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New Periodic Class Ii Methanol Maser From Methanol Multi Beam Survey Catalogue

1517 words - 7 pages

\section{Discussion and analysis}

From the eight class II methanol maser sample selected from 6.7-GHz MMB survey catalogues I \citep{caswell2010} and II \citep{green2010}. The most exciting source is G358.460-0.391 which shows periodic variation over the monitoring period. This adds onto nine known class II methanol masers which show periodic variation \citep{goedhart2003,goedhart2004,goedhart2009,araya2010,szymczak2011,goedhart2013}.

The waveform of this source is like that of the absolute cosine function. Figure \ref{fig:G358.460-0.391_abs_cosine}, gives the absolute cosine fitted to the time series. The function fitted to the time series in Figure \ref{fig:G358.460-0.391_abs_cosine} was: $f(t) = A\cos{\left( \frac{\omega t}{2} + \phi \right) } + mt + c $, where $A$ is the amplitude, $\omega$ is a frequency, $t$ is time in days, $\phi$ is the phase, $m$ is the gradient for long term behaviour and $c$ is the y-intercept for the long term variation behaviour. The fitted parameters were: $A$, $\phi$, $m$ and $c$. The absolute cosine waveform was also noticed in G338.93-0.06 \citep{goedhart2003,goedhart2013}. The amplitude of the time series is slowly decreasing over the monitoring period. This could be due to changes on the surroundings of a masing cloud.

\begin{figure}
\centering
\resizebox{\hsize}{!}{\includegraphics[clip]{../figures/G358.460-0.391_67_full_abs_cosine.eps}}
\caption{Fitted absolute cosine with 219 days period to the 1.129 km.s$^{-1}$ time series. The bottom panel is for the residual flux after the fitted absolute cosine had been subtracted from the 1.129 km.s$^{-1}$ time series.}
\label{fig:G358.460-0.391_abs_cosine}
\end{figure}

From the chi-square ($\chi^2$) to produce Figure \ref{fig:G358.460-0.391_abs_cosine}, The root-mean-square error (RMSE), mean absolute error (MAE), mean bias error (MBE) and mean-square error (MSE). These parameter give the information about the goodness of the model to the data which is how an absolute cosine model. The determined values are: RMSE = $3.06$, MSE = $9.35$ MAE = $2.38$ and MBE = $0.008$. \citet{willmott2005} argued that MBE should be interpreted careful because it not an underestimate but is related to typical-error magnitude. The MBE hold information about the average model bias. The RMSE on the other hand, depends on the error magnitude, average error magnitude and square root of the size of the data ($\sqrt{n}$), and its boundary are MAE $\leq$ RMSE $\leq$ $\sqrt{n}$. The RMSE is not reliable in measuring the average error due to inconsistent relationship between MAE and RMSE \citep{willmott2005}. This inconsistency is due to the fact that the difference between MAE and RMSE increase non-monotonically though MAE $\leq$ RMSE.

The time series for class II methanol masers associated with G358.460-0.391 (see Figure \ref{fig:G358.460-0.391_67_timeseries}) were tested for the existence of periods using the Jurkevich (Figure \ref{fig:G358.460-0.391_jurkevich}),...

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