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Is There A Distinction Between Periodic And Quasi-Periodic Class II Methanol Masers?
(Phd student at North-West University, Potchefstroom, South Africa )
Supervisors: Prof. J. D. Van der Walt (North-West Univeristy), Dr. M. J. Gaylard (HartRAO) and Dr. S. Goedhart (SKA South Africa)

Jabulani P. Maswanganye

A Neapolitan of Masers: Variability, Magnetism and VLBI 20-22 May 2013, Sydney, Australia

Class II methanol masers
High mass stars are form in optiacal depth and are giant molecular typically formed clouds with high in clusters. The two Class II methanol masers (6.7GHz and 12.2 GHz emission lines) are found in massive star forming regions and reside near ultra-compact ionised hydrogen (H II) region(e.g., Norris et al. 1993; Bartkiewicz et al. 2009; Sanna et al. 2010). Monitoring these masers in the indirect way of studying the dynamics in massive star forming region.

Class II methanol Masers
Goedhart et al. (2003) reported regular varying Class II methanol maser in some of massive star forming region (G9.621+0.196). Since then, at least 900 methanol masers (6.7 GHz) had been observed (e.g., Pestalozzi et al. 2005; Caswell et al. 2011; Green et al. 2012), and Eleven have been reported to periodic or quasi-periodic (Goedhart et al. 2003, 2004 2007, 2009; Araya et al. 2010; Szymczak et al. 2011,Sanna et al. (2009); Xu et al. 2011; Green & McClure-Gri ths (2011); Reid et al. 2009A; Honma et al. 2007). The periods range: 29 - 668 days.

Example of periodic or quasi-periodic class II methanol masers G9.62+0.20 G188.95+0.89 G328.24-0.55

G331.13-0.24

G338.93-0.06

G339.62-0.12

Period determination methods used

Lomb-Scargle method derived by Lomb (1976), then modified by Scargle (1982) Jurkevich method derived by Jurkevich (1971) Epoch-folding using L-statistics (Davies, 1990)

Lomb-Scargle method
This just a modified classical periodogram. Use false alarm probability statistics to test the significant of the determined period.

Lomb-Scargle applied to G9.62+0.20

Lomb-Scargle Periodogram (Red-dash line significant test line)

Procedure: Fit Fourier series, shuffle residuals, create Noise. Create 1000 Synthetic time series {fitted Fourier series + Noise + shuffle residual} with different shuffled residuals and noise.

Monte Carlo simulation (Hakala et al. 2003)

(Example for the third and tenth order Fourier series fitted to G9.62-0.20 at 12 GHz )

Monte Carlo simulation (Hakala et al. 2003)

3rd order

10th order

Weighted mean of the harmonics improve the accuracy of the determine period (Gradari et al. 2009)

G9.62+0.20 (12GHz) Peak one 243.1 +/Peak two: 121.5 +/Peak three: 81.03 +/Peak four: 60.76 +/Peak five: 48.61 +/-

1.631 km/s 0.6 days 0.2 days (2) 243.0 +/0.08 days (3) 243.1 +/0.05 days (4) 243.0 +/0.03 days (5) 243.0 +/-

0.3 0.2 0.2 0.2

days days days days

Periods determine by Lomb-Scargle method

source G9.62+20 G12.89+0.49 G188.95+0.89 G328.24+0.55 G331.13-0.24 G338.93-0.06 G339.62-0.12

Period for MC Simulation (days) 243 29 400 221 510 133 200

Determined period (days)

243.05 (4) 29.453 (5) 394.1 (6) 221.0 (3) 511 (1) 132.80 (6) 200.1 (3)

Jurkevich method

It is based on the expected mean square deviation and it is less inclined to generate spurious periodicities than Fourier analysis (Fan et al. 1997 ) It folds the time series in bins (with a trial period), calculate the variance in each bin and sums all the variances across the bins (for each trial period). If the trial period is a true period, the sum of the variances across the bins will be absolute minimum. Kidger et al. (1992) used the minimum as the measure of time series periodicity.

Example of the folded G331.13-0.24 time series

G338.93-0.06 at 6.7 GHz time series

Jurkevich method applied to G338.93-0.06

Periods determine by Jurkevich method
source Period in days Periodicity measure f (sum of varianceV^2) 1.30 (0.46) 0.30 (0.77) 0.48 (0.68) 0.55 (0.64) 1.29 (0.44) 2.01 (0.33) 0.59 (0.63) Periodic Periodic Periodic Periodic Periodic ? Periodic Periodic

G9.62+20 G12.89+0.49 G188.95+0.89 G328.24+0.55 G331.13-0.24 G338.93-0.06 G339.62-0.12

243 (2) 29.51 (7) 394 (7) 221 (2) 509 (10) 133 (1) 201 (3)

Epoch-folding using L-statistics
This method folds the time series like Jurkevich method, It determines the period using either Phase Dispersion Minimisation (Stellingwerf 1978) or Epochfolding but it tests the significancy of the period using L-statistics.

G331.13-0.24 time series at 6.7 GHz

Epoch-folding using L-statistics applied for G331.13-0.24 time series at 6.7 GHz

Epoch-folding using L-statistics Results
source
G9.62+20 G12.89+0.49 G188.95+0.89 G328.24+0.55 G331.13-0.24 G338.93-0.06 G339.62-0.12

Period in days
243.2 (3) 29.47 (4) 395 (7) 220.3 (6) 509 (7) 132.8 (9) 200.1 (2)

Comparing the methods
source Lomb-scargle (days)
243.05 (4) 29.453 (5) 394.1 (6) 221.0 (3) 511 (1) 132.80 (6) 200.1 (3) Epochfolding Jurkevich (days) (days) Best Approx. Period (days) 243.05 (4) 29.453 (5) 394.1 (6) 220.9 (3) 511 (1) 132.80 (6) 200.1 (3)

G9.62+20 G12.89+0.49 G188.95+0.89 G328.24+0.55 G331.13-0.24 G338.93-0.06 G339.62-0.12

243.2 (3) 29.47 (4) 395 (7) 220.3 (6) 509 (7) 132.8 (9) 201 (2)

243(2) 29.51 (7) 394 (7) 221 (2) 509 (10) 133 (1) 201 (3)

Summary

All sources have been shown to be periodic. Using Jurkevich method: Kidger et al. (1992) proposed that if f >= 0.5 suggests there is a very strong periodicity and if f < 0.25 there is no periodicity, if periodic, it is a weak one.

But?

there is one source: G331.13-0.24.

It should be quasi-periodic because one maser group is strongly periodic, and the other is quasi-periodic.

G331.13-0.24 maser spot map at 6.7 GHz

~ 0.5 arcsec

Phillips et al. (1998)

(Vertical lines prove that the bottom three time series have a varying time delay with the top two time series)

G331.13-0.24 time series

The End Thank you