text:
\section{Introduction}

\noindent Population I Wolf-Rayet (WR) stars are characterised by dense, fast
stellar winds giving the stars their broad emission-line spectra and carrying
heavy mass loss: they represent the last stable stage in the evolution of massive
stars. One of the earliest results from infrared (IR) astronomy was the
discovery of `excess' radiation by heated circumstellar dust from a variety of
stars known to be losing mass. Amongst these were three WC9 type WR stars,
observed by Allen, Harvey \& Swings (1972). Subsequent studies (e.g. Cohen,
Barlow \& Kuhi 1975) found circumstellar dust emission from most WC9 and
many WC8 stars. The process was soon inverted, and bright IR sources discovered
in space- or ground-based IR surveys were found to harbour optically faint dusty
WC8--9 stars (e.g. AFGL\,2104 = WR\,112, Cohen \& Kuhi 1977).  Amongst these was
WR\,48a, discovered by Danks et al. (1983, hereafter DDWS) in a survey of the
H\,{\sc ii} region G305.5 +0.0. They observed WR\,48a to be undergoing an infrared
outburst similar to that shown in 1977 by HD 193793 (Williams et al. 1978,
Hackwell, Gehrz \& Grasdalen 1979). DDWS tracked the rise of the IR emission to
maximum in 1979 and its initial fading, and presented a spectrum showing He and C
emission lines, most conspicuously He\,{\sc i} 10830\AA\ and C\,{\sc iii} 9710\AA,
from which they classified WR\,48a as a WC9 star.

In their survey of IR dust emission by late subtype WC stars, Williams,
van der Hucht \& Th\'e (1987a, hereafter WHT), reported photometry of WR\,48a
in 1982--86 which showed continuing fading of its dust emission. They also
extended the spectroscopy to the yellow (5550--5950\AA), and argued from the
approximately equal intensities in the C\,{\sc iii} 5696-\AA\ and C\,{\sc iv}
5808-\AA\ classification lines that WR\,48a was a WC8 star. Further IR photometry
of WR\,48a was reported by Williams et al. (2003, hereafter Paper~I), showing
that the fading continued to about 1997, but
that the spectral energy distribution (SED) at that time still showed  dust
emission, indicating that dust was still being formed by WR\,48a.
In this respect it differed from `episodic' dust makers like HD 193793 (WR\,140),
which form dust for only a fraction of their periods (Williams et al. 1990).
The IR photometry of WR\,48a also showed secondary dust-formation episodes,
`mini eruptions', in 1990 and 1994. These resembled those observed by Williams
et al. (2001) in another episodic dust maker, the WC7+O9 system WR\,137 (HD 192641).
In Paper~I, the 2.4--25-$\mu$m SED of WR\,48a observed with the short-wavelength
spectrometer (SWS) on {\em ISO} in a survey of WR spectra (van der Hucht et al.
1996) was compared with that of WR\,104 (Ve2--45), the classical dust-making
WC9 star, and found to be significantly cooler. This difference was consistent
with the radial dust density distribution around WR\,48a being flatter than
the $\propto r^{-2}$ law expected of a system making dust at a constant rate
like WR\,104: the evolution of the dust density distribution
of WR\,48a is considered further in Section \ref{SModels}. The {\em ISO}-SWS
spectrum of WR\,48a presented in Paper~I showed an emission feature near
7.7 $\mu$m similar to that observed in WR\,104 and WR\,112 by Cohen, Tielens
\& Bregman (1989) and ascribed to a carbonaceous carrier with small aromatic
domains, a possible precurson to carbon grains; an independent study of the
SWS spectrum by Chiar, Peeters \& Tielens (2002) identified and discussed
emission features at 6.4$\mu$m and 7.9$\mu$m.

The enduring interest of dust formation by WR stars is the great difficulty
in forming dust in such hostile environments: close to the stars, the stellar
radiation fields would heat any dust to above its evaporation temperature
but at greater distances, where the radiation field is sufficiently diluted,
the density of the WR stellar wind is too low to allow homonuclear dust
condensations -- as recognised early on by Hackwell et. al. (1979) in the case
of WR\,140 and discussed by WHT for the WC8--9 stars making dust persistently.
Zubko (1998) found that carbon
grains having drift velocities relative to the WC8--9 wind could grow via
collision with carbon ions, but the question of grain nucleation remains open.
A chemical kinetic study of the formation of molecular species and carbon
grain precursors in WC9 winds by Cherchneff et al. (2000) found that only
C$_2$ was formed in useful amounts, and even that required significantly
(factor $>10^3$) higher densities than expected in the regions of isotropic,
smooth WR winds where dust grains are observed.
Understanding the physicochemical process of dust formation by WR stars
appears to have stalled, but the incidence of observed dust formation by
WR stars in different systems provides valuable information on the origin
of the significantly higher densities demanded.

Large-scale, high-density structures in a WR wind are provided by compression of
the stellar wind in strong shocks formed where the wind of a WR star collides
with that of a sufficiently luminous companion in a binary system -- a colliding
wind binary (CWB) -- as occurs in WR\,140. Usov (1991) suggested that very
high compression factors ($10^{3} - 10^{4}$) could be produced in WR\,140
if the heated and compressed wind was able to cool efficiently.
The link between the dust-formation episodes and binary orbit in WR\,140 is
provided by the periodic increases by factor of $\sim$ 40 of the pre-shock wind
density at the wind-collision region (WCR) for a brief time around periastron
passage (Williams 1999) in its very elliptical orbit.
Similarly, Lef\`evre et al. (2005) showed that the episodic dust-maker WR\,137
was a spectroscopic binary having a period (13.05 yr) equal to that of the
dust-formation episodes (Williams et al. 2001), with periastron passage about
a year before maximum dust emission.
More recently, Williams, Rauw \& van der Hucht (2009a) showed that the radial
velocities of the WC5+O9 system WR\,19 were consistent with its being a
high-eccentricity ($e = 0.8$) binary, having periastron passage shortly
before its brief, periodic (10.1-yr) dust-formation episodes.

The connection between the persistent dust-formation by the WC9 stars and their
movement in binary orbits comes from IR images of the dust, which show rotating
`pinwheel' structures around WR\,104, WR\,98a (IRAS 17380--3031)
and WR\,112, interpreted to be dust formed and ejected in a stream to one side
of a rotating binary system observed at a relatively low orbital inclination
(Tuthill, Monnier \& Danchi 1999, Monnier, Tuthill, \& Danchi 1999, and
Monnier et al. 2007).
The observation of non-thermal radio emission from the `pinwheel' systems
(Monnier et al. 2002) provides further support for their being CWBs; but their
stellar components have not yet been resolved, so that it has not been
possible to relate the positions of the stars and WCRs to that of the dust.

Monnier et al. (2007) found the dust emission by WR\,48a to be extended at
2$\mu$m; and the dust cloud was imaged at 12.3$\mu$m by Marchenko \& Moffat
(2007), showing the dust emission to be extended E--W, suggesting a flattened
structure, possibly a fragmentary spiral, seen at moderately high inclination.

DDWS and Danks et al. (1984) associated WR\,48a with two newly discovered
galactic clusters, Danks~1 (C 1310--624) and Danks~2 (C 1309--624) at a
distance between $\sim$ 3.3 and 4.6 kpc. Bica et al. (2004) derived
colour-magnitude diagrams from deeper photometry and derived distances
to the clusters of $3.6\pm0.5$ and $3.4\pm0.2$ kpc respectively.
The connection between WR\,48a and the clusters was reinforced by
Clark \& Porter (2004) in their study of star formation in the region.
They suggested that star formation
might have been triggered by WR\,48a and adopted a distance of 4 kpc
for the complex. This gives a greater distance to WR\,48a than that
(1.2~kpc, van der Hucht 2001) implied by its spectral type, and these
estimates need to be reconciled.

By all accounts, WR\,48a is heavily reddened, but the exact value is not
certain. DDWS derived A$_v \simeq$ 9.2 from the 7000--10000-\AA\ colour
in their spectrum. Williams, van der Hucht \& Th\'e (1987b) derived
A$_v \simeq 8.3$ from the 5000--7000-\AA\ slope in their spectrum observed
in 1986, and noted that this was consistent with the strength of the
6284-\AA\ diffuse interstellar absorption band (DIB) and the relation
between these quantities from other reddened stars.
From the $ISO$ SWS spectrum of WR\,48a, Schutte et al. (1998) found the
interstellar `silicate' feature to have $\tau_{9.7} = 0.52$. The ratio of
visual extinction to `silicate' optical depth in the spectra of WR stars
and Cyg OB2 No.\ 12 showed significant scatter, $A_V/\tau_{9.7} = 16.6\pm4.6$.
Applying this ratio to the $\tau_{9.7}$ observed in WR\,48a gives
$A_V = 8.6\pm2.4$. (A lower value, $A_V$ (6.1), was derived from $\tau_{9.7}$
in Paper~I but this used a different and probably inappropriate calibration.)
Baume, Carraro \& Momany (2009) observed $UBVIc$ photometry in 2006, and
derived $E(B-V) \simeq 2.4$. For a standard reddening law, this implies
a lower extinction and, from their observed $(V-Ic) = 3.88$, an intrinsic
$(V-Ic) \simeq 0.9$, which is abnormally red for an early type star.
If some of the extinction occurs in the carbon dust made by WR\,48a, the
extinction law may not be standard. For example, Menzies \& Feast (1997)
found an anomalous reddening law for the carbon dust made by the RCB star
RY Sgr, so the sightline to WR\,48a may have a reddening law intermediate
between the standard interstellar and that for carbon dust.
On the other hand, the circumstellar component of the reddening is unlikely
to be very great, given the strength of the `silicate' feature and the
reddening to the associated clusters $A_V = 8.1$ and $9.3$ respectively
(Bica et al.).  For the present, therefore, we adopt $A_V = 9.0$ and a
standard interstellar law for the reddening of WR\,48a.

Zhekov, Gagn\'e \& Skinner (2011) have identified a strong, highly obscured
X-ray source with WR\,48a. They pointed out that, if WR\,48a was physically
associated with the clusters Danks 1 and Danks 2 at a distance of $\sim 4$kpc,
it would be the most X-ray luminous WR star in the Galaxy, after Cyg X-3.
They also derived a high extinction, $N_H = 2.29 \times 10^{22}$ cm$^{-2}$,
from their NEI shock modelling of the X-ray spectrum and noted that this was
consistent with $A_V = 10$ using the standard conversion,
$N_H = 2.22 \times 10^{21} A_V$ cm$^{-2}$; but $A_V$ could be 40-50\% higher
using more recent conversions. As one of several possible origins for the
X-ray emission, they considered colliding stellar winds in a wide WR+O binary.
As noted by Zhekov et al., and also Mauerhan, van Dyk \& Morris (2011),
WR\,48a was detected with {\em Chandra} as a very strong X-ray source.

In this paper, we report almost three decades (1982--2011) of IR photometry
tracking the emission by the dust cloud made by WR\,48a and showing that
the 1978--9 dust-formation was not an isolated event, but one which appears
to be recurring after an interval of over 32 yrs.
We present optical spectra which suggest that the WC8 star in WR\,48a has an
OB companion, apparently an Oe or Be star.
We use the IR colours and simple modelling of the SEDs to describe the
evolution of the dust cloud and develop a preliminary picture of WR\,48a
as a colliding-wind binary.

\section{Observations}\label{SObs}

\subsection{Infrared photometry}

\begin{table
\caption{Near-infrared photometry of WR\,48a with ESO telescopes: except
where marked (* 3.6m, + 2.2m), observations were made with the 1-m
photometric telescope.}
\label{TESOa}
\centering
\begin{tabular}{llllll}
\hline
Date    &  $J$ &  $H$ &  $K$ &  \Lp &  $M$  \\
\hline
2445418 & 7.80 & 5.21 & 3.01 & 0.29 & -0.42 \\
2445419 & 7.88 & 5.25 & 3.10 & 0.41 & -0.37 \\
2445839 & 8.27 & 5.61 & 3.39 & 0.52 & -0.31 \\
2446278 & 8.46 & 5.94 & 3.71 & 0.80 &  0.04 \\
2446632 & 8.57 & 6.23 & 4.07 & 1.13 &  0.27 \\
2446829 & 8.68 & 6.40 & 4.22 & 1.18 &  0.32 \\
2446831 & 8.69 & 6.38 & 4.12 & 1.27 &  0.25 \\
2447258 & 8.72 & 6.46 & 4.35 & 1.41 &  0.58 \\
2447259 & 8.73 & 6.45 & 4.32 & 1.36 &  0.63 \\
2447260 & 8.70 & 6.45 & 4.33 & 1.40 &  0.63 \\
2447261 & 8.70 & 6.46 & 4.36 & 1.42 &  0.61 \\
2447519 & 8.91 & 6.69 & 4.57 & 1.54 &  0.64 \\
2447520 & 8.94 & 6.69 & 4.57 & 1.54 &  0.73 \\
2447540 & 9.17 & 6.78 & 4.56 & 1.59 &  0.67 \\
2447453 & 8.94 & 6.75 & 4.55 & 1.56 &  0.66 \\
2447544 & 8.93 & 6.70 & 4.56 & 1.58 &  0.69 \\
2447552 & 8.85 & 6.73 & 4.55 & 1.55 &  0.70 \\
2447573 & 8.87 & 6.71 & 4.60 & 1.58 &  0.74 \\
2447670 & 8.73 & 6.67 & 4.63 & 1.69 &  0.91 \\
2447671 & 8.86 & 6.80 & 4.70 & 1.66 &  0.73 \\
2447672 & 8.86 & 6.82 & 4.73 & 1.71 &  0.78 \\
2447910 & 8.89 & 6.83 & 4.80 & 1.79 &  0.89 \\
2447966 & 8.87 & 6.87 & 4.86 & 1.85 &  0.94 \\
2447967 & 8.93 & 6.89 & 4.86 & 1.87 &  0.96 \\
2447968 & 8.90 & 6.87 & 4.83 & 1.83 &  0.92 \\
2447970 & 8.91 & 6.88 & 4.85 & 1.84 &  0.96 \\
2447971 & 8.90 & 6.88 & 4.84 & 1.83 &  0.95 \\
2447991 & 8.91 & 6.89 & 4.87 & 1.87 &  0.93 \\
2447992 & 8.86 & 6.88 & 4.86 & 1.84 &  0.95 \\
2447993 & 8.89 & 6.88 & 4.87 & 1.85 &  0.97 \\
2448316 & 8.89 & 6.91 & 4.89 & 1.94 &  1.01: \\
2448317 & 8.89 & 6.89 & 4.89 & 1.92 &  1.02 \\
2448318 & 8.91 & 6.90 & 4.88 & 1.93 &  1.02 \\
2448347* & 8.91 & 6.93 & 4.93 & 1.97 &  1.07\\
2448348 & 8.94 & 6.96 & 4.95 & 1.97 &  1.04 \\
2448349 & 8.96 & 6.96 & 4.96 & 1.98 &  1.09 \\
2448350 & 8.95 & 6.98 & 4.97 & 1.97 &  1.08 \\
2448639 & 8.91 & 6.92 & 4.95 & 2.03 &  1.16 \\
2448698 & 8.96 & 7.02 & 5.04 & 2.08 &  1.14 \\
2448749 & 8.98 & 7.07 & 5.10 & 2.11 &  1.21 \\
2448752 & 9.00 & 7.07 & 5.10 & 2.12 &  1.20 \\
2448753 & 8.92 & 7.05 & 5.09 & 2.12 &  1.21 \\
2448799 & 9.16 & 7.14 & 5.13 & 2.13 &  1.20 \\
2449050+ & 9.01 & 7.15 & 5.24 & 2.26 &  1.35 \\
2449052+ & 8.98 & 7.14 & 5.24 & 2.26 &  1.35 \\
2449179 & 8.97 & 7.09 & 5.20 & 2.29 &       \\
2449180 & 8.96 & 7.10 & 5.21 & 2.30 &  1.37 \\
2449181 & 8.94 & 7.11 & 5.22 & 2.31 &  1.38 \\
2449182 & 8.92 & 7.11 & 5.23 & 2.32 &  1.39 \\
2449183 & 8.96 & 7.11 & 5.22 & 2.31 &  1.36 \\
2450198+ &      & 7.11 & 5.37 & 2.49 &  1.61 \\
2450890+ & 9.07 & 7.12 & 5.20 & 2.54 &  1.78 \\
\hline
\end{tabular}
\end{table}

\begin{table
\caption{Long-wavelength photometry of WR\,48a with ESO telescopes}
\label{TESOb}
\begin{tabular}{rlrlllll}
\hline
Date    &  \Lp &  $M$  & $N1$ &  $N2$ &  $N3$  &  $Q0$ & Tel. \\
\hline
2445150 & 0.08 & -0.67 & -1.6 & -1.4  &  -1.9  &  -1.7 & 3.6m \\
2445425 & 0.29 & -0.46 & -1.4 & -1.3  &  -1.6  &  -1.5 & 3.6m \\
2446194 & 0.86 & -0.03 & -1.3 & -1.1  &  -1.7  &       & 3.6m \\
2447519 & 1.54 &  0.73 & -0.9 & -0.5  &  -1.4  &       & 1.0m \\
2447987 & 1.81 &  0.80 & -0.8 & -0.6  &  -1.2  & -1.2  & 2.2m \\
2447988 & 1.88 &  0.91 & -0.7 & -0.5  &  -1.3  & -1.3  & 2.2m \\
2448346 & 1.95 &  1.10 & -0.6 & -0.4  &  -1.1  & -1.2  & 3.6m \\
2448347 & 1.96 &  1.09 & -0.6 & -0.3  &  -1.1  & -1.1  & 3.6m \\
\hline
\end{tabular}
\end{table}

\begin{table*}
\caption{SAAO photometry of WR\,48a with the Mk II IR photometer on the 0.75-m
telesope using the 36\arcsec (*or 24\arcsec) aperture.}
\label{TSAAO}
\begin{minipage}{5.5cm}
\centering
\begin{tabular}{lcccc}
\hline
Date & $J$ & $H$  &  $K$  &  $L$  \\
\hline
2445417 & 7.78 & 5.19 & 3.05 & 0.65 \\
2447547 & 8.38 & 6.50 & 4.50 & 1.98 \\
2447553 & 8.34 & 6.49 & 4.57 & 1.98 \\
2447607 & 8.34 & 6.55 & 4.57 & 2.00 \\
2447634 & 8.42 & 6.64 & 4.63 & 2.11 \\
2447669 & 8.39 & 6.59 & 4.62 & 2.08 \\
2447687 & 8.43 & 6.63 & 4.63 & 2.08 \\
2447737 & 8.42 & 6.65 & 4.67 & 2.17 \\
2448028 & 8.36 & 6.66 & 4.77 & 2.24 \\
2448108 & 8.31 & 6.46 & 4.61 & 2.30 \\
2448285 & 8.40 & 6.87 & 4.78 & 2.29 \\
2448289 & 8.42 & 6.70 & 4.78 & 2.31 \\
2448327 & 8.41 & 6.73 & 4.82 & 2.34 \\
2448365 & 8.43 & 6.76 & 4.87 & 2.35 \\
2448378 & 8.38 & 6.73 & 4.85 & 2.41 \\
2448385 & 8.41 & 6.76 & 4.87 & 2.35 \\
2448427 & 8.42 & 6.74 & 4.88 & 2.42 \\
2448437 & 8.41 & 6.74 & 4.89 & 2.41 \\
2448451 & 8.40 & 6.73 & 4.86 & 2.39 \\
2448457 & 8.41 & 6.71 & 4.85 & 2.39 \\
2448462 & 8.40 & 6.72 & 4.85 & 2.38 \\
2448500 & 8.33 & 6.62 & 4.78 & 2.37 \\
2448701*& 8.47 & 6.80 & 4.96 & 2.48 \\
2448734*& 8.54 & 6.83 & 4.98 & 2.51 \\
2448760*& 8.44 & 6.83 & 5.00 & 2.51 \\
2448783 & 8.40 & 6.82 & 5.00 & 2.52 \\
2448792 & 8.46 & 6.85 & 5.01 & 2.54 \\
2448817 & 8.45 & 6.86 & 5.03 & 2.56 \\
2448851 & 8.51 & 6.90 & 5.07 & 2.63 \\
2449001 & 8.48 & 6.94 & 5.11 & 2.60 \\
2449106 & 8.52 & 6.91 & 5.14 & 2.68 \\
2449146 & 8.42 & 6.87 & 5.12 & 2.69 \\
2449221 & 8.44 & 6.90 & 5.14 & 2.75 \\
\hline
\end{tabular}
\end{minipage}
\hfill
\begin{minipage}{5.5cm}
\centering
\begin{tabular}{lcccc}
\hline
 Date & $J$ & $H$  &  $K$  &  $L$  \\
\hline
2449382 & 8.56 & 6.97 & 5.23 & 2.79 \\
2449406 & 8.46 & 6.86 & 5.14 & 2.77 \\
2449501 & 8.35 & 6.62 & 4.91 & 2.68 \\
2449519 & 8.28 & 6.55 & 4.85 & 2.67 \\
2449583 & 8.32 & 6.58 & 4.84 & 2.62 \\
2449590 & 8.34 & 6.59 & 4.84 & 2.59 \\
2449735 & 8.43 & 6.75 & 4.96 & 2.61 \\
2449820 & 8.46 & 6.79 & 4.98 & 2.68 \\
2449887 & 8.46 & 6.85 & 5.04 & 2.68 \\
2450091 & 8.47 & 6.91 & 5.13 & 2.76 \\
2450127 & 8.44 & 6.89 & 5.13 & 2.77 \\
2450178 & 8.45 & 6.95 & 5.21 & 2.75 \\
2450206 & 8.42 & 6.95 & 5.20 & 2.83 \\
2450237 & 8.47 & 6.95 & 5.22 & 2.86 \\
2450259 & 8.49 & 6.95 & 5.23 & 2.90 \\
2450320 & 8.48 & 6.99 & 5.28 & 2.90 \\
2450484 & 8.46 & 7.02 & 5.32 & 2.90 \\
2450591 & 8.46 & 7.07 & 5.44 & 3.03 \\
2450618 & 8.52 & 7.06 & 5.43 & 3.07 \\
2450798 & 8.41 & 6.82 & 5.12 & 2.89 \\
2450980 & 8.44 & 6.92 & 5.23 & 2.98 \\
2451234 & 8.40 & 6.83 & 5.14 & 2.92 \\
2451298 & 8.46 & 6.93 & 5.23 & 2.94 \\
2451358 & 8.45 & 6.93 & 5.21 & 2.99 \\
2451576 & 8.34 & 6.68 & 5.02 & 2.89 \\
2451614 & 8.39 & 6.71 & 4.99 & 2.86 \\
2451677 & 8.42 & 6.75 & 5.02 & 2.86 \\
2451685 & 8.45 & 6.77 & 5.02 & 2.87 \\
2451715 & 8.42 & 6.79 & 5.05 & 2.84 \\
2451743 & 8.43 & 6.82 & 5.06 & 2.86 \\
2451785 & 8.44 & 6.84 & 5.08 & 2.88 \\
2451967 & 8.42 & 6.86 & 5.14 & 2.93 \\
\hline
\end{tabular}
\end{minipage}
\hfill
\begin{minipage}{5.5cm}
\centering
\begin{tabular}{lcccc}
\hline
Date & $J$ & $H$  &  $K$  &  $L$  \\
\hline
2451981 & 8.42 & 6.86 & 5.14 & 2.89 \\
2452070 & 8.40 & 6.78 & 5.06 & 2.90 \\
2452093 & 8.41 & 6.79 & 5.06 & 2.87 \\
2452116 & 8.45 & 6.80 & 5.07 & 2.88 \\
2452290 & 8.52 & 6.85 & 5.10 & 2.90 \\
2452322 & 8.41 & 6.81 & 5.08 & 2.91 \\
2452351 & 8.41 & 6.84 & 5.12 & 2.90 \\
2452383 & 8.42 & 6.80 & 5.11 & 2.94 \\
2452426 & 8.36 & 6.75 & 5.07 & 2.93 \\
2452451 & 8.38 & 6.74 & 5.05 & 2.91 \\
2452694 & 8.44 & 6.87 & 5.18 & 2.97 \\
2452755 & 8.36 & 6.72 & 5.03 & 2.92 \\
2452798 & 8.55 & 6.82 & 5.05 & 2.94 \\
2452868 & 8.38 & 6.68 & 4.97 & 2.86 \\
2453065 & 8.41 & 6.72 & 4.92 & 2.76 \\
2453118 & 8.36 & 6.66 & 4.90 & 2.74 \\
2453177 & 8.22 & 6.42 & 4.70 & 2.61 \\
2453194 & 8.24 & 6.39 & 4.66 & 2.60 \\
2453408 & 8.26 & 6.37 & 4.54 & 2.43 \\
2453442 & 8.31 & 6.42 & 4.55 & 2.42 \\
2453507 & 8.30 & 6.43 & 4.60 & 2.43 \\
2453562 & 8.28 & 6.38 & 4.55 & 2.45 \\
2453906 & 8.19 & 6.05 & 4.19 & 2.14 \\
2453935 & 8.13 & 6.06 & 4.20 & 2.13 \\
2454184 & 7.99 & 5.77 & 3.88 & 1.84 \\
2454234 & 7.93 & 5.70 & 3.81 & 1.75 \\
2455011 & 7.52 & 5.04 & 3.16 & 1.08 \\
2455353 & 7.56 & 4.90 & 2.99 & 0.99 \\
2455621 & 7.21 & 4.71 & 2.86 & 0.82 \\
2455642 & 7.25 & 4.75 & 2.92 & 0.99 \\
2455731 & 7.26 & 4.73 & 2.84 & 0.77 \\
2455733 & 7.24 & 4.72 & 2.85 & 0.77 \\
\hline
\end{tabular}
\end{minipage}
\end{table*}

Photometry of WR\,48a was obtained using aperture photometers on the 1-m, 2.2-m
and 3.6-m telescopes of the European Southern Observatory (ESO) at La Silla, Chile,
(Tables \ref{TESOa} and \ref{TESOb}), the Mk II photometer on 0.75-m telescope of
the South African Astronomical Observatory (SAAO), Sutherland, South Africa
(Table \ref{TSAAO}), and the Infrared Photometer/Spectrometer (IRPS) on the
Anglo-Australian Telescope (AAT) at Siding Spring, Australia (Table \ref{TAAT}).
The final two observations in Table \ref{TESOa} were obtained with the array camera
IRAC-1 on the 2.2-m telescope at La Silla.

During our campaign, the near-infrared (NIR) photometric systems on the three ESO
telescopes were the same, and as described by Bouchet, Manfroid \& Schmider (1991)
and Bersanelli, Bouchet \& Falomo (1991). The final (`Postscript') photometry by
DDWS was on this system, whereas that in the body of their paper was on the earlier
ESO system (Wamsteker 1981), which differed principally in using a filter having
$\lambda_{\rmn{eff}} \simeq$ 3.5--3.6 $\mu$m instead of 3.8 $\mu$m for $L$.
The 3.8-$\mu$m filter is often called `\Lp' to distinguish it from the
shorter-wavelength $L$, a convention we follow here.
The SAAO photometry (Carter 1990) uses a shorter-wavelength ($\lambda_{\rmn{eff}}
\simeq 3.5 \mu$m) $L$ filter.
The  NIR system at the AAT (Allen \& Cragg 1983) also used a 3.8-$\mu$m filter
for \Lp, but their $J$ filter had a slightly shorter $\lambda_{\rmn{eff}}$ than
the ESO $J$ filter and closer to that of the $J$ filter in the SAAO Mk II
photometer (see Glass 1993).

Observations of WR\,48a can be affected by the nearby 11th magnitude star
CPD -62$\degr$ 3058. From HST WFPC2 images, Wallace et al. (2003) measured a
separation $9\farcs2$ and position angle $194\fdg2$, placing it within or
near the edges of some of the apertures used for the photometry of WR\,48a.
To determine the effect of this contribution on the photometry, we observed
CPD -62$\degr$ 3058 with IRIS on the AAT through a 5$\arcsec$ aperture and give the
results, together with magnitudes from the DENIS (Epchtein et al. 1999) and 2MASS
(Skrutskie et al. 2006) surveys, in Table \ref{TCPD}. Despite the scatter in
the data, we assume that the CPD star is not significantly variable in the NIR.
In the $J$ band, the CPD star is 0.2 mag.\, fainter than WR\,48a at its minimum
(2.4 mag. at maximum) and so makes a significant contribution to the $J$
magnitudes observed with the SAAO 0.75-m telescope, which used 36$\arcsec$ or,
occasionally, 24$\arcsec$ apertures (see Table \ref{TSAAO}).
This contribution is much smaller at longer wavelengths, with differences (WR\,48a
minus CPD star) in the ranges $\Delta H = 2 - 5$ mag., $\Delta K = 3.5-6.2$ mag.,
and $\Delta L \simeq 5-8$ mag. corresponding to minima and maxima in WR\,48a.
The AAT photometry used apertures of 5$\arcsec$ or 6$\arcsec$ and that with the
ESO 3.6-m telescope used a $7\farcs5$ aperture, so the CPD star should have been
well excluded.
Depending on the seeing and centring, there might have been some contamination
of observations with the ESO 1-m and 2.2-m photometers, which generally used
15$\arcsec$ and 12$\arcsec$ apertures. We searched for this by comparing the
dispersion in the $J$ magnitudes when WR\,48a was observed on successive nights
in an observing run (Table \ref{TESOa}) with the dispersion in $K$,
where any contamination by the CPD star would be at least a factor of 20 smaller,
but found no significantly greater dispersion in $J$.

\begin{table}
\caption{Infrared photometry of WR\,48a with the IRPS on the AAT}
\label{TAAT}
\centering
\begin{tabular}{lccccc}
\hline
Date    & $J$  &  $H$ &  $K$ &  \Lp & $M$   \\
\hline
2446309 & 8.61 & 5.94 & 3.73 & 1.00 & -0.11 \\
2446595 & 8.88 & 6.17 & 4.00 & 1.11 &       \\
2446716 & 8.98 & 6.28 & 4.07 & 1.18 &       \\
2446888 & 8.76 & 6.40 & 4.26 & 1.31 &       \\
2447614 & 8.97 & 6.77 & 4.70 & 1.71 &       \\
\hline
\end{tabular}
\end{table}

\begin{table}
\caption{Infrared photometry of CPD -62$\degr$ 3058 with the IRPS or from surveys.}
\label{TCPD}
\centering
\begin{tabular}{lcccccc}
\hline
Date    & $J$  &  $H$ & $Ks$ &  $K$ &  \Lp & source  \\
\hline
2446888 & 9.48 & 9.20 &      & 8.99 &      & AAT  \\
2447614 & 9.39 & 9.13 &      & 8.97 & 8.53 & AAT  \\
2450501 & 9.33 &      & 8.86 &      &      & DENIS \\
2450973 & 9.28 &      &      &      &      & DENIS \\
2451595 & 9.30 & 9.13 & 8.90 &      &      & 2MASS \\
\hline
\end{tabular}
\end{table}

\subsection{Homogenizing the NIR photometry}

\begin{table}
\caption{Zero points for the photometric systems employed and our {\em ad hoc}
adjustments applied to the $L/L^{\prime}$ photometry of WR\,48a, the bands being
identified by their wavelengths.}
\label{Tzero}
\centering
\begin{tabular}{lcccccc}
\hline
System          &  $H$  &  $K$  &  3.5  &  3.6  &  3.8  \\
\hline
AAT             & -0.02 & -0.01 &       &       & -0.03 \\
pre-1982 ESO    & -0.03 & -0.01 &       & 0.04  &       \\
post-1982 ESO   & -0.06 & -0.03 &       &       & -0.01 \\
SAAO            & 0.00  & 0.00  &  0.00 &       &       \\
adjustments  &       &       &  0.00 & 0.18  & 0.38  \\
\hline
\end{tabular}
\end{table}

In order to determine the evolution of the dust emission by WR\,48a from the IR
photometry, it is necessary to consider the relations between the different systems.
The zero points of the systems are fairly similar (Table \ref{Tzero}, compiled from
Cohen et al. 1999) but the redness of WR\,48a compared with the photometric standards
is more of a problem.
Bouchet et al. (1991),
Carter (1990), and Allen \& Cragg (1983) all derive colour transforms between their
and other NIR photometric systems, none of these extend to objects as red as
WR\,48a: most comparisons are based on stars having ($J-K$) $<$ 1.1, whereas
WR\,48a generally has ($J-K$) $\simeq 4.0$.
We therefore estimated {\em ad hoc} transformations for WR\,48a, concentrating
on the various $L$ and $L^{\prime}$ systems, as the filters for these have very
different wavelengths. We relate the AAT and two sets of ESO photometry
to the corrected SAAO data as the last forms the largest homogeneous dataset.

To relate the post-1982 ESO photometry of WR\,48a to the corrected SAAO photometry,
we compared contemporaneous observations, i.e., those made within about 0.02 yr of
each other, sometimes using successive observations at one observatory to bracket
those made at the other and avoiding times when WR\,48a appeared to be changing rapidly.
This gave eight useful comparisons between 1983 and 1993, yielding differences in
the sense SAAO minus ESO: $\Delta J = -0.09\pm0.04$, $\Delta H = 0.07\pm0.03$,
$\Delta K = 0.04\pm0.01$ and $L-L^{\prime} = 0.38\pm0.06$, while the ESO ($J-K$)
colour of WR\,48a was in the range 4.8--3.9. The difference $L-L^{\prime}$ is
much greater than that found by Bouchet et al. (1991) for stars having
($J-K$)$<$1.0, but not surprising given the difference between the two
filters and the extreme redness of WR\,48a.
Attempts to derive a colour equation, such as a linear fit of the differences to
($J-K$), did not yield statistically significant coefficients, so we restricted
ourselves to applying a constant difference, $L-L^{\prime} = 0.38$, to our ESO
photometry (and to the final, 1982, observation by DDWS) of WR\,48a to bring the
data into line with the SAAO photometry for the production of homogeneous light
and colour curves.

For the earlier ESO photometry of WR\,48a in DDWS, we do not have
contemporaneous SAAO observations for direct comparison.
Instead, we used the photometry of WR stars by Pitault et al. (1983), which was also
on the older ESO system and included two dust-emitting WC9 stars having ($J-K$)
comparable to that of WR\,48a as an intermediate step. Comparison of their
photometry of WR\,104 and WR\,106 with observations of these stars by WHT, which
was on the post-1982 ESO system, suggests an offset $L$--\Lp = 0.20.
This is about half the difference between \Lp and the SAAO $L$,
as one might expect from the fact that the efective wavelength of the older ESO $L$
filter lies between those of \Lp and the SAAO $L$. To convert DDWS $L$ magnitudes of
WR\,48a to the SAAO $L$ scale, we therefore added 0.18 mag., and made no adjustments
to $H$ or $K$.

Four of the AAT observations of WR\,48a are contemporaneous with observations at ESO
or SAAO, from which we infer an offset $L$--\Lp = 0.34, comparable to that for the
ESO photometry, as one might expect from the similarity of the filter wavelengths.
Inspection of the AAT $H$ and $K$ data suggests that there is no significant shift
between them and the ESO data.

We applied these differences to the AAT and the two sets of ESO photometry and
combined them with the corrected SAAO photometry to produce a homogeneous photometry
set in $HKL$. The light curves from these data and the mid-IR photometry in Table
\ref{TESOb} are discussed below, and the trajectory in the near-IR colour-magnitude
diagram is discussed in Section \ref{SCMD}. The adjusted $L/L^{\prime}$ magnitudes
are not used for production of the SEDs in Sections \ref{SSED} and \ref{SModels}
where the calibrated fluxes are entered at their respective wavelengths.

\subsection{Optical spectroscopy}
\label{SOpt}

\begin{figure}
\centering
\includegraphics[width=9cm]{wr48arn.eps}
\includegraphics[width=8.8cm]{wr48abn1.eps}
\includegraphics[width=8.5cm]{wr48asc3.eps}
\caption{Optical spectra of WR\,48a. Top: 18-\AA-resolution spectrum observed in
1993. The 10830-\AA\ line is truncated to allow the weaker lines to be more easily
seen. Middle: 7.4-\AA-resolution spectrum observed with the blue arm on the same time.
Bottom: blue spectrum of WR\,48a observed in 2001 with EMMI on the NTT,
blocked to 3-\AA\ bins.}
\label{FOpt}
\end{figure}

New spectra were observed for us with the RGO spectrograph on the Anglo
Australian Telescope on 1993 June 21, when the NIR emission had faded about
2.5 mag.\ from maximum (cf. Fig\,\ref{FHKL}). In the blue, the resolution
was 7.4\AA\ while that in the red, observed simultaneously, was 18\AA.
A spectrum of the metal-poor star HD 184711 observed on the same night was
used to help with removal of telluric absorption features in the red.
Rectified spectra are shown in the first two panels of Fig. \ref{FOpt}.
The correction for the strong telluric absorption in the A band (7630\AA)
was incomplete because HD 184711 was observed at a rather lower airmass
than WR\,48a.

The `red' spectrum resembles that in DDWS, but the emission lines appear
more strongly.
We measured equivalent widths (EWs) of the strong He\,{\sc i} 10830-\AA\
and C\,{\sc iii} 9715-\AA\ lines to be 280\AA\ and 118\AA\ respectively,
compared with EWs of $\sim$ 63\AA\ and 46\AA\ estimated from fig.\,3 of DDWS.
Taken at face value, these differences suggest that, at the time (1980 January)
DDWS's spectrum was observed, these emission lines were diluted by additional
contimuum emission of factors 1.6 -- 3.4 above the stellar continuum between
9715\AA\ and 10830\AA\, possibly by the newly formed dust, which is considered
below.

The 10830-\AA\ emission line falls close to the blue edge of the $J$ filter
and line emission can contribute to the $J$ magnitudes. For example, the
transmission of the $J$ filter in the SAAO Mk II IR photometer (Glass 1993)
is about 50\% maximum at this wavelength while that of the post-1982 ESO $J$
filter (Bersanelli et al.) is nearer 20\%. The other optical components and
the atmosphere will reduce these percentages.
The corresponding contributions of the 10830-\AA\ line to $J$ magnitudes
observed with the Mk II photometer at the times of the 1980 and 1993 spectra
would then be 0.01 and 0.05 mag. for a flat continuum across the $J$-filter
passband, and somewhat less for a rising dust continuum, while the contributions
to the ESO $J$ magnitudes would be about half these values. We did not adjust
$J$ photometry {\em en masse} but did adjust the SAAO $J$ magnitude used for
the SED near minimum (Section \ref{SSED}) for the 10830-\AA\ line contribution.

We were not able to measure a P~Cygni absorption component of the 10830-\AA\
line, but its FWZI of 90~\AA\ allows us to estimate the wind velocity to be
$v_{\infty} \simeq 1200\pm170$ km~s$^{-1}$. This is lower than the average
(1700 km~s$^{-2}$) for WC8 stars (van der Hucht 2001, table 27) and equal to
that for WC9 stars. This line needs to be re-observed  at higher resolution
and higher S/N ratio to to refine our measurement. (The broad C\,{\sc iii}
feature at 9715\AA\ is a multiplet with components ranging 9704--9720\AA.)

We measured the 6284-\AA\ diffuse interstellar band to have an EW of 3.1~\AA,
comparable to the value (2.8\AA) in the 1986 spectrum, observed when the dust
emission was greater (Williams, van der Hucht \& Th\'e 1987b) , so it is
unlikely that this feature has a circumstellar component.

After the 10830-\AA\ line, the strongest emission line is that at 6570\AA\
(EW 73\AA). This is much stronger than the C\,{\sc iii} 9715-\AA\ feature,
whereas it is weaker than the C\,{\sc iii} lines in the spectra of the WC8+O9
systems WR\,11 ($\gamma$ Vel) and WR\,70 presented by Vreux, Dennefeld \&
Andrillat (1983), and significantly weaker in the single WC8 star in their
sample, WR\,53 (since reclassified WC9 by Crowther, de Marco \& Barlow 1998).
The identification of the 6570-\AA\ feature is difficult.
DDWS identified it with $\lambda$6560 He\,{\sc ii} (Hu$\beta$),
but we consider any contribution of He\,{\sc ii} -- which we cannot rule
out given the resolution of the spectrum -- to be small, because of the
weakness or absence of the Hu$\alpha$ line at 10124\AA. There may be a
small Hu$\alpha$ contribution to the C\,{\sc iii-iv} feature at 10130\AA,
but the Hu$\beta$ line would be even smaller.
Another contributor to the 6570\AA\ feature is multiplet~2 of C\,{\sc ii}.
The spectra of WR\,11, WR\,53 and WR\,70 (Vreux et al.) suggest that the
strength of this should be comparable (within a factor of 2) to that of
multiplet~3 of C\,{\sc ii} at 7236\AA; but the 6570-\AA\ line is a factor
of about 16x stronger in our spectrum of WR\,48a, so C\,{\sc ii} cannot be
the dominant contributor. Another possible
contributor to the 6570\AA\ feature in low-resolution spectra of WR\,48a is
the C\,{\sc iv} line at 6592\AA. This line accounts for the rising ratio of
the 6570\AA\ and 7236\AA\ C\,{\sc ii} lines in the spectra of earlier
subtype WC stars (cf. Vreux et al.), but nowhere is the ratio as high as it
is observed in WR\,48a -- nor are the other C\,{\sc iv} lines in our
spectrum found to be anomalously strong.
No other plausible WC8 lines seem capable of explaining
the strength of the 6570\AA\ feature. We suggest it comes from H$\alpha$,
either from a nebula very close to the star (not resolved in the long-slit
spectrum) or from an Oe or Be stellar companion to the WC star.

Owing to the heavy reddening of WR\,48a, the blue spectrum
is very noisy at short wavelengths, and only that longward of 4200\AA\ is
considered useful. The only convincing feature in the blue is the blend of
C\,{\sc iii} 4649\AA\ and He\,{\sc ii} 4686\AA. This is very weak, having an
equivalent width (EW) of 36\AA, compared with the EW of 410\AA\ of the same
feature measured from the low-resolution spectrum of the single WC8 star
WR\,135 observed by Torres \& Massey (1987). There is a possible feature at
the position of the 4325-\AA\ C\,{\sc iii} line and a stronger, narrow line
at 4868 \AA\ which might be H$\beta$ emission from the proposed companion.

The spectrum in the yellow is similar to that observed in 1986 (WHT).
Compared with the WC8 spectra in Torres \& Massey, the He\,{\sc i} 5896-\AA\
line in WR\,48a appears abnormally strong relative to the C\,{\sc iii} and
C\,{\sc iv} lines. This is not a question of the classification of WR\,48a:
the WC9 spectra in Torres \& Massey have the He\,{\sc i} comparable in
strength to the C\,{\sc iv} line but much weaker than C\,{\sc iii}.
The carbon lines are much weaker: the EWs of the 5696-\AA\ and
5813-\AA\ features in WR\,48a are 49~\AA\ and 41~\AA\ repectively, one
quarter their values in WR\,135 (197~\AA\ and 185~\AA\ respectively).

We take relative weakness of the C\,{\sc iii} and C\,{\sc iv} lines as evidence
for their dilution, in this wavelength region, by the proposed stellar companion.
Taking the ratios of 5696-\AA\ and 5813-\AA\ lines in WR\,48a and the WC8 standard
WR\,135, the companion would be $\sim 3 \times$ (1.2 mag.) brighter than the WC8
star in $V$ and the total luminosity $\sim 4 \times$ (1.5 mag.) brighter.
If the WC8 star had $M_V = -3.7$ (cf. $M_v = -3.7\pm0.5$ for WC8 stars in clusters
and associations, van der Hucht 2001), the companion would have $M_V \simeq -4.9$,
comparable to that of an O6V star (Martins, Schaerer \& Hillier 2005), and the
system would have $M_V \simeq -5.2$. At 4 pc, this would be $V_0 = 7.8$ which,
reddening by $A_V = 9$, would give $V=16.8$, close to the $V=17.1$ observed by
Baume et al. and potentially resolving the discrepancy between the spectroscopic
distance to WR\,48a and that of the clusters. Fitting the observed $V$ magnitude
and retaining the adopted distance and reddening would give O5V for the companion
and $M_V = -4.0$ for the WC8 star, still within the range for its spectral type.
The total luminosity of the WR\,48a system would be $\sim 4\times 10^5L_\odot$,
which matches that found by Clark \& Porter (2004).

In an attempt to classify the companion, we re-observed WR\,48a in the blue
using the ESO Multi-mode Instrument (EMMI) on the 3.6-m New Technology Telescope
(NTT) at La Silla on 2001 June 17-19 to look for absorption lines.
The spectrum in the bottom panel of Fig.\,\ref{FOpt}
is blocked down to 3-\AA\ bins to improve the S/N ratio. The C\,{\sc iii}
4649-\AA\ triplet is present about 50\% stronger than in the low-resolution
spectrum but we do not confirm the C\,{\sc iii} 4325-\AA\ line, nor do we see
any evidence for emission at the position of C\,{\sc iv} 4441\AA\ usually seen
more strongly in WC8 and still present in WC9 spectra. Evidently, the continuum
from the companion is dominant in this wavelength region and it is disappointing
not to observe absorption lines from it, apart from a possible weak line at the
position of B$\gamma$, which may owe its weakness to partial infill by emission.

The formal classification of the WC star is clearly WC8 from the ratio of
the C\,{\sc iii} 5696-\AA\ and C\,{\sc iv} 5813-\AA\ features but it appears
to be atypical in terms of He\,{\sc i} strength and wind velocity. Without the
absorption lines, the companion cannot be classified, but estimates of its
luminosity adopting a distance of 4~kpc and $A_V = 9$ suggests an O5Ve star
and gives $M_V = -4.0$ for the WC8 star.

\subsection{Infrared spectroscopy}

\begin{figure}
\centering
\includegraphics[width=9cm]{wr48aksc.eps}
\caption{Two-micron spectrum of WR\,48a observed with IRIS and formed from
the 5th and 6th order HK echelle spectra. The spectrum of WR\,48a at this
wavelength is dominated by the dust emission, most of which is suppressed
in the figure to show up the lines.}
\label{FIRISK}
\end{figure}

The infrared spectrum of WR\,48a is dominated by dust emission, but it is
still possible to see the line spectrum on top of this in the near IR.
Low-resolution NIR spectra were observed for us using the InfraRed Imaging
Spectrograph (IRIS) on the AAT on 1995 August 15.
The $HK$ echelle gave a spectral resolution of $R = 400$. The spectrum
in the 2-micron region is shown in Fig.\,\ref{FIRISK}. Comparison with the
spectra of WC8 and WC9 stars discussed by Eenens, Williams \& Wade (1991)
and Figer, McLean \& Najarro (1997), particularly the relative strengths
of the C\,{\sc iv} triplet at 2.07-08 $\mu$m and C\,{\sc iii}/He\,{\sc i}
blend at 2.11 $\mu$m shows that WR\,48a is a closer match to the WC9 spectra
than the WC8 star WR\,135. Stronger than either of these features in WR\,48a
is the He\,{\sc i} 2.06-$\mu$m line, also strong in the WC9 stars WR\,121
and WR\,119 (cf. Figer et al.) but not WR\,88 (cf. Eenens et al.).
Of particular interest is the strength of the 2.16-$\mu$m He\,{\sc i}
feature, which is stronger then the other lines in any of the WC8 or WC9
spectra in Eenens et al. and Figer et al. We suggest one possible reason
for this is a contribution from Br $\gamma$ from the companion to the WR star.

\section{Evolution of the dust emission from WR\,48a}
\subsection{Infrared light curves}
\label{SCurves}

\begin{figure*}
\centering
\includegraphics[width=13cm]{HKLLp1.eps}
\caption{Synoptic $H$, $K$ and $L$ light curves of WR\,48a from SAAO data
corrected for contamination from CPD -62$\degr$ 3058 and the ESO and AAT data
adjusted as described in the text. Given the long time-scales, we use
civil dates for discussion of the dust emission. The $L$ magnitudes from
different sources are plotted with different symbols and show concordance
where they overlap.}
\label{FHKL}
\end{figure*}

The light curves in $H$, $K$ and $L$ from the homogenized NIR data are shown in
Fig.\,\ref{FHKL}. We see that the flux faded until about 1997, after which it grew
very slowly until about 2003, and then began rising again. In $K$ it reached the
level of DDWS's first (1978) observation in 2010 and continued brightening,
albeit more slowly.

Superimposed on the long-term variation are secondary episodes in 1990, 1994--5,
1999--2000, 2004 and perhaps 1997--8 and 2010--11. The best defined is that in 1994--95.
From 1994.1, the flux rose to maximum in 1994.4 ($J$ and $H$) to 1994.6 ($K$ and $L$)
and then gradually faded through 1995 and 1996. The rates of fading are strongly
wavelength dependent ($\simeq$ 0.38 mag.y$^{-1}$ in $J$, 0.34 mag.y$^{-1}$ in $H$,
0.22 mag.y$^{-1}$ in $K$ and 0.15 mag.y$^{-1}$ in $L$) and the evolution of the IR
colour (Section \ref{SCMD}) is consistent with the formation and cooling of extra dust.
Within the coverage of the observations, the other episodes have similar shapes: a
steep rise for about 0.4 yr followed by a slower decline. Simple modelling of the
SED of the epsiode is discussed in Section \ref{SModels}.
To determine the timing of other episodes, we shifted the $H$ and $K$ light curves
defining the 1994 mini outburst to those near the other events and used the best
fits to measure the shifts to the other events, deriving --3.95 yr, +3.3 yr, +5.4 yr
and +10.2 yr, giving intervals between the mini epsiodes of 3.95 yr, 3.3 yr, 2.1 yr
and 4.8 yr. There is no suggestion of periodicity in these data.
The $J$, $H$ and $L$ photometry of DDWS suggests that there was another in 1980, but
this is not evident in their $K$ photometry. It is possible that there
were mini episodes between then and 1990, but the data are too sparse to be certain.
As discussed in Section \ref{SCMD}, the trajectory in the NIR colour-magnitude
diagram points to more secondary outbursts, including a possible one in 2010--11.
These irregularities suggest that the IR light curves will not repeat exactly and
will make it hard to determine a photometric period without several more years
observations but the present data suggests a period a little longer than 32 years
and we will discuss WR\,48a in the framework of its being a long-period CWB.

\begin{figure}
\centering
\includegraphics[width=7cm]{LMNN.eps}
\caption{Mid-IR light curves of WR\,48a during 1979 maximum and subsequent fading.
}
\label{LMNN}
\end{figure}

We tracked the fading of the dust emission at longer wavelengths and show light
curves in $N3$ (12.8$\mu$m), $N1$ (8.4$\mu$m), $M$ and $L$, together with $N$ from
DDWS in Fig.\,\ref{LMNN}. As can be seen from Table \ref{TESOb}, the $N2$ and $Q$
magnitudes follow the same trend ($N2$ is always fainter than $N1$ and $N3$ owing
to the coverage by this band of the strong silicate absorption feature) but are
omitted from Fig.\,\ref{LMNN} for clarity.
Between 1983 and 1991, the rates of fading are strongly wavelength dependent:
0.07 mag~yr$^{-1}$ in $N3$, 0.08 mag~yr$^{-1}$ in $N1$, 0.16 mag~yr$^{-1}$ in $M$
and 0.17 mag~yr$^{-1}$ in $L$, showing continued cooling of the dust.
Between the 1979 maximum and our first mid-IR photometry the fading appears to
be slower, and at 20 microns our $Q0 = -1.7\pm0.2$ is comparable to $O = -1.652\pm0.2$
observed by DDWS, reminiscent of the behaviour of WR\,140, where the long-wavelength
fluxes brightened a year after maximum (Williams et al. 2009b).

\subsection{Synopsis of dust evolution from the infrared colour-magnitude diagram}
\label{SCMD}
\begin{figure}
\centering
\includegraphics[width=8.5cm]{KLHCMDg2p1.eps}
\caption{Trajectory of WR\,48a in the ($H-L$), $K$ colour-magnitude diagram from
the first observation by DDWS in 1978 to 2011.5. The data are gridded to 0.2-yr
bins and the numbers of observations contributing to
each point are marked with different symbols.}
\label{CMD}
\end{figure}

There are three principal processes determining the evolution of the dust made by
a system like WR\,48a and its infrared emission (cf. consideration of the dust
made by the archetypal dust-making CWB WR\,140 by Williams et al. 2009b).
These are the nucleation of new grains within the compressed stellar winds, the
growth of the grains by accretion of carbon ions as they are accelerated through
the wind by radiation pressure, and the cooling of the grains as they move away
from the stars and the stellar radiation heating them is progressively diluted.
The nucleation process is not understood, observations indicate that the newest
grains have temperatures in the region of 1200~K (e.g. WHT, Williams et al. 2009b).
The growth of the grains can also cause them to cool as they become relatively
more efficient coolants than small grains. Their velocity from the stars is
initially that inherited from the compressed wind, and is increased by radiation
pressure on the grains until they reach a drift velocity relative to the wind
when the radiative acceleration is balanced by supersonic drag.

Compared with the case of WR\,140, we know less about the WR\,48a system, e.g.
velocity of the dust and its distance from the stars and stellar luminosity,
and modelling is premature, but we can at least qualitatively identify these
processes from the SEDs of WR\,48a and its IR colour and magnitude.

\begin{figure}
\centering
\includegraphics[width=8.5cm]{KLHCMDhs2.eps}
\caption{Detailed view of WR\,48a in the ($H-L$), $K$ colour-magnitude diagram
in 1993--2004 showing trajectories around the mini-outbursts in 1994--5,
1999--2000 and, possibly, 1997--8. The symbols are as in Fig.\,\ref{CMD}, and
are joined by solid lines when the time bins are consecutive and by broken lines
when the gaps are greater than 0.2 yr.}
\label{CMDhs}
\end{figure}

We formed a colour-magnitude diagram from our corrected and adjusted photometry
to track the evolution of the dust. For the amount of hot dust, we chose $K$
magnitudes, and straddled this with ($H-L$) as the best indicator of the
temperature of the newly formed hot dust.
Sometimes WR\,48a was observed several times in a short interval, so we have
gridded the data to avoid confusion in the diagram and also increase the accuracy
of the points where they come from averages of two or more observations. From
experimentation, we found a grid size of 0.2 yr gave a good balance preserving
information and providing clarity. The CMD is shown in Fig.\,\ref{CMD}.

Initially, in 1978--1979.2 (DDWS's observations between JD 2443739 and 2443954),
we observe the flux brightening while the colour did not change.
We attribute this to the formation of new dust at a higher rate than before.
The constant colour implies a constant temperature, that at which the dust
was condensing, and its persistence shows that the SED was dominated by emission
from the hottest, newest dust, -- i.e. that the nucleation rate exceeded the
rate at which the dust was carried away in the wind.
During 1979, the dust emission cooled while the $K$ flux barely changed.
This can also be seen in DDWS's light curves: after JD 2443954, the $L$ and $M$
fluxes grew while $K$ and $H$ fell slightly.
(DDWS consider their $J$ magnitudes might be affected by emission-line flares.)
We interpret this phase as the continued growth of the newly formed grains
while the nucleation process itself had slowed; if the grains did not grow,
then the flux at all the wavelengths would {\em start falling  at the same time}
as the grains were carried away from the star and cooled as the stellar
radiation heating them was progressively diluted.
After 1979 (DDWS's photometry on JD 2444215), fluxes at all wavelengths faded
and the colour became redder owing to cooling of the dust as the condensation rate
slowed. The CMD shows continued fading, with ($H-L$) reaching a maximum at 1987.2.
The fall in average dust temperature implied by the reddening in ($H-L$) is
interpreted as indicating that the dust being continually carried away from the
star was no longer being replenished by the condensation of new grains at the
same rate as before.
After 1987, the ($H-L$) gets bluer again while the $K$ flux continues to fade.
We interpret this as an indication that the dust formed in the 1979 maximum had
now cooled sufficiently that its SED was no longer dominating the $L$ band emission.
At longer wavelengths, continued cooling after 1987 can be seen from the the
mid-IR colours (Table \ref{TESOb}): e.g. ($L^{\prime}-N1$), which had increased
from 1.6 in 1982 to 2.4 in 1988 (JD 2447519), continued increasing to 2.6 in 1991
(JD 2448345,7). Some of the SEDs are compared in Fig.\,\ref{Cooling} below.

Sharp blueward movement in ($H-L$) accompanied by rises in $K$ were observed in
1990 and 1994, the times of the mini episodes seen in the light curves.
These changes are interpreted as the consequence of additional episodes of dust
formation: the bluer ($H-L$) being a consequence of the addition of hot dust at
the condensation temperature, while the total NIR emission rises.
We have sufficiently frequent observations to track the evolution of the dust
emission in the 1994--95 event. This is shown in more detail in Fig.\,\ref{CMDhs}.
After the minimum in ($H-L$), the emission gets redder while $K$ continues rising
(1994.4--1994.6). This implies that nucleation of grains has ceased but that the
mass of dust continues to rise as the grains grow by accretion. After 1994.6,
the emission fades and the dust continues cooling as it is carried away in the
wind. Part of a similar clockwise trajectory can be seen in 2000.0--2000.6, and
smaller bits of the others can be discerned.

After the $K$ minimum in 1997.4, and mini eruptions, the ($H-L$) is increasingly
influenced by newly formed hot dust and remains blue as the $K$ brightens, with
a superimposed secondary outburst in 2010.4--2011.3. Generally, however, the
$K$, ($H-L$) slope in the CMD of the major rise to maximum differs from those
of the mini episodes in that the brightening $K$ due to increased dust is not
accompanied by further blueing of ($H-L$): the blue limit must be set by the
dust condensation temperature.

\subsection{Spectral Energy Distributions (SEDs)}
\label{SSED}

\begin{figure}
\centering
\includegraphics[width=8cm]{Cooling.eps}
\caption{SEDs of WR\,48a as it faded after maximum in 1979: $\triangle$ photometry
by DDWS in 1979.5; $\oplus$ our mid-IR photometry on JD 2445150 combined with
DDWS's NIR photometry of 33 days later; $\bullet$ our photometry in mid-1985; and
$\diamond$ our photometry in 1990.3. The optical data come from $B$ and $V$
observed in 2006 by Baume et al. (2009), see text. All the photometry was de-reddened
by $A_V = 9$. The dashed line through the 1979
points is a 1210-K Planck function for reference.}
\label{Cooling}
\end{figure}

A set of SEDs illustrating the cooling and fading of the dust between maximum and
our photometry in early 1990 (before the mini dust-formation episode described
above) derived from the photometry is given in Fig.\,\ref{Cooling}. Following
the discussion in Section 1, we de-reddened the photometry with a standard
interstellar law for $A_V = 9.0$.
The dashed line through the fluxes at maximum is a 1210-K Planck function for
reference -- but it may be a good description of the dust SED at this phase if
the emission is optically thick. The IR luminosity at maximum
($5.6\times10^{-11}$Wm$^{-2}$, about $2.8 \times 10^5 L_{\odot}$ at the adopted
distance of 4~kpc) is about 70 per cent of the total stellar luminosity,
$\sim 4\times10^5 L_{\odot}$ for the WC8 star plus its proposed O companion.
This is the fraction of the stellar UV-optical flux that is absorbed and
re-radiated by the dust, and would give the UV-optical depth in the dust if it
were uniformly distributed around the stars; but we know from the images that
the dust is not symmeterical, so some sightlines will have greater optical depth.

A Planckian SED in the $\log\lambda F_{\lambda}$ {\em vs.} $\log\lambda$ plane is
isomorphic with temperature and flux level, so the broader SEDs seen as the dust
cools in 1979--90 indicate that we are observing dust having a greater range of
temperature.

We can extrapolate the 1979.5 SED shortwards to 1 micron to investigate the
possible dilution of the 10830-\AA\ and 9710-\AA\ emission lines in DDWS's
1980 spectrum by dust emission. This extrapolation, reddened by $A_V = 9$,
gives a dust-emission magnitude at 1 micron of 10.4.
This is significantly brighter than the 1-micron magnitude ($\sim$ 12.1)
extrapolated from the 2006 $BVIc$ photometry by Baume et al. (2009) and
would provide the additional wavelength-dependent continuum emission implied
by the dilution of the longest wavelength lines in the 1980 spectrum. At
shorter wavelengths, this is not a problem: the reddened dust-emission $Ic$
is 14.8, significantly fainter than the $Ic = 13.25$ observed by Baume et al.

Even at minimum, we can see from the spacing of light curves that there was still
significant dust emission by WR\,48a. We examine the SED in 1996, near IR minimum
by combining the SAAO $JHKL$ photometry observed on JD 2450127, contemporaneously
with the {\em ISO}-SWS spectrum presented in Paper~I. Convolution of the SWS
spectrum with the $L$ filter passband recovers the observed $L$ magnitude.
The SED (Fig.\,\ref{SEDs3}) showing strong dust emission, and the absence of further
fading after 1997 to the stellar wind level, demonstrate continuing dust formation,
which replenishes that carried away in the stellar wind.
In this respect, WR\,48a differs from the episodic dust makers like WR\,140, and
resembles the variable dust-maker WR\,98a discussed in Paper I.

To estimate the SED during the rising branch of the light curve, we retrieved mid-IR
fluxes for WR\,48a observed (as AKARI-IRC-V1 J1312398-624255) in the {\em AKARI}
IRC Survey (Ishihara et al. 2009) from the ISAS/JAXA Archive. These data come from
six scans made between 2006 May and 2007 August and we combined them with $JHKL$
observed in 2006 (JD 2453906 and 2453935). Comparison of the {\em AKARI} 9-$\mu$m
and 18-$\mu$m fluxes with the {\em ISO}-SWS SED (Fig.\,\ref{SEDs3}) suggests that
the mid-IR flux from WR\,48a barely changed over the decade between the two
missions, although we note that the breadth of the $S9W$ and $L18W$ filters used
for the IRC survey and their coverage of the `silicate' bands requires
care in the conversion of in-band fluxes to monochromatic fluxes for a SED and
the observed and extinction-corrected {\em ISO}-SWS spectra need to be convolved
with the {\em AKARI} IRC optics to examine this further.
For the present, we note that while the mid-IR flux barely changed, the near-IR
has increased significantly between 1996 and 2006, indicating the formation of
new hot dust.

The optical data in Figs \ref{Cooling} and \ref{SEDs3} ($B$, $V$ and $Ic$) come
from the photometry in 2006 by Baume et al. (2009).
Their $V = 17.13$ agrees well with the HST WFPC2 magnitude $F555W = 17.08$ observed
on 1996 July 4\footnote{Date is from the HST archive.} by Wallace et al. (2003),
while the difference between their $B = 19.37$ and Wallace et al.'s $F439W = 19.79$
is readily understood in terms of the longer wavelength cutoff of the $B$ filter
and the red colours of WR\,48a, which lie outside the range of colours for which
the transformations between WFPC2 and $UBV$ colours given by Holtzman et al.
(1995) apply. Hence, the $B$ and $V$ are a good measure of the optical flux from
WR\,48a at the times of our SEDs in both 2006 and 1996 at least.
We note that the $Ic = 13.25$ measured by Baume et al. is significantly fainter
than the $i$ = 12.50 and 12.58 observed in the DENIS survey (Epchtein et al. 1999)
in 1997 and 1998 respectively.
This cannot be emission by the hot dust as we can see (Fig.\,\ref{SEDs3}) that
there was more hot dust emission in 2006 than in 1997, and further observations in
this wavelength region are needed to look for variability.

\begin{figure}
\centering
\includegraphics[width=8cm]{SEDs3ir.eps}
\caption{SEDs of WR\,48a at three phases: $\triangle$ the IR maximum 1979.5 observed
by DDWS; $\oplus$ close to IR minimum from our $JHKL$ photometry in mid-1996 soon
after the {\em ISO}-SWS spectrum from Paper~I, solid line; and $\diamond$ while
the IR flux was rising from our $JHKL$ photometry in mid-2006 with 9-$\mu$m and
18-$\mu$m fluxes observed by {\em AKARI} in 2006--07.
The optical flux points come from $BVIc$ photometry by Baume et al. in 2006, with
$B$ and $V$ supported by HST WFPC2 $439W$ and $556W$ photometry in 1996, see
text. All the photometry was de-reddened by $A_V = 9$; the {\em ISO} spectrum was
der-reddened by nulling the 9.7-$\mu$m silicate feature.}
\label{SEDs3}
\end{figure}

\subsection{Modelling the SED of the `mini' eruption}
\label{SModels}

At its simplest, the IR SED of dust emission is given by the convolution
of the grain emissivity, $\kappa_{\lambda}$, and the Planck function for
the dust temperature, $T_{\rmn{g}}$:
\[
4 \pi d^2 F_{\lambda} = m_{\rmn{d}} \kappa_{\lambda} B(\lambda, T_{\rmn{g}})
\]
\noindent where $d$ is our distance to the dust, $m_{\rmn{d}}$ is the dust
mass and the emission is optically thin in the IR. Given $\kappa_{\lambda}$,
the temperature of the grains can be found by fitting the SED over a suitable
wavelength range, followed by the dust mass from the overall fit and distance, $d$.
We calculated $\kappa_{\lambda}$ from the optical properties of the `ACAR'
amorphous carbon grains prepared in an inert atmosphere in the laboratory
by Colangeli et al. (1995) and tabulated by Zubko et al. (1996).
Model SEDs calculated using the `ACAR' data gave a better fit to broad
features in the 5.5--6.5 $\umu$m {\em ISO} spectra of dust-making WC8--10
stars (Williams, van der Hucht \& Morris, 1998) than those based on the
`ACH2' grains produced by Colangeli et al. in a hydrogen atmosphere --
as one might expect for grains formed in hydrogen-poor WC stellar winds.
A comparison of several laboratory analogues of cosmic amorphous carbon grains
by Andersen, Lodl \& H\"ofner (1999) shows that their absorption efficiencies
have fairly similar wavelength dependencies, $\kappa \propto \lambda^{-1.1}$,
in the IR, but absolute values ranging by a factor of $\sim$ 5. Consequently,
the grain temperatures derived from fitting IR SEDs are relatively insensitive
to the choice of grain sample, but not the masses of the dust clouds.
Usually, circumstellar grains are not all at the same temperature, but have a
range of temperature depending on their distances, $r_*$, from the star(s)
heating them, and also on their size. For small `ACAR' grains and in the absence
of significant UV-visual optical depth, the temperatures of grains in thermal
equilibrium with the stellar UV-visual radiation field falls off with distance
as $T_{\rmn{g}} \propto r_*^{-0.38}$ (Williams et al. 2009). This dependence
is also relatively insensitive to grain sample, and was found to apply on
average even in the full radiative transfer modelling of the thick dust spiral
of the classical persistent dust-making WC9 star WR\,104 by Harries et al. (2004).

Similar techniques will be required for modelling of the dust made by WR\,48a
owing to its optical depth. This will require knowledge of the dust geometry, and
is beyond the scope of the present paper; for the present, we consider simple
optically thin, isothermal modelling of the 1994--5 `mini' eruption. We model the
SEDs at two epochs: the maximum in $J$ and $H$ at 1994.45 (data from JD 2449519)
and that in $K$ and $L$ in 1994.64 (averaging data of JD 2449583 and 2449590).
This emission is in excess of the continuous `baseline' dust emission
by WR\,48a at the time, and we formed a `baseline' SED interpolating between
the light curves before and after the `mini' dust-formation episode.
The additional IR luminosity in the 1994 sub-peak at maximum (i.e. subtracting
the baseline emission) was $\sim$ 10$^{-11}$ Wm$^{-2}$, equivalent to
$\sim 5 \times 10^3 L_{\odot}$ at the adopted distance of 4~kpc, is only one
per cent of the total stellar luminosity, so we treat its emission as being
optically thin -- although it may suffer extinction in the cooler dust in our
sightline. Also, if the dust is newly formed, the spread in $r_*$ and grain
size may be small enough for the dust to be approximately isothermal, and we
can usefully derive an average temperature $\langle T_{\rmn{g}} \rangle$ from
the observed SED.

The results of fitting these differential SEDs are given in Table \ref{Mods},
in which the uncertainties were estimated from those in the photometry
(0.02 mag. in $JHK$ and 0.03 mag. in $L$). The two epochs roughly separate
three phases in the evolution of the dust: (a) nucleation of new grains near
the stars until 1994.45, (b) growth of the grains as they moved away from the
stars causing the dust mass to increase between then and 1994.64 and (c) the
continued fading of the dust emission. The grain temperature from the 1994.45 fit
($\langle T_{\rmn{g}} \rangle = 1220\pm$90~K) is close
to that at which the grains nucleate; the relatively large uncertainty comes
from fitting the small difference between the two SEDs, and there must be
some range in temperature as the first grains to form will have moved further
from the stars. There was no emission from the `mini' episode in the 1994.06
photometry, so we determine an average dust formation rate, presumably a
combination of nucleation and growth of the oldest grains, for this phase.
The lower $\langle T_g \rangle$ two months later results primarily from the
movement of the mini dust cloud away from the stars.  There may be a component
from more efficient cooling by the largest grains, but we do not have the data
(e.g. velocity of the dust grains) to separate the contributions. The formation
rate in this second phase is about four times that in the first and must be
almost entirely due to the growth of the existing grains as the $J$ and $H$
fluxes were falling at the time, implying that nucleation had ceased. The
three-fold increase in dust mass implies a 40\% increase in average grain
radius in the two months of the second phase.

The average dust-formation rate, $1.4\pm0.3 \times 10^{-7} M_{\odot}$ yr$^{-1}$,
seems high for a minor dust-formation episode compared with the likely mass-loss
rate of WR\,48a ($\sim  10^{-5} M_{\odot}$ yr$^{-1}$) and abundance of carbon in
its wind, but we recall the range in the scales of $\kappa_{\lambda}$ for
different laboratory grain samples resulting in a similar range of derived
dust mass.

\begin{table}
\caption{Isothermal model fits to $JHKL$ SEDs during the 1994 mini dust-formation episode.}
\label{Mods}
\centering
\begin{tabular}{lrcc}
\hline
Date    & $\langle T_d \rangle$ &  $M_d$                   & formation rate         \\
        &          (K)          &  ($M_{\odot}$)           & ($M_{\odot}$ yr$^{-1}$) \\
\hline
1994.45 &     1220$\pm$90 &     $1.4\pm0.7 \times 10^{-8}$ & $3.6\pm1.8 \times 10^{-8}$  \\
1994.64 &     1050$\pm$20 &     $4.1\pm0.8 \times 10^{-8}$ & $1.4\pm0.3 \times 10^{-7}$  \\
\hline
\end{tabular}
\end{table}

\section{Discussion}
\label{SDisc}

The long-term infrared photometry of WR\,48a shows complex behaviour different
from that of any other WR star: a slow, large-amplitude variation on which are
superimposed briefer variations of lower amplitude. In all cases in which they
can be determined, the trajectories in the ($H-L$), $K$ colour-magnitude diagram
are loops (clockwise in Figs \ref{CMD} and \ref{CMDhs}) indicative of the formation
of new, hot dust, followed by its cooling. The recurrence time-scale for the
slow variation is 32+ yrs; although the 2010--11 NIR photometry reached the
levels of the earliest (1978--79) pre-maximum photometry by DDWS,
the interval cannot be translated into a period owing to the superimposed
short-term variations, and further observations capturing at least the maximum
and early decline are needed for a period\footnote{Strictly, observations over
another whole cycle, but these would take the first author to his centenary and
are not planned}.
Even without a period, there is enough evidence to consider WR\,48a as a CWB
periodic dust-maker and discuss it in that context.

The total dust luminosity at maximum (1979) is 13$\times$ that in 1996, near
minimum, implying a variable rate of dust formation assuming a constant wind
dispersing the dust. The rate of dust formation is better estimated from the
short wavelength flux sensitive to the hottest, newly formed dust and the range
in $H$ between maximum and minimum (adjusted for the stellar contribution)
gives a factor $\simeq 16$. The fraction of the WC8 wind going into the WCR
is determined by the angular size of the WCR, which depends on the wind-momentum
ratio $\eta = (\dot{M}v_\infty)_{OB}/(\dot{M}v_\infty)_{WC}$,
which does not change around the orbit if the winds collide at their terminal
velocities, but the pre-shock wind density at the WCR does change with the
stellar separation if the orbit is elliptical. If maximum and minimum dust
formation coincide with periastron and apastron passages in an elliptical
orbit, and if the dust formation rate is proportional to the pre-shock wind
density at the WCR, the stellar separation varies by a factor of $\simeq 4$
and the orbital eccentricity would be $e \simeq 0.6$, with periastron passages
in 1979 and some time after mid-2011.

The mini eruptions appear not to be periodic, arguing against the suggestion
in Paper I of a third stellar component in WR\,48a, and other large-scale
overdensity structures which are intercepted by the WCR as it moves through
the winds are implied.
The only other system having mini outbursts superimposed on its long-term
dust-formation variation is WR\,137. This is one of the few WR stars to have
significant continuum polarization and wind asymmetry (Harries, Hiller \&
Howarth 1998). Harries, Babler \& Fox (2000) pointed out the similarity of
WR\,137 to WR\,6 and WR\,134, which display periodic variability in their
emission-line morphology possibly caused by the rotation of large-scale
azimuthal structures within their flattened winds. Polarization observations
of WR\,48a are needed to to see if this is the case here. Also, the H$\alpha$
emission associated with the companion suggests that this might have a
flattened wind and large-scale structures.

The persistence of dust formation even at IR minimum classifies WR\,48a as a
variable dust maker like WR\,98a, which has a period near 564 d. determined
from both the rotation of its dust pinwheel (Monnier et al. 1999) and NIR
photometry (Paper~I). The recurrence time-scale of WR\,48a much longer than
this, and the periods of the episodic dust makers, of which the longest is
13.05 yrs for WR\,137, both from IR photometry (Williams et al. 2001) and the
RV orbit (L\`efevre et al. 2005), and even the orbital period, 24.8 yr, of
the persistent dust-maker WR\,112 inferred from its multi-arc dust cloud
(Marchenko et al. 2002). The relevance of the long period is
the implied size of the orbit (for stellar systems of similar mass), with
implications for the wind-collision process, particularly whether the post-shock
WC wind is radiative or adiabatic.

Radiative cooling in the post-shock WC wind is important for dust formation
(Usov 1991). It was discussed by Stevens, Blondin \& Pollock (1992), who
introduced the cooling parameter, $\chi$: the ratio of the time-scales for
cooling of the shocked gas and its escape from the apex of the WCR to flow
downstream, and given by
\[
\chi = \frac{v^4_8d_{12}} {\dot{M}_{-7}}
\]
\noindent
where $v_8$ is the wind velocity in units of 1000 km~s$^{-1}$, $d_{12}$ is
the separation of the stars in units of $10^{12}$ cm, and $\dot{M}_{-7}$
is the star's mass-loss rate in units of  $10^{-7}$ M$_{\odot}$ yr$^{-1}$.
Stevens et al. considered a wind with $\chi \geq 1$ to be adiabatic and
$\chi \ll 1$ to be radiative; recent hydrodynamical simulations by Parkin
\& Pittard (2008) find a higher threshold, with the compressed wind
cooling rapidly if $\chi \leq 3$. The WCR in a system having a very
elliptical orbit, like WR\,140, can vary between adiabatic and radiative
as the stellar separation varies, becoming radiative close to periastron
-- the only time that dust forms in that system.
In the case of WR\,48a we know none of $v_8$, $d_{12}$ and $\dot{M}_{-7}$,
but can estimate $\chi$ very roughly. If the stars in WR\,48a have masses
comparable to those in the $\gamma$ Vel system they would have
$d_{12} \simeq 530$ in a $P = 33$ yr period circular orbit. Adopting a wind
velocity of 1200 km~s$^{-1}$ (Section \ref{SOpt}) and assuming a mass-loss
rate of $10^{-5}$ M$_{\odot}$ yr$^{-1}$, we have $\chi \simeq 11$ for the
WR\,48a WCR. This is significantly above the threshold and indicates an
adiabatic WCR -- which does not favour dust formation. In an elliptical
orbit, the separation and hence $\chi$ would be smaller near periastron
(e.g. $\chi \simeq 4$ for $e = 0.6$); but they would be larger at apastron
-- and we know from the observations that dust forms throughout the orbit.
The dust formation by WR\,112 raises a similar problem: for the same
stellar masses, the stars would have $d_{12} \simeq 390-490$ in an orbit
having $e = 0.11$ (Marchenko et al. 2002) and $\chi \simeq 8-10$ for the
same estimates of mass loss and velocity, which are also those used in
their modelling by Marchenko et al. Higher mass-loss rates would result
in lower values of $\chi$, as would lower wind velocities, which enter with
the fourth power. Wind velocities below $\sim 900$ km~s$^{-1}$ would give
values of $\chi \simeq 3$ and possibly radiatively cooling winds.
The velocities of both stars need to be measured from high-resolution
spectra to advance the question of the cooling of the post-shock winds
and the conditions allowing their dust formation. Velocities are also
needed to aid interpretation of the dust images of the two stars.

The recurrence of dust formation, the dilution of the WC emission lines
implying presence of a luminous companion, the anomalous emission in
H$\alpha$ (and possible H$\beta$ and Br$\gamma$) supporting this, and
the strong X-ray emission reported by Zhekov et al. (2011) and Mauerhan et al.
(2011) all point to WR\,48a being a long-period CWB. The IR photometry needs
to be extended to determine a period and characterise the `mini' outburst
and the spectrum needs to be re-observed at higher resolution and S/N to
elucidate the types of both components and determine the WC wind velocity
to further the consideration of the conflict between observed dust formation
and an apparently adiabatic post-shock wind. Knowledge of the wind cooling
will also be valuable in understanding the X-ray flux from WR\,48a and its
long term variation. The long period of the system suggests that any non-thermal
radio emission from the WCR  will have little difficulty in escaping the
wind (cf. Dougherty \& Williams 2000). Its distance is comparable to
that of WR\,112 (4~kpc, van der Hucht 2001), which shows variable non-thermal
radio emission at the level of $\sim$ a few mJy (Chapman et al. 1999,
Monnier et al. 2002), so we expect the similar flux levels from WR\,48a
if the stars have similar winds, but with greater amplitude of variation
given the greater eccentricity and inclination of the WR\,48a system.

\section*{Acknowledgments}

The long-term observing campaign reported here would have been impossible without
the active support of many individuals and observatories. We would like to thank
the Directors and Staff at the SAAO, ESO and the AAO for continued access to
facilities and their support over a long period, and Pik Sin Th\'e, Frank Spaan,
R. de Jong and D. de Winter for contributing or helping with the observations at ESO.
It is a pleasure to thank Martin Cohen for helpful discussions.
This research has made use of the NASA / IPAC Infrared Science Archive,
which is operated by the Jet Propulsion Laboratory, California Institute
of Technology, under contract with the National Aeronautics and Space
Administration; the Vizier database, operated by the CDS, Strasbourg,
the data archive at the Space Telescope Coordinating Facility (ST-ECF)
at ESO, and the DARTS archive developed and maintained by C-SODA at ISAS/JAXA.
PMW is grateful to the Institute for Astronomy for hospitality and continued
access to facilities of the Royal Observatory, Edinburgh. PAW acknowledges
a grant from the SA National Science Foundation.

redpajama_set_name: RedPajamaArXiv


text:
Peter Marki-Zay - Photo: Facebook
Kovacs accuses opposition PM candidate of 'lying again'; no weapons delivery to Ukraine
No Hungarian military plane is involved in delivering weapons to Ukraine, Zoltan Kovacs, the state secretary for international communications and relations, wrote on Facebook on Monday, accusing the opposition's prime ministerial candidate, Peter Marki-Zay, of "lying yet again" and spreading "fake news" to that effect.
No weapons are passing through Hungarian territory to Ukraine and none are being handled by Hungarian personnel, Kovacs wrote.
The state secretary said, however, that three Hungarian aircraft were performing tasks related to NATO's heavy air transport capability in cooperation with several nations by providing international strategic military airlift capabilities to participating countries.
Each participant can purchase flight hours for use of the aircraft for their own purposes, Kovacs said. The purpose for which the aircraft were being used had not been requested by Hungary or the Hungarian Armed Forces, he added.
DK calls on government to release names of Russian residency bond buyers
Paks II project advancing 'according to plan'

redpajama_set_name: RedPajamaCommonCrawl


While sitting, contemplating, staring at my computer screen, tracing the lip of my coffee cup with my finger, it dawned on me that we don't play with shapes enough in wedding invitations. So while the round shape of this invitation set may be a little left field, the classic color scheme and elegant scroll detailing and fonts keep these pieces well grounded in wedding tradition. You could print on any color card, though I don't think you can go wrong with black and white. This set is sure to make a bold statement in the mail, and with just three easy steps to put together, you will be patting yourself on the back for your bold choice to make them at home.
Download the template files and open the invitation and RSVP in MS Word, and the envelope liner in Acrobat. Customize the Word files with your wedding details.
The script font used in the template sample is Snell Roundhand, and the information text is Copperplate Light, both of which are available to download for free. If you do not have these fonts installed on your computer Word will substitute different fonts. You can pick any fonts that you like.
Print the files on white or cream cardstock.
TIP: I recommend printing one sample of the invitation and RSVP to check for spelling and punctuation errors. Have a second set of eyes look at the sample before you commit to printing them all!
Cut the invitation and RSVP circles along the trim lines using your scissors. The trick to cutting circles is to keep your scissors stationary and move the paper. For smooth circles use long, deep cuts along the entire blade rather than small snips.
Also cut out the envelope liner.
Place the envelope liner into a 5.75" square envelope. Line up the top flap so that is sits just below the edge of the envelope. Fold over the liner along the fold line of the envelope, using a bone folder if available for a sharp crease. Add some glue or double sided tape to the back of the liner flap. Fold the envelope flap over and onto the liner and push down firmly to attach the liner to the envelope.
The invitations are now ready for stuffing and mailing.
This entry was posted in Templates, Tutorial, Wedding and tagged 1704, diy, elegant, scroll.


text:
ALL-IN-ONE MASTER TONIC
12 THINGS THE NEGRO MUST DO FOR HIMSELF
25 THINGS THAT REALLY MATTER IN LIFE
Black InterestsBlack Men
The October Column: The Manhood Line: Live! By Mike Ramey
By Black Men In America.com October 3, 2018 0524 views
A TRULY SCARY TIME FOR MEN, PERIOD
With our coming into the Halloween season, it's good to discuss spiritual things and how much they impact the physical realm. For, my brothers, if you understand the spiritual, you'll have a better understanding of the physical.
Let's explain a basic truth. If one does NOT have a firm relationship with Jesus Christ and have Him in their lives, not only do they NOT have protection from evil spirits; they also do NOT have a true understanding of the spiritual side of life.
Spiritual warfare is NOT an imaginary 'suggestion' in the KJV Bible, but an unadulterated FACT. The reason why a lot of young Christian men are failing in their lives is that they don't take the war against them from the forces of Satan and his demons as a real event. Jesus himself had to deal with the unseen realm on multiple occasions. Mark, chapter five points out the demoniac who was possessed by a legion of demons. Jesus, throughout his earthly ministry had to case unclean spirits out of MANY people.
If the Lord had to deal with evil spirits; and his apostles had to deal with evil spirits, make no mistake about it: Those who follow Christ are going to have to deal with evil spirits. In short, brothers? The armor of God is ONLY for the Christian man–and you NEED to know how to use it!
Mental Illnesses have increased in their frequency and scope at just about every level of society. Many of these illnesses are directly linked to occult involvement. Playing with Ouija boards, binge watching horror movies or playing violent video games on line will leave doorways open in one's soul…doorways that need little prompting from Satan and his forces to become permanent residences of evil spirits.
One of the best books on this subject is "Between Christ and Satan" by Kurt Koch. Check it out. You won't regret the investment.
THE NFL IS ANTI-GOD? WHAT A SHOCK:
The Ol' P-School Ranger just happened to think of a few items of interest involving the National Football League (NFL) and its low viewership. You can file this under "God don't like ugly, and ain't too thrilled with pretty":
*Back in the nineties, Christian NFL football players of competing teams used to kneel at midfield to PRAY at the END of football games. The cameras were rolling–and the NFL got upset. Fast forward some 20 years. Now, we have the NFL silent as a few players are taking a knee AGAINST the things that make this country great–INCLUDING God. Viewership continues to fall. What a shock!
*Back in the nineties, football stadiums were packed to capacity for Promise Keepers rallies to lead men to Christ, and to teach men the concepts of biblical manhood. The NFL got upset about the practice and the preaching. Fast forward some 20 or more years. NOW the NFL has problems FILLING stadiums. What a shock!
*Remember Tim Tebow? Had Bible verses written on his eye protectors in college. Was a warrior for Jesus Christ on the NFL football field, and wasn't ashamed to tell the world about Christ. The NFL didn't like it. Fast forward some 20 or more years. Tebow has moved on, is more prosperous…and the NFL is still begging for fans to come back. What a shock!
*Lastly, back in the nineties, Christian football players would thank God for their touchdowns in the end zone. The NFL passed a variety of rules prohibiting such displays 'of religion', saying that they weren't 'proper' for family viewing. Fast forward some 20 years. Now the NFL approves of all kinds of 'antics' in the end zone…but no praise to God. Bottom line? God has a way of paying back those who disrespect Him, and his people. What a shock!
READY FOR MARRIAGE? ARE YOU PREPARED, BROTHERS?
One thing that I can say about the sixth wave feminists involved with the #MeToo crowd…they represent the kind of women that a man should NOT date, NOR marry. They are anti-Christ, anti-common sense, anti-family, anti-responsibility, and anti-conservative woman. Don't believe the hype, brothers: Feminism has ALWAYS been about power, and making the woman the head of the home and society. God took woman from man's rib…not his brain, nor his backbone. No matter how loudly a shrew screeches, she's still NOT the marrying kind. Leave her alone to mess up her OWN life!
There are some who may not like President Donald Trump. However, truth IS truth, and right IS right. MAGA, baby! His best quote for men? "It's a very scary time for young men in America." Thus, IF you are thinking of marriage, you had better be aware of the times, and the women that are 'on the landscape'. Like they said in the first "Men In Black" movie: "Nothing is as it seems."
The best booklet on marriage I have found? It's available at the www.chapellibrary.org website. You can either order by snail mail. This 28 page masterpiece comes complete with a 10 question study guide in the back, just to check on your reading this booklet.
Two items hit you as you start reading: First, a man MUST have HIS relationship right with God; second, you MUST seek your spouse from God. Yes, it is a blessing to find a wife…but God, through Christ, is the one who will lead you to the right one, baby! More on this subject, next month. One other thing: Pre-marital counseling from a true Man of God at a Bible-believing church. It WILL make a difference!
TWO WARHEADS–FROM THE PAST:
*A Black man with a job and a future will build a family. A Black man without a job and a bleak future will help destroy a community. What are we seeing on our streets?
Black Business Owner; put your corporate logo and 'party money' into your brothers and sisters. A party lasts but a weekend. A young brother with an education and some job training will be able to start his employment career with Y-O-U!
There is no BETTER party…than helping someone get their first paycheck!
*It's not JUST about registering. It's about VOTING. If you can look in the mirror and support people who believe in abortion, your mirror is cracked and you are wrong! Don't be fooled by the screams and the protests. Get out and VOTE!
Mike Ramey is a Minister, Book Reviewer, P-School Ranger and Syndicated Columnist who lives in Indianapolis, Indiana. "The Manhood Line: Live" is one of a variety of columns that Ramey has in cyberspace. To drop him a line…or a whine…the address is still the same: manhoodline@yahoo.com. ©2018 Barnstorm Communications.
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Mike Ramey
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text:
Q: problema al pocicionar algo en tkinter Hola estoy haciendo un programa en tkinter el cual tiene una segunda ventana y conexion con mySQL, el problema es al pocicionar unos odjetos en tkinter ya que he usado tanto el .grid como el .place pero los odjetos siguen estando en la esquina de la segunda ventana que es exactamente no quiero que este, y aun no se como solucionar este problema. si alguien sabe como ayudarme lo agradeceria mucho.
aqui mi codigo:
from tkinter import *
from tkinter import ttk
import pymysql
import os

ventana = Tk()

ventana.title("softnum_empleados")

ventana.geometry('900x800')

#sensure la conexion por obvias rasones

ventana2=Toplevel()
ventana2.geometry('900x800')
etiqueta1=Label(ventana2, text="nombre")
etiqueta1.place(x=4, y=3)#-------------------------# aqui el problema#
Rnombre=Entry(ventana2, width=60)
Rnombre.place(x=5, y=6)#-------------------------# aqui el problema#

def hola():
    pass

tad_control=ttk.Notebook(ventana)
tad_control.pack()
tad_control.grid(column=0, row=1)
tad1=ttk.Frame(tad_control)
tad2=ttk.Frame(tad_control)
tad3=ttk.Frame(tad_control)

tad_control.add(tad1, text="ventas 1")
tad_control.add(tad2, text="ventas 2")
tad_control.add(tad3, text="compras")

boton1=Button(tad1, text="VENTAS", width=19, height=6, bg="yellow")
boton1.place(x=200, y=400)
boton1.pack()

boton2=Button(tad1, text="DEVOLUCIONES", width=19, height=6, bg="yellow")
boton2.place(x=500, y=400)
boton2.pack()

boton3=Button(tad2, text="SEGUNDAS VENTAS", width=19, height=6, bg="yellow")
boton3.place(x=200, y=400)
boton3.pack()

boton4=Button(tad3, text="COMPRAS", width=19, height=6, bg="yellow")
boton4.place(x=200, y=400)
boton4.pack()
ventana.mainloop()

A: Cuando tu posicionas a un widget en una ventana o frame deberías hacerlo solo de un forma, no de dos formas como lo estas haciendo.
# Esto esta mal
boton1.place(x=200, y=400)
boton1.pack()

# Esto esta bien
boton1.place(x=200, y=400)

El método pack si no le pasas ningún argumento te va empaquetar tus widgets arriba y al medio de tu ventana uno pegado de otro.
pack puede recibir las siguientes opciones: expand, fill y side como las mas utilizadas, también tiene otras muchas opciones mas.
Geometry Management pack()
El método place te permite posicionar tus widgets en una posición absoluta, lo puedes dejar donde desees, place funciona con coordenadas x e y donde x vendría siendo el posicionamiento horizontal e y el posicionamiento vertical.
Ejemplo
widget.place(x=100, y=50) # x = 100 pixeles, y = 50 pixeles

Geometry Management place()
En el caso de que uses place tendrás que darle geometría(ancho y alto) a tus frames de esta forma.
tad1=ttk.Frame(tad_control, width=700, height=700)
tad2=ttk.Frame(tad_control, width=700, height=700)
tad3=ttk.Frame(tad_control, width=700, height=700)

tus widgets de la segunda ventana aparecen en la esquina por que los estas posicionando ahí.
etiqueta1.place(x=4, y=3)
Rnombre.place(x=5, y=6)

si le das mas pixeles puedes dejarlos donde quieras, recuerda que place trabaja con coordenadas (x e y) y grid con filas y columnas.
etiqueta1.place(x=40, y=30)
Rnombre.place(x=50, y=60)

redpajama_set_name: RedPajamaStackExchange


text:
Burleigh County commissioners vote no on turbines in Morton Township
By Megan Hoffman |
Posted: Tue 11:49 AM, Jan 08, 2019
BISMARCK N.D. - A controversial wind farm project in Morton Township in southern Burleigh County has been denied. County commissioners voted tonight to reject the 30 applications for turbines in the municipality.
Nearly a month after a public hearing on the issue, Burleigh County commissioners made the decision to turn down the special permit applications for wind turbines in Morton Township, and the decision was met with enthusiasm from the crowd.
"Wind is okay but this was a bad place it would be bad to ruin the beauty of the capital city," Burleigh County resident Jerry Doan said.
According to Building Official Ray Ziegler, 18 of the towers were in violation of the county's ordinance for being too high, for standing at 567 feet. The official report from the planning and zoning commission cited that the plans could hinder future development of the airport, be unsafe for pilots and could affect land owner's rights.
Pure New Energy officials were on hand to refute the claims, but it wasn't enough.
"It's a very dark day for property rights in North Dakota and essentially what this decision said is as long as enough of your neighbors get together they can dictate what you can and can't do on your property," Pure New Energy Director of Business Development Courtney Timmons said.
Burleigh County State's Attorney Julie Lawyer said she believes the report was insufficient and there were too many inconsistencies for the board to make a decision.
"It's very unfortunate that the county commission took a stand today that contradicted the advice of the state's attorney and I think they have left themselves open to legal action," Timmons said.
Timmons says the company will look at all options before deciding what its next steps are. But residents are glad they won this battle.
"The vast majority of the citizens out there and the residents are saying no and not let these out of state Minneapolis and Chicago lawyers come in and run all over us in Burleigh County so we're proud of them," Doan said.
The vote was 4 to 1 in favor of denying, with commissioner Brian Bittner the only no vote.
Timmons says they will continue developing the other parts of the project in areas outside of Morton Township in Burleigh and Emmons counties.
Doan says those against will continue fighting the issue in those areas.
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kfyrtv.com/a?a=504055701