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Chapter 27: Problem 32

(a) If a Population III star had a surface temperature of \(10^{5} \mathrm{~K}\), what was its wavelength of maximum emission? In what part of the electromagnetic spectrum does this wavelength lie? (b) To ionize a hydrogen atom requires a photon of wavelength \(91.2 \mathrm{~nm}\) or shorter. Explain how Population III stars caused reionization. (c) If reionization occurred at \(z=11\), what do we measure the wavelength of maximum emission of a Population III star to be? In what part of the electromagnetic spectrum does this wavelength lie? (d) The image that opens this chapter was made using infrared wavelengths. Suggest why these wavelengths were chosen.

Short Answer

Expert verified
A Population III star with a temperature of \(10^{5}K\) emits majorly in the UV part of the spectrum. The high energy of the emitted photons can cause reionization by ionizing hydrogen atoms. Due to redshift, this light is observed at longer (infrared) wavelengths. Infrared astronomy is therefore important for observing objects in the early universe, such as Population III stars.

Step by step solution

01

Calculate Wavelength of Maximum Emission

The wavelength of maximum emission for a blackbody is given by Wien's law, expressed as \( \lambda_{max} = \frac{b}{T} \), where b is Wien's constant (\(2.898 \times 10^{-3} m.K\)) and T is the temperature in Kelvin. On substituting the temperature \( T= 10^{5}K \), we get \( \lambda_{max} = \frac{2.898 \times 10^{-3} m.K}{10^{5} K} \)
02

Identify part of Electromagnetic Spectrum

The part of the electromagnetic spectrum that a particular wavelength lies in can be determined by its range. From the calculation in step 1, if the value of \( \lambda_{max} \) falls within the range of UV rays (10nm to 400nm), then the maximum emission lies in the ultraviolet part of the electromagnetic spectrum.
03

Explain Reionization

Population III stars caused reionization by emitting photons of sufficiently short wavelength (and thus high energy) to ionize hydrogen atoms. To ionize a hydrogen atom, a photon with a wavelength of 91.2nm or shorter is required. A Population III star with a surface temperature of \(10^{5}K\) emits a significant fraction of its radiation at these high energies, and so can contribute to the reionization of the universe.
04

Calculation Taking Redshift Into Account

Light from distant objects is redshifted due to the expansion of the universe. The observed wavelength of light is longer than the emitted wavelength by a factor of \(1+z\), where \(z\) is the redshift. Given \(z=11\), the observed wavelength of maximum emission from a Population III star is \((1+11)\lambda_{max}\).
05

Identify part of Electromagnetic Spectrum

Similar to Step 2, based on the calculated value from Step 4, the part of the electromagnetic spectrum can be determined.
06

Explanation for Use of Infrared Wavelengths

Infrared wavelengths were likely used because they are capable of observing objects at high redshifts. Matter from the early universe (including Population III stars) is observed at high redshifts, which shifts the light they emitted into longer (infrared) wavelengths.

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