In 2016, Dr Roy Axelsen was awarded the Berenice and Arthur Page Medal for high-precision photometric observations and the Fourier analysis of Delta Scuti variables.

Details of his achievements are as follows.

### Summary

Roy Axelsen is the Director of the Variable Star Section of the Astronomical Association of Queensland (AAQ) and has held that position since 2005. His research interests have been the measurement of pulsating variable stars of δ Scuti type, and the analysis of the resulting light curves and times of maximum light (TOM). He has published seven papers reporting photoelectric and DSLR photometric observations in this field, which are the subject of this nomination. He has published new TOM for several southern δ Scuti stars and has calculated ephemerides which report the periods of these stars with improved precision. He has studied and published changes in the periods of such stars, and has utilized Fourier analysis to reveal previously undiscovered periods. By recording and analysing times of maximum light, he has discovered and published the highest recorded rate of increase in the period of a radially pulsating δ Scuti star (RS Gru), has found evidence which does not support (and arguably refutes) a hypothesis by others of an unseen companion to BS Aqr, has discovered a reversal in the direction of change in the period of ZZ Mic and fitted a third order polynomial ephemeris to the observational data on ZZ Mic. While drafting reports of his results and analyses, he found no clear step-by-step description for amateurs of methods for O-C diagrams, nor of methods for calculating ephemerides of variable stars and the rates of change in their periods, particularly for quadratic ephemerides. He therefore published a paper on these methods for use by other amateur astronomers.

### Publications Attached to this Nomination

- Axelsen, R.A. 2014, New Light Elements for the High Amplitude δ Scuti Star BS Aquarii. JAAVSO , 42, 37.
- Axelsen, R.A. 2014, New Light Elements for the High Amplitude δ Scuti Star RS Gruis. JAAVSO 42, 44.
- Axelsen, R.A. 2014, EQ Eridani, a Multiperiodic δ Scuti Star. JAAVSO, 42, 287.
- Axelsen, R.A. 2014, Current LIght Elements of the δ Scuti Star V393 Carinae. JAAVSO 42, 292.
- Axelsen, R.A. 2014, Methods for O-C (Observed Minus Computed) Diagrams and for the Determination of Light Elements of Variable Stars with Linear and Second Order Polynomial Ephemerides. JAAVSO 42, 451.
- Axelsen, R.A. and Napier-Munn, T. 2015. Recently Determined Light Elements for the δ Scuti Star ZZ Microscopii. JAAVSO 43, 50.
- Axelsen, R.A. 2015, Recently Refined Periods for the High Amplitude δ Scuti Stars V1338 Centauri, V1430 Scorpii and V1307 Scorpii. JAAVSO 43 (In press).

### Description of Research

#### BS AQUARII (Reference 1)

The period of the high amplitude δ Scuti star BS Aqr had previously been found to change over time. It was suggested in 1997 that the shape of the O-C diagram could be explained by the light time travel effect due to an unseen companion.

DSLR time series photometry of BS Aqr was taken during five nights in 2013. Five times of maximum are added to the data on this star. A new linear ephemeris was defined for recent decades, with no significant change in the period from 1973 to 2013. A refined period of 0.197822765 (+/- 0.000000010) d was calculated. The results do not support, and arguably refute, the previously published hypothesis of an unseen companion.

#### RS GRUIS (Reference 2)

RS Gru is a high amplitude δ Scuti star with a period that decreased at a constant rate from 1952 to 1988, then increased between 1988 and 2010.

Photoelectric photometry was taken from 2007 to 2010, and DSLR time series photometry from 2011 to 2013. Sixteen times of maximum calculated by Axelsen are added to the data for RS Gru. This is the largest collection of such data for this star by a single observer, or group of observers publishing together. A quadratic ephemeris was calculated from data by other observers and by Axelsen from 2003 to 2013, which revealed that the period of RS Gru during this span of years has been increasing at a constant rate of dP/Pdt = 84.95 (15.74) x 10-8 yr-1 which is the highest published rate of increase in the period of a radially pulsating δ Scuti star.

#### EQ ERIDANI (Reference 3)

EQ Eri is δ Scuti star reported to have a single period of 0.0700 d. The most recent pervious photometric study was published in 1995.

DSLR time series photometry was taken during 6 nights in 2013. The light curve had an irregular shape and varying amplitude, indicating the existence of two or more periods. Fourier analysis revealed at least three periods, 0.0696 d, 0.0856 d and 0.1386 d. The existence of multiple periods is a new discovery. None of the period ratios fall within the range 0.74 – 0.78 expected for the ratio of the first overtone to the fundamental mode of a radially pulsating δ Scuti star. The pulsations may therefore be in the non-radial mode.

#### V393 CARINAE (Reference 4)

V393 Car is a δ Scuti star with a dominant period of 0.1412937 (+/- 0.0000002) d. A suggestion of a second period from results in the literature has never been confirmed.

DSLR time series photometry was taken during six nights from December 2013 to March 2014. Six times of maximum have been added to the data on V393 Car. Fourier analysis revealed a dominant period of 0.141297 (+/- 0.000001) d, almost identical to that determined 37 years previously by another observer and published in 1984. No second period could be found. A linear ephemeris was calculated from the data of Axelsen and the data published in 1984, which yielded a refined period of 0.14129328 (+/- 0.00000001) d.

#### METHODS FOR 0-C (OBSERVED MINUS COMPUTED) DIAGRAMS AND FOR THE CALCULATION OF EPHEMERIDES OF VARIABLE STARS (Reference 5)

In the process of analysing his results from the photometry of δ Scuti stars, Axelsen found no single, clear source of information in the literature readily available to amateur astronomers that provided step-by-step methods for constructing O-C diagrams, for calculating linear and quadratic (second order polynomial) ephemerides, or explaining the formula for the constant rate of change in the period of a variable star with a quadratic ephemeris.

This paper therefore provides, for amateur astronomers, a step-by-step description and explanation of the methods used by Axelsen for the analyses and calculations described in the paragraph above.

#### ZZ MICROSCOPII (Reference 6)

The period of the δ Scuti star ZZ Mic had been found by other observers to be increasing at a constant rate between 1960 and 2003.

Photoelectric photometry was taken during 3 nights in 2008, and DSLR time series photometry during 3 nights in 2014. Eighteen times of maximum are added to the data on ZZ Mic, four from photoelectric photometry, and fourteen from DSLR photometry. An O-C diagram of the results of Axelsen and those of other observers confirmed the previous increase in the period. The new data by Axelsen reveals that the period has decreased in recent years. A cubic ephemeris was derived (acknowledging the assistance of co-author Tim Napier-Munn with analysis and discussion of the statistics), with the formula:

Tmax (HJD) = 2456858.0131 (0.0002) – 7.644 (2.532) × 10–19 E3 – 2.646 (0.973) × 10–13 E2 + 0.06717917 (0.00000001) E

#### V1338 CENTAURI, V1430 SCORPII AND V1307 SCORPII (Reference 7)

The most recent previously published periods and epochs for these high amplitude δ Scuti stars were in January 2006, March 2004 and May 2001 respectively.

DSLR time series photometry was taken by Axelsen between April and August 2015, comprising six nights of data for V1338 Cen, six nights of data for V1430 Sco, and four nights of data for V1307 Sco. Ten new times of maximum are added to the data for both V1338 Cen and V1430 Sco, and four new times of maximum for V1307 Sco. The periods of these stars were recalculated from linear ephemerides based on previously published epochs and the new epochs of Axelsen, resulting in improved accuracy of the periods, namely: 0.13093808 (+/- 0.00000003) d for V1338 Cen, 0.08377709 (+/- 0.00000001) d for V1430 Sco and 0.11703066 (+/- 0.00000001) d for V1307 Sco. In addition, Fourier analysis discovered a previously unknown low amplitude oscillation for V1430 Sco. The ratio of the dominant frequency to the newly discovered frequency is 0.644, which is not in the range of 0.74 – 0.78 expected for a fundamental to first overtone ratio for a δ Scuti star pulsating in the radial mode. The new frequency may therefore be a non-radial mode.