CCD Photometry of the High‐Amplitude δ Scuti Stars V798 Cygni and V831 Tauri

CCD Photometry of the High‐Amplitude δScuti Stars V798 Cygni and V831 TauriAuthor(s): F. Musazzi, E. Poretti, S. Covino, and A. Arellano FerroSource: Publications of the Astronomical Society of the Pacific, Vol. 110, No. 752 (October1998), pp. 1156-1163Published by: The University of Chicago Press on behalf of the Astronomical Society of the PacificStable URL: http://www.jstor.org/stable/10.1086/316234 .

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1156

Publications of the Astronomical Society of the Pacific, 110:1156–1163, 1998 Octoberq 1998. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.

CCD Photometry of the High-Amplitude d Scuti Stars V798 Cygni and V831 Tauri

F. Musazzi, E. Poretti, and S. Covino

Osservatorio Astronomico di Brera, Via Bianchi 46, I-23807 Merate, Italy; [email protected], [email protected]

andA. Arellano Ferro

Departamento de Astronomıa, Universidad de Guanajuato, Apdo Postal 144, Guanajuato, Gto. Mexico 36000; [email protected]

Received 1998 May 8; accepted 1998 June 19

ABSTRACT. New CCD measurements of the two high-amplitude d Scuti stars V798 Cyg and V831 Tau werecarried out. The double-mode pulsation of V798 Cyg is demonstrated beyond any doubt. The ratio of 0.800f /f1 2

is confirmed to be related to the unusual shape of the light curve. The properties of the Fourier parametersf1

were revisited also by considering the new light curve of V831 Tau. In particular, the classical double-modepulsators cannot fill the gap in the distribution. Two new variable stars were discovered in the field of V798R21

Cyg.

1. INTRODUCTION

In the recent past, an increasing number of theoretical andobservational studies were devoted to the d Scuti stars showinglight curves having a V amplitude larger than ∼0.20 mag andpulsating in one or two stable frequencies (HADS; see alsoPetersen & Christensen-Daalsgard 1996). They were mainlyconcerned with the understanding of their pulsational and phys-ical properties. Rodrıguez et al. (1996) investigated the natureof the large amplitude modes, concluding that they are radial;Garrido & Rodrıguez (1996) refined this conclusion, findingpossible nonradial terms having very small amplitudes inSX Phe and DY Peg. Breger & Pamyatnykh (1998) foundevidence of period changes in a number of HADS, but it wasnot possible to relate them to stellar evolution; hence, theirnature is still unclear.

Antonello et al. (1986) and Poretti, Antonello, & LeBorgne(1990) proposed a synthetic description of the HADS lightcurves, trying to obtain their quantitative classification. Theresult was successful, since regular trends were observed in theFourier parameter space, as in the f21-P and f31-P planes. Abimodal distribution was observed in R21-P plots, and no sat-isfactory explanation can be given at the moment, since theaction of a resonance is not confirmed by the phase plots.Moreover, Poretti & Antonello (1988) emphasized the simi-larities between the light curves of V1719 Cyg, V798 Cyg,and V974 Oph, which show a descending branch steeper thanthe ascending one. Later, V974 Oph was dropped from thisshort list since it is actually a multiperiodic variable (Poretti& Mantegazza 1992).

Recently, Hintz & Joner (1997) reported new results onCY Aqr, XX Cyg, and V798 Cyg. Their result for the first twostars confirms the Fourier parameters obtained by Antonello et

al. (1986). On the other hand, Hintz & Joner questioned thedouble-mode nature of V798 Cyg suggested by Poretti & An-tonello (1988). In this paper, we present new CCD data thatcorroborate the double-mode hypothesis; we also rediscuss theproperties of the Fourier parameters considering the first CCDmeasurements of the short-period variable V831 Tau.

2. NEW OBSERVATIONS

After the detection of a possible second periodicity in thelight curve of V798 Cyg, we planned new photometric meas-urements to confirm it. On four nights between 1987 August29 and September 4, 135 CCD images were obtained with the152 cm Cassini telescope of the Bologna Astronomical Ob-servatory, located at Loiano. The observations were obtainedthrough a V filter, and the exposure time was 20 s (15 s forthe first 20 images). Figure 1 shows a typical frame.

More recently, we carried out an observing run on someextragalactic objects with the 1.5 m telescope at San PedroMartir Observatory (Baja California, Mexico) in 1996 Decem-ber. When seeing conditions were not adequate (owing to strongwind) to take CCD frames of 20th magnitude objects, we con-sidered the 17th magnitude variable star V831 Tau (named asGR 269 and ZB 33 in Romano 1973 and Huang 1982, re-spectively) as a good backup program. Exposure times rangedfrom 7 to 15 minutes depending on weather conditions. On sixnights from 1996 December 11 to 18, 81 CCD V images wereobtained. The rapid and large amplitude variability made V831Tau an interesting object since the light curve reported byHuang (1982) is sinusoidal, and such a shape is quite unex-pected for short-period variables. Figure 2 shows a typical CCDframe of the field.

The data reduction was performed by using the MIDAS



CCD PHOTOMETRY OF V798 CYG AND V831 TAU 1157

1998 PASP, 110:1156–1163

Fig. 1.—Typical frame of the V798 Cyg field. North is down and west isright. The field is 2.5 # 4.4 arcmin2. V798 Cyg is labeled as star 1; stars 2and 4 are the selected comparison stars; star 6 is probably a new eclipsingbinary; star 8 is probably a multiperiodic new variable star.

package; both photometry aperture and DAOPHOT routineswere used. Because the target stars in our frames are verybright, the methods are equivalent. For a full description of theanalysis, see Musazzi (1997). The results described here areobtained using a photometric aperture of 140 for the San PedroMartir frames and 100 for the Loiano frames. Photometry wasperformed for all the stars in each field; differential magnitudeswere calculated with respect to the adequate comparison star.In the case of V798 Cyg (Fig. 1), DV values were derived withrespect to star 2; they were transformed into an instrumentalV system by assuming for V798 Cyg (Poretti &AV S 5 12.504Antonello 1988). An estimation of the errors was achieved fromthe standard deviation of the measurements of star 4 in theV798 Cyg frames and of the star 3 ones in the V831 Tau frames:the whole data sets yielded 5 and 7 mmag, respectively.

As a by-product of our analysis, we detected two new var-iables in the rich field of V798 Cyg. The first one, labeled “6”in Figure 1, is probably an eclipsing binary. Figure 3 showsits light curve on the three longest nights: the regular decreasein the top panel is about 0.5 mag, while on the other nights itis constant at the maximum level. The second new variable,labeled “8” in Figure 1, is probably a multiperiodic pulsatingstar. Figure 4 shows its light curve: cycle-to-cycle variationsare clearly evident. A frequency analysis revealed two possibleterms at 13.95 and 19.58 cd21, but further observations arenecessary to disclose its true nature.

3. FREQUENCY ANALYSIS

The least-squares power spectrum method (Vanicek 1971)was used to detect the frequency content of the light curves.This method allows each constituent to be detected one by one:in the search for a new term, only the frequencies of the pre-viously identified terms (the known constituents, or k.c.’s) aretaken into account, since their amplitudes and phases are re-calculated as unknowns in the least-squares routine. We rou-tinely apply this algorithm to multiperiodic d Sct stars; recently,Pardo & Poretti (1997) used it to detect the frequency contentof the light curves of double-mode Cepheids.

3.1. V798 Cyg

The new CCD measurements were analyzed to confirm thepresence of a second excited mode. The frequency analysisimmediately evidenced the peak at 5.13 cd21 (Fig. 5, top panel),corresponding to the well-known first period (Poretti & An-tonello 1988). There is no doubt about it, since when intro-ducing the neighboring alias (4.13 or 6.13 cd21) a residualsignal is left at 5.13 cd . By proceeding in the analysis, the21

harmonics 2 , 3 , and 4 (or its aliases) were detected as thef f f1 1 1

highest peaks. This is not surprising since the light curve ofis known to be quite asymmetrical.f1

The crucial point was to verify what happened when andf1

its first three harmonics were introduced as k.c.’s in the searchfor new frequencies. The middle panel of Figure 5 shows thepower spectrum we obtained: the structure centered around 6.41cd21 is clearly visible. This panel can be compared with Figure5 in Poretti & Antonello (1988): in that figure, the uncertaintybetween 6.41 and 7.41 cd21 is strong because of the interactionbetween noise effects and the spectral window, since in allthese cases the time sampling is not particularly good. We canconclude that the spectral analysis of the new, more accurate,CCD data suggests 6.41 cd21 as the true value for the term.f2

Figure 6 shows the light curves obtained by subtracting fromthe data the curve related to one of the two frequencies andthen plotted against the phase related to the other one. As canbe seen, the CCD light curves in Figure 6 are of better qualitywith respect to the photoelectric ones (Fig. 6 in Poretti & An-tonello 1988); in particular, the scatter around the minimum ofthe light curve of is considerably reduced, and it can bef1



1158 MUSAZZI ET AL.

1998 PASP, 110:1156–1163

Fig. 2.—Typical frame of the V831 Tau field. North is up and west is left. The field is about 7 # 7 arcmin2. V831 Tau is labeled as star 1; star 3, the brightestof the field, is the comparison star.

ascribed to the low signal in the photoelectric measurementswhen the star is very faint. Also considering the middle panelof Figure 5, no doubt is left of the fact that a second periodicitydoes exist. The two frequency analyses carried out on twoindependent data sets show the same structure over the wholespectral pattern and its three harmonics, ), strongly sup-( f f1 2

porting its real nature.It is now necessary to understand why Hintz & Joner (1997)

failed to find the term. It should be noted that they did notf2

report any power spectrum and did not give any details aboutthe method used to analyze their time series, and no observinglog is presented. A careful rediscussion of their measurementswas therefore considered necessary. The authors kindly put atour disposal their unpublished measurements, and we processedthem. The data were obtained on only two nights spaced by

one night. As a result, the peaks in the power spectrum arequite large and the aliases at 0.5 cd21 are also prominent. SinceHintz & Joner (1997) performed a prewhitening at each step,some power belonging to may be arbitrarily subtracted whenf2

removing the light curve, owing to the leakage between thef1

large and numerous peaks. Hence, the importance of hasf2

been underevaluated. To verify this hypothesis, we analyzedthe Hintz & Joner measurements by using our method, whichdoes not require any prewhitening: the bottom panel of Figure5 shows the power spectrum we obtained. In spite of its ratherpoor look (owing to the bad spectral window), the presence ofa signal around 5–7 cd21 is clearly evidenced. We can concludethat their measurements also support the presence of a secondperiodicity.

Why did they miss it? They observed on two nights only,




1998 PASP, 110:1156–1163

Fig. 3.—Light curves of a probable new eclipsing variable in the field ofV798 Cyg (star 6 in Fig. 1).

Fig. 4.—Light curves of a possible new multiperiodic variable in the fieldof V798 Cyg (star 8 in Fig. 1).

Fig. 5.—Power spectra of V798 Cyg. Top: Loiano CCD measurements, nok.c.’s. Middle: Loiano CCD measurements, , 2 , 3 , and 4 k.c.’s. Bottom:f f f f1 1 1 1

Hintz & Joner (1997) measurements, , 2 , 3 , and 4 k.c.’s. The presencef f f f1 1 1 1

of a residual signal is quite evident in the middle and bottom panels.

and the influence of shifted the light curve built onf f 52 1

cd21. Hence, they could obtain a good fit with a slightly5.1343different value for the frequency (5.1261 cd21); the prewhiten-ing of in their data may have subtracted power from .f f1 2

However, the 5.1261 cd21 value is fully inadequate to fit allthe available data on V798 Cyg (not only our CCD and pho-toelectric sets but also the former photographic measurements);this different frequency value can be considered as an artifactof the analysis, just good enough to link the light curves oftwo nights only of a double-mode variable with a single (butwrong) period. To verify once more the action of the termf2

in the Hintz & Joner data, Figure 7 shows the light curves ofand as obtained from the Hintz & Joner measurements:f f1 2

the sine-shaped light curve is quite evident. When comparingf2

Figures 6 and 7, the light curves of the term seem to bef1

different in shape at maximum light, but this must be consideredwith caution because our CCD measurements cover only onecycle around the maximum. Indeed, the Fourier parameters arevery similar. They are summarized in Table 1, together withthe parameters of the least-squares fit. The small differencesin the amplitudes can be entirely due to the different instru-mental systems; this fact hampered us from merging all themeasurements in a reliable way.

3.2. V831 Tau

The analysis of the 81 CCD V measurements of V831 Tauwas much easier than in the previous case. The terms f 51

cd21, 2 , 3 , and 4 were clearly identified in the power15.551 f f f1 1 1



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1998 PASP, 110:1156–1163

Fig. 6.—Light curves of V798 Cyg as obtained from new CCD measure-ments. Top: first frequency (5.134195 cd21); Bottom: second frequency(6.409439 cd21).

Fig. 7.—CCD measurements of V798 Cyg by Hintz & Joner (1997) rein-terpreted in the double-mode scenario. Top: phased with , subtracted fromf f1 2

the data. Bottom: phased with , subtracted from the data.f f2 1

TABLE 1Least-Squares Fit of the Three Data Sets Available on V798 Cyg

Term(cd )21

Photoelectric Loiano CCD Hintz & Joner CCD

Ai

(mag)fi

(rad)Ai

(mag)fi

(rad)Ai

(mag)fi

(rad)

5 5.134915 . . . . . . . . . . . .f1 0.182 5 0.002 3.19 5 0.01 0.165 5 0.001 3.05 5 0.01 0.159 5 0.001 3.19 5 0.012 . . . . . . . . . . . . . . . . . . . . . . . .f1 0.032 5 0.002 2.62 5 0.06 0.032 5 0.001 2.46 5 0.03 0.027 5 0.001 2.80 5 0.043 . . . . . . . . . . . . . . . . . . . . . . . .f1 0.019 5 0.002 3.34 5 0.09 0.018 5 0.001 2.99 5 0.05 0.012 5 0.001 3.48 5 0.094 . . . . . . . . . . . . . . . . . . . . . . . .f1 0.005 5 0.002 4.53 5 0.35 0.008 5 0.001 3.48 5 0.12 0.004 5 0.001 4.73 5 0.29

5 6.409439 . . . . . . . . . . . .f2 0.012 5 0.002 0.51 5 0.16 0.016 5 0.001 4.57 5 0.06 0.013 5 0.001 1.20 5 0.08. . . . . . . . . . . . . . . . . . . . . . . . .V0 12.504 5 0.001 12.504 5 0.001 0.3815 5 0.001

Residual rms (mag) . . . . . . 0.018 0.007 0.009N . . . . . . . . . . . . . . . . . . . . . . . . . . 204 134 182

(HJD) . . . . . . . . . . . . . . . . . .T0 2,446,639.2526 2,447,036.5840 2,449,621.5182

Note.—The Loiano data are in an instrumental V system. The Hintz & Joner values are magnitude differences.

spectrum; they correspond to the already known period of0.0643 days. The fit with these four terms leaves an rms residualof 0.014 mag (Table 2); it is larger than the expected one, butwe have to consider that V831 Tau is 2 mag fainter than star2 in Figure 2. Moreover, owing to the large amplitude and shortperiod, during the exposure time V831 Tau showed an intrinsic,

not linear, variability, and hence ascribing the observed flux tothe middle time is not always an exact procedure. The residualpower spectrum does not allow any identification of a secondperiod or a higher harmonic. Figure 8 shows the light curve;as can be noted, it is quite asymmetrical, and the ascendingbranch is very steep. Moreover, it is quite regular; a small




1998 PASP, 110:1156–1163

TABLE 2Least-Squares Fit of the Measurements of V831 Tau

Term(cd )21

Ai

(mag)fi

(rad)

5 15.5528 . . . . . . . . . . . . .f1 0.270 5 0.003 2.66 5 0.022 . . . . . . . . . . . . . . . . . . . . . . . .f1 0.098 5 0.003 2.79 5 0.053 . . . . . . . . . . . . . . . . . . . . . . . .f1 0.039 5 0.004 2.72 5 0.144 . . . . . . . . . . . . . . . . . . . . . . . .f1 0.014 5 0.003 3.39 5 0.39

. . . . . . . . . . . . . . . . . . . . . . .DV0 2.809 5 0.002Residual rms (mag) . . . . . . 0.014N . . . . . . . . . . . . . . . . . . . . . . . . . . 81

(HJD) . . . . . . . . . . . . . . . . . .T0 2,450,062.050

Fig. 8.—The light curve of V831 Tau as obtained from CCD measurementscarried out at San Pedro Martir Observatory; the period is 0.0643 days, i.e.,92.6 minutes.

scatter is observed only at the turning points, where the shapeof the light curve is changing nonlinearly during the exposures.The sine-shaped light curve presented by Huang (1982) is notconfirmed; it probably originated from the very long photo-graphic exposures. It should be noted that its period is one ofthe shortest among HADS, very close to that of CY Aqr.

4. DISCUSSION

4.1. The Search for a Second Term

From a methodological point of view, it was once moredemonstrated that the detection of a second periodicity is notan easy task when it has a very small amplitude. A carefulfrequency analysis must be performed, and the quality of thefit cannot be considered a powerful diagnostic of the absenceof a second term. Harmonics and cross-coupling terms can bedetected one by one using our iterative least-squares technique,as Pardo & Poretti (1997) extensively demonstrated in the caseof double-mode Cepheids. In such a context, the approach ofHintz & Joner (1997) aiming at searching for the best solutionis inadequate and is not recommended for future works: as itwas demonstrated by the power spectra and the light curves(Figs. 3, 4, and 5), the second term is clearly evident in thef2

measurements of V798 Cyg. Moreover, it should be emphasizedthat Hintz & Joner did not verify whether their solution couldfit the previous data sets. In such a case, they could easilyverify that their period was wrong; from a general point ofview, two short nights cannot invalidate the well-proven resultsobtained on a larger baseline.

When the presence of a second periodicity is claimed orrefused on the basis of qualitative statements, some contradic-tions may arise. As an example, Hintz & Joner (1997) consid-ered V567 Oph as a possible double-mode pulsator becausePowell, Joner, & McNamara (1990) had found amplitude var-iations and phase shifts. Since Powell et al. (1990) did notdetect any second term in the power spectrum of V567 Oph,we cannot consider it as a double-mode pulsator; moreover,Poretti et al. (1990) found its light curve to be very stable. Onthe other hand, they considered CY Aqr as a monoperiodicpulsator, but this star shows the same cycle-to-cycle variations(McNamara et al. 1996 and references therein). Such variations

are the definition of the well-known (but also not well-under-stood) Blazhko effect, typical of HADS and RR Lyrae stars.As a rule, it is not possible to explain it as the action of asecond periodicity, since the frequency analysis of well-ob-served stars failed to detect it. As a last comment, it should benoted that Hintz & Joner (1997) considered V1719 Cyg as asuspected double-mode pulsator in their discussion; however,as clearly demonstrated by Poretti & Antonello (1988), thedouble-mode pulsation is quite evident, and there is no reasonto doubt it. In our opinion, only a frequency power spectrumobtained on the basis of good-quality data (both for precisionand for time sampling) should be used to argue in favor of oragainst a double-mode behavior.

5. THE FOURIER DECOMPOSITION

To perform the decomposition, we fitted the original meas-urements by the formula

n

DV(t) 5 DV 1 A cos [2pif (t 2 T ) 1 f ]O0 i 1 0 ii

m

1 A cos [2pif (t 2 T ) 1 f ]. (1)O i 2 0 ii

In the case of V831 Tau, , 2 , 3 , and 4 were identified inf f f f1 1 1 1

the frequency analysis; i.e., there was no term. The corre-f2

sponding phase and amplitude pa-f 5 jf 2 if R 5 A /Aij i j ij i j

rameters can be derived. In the case of V798 Cyg, the , 2 ,f f1 1



1162 MUSAZZI ET AL.

1998 PASP, 110:1156–1163

3 , 4 , and terms were identified; because , no Fourierf f f m 5 11 1 2

parameter can be calculated for the term.f2

5.1. V831 Tau

The Fourier decomposition of the V CCD measurementsyields rad andf 5 f 2 2f 5 3.75 5 0.09 R 521 2 1 21

for V831 Tau. This star provides a goodA /A 5 0.36 5 0.032 1

confirmation of the regular trend in the short-period region ofthe f21-P plots (see Fig. 8 in Poretti et al. 1990): in fact, from0.10 to 0.04 days we can see a drop of the values fromf21

4.0 rad to about 3.0 rad. The reason for such an abrupt changein the light curve shape is unknown at present. V831 Tau takesplace in the group having large values, as is often the caseR21

for short-period variables. The asymmetrical light curve be-havior is the expected one for such a variable and is more likelythan the previously reported sinusoidal shape.

5.2. V798 Cyg and the Double-Mode Pulsators

The least-squares fits reported in Table 1 allowed us to obtainvalues in good agreement with each other: ,f 2.53 5 0.0821

, and rad, respectively. Poretti & An-2.64 5 0.05 2.70 5 0.06tonello (1988) determined a value of rad from2.52 5 0.05uvby photometry of V1719 Cyg. Since the two values areR21

also very similar (0.18, 0.19, and 0.17 in the three data setsof V798 Cyg; 0.20 for V1719 Cyg), the close similarity be-tween their light curves is now a well-established result. Thef1

light curves are slightly different; in V798 Cyg the am-f f2 2

plitude is shallow, and hence cross-coupling terms are not de-tected, while they are observed in the V1719 Cyg light curve.f2

The ratio is for V1719 Cyg andf /f 0.7998 5 0.00011 2

for V798 Cyg: since the separation is about0.8012 5 0.00021 order of magnitude greater than the formal errors, a slightdependence from is suggested.f1

Hintz & Joner (1997) argued that double-mode pulsators canfill the gap in the distribution, supplying values aroundR21

0.27. They quoted the Rodrıguez et al. (1992) results to supporttheir thesis and in particular the 0.27 value obtained in thecases of BP Peg and RV Ari. However, as can be easily verified,this intriguing hypothesis is wrong, as Rodrıguez et al. report0.303 for RV Ari and 0.315 for BP Peg; the same values areobtained from their least-squares fit. So the gap around 0.27still exists.

It should be emphasized once more that the ratio forf /f1 2

AE UMa, BP Peg, and RV Ari is about 0.773. Petersen &Christensen-Daalsgard (1996) showed how the 0.77 ratio is ingood agreement with the predictions of the theoretical modelsfor the fundamental (P0) and the first overtone (P1) radialmodes. Small deviations can be obtained by varying the me-tallicity or assuming different relationships, but for log P0M-L! 20.8, all the theoretical values are within 0.765 and 0.790.When discussing the case of VZ Cnc, Petersen & Høg (1998)

argued against the hypothesis of a ratio modified byP /P1 0

secondary parameters as diffusion or rotation and consideredthe 0.800 ratio as an indicator of the pulsation in a differentcouple of modes, i.e., the second (P2) and the first radial over-tone. In this scenario, we should consider V1719 Cyg and V798Cyg as two pulsators; however, we pointed out theP /P2 1

unusual shape of their light curve (considering it both a P0f1

or a P1 mode), very different from that of other double-modepulsating stars, both HADS and Cepheids. Since in the case ofCepheids the deviations from regular trends in the Fourier pa-rameter planes were recognized as indicators of different phys-ical conditions (other pulsation modes, resonances: Poretti 1994and references therein; Welch et al. 1995), further theoreticalinvestigations are needed to give a full description of the ob-served peculiarities emphasized above.

6. CONCLUSIONS

The possibility of performing a frequency analysis of thelight variation of V798 Cyg on the basis of a more accurateset of data and the Fourier decomposition of the new lightcurve of V831 Tau allowed us to improve the knowledge ofthe HADS. The following points are now better defined:

1. V798 Cyg is confirmed to be a double-mode pulsator,and its similarity with V1719 Cyg is definitely established: thepeculiar light curve of (descending branch steeper than thef1

observed one) and the double-mode pulsation with ratio 0.800have to be considered together in modeling these stars.

2. The detection of additional periodicities in light curvesis confirmed to be a delicate matter. A thorough discussionwould be needed to invalidate previous results established onthe basis of better time series, as otherwise confusing resultsare obtained, as in the case of V798 Cyg.

3. The short-period variable V831 Tau shows a light curvevery similar to other stars having the same period; the previ-ously reported sinusoidal light curve is not confirmed. The lightcurves of HADS toward short periods have a very regularprogression in the Fourier parameter space.

4. The gap around 0.25–0.30 in the distribution ofR21

HADS light curves is confirmed. Hintz & Joner (1997) claimedthat it can be filled by the values obtained from double-modepulsators, but the available photometry does not support thatclaim, which seems the result of improper handling of the data.

E. Poretti wishes to thank V. Zitelli for help in the observingrun in Loiano. E. Poretti and A. Arellano Ferro acknowledgethe financial support of a CNR-CONACyT contract. The au-thors wish to thank J. Vialle for the improvement of the Englishform of the manuscript.




1998 PASP, 110:1156–1163

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Documents

CCD Photometry of the High‐Amplitude δ Scuti Stars V798 Cygni and V831 Tauri