FRECUENCIA DE FALLAS

After each of the 10 kHz fine channel images are created, they are corrected for the primary beam shape by dividing by the beam model created for the coarse channel in which the fine channels originated and corrected for the position o↵set caused by the ionosphere as determined for that coarse channel. Once these corrections are completed, the corrected fine channels are built into a three-dimensional data cube using the python script cube make.py (See Section 2.9 for the github repository for the code). This is represented on line five of Figure 2.3 and is completed for each coarse channel of each observation.

Once a data cube is created for each coarse channel of each observation, the observations from each coarse channel are individually integrated together to form a full continuum plus line three-dimensional data cube. From there the continuum can be subtracted to reveal the spectral lines, as per the sections below.

2.5.1

Stacking Observation with Inverse Variance Weight-

ing

The average, or arithmetic mean (AM), of a group of values is determined by calculating the sum of the values and dividing by the quantity of items within that group: Mean = 1 n n X n=1 ai = 1 n(a1+ a2+ ... + an). (2.3) A modification to the average, created by specifying a weight to each value before the data are averaged, is a process called weighted averaging. Inverse variance weighting is, therefore, averaging the results but dictating the level of importance of any individual value (a) based on one over the square of the stan- dard deviation ( ) or root mean square (RMS) of the value:

Weighted Mean = P ai/ 2i P 1/ 2 i . (2.4)

For the spectral line work, the MWA observations are taken in either five- minute or two-minute snapshots that, once calibrated, are combined to create a single integrated data cube for the region. By using inverse variance weighting, any observation with higher RMS will be down-weighted in importance when the observations are averaged together. If all the observations have similar variance, the weighted average will be similar to the arithmetic mean.

To obtain the RMS for each observation, an area average RMS from the associated coarse channel is determined using a python script and then writing it into a list in a text file. To integrate the data cube together, the fits cubes are first converted into a miriad file format. In miriad all the snapshot images for each coarse channel are averaged together after the coordinates for each image are gridded to match the first input data cube.

2.5.2

Continuum Subtraction

To obtain an unobscured view of any possible spectral line detections, the contin- uum and the associated artefacts (i.e. sidelobes or deconvolution errors), within the image, must be removed (Cornwell et al., 1992). Traditionally, continuum subtraction by fitting a polynomial to the visibility data through an identified list of line-free channels is considered a robust method regardless of any system- atic errors that may exist (Cornwell et al., 1992; Sault, 1994).

As an initial pass to subtract the continuum in the visibility plane, the casa task uvcontsub was used to apply a first order polynomial across the spectral channels in each snap-shot observation. This casa task subtracts the continuum on the real and imaginary separately. The continuum subtraction of the widefield image using casa removed approximately 71% of the continuum. To remove the remaining bright sources in the field, a second method was used to subtract the continuum by using the miriad task moment with “mom” set as “-1”, which created an average intensity map. This average intensity map was subtracted from each fine channel within the cube, removing approximately 99% of the total continuum.

Although this method produced a data cube that appeared to be clear of the continuum, the use of CASA to subtract the continuum produced an image in which some artefacts around bright continuum sources were visible in the image plane. These “streaking” artefacts, shown in Figure 2.9 may have been caused by uvcontsub not correcting for the w-terms when the continuum subtraction was done. However, it may have also been an e↵ect of sources further from the phase centre will have a more sinusoidal response as a function of frequency.

When the continuum subtraction can not be performed on the visibilities, the common suggestions are subtracting a continuum image made from channels free of spectral lines or fitting a polynomial to the spectral data before decon- volution. This is because “..if the continuum is removed before deconvolution, no deconvolution errors are propagated to the line images” (Sault, 1994). Both

Figure 2.9: Residual continuum in the three-dimensional data cube after con- tinuum subtraction was done in casa on the Galactic Centre data from 2014. (Image Credit: This image was created by Amr Hassan using spectral line cube visualisation software he created.)

of these methods are robust against calibration artefacts that are independent in frequency. However, any residual continuum within the image will have large unsubtracted side lobes from the weak emission.

Continuum subtraction completed by subtracting an image free of spectral lines from the continuum image is only recommended if the fractional bandwidth is small. Otherwise, the bandwidth could be smeared, or the spectral index of bright sources may be altered (Sault, 1994). The MWA has a 30.72 MHz bandwidth with observing frequencies of 99-170 MHz for these surveys, so the fractional bandwidth is large and these methods are not recommended.

A requirement to stray from traditional methods is not unique to MWA data. We adopted a method created by the Southern Parkes Large-Area Survey in Hy- droxyl (SPLASH) survey published by Dawson et al. (2014) where they binned the spectral data, creating a smooth curve that fits the spectral curvature at each pixel, and then subtract the binned spectra. This method creates a smooth sub- traction across the field-of-view and frequency band, correcting for any residual bandpass shape. However, this can also result in some loss of intensity for each spectral transition.

MWA survey regions, the data were binned in sizes of 5, 10, 15 and 20 channels and the impact on an injected 5 detection was evaluated. For a region around a potential 5 source, the di↵erence in intensity between the binned data and the uncorrected data was approximately 1% with the 15 channel bin giving the closest intensity to the unsubtracted line intensity. The data in which 15 or 20 channels are binned, show the smoothest spectra and identifies the likely true spectral characteristics of the sky.

The continuum subtraction technique of binning 15 spectral fine channels together, regridding the data based on the original observation to extrapolate the missing information, and then subtracting the two data cubes was used for both surveys. All the steps involved were completed in miriad on the final integrated data cube, as explained in Chapter 4.

Noise Reduction

Noise is normally defined as the unwanted signal and lowest threshold in which any signal may reside. However, noise can also mean unpredictable signals that carry no useful information. In signal processing noise can be considered uncor- related to the signal of interest.

Signal averaging is a signal processing technique where signals, or potential areas of signal, are averaged over time to increase the strength of a signal of interest relative to the noise. If we can assume that the signal power (S) is constant in replicated measurements then:

S = Z T

0

E[s(t)2]dt, (2.5)

where s(t) is the signal strength in respect to time and T is the total length of time. When the noise varies about a mean of zero with constant variance ( ) we can define the signal-to-noise ratio (SNR) as:

SNR = S₂ (2.6)

and we would expect the noise to decrease as a function of square root of the averaged time or number of replicate measurements. To see if the MWA spectral line observations behaved in this manner, observations were randomly averaged together in sets and the image RMS in the coarse channel continuum image was determined. As shown in Figure 2.10, the noise continues to decrease as a function of square root of time as more observations are averaged together.

However, in the observations of Orion (bottom plot), this was not immediately evident until the sensitivity of the primary beam was applied. This is likely due to the observations being done close to the horizon, where e↵ects of the changing primary beam are more evident.

This check is published in Chapter 5 and also had the added benefit of allowing us to predict how much time the MWA would need to start detecting thermal emission from molecules. The distance of 400 pc matches that of Orion and the distance of 8.6 kpc matches that of the Galactic Centre. This suggests that if the noise were continued to decrease in the same manner, we would require 30 hours of observations to be able to match the column densities calculated at higher frequencies for molecules which have transitions at the MWA frequencies.