Radiometer equation
Definition: The thermal-noise scaling that relates rms uncertainty to system sensitivity and independent time-frequency samples.
Why it matters here: It is needed to answer If a spectral channel is narrowed by a factor of 16, how much longer must you integrate to preserve the same thermal rms, all else equal? and to interpret Thermal noise is reduced by averaging independent time-frequency-polarization samples.
Relationships: Use it with Confusion noise and SEFD; the lecture model is \(\sigma_S=\frac{\mathrm{SEFD}}{\eta_s\sqrt{n_{\rm pol}\,\Delta\nu\,\tau}}\).
Boundary or common confusion: The radiometer result is a thermal lower bound. RFI flagging, quantization/correlator efficiency, calibration drift, and confusion can dominate, so ideal sqrt(t) extrapolation eventually fails.
SEFD
Definition: System-equivalent flux density: the source flux that would double the system noise power.
Why it matters here: It is needed to answer If a spectral channel is narrowed by a factor of 16, how much longer must you integrate to preserve the same thermal rms, all else equal? and to interpret Thermal noise is reduced by averaging independent time-frequency-polarization samples.
Relationships: Use it with Radiometer equation and Channel width; the lecture model is \(\sigma_S=\frac{\mathrm{SEFD}}{\eta_s\sqrt{n_{\rm pol}\,\Delta\nu\,\tau}}\).
Boundary or common confusion: The radiometer result is a thermal lower bound. RFI flagging, quantization/correlator efficiency, calibration drift, and confusion can dominate, so ideal sqrt(t) extrapolation eventually fails.
Channel width
Definition: The frequency interval represented by one spectral sample after channelization.
Why it matters here: It is needed to answer If a spectral channel is narrowed by a factor of 16, how much longer must you integrate to preserve the same thermal rms, all else equal? and to interpret Thermal noise is reduced by averaging independent time-frequency-polarization samples.
Relationships: Use it with SEFD and Integration time; the lecture model is \(\sigma_S=\frac{\mathrm{SEFD}}{\eta_s\sqrt{n_{\rm pol}\,\Delta\nu\,\tau}}\).
Boundary or common confusion: The radiometer result is a thermal lower bound. RFI flagging, quantization/correlator efficiency, calibration drift, and confusion can dominate, so ideal sqrt(t) extrapolation eventually fails.
Integration time
Definition: The accumulated duration over which statistically independent measurements are averaged.
Why it matters here: It is needed to answer If a spectral channel is narrowed by a factor of 16, how much longer must you integrate to preserve the same thermal rms, all else equal? and to interpret Thermal noise is reduced by averaging independent time-frequency-polarization samples.
Relationships: Use it with Channel width and Confusion noise; the lecture model is \(\sigma_S=\frac{\mathrm{SEFD}}{\eta_s\sqrt{n_{\rm pol}\,\Delta\nu\,\tau}}\).
Boundary or common confusion: The radiometer result is a thermal lower bound. RFI flagging, quantization/correlator efficiency, calibration drift, and confusion can dominate, so ideal sqrt(t) extrapolation eventually fails.
Confusion noise
Definition: Brightness fluctuations from unresolved sources that impose a non-thermal sensitivity floor.
Why it matters here: It is needed to answer If a spectral channel is narrowed by a factor of 16, how much longer must you integrate to preserve the same thermal rms, all else equal? and to interpret Thermal noise is reduced by averaging independent time-frequency-polarization samples.
Relationships: Use it with Integration time and Radiometer equation; the lecture model is \(\sigma_S=\frac{\mathrm{SEFD}}{\eta_s\sqrt{n_{\rm pol}\,\Delta\nu\,\tau}}\).
Boundary or common confusion: The radiometer result is a thermal lower bound. RFI flagging, quantization/correlator efficiency, calibration drift, and confusion can dominate, so ideal sqrt(t) extrapolation eventually fails.