1. DSLR Photometry of the High Amplitude δ Scuti Stars V1338 Cen, V1430 Sco and V1307 Sco Roy Axelsen Astronomical Association of Queensland

2. δ Scuti Stars Pulsating variable, main sequence (MS), pre-MS and post-MS stars Spectral classes: A and F Low order gravity (g) and pressure (p) modes of pulsation Periods: 15 minutes to 5 hours Masses: ~ 1.5 – 2.5x solar Pulsations are self excited via the κ-mechanism

3. The κ Mechanism Involves cyclical changes in gravity-induced compression and heat-induced expansion, with consequent cyclical changes in opacity of partial ionization layers of H and He Heat trapped beneath the opaque layers of gas on compression correlates with maximum brightness of the star

4. Radial and Non-Radial Pulsations

5. Radial Pulsation http://www.physics.us yd.edu.au/~bedding/a nimations/visual.html Animation by Beau Bellamy, School of Physics, University of Sydney

6. Non Radial Pulsation http://www.physics.us yd.edu.au/~bedding/a nimations/visual.html Animation by Alexandra Chambers and Darran Baker, School of Physics, University of Sydney.

7. Target Stars

8. V1338 Cen Variability first reported in 1968 – Strohmeier, W., Ott, H. and Schoffel, E. 1968, Inf. Bull. Var. Stars 261 Period 0.1309382 d, epoch JD 2453764.8191 – Approx. 3h 9m, in January 2006 – Samus N.N., Durlevich O.V., Kazarovets E V., Kireeva N.N., Pastukhova E.N., Zharova A.V., et al., General Catalogue of Variable Stars (Samus+ 2007- 2012),VizieR On-line Data Catalog: B/gcvs.VizieR On-line Data Catalog: B/gcvs Magnitude range – ~10.2 – 10.7 (V)

9. V1430 Sco Variability first reported in 2007 – Otero, S.A. 2007, Open European Journal on Variable Stars, 56, 10 Period 0.0837770 d, epoch JD 2453096.878 – Approx. 2h 1m, in April 2004 Magnitude range – ~9.5 – 9.8 (V)

10. V1307 Sco Variability first reported in 1967 – Strohmeier, W. 1967, Inf. Bull. Var. Stars 178 Period 0.117031 d, epoch HJD 2452057.700 – Approx. 2h 49m, in May 2001 – Wils, P., Greaves, J. and Otero, S.A. 2004, Inf. Bull. Var. Stars 5490, 1. Magnitude range – ~9.9 – 10.5 (V)

11. Aims and Methods

12. Aims Obtain time series DSLR photometric data, and construct light curves for each night Perform Fourier analyses of the data (Period04) and create phase diagrams Determine the times of maximum (TOM) of the light curves (PERANSO) Create O-C (observed minus computed) diagrams Calculate ephemerides based on historical and personal TOM

13. Instrumentation Canon EOS 500D digital single lens reflex camera Celestron C9.25 SCT Losmandy GM-8 German equatorial mount – No autoguiding Images downloaded to a laptop computer

14. Imaging All images – Canon RAW (CR2) Light frames (variable, comparison and check stars) – 120 second exposure at ISO 800 – One image every 140 seconds Dark frames – During the meridian flip – Four or five frames Exposures same as for target stars

15. Imaging Flat fields – Near dawn – Four or five frames – Telescope aimed at the zenith – Sheet of white acrylic as diffuser – Exposures taken to half saturate the DSLR sensor Half saturation determined in AIP4Win

16. Fourier Analysis (Period04) Identify frequencies of pulsation (and thus the periods) Identify any harmonics of those frequencies Calculate period ratios (if more than one period) – Radial or non-radial pulsations? Construct phased light curves

17. Results

18. Data StarNo. of Nights No. of Images No. of Peaks* V1338 Cen697911 V1430 Sco689810 V1307 Sco45614 * Light curve peaks

19. Examples of Light Curves

23. Fourier Analysis

24. Fourier Analysis of V1430 Sco

25. Fourier Analysis: V1338 Cen Frequency No.Frequency (d -1 )ErrorSNR f17.63720.0001-- f2 (2 x f1)15.27390.000293.8 f3 (3 x f1)22.91120.000655.0 f4 (4 x f1)30.5460.00123.4 f51.020*0.0019.4 F6 (5 x f1)38.1870.00216.5

26. Fourier Analysis: V1338 Cen Frequency No.Frequency (d -1 )ErrorSNR f17.63720.0001-- f2 (2 x f1)15.27390.000293.8 f3 (3 x f1)22.91120.000655.0 f4 (4 x f1)30.5460.00123.4 f51.020*0.0019.4 F6 (5 x f1)38.1870.00216.5 * Considered to be a spurious result, possibly due to: -Small instrument effects, and -One cycle/day aliasing (observing nights clustered into 3 pairs, one night apart – see next frame)

28. Fourier Analysis: V1430 Sco Frequency No.Frequency (d -1 )ErrorSNR f111.936290.00004-- f2 (2 x f1)23.87270.000260.3 f3 (3 x f1)35.81050.000626.7 f418.4335*0.000811.7 F5 (4 x f1)47.74550.00116.4

29. Fourier Analysis: V1430 Sco Frequency No.Frequency (d -1 )ErrorSNR f111.936290.00004-- f2 (2 x f1)23.87270.000260.3 f3 (3 x f1)35.81050.000626.7 f418.4335*0.000811.7 F5 (4 x f1)47.74550.00116.4 f4 is not a Fourier harmonic, nor a combination of frequencies f1/f4 = 0.644, not in the range 0.74 – 0.78 Therefore, not a fundamental to first overtone ratio f4 may therefore by a non-radial pulsation

30. Fourier Analysis: V1307 Sco Frequency No.Frequency (d -1 )ErrorSNR f18.544750.00007 f2 (2 x f1)17.08900.000283.9 f3 (3 x f1)25.63370.000428.8 F4 (4 x f1)34.17810.000816.3 F5 (5 x f1)42.71800.00215.4

31. Phase Diagrams

32. V1338 Cen Phase Diagram

33. V1430 Sco Phase Diagram

34. V1307 Sco Phase Diagram

35. Times of Maximum Light

39. O-C Diagrams

46. Calculating Linear Ephemerides

50. Linear Ephemerides StarEphemeris V1338 CenT max (HJD) = 2,457,136.9978 (2) + 0.13093808 (3) E V1430 ScoT max (HJD) = 2,457,179.0027 (2) + 0.08377709 (1) E V1307 ScoTmax(HJD) = 2,457,222.0291 (3) + 0.11703066 (1) E

51. Conclusions Updated ephemerides are calculated for V1338 Cen, V1430 Sco and V1307 Sco

52. Conclusions The periods have been calculated, and are similar to those in the literature, but presented with enhanced precision

53. Conclusions All three stars have one principle frequency, accompanied by harmonics

54. Conclusions In the case of V1430 Sco, an additional unique frequency of approximately 18.4 c/d is discovered, which may represent a non-radial pulsation