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In class we showed an animated map of the Milky Way HI data as seen in individual velocity slices of 21cm emission. What frequency resolution would be needed to observe the 21cm line with a velocity resolution of 0.2 km/s? Give your response in kHz, to two decimal places.

In class we showed an animated map of the Milky Way HI data as seen in individual velocity slices of 21cm emission. What frequency resolution would be needed to observe the 21cm line with a velocity resolution of 0.2 km/s? Give your response in kHz, to two decimal places.

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For each problem, use the following values: - \( c = 3 \times 10^8 \) m/s - Mass of the sun = \( 1.989 \times 10^{30} \) kg - Luminosity of the sun = \( 3.828 \times 10^{26} \) W - 1 AU = \( 1.496 \times 10^{11} \) m - 1 pc = 3.262 light years = \( 3.086 \times 10^{16} \) m - 1 year = \( 3.154 \times 10^7 \) seconds - Critical density of our Universe (expressed as a mass density): \( \rho_{\text{crit}} = 8.7 \times 10^{-27} \) kg m\(^{-3}\) - Critical energy density of our Universe: \( \epsilon_{\text{crit}} = \rho_{\text{crit}} c^2 \) - \( G = 6.674 \times 10^{-11} \) m\(^3\) kg\(^{-1}\) s\(^{-2}\) - \( 1 \) eV = \( 1.60218 \times 10^{-19} \) J - Boltzmann constant: \( k_B = 1.381 \times 10^{-23} \) J K\(^{-1} = 8.617 \times 10^{-5} \) eV K\(^{-1} \) - Energy density constant (in Stefan Boltzmann Law): \( \alpha = 7.566 \times 10^{-16} \) J m\(^{-3}\) K\(^{-4} = 4.7 \times 10^{-3} \) MeV m\(^{-3}\) K\(^{-4} \) - Constant in Wien displacement law: \( b = 2.898 \times 10^{-3} \) m K - Baryon-to-photon ratio, \( \eta = 6 \times 10^{-10} \)
Transcribed Image Text:For each problem, use the following values: - \( c = 3 \times 10^8 \) m/s - Mass of the sun = \( 1.989 \times 10^{30} \) kg - Luminosity of the sun = \( 3.828 \times 10^{26} \) W - 1 AU = \( 1.496 \times 10^{11} \) m - 1 pc = 3.262 light years = \( 3.086 \times 10^{16} \) m - 1 year = \( 3.154 \times 10^7 \) seconds - Critical density of our Universe (expressed as a mass density): \( \rho_{\text{crit}} = 8.7 \times 10^{-27} \) kg m\(^{-3}\) - Critical energy density of our Universe: \( \epsilon_{\text{crit}} = \rho_{\text{crit}} c^2 \) - \( G = 6.674 \times 10^{-11} \) m\(^3\) kg\(^{-1}\) s\(^{-2}\) - \( 1 \) eV = \( 1.60218 \times 10^{-19} \) J - Boltzmann constant: \( k_B = 1.381 \times 10^{-23} \) J K\(^{-1} = 8.617 \times 10^{-5} \) eV K\(^{-1} \) - Energy density constant (in Stefan Boltzmann Law): \( \alpha = 7.566 \times 10^{-16} \) J m\(^{-3}\) K\(^{-4} = 4.7 \times 10^{-3} \) MeV m\(^{-3}\) K\(^{-4} \) - Constant in Wien displacement law: \( b = 2.898 \times 10^{-3} \) m K - Baryon-to-photon ratio, \( \eta = 6 \times 10^{-10} \)
**Text:** In class we showed an animated map of the Milky Way HI data as seen in individual velocity slices of 21cm emission. What frequency resolution would be needed to observe the 21cm line with a velocity resolution of 0.2 km/s? Give your response in kHz, to two decimal places. **Explanation:** This text discusses the visualization of the Milky Way galaxy using neutral hydrogen (HI) data. The HI emissions are particularly viewed at a wavelength of 21 centimeters, which helps in observing different velocity slices of the galaxy. The question asks for the necessary frequency resolution to achieve a velocity resolution of 0.2 kilometers per second for these observations, with the answer expected in kilohertz to two decimal places.
Transcribed Image Text:**Text:** In class we showed an animated map of the Milky Way HI data as seen in individual velocity slices of 21cm emission. What frequency resolution would be needed to observe the 21cm line with a velocity resolution of 0.2 km/s? Give your response in kHz, to two decimal places. **Explanation:** This text discusses the visualization of the Milky Way galaxy using neutral hydrogen (HI) data. The HI emissions are particularly viewed at a wavelength of 21 centimeters, which helps in observing different velocity slices of the galaxy. The question asks for the necessary frequency resolution to achieve a velocity resolution of 0.2 kilometers per second for these observations, with the answer expected in kilohertz to two decimal places.
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