Matched Filtering for the Canadian Hydrogen Observatory and Radio-Transient Detector Galaxy Search

Abstract

We present the spatial part of the point source signal extraction strategy for the upcoming CHORD galaxy survey. CHORD, the Canadian Hydrogen Observatory and Radio-transient Detector, is an under-construction drift-scanning compact interferometric radio telescope. CHORD comprises 512 six meter dishes and observes in the 300 to 1500 MHz frequency range. One of its science goals is producing a catalogue of galaxies detected by the neutral hydrogen (HI) 21 cm emission line. CHORD's highly redundant dish layout creates the problem of spatial aliasing, the effect where the same signal could be feasibly produced from sources at multiple locations on the sky. The search will be done with a matched filter in the visibility plane. This paper presents the search strategy and a prediction tool that can quickly estimate the matched filter response at a given sky position, allowing a prediction of alias locations and severity. This tool confirms that although aliases are impossible to distinguish in a single snapshot, they become possible to distinguish when combining data over a period of time. It predicts that aliases will be harder to distinguish for observations closer to the celestial equator, but that scanning with offset adjacent strips can remove this degeneracy. It predicts that the optimal strategy for a single offset to disambiguate aliases is to re-point the array in declination by about two degrees. A future paper will combine these findings with realistic noise estimates and galaxy population statistics to make forecasts of the population of galaxies that CHORD will detect.

Figures (15)

• Figure 1: The correlation coefficient $R(\boldsymbol n, \boldsymbol n_s)$ (equation \ref{['eqn:instantaneousmainresult']}) plotted in equatorial (RA, Dec) sky coordinates. The direction that CHORD is pointing at an instant, $\boldsymbol n_p$, is indicated with the ✕. In this case, CHORD is pointed at its zenith. The source position $u_s$ is indicated by the box $\Box$. The wavelength is set to 21 cm. A grid of locations yield $R(\boldsymbol n, \boldsymbol n_s) = 1$, which are perfect aliases.
• Figure 2: Predicted primary beam power for the true source location and closest alias locations as they move across the meridian. The north alias is about 1.4 degrees away, and the east alias is about 1.9 degrees away. Since the source is moving across the sky at a constant rate, the horizontal axis also corresponds to time. The source is located at the declination CHORD is pointed to. The matched filter expects the signal to peak as the source transits the meridian, passing closest to the center of the primary beam, as shown in the "True source" curve. For an aliased position to the east (blue dotted curve), the matched filter expects the signal to peak at the wrong time. For an aliased position to the north, the peak occurs at the correct time, but the detailed shape of the peak and its lobes do not match the data perfectly.
• Figure 3: The deviation of an alias's path from a path of constant declination. In this example, CHORD is pointed at a high 70 degree declination, and there is a source at that same declination. The position of the first northern alias is shown with a dashed line. In this tangent-plane projection, the alias follows a path that is a constant vertical offset from the true source path. In contrast, a real source would follow a constant-declination path, shown with a dotted line. These paths diverge slightly at large hour angles.
• Figure 4: Left: The correlation coefficients given by equation \ref{['eqn:integratedmain']} with CHORD pointing straight up and a source passing nearby. The dashed line indicates the path of CHORD's pointing direction. The true source position is indicated by the box $\Box$. The first aliases to the north and south remain prominent, while the aliases to the east and west are significantly reduced in amplitude. Right: a copy of Figure \ref{['fig:instantaneous']}, the instantaneous case, for comparison.
• Figure 5: A map of the log correlation coefficients for the case of a source near the north pole. The position of the source is indicated by the box $\Box$. The purple declination grid lines are separated by 1 degree. CHORD's pointing declination at 89 degrees is indicated by the dashed line. The concentric rings of higher correlation coefficient are aliases that rotate around the true source position at a fixed angular distance over the course of a sidereal day. This smears out the power of the aliases into rings rather than discrete peaks.