Period Analysis of All-Sky Automated Survey for Supernovae (ASAS-SN) Data on Pulsating Red Giants

TL;DR

This study critically examines ASAS-SN data on pulsating red giants, revealing inaccuracies in automated period determinations due to the complex variability of these stars.

Contribution

It provides a detailed comparison between ASAS-SN automated classifications and manual analysis, highlighting common errors in period estimation for pulsating red giants.

Findings

ASAS-SN often misidentifies periods as multiples of the true period.

Long-period Mira stars frequently have their periods underestimated.

Complex variability of PRGs challenges automated classification accuracy.

Abstract

The All-Sky Automated Survey for Supernovae (ASAS-SN) has recently used over 2000 days of data to identify more than 50,000 variable stars, automatically classify these, determine periods and amplitudes for those that are periodic -- part of a remarkable project to classify 412,000 known variable stars, and determine their basic properties. This information about the newly-discovered variables, along with the photometric data is freely available on-line. In this paper, we analyze ASAS-SN data on two small random samples of pulsating red giants (PRGs) in detail, and compare our results with those found by ASAS-SN. For the majority of a sample of 29 mostly semi-regular (SR) PRGs, the ASAS-SN results are incorrect or incomplete: either the ASAS-SN periods are 2, 3, or 4 times the actual period, or the ASAS-SN period is a "long secondary period" with a shorter pulsation present, or the star is multi-periodic or otherwise complex, or the star's data are contaminated by instrumental effects. For almost all of a sample of 20 of the longest-period Mira stars (period 640 days or more), the ASAS-SN period is actually 2 or more times the actual period. Our results are not surprising, given the very complex behavior of PRGs.

Figures

Tables

Table 1. Table 1: Table 1. Analysis of ASAS-SN Observations of 29 Pulsating Red Giants

Name - ASAS-SN-V	Type	PA(d)	P(d)	$\Delta$V	V$>$	J-K	Notes (see text)
J053227.48-691652.8	SR	469	227	1.2	12.7	1.112	x2?, Fig. 7
J055444.75-694714.7	SR	544	264	1.5	12.86	0.951	x2, lsp
J061214.08-694558.6	SR	643	318	1.5	16.82	1.725	x2
J054102.00-704309.9	SR	702	702	1.2	15.78	1.357	OK, spp
J191920.70-195042.1	SR	82	81	0.8	13.43	1.201	OK, tpp?
J054747.21-602210.3	SR	418	139	2.5	13.27	0.944	x3, Fig. 2
J191639.10-215848.8	SR	25	38	0.3	11.61	1.245
J205350.26-593921.1	SR	168	168	1.2	11.81	1.209	tpp
J054606.99-694202.8	SR	544	538	1.5	15.92	1.381	OK, spp, *
J191715.66-200034.1	SR	59	59	0.8	12.75	1.191	OK
J051623.43-690014.3	SR	466	233	0.7	14.95	1.287	x2
J053035.52-685923.2	SR	643	295	0.9	13.13	1.194	lsp?, tpp, *
J052011.96-694029.4	SR	662	662	1.1	15.1	1.494	OK, spp, Fig. 9, *
J052337.99-694445.8	SR	636	400	1.2	16.38	1.228
J054036.77-692620.6	SR	505	458	1.0	13.39	1.172	tpp
J054110.62-693804.1	SR	702	694	1.4	12.65	1.158	OK, *
J045337.64-691811.2	SR	430	80	0.2	13.3	1.115	x5, *
J045412.77-701708.6	SR	437	204	0.5	13.58	1.181	tpp
J050354.98-721652.3	SR	138	138?	1.5	16.21	0.898	OK, Fig. 1
J171247.59+265024.8	M	889	–	0.0	13.4	0.785
J195424.95-114932.2	M/SR	848	424	0.2	13.5	1.269	lsp, Fig. 6
J175514.90+184006.9	M	815	204	2.7	13.68	1.186	x4
J182825.60+171943.2	M	728	243	2.35	13.23	1.538	x3
J185653.55-392537.4	M	645	215	2.30	13.76	1.272	x3, *
J020359.53+141132.4	L/SR	irr	389	1.25	12.01	1.148	SR, lsp?
J181616.35-281634.1	L/SR	irr	121	1.38	13.69	1.149	SR, Fig. 8
J194755.85-611127.5	L/SR	irr	400	1.14	13.07	1.151	SR
J042630.05+255344.6	SR	1022	30	0.95	13.66	1.759	x2, lsp, Fig. 3-5, *
J082819.18-143319.3	SR	1020	78/128	0.63	11.66	1.251	tpp

Table 2. Table 2: Table 2. Analysis of ASAS-SN Observations of 20 Long-Period Mira Stars

Name - ASASSN-V	PA(d)	V$>$	$\Delta$VA	Notes (see text)
J171247.59+265024.8	888.8	13.5	3.05	*
J195424.95-114932.2	848.4	13.6	2.5	lsp?, *
J175514.90+184006.9	814.7	13.7	2.7	x4
J182825.60+171943.2	814.7	13.2	2.35	x3
J065708.96+473521.9	725.8	13.48	2.02	x2, QX Aur
J202918.27+125429.1	721.0	13.31	2.22	x5, XZ Del
J190214.90+471259.7	716.1	13.49	2.71	x2, WZ Lyr
J175727.78+243018.0	695.1	13.31	2.56	x2
J184802.27-293034.0	675.7	13.27	2.36	dd
J184706.22-314645.6	675.3	13.62	4.61	x3, V962 Sgr
J181958.07-395457.8	665.9	12.75	2.78	*
J082915.17+182307.3	655.8	13.66	2.1	x2
J124209.54-435503.3	645.6	13.93	2.79	OK, V1132 Cen
J182037.28-385833.5	645.5	13.8	2.02	x4
J182346.68-363942.1	645.5	13.73	2.39	Fig. 10, *
J185653.55-392537.4	645.0	13.76	2.29	x3, AB CrA, *
J144304.69-753418.9	641.8	12.25	2.5	Fig. 11, *
J141547.57-480350.7	641.0	13.65	3.02	x3
J175730.94-744810.7	640.5	13.45	2.05	x4
J184614.49-301856.4	639.6	13.64	2.02	x3, V1935 Sgr

Full text

Period Analysis of All-Sky Automated Survey for Supernovae (ASAS-SN) Data on Pulsating Red Giants

**John R. Percy and Lucas Fenaux

Department of Astronomy and Astrophysics, and

Dunlap Institute of Astronomy and Astrophysics

University of Toronto

Toronto ON

Canada M5S 3H4**

Abstract The All-Sky Automated Survey for Supernovae (ASAS-SN) has recently used over 2000 days of data to identify more than 50,000 variable stars, automatically classify these, determine periods and amplitudes for those that are periodic – part of a remarkable project to classify 412,000 known variable stars, and determine their basic properties. This information about the newly-discovered variables, along with the photometric data is freely available on-line. In this paper, we analyze ASAS-SN V data on two small random samples of pulsating red giants (PRGs) in detail, and compare our results with those found by ASAS-SN. For the majority of a sample of 29 mostly semi-regular (SR) PRGs, the ASAS-SN results are incorrect or incomplete: either the ASAS-SN periods are 2, 3 or 4 times the actual period, or the ASAS-SN period is a “long secondary period” with a shorter pulsation period present, or the star is multi-periodic or otherwise complex, or the star’s data are contaminated by instrumental effects. For almost all of a sample of 20 of the longest-period Mira stars (period 640 days or more), the ASAS-SN period is actually 2 or more times the actual period. Our results are not surprising, given the very complex behaviour of PRGs.

AAVSO keywords = Photometry, CCD; pulsating variables; giants, red; period analysis; amplitude analysis

ADS keywords = stars; stars: late-type; techniques: photometric; methods: statistical; stars: variable; stars: oscillations

1. Introduction

Red giant stars are unstable to pulsation. In the General Catalogue of Variable Stars (GCVS; Samus et al. 2017), pulsating red giants (PRGs) are classified according to their light curves. Mira (M) stars have reasonably regular light curves, with visual ranges greater than 2.5 magnitudes. Semi-regular (SR) stars are classified as SRa if there is appreciable periodicity, and SRb if there is little periodicity. Irregular (L) stars have very little or no periodicity.

Mira stars have periods which “wander” by a few percent; this wandering can be described and modelled as random, cycle-to-cycle fluctuations (Eddington and Plakidis 1929). Their maximum magnitudes vary from cycle to cycle, as observers of Mira itself know. The variability of SR stars is even more complicated. Some stars are multiperiodic; both the fundamental and first overtone modes are excited (e.g. Kiss et al. 1999). About a third show long secondary periods (LSPs), 5-10 times the pulsation period (Wood 2000); their cause is unknown. The amplitudes of PRGs vary by up to a factor of 10 on time scales of 20-30 pulsation periods (Percy and Abachi 2013). There are also very slow variations in mean magnitude (Percy and Qiu 2018). In a very few stars, thermal pulses cause large, secular changes in period, amplitude, and mean magnitude (Templeton et al. (2005) and references therein).

Our previous studies of PRGs have used long-term visual and sometimes photoelectric observations from the American Association of Variable Star Observers International Database (AID; Kafka 2019). Now, an important and very useful new source of data is available: the All-Sky Automated Survey for Supernovae (ASAS-SN).

ASAS-SN uses a network of up to 24 telescopes around the world to survey the entire visible sky every night down to about 18th magnitude (Shappee et al. (2014), Jayasinghe et al. (2018)). It has been doing so for over 2000 days (since about JD 2456500). ASAS-SN has identified over 50,000 variable stars, classified these using machine learning, determined periods and amplitudes for those that are periodic, ane made this information, and the data on-line (asas-sn.osu.edu/variables). It has also used machine learning to uniformly classify 412,000 known variables (Jayasinghe et al. 2018).

The purpose of the present project was to look at a small, random sample of the PRG data in more detail, and investigate the reliability of the ASAS-SN classifications and periods and amplitudes of PRGs. Jayasinghe et al. (2018) comment only briefly on the ASAS-SN classification of these very complex variables.

Vogt et al. (2016) have recently carried out a related study: analysis of 2875 Mira stars observed in the original ASAS project, which extended from 2000 to 2009. They used a semi-automatic method based on the observed times of maximum light. They found that, whereas their periods agreed with those in the VSX Catalogue (Watson et al. 2014) in more than 95 percent of the stars, their periods agreed with those obtained by Richards et al. (2012), who used an automatic machine-learning method, in only 76 percent of the stars. Most often, the latter periods differed from the Vogt et al. (2016) periods by a ratio of small whole numbers.

2. Data and Analysis

For our initial project, we analyzed a sample of 22 stars classified as SR, five as M, and three as L. They were randomly chosen around a random position on the sky. The SR and L stars were chosen to have ASAS-SN amplitudes of at least 0.5 magnitude (with one accidental exception), so that the results would not be unduly affected by noise, and would therefore be meaningful. A study of smaller-amplitude ASAS-SN stars would be the subject of a future project. The datasets were approximately 2000 days in length, significantly shorter than visual datasets from the AID. For each of the SR and M stars, ASAS-SN provides a period and amplitude, and a light curve and phase curve, and a quantity T which is a statistical measure of the confidence of the period; lower values indicate higher confidence.

The data were downloaded, and analyzed using the AAVSO VSTAR time-series package (Benn 2013) which includes a Fourier analysis routine. For one star, we also used a new self-correlation (e.g. Percy et al. 2003) program written by author LF.

The results were interesting, so we carried out a subsidiary project, to analyze a sample of 20 Mira stars with the longest ASAS-SN periods – longer than 639 days. Miras with such long periods would be especially interesting and important, astrophysically.

3 Results

Of the 29 stars in our initial project, 7 were acceptably analyzed (e.g. Figure 1). For 9 stars, the ASAS-SN period was exactly 2, 3, or 4 times the actual period; the phase curve had not one, but 2, 3, or 4 cycles in it. While this is a mathematical possibility, it is unphysical for a radial pulsator such as a PRG. Figure 2 shows an example with 3 cycles per unit phase.

For 5 stars, the light curve also showed periodic variability on a time scale 5-10 times shorter than the ASAS-SN period. The latter was clearly a “long secondary period”, whereas the shorter period was the pulsation period. Figures 3-5 show an example in which the LSP is actually half the ASAS-SN period of 1022 days. The shorter pulsation period of 55$\pm$2 days is clearly visible.

For a very few stars, the light curve included some highly-discordant data, and it appeared that ASAS-SN had used all the data for analysis. Figure 6 shows an example. These discordant photometric points are probably due to astrometry problems, and their effect on the image-subtraction process (Kochanek and Jaysinghe, private communication, April 2, 2019). The non-discordant data show periods of 423.9 and 66.9 days, with V amplitudes of 0.09 and 0.07, respectively, rather than the (artificial) ASAS-SN amplitude of 2.5. The longer period is probably a long secondary period.

For a few other stars, the variability appears to be either bimodal or more complex. Figure 7 shows an example in which there may be periods of 469 days (the ASAS-SN period) and about half that value – typical of PRGs which are pulsating in the fundamental and first overtone modes. Bimodal pulsators can be useful for determining the physical properties of the stars.

Figure 8 shows the light curve of a star which ASAS-SN classifies as irregular (L type) but which clearly shows some periodicity; we obtain a best period of 121 days.

Figure 9 shows a star with a very unusual light curve. There are two maxima which take the form of slow “eruptions”. They may, however, be maxima of a faint Mira star which has a 15.3-magnitude non-variable companion.

Table 1 lists the results of the initial project. It gives: the ASAS-SN name of the star, minus ASAS-SN-V J; the period PA in days given by ASAS-SN; the pulsation period PP in days obtained by us; the V amplitude $\Delta$V; the mean V magnitude $<$V$>$; the (J-K) color; the ASAS-SN classification; and the following notes: x2, x3, x4: the ASAS-SN period is 2, 3, or 4 times the correct pulsation period; lsp: the ASAS-SN period is a long secondary period, and a shorter pulsation period can be seen in the light curve; tpp: the star shows evidence of two pulsation periods, differing by a factor of approximately two; dd: the analysis is affected by contamination by discordant data (see above); spp: the pulsational phase curve is more sawtooth than sinusoidal; OK: the ASAS-SN analysis is correct; *: see “Notes on Individual Stars” below. This Table, and Figures 1-9 show the remarkable diversity of results which occur in a sample of less than 30 stars.

In the 20 long-period Mira stars in the subsidiary project, the ASAS-SN period was in almost every case exactly 2, 3, 4, or 5 times the actual period.

Table 2 lists 20 Mira stars with mean V magnitudes between 12 and 14, and with the longest periods. The magnitude range was chosen because it is optimal for ASAS-SN data. They are listed in order of decreasing ASAS-SN period. The columns list: the name of the star, minus ASAS-SN-V J; the period PA in days given by ASAS-SN; the mean V magnitude $<$V$>$; the ASAS-SN amplitude $\Delta$VA; and the following notes: x2, x3, x4, x5: the ASAS-SN period is 2, 3, 4, or 5 times the correct pulsation period; dd: the analysis seems to have been complicated by discordant data (see above); OK: the ASAS-SN analysis is correct; *: see “Notes on Individual Stars”, below.

3.1 Notes on Individual Stars in Table 1

Figures 1-9 and their captions provide both light/phase curves and notes about seven illustrative stars in the sample.

ASAS-SN-V J054606.99-694202.8: The light curve is unusual; it is non-sinusoidal, and there are two maxima in the 544-day cycle. It is not clear whether the behavior is periodic.

ASAS-SN-V J053035.52-685923.2: The light curve shows a slow decline, with some cyclic variations superimposed; their time scale is about 200 days. The slow decline could be part of a long secondary period.

ASAS-SN-V J052011.96-694029.4: The light curve (Figure 9) seems to show outbursts, but they may be maxima of a faint Mira star which has a non-variable companion.

ASAS-SN-V J054110.62-693804.1: The star has a double-humped maximum.

ASAS-SN-V J045337.64-691811.2: Unlike the other stars in the sample, this star had a very small amplitude, but it was possible to show that the actual period is 1/5 of the ASAS-SN period.

ASAS-SN-V J 185653.55-392537.4: The pulsation amplitude is slowly decreasing during the time of observation.

ASAS-SN-V J042630.05+255344.6: One-half the ASAS-SN period is a long secondary period. A shorter pulsation period is also present.

3.2 Notes on Individual Stars in Table 2

ASAS-SN-V J171247.59+265024.8: There are a few points between JD 2457850-2457896 which are four magnitudes fainter than the rest, which are almost constant; these are presumably due to instrumental effects, as discussed above. For the rest of the points, the highest peak has an amplitude of only 0.017 mag.

ASAS-SN-V J195424.95-114932.2: There are discordant points. For the rest, the highest peak is at 423.9 days (half the ASAS-SN period) with an amplitude of 0.09 mag; the second-highest is at 66.9 days, with an amplitude of 0.07 mag. These may be an LSP and a pulsation period. The ASAS-SN amplitude is given as 2.5 magnitudes.

ASAS-SN-V J181958.07-395457.8:: there are a few discordant points.

ASAS-SN-V J182346.68-363942.1: There are discordant points. For the rest, periods of 158$\pm$8 days and 83$\pm$4 days are present, with small amplitudes (Figure 10). They may possibly be the fundamental and first overtone pulsation periods.

ASAS-SN-V J144304.69-753418.9: The light curve is unusual; there are variations on a time scale of about 100 days, superimposed on irregular long-term variations (Figure 11). The ASAS-SN period of 641.8 days is unlikely.

4. Discussion

The ASAS-SN data begin about JD 2456500 so, as of the time of carrying out this project, there is only about 2000 days of data. This is adequate for studying many aspects of PRG variability, but not the very long-term variations in period, amplitude, and mean magnitude. Only the visual data can presently do that. Nevertheless, these new data provide a remarkable resource for studying these and other variable stars.

It is interesting to note that, when Vogt et al. (2016) compared their results with those of Richards et al.’s (2012) results which were obtained using a machine-learning approach, the discrepancy was most often by a ratio of small whole numbers, such as 2 or 1/2. We find a similar result.

Pulsating red giants are certainly a challenge for automated analysis and classification. Jayasinghe (private communication, April 10, 2019) has been refining the analysis and classification procedure, and has provided a list of updated periods for the stars in Table 1. About two-thirds now agree with our values, so a detailed inspection and analysis of the light curve is still recommended for individual SR and Mira stars.

It is not surprising that a few of these stars, especially the longer-period stars, have sawtooth phase curves. The same was found by Percy and Qiu (2018), from AAVSO visual data.

Most of this project was carried out by undergraduate math major LF. It illustrates the great educational potential of the ASAS-SN data, with its immense quantity, quality, and variety. We can envision a large number and variety of projects which could be carried out by students, using the ASAS-SN data. The AAVSO VSTAR time-series analysis package is well-suited for use with these and other data.

5. Conclusions

We have analyzed ASAS-SN observations of pulsating red giants (mostly semi-regular and Mira stars) and compared our results with the periods, amplitudes, and classifications given by ASAS-SN. For many stars, the actual periods are a small integral fraction of the ASAS-SN period, because the ASAS-SN phase curve contains two or more cycles of variability, rather than one. In other cases, the ASAS-SN period is a long secondary period, and the shorter pulsation period is visible in the light curve. In a few stars, the ASAS-SN analysis is complicated by the presence of data which are discordant, due to instrumental problems. In a few others, the star is bimodal or otherwise complex. The few irregular (type L) stars that we analyzed were probably semi-regular (type SR).

Given the complexity of pulsating red giants, it is not surprising that the ASAS-SN automatic analysis procedure produced incorrect or incomplete results. Perhaps the procedure can be trained to “solve” these very complex stars! Indeed, the ASAS-SN variable star data and website have been significantly updated and improved in the weeks since we completed this project (in February 2019), and some of the problems with the PRG analysis and classification have been fixed.

The ASAS-SN data on PRGs can be exceptionally useful for analyzing these stars, and is invaluable for both scientific and educational purposes. But the data for individual PRGs in the ASAS-SN catalogue should still be confirmed by careful inspection of the light curve, and by detailed analysis if necessary.

Acknowledgements

This paper made use of ASAS-SN photometric data. We thank the ASAS-SN project for their remarkable contribution to stellar astronomy, and for making the data freely available on-line. Thanks also to Chris Kochanek and especially Tharindu Jayasinghe for helpful comments. We acknowledge and thank the University of Toronto Work-Study Program for financial support. The Dunlap Institute is funded through an endowment established by the David Dunlap Family and the University of Toronto.

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