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No.49

Apr. 2009ISSN 0917-2211

Variable Star Bulletin
Rebrightening Phenomenon in Classical Novae
Taichi Kato1 , Kazuhiro Nakajima2 , Hiroyuki Maehara3 , Seiichiro Kiyota4
1

Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japantkato@kusastro.kyoto-u.ac.jp

2

Variable Star Observers League in Japan (VSOLJ), 124 Isatotyo, Teradani, Kumano, Mie 519-4673, Japan
3

Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto 607-8471, Japan
4

VSOLJ, 405-1003 Matsushiro, Tsukuba, Ibaraki 305-0035, Japan

Abstract
Two classical novae V1493 Aql and V2362 Cyg were known to exhibit unprecedented large-amplitude
rebrightening during the late stage of their evolution. We analyzed common properties in these two light
curves. We show that these unusual light curves are very well expressed by a combination of power-law
decline, omnipresent in fast novae, and exponential brightening. We propose a schematic interpretation of
the properties common to these rebrightenings can be a consequence of a shock resulting from a secondary
ejection and its breakout in the optically thick nova winds. This interpretation has an advantage in explaining
the rapid fading following the rebrightening and the subsequent evolution of the light curve. The exponential
rise might reﬂect emerging light from the shock front, analogous to a radiative precursor in a supernova shock
breakout. The consequence of such a shock in the nova wind potentially explains many kinds of unusual
phenomena in novae including early-stage variations and potentially dust formation.

1

Introduction

Classical novae are thermonuclear runaways (cf. Starrﬁeld et al. 2000) on a mass-accreting white dwarf incataclysmic variables (CVs). The light curves of classical novae usually are comprise of rapid premaximum riseand slower decline from the maximum. While many of fast (rapidly fading) novae show a relatively smoothdecline, which is often well approximated by a power-law (cf. Hachisu, Kato 2006), slow (slowly fading) novae
tend to show more complex behavior.
In recent years, two fast novae (V1493 Cyg and V2362 Cyg) drastically violated this picture. The light
curves of these novae initially showed smooth decline typical for fast novae, but was followed by acceleratingbrightening (hereafter rebrightening), then by a rapid drop (cf. Venturini et al. 2004; Kimeswenger et al. 2008).
The overall feature of the light curves in these novae was extremely similar (Goranskij et al. 2006; Munari et al.
2008) suggesting a common underlying mechanism.
We here show that the light curves of these two novae can be very well represented by a combination of
power-law decline and exponential brightening and discuss the origin of the peculiar light variation.

2

Data analysis

The photometric data were taken by us and from observations to VSNET (Kato et al., 2004), supplemented for
discovery and early observations from IAU Circulars. For V1493 Aql,1 we adopted visual observations because
1 The

magnitudes at the epoch of the discovery (mpg = 8.8 on 1999 July 13) were (Nakano et al., 1999)
later found to be incorrect due to the problem in comparison stars (vsnet-alert 3254, <http://www.kusastro.kyotou.ac.jp/vsnet/Mail/alert3000/msg00254.html>). The resultant t2 was ∼ 4 d, in contrast to the unexpectedly small t2 < 3 d,claimed to be the fastest known nova (Bonifacio et al., 2000).

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Figure 1: Best ﬁts to the V -band light curve of V2362 Cyg. Individual circles represent observations and straightlines represent ﬁts with parameters equation 4. (Upper): the early decline is well represented by a power law.
(Lower): excess rebrightening component (in magnitude scale) is well represented by an exponential rise.

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Figure 2: Best ﬁt of the two-component model (equation 3) to the V -band light curve of V2362 Cyg. The thindotted curve and line represent the components of power-law decline and exponential rise, respectively. The thincurve represents the best ﬁt.

CCD observations did not cover the entire stage of the outburst. For V2362 Cyg, we adopted CCD V observations.
The typical errors of visual and CCD V observations were 0.1–0.2 and 0.01–0.03 mag, respectively.
The early part of the light curve is well represented by a power law-type decline (cf. ﬁgure 1, upper panel),
as is typical for a fast nova. Subtracting the extrapolated power law decline, we found that the excess componentof the rebrightening is well expressed by an exponential rise (cf. ﬁgure 1, lower panel). Upon this knowledge, we
modeled the light curve as a combination (equation 3) of two components: a power-law decline (equation 1) andan exponential rebrightening (equation 2).
Vdec = a + b log(t − c)(1)

Vreb = d(t − t0 ) + e(2), where t0 = 2453920 is an arbitrary value to avoid large coeﬃcients.
V = −2.5 log(10−0.4Vdec + 10−0.4Vreb )(3)

The best-ﬁt parameters werea = 7.64(0.16), b = 2.35(0.10), c = 2453829.7(0.3),
d = −0.0248(0.0011), e = 14.71(0.17)(4), for the interval of 2453831 < t(JD) < 2454073.
Figure 2 shows the overall ﬁt. The observed light curve before the rapid fade following the rebrightening
maximum is well expressed by this simple combination of components. We could not, however, reproduce theresult by Kimeswenger et al. (2008) reporting that an extrapolation of a power-law decline determined from theﬁrst 60 d perfectly ﬁts to the post-rebrightening light curve. This discrepancy could have originated from thediﬀerent power indices between Kimeswenger et al. (2008) and ours. In order to estimate the eﬀect of this potential
uncertainty in determining the power index, we calculated ﬁts to diﬀerent portions of the early light curve, and aﬁt to the entire light curve excluding the rebrightening portion (this simulates the result by Kimeswenger et al.
2008) and subtracted each of them from the light curve. The overall trend in unchanged in all cases in that theresidual can be well-expressed by an exponential rise. The power law index simulating the result by Kimeswenger
et al. (2008) was b = 3.08(0.04), which is signiﬁcantly smaller than that (4.4 = 1.75 × 2.5) expected from the“universal decline law” of F ∝ t−1.75 (Hachisu, Kato, 2006).
The same procedure was applied to the light curve of V1493 Aql, yielding the best ﬁt values (equation 5)
and the ﬁt (ﬁgure 3).
a = 8.75(0.43), b = 3.27(0.37), c = 2451371.8(0.6),
d = −0.0744(0.0008), e = 13.47(0.16)

(5)

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Figure 3: Best ﬁt of the two-component model to the visual light curve of V1493 Aql. The line are curves are as
in ﬁgure 2.

, for the interval of 2451372 < t(JD) < 2451422, using t0 = 2451400.

3

Discussion

3.1

Unusual Rebrightenings and Role of Shocks

Several authors have pointed out that the light curves of these two novae were very unusual but closely resembled
each other, but the the phenomenon still awaits physical interpretation.
Kimeswenger et al. (2008) tried to reproduce the rebrightening spike of V2362 Cyg by assuming a temporary
expansion of the pseudo-photosphere of the nova and estimated its temperature and radius. Kimeswenger et al.
(2008) suggested that this temporary expansion was caused by a fast ejecta reaching the photosphere, resulting asigniﬁcant increase in the density. Although the authors attributed the rapid fading following the rebrightening
peak to dust obscuration, the reason is unclear why and how dust formation took place around the peak. If thisinterpretation is also applicable to the extremely similar nova V1493 Aql, the apparent lack of evidence of dust
formation (Venturini et al., 2004) could be problematic. Furthermore, a drastic expansion of the photosphereshould aﬀect the free-free component of the light curve, which is considered to dominate at this stage of nova
evolution (see equation 9 of Hachisu, Kato 2006). If such an expanded photosphere was obscured by dust
formation, and the remaining light is from a “detached shell”, the subsequent evolution of the light curve should
follow a steeper decline (corresponding to the epoch after the wind stops, cf. Hachisu, Kato 2006) rather than asmooth extrapolation of the early decline. Emission lines would be also aﬀected, while observations of strength ofﬁtted emission of the main outburst (see ﬁgure 4 of Kimeswenger et al. 2008) smoothly declined regardless of therebrightening. These diﬃculties probably arise from an assumption of a continuous input of substantial amountof new ejecta into the preexisting one. We probably need a more dynamic, rather than this static, process.
We then propose an alternative idea that the thin shock front formed by a limited amount of newly ejected
matter, and potentially its breakout in the optically thick nova winds, comprises the rebrightening phenomenon.
The spectra of V2362 Cyg taken around the rebrightening maximum (Munari et al. 2008; Kimeswenger et al.
2008) showed temporary appearance of strong and blue-shifted absorption components in the Balmer-emission-line
proﬁles. Kimeswenger et al. (2008) also noted an enhancement of a new component of emission lines during therebrightening. Such high-velocity component is expected to collide with the exterior, slower, preexisting winds,
and will naturally produce a shock front (cf. Munari et al. 2007). The detection of hard X-rays (Ness, Starrﬁeld,2006) can also be attributed to the presence of a shock (Balman et al., 1998). The presence of optically thickwind provides a favorable condition that a breakout, if present, of such a shock becomes observable (e.g. Li 2007
for a supernova/GRB case). After the optically thick, geometrically thin shock front reaches the photosphere,
and the energy loss via a kinetic motion dominates over the radiative transport, the subsequent rapid expansion
and cooling of a thin shell can be naturally expected. The visibility of the high-velocity component only aroundthe peak indicates that the velocity structure dramatically varied around the rebrightening peak. In the present

5
picture, the matter outside the photosphere would remain largely untouched, preserving the general power lawtype decline trend and behavior of emission lines arising from the outer optically thin region. Dust formation
may be associated with the quick expansion of the shock front, as discussed later, probably naturally explaining
the temporal coincidence of the suggested dust formation around the rebrightening peak.
The rising stage of the rebrightening, the exponential rise, commonly observed in these two novae appears tobe harder to explain in any mechanism, and would be a challenge for theoreticians. Within the present picture,
we propose a working hypothesis that that photons emerging from a shock front constitute the exponentiallyrising, excess component. Before the shock front reaches the photosphere, the photons from the shock front havean escape probability of e−τ , where τ is the optical depth from the shock front to the observer. The observer
can thus see photons from the shock front attenuated by e−τ as an additional component. This interpretation
corresponds to the “radiative precursor” phase of a shock breakout in a supernova (Schawinski et al., 2008).
Under the condition that the front is approaching the photosphere, τ is expected to decrease with time. A
simple assumption of a constant rate of decrease of τ can explain an exponential rise. The parameter ﬁts give
characteristic time-scales of the rise corresponding to ∆τ = 1 of 44(1) d and 14.6(2) d for V2362 Cyg and V1493
Aql, respectively. The values of t2 being ∼9 d and ∼4 d for respective novae, the result might suggest a positive
relation between t2 and the time-scale of the rise.
Our interpretation is diﬀerent from that by Kimeswenger et al. (2008) in that they assumed continuous mass
input to the photosphere during the entire rising stage of the rebrightening (since day 170, resulting an expansionof the photosphere) while we assume the continuous presence of a shock front under the photosphere before thepeak of rebrightening (i.e. the front reaches the photosphere around the time of the peak). Our interpretation inturn requires the presence of optically thick wind at the time of the shock formation. This can be tested whether
the light curve follows by F ∝ t−1.75 or by a steeper (F ∝ t−3.5 ) power law (Hachisu, Kato, 2006). We analyzed
the fading part after the end of rebrightening (2454098 < t < 2454283). The best ﬁt powers p for t−p were 1.6(1)for the V -band and 1.2(2) for the y-band (less aﬀected by emission lines), which were closer to p = 1.75. This
result suggests that the optical thick winds had not yet stopped at the epoch in question.
The bluer color around the rebrightening peak, compared to the initial maximum (Munari et al., 2008)
also favors the presece of a hot shock front. Most recently, Arai et al. (2009) reported B − Ks multicolor light
curves and attributed the later infrared peak to transient dust formation. The duration of the infrared peak was
unusually short and it quickly decayed despite its optical thickness. This makes a contrast to other well-known
novae with substantial dust formation (Bode, Evans, 2008). Although this shortness may be attributed to the
only transient formation of the dust, these light curves, alternatively, can be also interpreted as progressively
slower maxima with longer wavelengths; the same tendency is inferred from the optical work by Munari et al.
(2008). This characteristic may be understood as a manifestation of a shock breakout, analogous to the supernova
case (e.g. Klein, Chevalier 1978), although a red V − I color would also require an excess reddening, i.e. thecoexisting dust. This dependence between maxima times and wavelengths would be worth further investigation.

3.2

Shock and Dust in Novae

A shock formed in an optically thick wind, and its potential subsequent breakout, is attractive in that it can not
only naturally produce a rapid fade but also enable eﬃcient dust production after its compression and subsequent
rapid expansion in post-shock cooling as in wind-wind collision binaries (e.g. Usov 1991). In V2362 Cyg, at theepoch following the rapid fade, Rayner et al. (2006) and Kimeswenger et al. (2008) reported an infrared excess
and reddening which were attributed to dust formation in the inner region. The dust formation related to the
expansion after a shock around the contracted photosphere is compatible with observations only slightly aﬀecting
emission lines and the power-law decline component, which is considered to arise from free-free emission in outer
ejecta (Hachisu, Kato, 2006).2

3.3

Implications to Other Novae and Future Prospects

We note that similar brightening phenomena accompanied by gradual brightening and rapid fade, although lessconspicuous, are present in some other novae. The noteworthy examples include the fast nova V2491 Cyg 15 dafter maximum (cf. ﬁgure 4, vsnet-alert 10129) and the unusual, slowly evolving nova V1280 Sco (Das et al. 2008;
2 In V1493 Aql, Venturini et al. (2004) obtained a spectrum around the rebrightening maximum, and detected strong continuum

emission and low-excitation emission lines. These ﬁndings suggested that a second period of continuous mass loss can be responsible
for the phenomenon (Venturini et al., 2004). It is, however, diﬃcult to see whether the shock component was present in the spectrum
because of the low resolution and the very broad emission lines. Venturini et al. (2004) did not report evidence for dust formation.

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Figure 4: Fit to the V (circles) and visual (crosses) light curve of V2491 Cyg. The line are curves are as in ﬁgure
2. The parameters were a = 6.6(1.2), b = 3.6(1.4), c = −1.1(1.1), d = 0.18(0.08), e = 11.2(0.8) for the given
t0 = 2454575. The data were from VSNET.

Chesneau et al. 2008), and potentially V5579 Sgr (vsnet-alert 10201). Hachisu, Kato (2009) tried to explain the
behavior of V2491 Cyg by introducing the polar-type magnetism and nova explosion-induced asynchronization.
Although this interpretation was apparently motivated by the diﬃculty in reproducing the rapid decline following
the rebrightening, we do not consider this possibility in the present paper because the quiescent brightness of
V2491 Cyg is incompatible with a polar and because similar anomalies (high quiescent X-ray luminosity) wereneither detected in V2362 Cyg nor V1493 Aql.
The fading in V1280 Sco was accompanied by dust formation occurring at an unexpectedly early epoch.
Although the mechanism of unusual variation in these novae is not well known, V2362 Cyg/V1493 Aql-typeejection of and shock formation at an early epoch may have played a role in producing unusual light variationand in dust production in a harsh environment (cf. Gallagher 1977). Another commonly seen feature of a bump(maximum) following a premaximum halt in slow novae (Kato et al. 2002 and references therein) might be an
extension of the same phenomenon. If this is the case, the fading rate (such as t2 ) derived from the fading portionof the bump would easily be an overestimate. The apparent discrepancy between the presence of a premaximum
halt and very rapid fading in V463 Sct (Kato et al., 2002) might then be solved.
A model incorporating more elaborate treatment of a shock formation in realistic nova winds and radiativetransfer, which is beyond the scope of this paper, is needed for a comparison with observed light curves, color
variations, and change in the proﬁle of emission lines. Considering the variety of phenomena potentially arisingfrom this mechanism, a survey in a wide parameter space is encouraged. The reason why only some novae show
this kind of late-stage rebrightening is still poorly known. The present interpretation suggests that if a second
ejection in the late stage somehow occurs when the optically thick wind is still present, the resultant light curveshould generally resemble those of the two objects investigated. Such phenomena may have been overlooked in
the past due to the limited high-precision observation. Future systematic multiwavelength photometry and highresolution spectroscopy are desired to better understand the phenomenon. X-ray observations are also expected toprovide evidence for the shock in the nova wind. These observations should be aimed prospectively starting fromthe early rising stage of rebrightening. A deviation of the light curve from the power-law decline, as empiricallyshown in this paper, would provide a promising early warning signal for coordinating such observations, that is,real-time examination of nova light curves on log t − mag plots will become a powerful diagnostic tool.
The author is grateful to VSOLJ and VSNET observers who supplied vital data.

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VSOLJ
c/o Keiichi Saijo National Science Museum, Ueno-Park, Tokyo Japan
Editor Seeichiro Kiyota
e-mail:skiyota@nias.aﬀrc.go.jp
Publishing Masahiko Momose