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courses:ast201:2 [2023/06/10 09:05] – [5.3 Brightness from magnitude] asadcourses:ast201:2 [2023/10/04 00:39] (current) – [1. Probes in astronomy] asad
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 ===== - Probes in astronomy ===== ===== - Probes in astronomy =====
 +Astronomy deals with particles or waves of matter or energy coming from outer space. Many of the fundamental particles illustrated in the **standard model of particle physics** below can be found in space.
 +
 +{{https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/803px-Standard_Model_of_Elementary_Particles.svg.png?nolink&500}}
 +
 +Quarks are not found in isolation, but in packets called protons or neutrons. We detect mostly protons from space using specialized detectors. Among the leptons, electrons and neutrinos are the most common particles found streaming through space. Quarks and leptons are particles of matter ([[wp>fermions]], named after [[wp>Enrico Fermi]]) and they are commonly called **cosmic rays** in astronomy; **cosmic-ray astronomy** is a large community.
 +
 +The particles of energy or force carriers ([[wp>bosons]], named after [[wp>Satyendranath Bose]]) constitute two more communities within astronomy. The **photons** or **electromagnetic waves** create the largest community of astronomers and they are the ones who use **telescopes**. The **gravitational waves** are detected by specialized detectors creating the most recent community of astronomy and astrophysics. Note that only the photon collectors and detectors are called telescopes, the detectors of cosmic rays or gravitational waves are simply called detectors.
 +
 +Fermions are massive, bosons are massless. The two are described below in the context of observational astronomy.
  
 ==== - Massive particles ==== ==== - Massive particles ====
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 ==== - As a particle ==== ==== - As a particle ====
 +From the beginning of the twentieth century, quantum mechanics claimed that there are situations where light cannot be described as a wave, but rather as a stream of particles called **photons**.
 +
 +The energy of a photon, however, is related to the frequency of the light when it exhibits its wave property according to the equation
 +
 $$ E = h\nu = \frac{hc}{\lambda} $$ $$ E = h\nu = \frac{hc}{\lambda} $$
 +
 +where $h=6.626\times 10^{-34}$ J s is Planck's constant. 
 ==== - As a ray ==== ==== - As a ray ====
 Photometry Photometry
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 Now if we can resolve the source, the solid angle subtended by a spherical source of radius $a$ at a distance $r$ (when $a\ll r$) Now if we can resolve the source, the solid angle subtended by a spherical source of radius $a$ at a distance $r$ (when $a\ll r$)
  
-$$ \Omega \approx \frac{\pi a^2}{r^2}. $$+$$ \Omega \approx \frac{\pi a^2}{r^2} $$
  
-Then the surface brightness+whose is angle is [[un:steradian]]. Then the surface brightness
  
 $$ S = \frac{F_o}{\Omega} = \frac{F_s}{\pi} $$ $$ S = \frac{F_o}{\Omega} = \frac{F_s}{\pi} $$
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 which is shown in the units of nW sr$^{-1}$ m$^{-2}$ Hz$^{-1}$. which is shown in the units of nW sr$^{-1}$ m$^{-2}$ Hz$^{-1}$.
  
-[{{:courses:ast201:blackbody-nw-thz.png?nolink&550|[[https://colab.research.google.com/drive/1vhrIuzj8mA5RnksjLuWGsPMko6J993gi?usp=sharing|Made using Google Colab here]].}}]+[[https://colab.research.google.com/drive/1vhrIuzj8mA5RnksjLuWGsPMko6J993gi?usp=sharing|{{:courses:ast201:blackbody-nw-thz.png?nolink&570}}]]
  
 The same brightness can be represented as a function of wavelength as The same brightness can be represented as a function of wavelength as
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 and the corresponding plot in the units of kW sr$^{-1}$ m$^{-2}$ nm$^{-1}$ is given below. and the corresponding plot in the units of kW sr$^{-1}$ m$^{-2}$ nm$^{-1}$ is given below.
  
-[{{:courses:ast201:blackbody-kW-nm.png?nolink&550|[[https://colab.research.google.com/drive/1vhrIuzj8mA5RnksjLuWGsPMko6J993gi?usp=sharing|Made using Google Colab here]].}}]+[[https://colab.research.google.com/drive/1vhrIuzj8mA5RnksjLuWGsPMko6J993gi?usp=sharing|{{:courses:ast201:blackbody-kW-nm.png?nolink&570}}]]
 \\ \\
-Why total power emitted by a blackbody at all angles is $\pi B$?+Why total power emitted by a blackbody at all angles is $\pi S$?
  
 At long wavelengths At long wavelengths
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 For a star, we could write either $m_B=5.67$ or $B=5.67$ for the magnitude at B band. For a star, we could write either $m_B=5.67$ or $B=5.67$ for the magnitude at B band.
 +
 +[{{:courses:ast201:apparent-magnitude-scale.jpg?nolink&700|Credit: Pasachoff & Filippenko.}}]
  
 ==== - Absolute ==== ==== - Absolute ====
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 Now if we take two pictures, one of our target star and another of Vega as a standard star, then we can measure the magnitude of the target star with respect to Vega as Now if we take two pictures, one of our target star and another of Vega as a standard star, then we can measure the magnitude of the target star with respect to Vega as
  
-$$ m_\star-m_{Vega} = -2.5 \log_{10} \frac{F_\star}{F_{Vega}} = -2.5 \log_{10} \frac{\sum (S_{xy}-B)_\star}{(S_{xy}-B)_{Vega}}. $$+$$ m_\star-m_{Vega} = -2.5 \log_{10} \frac{F_\star}{F_{Vega}} = -2.5 \log_{10} \frac{\sum (S_{xy}-B)_\star}{\sum (S_{xy}-B)_{Vega}}. $$
  
 Instead of Vega we can use any other standard star. Instead of Vega we can use any other standard star.
  
-  - Differential photometry +  - Differential photometry: two stars on the same image. 
-  - All-sky photometry+  - All-sky photometry: two stars on different images.
  
  
  
courses/ast201/2.1686409511.txt.gz · Last modified: 2023/06/10 09:05 by asad
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