[vsnet-chat 673] SW UMa ref. Wyoming proceeding preprint

[Taichi Kato <tkato>]

Dear Rudolf and VSNET colleagues,

   Attached is a summary of superhump matters I talked at the Wyoming CV
Conference.  Hope this would help before it will appear in the proceeding
book.

Regards,
Taichi Kato
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\documentstyle[11pt,paspconf]{article}

\markboth{Kato, et al.}{Photometry during superoutburst}
% \setcounter{page}{33}

\begin{document}

\title{Photometric Observations During Superoutburst}

\author{Taichi Kato, Daisaku Nogami, Hajime Baba and Katsura Matsumoto}
\affil{Department of Astronomy, Kyoto University,
       Sakyo-ku, Kyoto 606-01, Japan}

\begin{abstract}
SU UMa-type dwarf novae show {\it superhumps} during superoutbursts.
We present recent observational findings regarding superhumps and
superoutbursts, especially stressing on new findings in WZ Sge-type
dwarf novae, whose newly identified members have provided us a wealth
of observational tests on the process working in WZ Sge-type superoutburst.
An observational overview of the 1996 -- 1997 superoutburst of EG Cnc
(Huruhata's variable), is presented as an example.
\end{abstract}

\keywords{accretion disks, cataclysmic variables, dwarf novae}

\section{SU UMa-Type Dwarf Novae and Superoutbursts}
SU UMa-type dwarf novae are a subgroup of dwarf novae, which shows
bright, long outbursts called ``superoutbursts" in addition to usual
normal outbursts.  The superoutburst shows a rapid rise, typically in
several hours, and a slow linear decline typically lasting 10 days,
the phase sometimes called as ``plateau", then followed by a rapid decline.
Some stars tend to show rebrightenings after a week or so.
SU UMa-type dwarf novae (SU UMa stars) show {\it superhumps}
during superoutbursts.

Superhumps are semi-periodic oscillations with an amplitude of a few tenth
of magnitude, and are most uniquely characterized by the periods a few
percent longer than the orbital periods.  Superhumps are prominently
observed only during superoutbursts, and are considered to be one of the
defining characteristics of SU UMa-type dwarf novae.  Superhumps are
observed in other classes of cataclysmic variables (CVs), but are the
most prominent signals in SU UMa-type dwarf novae.  Superhumps start with
a very low-amplitude oscillation, then grow to a full amplitude typically
in one or few days.  Superhumps then decay gradually.

\begin{figure}
\vspace{2in}
\caption{A typical example of superoutburst (SW UMa, 1996) and superhumps
        (AW Gem, 1995)} \label{fig-1}
\end{figure}

\section{Origin of Superhumps}
The origin of superhumps had been a longstanding problem.
The theory should explain the basic two characteristics: the period a few
percent longer than the orbital period, and the fact that superhumps
only exist during superoutbursts of SU UMa-type dwarf novae, and not
observed in SS Cyg and Z Cam stars.

The situation was changed dramatically by the discovery of
``tidal instability" by numerical simulation by Whitehurst (1988).
The tidal instability is also called ``tidally driven eccentric
instability", which means the accretion disk becomes unstable to eccentric
perturbation to tidal force under some extreme mass-ratio condition.
The excellent point of Whitehurst's idea was that the required mass-ratio
condition naturally explains the difference between SU UMa stars and
SS Cyg stars.  SU UMa stars are now explained as short-orbital period
systems whose mass ratios are large enough to induce tidal instability.
The superhump is explained as periodic modulation of tidal dissipation
in the disk due to the secondary force, and the superhump period as
the beat period between the binary rotation and the apsidal precession of
the eccentric disk.
The combination of thermal and tidal instabilities is then shown
by Osaki (1989) to well reproduce the basic outburst patterns of
SU UMa stars.

\section{Problems of Superhumps}
Several continuing and new problems regarding superhumps are selected here.

\subsection{Universality of the Tidal Instability Criterion}
Numerical simulations suggests mass ratios ($q=M_1/M_2$) larger than 3 or 4
are required,
but recent extensive photometric studies by Skillman and Patterson
have shown novalike systems (permanent superhumpers) having
relatively short orbital periods, but definitely longer than those of
SU UMa stars, more generally show low-amplitude superhumps.  Some of these
objects are reported to show ``positive" and ``negative" superhumps
at the same time (e.g. V603 Aql, Patterson et al. 1997).
Patterson et al. (1997) tried to interpret the latter being caused by
nodal precession, but the exact mechanism still awaits to be worked.

   These may be an indication of a certain limit of our understanding of
the classical mass-ratio criterion, or the excitation mechanism of
superhumps.

\subsection{``How Superhumps Grow"}
Theoretically, the growth rate of tidal instability is generally accepted
to be correlated with inverse square of the mass ratio (e.g. Lubow 1991).
This predicts the superhumps grow more slowly in short orbital-period
systems, that is, high mass-ratio systems.
   This prediction generally agrees with the ``textbook" superhump delay;
superhumps take one or a few days to grow in long orbital-period SU UMa
stars, several to ten days in very short period systems (e.g. Vogt 1993).

   However, the recently recognized small group of SU UMa stars, called
ER UMa stars or RZ LMi stars, is known to develop large-amplitude
superhumps within a day of the start of superoutburst (Kato et al. 1996),
in spite of their short orbital periods.
These ``precocious" superhumps have the same period
as the later developing superhumps.  This might suggest our basic 
understanding of the superhump delay is in some point incomplete.

\subsection{Early Superhumps}
   There are another type of objects showing unusual superhump-like feature
in the early stages of superoutburst.  As first pointed out by
Patterson et al. (1981) in WZ Sge, all known systems similar to WZ Sge
are known to show humps having periods about 1 percent shorter than the
later superhump period.
In WZ Sge and AL Com, these humps are shown to have the same period as
the orbital one, so some call them ``orbital superhumps"
(Kato et al. 1996; Patterson et al. 1996; Nogami et al. 1997b).

\begin{figure}
\vspace{2.25in}
\caption{Comparison of early superhumps of
        WZ Sge-type dwarf novae} \label{fig-2}
\end{figure}

   It is in debate whether these humps represent heavily enhanced orbital
humps arising from hot spots, reflection effect on the secondary,
or a kind of superhumps showing the period close to the orbital period
during their development.  The double-humped feature common to all
these ``early" superhumps seem to preclude the possibility of the single
hot spot model or the reflection-effect model.  In T Leo, a smooth
transition from the orbital to the usual superhump period is reported
(Kato 1997).

   This suggests that these ``early" superhumps represent the growing
stage of usual superhumps, and is somehow related to the excitation
mechanism of the tidal instability.

\subsection{Period Changes}
   Superhumps are not strictly periodic, and usually change in periods
during the course of superoutburst.  More precisely, the superhump period
usually decrease in time.  This period derivative
($P_{\rm dot} = \stackrel{.}{P}/P$)
has a rather common negative value ($\sim 5 \times 10^{-5}$), which has
been generally attributed to the decreasing
apsidal motion due to the decreasing disk radius, or to the eccentricity
wave propagating inward.  However, there have recently arisen systems
(best examples: SW UMa, AL Com, V1028 Cyg and HV Vir) definitely positive
$\stackrel{.}{P}$, which do not seem to allow the above interpretation.

\begin{figure}
\vspace{1.75in}
\caption{O-C diagram of superhumps in SW UMa (from Nogami et al. 1997a).
        The period is clearly increasing.} \label{fig-3}
\end{figure}

\subsection{Superhump Development and Outburst Development}
   The original motivation of this issue arose from a question
whether the mechanism producing superhumps cause superoutbursts,
or inversely, the length of superoutburst is responsible for superhumps.
This question seems to have reached a fair observational solution
supporting the former interpretation.

   Recently a similar problem has arisen in peculiar rebrightenings,
particularly ``double superoutburst-looking" outbursts of
WZ Sge-like stars.  The recent example, AL Com (Patterson et al. 1996;
Nogami et al. 1997b) showed this pattern.
During the second outburst, a rather usual pattern of superoutburst --
a short outburst looking like a triggering normal outburst,
and a later plateau phase showing development of superhumps.
Nogami et al. (1997) interpreted the second outburst is indeed a
superoutburst, newly triggered by a normal outburst.

\section{EG Cancri}
   As an another remarkable example, we give an example of the recent
spectacular postoutburst brightenings in EG Cnc.

   EG Cnc is a dwarf nova, which has been shown to remarkably similar to
WZ Sge in the following points (Kato et al. 1997; Matsumoto et al. 1997).

\begin{itemize}
\item Long outburst interval of 19 years
\item Apparent lack of normal outbursts
\item Large outburst amplitude ($\sim 9$ mag)
\item Development of early and usual superhumps as in WZ Sge and AL Com
\item Long-lasting outburst more than 100 days
\end{itemize}

   Surprisingly enough, EG Cnc further showed an unprecedented series
of six postoutburst rebrightenings (Kato et al. 1997).

\begin{figure}
\vspace{1.75in}
\caption{Repetitive rebrightenings of EG Cnc} \label{fig-4}
\end{figure}

   The rebrightenings resemble normal outbursts in shape, but during this
period and the long fading tail, superhumps were persistently observed
having the same period as in the main superoutburst.
   The strong superhump modulation in the fading tail safely precludes
the possibility of the cooling white dwarf as a main source of
the fading tail of WZ Sge-type dwarf novae, which was suggested by
Smak (1993).
   The invariance of the pulsed superhump flux across the rebrightening
suggests that these persistent superhumps and rebrightenings
are independent phenomena.
   One may argue the possibility of superhumps arising from the inner disk,
and seemingly outside-in type rebrightenings from the outer disk.

\section{Activity Sequence of WZ Sge Stars}
   Considering the similarity of EG Cnc with other WZ Sge-like objects,
it would be natural to consider a sequence of post-superoutburst activity:
from superoutbursts without noticeable rebrightenings (as in usual SU UMa
stars), with single rebrightenings, with double to multiple rebrightenings,
then to double superoutbursts.

\begin{itemize}
\item Without noticeable rebrightenings: WZ Sge (1913 and 1946)
\item Single rebrightenings: EG Cnc (1977), possibly HV Vir (1992)
\item Double to multiple rebrightenings: EG Cnc (1996-1997), UZ Boo (1994)
\item Double superoutbursts: WZ Sge (1978-1979), AL Com (1975, 1995)
\end{itemize}

   An ideal model of WZ Sge-type dwarf novae should reproduce this wide
and continuous variety of outburst activity by changing some input
parameters.

\begin{figure}
\vspace{1.75in}
\caption{Occurrence of post-superoutburst rebrightenings vs.
       superhump period.} \label{fig-5}
\end{figure}

   The second of this activity sequence are not unique to WZ Sge-like stars,
but its appearance is strongly correlated with the orbital period;
post-superoutburst rebrightenings thus predominantly occur in
short-period systems.
   These systems have been recently known to show another unique feature:
{\it increasing} superhump period, rather than common decreasing period.
Positive $\stackrel{.}{P}$ systems also predominantly occur in the
short-orbital regime.  The close encounter of these peculiar new features
suggests that they are a result of single common physical condition.

\begin{figure}
\vspace{1.75in}
\caption{Superhump $\stackrel{.}{P}$ vs.
       superhump period.} \label{fig-6}
\end{figure}

\section{Discussion}
   Superoutburst after superoutburst should require excessive matter
with a large proper angular momentum even after superoutburst,
and the positive $\stackrel{.}{P}$ may be a result of the eccentricity
wave propagating outward.
   These requirements may be fulfilled by assuming the tidal instability
working in the middle region of the accretion disk.
The eccentricity wave then can propagate outward,
and the weak tidal heating in the outer region may result in premature
quenching of the outburst hot state, possibly leaving matter of
high angular momentum.

   In the thermal-tidal instability scheme, superoutbursts of usual
SU UMa-type dwarf novae occur when the disk radius first time reaches
the tidal resonance radius after successive normal outbursts.
In this case, the maximum disk radius being critically close to the
tidal resonance radius, the tidal instability always occur in the
outermost region of the disk.
   However, in systems having little experienced normal outbursts,
the disk matter is expected to accumulate so that the disk can expand
during outburst beyond this radius. (And extreme mass-ratios can hold
the resonance radius well inside the Roche lobe).
   This condition well matches the outburst characteristics and physical
parameters of so-called WZ Sge-type dwarf novae.  Although the mechanism
of WZ Sge-type outbursts is still controversial, the wide variety of
these peculiar phenomena may be considered as a natural consequence of
conditions causing only superoutbursts.

\acknowledgments
   The authors are grateful to Y. Osaki for fruitful discussions at
the Annual Meeting of the Astronomical Society of Japan.  The authors
are also grateful to the contributors to VSNET
(http://vsnet.kusastro.kyoto-u.ac.jp) for promptly notifying important
outbursts and for valuable and timely online discussions.

\begin{references}
\reference Kato, T. 1997, \pasj, in press
\reference Kato, T., Nogami, D., Baba, H., Matsumoto, K., Arimoto, J.,
     Tanabe K., \& Ishikawa, K. 1996, \pasj, 48, L21
\reference Kato, T., Nogami, D., \& Masuda, S. 1996, \pasj, 48, L5
\reference Kato, T., Nogami, D., Matsumoto, K., \& Baba, H. 1997, \apj,
     submitted
\reference Lubow, S. H. 1991, \apj, 381, 259
\reference Matsumoto, K., Nogami, D., Kato, T., \& Baba, H. 1997, \pasj,
     submitted
\reference Nogami, D., Baba, H., Kato, T., \& Novak, R. 1997a, in preparation
\reference Nogami, D., Kato, T., \& Baba, H. 1997b, \apj, in press
\reference Osaki, Y. 1989, \pasj, 41, 1005
\reference Patterson, J., Augusteijn, T., Harvey, D. A., Skillman, D. R.,
      Abbott, M. C., \& Thorstensen, J. 1996, \pasp, 108, 748
\reference Patterson, J., Kemp, J., Saad, J., Skillman, D. R., Harvey, D. A.,
     Fried, R., Thorstensen, J. R., \& Ashley, R. 1997, \pasp, 109, 468
\reference Patterson, J., McGraw, J. T., Coleman, L., \& Africano J. L.
     1981, \apj, 248, 1067
\reference Smak, J. I. 1993, Acta. Astron. 43, 101
\reference Vogt, N. 1993, in ``Cataclysmic Variables and Related Physics",
          ed. O. Regev, G. Shaviv (Ann. Israel Phys. Soc. 10)
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\reference Whitehurst R. 1988, \mnras, 232, 35
\end{references}

\end{document}

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