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+% MNSAMPLE.TEX
+%
+% A sample plain TeX single/two column Monthly Notices article.
+%
+% v1.5 --- released 25th August 1994 (M. Reed)
+% v1.4 --- released 22nd February 1994
+% v1.3 --- released 8th December 1992
+%
+% Copyright Cambridge University Press
+
+% The following line automatically loads the mn macros if you are not
+% using a format file.
+\ifx\mnmacrosloaded\undefined \input mn\fi
+
+% If your system has the AMS fonts version 2.0 installed, MN.tex can be
+% made to use them by uncommenting the line: %\AMStwofontstrue
+%
+% By doing this, you will be able to obtain upright Greek characters.
+% e.g. \umu, \upi etc. See the section on "Upright Greek characters" in
+% this guide for further information.
+
+\newif\ifAMStwofonts
+%\AMStwofontstrue
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+ \def\umu{\mu}
+ \def\upi{\pi}
+ \def\upartial{\partial}
+ \fi
+\fi
+
+
+% Marginal adjustments using \pageoffset maybe required when printing
+% proofs on a Laserprinter (this is usually not needed).
+% Syntax: \pageoffset{ +/- hor. offset}{ +/- vert. offset}
+% e.g. \pageoffset{-3pc}{-4pc}
+
+\pageoffset{-2.5pc}{0pc}
+
+\loadboldmathnames
+
+% \Referee % uncomment this for referee mode (double spaced)
+
+% \pagerange, \pubyear and \volume are defined at the Journals office and
+% not by an author.
+
+% \onecolumn % enable one column mode
+% \letters % for `letters' articles
+\pagerange{1--7} % `letters' articles should use \pagerange{Ln--Ln}
+\pubyear{1989}
+\volume{226}
+% \microfiche{} % for articles with microfiche
+% \authorcomment{} % author comment for footline
+
+\begintopmatter % start the two spanning material
+
+\title{Dust envelopes around RV Tauri stars}
+\author{A. V. Raveendran}
+\affiliation{Indian Institute of Astrophysics, Bangalore 560034, India}
+
+\shortauthor{A. V. Raveendran}
+\shorttitle{Dust envelopes around RV Tauri stars}
+
+% \acceptedline is to be defined at the Journals office and not
+% by an author.
+
+\acceptedline{Accepted 1988 December 15. Received 1988 December 14;
+ in original form 1988 October 11}
+
+\abstract {In the {\it IRAS\/} [12]--[25], [25]--[60]
+colour--colour diagram, RV Tauri stars are found to populate
+cooler temperature regions $(T<600\,{\rm K})$, distinctly
+different from those occupied by the oxygen and carbon Miras.
+The {\it IRAS\/} fluxes are consistent with the dust density in
+the envelope varying as the inverse square of the radial
+distance, implying that the grain formation processes in these
+objects are most probably continuous and not sporadic. It is
+found that the spectroscopic subgroups A and B are
+well separated in the far-infrared two-colour diagram, with
+group B objects having systematically cooler dust envelopes. We
+interpret this as being due to a difference in the nature of
+grains, including the chemical composition, in the two cases.}
+
+\keywords {circumstellar matter -- infrared: stars.}
+
+\maketitle % finish the two spanning material
+
+
+\section{Introduction}
+
+It has been well established that RV Tauri variables
+possess infrared emission far in excess of their expected
+blackbody continuum, arising from their extended cool dust
+envelopes (Gehrz \& Woolf 1970; Gehrz 1972; Gehrz \& Ney 1972).
+Recently, Lloyd Evans (1985) and Goldsmith et~al.\ (1987)
+have given detailed descriptions of the near-infrared
+properties of RV Tauri stars. In this paper we present an
+analysis of the {\it IRAS\/} data of RV Tauri stars with the help
+of the far-infrared two-colour diagram and a grid computed
+using a simple model of the dust envelope. Such two-colour plots
+have already been employed extensively by several investigators
+to study the circumstellar envelopes around oxygen-rich and
+carbon-rich objects which are in the late stages of stellar
+evolution (Hacking et~al.\ 1985; Zuckerman \& Dyck 1986;
+van der Veen \& Habing 1988; Willems \& de Jong 1988).
+
+Table~1 summarizes the basic data on the 17 objects
+detected at 60$\,\umu$m. Apart from the {\it IRAS\/} identification
+and the flux densities at 12-, 25-, 60- and 100-$\umu$m wavebands,
+it gives the spectroscopic groups of Preston et~al.\ (1963),
+the light-curve classes of Kukarkin et~al.\ (1969) and the periods of
+light variation. The list, which
+contains about 20 per cent of all the known RV Tauri stars,
+is essentially the same as that given by Jura (1986). The
+spectroscopic subgroups are from either Preston et~al.\ (1963) or
+Lloyd Evans (1985).
+%
+\begintable*{1}
+\caption{{\bf Table 1.} Data on the RV Tauri stars detected by {\it IRAS}.}
+\halign{%
+\rm#\hfil&\qquad\rm#\hfil&\qquad\rm\hfil#&\qquad\rm\hfil
+#&\qquad\rm\hfil#&\qquad\rm\hfil#&\qquad\rm#\hfil
+&\qquad\rm\hfil#&\qquad\rm#\hfil&\qquad\hfil\rm#\cr
+Name&&\multispan4\hskip23pt\hss Flux density (Jy)$^a$\hss \cr
+Variable&{\it IRAS}&12$\;\umu$m&25$\;\umu$m
+&60$\;\umu$m&100$\;\umu$m&Sp.&Period&Light-&$T_0({\rm K})$\cr
+&&&&&&group&(d)\hfill&curve\cr
+&&&&&&&&type\cr
+\noalign{\vskip 10pt}
+TW Cam&04166$+$5719&8.27&5.62&1.82&$<$1.73&A&85.6&a&555\cr
+RV Tau&04440$+$2605&22.53&18.08&6.40&2.52&A&78.9&b&460\cr
+DY Ori&06034$+$1354&12.44&14.93&4.12&$<$11.22&B&60.3&&295\cr
+CT Ori&06072$+$0953&6.16&5.57&1.22&$<$1.54&B&135.6&&330\cr
+SU Gem&06108$+$2734&7.90&5.69&2.16&$<$11.66&A&50.1&b&575\cr
+UY CMa&06160$-$1701&3.51&2.48&0.57&$<$1.00&B&113.9&a&420\cr
+U Mon&07284$-$0940&124.30&88.43&26.28&9.24&A&92.3&b&480\cr
+AR Pup&08011$-$3627&131.33&94.32&25.81&11.65&B&75.0&b&450\cr
+IW Car&09256$-$6324&101/06&96.24&34.19&13.07&B&67.5&b&395\cr
+GK Car&11118$-$5726&2.87&2.48&0.78&$<$12.13&B&55.6&&405\cr
+RU Cen&12067$-$4508&5.36&11.02&5.57&2.01&B&64.7&&255\cr
+SX Cen&12185$-$4856&5.95&3.62&1.09&$<$1.50&B&32.9&b&590\cr
+AI Sco&17530$-$3348&17.68&11.46&2.88&$<$45.62&A&71.0&b&480\cr
+AC Her&18281$+$2149&41.47&65.33&21.12&7.79&B&75.5&a&260\cr
+R Sct&18448$-$0545&20.88&9.30&8.10&$<$138.78&A&140.2&a\cr
+R Sge&20117$+$1634&10.63&7.57&2.10&$<$1.66&A&70.6&b&455\cr
+V Vul&20343$+$2625&12.39&5.72&1.29&$<$6.96&A&75.7&a&690\cr
+}
+\tabletext{\noindent $^a$Observed by {\it IRAS}.}
+\endtable
+
+
+\section{Description of the envelope model}
+
+If we assume that the dust grains in the envelope are
+predominantly of the same kind and are in thermal equilibrium,
+the luminosity at frequency $\nu$ in the infrared is given by
+$$
+ L(\nu)=\mskip-25mu\int\limits_{\rm envelope}\mskip-25mu
+ \rho(r)Q_{{\rm abs}}
+ (\nu)B[\nu,T_{\rm g}(r)]\exp [-\tau(\nu,r)]\> {\rm d}V, \eqno\stepeq
+$$
+where
+$Q_{{\rm abs}}(\nu)$ is the absorption efficiency at frequency $\nu$,
+$\rho(r)$ is the dust grain density,
+$T_{\rm g}(r)$ is the grain temperature,
+$B[\nu,T_{\rm g}(r)]$ is the Planck function and
+$\tau(\nu,r)$ is the optical depth at distance {\it r\/} from the
+centre of the star.
+
+The temperature $T_{\rm g}(r)$ is determined by the condition of
+energy balance: amount of energy radiated = amount of energy
+absorbed. The amount of energy absorbed at any point is
+proportional to the total available energy at that point, which
+consists of:
+\beginlist
+\item (i) the attenuated and diluted stellar radiation;
+\item (ii) scattered radiation, and
+\item (iii) reradiation from other grains.
+\endlist
+
+Detailed solutions of radiative transfer in circumstellar
+dust shells by Rowan-Robinson \& Harris (1983a,b) indicate that
+the effect of heating by other grains becomes significant only at
+large optical depths at the absorbing frequencies $[\tau({\rm
+UV})\gg 10]$, and at optical depths $\tau({\rm UV})<1$ the grains
+have approximately the same temperature that they would have if
+they were seeing the starlight unattenuated and no other
+radiation.
+
+The Planck mean optical depths of circumstellar envelopes
+around several RV Tauri stars, derived from the ratios of the
+luminosities of the dust shell (at infrared wavelengths) and
+the star, range from 0.07 to 0.63 (Goldsmith et~al.\ 1987).
+There is much uncertainty in the nature of the optical
+properties of dust grains in the envelope. The carbon-rich RV
+Tauri stars are also reported to show the 10-$\umu$m silicate
+emission feature typical of oxygen-rich objects (Gehrz \& Ney
+1972; Olnon \& Raimond 1986). The pure terrestrial silicates or
+lunar silicates are found to be completely unsuitable to account
+for the infrared emission from circumstellar dust shells around
+M-type stars (Rowan-Robinson \& Harris 1983a). We assume that
+the absorption efficiency $Q_{{\rm abs}} (\nu)$ in the infrared
+varies as $\nu^{\gamma}$. ${\gamma}=1$ appears to provide a
+reasonable fit in a variety of sources (Harvey, Thronson \&
+Gatley 1979; Jura 1986). Under these circumstances the
+condition of energy balance implies that the dust temperature
+$T_{\rm g}$ will vary as $r^{\beta}$.
+
+In view of the low value of the observed Planck mean optical
+depth for the stellar radiation and the nature of the assumed
+frequency dependence of the absorption efficiency, the
+extinction of the infrared radiation by the dust envelope can
+be neglected. If we consider the envelope to be spherically
+symmetric, equation (1) reduces to
+$$
+ L(\nu)=\!\!\int_{r_{1}}^{r_{2}}\!\!4\upi r^2\rho(r)\> Q_{{\rm abs}}
+ (\nu)B[\nu,T_{\rm g}(r)]\> {\rm d}r, \eqno\stepeq
+$$
+where $r_1$ and $r_2$ are the inner and outer radii of the
+shell. For a dusty density distribution $\rho(r)\propto
+r^{\alpha}$ and $r_2\gg r_1$, equation (2) reduces to
+$$
+ L(\nu)\propto \nu^{2+\gamma-Q}
+ \int_{X_0}^{\infty}{{x^Q}\over{{\rm e}^x-1}}{\rm d}x, \eqno\stepeq
+$$
+where $Q=-(\alpha+\beta+3)/\beta$ and $X_0=(h\nu /kT_0)$.
+$T_0$ represents the temperature at the inner boundary of the
+dust shell where grains start condensing. In a steady radiation
+pressure driven mass outflow in the optically thin case, values of
+$\alpha$ lie near $-2$ (Gilman 1972). $\gamma$ and $\beta$ are
+related by $\beta=-2/(\gamma+4)$.
+
+In the {\it IRAS\/} Point Source Catalog (PSC, Beichman et~al.\ 1985a),
+the flux densities have been quoted at the effective
+wavelengths 12, 25, 60 and 100$\,\umu$m, assuming a flat energy
+spectrum $[\nu F(\nu)=1]$ for the observed sources. For each model
+given by equation (3), using the relative system response, the
+colour-correction factors (Beichman et~al.\ 1985b) in each
+of the {\it IRAS\/} passbands were calculated and the fluxes
+were converted into flux densities expected for a flat energy
+distribution, as assumed in the {\it IRAS\/} PSC, so that the
+computed colours can be directly compared with the colours
+determined from the catalogue quantities. Such a procedure
+is more appropriate than correcting the {\it IRAS\/}
+colours for the energy distribution given by a particular model
+and then comparing them with those computed by the model.
+
+
+\subsection{Colour--colour diagram}
+
+The IR colour is defined as
+$$
+ [\nu_1]-[\nu_2]=-2.5\log [f(\nu_1)/f(\nu_2)],
+$$
+where $\nu_1$ and $\nu_2$ are any two wavebands and
+$f(\nu_1)$ and $f(\nu_2)$ are the corresponding flux densities
+assuming a flat energy spectrum for the source.
+%
+\beginfigure{1}
+\vskip 91mm
+\caption{{\bf Figure 1.} Plot of [25]--[60] colours of
+RV Tauri stars against their [12]--[25] colours after normalizing
+as indicated in Beichman et~al.\ (1985b). Some of the objects
+are identified by their variable-star names. Typical error bars
+are shown in the bottom right-hand corner. The lines represent
+the loci for constant inner shell temperature and the quantity
+$Q$. Note the separation of group A and B stars at $T_0 \sim$
+460$\,$K. Positions occupied by a sample of carbon and oxygen
+Miras are also shown. The $Q=1.0$ line differs from the
+blackbody line by a maximum of $\sim 0.05$.}
+\endfigure
+
+In Fig.~1, we have plotted the [25]--[60] colours of
+RV Tauri stars against their corresponding [12]--[25] colours
+derived from the {\it IRAS\/} data. Filled circles represent
+stars of group A and open circles stars of group B. The two
+sets of near-parallel lines represent the loci of constant
+inner shell temperature $T_0$ and the quantity $Q$ defined
+above. The models correspond to the case of absorption
+efficiency $Q_{{\rm abs}}(\nu)$ varying as $\nu$ (with
+$\gamma=1$ and hence $\beta=-0.4$). We have omitted R Sct in
+Fig.~1 because it shows a large deviation from the average
+relation shown by all the other objects. R Sct has a
+comparatively large excess at 60$\,\umu$m, but the extent of a
+possible contamination by the infrared cirrus (Low et~al.\ 1984)
+is unknown. Goldsmith et~al.\ (1987) found no
+evidence of the presence of a dust envelope at near-IR
+wavelengths and the spectrum was consistent with a stellar
+continuum. This explains why R Sct lies well below the mean
+relation shown by stars of groups A and C between the
+[3.6]--[11.3] colour excess and the photometrically determined
+(Fe/H) (Dawson 1979). R Sct has the longest period of 140$\,$d
+among the RV Tauri stars detected at far-infrared wavelengths
+and does not have the 10-$\umu$m emission feature seen in other
+objects (Gehrz 1972; Olnon \& Raimond 1986). R Sct is probably
+the most irregular RV Tauri star known (McLaughlin 1932).
+
+The inner shell temperatures $(T_0)$ derived for the various
+objects are also given in Table~1 and we find the majority of
+them to have temperatures in the narrow range 400--600$\,$K. If
+the dependences of $Q_{{\rm abs}}(\nu)$ on $\nu$ and $\rho(r)$ on
+$r$ are similar in all the objects considered, then in the
+colour--colour diagram they all should lie along a line
+corresponding to different values of $T_0$ and in Fig.~1 we find
+that this is essentially the case. In view of the quoted
+uncertainties in the flux measurements, we cannot attach much
+significance to the scatter in Fig.~1.
+%
+\beginfigure*{2}
+\vskip 5.9cm
+\caption{{\bf Figure 2.} Plot of the [60]--[100] colours
+of RV Tauri stars against their [25]--[60] colours after normalizing
+as indicated in Beichman et~al.\ (1985b). The solid lines
+represent the loci for constant inner shell temperature and the
+quantity $Q$. The dashed line shows the locus for a blackbody
+distribution.}
+\endfigure
+
+At 100$\,\umu$m the infrared sky is characterized by emission,
+called infrared cirrus, from interstellar dust on all spatial
+scales (Low et~al.\ 1984), thereby impairing the
+measurements at far-infrared wavelengths. In Fig.~2, we have
+plotted the [60]--[100] colours of the six RV Tauri stars
+detected at 100$\,\umu$m against their [25]--[60] colours, along
+with the grid showing the regions of different values for inner
+shell temperature $T_0$ and the quantity $Q$, as in Fig.~1. The
+results indicated by Fig.~2 are consistent with those derived
+from Fig.~1. AR Pup shows a large excess at 100$\,\umu$m but, in
+view of the large values for the cirrus flags given in the
+catalogue, the intrinsic flux at 100$\,\umu$m is uncertain.
+
+
+\subsection{Radial distribution of dust}
+
+From Fig.~1, it is evident that all RV Tauri stars lie
+between the lines corresponding to $Q=1.5$ and $0.5$. With
+$$
+ \alpha=-(1+Q)\beta-3,
+$$
+these values suggest limits of $r^{-2.0}$ and $r^{-2.4}$
+for the dust density variation, indicating a near-constant
+mass-loss rate. Jura (1986) has suggested that the density in
+the circumstellar envelope around RV Tauri stars varies as
+$r^{-1}$, implying a mass-loss rate that was greater in the
+past than it is currently. By fitting a power law to the
+observed fluxes, such that $f(\nu)$ varies as $\nu^q$, values
+of $q$ determined by him for the various objects given in
+Table~1 lie in the range 0.6--1.2, with a mean $\bar q=0.98$. The
+assumption of a power law corresponds to the case of $X_0=0$ in
+equation (3) and hence we get
+$$
+ q=2+\gamma -Q.
+$$
+Since we assume that $Q_{{\rm abs}}(\nu)$ varies as $\nu$,
+the resulting value for $Q$=2.0. None of the objects is found
+to lie in the corresponding region in the colour--colour
+diagram. Even this extreme value for $Q$ implies a density
+which varies as $r^{-1.8}$.
+
+Goldsmith et~al.\ (1987) have reported that the
+simultaneous optical and near-IR data of AC Her can be fitted
+by a combination of two blackbodies at 5680 and 1800$\,$K,
+representing, respectively, the stellar and dust shell
+temperatures, and suggested that in RV Tauri stars the grain
+formation is a sporadic phenomenon and not a continuous
+process. Apparently, they have been influenced by the remark by
+Gehrz \& Woolf (1970) that their data in the 3.5--11$\,\umu$m
+region of AC Her indicated a dust temperature of $\sim300\,$K. We
+find that the {\it K--L\/} colours given by Gehrz (1972), Lloyd
+Evans (1985) and Goldsmith et~al.\ (1987) are all
+consistent with each other. Surely, hot dust ($\sim 1800\,$K), if
+present at the time of observations by Goldsmith et~al.\ (1987),
+would have affected the {\it K--L\/} colour
+significantly. AC Her, like other members of its class, is
+found to execute elongated loops in the ({\it U--B\/}), ({\it
+B--V\/}) plane (Preston et~al.\ 1963), indicating that
+significant departure of the stellar continuum from the
+blackbody is to be expected. Further, their data show only a
+marginal excess at the near-IR wavelengths. We feel that the
+case for the existence of hot dust around AC Her and hence for
+the sporadic grain formation around RV Tauri stars is not
+strong. In Fig.~3 we find that AC Her and
+RU Cen lie very close to R Sct which, according to Goldsmith
+et~al.\ (1987), shows no evidence for the presence of a hot
+dust envelope.
+
+
+\subsubsection{Comparison with oxygen and carbon Miras}
+
+In Fig.~1 we have also shown the positions of a sample of
+oxygen-rich and carbon-rich Miras. At the low temperatures
+characteristic of the Miras, a part of the emission at 12$\,\umu$m
+comes from the photosphere. For a blackbody at 2000$\,$K, the ratio
+of fluxes at wavelengths of 12 and 2$\,\umu$m $(f_{12}/f_{2})\sim
+0.18$. The Miras shown in Fig.~1 have $(f_{12}/f_{2})$
+ratios larger than twice the above value. It is clear that the
+three groups of objects populate three different regions of the
+diagram. Hacking et~al.\ (1985) have already noticed that
+there are distinct differences between the {\it IRAS\/} colours
+of oxygen-rich and carbon-rich objects. On the basis of an
+analysis, using a bigger sample of bright giant stars in the
+{\it IRAS\/} catalogue, this has been interpreted by Zuckerman \&
+Dyck (1986) as being due to a systematic difference in the dust
+grain emissivity index. U Mon shows the 10-$\umu$m silicate
+emission convincingly and, in most of the other objects for
+which low-resolution spectra in the near-infrared have been
+reported (Gehrz 1972; Olnon \& Raimond 1986), the 10-$\umu$m
+emission may be partly attributed to silicates. Hence it is
+reasonable to expect that, in the envelopes around at least some
+of the RV Tauri stars, the dust grains are predominantly of
+silicates, as in the case of oxygen Miras (Rowan-Robinson \&
+Harris 1983a). The fact that none of the RV Tauri stars is
+found in the region of the two-colour diagram occupied by the
+oxygen Miras indicates that the emissivity indices of the
+silicate grains in the two cases are different. Because of the
+higher temperatures and luminosities, the environment of grain
+formation will be different in RV Tauri stars.
+
+
+\subsubsection{Correlation with subgroups}
+
+Preston et~al.\ (1963) have identified three spectroscopic
+subgroups, which are designated as groups A, B and C. Objects of
+group A are metal-rich; group C are metal-poor; group~B objects are
+also metal-poor, but show carbon enhancements (Preston et~al.\ 1963;
+Lloyd Evans 1974; Dawson 1979; Baird 1981). It is interesting
+to see that Table~1 contains no group C objects and that in Fig.~1
+there is a clear separation of the two spectroscopic subgroups A
+and B, with the demarcation occurring at an inner shell
+temperature of about 450$\,$K, group~B stars having lower
+temperatures than group A. SX Cen is the only exception. Lloyd
+Evans (1974) has reported that metal lines are stronger in SX Cen
+than in other group~B objects. It may be worth noting that SX Cen
+has the shortest period among the 100 or so objects with the RV
+Tauri classification. RU Cen has the coolest inner shell
+temperature, as already suggested by the near-infrared spectrum
+(Gehrz \& Ney 1972).
+%
+\beginfigure{3}
+\vskip 59mm
+\caption{{\bf Figure 3.} Plot of $(K$--$L)$ colours of
+RV Tauri stars detected by {\it IRAS\/} against their corresponding
+$(J$--$K)$ colours. The position of AR Pup is indicated. The three
+objects lying close to the blackbody line are AC Her, RU Cen and R Sct.}
+\endfigure
+
+Group~B objects follow a different mean relationship from those
+of group~A, having systematically larger 11-$\umu$m excess for a
+given excess at 3$\,\umu$m (Lloyd Evans 1985). For a general
+sample of RV Tauri stars, the distinction between the
+oxygen-rich and carbon-rich objects is not that apparent in the
+{\it JHKL\/} bands. In Fig.~3 we have plotted the near-IR
+magnitudes of the objects given in Table~1 (except V Vul which
+has no available measurements) in the {\it J--K, K--L\/} plane.
+The colours, taken from Lloyd Evans (1985) and Goldsmith
+et~al.\ (1987), are averaged if more than one observation
+exists, because the internal agreements are found to be often
+of the order of observational uncertainties, in accordance with
+the earlier finding by Gehrz (1972) that variability has
+relatively little effect on colours. Barring RU Cen and AC Her,
+it is evident that stars belonging to group~B show
+systematically larger excesses at {\it L\/}~band for a given
+excess at {\it K}. The low excesses at near-IR wavelengths for
+AC Her and RU Cen are consistent with the very low dust
+temperatures indicated by the far-infrared colours.
+%
+\ifsinglecol
+ \pageinsert
+ \vfil
+ \centerline{Landscape figure to go here. This figure was not
+ part of the original paper and is inserted here for illustrative
+ purposes.}
+ \centerline{See the author guide for details on how to handle landscape
+ figures or tables, and {\tt mnland.tex}.}
+ \centerline{{\bf Figure 4.}}
+ \vfil
+ \endinsert
+\else
+ \beginfigure*{4}
+ \vbox to 646pt{\vfil
+ \centerline{Landscape figure to go here. This figure was not
+ part of the original paper and is inserted here for illustrative
+ purposes.}
+ \centerline{See the author guide for details on how to handle landscape
+ figures or tables, and {\tt mnland.tex}.}
+ \caption{{\bf Figure 4.}}
+ \vfil}
+ \endfigure
+\fi
+
+It is already well established that from {\it UBV\/} photometry
+one can distinguish between groups A and~B, members of group~A
+being significantly redder than those of group~B (Preston
+et~al.\ 1963). Similarly, Dawson (1979) has found that the two
+spectroscopic groups are well separated in the DDO
+colour--colour diagrams when mean colours are used for the
+individual objects.
+
+The clear separation of the spectroscopic subgroups A and~B in
+the IR two-colour diagram suggests that the natures of dust
+grains in the envelopes in the two cases are not identical.
+This is to be expected because of the differences in the
+physical properties of the stars themselves. The average
+colours of group~B stars are bluer than group A, but the
+envelope dust temperatures of B are cooler than those of~A. The
+near-IR spectra of AC Her and RU Cen are extremely similar
+(Gehrz \& Ney 1972). The striking similarities in the optical
+spectra of AC Her and RU Cen have been pointed out by Bidelman
+(O'Connell 1961). We feel that the physical properties,
+including the chemical composition, of the grains formed in
+the circumstellar envelope strongly depend on those of the
+embedded star. This, probably, explains the diversity of the
+energy distributions of RV Tauri stars in the near-infrared
+found by Gehrz \& Ney (1972). On the basis of the observed
+differences in chemical abundances and space distribution of RV
+Tauri stars, Lloyd Evans (1985) has already pointed out that
+there is no direct evolutionary connection between group~A and
+group~B objects, thus ruling out the possibility that group~B
+objects are the evolutionary successors of group~A, in which
+grain formation has stopped and the cooler temperatures for the
+former are caused by an envelope expansion.
+
+Kukarkin et~al.\ (1969) have subdivided RV Tauri stars
+into two classes, RVa and RVb, on the basis of their light
+curves; the former shows a constant mean brightness, whereas
+the latter shows a cyclically varying mean brightness.
+Extensive observations in the near-infrared show that, on
+average, RVb stars are redder than RVa stars, and Lloyd Evans
+(1985) has suggested that in RVb stars dust shells are denser
+in the inner regions and hence radiate strongly in the
+1--3$\,\umu$m region. Fig.~3 confirms this; RVb objects show
+systematically larger ({\it J--K\/}) and ({\it K--L\/}) colours than RVa
+objects. Apparently, there is no distinction between objects of
+the two light-curve types at far-infrared wavelengths (Fig.~1).
+
+
+\section{Conclusions}
+
+In the [12]--[25], [25]--[60] colour diagram, RV Tauri
+stars populate cooler temperature regions $(T<600\,\rm {K})$,
+distinctly different from those occupied by the oxygen and
+carbon Miras. Using a simple model in which
+\beginlist
+\item (i) the envelope is spherically symmetric,
+\item (ii) the IR-emitting grains are predominantly of the same kind, and
+\item (iii) in the IR the absorption efficiency $Q_{{\rm abs}} (\nu)\propto\nu$,
+\endlist
+we find that the {\it IRAS\/} fluxes
+are consistent with the density in the envelope $\rho(r)\propto
+r^{-2}$, where {\it r\/} is the radial distance. Such a
+dependence for the dust density implies that the mass-loss
+rates in RV Tauri stars have not reduced considerably during
+the recent past, contrary to the suggestion by Jura (1986). In
+the two-colour diagram, the blackbody line and the line
+corresponding to $\rho(r)\propto r^{-2.2}$ nearly overlap and
+the present data are insufficient to resolve between the two
+cases. The latter case is more physically reasonable, however.
+
+The spectroscopic subgroups A and B are well separated in
+the {\it IRAS\/} two-colour diagram, with group B objects having
+systematically cooler dust envelopes. If we consider only the
+objects detected by {\it IRAS}, we find that stars
+belonging to group B show systematically larger excess at {\it
+L\/}~band for a given excess at {\it K}. Apparently, there is no
+correlation between the light-curve types (RVa and RVb) and the
+far-infrared behaviour of these objects. It is fairly certain
+that the physical properties, including the chemical
+composition, of the embedded stars are directly reflected by
+those of the dust grains. Most probably, the grain formation
+process in RV Tauri stars is continuous and not sporadic as
+suggested by Goldsmith et~al.\ (1987).
+
+
+\section*{Acknowledgments}
+
+I thank Professor N. Kameswara Rao for some helpful
+suggestions, Dr H. C. Bhatt for a critical reading of the
+original version of the paper and an anonymous referee for
+very useful comments that improved the presentation of the paper.
+
+
+\section*{References}
+
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+
+
+\appendix
+
+\section{Large gaps in {$\bf L\lowercase{y}\balpha$} forests
+ due to fluctuations in line distribution}
+
+(This appendix was not part of the original paper by A.V.~Raveendran and is
+included here just for illustrative purposes.)
+
+Spectroscopic\looseness=1\ observations of bright quasars show that the mean number
+density of ${\rm Ly}\alpha$ forest lines, which satisfy certain criteria,
+evolves
+like ${\rm d}N/{\rm d}z=A(1+z)^\gamma$, where $A$ and~$\gamma$ are two
+constants. Given
+the above intrinsic line distribution we examine the probability of finding
+large gaps in the ${\rm Ly}\alpha$ forests. We concentrate here only on
+the statistics and neglect all observational complications such as the line
+blending effect (see Ostriker, Bajtlik \&~Duncan 1988).
+
+Suppose we have observed a ${\rm Ly}\alpha$ forest between redshifts $z_1$
+and~$z_2$
+and found $N-1$ lines. For high-redshift quasars $z_2$~is usually the emission
+redshift $z_{\rm em}$ and $z_1$ is set to $(\lambda_{\rm Ly\beta}/\lambda_{\rm
+Ly\alpha})(1+z_{\rm em})=0.844(1+z_{\rm em})$ to avoid contamination by
+Ly$\beta$ lines. We want to know whether the largest gaps observed in the
+forest are significantly inconsistent with the above line distribution. To do
+this we introduce a new variable~$x$:
+$$
+ x={(1+z)^{\gamma+1}-(1+z_1)^{\gamma+1} \over
+ (1+z_2)^{\gamma+1}-(1+z_1)^{\gamma+1}}. \eqno\stepeq
+$$
+$x$ varies from 0 to 1. We then have ${\rm d}N/{\rm d}x=\lambda$,
+where $\lambda$ is the mean number of lines between $z_1$ and $z_2$ and is
+given by
+$$
+ \lambda\equiv{A[(1+z_2)^{\gamma+1}-(1+z_1)^{\gamma+1}]\over\gamma+1}.
+ \eqno\stepeq
+$$
+This means that the ${\rm Ly}\alpha$ forest lines are uniformly distributed
+in~$x$.
+The probability of finding $N-1$ lines between $z_1$ and~$z_2$, $P_{N-1}$, is
+assumed to be the Poisson distribution.
+%
+\beginfigure{5}
+\vskip 11pc
+\caption{{\bf Figure A1.} $P(>x_{\rm gap})$ as a function of
+$x_{\rm gap}$ for, from left to right, $N=160$, 150, 140, 110, 100, 90, 50,
+45 and~40.}
+\endfigure
+
+\subsection{Subsection title}
+
+We plot in Fig.~A1 $P(>x_{\rm gap})$ for several $N$ values.
+We see that, for $N=100$ and $x_{\rm gap}=0.06$, $P(>0.06)\approx 20$
+per cent. This means that the
+\ifsinglecol\else \vadjust{\vfill\eject}\fi
+probability of finding a gap with a size
+larger than six times the mean separation is not significantly small.
+When the mean number of lines is large, $\lambda\sim N>>1$, our
+$P(>x_{\rm gap})$ approaches the result obtained by Ostriker et~al.\ (1988)
+for small (but still very large if measured in units of the mean separation)
+$x_{\rm gap}$, i.e., $P(>x_{\rm gap})\sim N(1-x_{\rm gap})^{N-1}\sim N
+{\rm exp}(-\lambda x_{\rm gap})$.
+
+
+\bye
+
+% end of mnsample.tex