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5  Sensitivity

The theoretical sensitivity that can be reached using the LWA1 can be estimated (Sect. 5.1). However, with a single station the instrument is severely limited by confusion noise (Sect. 5.2).

5.1  Theoretical Noise

The theoretical rms noise is derived using the effective collecting area Ae of the station, the system temperature Tsys, number of polarizations Npol, the bandwidth Δν and the integration time Δ t:

Δ S=
NpolΔνΔ t
 W m−2 Hz−1 sr−1     (1)


Δ S=
2NpolΔνΔ t
 Jy/beam     (2)

where SEFD is known as the System Equivalent Flux Density:

2k Tsys
1026 Jy     (3)

Ae is estimated from the collecting area of an LWA dipole, Adip times 256 for the number of dipoles in the array. Adip depends on the zenith angle, and can be expressed as:

cosθ1.6     (4)

where λ is the wavelength, θ is the zenith angle and G(λ) is the antenna zenith gain ranging from 8.5 dB at 20 MHz to 5.9 dB at 88 MHz [Ellingson et al. (2009)].
The system temperature is a combination of external noise (cosmic, atmospheric and earth-generated noise) and internal noise (noise generated in the active parts of the antenna, and in the receiver). Except for night time atmospheric noise at the lowest frequencies around 10−20 MHz, and excluding man made interference signals, the system temperature between 10−88 MHz is dominated by the Galactic background radio emission, and can be approximated by a power law:

Tsys≈ 50 λ2.56 
K     (5)

Table 5.1 gives the LWA1 theoretical noise in steps of 10 MHz, assuming dual polarizations, a bandwidth of 4 MHz, a 10 min integration time and a zenith pointing direction.

Frequency (MHz)Ae1 (m2)Tsys (K)SEFD (Jy)Δ S (mJy)
152.56× 1041.07× 10511540118
2592002.89× 104867088
3547001.21× 104718073

Ae calculated in the zenith direction, assuming a zenith gain G=6 dB.
Table 3: LWA1 theoretical noise estimates using dual polarizations, a bandwidth of 4 MHz, a 10 min integration time and a zenith pointing direction.

5.2  Confusion Limit

The rms fluctuations are affected by unmodeled sources in the field of view as well as sources passing through the sidelobes. These effects are large at low frequencies, and will limit the sensitivity of the LWA1.

The confusion noise limit σc at 74 MHz using a 2 beam and resolution θ is given by [Cohen (2004)]:




 29   µ Jy/beam     (6)

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