Specific intensity
Definition: Radiant power per projected area, solid angle, and frequency interval, conserved along an empty ray.
Why it matters here: It is needed to answer An unresolved source is observed with two beam sizes. Which reported quantity should remain stable under ideal imaging: peak Jy/beam, integrated Jy, or brightness temperature? State conditions. and to interpret A telescope measures sky brightness convolved with its point-spread function, not the unconvolved sky field.
Relationships: Use it with Jy per beam and Brightness temperature; the lecture model is \(T_b=\frac{\lambda^2 S_\nu}{2k\Omega_b},\qquad\Omega_b=\frac{\pi\theta_{\rm maj}\theta_{\rm min}}{4\ln2}\).
Boundary or common confusion: The Rayleigh-Jeans brightness temperature is a coordinate on specific intensity; for coherent and synchrotron sources it can greatly exceed the kinetic temperature.
Brightness temperature
Definition: A Rayleigh-Jeans re-expression of specific intensity, not necessarily a gas kinetic temperature.
Why it matters here: It is needed to answer An unresolved source is observed with two beam sizes. Which reported quantity should remain stable under ideal imaging: peak Jy/beam, integrated Jy, or brightness temperature? State conditions. and to interpret A telescope measures sky brightness convolved with its point-spread function, not the unconvolved sky field.
Relationships: Use it with Specific intensity and Beam solid angle; the lecture model is \(T_b=\frac{\lambda^2 S_\nu}{2k\Omega_b},\qquad\Omega_b=\frac{\pi\theta_{\rm maj}\theta_{\rm min}}{4\ln2}\).
Boundary or common confusion: The Rayleigh-Jeans brightness temperature is a coordinate on specific intensity; for coherent and synchrotron sources it can greatly exceed the kinetic temperature.
Beam solid angle
Definition: The effective angular area of the normalized telescope response.
Why it matters here: It is needed to answer An unresolved source is observed with two beam sizes. Which reported quantity should remain stable under ideal imaging: peak Jy/beam, integrated Jy, or brightness temperature? State conditions. and to interpret A telescope measures sky brightness convolved with its point-spread function, not the unconvolved sky field.
Relationships: Use it with Brightness temperature and Beam dilution; the lecture model is \(T_b=\frac{\lambda^2 S_\nu}{2k\Omega_b},\qquad\Omega_b=\frac{\pi\theta_{\rm maj}\theta_{\rm min}}{4\ln2}\).
Boundary or common confusion: The Rayleigh-Jeans brightness temperature is a coordinate on specific intensity; for coherent and synchrotron sources it can greatly exceed the kinetic temperature.
Beam dilution
Definition: Reduction of observed peak brightness when a source occupies only part of the beam.
Why it matters here: It is needed to answer An unresolved source is observed with two beam sizes. Which reported quantity should remain stable under ideal imaging: peak Jy/beam, integrated Jy, or brightness temperature? State conditions. and to interpret A telescope measures sky brightness convolved with its point-spread function, not the unconvolved sky field.
Relationships: Use it with Beam solid angle and Jy per beam; the lecture model is \(T_b=\frac{\lambda^2 S_\nu}{2k\Omega_b},\qquad\Omega_b=\frac{\pi\theta_{\rm maj}\theta_{\rm min}}{4\ln2}\).
Boundary or common confusion: The Rayleigh-Jeans brightness temperature is a coordinate on specific intensity; for coherent and synchrotron sources it can greatly exceed the kinetic temperature.
Jy per beam
Definition: An image unit giving flux density assigned to one synthesized-beam area.
Why it matters here: It is needed to answer An unresolved source is observed with two beam sizes. Which reported quantity should remain stable under ideal imaging: peak Jy/beam, integrated Jy, or brightness temperature? State conditions. and to interpret A telescope measures sky brightness convolved with its point-spread function, not the unconvolved sky field.
Relationships: Use it with Beam dilution and Specific intensity; the lecture model is \(T_b=\frac{\lambda^2 S_\nu}{2k\Omega_b},\qquad\Omega_b=\frac{\pi\theta_{\rm maj}\theta_{\rm min}}{4\ln2}\).
Boundary or common confusion: The Rayleigh-Jeans brightness temperature is a coordinate on specific intensity; for coherent and synchrotron sources it can greatly exceed the kinetic temperature.