Flux to brightness temperature

Tbright.ipynb

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   "source": [
    "import numpy as np\n",
    "import astropy"
   ]
  },
  {
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   "execution_count": 5,
   "id": "176b22ab-b54a-4f81-9822-ffe8149807ed",
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   "source": [
    "from astropy import units as u"
   ]
  },
  {
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   "source": [
    "freq = 1*u.MHz\n",
    "equiv = u.brightness_temperature(freq)\n",
    "\n",
    "# angular size of source (Jupiter ranges from 30 to 60 arcsec)\n",
    "# I'm just including a factor of 10 to include its magnetosphere\n",
    "source_diameter = 10*u.arcmin\n",
    "source_area = np.pi*(source_diameter/2)**2"
   ]
  },
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   "source": [
    "# From Cassini at Jupiter (Figure 2 in https://www.nature.com/articles/415985a)\n",
    "# Flux was integrated over 0.5-5.6 MHz\n",
    "Delta_nu = 5.1 * u.MHz\n",
    "flux = 1e-10 * u.W / u.m**2 / (4*np.pi*u.sr) / Delta_nu"
   ]
  },
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    {
     "data": {
      "text/latex": [
       "$5.0786477 \\times 10^{9} \\; \\mathrm{K}$"
      ],
      "text/plain": [
       "<Quantity 5.0786477e+09 K>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flux.to(u.K, equivalencies=equiv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1d22f73f-e368-4d6b-a538-47c704d08483",
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    {
     "data": {
      "text/latex": [
       "$56586167 \\; \\mathrm{K}$"
      ],
      "text/plain": [
       "<Quantity 56586167.27900947 K>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Numbers from Karl's code\n",
    "# Cassini was at approximately 9.5e10 m from Jupiter\n",
    "# Correct to the farthest distance between Moon and Jupiter (9.0e11 m)\n",
    "dist_ratio = 9e11 / 9.5e10\n",
    "flux_at_moon = flux / dist_ratio**2\n",
    "flux_at_moon.to(u.K, equivalencies=equiv)"
   ]
  },
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