D2 Stellar characteristics and stellar evolution - D2.1 Stellar spectra

Sep 22, 2026

Uploaded by Logic

Learning objectives and instructional content explain how to use stellar spectra to determine surface temperature and chemical composition of stars. The material covers black-body radiation profiles and applies Wien’s displacement law to relate peak wavelength to temperature. Worked examples include calculations using the Sun’s radiation. It also discusses absorption spectra: dark lines indicate specific elements, with hydrogen line visibility depending on stellar temperature and electron ionisation or energy-level populations. Additional notes introduce spectral classes, the HR diagram, and related stellar properties.

LanguageEnglish

CategoryExam

FormatPDF

Pages12

Reading Time30 min

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Learning objectives

D2 Stellar characteristics and stellar evolution

D2.1 Stellar spectra

Worked examples

The Hertzsprung–Russell diagram

Learning objectives • Describe the use of stellar spectra. • Work with the HR diagram, including representation of stellar evolution. • Apply the mass–luminosity relation. • Describe Cepheid variables and their use as standard candles. • Describe the nature of the stars in the main regions of the HR diagram. • Understand the limits on mass for white dwarfs and neutron stars. D2 Stellar characteristics and stellar evolution This section deals with the lives of stars on the main sequence and their evolution away from it. We will see how stellar spectra may be used to determine the chemical composition of stars, and will study an important diagram called the Hertzsprung–Russell (HR) diagram. We will follow the stellar evolution on the HR diagram and meet important classes of stars such as Cepheid variables, white dwarfs and red giants. D2.1 Stellar spectra The energy radiated by a star is in the form of electromagnetic radiation and is distributed over an in nite range of wavelengths. A star is assumed to radiate like a black body. Figure D.9 shows black-body spectra at various temperatures. 4000 K 5000 K 6000 K I 10 8 6 4 2 0 5 10 15 λ / 10–7 m Figure D.9 Black-body radiation proﬁles at various temperatures. The broken lines show the variation with temperature of the peak intensity and the wavelength at which it occurs. Much information can be determined about a star by examining its spectrum. The rst piece of information is its surface temperature. Most of the energy is emitted around a wavelength called the peak wavelength. Calling this wavelength λ 0 , we see that the colour of the star is mainly determined by the colour corresponding to λ 0 . The Wien displacement law relates the wavelength λ0 to the surface temperature T: λ0T = constant = 2 .90 × 10 −3 Km This implies that the higher the temperature, the lower the wavelength at which most of the energy is radiated. 10 D ASTROPHYSICS PHYSICS FOR THE IB DIPLOMA © CAMBRIDGE UNIVERSITY PRESS 2015 Worked examples D.9 The Sun has an approximate black-body spectrum with most of its energy radiated at a wavelength of 5.0 × 10−7 m. Find the surface temperature of the Sun. From Wien’s law, 5.0 × 10−7 m × T= 2 .9 × 10−3 Km; that is, T = 5800 K. D.10 The Sun (radius R = 7.0 × 108 m) radiates a total power of 3 .9 × 1026 W. Find its surface temperature. From L= σAT4 and A = 4πR2 , we nd L 1/4 T = σ4πR2 ≈ 5800 K The surface temperature ofa star is determined by measuring the wavelength at which most of its radiation is emitted (see Figure D.10). I / 1011 W m–3 80 60 40 20 0.2 0.4 0.6 0.8 1 λ / 10–6 m Figure D.10 The spectrum of this star shows a peak wavelength of 500 nm. Using Wien’s law, we can determine its surface temperature. The second important piece of information from a star’s spectrum is its chemical composition. It is common to obtain an absorption spectrum in which dark lines are superimposed on a background of continuous colour (as in Figure D.11). Each dark line represents the absorption of light of a speci c wavelength by a speci c chemical element in the star’s atmosphere. Figure D.11 Absorption spectrum of a star, showing the absorption lines of hydrogen. A real spectrum would show very many dark lines corresponding to other elements as well. It is known that most stars have essentially the same chemical composition, yet show di􀀛erent absorption spectra. The reason for this di􀀛erence is that di􀀛erent stars have di􀀛erent temperatures. Consider two stars with the same content of hydrogen. One is hot, say at 25 000 K, and the other cool, say at 10 000 K. The hydrogen in the hot star is ionised, which means the electrons have left the hydrogen atoms. These atoms cannot absorb any light passing through them, since there are no bound electrons to absorb the photons and make transitions to higher-energy states. Thus, the hot star will not show any absorption lines at hydrogen PHYSI

FAQs

How does a star’s black-body spectrum help determine its surface temperature?

The star’s energy peaks at a peak wavelength, and the surface temperature can be found using Wien’s displacement law relating peak wavelength to temperature.

Why do hot and cool stars show different hydrogen absorption lines?

In a hot star, hydrogen is ionised so there are no bound electrons to absorb photons, so hydrogen absorption lines are absent. In a cooler star, hydrogen electrons occupy energy states (e.g., n=2), allowing absorption at specific wavelengths and producing characteristic lines.

What information can be extracted from an absorption spectrum?

An absorption spectrum contains dark lines superimposed on continuous radiation. Each dark line corresponds to absorption of a particular wavelength by a specific chemical element in the star’s atmosphere.

Sep 22, 2026

Uploaded by Logic