WJEC AS Physics Unit 1.6 - Using Radiation to Investigate Stars

Stellar spectra of stars

• Analysis of a star’s stellar spectrum, can identify the EM radiation emitted from the star

• Consists of a continuous emission spectrum, from the dense gas of the surface of the star, and a line absorption spectrum arising from the passage of the emitted electromagnetic radiation through the tenuous atmosphere of the star

Continuous emission spectrum

• Spectrum of the wavelengths of light being emitted from a gas cloud (wavelengths it had previously absorbed when light passed through it)

• From the dense gas of the surface of the star

• Emitted light from photons being emitted

• Coloured lines on black background

• Lines of light produced by the atoms emitting photons of light

• Used to identify unknown elements via diffraction grating

Line absorption spectrum

• A continuous spectrum of light crossed by black absorption lines

• Absorption lines where photons have been absorbed by the gas cloud

• Transmitted light

• Black lines correspond to particular photons

• Gas absorbed certain wavelengths of like

• Atoms absorb photons of light

Black bodies

A black body is a body/surface which absorbs all the electromagnetic radiation that falls upon it. No body is a better emitter of radiation at any wavelength that than a black body at the same temperature. Stars are very good approximations to back bodies

Best emitter of radiation at any wavelength

A black body, no body is a better emitter of radiation at any wavelength than a black body at the same temperature

Good approximations to black bodies

Stars, although not black, they are almost perfect emitters of electromagnetic radiation

How intensity of radiation emitted from black bodies varies

With wavelength

Absolute or Kelvin temperature

The temperature, T in Kelvin (K) is relayed to the temperature, θ, in Celsius (°C) by;

T/K=θ/°C + 273.15

At 0K (-273.15°C), the energy of particles in a body is the lowest I can possibly be

θ = T-273

T=θ+273

Relationship between peak wavelength and the absolute temperature

Inversely proportional

Relationship between temperature and intensity

Directly proportional

Higher temperature=higher the peak intensity, lower the peak intensity wavelength, more curve + more blue light

Black Body spectrum

• y-axis=spectral intensity (au)

• x-axis=wavelength

• Shows how intensity of the radiation varies with wavelength for black bodies at different temperatures

• the shape of the curve is similar for each temperature

• the high the temperature, the higher the peak intensity

• the higher the temperature, the lower the peak intensity wavelength so peak is shifted to the left at high temperatures

• the lower temperature, the longer the flat section is before the curve ‘lifts off’

Wien’s displacement law

• The wavelength of peak emission from a black body is inversely proportional to the absolute (kelvin) temperature of the body. λmax = W/T [W = the Wien constant = 2.90 × 10-3 m K]

• max wavelength is inversely proportional to 1/T

• Used to determine to temperatures of objects, including distant stars

• Units; m=mK/K

Stefan’s law

• The total electromagnetic radiation energy emitted per unit time by a black body is given by power = A σT4 in which A is the body’s surface area and σ is a constant called the Stefan constant. [σ = 5.67 × 10-8 W m-2 K-4]

• Power or Luminosity

• Luminosity of a star is directly proportional to; r², surface area and the surface absolute temeperature

Inverse square law

• The intensity is inversely proportional to the square of the distance that star is away (Intensity∝1/d²)

• Intensity = Luminosity/Area that light covers = 4πr²σT⁴/4πd²

Multiwavelength astronomy

• A galaxy can be studied using different telescopes which are sensitive to different wavelengths or different photon energies of the EM spectrum

• by studying a region of space at different wavelengths (different photon energies) the different processes which took place there can be revealed

• Studying stars and space by making observations outside of the visible light spectrum —> more information about the process which took place

• With the exception of visible light astronomy, the colours are ‘false colours’ - the colour is an intensity code rather than an actual colour

• Observe areas of the universe using instruments sensitive to other aprts of the spectrum —> understand other processes that are goining on which do not emit light

Wavelength colours for spectra

• 450-700 = white

• <450 = blue

• >700 = red

Light years

• ly

• measure of distance

• x=vt = 3×10^8 × 365 × 24 × 60 × 60

• 1ly = 9.5 × 10^15 m

Parsecs

• 1 parasec is the distance at which 1AU subtends an angle of 1 arcsecond

• 1° = 60 arcminutes

• 1 arc minute = 60 arcseconds

• 1° = 3600 arcseconds

• 1 parsec = 3.09 × 10^16 m

Parallax

• used to measure the distances to stars that are closer to the earth

• the apparent shift in the position of a relatively close star against the backdrop of much more distant stars as the Earth orbits the Sun

• using the radius of the orbit, can measure the angle and the distance to the star

  • tanθ=r/d so; d = r/tanθ

  • As θ is very small, we can use the approximation tanθ=θ (with θ in radians) to calculate the distance using the Earth’s orbital radius of 1.5×10^11m

  • d = r/θ (with θ in radians)

Luminosity of a star

The luminosity of a star is the total energy it emits per unit time in the form of electromagnetic radiation. UNIT: W [Thus we could have written luminosity instead of power in Stefan’s law (above).]

Intensity

The intensity of radiation at a distance R from a source is given by I = P/4πR²

UNIT: Wm^-2

How light from stars is analysed

By separating out the different wavelengths via a prism or diffraction grating.

How stars emit light

As a continuous spectrum of radiation.

Absorption lines

Black lines crossing an absorption spectrum

Cause of absorption lines

Atom’s in the gases of a star's atmosphere absorb certain wavelengths of light. Creating black (absorption) lines on the spectrum.

Unit for luminosity

Watts (W)

Equivalent to luminosity

The power of a star.

Relationship between colours and temperature of stars

The more blue a star the higher its temperature, the more red a star the lower its temperature.

Why hotter stars appear blue and colder stars appear red

Higher energy light has shorter wavelengths, thus

the higher an object's temperature, the shorter the wavelength of light it’s black body curve peaks at. Thus hotter stars black body curves peak towards the ultraviolet side of the spectrum appearing blue and the opposite for colder stars.

Difference between Luminosity and Intensity

The luminosity of a star is the total energy it emits per unit time in the form electromagnetic radiation.

Intensity is the electromagnetic radiation received by an observer per unit time.