Photoelectric Photometry Newsletter

Volume 21, No. 2, August 2002

Contributions to this Newsletter are gratefully received at any time. Please send them to: John Percy, Erindale Campus, University of Toronto, Mississauga ON, Canada L5L 1C6; e-mail: jpercy@erin.utoronto.ca All material in this Newsletter has been written by the Editor unless otherwise indicated.

Contents:

• What the Editor Did This Summer
• Pulsating Red Giants - New Results in 2001-2002
• Cycle-to-Cycle Behaviour of RV Tauri Stars
• Amateurs' Contributions to Be Star Research
• V2048 (66) Ophiuchi
• Reports on the AAVSO Photoelectric Program

What the Editor Did This Summer

The following week, in Tucson AZ, I attended a delightful meeting honouring a lifetime of work by my University of Toronto colleague Bob Garrison. The meeting was entitled "Probing the Personalities of Stars and Galaxies", and was organized by Christopher Corbally (Vatican Observatory) and Richard Gray (Appalachian State University). Bob Garrison is the world leader in the field of spectral classification of stars. He has also been a strong supporter of the role of small telescopes in astronomy; for three decades, he was the Director of the University of Toronto's Southern Observatory, in Chile, where our 0.6m telescope was arguably the most productive telescope in the world, per dollar. He is also a strong supporter of the work of amateur astronomers and the AAVSO; he has just completed a two-year term as President of the Royal Astronomical Society of Canada, and edits the Bright Stars section of the RASC's famous Observer's Handbook. He is also an award-winning teacher.

At the Tucson meeting, I thought it appropriate to present a paper, with Akos Bakos as co-author, on the pulsation modes of small-amplitude pulsating red giants (SAPRGs), described below. Bob Garrison has a long interest in Mira stars - the large-amplitude cousins of SAPRGs. He has also been very active in supervising undergraduate research, and this project was carried out by Akos Bakos as an undergraduate research project.

For the first two weeks of July, it was off to northern Finland for the Sixth Annual Summer School of the European Association for Astronomy Education, where I was keynote speaker (on "The Sun and Stars in your Classroom"). This school attracted 100 teachers and teacher educators from across Europe. Fortunately it did not attract the number of mosquitos that had been forecast. The Midnight Sun did appear on one night and, of course, there was no observing - except of the sun. I offered an impromptu workshop on variable star observing - indoors, using the slides from the AAVSO's Hands-On Astrophysics project.

The final trip was to a workshop on The Interplay between Periodic, Cyclic, and Stochastic Variability, held at the University of Brussels, Belgium, and hosted by Christiaan Sterken - well remembered as the host of the AAVSO's first European meeting, which was also in Brussels. There, I presented a summary of the various projects on SAPRGs which my students had done, and a poster on RV Tauri stars and related objects, described below.

Pulsating Red Giants - New Results in 2001-2002

Figure 1. Observed Q-values for a large sample of SAPRGs. Theoretical values are: 0.06­ -.07 (F), 0.037-0.040 (1H), 0.025-0.030 (2H) and 0.020-0.025 (3H). There appears to be no trend in the observed values, with temperature.

Giants cooler than K5III are almost all variable in brightness. K5-M9 giants make up about 10 per cent of the stars in the Bright Star Catalogue. Generally, the cooler the star, the larger the V amplitude. The coolest stars are the rare large-amplitude Miras. The primary periods of the SAPRGs are consistent with low-order radial periods, according to the small sample studied by Percy & Parkes in 1998. The high-overtone periods in a small number of SAPRGs in the Hipparcos catalogue are almost certainly spurious. Many SAPRGs do, however, have well-established long secondary periods, whose nature and cause are unclear.

Akos Bakos recently carried out, under my supervision, a pulsation mode analysis of 77 SAPRGs - all those in our dataset which have luminosity class III, and have well-established periods and physical data. Modes are assumed to be radial (based on radial velocity observations), and are determined by comparing observed Q-values (pulsation constants) with theoretical values. The Q-value is the period in days, times the root of the mean density in solar units. Temperatures were determined in as many ways as possible: spectral types, (V-K) and (V-I) colours and, in a few cases, from angular diameters. Luminosities were determined from the mean magnitudes which were determined from the differential photometry, the Hipparcos parallaxes which gave absolute magnitudes, and bolometric corrections which gave bolometric magnitudes and hence luminosities. Radii were determined from luminosities and temperatures, from calibrations of radius with spectral type or colour or, in a few cases, from angular diameters. For most stars, there were two or more radius determinations which could be examined for consistency. Masses cannot be observed for these stars, but are believed to be 1.0 to 1.5 suns. The Q-value is not as sensitive to mass as to radius.

The Q-values which we determined range from 0.02 to 0.09 day with no apparent trend with temperature; this is different from the situation in other types of pulsating stars. The theoretical Q-values are: 0.06-0.07 (F: fundamental mode), 0.037-0.040 (1H: first harmonic or overtone mode), 0.025-0.030 (2H: second harmonic or overtone mode) and 0.020-0.025 (3H: third harmonic or overtone mode) but these vary somewhat with temperature. About 30 per cent of the stars in our sample pulsate in the F mode, about 50 per cent in the 1H mode, about 10 per cent in the 2H mode, and about 5 per cent in the 3H mode. Percy & Parkes found a slightly larger fraction to be pulsating in 2H and 3H modes, but their sample was much smaller. About one per cent of the red giants in the Hipparcos catalogue have very short periods which imply that the stars are pulsating in very high overtones. Is this really the case? Undergraduate student JoAnne Hosick and I have amassed several arguments which suggest that these short periods are spurious, and arise from the peculiar time distribution and aliasing properties of the Hipparcos photometry. Our results have just appeared in the Monthly Notices of the Royal Astronomical Society, volume 334, pages 669-672 (2002).

The 200-day light curves of some SAPRGs show evidence of possible multiperiodicity. Undergraduate students Gurtina Besla and Vince Velocci analyzed five of these stars which appeared to have periods of 50 days or less. We chose such short-period variables so we could determine reliable periods from individual seasons of data.

Figure 2. The 200-day light curve of RZ Ari (left) and BC CMi (right), showing evidence of multiperiodicity.

We checked, using simulations, that using 200-day datasets would not have a systematic effect on our period determinations. Each season was analyzed using the Fourier/CLEAN program TS available on the web site of the AAVSO. For each star, it was observed, using stem-plot analysis, that two or three consistent periods recurred each season. The average values were determined for each star. These periods could be used to determine a Q-value, and hence a pulsation mode, as described in the previous section. Their ratio could also be used to check the pulsation mode. The details of this study will be published elsewhere, but a summary of the results is as follows:

RZ Ari (M61II, Te = 3305 K, R = 145 R(D); periods 37 and 56 days; Q-values 0.028 (2H) and 0.042 (1H); the period ratio of 1.514 favours F and 111, but the disagreement can be avoided by adjusting the mass.

V523 Mon (Mb, Te = 3439 K, R = 110 RD); periods 27, 34 and 47 days; Q-values 0.029 (3H), 0.037 (2H) and 0.051 (1H); the period ratios of 1.259 and 1.382 are consistent with these modes.

BC CMi (M411I, Te = 3495 K, R = 71 RD); periods 20, 27 and 42 days; Q-values 0.033 (2H), 0.045 (1H) and 0.069 (F); the period ratios of 1.350 and 1.556 are consistent with these modes.

UX Lyn (M6III, Te = 3328 K, R = 133 Ro); periods 36 and 51 days; Q-values 0.029 (2H) and 0.041 (1H); the period ratio of 1.420 is consistent with these modes.

FS Com (M5III, Te = 3418 K, R = 136 RD); periods 37 and 54 days; Q-values 0.031 (2H) and 0.045 (1H); the period ratio of 1.460 is consistent with these modes.

The discovery of multiperiodicity in SAPRGs raises the question of how the amplitudes of the modes vary with time. Are the amplitudes constant? Do they rise and fall in unison? Is the total pulsation energy constant with time? Or is the situation more complex?

For each of the five stars, Vince Velocci fit the seasonal light curves using the two or three periods given above, using the Period98 program available on the web site of the University of Vienna. The amplitudes of each period, for each season, were plotted against time. The data for the first two or three seasons are slightly more sparse than for the rest.

The amplitudes definitely change significantly from season to season. In four of the five stars, there are one or two epochs when all of the modes have lower amplitude: BC CMi: JD 2449400; V523 Mon: JD 2447000 and 2450000; UX Lyn: JD 2448600; FS Com: JD 2447200. In these stars, the amplitudes of the different modes fell in unison before these dates, and rose in unison after. From a purely statistical point of view, however, there were almost as many instances of the amplitudes changing in the opposite sense from one season to the next, as changing in the same sense.

We must keep in mind that the two-period and three-period fits still left significant residuals. These may be due to additional modes, or other sources of irregular variability such as convection. Another caveat is that our results depend slightly on whether we fit each season of data with the mean periods given above, or with the periods which were actually determined for that season.

Many semi-regular red variables show long secondary periods; Houk, in 1963, found an average period ratio of 9.4 for M-type stars, and 12.2 for N-type stars. Kiss et al., in 1999, analyzed the multiperiodicity of a large sample of red semi-regular variables, using visual data, and found many of these to have secondary periods which are about 10 times the primary period. In our sample of small-amplitude variables with periods that were unambiguously determined, 26 have long secondary periods, and 45 do not. A long secondary period is defined as one which is at least three times the short radial period. Our results may be incomplete; the K5-MOIII stars with very small amplitudes have only two seasons of data, for instance. Among the 26 K-M III stars with long secondary periods, the median period ratio is 10.0, which is similar to Houk's result.

There are several possible explanations for the long secondary periods. Non-radial pulsation is unlikely to produce the large amplitudes which are associated with some of these long secondary periods. Episodic dust ejection is unlikely in these stars which have just begun to ascend the giant branch, and which do not have large observed mass loss rates. Irene Cum­mings, in her 1998 New Zealand doctoral thesis, on the basis of a detailed study of southern SAPRGs, suggested that the long secondary periods might be due to rotation. Peter Wood has hypothesized convection-induced oscillatory thermal (COT) modes, but found them to be stable in the models which he tested. He also suggested binarity as a possible cause.

We note that one of our stars - EG And - is a symbiotic star with a pulsation period of 29 days (probably F mode pulsation) and a long secondary period of 241 days, which is half of the known binary period. This suggests that the long secondary variability is ellipsoidal in nature.

We have also considered two samples of binary systems containing red giants: a list provided by Petr Harmanec, and the systems in the spectroscopic binary catalogue of Batten, Fletcher & MacCarthy. These two samples include 17 systems in which the cool component was a K or M giant. In almost all cases, the variability of this component has not been studied, so the pulsation period is unknown. We therefore assumed that the period was the median value found in our database for giants of the same spectral type. We then calculated the ratio of the binary period to the assumed pulsation period. Despite all of the uncertainties and assumptions made, we found that, in 10 of 17 stars in the sample, the ratio was between 8 and 12. This suggests that the binary hypothesis may be correct in some of the stars, and should be investigated further.

Cycle-to-Cycle Behaviour of RV Tauri Stars

RV Tauri Stars are pulsating yellow supergiant stars whose light curves are characterized by alternating deep and shallow minima. There are two on the AAVSO PEP program, and dozens more on the AAVSO visual program. RV Tauri stars are related to (and sometimes confused with) Population II Cepheids and SRd (yellow semi-regular) variables. The cause of their alternating deep and shallow minima, and their precise evolutionary status are not known. One hypothesis for the alternating minima is that the RV Tauri stars are double mode pulsators in which the period ratio is 2:1; a second hypothesis (which is not totally independent of the first) is that they are exhibiting low-dimensional chaos.

Alcock et al., using MACHO data, have recently reported the discovery of 12 definite or probable RV Tauri stars in the LMC, and have studied these and 21 other related stars. They determined periods, Fourier decomposition parameters, and intrinsic colours and absolute magnitudes for these 33 stars, and derived a new period-luminosity relation. The RV Tauri stars appear to be a direct extension of the Type II Cepheids to longer periods; variables with periods greater than 20 days show increasingly strong RV Tauri characteristics.

The goal of this project was to develop a deeper understanding of the RV Tauri phenomenon, and its relationship to Population II Cepheids and to SRd variables. Is the transition between these types smooth or discontinuous? Is there an index of "RV Tauri-ness", other than the qualitative alternation of deep and shallow minima? If the RV Tauri phe­nomenon is due to the presence of two periods in the ratio 2:1, what would happen if the ratio was close to, but not exactly 2:1?

Light curves and Fourier analysis (power spectra) are commonly used for analyzing variable star data. We have found that self-correlation - a form of autocorrelation or variogram analysis - can be useful, in conjunction with the other two techniques, for some kinds of stars, especially if the stars are somewhat irregular. It can detect characteristic time scales T in the data. It determines the cycle-to-cycle behaviour of the star, averaged over all the data. The measurements do not have to be equally-spaced. We have used this technique successfully on a wide variety of variable star types, from short-period Beta Cephei and Be stars, to long-period pulsating red giants. The self-correlation diagram contains features which enable the estimation of the period, mean amplitude, and observational error.

The self-correlation diagram is constructed from measurements which are typically up to a dozen cycles apart. Because RV Tauri stars are defined on the basis of their cycle-to-cycle behaviour, our method is well suited for analyzing them. It can, for instance, investigate the correlation between minima which are more than two cycles apart, and can therefore provide information about whether the alternating minima persist.

We first tested self-correlation analysis on photoelectric and visual measurements of bright RV Tauri stars, obtained by the AAVSO. We then applied the method to 13 RV Tauri and 20 related stars in the LMC, obtained as part of the MACHO project by Alcock et al.

Figure 3. The self-correlation diagram for the RV Tauri star MACHO 81.9362.25 in the Large Magellanic Cloud. The minima indicate time scales on which the measurements correlate i. e. a period. Note that alternating minima are deeper and shallower. In fact, the 4th and 8th minima are deeper than the 2nd, 6th and 10th, which suggests an additional dimension to the RV Tauri phenomenon.

The detailed results of our analysis will be published elsewhere; we present only a summary here:

• The height of the minima above the zero line in the self-correlation diagram is consistent (as it should be) with the expected photometric error seen in the scatter in the light curves of the non-RVT stars by Alcock et al.

• In the self-correlation diagrams, there is often enhanced scatter for t between 150 and 200 days; this is because of the shortage of t's in this range, because of seasonal gaps in the measurements.

• The periods of the stars were determined from the multiple minima in the self-correlation diagrams; the periods agree with those determined by Fourier analysis by Alcock et al. to within 0.1 to 1 per cent.

• The stars classified by Alcock et al. as RV Tauri stars had self-correlation diagrams which showed alternating deep and shallow minima though, in some stars, this behaviour was marginal.

• In some stars, the alternation persisted for many cycles; in others, it persisted for two to four cycles only; this suggests that the RV Tauri phenomenon may be more complex than a simple "alternating deep and shallow minima" description. In the "period ratio 2:1" hypothesis, it may be due to a period ratio which is not exactly this value.

• One star - MACHO 81.9362.25 - showed alternating deep and shallow minima in the self-correlation diagram, but the 4th and 8th minima were deeper than the 2nd, 6th, and 10th; this may be due to period-quadrupling in the star.

In order to understand the light curves and self-correlation diagrams better, we made the hypothesis that the variability might be due to the superposition of two periods, in a ratio close to 2:1. We generated the sum of two sine curves with various periods, amplitudes, and phases, and sampled this at the same times as the MACHO observations were made, and then generated self-correlation diagrams.

A sine curve with a period of 20 days and an amplitude of 1.0, plus a sine curve with a period of 40 days and an amplitude of 0.1, produced a self-correlation diagram which was qualitatively identical to that of the RV Tauri star MACHO 2.5026.30. If the period ratio was 0.45 instead of 0.50, then the diagram was similar to that of MACHO 47.2496.8 or 81.9728.14: the alternating deep and shallow minima persisted for two cycles only.

If the amplitude of the shorter period was smaller, then the self-correlation diagram showed a shallow secondary minimum. This is observed in MACHO 47.2496.8, 78.5856.2363 and 79.5501.13.

In conclusion: the self-correlation analysis provides useful, and sometimes new informa­tion about stars such as RV Tauri stars. The behaviour of these stars can be explained by the superposition of two pulsation modes with a ratio of 2:1.

Amateurs' Contributions to Be Star Research

Not only the most grandiose projects, but also hundreds of small telescopes operated by advanced amateurs can contribute to the progress of our field. We can meet amateur as­tronomers, who show incredible enthusiasm and remarkable knowledge, and who own pho tometric or spectroscopic facilities producing data of nearly professional quality. These amateurs could at least partly close the gap which appeared after many smaller telescopes at professional observatories were closed. The present age of the Internet enables them to be involved in professional projects. Please, forget about our professional conceit and lend a helping hand to these people, who devote their free time, energy, and money to astronomy. In the present world of pragmatic business and cheap amusement, they deserve our sincere respect.

I had no part in the writing of this editorial, and Stan is not a regular part of the pro-am community, so I regard him as an impartial observer. And it's people like AAVSO-ers that he is talking about! By the way, you can access the Be Star Newsletter on-line at:

www.astro.virginia.edu/~dam3ma/benews/

V2048 (66) Ophiuchi

"66 Oph is a Be star seen under a moderate inclination angle that shows strong variability from UV to IR wavelengths. A concise review of long-term variability history is given. High resolution, high signal/noise spectroscopic observations obtained in 1997, 1998 and 2001 and spectropolarimetric observations obtained in 2000 are presented. These observations occurred during a long-term decrease in H-alpha intensity. Fundamental parameters of the star have been revisited from Barbier-Chalonge-Divan (BCD) calibrations. New v sin i values are obtained using Fourier transforms applied to observed helium lines, and a rotational frequency of 1.29 cycles/day is determined. Time series analysis and Fourier Doppler Imaging (FDI) of helium I lines (4713, 4921, 5876 and 6678 A) lead, for the first time, to the detection of multi-periodicity in 66 Oph. The two main frequencies found are f = 2.22 cycles/day and 4.05 cycles/day. They are attributed to non-radial pulsations, and can be associated with mode degrees l = 2 and 3, respectively. Inspection of Stokes V profiles suggests the presence of a weak Zeeman signature but further observations are needed to confirm the detection of a magnetic field in 66 Oph."

Figure 4. The V light curve of V2048 (66) Ophiuchi. Note the great activity of the star, in the form of quasi-regular "outbursts".

Editor's Comments. The cause of the brightenings of Be stars are still not known. They may be connected with the short-period variations mentioned in Floquet's abstract. The cause of these is also not clear. One hypothesis is that they are due to non-radial pulsation; another is that they are due to the rotation of a non-uniform star. The discovery of multi-periodicity would be strong evidence for the non-radial pulsation hypothesis. On the other hand, the rotation hypothesis probably requires the presence of a magnetic field, and magnetic fields have not been observed on any normal B star. Hence the possible observation of a magnetic field in 66 Oph would be significant.

Reports on the AAVSO Photoelectric Program

The Infrared Photometry Project, discussed in the previous issue of this newsletter, has made some progress in 2002, but is presently waiting for the manufacturers of the filters to resolve a problem. Given that so many variable stars are bright in the infrared, this will be a very exciting and worthwhile project.

The IM Pegasi Project, also discussed in the previous issue of this newsletter, is also progressing well. You will remember that IM Peg is the guide star for the Gravity Probe B satellite, which is testing current theories of gravitation. This star is an RS CVn binary star; its importance is that it is also a point radio source, as well as a point optical source. AAVSO observers have accumulated 126 observations during the current "ramp-up" phase of the project (the satellite launch is still some time away). It is particularly important to observe this star during the summer, since the robotic telescope which is also observing the star is "rained out" in the summer by the Arizona monsoons.

Phil Manker, chair of the AAVSO Photoelectric Photometry Committee, has submitted the following semi-annual report to the 91st (2002) Spring Meeting, in Hawaii.

During the fiscal year 2001-2002, 15 observers contributed to the AAVSO PEP data base. The total observations up to the middle of the fiscal year 2001-2002 was: 1676. The contributing observers, their locations, and the number of observations contributed were: Beresky (Missouri) 9; Clark (Missouri) 42; Cox (Canada) 140; Dempsey (Canada) 35; Dallaporta (Italy) 58; DeVilliers (South Africa) 10; Fox (Minnesota) 67; Grim (Utah) 15; Jones (South Africa) 373; Kneipp (Louisiana ) 17; Lopata (Canada) 9; Luedeke (New Mexico) 430; Thompson (Canada) 332; Wood (Canada) 12; Stoikidis (Greece) 127.

New PEP observers include: Thomas Baskins (Arkansas), Larry Sumner (Virginia), Jo Nylands (Australia), Doug West (Kansas).

Dr. Doug West is working with Optec Inc. to design an IR photometer. Several of the prototypes will be handed over to our most experienced observers for trials. This will take place next year.

Support of the Gravity Probe B Satellite. During this fiscal year, the PEP Division supported the Gravity Probe B satellite. Our task is to monitor IM Peg prior to launch. Launch will be early 2003. IM Peg is the guide/navigation star. The camera locks on the star and keeps the satellite's platform stable.

IM Peg is a K2 star with a high level of activity due to short-lived flares, photospheric spots, and IM Peg is also a spectroscopic binary. The period is about 24.7 days.

We need to know exactly when the maximum occurs. If the star flares, the camera may reject the star because the magnitude has changed. The result is that the satellite platform will become unstable, and the data will be flawed.

At this time (mid 2001-2002), we have 93 observations of IM Peg. The following observers contributed to this project: Wayne Clark, Frank Dempsey, Sergio Dallaporta, Jim Fox, Phil Kneipp, Ken Luedeke, Nick Stoikidis, and Ray Thompson.

Editor's Comments. I welcome Phil Manker to the important position of Chair of the PEP Committee. I am pleased to see the number of PEP observers from Canada, and overseas, but would be very happy to see more observers from the US - and elsewhere!

We are happy to announce that the PEP charts are now available via the AAVSO web site (www.aavso.org)! Information on the changes made and how to obtain the charts either by downloading them from the web or ordering them through AAVSO Headquarters will be detailed in the next edition of the PEP Newsletter.

Please note that these charts will go into effect on January l, 2003 and must not be used prior to this date.