From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- .../macros/latex209/contrib/mnras/mnsample.tex | 743 +++++++++++++++++++++ 1 file changed, 743 insertions(+) create mode 100644 obsolete/macros/latex209/contrib/mnras/mnsample.tex (limited to 'obsolete/macros/latex209/contrib/mnras/mnsample.tex') diff --git a/obsolete/macros/latex209/contrib/mnras/mnsample.tex b/obsolete/macros/latex209/contrib/mnras/mnsample.tex new file mode 100644 index 0000000000..ec0105d7a4 --- /dev/null +++ b/obsolete/macros/latex209/contrib/mnras/mnsample.tex @@ -0,0 +1,743 @@ +% mnsample.tex +% +% v1.2 released 5th September 1994 (M. Reed) +% v1.1 released 18th July 1994 +% v1.0 released 28th January 1994 + +\documentstyle{mn} + +% If your system has the AMS fonts version 2.0 installed, MN.sty 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. +% +% If you are using AMS 2.0 fonts, bold math letters/symbols are available +% at a larger range of sizes for NFSS release 1 and 2 (using \boldmath or +% preferably \bmath). + +\newif\ifAMStwofonts +%\AMStwofontstrue + +%%%%% AUTHORS - PLACE YOUR OWN MACROS HERE %%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ifoldfss + % + \newcommand{\rmn}[1] {{\rm #1}} + \newcommand{\itl}[1] {{\it #1}} + \newcommand{\bld}[1] {{\bf #1}} + % + \ifCUPmtlplainloaded \else + \NewTextAlphabet{textbfit} {cmbxti10} {} + \NewTextAlphabet{textbfss} {cmssbx10} {} + \NewMathAlphabet{mathbfit} {cmbxti10} {} % for math mode + \NewMathAlphabet{mathbfss} {cmssbx10} {} % " " " + \fi + % + \ifAMStwofonts + % + \ifCUPmtlplainloaded \else + \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 + \fi + % + \fi +% +\fi % End of OFSS + +\ifnfssone + % + \newmathalphabet{\mathit} + \addtoversion{normal}{\mathit}{cmr}{m}{it} + \addtoversion{bold}{\mathit}{cmr}{bx}{it} + % + \newcommand{\rmn}[1] {\mathrm{#1}} + \newcommand{\itl}[1] {\mathit{#1}} + \newcommand{\bld}[1] {\mathbf{#1}} + % + \def\textbfit{\protect\txtbfit} + \def\textbfss{\protect\txtbfss} + \long\def\txtbfit#1{{\fontfamily{cmr}\fontseries{bx}\fontshape{it}% + \selectfont #1}} + \long\def\txtbfss#1{{\fontfamily{cmss}\fontseries{bx}\fontshape{n}% + \selectfont #1}} + % + \newmathalphabet{\mathbfit} % math mode version of \textbfit{..} + \addtoversion{normal}{\mathbfit}{cmr}{bx}{it} + \addtoversion{bold}{\mathbfit}{cmr}{bx}{it} + % + \newmathalphabet{\mathbfss} % math mode version of \textbfss{..} + \addtoversion{normal}{\mathbfss}{cmss}{bx}{n} + \addtoversion{bold}{\mathbfss}{cmss}{bx}{n} + % + \ifAMStwofonts + % + \ifCUPmtlplainloaded \else + % + % Make NFSS 1 use the extra sizes available for bold math italic and + % bold math symbol. 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V. Raveendran] + {A. V. Raveendran \\ + Indian Institute of Astrophysics, Bangalore 560034, India} +\date{Accepted 1988 December 15. + Received 1988 December 14; + in original form 1988 October 11} + +\pagerange{\pageref{firstpage}--\pageref{lastpage}} +\pubyear{1994} + +\begin{document} + +\maketitle + +\label{firstpage} + +\begin{abstract} +In the {\it IRAS\/} [12]--[25], [25]--[60] colour--colour diagram, RV +Tauri stars are found to populate cooler temperature regions +$(T<600\,\rmn{K})$, 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. +\end{abstract} + +\begin{keywords} +circumstellar matter -- infrared: stars. +\end{keywords} + +\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 +\hbox{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). +\begin{table*} + \centering + \begin{minipage}{140mm} + \caption{Data on the RV Tauri stars detected by {\it IRAS}.} + \begin{tabular}{@{}llrrrrlrlr@{}} + Name & & \multicolumn{4}{c}{Flux density (Jy)% + \footnote{Observed by {\em IRAS}.}}\\ + Variable & {\it IRAS} & 12$\,\umu$m & 25$\,\umu$m & 60$\,\umu$m + & 100$\,\umu$m & Sp. & Period & Light- & $T_0\,(\rmn{K})$ \\ + & & & & & & group & (d) & curve \\ + & & & & & & & & type \\[10pt] + TW Cam & 04166$+$5719 & 8.27 & 5.62 & 1.82 & $<$1.73 & A & 85.6 & a & 555 \\ + RV Tau & 04440$+$2605 & 22.53 & 18.08 & 6.40 & 2.52 & A & 78.9 & b & 460 \\ + DY Ori & 06034$+$1354 & 12.44 & 14.93 & 4.12 & $<$11.22 & B & 60.3 & & 295 \\ + CT Ori & 06072$+$0953 & 6.16 & 5.57 & 1.22 & $<$1.54 & B & 135.6 & & 330 \\ + SU Gem & 06108$+$2734 & 7.90 & 5.69 & 2.16 & $<$11.66 & A & 50.1 & b & 575 \\ + UY CMa & 06160$-$1701 & 3.51 & 2.48 & 0.57 & $<$1.00 & B & 113.9 & a & 420 \\ + U Mon & 07284$-$0940 & 124.30 & 88.43 & 26.28 & 9.24 & A & 92.3 & b & 480 \\ + AR Pup & 08011$-$3627 & 131.33 & 94.32 & 25.81 & 11.65 & B & 75.0 & b & 450 \\ + IW Car & 09256$-$6324 & 101/06 & 96.24 & 34.19 & 13.07 & B & 67.5 & b & 395 \\ + GK Car & 11118$-$5726 & 2.87 & 2.48 & 0.78 & $<$12.13 & B & 55.6 & & 405 \\ + RU Cen & 12067$-$4508 & 5.36 & 11.02 & 5.57 & 2.01 & B & 64.7 & & 255 \\ + SX Cen & 12185$-$4856 & 5.95 & 3.62 & 1.09 & $<$1.50 & B & 32.9 & b & 590 \\ + AI Sco & 17530$-$3348 & 17.68 & 11.46 & 2.88 & $<$45.62 & A & 71.0 & b & 480 \\ + AC Her & 18281$+$2149 & 41.47 & 65.33 & 21.12 & 7.79 & B & 75.5 & a & 260 \\ + R Sct & 18448$-$0545 & 20.88 & 9.30 & 8.10 & $<$138.78 & A & 140.2 & a \\ + R Sge & 20117$+$1634 & 10.63 & 7.57 & 2.10 & $<$1.66 & A & 70.6 & b & 455 \\ + V Vul & 20343$+$2625 & 12.39 & 5.72 & 1.29 & $<$6.96 & A & 75.7 & a & 690 +\end{tabular} +\end{minipage} +\end{table*} + +\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 +\begin{equation} + L(\nu)=\mskip-12mu\int\limits_{\rmn{envelope}}\mskip-12mu + \rho(r)Q_{\rmn{abs}}(\nu)B[\nu,T_{\rmn{g}}(r)]\exp [-\tau(\nu,r)]\> + \rmn{d}V, +\end{equation} + where + $Q_{\rmn{abs}}(\nu)$ is the absorption efficiency at frequency $\nu$, + $\rho(r)$ is the dust grain density, + $T_{\rmn{g}}(\nu)$ is the grain temperature, + $B[\nu,T_{\rmn{g}}(r)]$ is the Planck function, and + $\tau(\nu,r)$ is the optical depth at distance {\it r\/} from the + centre of the star. + +The temperature $T_{\rmn{g}}(r)$ 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: +\begin{enumerate} + \item the attenuated and diluted stellar radiation; + \item scattered radiation, and + \item reradiation from other grains. +\end{enumerate} + +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 $[\tau(\rmn{UV})\gg 10]$, and at +optical depths $\tau(\rmn{UV})<1$ 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 $Q_{\rmn{abs}} (\nu)$ 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 $T_{\rmn{g}}$ 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 +\begin{equation} + L(\nu)=\!\!\int_{r_{1}}^{r_{2}}\!\!4\upi r^2\rho(r)\> Q_{\rmn{abs}}(\nu)B[\nu,T_{\rmn{g}}(r)]\> {\rmn{d}}r, +\end{equation} +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 +\begin{equation} + L(\nu)\propto \nu^{2+\gamma-Q}\int_{X_0}^{\infty}{{x^Q}\over + {\rmn{e}^x-1}}\rmn{d}x , +\end{equation} +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 \hbox{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. +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 $Q_{\rmn{abs}}(\nu)$ 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). + +\begin{figure} + \vspace{302pt} + \caption{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 $\sim 0.05$.} +\end{figure} +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 +$Q_{\rmn{abs}}(\nu)$ 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. + +At \hbox{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 \hbox{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 \hbox{100\,$\umu$m} but, in view of the +large values for the cirrus flags given in the catalogue, the intrinsic +flux at \hbox{100\,$\umu$m} is uncertain. + +\subsection{Radial distribution of dust} + +\begin{figure*} + \vspace*{174pt} + \caption{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.} +\end{figure*} + +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 $\skew5\bar q=0.98$. 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 $Q_{\rmn{abs}}(\nu)$ 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 $\sim$300\,K. We find that the {\it K--L\/} +colours given by Gehrz (1972), Lloyd Evans (1985) and Goldsmith et +al. (1987) are all consistent with each other. Surely, hot dust ($\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). +\begin{figure} + \vspace*{174pt} + \caption{Plot of ({\it K--L\/}) colours of RV Tauri stars detected by + {\it IRAS\/} against their corresponding ({\it 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.} +\end{figure} + +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. +% +\begin{figure*} +\vbox to 220mm{\vfil +Landscape figure to go here. This figure was not part of the original +paper and is inserted here for illustrative purposes.\\ See the author +guide for details on how to handle landscape figures or tables, and +\verb|mnland.tex|. +\caption{} +\vfil} +\label{landfig} +\end{figure*} + +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 $(T<600 \,\rmn{K})$, distinctly different from +those occupied by the oxygen and carbon Miras. Using a simple model +in which +\begin{enumerate} + \item the envelope is spherically symmetric, + \item the IR-emitting grains are predominantly of the same kind, and + \item in the infrared the absorption efficiency $Q_{\rmn{abs}} + (\nu)\propto\nu$, +\end{enumerate} +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. + + +\begin{thebibliography}{99} +\bibitem{b1} Baird S.R., 1981, ApJ, 245, 208 +\bibitem{b2} 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{b3} 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 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 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 $z_{\rmn{em}}$ and $z_1$ is set to +$(\lambda_{\rmn{Ly}\beta}/\lambda_{\rmn{Ly}\alpha})(1+z_{\rmn{em}})=0.844 +(1+z_{\rmn{em}})$ 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~$x$: +% +\begin{equation} +x={(1+z)^{\gamma+1}-(1+z_1)^{\gamma+1} \over + (1+z_2)^{\gamma+1}-(1+z_1)^{\gamma+1}}. +\end{equation} +% +$x$ varies from 0 to 1. We then have $\rmn{d}N/\rmn{d}x=\lambda$, where $\lambda$ +is the mean number of lines between $z_1$ and $z_2$ and is given by +% +\begin{equation} +\lambda\equiv{A[(1+z_2)^{\gamma+1}-(1+z_1)^{\gamma+1}]\over\gamma+1}. +\end{equation} +% +This means that the 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. +% +\newpage +% +\begin{figure} +\vspace{11pc} +\caption{$P(>x_{\rmn{gap}})$ as a function of $x_{\rmn{gap}}$ for, + from left to right, $N=160$, 150, 140, 110, 100, 90, 50, 45 and~40.} +\label{appenfig} +\end{figure} + +\subsection{Subsection title} + +We plot in Fig.~\ref{appenfig} $P(>x_{\rmn{gap}})$ for several $N$ values. +We see that, for $N=100$ and $x_{\rmn{gap}}=0.06$, $P(>0.06)\approx20$ +per cent. This means that the 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 +$P(>x_{\rmn{gap}})$ approaches the result obtained by Ostriker et al.\ +(1988) for small (but still very large if measured in units of the mean +separation) $x_{\rmn{gap}}$, i.e., $P(>x_{\rmn{gap}})\sim N(1- +x_{\rmn{gap}})^{N-1}\sim N {\rmn{exp}}(-\lambda x_{\rmn{gap}})$. + +\bsp + +\label{lastpage} + +\end{document} -- cgit v1.2.3