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diff --git a/Master/texmf-dist/doc/plain/mnras/mnsample.tex b/Master/texmf-dist/doc/plain/mnras/mnsample.tex new file mode 100644 index 00000000000..b19ea01c605 --- /dev/null +++ b/Master/texmf-dist/doc/plain/mnras/mnsample.tex @@ -0,0 +1,705 @@ +% 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 |