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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
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- \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}
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-\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