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).

The theoretical rms noise is derived using the effective collecting
area *A*_{e} of the station, the system temperature *T*_{sys}, number of
polarizations *N*_{pol}, the bandwidth Δν and the integration
time Δ *t*:

Δ S= |
| W m^{−2} Hz^{−1} sr^{−1}
(1) |

or

Δ S= |
| Jy/beam
(2) |

where *SEFD* is known as the System Equivalent Flux Density:

SEFD= |
| 10^{26} Jy
(3) |

*A*_{e} is estimated from the collecting area of an LWA dipole,
*A*_{dip} times 256 for the number of dipoles in the array. *A*_{dip}
depends on the zenith angle, and can be expressed as:

A_{e}=G(λ) |
| cosθ^{1.6}
(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:

T_{sys}≈ 50 λ^{2.56} 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) A_{e}^{1}(m^{2})T_{sys}(K)SEFD (Jy) Δ S(mJy)15 2.56× 10 ^{4}1.07× 10 ^{5}11540 118 25 9200 2.89× 10 ^{4}8670 88 35 4700 1.21× 10 ^{4}7180 73 45 2840 6420 6240 64 55 1900 3840 5570 57 65 1360 2500 5080 52 75 1020 1740 4680 48 85 800 1260 4370 45

- 1
A_{e}calculated in the zenith direction, assuming a zenith gainG=6 dB.

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 σ_{c} at 74 MHz using a 2^{∘} beam
and resolution θ is given by [Cohen (2004)]:

σ_{c}= | ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ |
| 29 µ Jy/beam
(6) |