
the progenitor in the last 60 yr before the explosion, assuming
a mass loss wind velocity of ∼100 km s−1 . The localized
formation of the dust grains indicates that they were formed
in high-density regions that were probably distributed in highdensity clumps. This supports the idea that the dust was formed
in a dense cooling shell created by the interaction between the

2
erg,

V
4000 km s−1

3

(4)

erg s−1 .
(5)These are comparable to the observed radiation output (∼4 ×1050 erg in the first 200 days, which should be added by
the smaller amount of the energy emitted after +200 days)
and the total observed luminosity in the optical and the NIR
at +550 days (∼6.5 × 1042 erg), assuming that about halfof the kinetic energy was converted to the radiation energy.
Detailed analysis is required to improve the above estimate, toaddress the conversion efficiency of the kinetic energy to theradiation energy and the shock velocity evolution (Moriya et al.
2013a), but the rough agreement above strongly supports that the
SN–CSM interaction is the main power source of the luminous
SN IIn 2010jl.
12The Astrophysical Journal, 776:5 (16pp), 2013 October 10

Maeda et al.

and we conclude that they are not the same component as
described in this paper. Andrews et al. (2011a) detected IR
excess at 3.6 and 4.5 μm (with the peak redder than 4.5 μm),
attributing it to an echo by pre-existing CSM dust grains.
The NIR dust emission in the late phase exceeds the NIR
magnitudes at day 108 reported in Andrews et al. (2011a). With
the monotonically decreasing SN luminosity (Zhang et al. 2012),
it is unlikely that the dust we observed was this pre-existing CSM
dust heated by the SN emission. Also, the estimated position of
the CSM dust (∼1018 cm from the progenitor) is too far away
to be shock heated by the SN forward shock. Indeed, if we
estimate the location of the materials emitting the NIR thermal
continuum, assuming a blackbody (while this is just a roughestimate, since the optical depth in the NIR as we derived is
below unity), we obtain a radius of ∼2.8 × 1016 cm from our
NIR spectrum. This is much smaller than the pre-existing dust
found by Andrews et al. (2011a). The blackbody estimate isindeed close to the expected radius reached by the shock wave(∼2 × 1016 cm for a constant shock velocity of 4000 km s−1 ,which is very likely an underestimate since the shock musthave experienced deceleration), strengthening the case for theformation of new dust grains at the dense cooling shell. Thus, thedust particles we observed in the late phase cannot be the same(pre-existing) dust particles reported in the early phase. Indeed,
the above estimate of the emitting radius (∼2–3 × 1016 cm) also
generally excludes a contribution from any pre-existing dust
grains to the NIR emission at ∼550 days, since at such a small
radius and with a large luminosity of SN 2010jl, any pre-existing
dust grains there must have been destroyed by the SN radiation(e.g., Fox et al. 2010).
In this context, we emphasize that our argument in theheating–cooling balance (Section 3.4) is totally independent
from any pre-existing CSM dust grains. Such pre-existing dust
grains never produce a “change” in the absorption (hence
the decrease in the optical luminosity). The possible mid-IR
emission from the pre-existing dust must not be added to thebolometric luminosity from the system, since these dust grainsat the distance of ∼1018 cm (Andrews et al. 2011a) would
reprocess the early phase radiation (and thus should not becounted in considering the instantaneous luminosity output).
From this argument, we conclude that we can neither support
nor reject the pre-existing CSM dust from our observations,but our analysis of the newly formed dust grains is essentiallyinsensitive to this.
Smith et al. (2012) reported a wavelength-dependent blueshift
in the hydrogen lines in the early phase ( +100 days), and they
attributed this behavior either to the newly formed dust or tothe optical depth effect of the emitting gas. We note that theblueshift we observe is more significant, as is shown by the Hαline profile evolution from the early to late phase (Zhang et al.
2012). Although no detailed analysis on the dust properties(including the mass and temperature) was presented in Smithet al. (2012), we suspect that the dust mass must have beenvery small, if not zero—otherwise the wavelength shift shouldhave been greater in the early epoch and the NIR flux shouldhave been much greater in the late phase. We speculate that
already in the early phase a small fraction of the shocked ejecta/
CSM might have started the dust formation, but the major dust
formation took place at ∼1 yr after the explosion.
We conclude that the newly formed dust grains are carbon
grains. One interesting question is how these were formed. As
we conclude that the dust formation took place either in theshocked H-rich CSM or the shocked H-rich SN envelope, we

SN and a dense CSM, since the dense cooling shell (or clumps)
is expected to be formed from regions that experience radiativeand hydrodynamic instabilities. The high-density CSM is further
supported by the relative strength of the hydrogen emission
lines.
We thus conclude that there is a very dense CSM aroundSN 2010jl, and we have found that the interaction of the SN
with the CSM defined above can roughly explain the luminosityand energy output of the luminous SN 2010jl. The high-density
CSM was likely produced by LBV-like eruptions, suggested totake place at the end of the evolution of a massive star withMms  30 M (Smith et al. 2011).
4.2. Discussions
As shown in this paper, the dust formation scenario provides aconsistent and straightforward interpretation to various featuresof SN 2010jl in the late phase. Still, one may consider different
scenarios, which may, in principle, partly contribute to eachfeature to some extent. Indeed, a combination of the blueshifted
Hα profile evolution and the flat optical light curve evolution up
to ∼400 days led Zhang et al. (2012) to hypothesize that these
could be explained by the CSM interaction without invoking thedust formation in this early epoch (before the epoch of the dust
formation we propose in this paper). Whether the extension ofthis idea could explain the later evolution, i.e., further blueshift
in the Hα emission and the accelerated fading, is another story.
For example, one may argue that the accelerated fading could
be caused by the end of the main CSM interaction that could be
related to the possible decrease in the Hα blueshift at 500 days
as compared to that at ∼400 days (while at 500 days it was
still larger than ∼200 days; Zhang et al. 2012). However, since
the starting epoch of the change in this optical luminosity
decrease and that of the possible Hα blueshift decrease were
not coincident, we speculate that such a scenario would require
some fine-tuning. In the dust formation scenario, the decreasein the degree of blueshift seen in Hα at 500 days could
be naturally explained if the dust formation were more or lesscompleted (which we attributed to be around 1 yr after the
V-band maximum) and then the optical depth simply decreased
following the expansion. In any case, it is definitely interesting toinvestigate details of the light curve and the line profile evolution
as well as their mutual relation (which has not been discussed
quantitatively so far). Such a study will lead to an accurate
evaluation of the properties of the dust grains.
Though investigating details of the CSM interaction is beyond
the scope of the present paper, we present some arguments that
this would not significantly change our result. For example, theCSM interaction would not cause the wavelength-dependentline shift. Given that the optical depth we estimate based
only on the line profiles at various hydrogen emission lines
is quite consistent with the difference between the observed
optical luminosity at ∼550 days and the extrapolation from theearly phase light curve evolution, there is no need to introduce
additional cause of the luminosity change. Furthermore, we
showed that the bolometric luminosity, including the NIR,
does not show significant change in the decline rate, strongly
indicating that the possible effect from the change in the
CSM interaction property should provide at most only a minor
contribution.
We estimate that the dust particles we observed were formedat ∼1 yr after the explosion. There were possible dust signatures
reported based on observations of SN 2010jl in the earlier phase,
13

The Astrophysical Journal, 776:5 (16pp), 2013 October 10

Maeda et al.

expect that the number fraction of oxygen atoms was higher thanthat of carbon. In such a situation, the formation of carbon dust
grains may be forbidden by the consumption of carbon atoms
into the CO molecules (Nozawa et al. 2011). Observationally,
we have not detected any clear signature of CO molecules in
the K-band spectrum despite a good S/N—thus, it seems thateven within the O-rich gas, the carbon dust grains can formby avoiding the formation of CO molecules. The investigationof such a process is beyond the scope of this paper (see, e.g.,
Clayton 2013), but we note that this could provide a hint forunderstanding the dust formation in SNe and other astrophysicalenvironments. It would also be interesting to see if the carbon
grain formation would have been preceded by formation of
CO molecules. Unfortunately, the Spitzer data around 100 days
(Andrews et al. 2011a), well before our claimed epoch for the
major formation of the dust grains, do not either support or rejectexistence of the CO. Nevertheless, this highlights the importanceof both multi-epoch and multi-band observations. Anotherinteresting possibility for the future is to follow SN 2010jl
further to see if silicate dust is also formed as the temperature
decreases.
In addition to the dust properties, our analysis allows us toconstrain the CSM environment independent from the opticallight curve. We note that the density and distribution have also
been constrained by X-ray observations. Chandra et al. (2012;see also Ofek et al. 2013) derived the density slope of ρCSM ∝r −1.6 and the mass loss rate of ∼5 × 10−3 M yr−1 normalized
at 1015 cm (we assume the shock velocity of 4000 km s−1 andthe wind velocity of 100 km s−1 in order to compare them toour result). This corresponds to the corresponding “local” massloss rate of ∼0.017 M yr−1 at the distance of 2 × 1016 cm.
Thus, our independent estimate of the mass loss rate throughthe dust formation signal is roughly consistent with the Xray measurement. Given uncertainties in both methods (e.g.,
ionization status in analyzing the X-ray absorption), we contend
that the agreement is fairly good.
The conclusion about the high-density CSM likely applies
to other luminous SNe IIn as well. Despite totally different
approaches to estimate these properties, we note a striking
similarity in the ejecta and CSM properties we derived for
SN 2010jl and those derived for SN IIn 2006tf by Smith et al.
(2008a). SN IIn 2006tf was similar to SN 2010jl regarding
luminosity, light curves, and spectral evolution (Zhang et al.
2012). Smith et al. (2008a) estimated the mass loss rate in thelast decade before the explosion of SN 2006tf reached a few
M yr−1 , which explains the luminosity of SN 2006tf (similar
to that of SN 2010jl) by the SN–CSM interaction. The CSM
density we estimated is a bit lower than this, but still much higher
than a usual stellar wind and close to the amount expected for
LBV-like eruptions of a massive star. Given uncertainties in both
estimates (i.e., from the interaction luminosity and from the dustmass), the situation we infer from these two SNe are strikingly
similar. Our analysis on the CSM properties around SN 2010jl
will provide a useful basis for analyzing other (luminous) SNe
IIn and potentially (at least a part of) SLSNe.

Figure 10. Comparison between the extracted SN spectrum (black) and thebackground spectrum (red). The background spectrum is scaled to the [O iii]
λλ4959,5007 seen in the SN spectrum (a), as this is very likely a residual
emission from the unresolved background region. The scaled background
spectrum is then compared to the SN spectrum in the wavelength ranges forHγ (b), Hβ (c), and Hα (d).
(A color version of this figure is available in the online journal.)

Pignata for valuable discussion. This research is supported byWorld Premier International Research Center Initiative (WPI
Initiative), MEXT, Japan. This work has also been supported
in part by the DST-JSPS Bilateral Joint Research Projects.
K.M. and R.Q. acknowledge financial support from Grant-inAid for Scientific Research for Young Scientists (23740141,
24740118). T.J.M. is supported by the Japan Society for the
Promotion of Science Research Fellowship for Young Scientists (23-5929). We have used the Weizmann interactive SN
data repository (www.weizmann.ac.il/astrophysics/wiserep) to
obtain the archive spectrum data for SN 2010jl around the
V-band maximum.
APPENDIX A
CONTAMINATION FROM THE UNRESOLVEDBACKGROUND REGION
In this section, we check how much the narrow componentof the hydrogen emission lines is contaminated by emissions
from the unresolved host and/or the SN environment, rather
than a narrow emission from the CSM just around the SN.
We assume that the HCT spectrum of the SN vicinity, used
for the background subtraction, represents a spectrum of theunresolved background region from the host galaxy and/or SN
environment (not affected by the SN emission). We estimate apossible contribution from the unresolved background region to
the narrow component of the hydrogen emission lines seen in the
SN spectrum as follows (Figure 10). The extracted SN spectrum(Figure 1) shows narrow emission lines of [O iii] λλ4959,5007,
which likely originated from the background rather than from

This research is based on observations obtained at theSubaru Telescope (S12A-047) operated by the Astronomical
Observatory of Japan, and at the Himalayan Chandra Telescope (HCT) operated by the Indian Institute of Astrophysics.
The authors thank the staff at the Subaru Telescope and the
HCT for excellent support in the observations. The authors
also thank Masayuki Tanaka, Filomena Bufano, and Giuliano
14

The Astrophysical Journal, 776:5 (16pp), 2013 October 10

Maeda et al.

the SN/CSM itself. We first scaled the background spectrumby the flux of the [O iii], then assumed that the scaled spectrum
is representative of the unresolved background region. Next,
we compared this spectrum with the hydrogen emission lines.
As shown in Figure 10, the possible contamination from thebackground to the narrow emission lines seen in the SN spectrum
is not negligible. Therefore, we decided not to discuss details of
the narrow component in the main text.
APPENDIX B
SN SITE METALLICITY
Stoll et al. (2011) reported that the metallicity around SN
2010jl is low, Z  0.3 Z . With the SN vicinity spectrum we obtained, we cross-checked this estimate. We firstmeasured the fluxes of the narrow emission lines, Hα , Hβ ,[N ii] λ6584, and [O iii] λ5007. Then, we used the N2 indicator (N2 ≡ log([N ii]/Hα )) and O3N2 indicator (O3N2 ≡log(([O iii]/Hβ )/([N ii]/Hα ))), in order to derive the oxygen
abundance (log(O/H)) using relations in Pettini & Pagel (2004).
Next, we derived the metallicity as 12 + log(O/H) ∼ 8.31 by
the N2 diagnostics and ∼8.36 by the O3N2 diagnostics. Given
the typical uncertainty of ∼0.1–0.2 dex in these methods, ourresult agrees with that presented by Stoll et al. (2011). Adopting
the solar metallicity as 12 + log(O/H) = 8.66 (Asplund et al.
2004) and representing the metallicity by the O abundance, weestimate that Z ∼ 0.3–0.7 Z . While the mean is greater thanthat derived by Stoll et al. (2011), the two results still agree
within the error. In the main text, we adopt Z = 0.3 Z as areference value for the metallicity, following Stoll et al. (2011).

Figure 11. Possible contribution of the CSM echo in the late-phase optical
spectrum. The HCT spectrum (black) is compared with a pseudo echo spectrum(red). This echo spectrum is constructed from the spectrum around V-band
maximum (Zhang et al. 2012) multiplied by the further dependence of fλ ∝λ−1.2 to mimic the scattered spectrum. The flux in the “echo” spectrum is scaled
as greatly as possible, while not to exceed the flux in the late-phase spectrum.
(A color version of this figure is available in the online journal.)

the echo contribution in the late-phase emission is definitely
interesting, and we will present detailed analysis on this issue
elsewhere.
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POSSIBLE ECHO CONTRIBUTION
IN THE OPTICAL SPECTRUM
As mentioned in Section 3.2, our optical spectrum in the latephase (∼+550 days) shows deviation from a single blackbody
fit especially in the blue, either due to unresolved lines or a lightecho caused by the CSM. While not a main focus of the present
paper, this itself is an interesting question, and we provide aconstraint with our data on this issue below.
Figure 11 shows a comparison between the late-phase spectrum and a pseudo echo spectrum. For the pseudo echo spectrum,
we simply adopt the maximum-phase spectrum at ∼24 days
since the V-band maximum (Zhang et al. 2012)14 and apply an
additional dependence of fλ ∝ λ−1.2 to mimic the scatteredspectrum (Miller et al. 2010). From this exercise, we see that
there is a hint of a light echo contribution below ∼5000 Å,
where the overall continuum slope is consistent with the expectation from the echo scenario. While this is not a probe of anecho contribution, it provides an upper limit of the contributionof an echo in the optical emission, which we estimate to be at
most 50% in luminosity. Since the thermal balance argument in
Section 3.4 already includes the uncertainty at this level (e.g.,in the value of α), this would not change our conclusion.
At the same time, there are emission features that cannot
be attributed to the echo (e.g., at ∼4500 and 5200 Å). Thus,
even if the echo is present, the unresolved lines are also present
as suggested by, e.g., Foley et al. (2007). Further investigating
14 The spectrum was obtained through The Weizmann interactive supernova

data repository (www.weizmann.ac.il/astrophysics/wiserep; Yaron & Gal-Yam2012).

15

The Astrophysical Journal, 776:5 (16pp), 2013 October 10

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