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diff --git a/Master/texmf-dist/doc/plain/mnras/mnsample.tex b/Master/texmf-dist/doc/plain/mnras/mnsample.tex deleted file mode 100644 index b19ea01c605..00000000000 --- a/Master/texmf-dist/doc/plain/mnras/mnsample.tex +++ /dev/null @@ -1,705 +0,0 @@ -% 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 - -\ifCUPmtplainloaded \else - \NewTextAlphabet{textbfit} {cmbxti10} {} - \NewTextAlphabet{textbfss} {cmssbx10} {} - \NewMathAlphabet{mathbfit} {cmbxti10} {} % for math mode - \NewMathAlphabet{mathbfss} {cmssbx10} {} % " " " - % - \ifAMStwofonts - % - \NewSymbolFont{upmath} {eurm10} - \NewSymbolFont{AMSa} {msam10} - \NewMathSymbol{\upi} {0}{upmath}{19} - \NewMathSymbol{\umu} {0}{upmath}{16} - \NewMathSymbol{\upartial}{0}{upmath}{40} - \NewMathSymbol{\leqslant}{3}{AMSa}{36} - \NewMathSymbol{\geqslant}{3}{AMSa}{3E} - \let\oldle=\le \let\oldleq=\leq - \let\oldge=\ge \let\oldgeq=\geq - \let\leq=\leqslant \let\le=\leqslant - \let\geq=\geqslant \let\ge=\geqslant - \else - \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} - -\beginrefs -\bibitem Baird S.R., 1981, ApJ, 245, 208 -\bibitem Beichman C.A., Neugebauer G., Habing H.J., Clegg P.E., - Chester T.J., 1985a, {\it IRAS\/} Point Source Catalog. Jet - Propulsion Laboratory, Pasadena -\bibitem Beichman C.A., Neugebauer G., Habing H.J., Clegg P.E., - Chester T.J., 1985b, {\it IRAS\/} Explanatory Supplement. 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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 |