Search for the optimal smoothing method to improve S/N in cosmic maser spectra

1 Introduction

Cosmic, or astrophysical, masers are naturally occurring sources of stimulated spectral line emission in the radio wave part of the electromagnetic spectrum. They can be observed in star-forming regions, planetary atmospheres and systems, molecular clouds, late-type star atmospheres, comets, and more (Gray 2012, Strel’nitskii 1974).

Cosmic masers are large in volume, approximately 1 0 7 meters in diameter. They emit very strong but narrow low-frequency electromagnetic waves, which can be sometimes difficult to distinguish from noise. The intensity of these emissions can oscillate over different time periods, ranging from a few seconds to up to eight years, based on past observations (Aberfelds 2024, Strel’nitskii 1974, Kegel 1975).

In the interstellar medium, masers consist of molecules with one to six atoms, most common being OH, CH₃OH, H₂O, and SiO (Gray 2012).

The study of astrophysical masers is crucial for enhancing our understanding of the universe. One of the institutes involved in observing galactic masers is Ventspils International Radio Astronomy Centre (VIRAC), utilizing the Irbene radio telescopes. These telescopes allow for resolution adjustments via computer settings, albeit with limitations. For instance, in the Ventspils monitoring program observing 6.7 GHz methanol masers (Aberfelds 2024, Aberfelds et al. 2023), a high velocity resolution of 0.017 km/s is used, even though the natural widths of the maser lines range from 0.2 to 0.3 km/s. As a result, the data are oversampled, leading to spectra with more noise than would be present with the appropriate velocity resolution.

The aim of this study is to find an optimal smoothing method, which in result increases the S/N value by not effecting the original peak values, keeping the original spectral form. It is hypothesized that the advanced mathematical functions will be better than the simple averaging down method.

Advanced mathematical methods differ from simple calculations like averaging over a number of spectral channels, they reduce noise via convolution-based filtering according to Fourier transform principles. Each convolution-based method applies various functions with specific parameters. For instance, the Savitzky–Golay method fits a polynomial with chosen polynomial order (p) to the central data point within a defined window (w) and replaces that point with the calculated polynomial value. Other parameters used are standard deviation ( σ ) and Gaussian order parameter (m) (Savitzky and Golay 1964, Press et al. 2002, Brandt 2019, Smith 2013).

Savitzky–Golay filtering has been previously applied in radio astronomy for spectral analysis, but past studies have only briefly explored its potential. Morabito et al. (2014) tested it alongside other smoothing methods for carbon radio recombination lines, while Stroe et al. (2015) mentioned its use without detailed results. More recently, Hussein and Mahdi (2024) applied it for radio signal enhancement but did not perform an extensive comparison. This study expands on previous work by systematically evaluating multiple smoothing techniques to determine the optimal approach for methanol maser spectra.

2 Method

In this article, VIRAC provided spectral data from nine different 6.7 GHz methanol maser sources (Aberfelds et al. 2023) and a pre-existing Python code for working with spectra, which included channel averaging smoothing method. The first course of action was to find additional smoothing methods for comparison. Ten more methods were identified, bringing the total to 11 methods (and their abbreviations):

• Channel averaging (Average);

• Fourier (F; Brandt 2019, Kleinman and Korn-Lubetzki 1997);

• Savitzky–Golay (S-G) (Savitzky and Golay 1964);

• Moving average (M-A);

• Median (M);

• Gaussian (G) (Draine 2011, Rudolph et al. 2023);

• Lorentzian (L) (Draine 2011);

• Voigt (Draine 2011);

• Hanning (H) (Essenwanger 1986);

• Bartlett (B) (Proakis and Monolakis 1996).

• Eilers Perfect Smoother (Eilers 2003)

The methods were compared based on their ability to preserve spectral details while smoothing the noise. Specifically, the radial velocity ( v LSR ) of the peak, peak flux density ( F p ), and integrated flux density ( F i ) should remain unchanged, while the noise root-mean-square (RMS) value and integrated noise flux density (noise F i ) should decrease, and the S/N ratio should increase. Additionally, the execution time for each method was compared to determine its practicality and ease of use.

Each method was implemented in the Python code with source codes listed in Table A1, and required various parameters, including window sizes (how many points are included in the calculations), standard deviation (affecting the smoothing level), the polynomial degree, and smoothing factor. The parameters were empirically found, meaning by trial and error and observing which parameters gave the best result.

Following the determination of the parameters, three different graphs were generated to visualize the effect of the smoothing methods on the original spectra, and additional data were outputted in the console to compare.

A code was made that completes all the mentioned tasks earlier, which was then used for testing smoothing methods on a range of maser sources. These sources varied in intensity, with either one or multiple peaks, and demonstrated differing levels of spectral complexity.

The used maser sources in this article, naming according to Galactic coordinates, were: G78.122+3.633, G109.871+2.114, G133.947+1.064, G94.602-1.796, G22.357+0.066, G32.744-0.076, G111.26-0.77, G196.454-01.67, G121.298+0.659.

3 Result

The values of each parameter used in different smoothing methods are displayed in Table 1. These values were determined to be optimal, working with Irbenes radio telescopes RT-32 and RT-16, which had the velocity resolution set as 0.017 km/s. The Voigt smoothing method combines parameters from Gaussian and Lorentzian methods.

An example result list for each smoothing method is given in Table 2. The results are from maser source G78.122+3.633. In addition, from the same maser source, a graph displaying the effect of smoothing method on the original spectrum is shown in Figure 1. The formula used for the difference calculations is given as follows:

Figure 1

Difference in flux densities between the original spectrum and smoothed spectrum for maser source G78.122+3.633.

The optimal smoothing method is chosen by first examining the graphs and then comparing the values.

The results for maser source G78.122+3.633 show that the optimal smoothing method is Savitzky–Golay. This proves to be true comparing the values in Table 2: the peak radial speed does not change, while the flux density changes slightly by 0.87 Jy (1.33%) and integrated flux by 0.64 Jy km/s (0.02%). The noise RMS is smaller by 0.31 Jy (40.26%), integrated flux by 0.91 Jy km/s (1.61%), and the S/N value is 1.64 times larger compared to the original values. Also by examining the Figure 1, it is noticeable that the Savitzky–Golay method evenly affects the whole spectrum, while other methods affect the peak values more.

The same result was achieved for the other maser sources except G32.744-0.076 and G111.26-0.77. The former consists of multiple peaks, which noticeably hinders the quality of smoothing for the Savitzky–Golay method. The effect of smoothing methods on original data points is shown in Figure A4. However, it was still considered the best method together with the channel averaging method, which is shown in Figure A2.

4 Conclusion

Based on the evaluation of 10 methods, Savitzky–Golay was identified as the optimal method for improving the S/N ratio in cosmic maser spectra for 7 out of 9 maser sources.

Execution time is not a significant factor in determining the optimal method, as all methods have an execution time of less than 1/100th of a second. Therefore, it was not taken into account.

Although the Savitzky–Golay method was identified as the optimal method, it did not improve the S/N ratio for low signal spectra. No other method improved it either, indicating that further research and evaluation of different methods are needed to find an optimal solution for low signal spectra.

After determining the optimal parameters for each method, the differences between the smoothing methods are minimal. The Savitzky–Golay, Hanning, Bartlett, and channel averaging methods are quite similar, each having minimal effect on the peak values. In contrast, the Fourier, Gaussian, Lorentzian, Voigt, and Eilers Perfect Smoother methods impact the peak values more noticeably. Finally, moving average and median methods affect the peak values the most.

The fitting parameters for all smoothing methods demonstrate a strong alignment, as the point count within the chosen window size closely matches the point count corresponding to the natural line width of a 6.7 GHz methanol cosmic maser. If the line width differs, it is advisable to adjust the window size accordingly.