H LO CM I Publications OFTHE Astronomical Society

>H CMLO i Publications OFTHE Astronomical Society of the Pacific CTi 99:425-438, May 1987

S< THE SPECTRAL VARIATIONS OF THE DELTA SCUTI STAR RHO PUPPIS r-cu \—Is s. YANG,* G. A. H. WALKER,* AND P. BENNETT Department of Geophysics and Astronomy, University of British Columbia, Vancouver, BC V6T 1W5, Canada Received 1986 December 12, revised 1987 February 9

ABSTRACT Precise differential radial velocities of the sharp-lined (υ sin ί = 14 km s _1) δ Scuti variable ρ Pup (P = 3.37 hours) with a time resolution < P/15givea2Kamplitude of 9.08 km s_1for Ca II λ8662 and 8.35 km s-1 for Η ΐλ8750. The amplitudes for the Fe I, Si I, and S I velocities are 9.46, 9.23, and 9.41 -1 1 -1 km s , respectively. The 2 Κ/Διηυ value of 93 km s mag is typical of a radial pulsator. The line intensities of the stellar lines vary out of phase with the observed radial velocities but closer in phase with the light curve. The amplitudes of the variations are between 0.3% and 1% of the continuum. Most lines are weaker near light maximum (temperature maximum) and stronger near light minimum (temperature minimum). The variations correspond to the changes in spectral type associated with the variations of eifective temperature over the pulsation cycle. A simple linear theory is developed in which the temperature dependence of both the stellar continuum opacity and line opacity are calculated. Key words: δ Scuti variable-radial velocities-equivalent widths

I. Introduction metric data and derived a period of 0^14088141 (3.3712 The star ρ Puppis (HR 3185, HD 67523) is a small-am- hours) and a blue-light amplitude of 0.126 mag. The light plitude, sharp-lined {v sin ¿ = 14 km s ^), δ Scuti variable curve was found to be nearly sinusoidal with the maxi- with a spectral type of F5 Hp (Morgan and Abt 1972). The mum slightly sharper than the minimum. Both the rising star is similar to the proto-Am (δ Delphini-type) stars and descending branches of the curve are equally steep. which show anomalous metal abundances. The enhanced Bappu (1959) measured a light amplitude of 0.16 mag at metal abundance in ρ Pup has been confirmed by Green- λ4050 together with a 300 Κ change in the color tempera- stein (1948), Bessell (1969), Breger (1970), and Kurtz ture. The simultaneous photometric and spectroscopic (1976). A value of 0.54 dex has been determined for observations by Danziger and Kuhi (1966) give a 2 Κ value -1 [Fe/H] by Kurtz (1976) who also found deficiencies in of 11 km s , a light amplitude of 0.15 mag at λ4566, and Ca i, Se II, Ti π, and V π. Meanwhile, Bidelman (1951), an effective-temperature variation of ± 140 K. Minimum McNamara and Augason (1962), and Morgan and Abt light was found to occur at about 0.08 of a period before (1972) have all pointed out that Ca π is weak in ρ Pup maximum radial velocity. when compared to stars of similar spectral type. Bessell (1969), using simultaneous radial-velocity and The star ρ Pup was first reported to exhibit variable photoelectric spectrum-scanner observations of the con- radial velocities by Reese (1903) and Campbell and Moore tinuum, measured a light amplitude of 0.130 mag at (1928). These early Lick velocities suggested a 2 Κ value X4255 and a 2 Κ value of 9.5 km s_1. One can measure (the peak-to-peak radial-velocity amplitude) of 8.4 km s_1. from his data that the radial-velocity minimum lags the Meanwhile, Spencer Jones (1928) derived a 2 Κ value of light maximum by about 0.075 in phase. Bessell (1969) has 11.6 km s-1 from Cape observations. The data from also reported a temperature variation of ± 65 Κ and a Struve, Sahade, and Zebergs (1956) has a 2 Κ amplitude of radius variation, AR, of ± 8 X 103 km. Thulasi Doss 9.7 km s-1 and a period of 0?1409. Additional radial-veloc- (1969) observed the photometric variations in the narrow ity measurements were also reported by Buscombe passbands at λ3858, λ4310, λ4720, and λ5875. The corre- (1957). Photometric variations were first reported by sponding amplitudes were given as 0.17, 0.14, 0.12, and Cousins (1951) and Eggen (1956, 1957). Ponsen (1963) 0.09 mag, respectively. An effective-temperature varia- reanalyzed all the early data together with his own photo- tion of ± 160 Κ and a period of 0^14088667 were also derived. Trodahl and Sullivan (1977) measured a light *Visiting Astronomer, Canada-France-Hawaii Telescope, which is amplitude of 0.105 mag at X4850 and an effective-temper- operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique of France, and the University of ature variation of ± 90 K. A corresponding amplitude of Hawaii. about 0.033 was given for AR/R, the relative radius varia-

425

tion. Dravins, Lind, and Sarg (1977), with simultaneous period of 0^141 (3.37 hours), respectively. Period cover- radial-velocity and photometric observations, have mea- age on the three nights was 83%, 112%, and 69%, respec- sured a phase lag of 0.06 between the radial-velocity tively. The mean S/N per diode (pixel) in the continuum of minimum and the light maximum. A temperature of ± each spectrum is 690, 800, and 400 for the three respec- 80 Κ was measured from the loop traveled by ρ Pup in the tive nights of observations. The midexposure time (in {c^ (b—y)) diagram over the pulsation cycle. Dravins et barycentric Julian day) of each observation is listed in al. (1977) also reported emission in the blue wing of the Table I. Ca π Κ line profile at about 0.28 in phase before maximum A spectrum of ρ Pup without the imposed HF lines is light. It has been suggested that the emission was caused shown in Figure 1. Lines from the same atomic or ionic by a shock wave propagating through the stellar atmo- species are indicated with the same number and are sphere (Dravins et al. 1977; Hill 1977; Smith 1982). identified in the caption. Simultaneous photometry and photoelectric radial veloc- The data reduction was performed using the program ities have also been given by Balona and Stobie (1983). RETICENT (Pritchet, Mochnacki, and Yang 1982). The With a Reticon detector, Campos and Smith (1980) mea- technique of preprocessing the Reticon spectra to obtain sured a 2 Κ value of 11.5 km s-1 from the Fe I λ4476 and the optimum S/N has been described in Walker et al. Fe π λ4508 lines. No line width or line-profile variation (1985). The procedure to measure radial velocities from greater than 5% of the continuum was detected. the stellar + HF spectra has been described in Yang et al. Smith (1982) adopted, for ρ Pup, a Δτη^ value (the peak- (1982) and Yang and Walker (1986α,&). The same stan- to-peak light amplitude in V) of 0.102 mag and a phase dard stellar and lamp + HF spectra were used to measure difference of 0.08 between the light maximum and the the radial velocities from all of the spectra. This ensures radial-velocity minimum. Reay, Hicks, and Atherton internal consistency for the measured velocities between (1983) used a servo-controlled Fabry-Perot-radial-veloc- the three time series. ity spectrometer to measure the radial-velocity variations TABLE I of Pup with a precision of ± 20 m s_1. From 226 minutes ρ Relative Radial Velocities of ρ Puppis (3.76 hours) of observations, there was no evidence of periodicity other than the period of 0^141. Fracassini et Mid-exposure Ca II mean mean mean time λ8662 Fe I Si I S I al. (1983) have reported a time series of IUE high-disper- BJD2445356+ (kms"1) (kms"1) (kms"1) (kms-1) sion observations of the Mg π H and Κ lines. Emission in 0.90112 -1.118 -1.119 -0.855 -0.950 the cores of the lines was found to be present over the 0.90839 +0.245 +0.211 +0.341 +0.462 0.91564 +1.484 +1.508 +1.715 +1.846 entire pulsation cycle. These emissions increased with 0.92289 +2.590 +2.694 +2.956 +3.056 increasing luminosity of the star. 0.93021 +3.702 +3.824 +3.968 +4.007 0.93748 +4.525 +4.600 +4.695 +4.793 Because it is so bright (V = 2.82 mag), ρ Pup offers a 0.94473 +4.771 +4.860 +4.976 +5.002 0.95197 +4.758 +4.655 +4.871 +4.767 rather unique opportunity to apply high S/N spectra to 0.95921 +4.079 +3.866 +4.107 +4.017 0.96646 +2.898 +2.793 +2.713 +2.803 the study of δ S cuti pulsation. In this paper, we report the 0.97372 +1.521 +1.162 + 1 .309 + 1 .244 results obtained with spectra having S/N in the range 400 0.98097 -0.213 -0.571 -0.651 -0.603 0.98821 -1.948 -2.384 -2.234 -2.332 to 800 per pixel. Radial velocities of ρ Pup were measured 0.99545 -3.220 -3.674 -3.447 -3.663 1.00271 -4.105 -4.526 -4.310 -4.518 using the hydrogen fluoride (HF) absorption-cell tech- 1.00996 -4.361 -4.761 -4.629 -4.799 nique (Campbell and Walker 1979; Yang and Walker 1.01844 -4.137 -4.544 -4.256 -4.629 2.84152 -4.644 -4.772 -4.768 -4.686 1986a). Precision was limited by line-profile variations 2.85246 -3.934 -4.097 -3.964 -4.046 2.86784 -2.259 -2.379 -2.267 -2.211 which were probably caused by temperature effects over 2.87868 -0.498 -0.592 -0.378 -0.440 the pulsation cycle. 2.88951 +1.460 +1.456 +1.652 + 1 .585 2.90036 +3.065 +3.191 +3.322 +3.283 2.91030 +4.206 +4.362 +4.450 +4.460 II. The Observations 2.91931 +4.587 +4.798 +4.746 +4.791 2.92924 +4.138 +4.228 +4.116 +4.319 One spectral time series was taken with the H F absorp- 2.94014 +2.433 +2.519 +2.548 +2.551 2.95098 +0.096 +0.058 +0.176 +0.141 tion cell at the Canada-France-Hawaii 3.6-m telescope on 2.96171 -2.288 -2.457 -2.367 -2.277 2.97244 -3.953 -4.094 -3.948 -3.972 each of 1983 January 22, 24, and 25 UT with the//7.4 2.98326 -4.472 -4.720 -4.464 -4.646 2.99401 -4.056 -4.196 -4.100 -4.138 coudé four-grating mosaic spectrograph (Brealey et al. 3.00474 -2.841 -2.964 -2.767 -2.862 1980) using a refrigerated RL1872F/30 EG&G Reticon as 3.01547 -1.067 -1.041 -0.875 -0.917 3.02621 +0.965 +0.987 +1.086 + 1 .146 detector (Walker, Johnson, and Yang 1985). The grating, 3.85436 -2.114 -2.220 -1.990 -1.955 3.86507 -0.336 -0.361 -0.178 -0.319 blazed at λ8000, gives a reciprocal dispersion in the first 3.87580 + 1 .383 +1.534 +1.807 + 1 .639 order of 4.8 A mm"1 at X8700. This corresponds to a 3.88652 +2.907 + 3.155 +3.398 +3.077 -1 3.89739 + 4..204 +4.262 +4.439 +4.151 dispersion of about 0.071 A pixel on the Reticon array. 3.90816 + 4..489 +4.500 +4.512 +4.393 3.91893 + 3..633 +3.689 +3.562 +3.647 The spectral coverage is about 130 A and the exposures 3.92969 M .862 +1.803 +1.887 + 1 .718 were one of 600, 750, or 900 seconds each. These corre- 3.94046 -0.553 -0.701 -0.901 -0.895 3.95118 -2.856 -3.136 -3.096 -3.230 spond to about 0.05, 0.062, and 0.074 of the cycle-count

1.00

0.75 -

0.50

0.25 8650 8675 8700 8725 8750 8775 Uaveiength (angstroms)

Fig. 1—A spectrum of ρ Pup with the major spectral lines identified: 1 — Ca π X8662; 2 — Η ι λ8665 and X8750; 3 — Fe I λ8675, λ.8689, λ8699, λ.8710, λ8713, λ8757, and λ8764; 4 - S ι λ8671, λ8680, and λ8695; 5 - Si ι λ8648, λ8686, λ8728, λ8742, and λ8752; 6 - Mg ι λ8718 and λ8736; 7 - Ν I λ8683; 8 - Μη ι λ8704; 9 - Al I λ8773 and λ8774.

III. The Line-Profile Variations Figure 3(b) are shown the corresponding residuals. The Individual radial-velocity curves were initially mea- average spectrum used to produce the residuals is calcu- sured with the conventional Fahlman-Glaspey differ- lated as the mean of the 15 spectra taken between ence-function technique (Fahlman and Glaspey 1973) for BJD2445358.879 and BJD2445359.026 and would repre- sent the mean spectrum over approximately one pulsa- the stellar lines Ca π X8662, Η i X8750, Mg i X8718, Fe I X8689, X8710, X8713, λ8757, λ8764, Si ι λ8686, λ8728, tion cycle. All the spectra in the plots have been λ8742, λ8752, S ι λ8680, and λ8695. The average, one- smoothed by a Gaussian transfer function with a σ value of standard-deviation uncertainties in the line-position mea- 0.075 A. It is evident from the residual plots that there are surements are ± 0.08 km s-1 and ± 0.16 km s1 for the line-profile variations at levels between 0.7% (the Sil 8752 line) and 1% (the Fe I 8689 line) of the continuum. strong Ca π λ8662 and Fe ι λ8689 lines, respectively. The λ λ corresponding values for the other lines are also large, The Ca π λ8662 residuals show a similar variation but at a e.g., ± 0.37kms_1fortheFe lX87571ine. As pointed out level of only 0.5% of the continuum. The Si I λ8686 and λ8728 lines show variations at a level of only 0.3% of the in Yang and Walker (1986a?¿), such large error estimates imply that the line profiles must vary through the series continuum. The line-profile variations can be described and provide a measure of the variations. Moreover, the as systematic variations in the line depth or equivalent magnitude of the errors is not random and appears to width of the line. Near the light minima at both correlate with pulsation phases. Two maxima in the error BJD2445358.90 and BJD2445359.03, the stellar absorp- curve occur about 0.07 in phase before the velocity maxi- tion lines are stronger than the mean line profile. And mum and minimum. Since the light minimum leads the the lines are weaker near the light maximum at velocity maximum by 0.08 in phase, the error curve BJD2445358.97. would be more in phase with the light curve than the Similar, but larger, equivalent-width variations have radial-velocity curve. One maximum would be close in been reported in the peculiar large-amplitude δ Scuti time to the light minimum and the other maximum close variable SX Phoenicis (Stock and Tapia 1971; Haefner, to the light maximum. Metz, and Schoembs 1976). The absorption-line intensi- The line-profile variations can best be examined from a ties were also found to be minimal near maximum light plot of the residuals obtained by subtracting an average while the maxima of the line intensities occurred near line profile from each spectrum after correcting for the light minima. This same sequence of line-intensity varia- observed velocity shifts. In Figures 2(a) and 2(b) are tions over a pulsation cycle occurs for the Cepheid vari- shown the Fe I λ8689 line profiles and the corresponding ables and corresponds to the well-known spectral-type residuals, respectively, for 1983 January 24 UT. In Figure variation. The spectral type of long-period Cepheids can 3(a) are shown the region of the Η ι λ8750. Si ι λ8752, vary between F5 and K1 over a pulsation cycle. The larger and Fe I λ8757 lines also for 1983 January 24 UT, while in effect in Cepheids is essentially caused by their much

0.84152 0.85246

0.86784 0.87868 0.88951 0.90036 0.91030 0.91931 0.92924 0.94014 0.95098 0.96171 0.97244 0.98326 0.99401 1.00474 1.0T547 1.02621

Mean

8687 8689

Fig. 2(a)-The Fe ι λ8689 line profiles for 1983 January 24 UT after correcting for the observed velocity shifts. The midexposure time from BJD2445358 is indicated.

larger change in effective temperature over the pulsation cycle. In ρ Pup, the effective-temperature amplitude is only about ± 140 K. The observed lines of Ca II, Fe I, and Si I are known to be stronger in stars of spectral types slightly later (or cooler) than ρ Pup. These lines are also weaker in stars of earlier (or hotter) spectral types. If the observed line-intensity variations are caused mainly by temperature variations over the pulsation cycle, they should be stronger near temperature minima which almost coincide with the Fig. 2(b)-The residuals of the individual X8689 line profiles after sub- light minima (Danziger and Kuhi 1966) and weaker near traction of a mean line profile.

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System THE DELTA SCUTI STAR RHO PUPPIS 429 temperature maxima which almost coincide with the light Despite the success of the simple theory in predicting the maxima. This is exactly the sequence of line-intensity sense of the observed variations, it is unable to account for variations that is observed in ρ Pup. their amplitudes. The degree of ionization and, hence, Temperature variations affect the observed line depth the associated depletion of neutral hydrogen atoms has to through the temperature dependence of both the stellar be taken into account. continuum level (where continuum opacity is mainly a The line of Ν IX8683 for which EL = 10.33 eV (Moore et function of the number of ΗΓ ions) and the energy-level al. 1966) also shows variations in the opposite sense to the population of the particular stellar-line transition (line Fe ι X8757 line. Equation (1) predicts this 180° phase opacity). Assuming LTE and considering only weak iso- difference with a Ad/d value of ± 0.15, while the ob- lated stellar lines and small temperature variations, one served value is about ± 0.19. The agreement between can derive a simple relation to describe the main effect of the predicted and observed values of Ad/d is less satisfac- the observed line-depth variations: tory for lines which have EL values close to 5.6 eV for which equation (1) would predict Δί/ value of zero. This kd/d = (1 — d) (ΔΤ/Γ) condition is true for most of the lines: Fe I X8699, X8710, X (EJikT) - 7.01316 Χ 104/Γ + 0.7475) . (1) X8713, X8764, Si X8680, X8695, Si ι X8646, X8686, In equation (1), d is the line depth, Τ is the temperature, X8728, X8742, and Mg I X8718. Equation (1) generally EL is the lower energy level of the line, and k is the gives lower-than-observed kdld values for these lines. Boltzmann constant. The derivation of equation (1) is Higher-order effects (e.g., other sources of opacity) may given in the Appendix. For ρ Pup, ΔΤ is about ± 140 Κ be important for these lines. Nevertheless, the good (Danziger and Kuhi 1966) and Τ is about 7100 Κ (Kurtz agreement between the predicted and observed direction 1976). Therefore, knowing £L and d for a line, the corre- of variations for most of the lines as well as between the sponding kd/d can be calculated. predicted and observed kd/d values of some of the lines The maximum line-depth change observed in the Fe I strongly strengthens the conclusion that temperature λ8757 line is about ± 0.8% of the continuum. Since the variations are responsible for the line-profile variations. line depth is about 10% of the continuum, the observed Moreover, the observed variations are consistent with a Δίί/d values are then +0.08 at temperature minimum and temperature variation of ± 140 K. —0.08 at temperature maximum. Using an jEl value of The Fe ι X8689 residual plot in Figure 2(b) appears to 2.84 eV (Moore, Minnaert, and Houtgast 1966) for this be more complicated than just simple line-depth or line, equation (1) gives a Ad/d value of —0.081 for ΔΓ = equivalent-width variations. The line core seems to vary + 140 Κ and a value of +0.081 for ΔΓ = —140 K. These inversely with the rest of the line. The amplitude of this agree very well with the observed values. In fact, the small reversal in the core is less than 0.3% of the contin- agreement is better than expected since the line is located uum and it remains stationary about —0.15 A from the in the far wing of a broad Paschen line and, hence, not line core. It can also be seen at a lower level in the Si I perfectly isolated. X8752 and Fe I X8757 lines in Figure 3(b). This apparent The agreement is less satisfactory for the strong Fe I core reversal is too marginal for a more detailed analysis λ8689 line. The calculated kd/d for this line is ± 0.08 with these spectra. while the observed value is only ± 0.03. The discrepancy The line-profile variations can also be described quanti- between the calculated and the observed values becomes tatively by the variations of the equivalent widths. Figure even larger for the Ca π λ8662 line. These inconsistencies 4 shows the equivalent-width variations of the Fe I X8689 were expected since equation (1) is valid only for isolated line. The corresponding radial-velocity curve of the line is weak lines. Nevertheless, the theory still predicts the also superimposed on the plot. The phase difference be- sense of the line-depth variations. tween the equivalent widths and radial velocities is very For a line with a sufficiently large Eh value, there will striking. Only partial equivalent widths were actually be a sign change in kd/d in equation (1). The line would measured. The line limits correspond to the two inflec- then vary in the opposite sense, being strongest at tem- tion points of the standard line profile which are identical perature maxima and weakest at temperature minima. to the line limits used to measure the radial velocities This condition is true for the Paschen λ8750 line for which (Yang and Walker 1986a). As with the radial velocities, Eh = 12.08 eV (Moore et al. 1966). It is well known that the mean value over a pulsation cycle has been subtracted the hydrogen lines become progressively weaker in stars from the measured, partial equivalent widths. For a given of spectral types later (or cooler) than ρ Pup. Examining line, the true equivalent width (integrated over the full the stacked residual plots in Figure 3(b), one can observe width of the line) differs from the corresponding partial that, at the position of the Paschen line, the variations do equivalent width by a scale factor of 1.7. Partial equiva- go in the opposite direction with respect to the other lent widths were used because they are less susceptible to lines. In fact, the Η I X8750 residuals are in marked the effects of line blending in the wings. contrast to the direction of the Si I λ8752 line residuals. The partial equivalent-width variations of the Fe I

0.84152 0.85246

0.86784 0.87868 0.88951 0*90036 0.91030 0.91931 0.92924 0.94014 0.95098 0.96171 0.97244 0.98326 0.99401 1.00474 1.01547 102621

Mean

8748 8750 8752 8754 8756 8758

Fig. 3(a)—Same as Figure 2(a) for the Η ι λ8750, Si I λ8752) and Fe I λ8757 lines.

λ8757, Si ι λ8742, Η ι λ8750, and S ι λ8695 lines are the Paschen and Fe I curves. The similar phase differ- shown in Figures 5, 6, 7, and 8, respectively. In both the ences between the Fe ι and S I (EL — 7.9 eV) curves are phase and amplitude, the Si I λ8742 curve is typical of the also predicted by equation (1). This reinforces the sugges- other equivalent-width curves of Si I, Fe I, and Ca π lines tion that the observed equivalent width and, hence, the while the S ι λ8695 curve agrees with the S ι λ8680 curve. line-profile variations are caused by temperature varia- The phase difference between the equivalent widths and tions. the radial velocities is about 0.19 or 0.03 for the Fe I λ8689, Si ι λ8742, and other similar curves. The Fe I FV. The Radial Velocities λ8757 radial velocities, however, lag the equivalent An optimizing difference function has been used in- widths by about 0^02 or 0.13 in phase. In any case, the stead of the conventional difference function (Fahlman equivalent widths appear to lead the radial velocities by and Glaspey 1973) to measure relative line shifts. This larger phase values than the light curve. As expected, modified difference function scales the individual line there is an approximately 180° phase difference between profile linearly in order to produce an optimized match

Fig. 3(b)-The residuals of the individual spectra (in Fig. 3(a)) after subtraction of a mean line profile. with the standard line profile. The new error estimates for 0.06 km s-1, and ± 0.08 km s-1 for the lines Ca II λ8662, the line-position measurements are ± 0.03 km s ^ ± Fe ι λ8689, and λ8757, respectively. In addition to the

ρ Pup : Fe I λ8689 0.85 0.89 0.93 0.97 1.01

mZD

3D Q_ω

o η -2

CD -4

0.85 0.89 0.93 0.97 1.01 — BJD2445358+

Fig. 4-The relative, partial (see text), equivalent widths and radial velocities of the Fe I λ8689 line. Stars - the equivalent widths; circles - the radial velocities; triangles — spectra without HF lines imposed. BJD stands for barycentric Julian day.

ρ Pup : Fe I λ8757 0.85 0.89 0.93 0.97 1.01

0.85 0.89 0.93 0.97 1.01 BJD2445358+

Fig. 5-Same as Figure 4 for the Fe ι λ8757 line. much smaller values, the periodic trends caused by the Figures 4, 5, 6, 7, and 8, respectively. To produce the line-intensity variations have also disappeared in the new relative radial velocities, a mean velocity (calculated over error curves. an approximate pulsation cycle) has been subtracted from The radial-velocity curves for the lines Fe ι λ8689, each individual radial-velocity curve. Barycentric correc- λ8757, Si ι λ8742, Η ι λ8750, and S ι λ8695 are shown in tions based on the algorithm of Stumpif (1980) have also

ρ Pup : Si I λ8742 0.85 0.89 0.93 0.97 1.01

ΠΖΌ)

ro< 30 CLω

< ΓΌ

-2

0.85 0.89 0.93 0.97 1.01 BJD2445358+

Fig. 6-Same as Figure 4 for the Si ι λ8742 line.

ρ Pup : Η I λ8750 0.85 0.89 0.93 0.97 1.01

0.85 0.89 0.93 0.97 1 .01 BJD2445358+ Fig. 7-Same as Figure 4 for the Η ι λ8750 line.

been applied to all velocities. In Figures 9,10, and 11 are λ8695). shown the Ca π λ8662 velocities for the three time series. The mean error introduced into the velocities by the In Table I we list the relative radial velocities derived uncertainties of the HE line positions was about 0.03 km from the Ca ιι λ8662 line as well as the mean velocities of s 1 for the data taken on the second night. In Figure 12 is the Fe ι lines (λ8689, λ8710, K8757, and λ8764), the mean shown the error estimate in the individual HE dispersion velocities of the Si ι lines (λ8686, λ8728, λ8742, and fit which is essentially a measure of the mean error in the λ8752), and the mean velocities of the S I lines (λ8680 and HE line positions. The effect of relative differences

ρ Pup : S I λ8695 0.85 0.89

0.85 0.89 0.93 0.97 1 .01 BJD2445358+

FiG.-8-Same as Figure 4 for the S I λ8695 line.

ρ Pup : Ca II λ8662 0.88 0.92 0.96 1 .00 1 .04

lo ε

"O ra er

OJ er

0.88 0.92 0.96 1.00 1 .04 BJD2445356+

Fig. 9-The relative radial velocities of the Ca π λ8662 line on the night of 1983 January 22 UT. Triangles-spectra without HF lines imposed.

among the spectra has been removed from the plot. In result of the line-intensity variations of the stellar lines, spite of the low values which are indicative of the high S/N The varying residuals produced by the imperfect numeri- of the data, one can notice that the errors are not random. cal line-profile cancellations with the standard stellar In fact, they appear to be periodic with the maxima spectrum would affect the line-position measurements of occurring near the light minima of ρ Pup. This is another the HF lines and, hence, the measured velocities. This

ρ Pup : Ca II λ8662 0.85 0.89 0.93 0.97 1 .01

ω ε

CJ o QJ

TO cn OJ>

OJ C£

0.85 0.89 0.93 0.97 1 .01 BJD2445358+

Fig. 10-Same as Figure 9 for 1983 January 24 UT.

p Pup : Ca II λ8662 0.82 0.86 0.90 0.94 0.98

t/i ε

CJ o

~α ΓΌ er

QJ er

0.82 0.86 0.90 0.94 0.98 BJD2445359+ Fig. 11-Same as Figure 9 for 1983 January 25 UT. represents a practical limit to the accuracy with which V Π* velocities can be measured for a similar type δ Scuti * lscusslon variable using the conventional HF technique no matter Using the algorithm of Morbey (1978), a period of how high the S/N. 0.14095 was determined from the Ca π velocities. In view

ρ Pup ; Standard error in HF dispersion fit 0.85 0.89 0.93 0.97

0.06 - ω ε

0.04 -

QJ U cz 0.02 - u o * QJ 0.00 -

0.85 0.89 0.93 0.97 1.01 BJD2445358+

Fig. 12-The uncertainties in the dispersion fit of the HF lines. These are essentially estimates of the mean errors in the HF line-position measurements. The maxima are near the times of minimum light for ρ Pup.

of the rather short time coverage, this agrees quite well^ ging behind the other curves is similar to the classical Van with the periods given by Ponsen (1963) and Thulassi Hoof effect (Van Hoof 1957) which has also been observed Doss (1969). in the δ Scuti star β Cassiopeiae (Yang et al. 1982). -1 The Ca π λ8662 velocities have a 2 Κ value of 9.08 km Using the 2 Κ value of the Fe I lines, avalué of 93 km s 1 -1 s while the value for the Η ι λ8750 velocities is 8.35 km mag is obtained for the 2 ΚΙΔπιν parameter. As Smith s_1. The corresponding values for the mean Fe I, Si I, and (1982) has also pointed out, such a value would imply that S I velocities are 9.46, 9.23, and 9.41 km s 1, respec- ρ Pup is pulsating radially. tively. These are all lower than the values of 11 and 11.5 1 The H F absorption cell used in this study was built with km s" given by Danzinger and Kuhi (1966) and Campos funds granted to Dr. Bruce Campbell from CFHT. This and Smith (1980), respectively. However, Struve et al. research was supported by funds granted to G. A.^H. (1956) and Bessell (1969) have measured the 2 Κ values of -1 Walker from the Natural Sciences and Engineering'Re- 9.7 and 9.5 km s , respectively. The discrepancy could search Council of Canada. not have been the artifact of phase smearing. The exposure times of the spectra reported here were only about APPENDIX 6% of the period. If this large discrepancy is a real effect, it may imply that the 2 Κ value is varying. This could be Derivation of Equation (1) caused by the presence of a low-amplitude long beat Considering only weak isolated lines, one can assume period. From the three nights of data, however, no con- that the continuum opacity, kc, is much larger than the vincing evidence for a varying 2 Κ value has been found. line opacity, κ^. The observed line depth, d, can then be The effect of differing 2 Κ values for different lines is approximated as probably real. Figure 13 shows the difference plot between the Ca π and the mean Fe I velocities. The effect of d = κ€/{κ€ + kc) . (2) the two different 2 Κ values is very apparent. In spite of This implies the fractional change in d is the amplitude differences, the Ca π λ8662 velocities are Ldld = {1 — d) (Δκ /κ — Ak^kJ . (3) in phase with almost all the other velocities. The minima € € of the Η ι λ8750 velocities, however, appear to lag the Assuming the line opacity to be proportional to the num- minima of the other velocities by about 0^003 or 2% of the ber of atoms at the particular energy level as well as a period. This phenomenon of the Η I velocity curve lag- Boltzmann distribution for the energy level population,

ρ Pup : Ca II λ8662 mean of Fe I lines 0.85 0.89 0.93 0.97

0.50

U1 ε 0.25 - uOJ

0.00 α

ë -0.25 -

-0.50 -

0.85 0.89 0.93 0.97 1 .01 BJD2445358+

Fig. 13-The residuals after subtracting the mean Fe I velocities from the Ca π λ8662 velocities. A difference between the 2 Κ values is apparent. Triangles-spectra without HF lines imposed.

the fractional change in the line opacity is AnH /nH- = (1/2) (ΔΚΗ/ΚΗ) - (ΔΚΗ-/ΚΗ-) . (9)

Δκ€/κ€ = (EJkT) (ΔΓ/Γ) . (4) Using the form of the Saha equation as given in Allen (1973), one obtains In equation (4), EL is the lower energy level of the line, k is the Boltzmann constant, and Τ is the temperature. The log (KH-) = -(xh-) θ - (3/2) log θ + ... . (10)

effect of induced emission (< 10% at λ8700 and Τ = — 7100 Κ) has been neglected in equation (4). To a first log (¾) = (Xh) θ — (3/2) log θ + ... . (11)

approximation, one can assume that the stellar continuum In equations (10) and (11), χΗ- is 0.75 eV, χΗ is 13.6 eV, of an F5 star is mostly due to free-free and bound-free and θ is 5040/Γ, where Τ is the temperature in Kelvins. transitions of the H~ ions and, in consequence, the con- The derivatives of equations (10) and (11) will then give tinuum opacity is proportional to the number of ΗΓ ions. The fractional change in the continuum opacity is then the ΔΚη-/^η- = 2.3 (ΔΓ/Γ) [(xh-) θ + 0.65] . (12) same as the fractional change in n -, the number density H ΔΚη/^η = 2.3 (ΔΓ/Γ) [(xh) θ + 0.65] . (13) of the H~ ions, i.e., Combining equations (12), (13), (9), (5), and (4) gives ¿íkJkc = ΔηΗ-/ηΗ- . (5) equation (1).

One can define KH and KH-, the dissociation constants for A more detailed theory would include sources of con- Η and H", respectively, as tinuum opacity other than H" ions. The Paschen line opacity is especially important to superimposed lines like n + n n ^ H J H (6) Si ι λ8752. Some Si I and Mg I lines are also blended with Kh~ ~ nHne^nH~ · (^) Ν I lines which vary in the opposite sense. Full model-at- mosphere calculations for a series of temperatures are In equations (6) and (7), n +, n , and n are the number H H e probably required for a more detailed comparison with densities of the H+ ions, the neutral atoms, and the Η the observations. electrons, respectively. Combining equations (6) and (7) and assuming that nH >> ne, one obtains REFERENCES nH- = [V(n3K„)]/KH- · (8) Allen, C. W. 1973, Astrophysical Quantities (3d ed. ; London: Athlone). Balona, L. Α., and Stobie, R. S. 1983, S. Afr. Astron. Ohs. Circ., No. 7, The derivative of equation (8) will then give p. 19.

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