Difference between revisions of "Specific Intensity"

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===Short Topical Videos===
 
===Short Topical Videos===
 
* [https://youtu.be/7Op36as0HX4 Specific Intensity: What's the Flux? (by Aaron Parsons)]
 
* [https://youtu.be/7Op36as0HX4 Specific Intensity: What's the Flux? (by Aaron Parsons)]
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* [http://youtu.be/YzqTpH9Y9y8 Photon Buckets: How (Radio) Telescopes Receive Power (by Aaron Parsons)]
  
 
===Reference Material===
 
===Reference Material===
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\usepackage{eufrak}
 
\usepackage{eufrak}
 
\begin{document}
 
\begin{document}
\subsection*{Units}
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\section{Units of Radiation}
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In order to motivate the useful properties of {\bf specific intensity}, it's helpful to list the variety of ways we have of describing the energy transfer coming from electromagnetic waves (or photons) striking a telescope.  Below are a few that are commonly used:
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\subsection{Voltage}
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Voltage (with units of Volts, $V$) gives the most direct view of the shape of the electromagnetic waves that are striking a (usually radio) telescope.  However, astronomical signals are usually noise, so the random fluctuations in voltage aren't usually terribly illuminating, and you can't average them directly.  This makes voltage a poor unit for learning about the sky.
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\subsection{Power}
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Power (with units of ergs/s, or watts, or dBm), which is generally proportional to voltage squared, is a much more useful quantity.  For example, it can be averaged over time.  However, it encodes no information about what frequency interval (bandwidth) that the measurement was made over, and the power of a measurement is generally proportional to the bandwidth of the signals you let in.
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The unit {\bf dBm} may not be familiar to most astronomers.  It refers to decibels relative to a milliwatt:
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\begin{equation}
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P_{\rm dBm} = 10\log_{10}\left(\frac{P}{1~{\rm mW}}\right)
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\end{equation}
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\subsection{Power Density}
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Power density (with units of ergs/s/Hz, or dBm/Hz), divides out by the bandwidth $B$ that the measurement is made over.  However, it contains no information about how large an area this signal was collected over. 
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\subsection{Flux}
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Flux (with units of ergs/s/cm$^2$) divides power received by the area the signal was collected over, but it does {\bf not} divide by the bandwidth.
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\subsection{Flux Density}
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Flux density (with units of ergs/(s cm$^2$ Hz), or Jy) combines power density and flux to get a measurement that divides out bandwidth and collecting area. 
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Most astronomers can agree on the flux density of a source, but {\bf if the beam of your telescope is smaller than the source on the sky}, you can get a different answer because you are not be getting all the photons from that source.
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Radio astronomers use Janskies (which are units of flux density) commonly.  A Jansky is defined as:
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\begin{equation}
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1~{\rm Jy}\equiv 1e-23 \frac{\rm erg}{{\rm s}\cdot {\rm cm}^2\cdot {\rm Hz}}
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\end{equation}
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\subsection{Specific Intensity}
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Specific intensity (with units of ergs/(s cm$^2$ Hz sr), Jy/beam) divides flux density by the angular area of the measurement (or of the source), and is intrinsic to source.  As
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- conserved along a ray
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\subsection{Brightness Temperature}
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Brightness temperature (with units of K) uses the Rayleigh-Jeans tail of a blackbody spectrum to define an equivalent temperature corresponding to a specific intensity.  It is often used as a proxy for specific intensity.
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\begin{equation}
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I_\nu=\frac{2kT_b)(\lambda^2}
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\end{equation}
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\section{Specific Intensity, Specifically}
  
 
Here are some terms pertaining to telescope observations:\par
 
Here are some terms pertaining to telescope observations:\par

Revision as of 12:22, 24 August 2016