Deducing Temperatures and Luminosities of Stars (and other objects…)

Deducing Temperatures and Luminosities of Stars(and other objects…)

Ultraviolet (UV) Radio waves Infrared (IR) Microwaves Visible Light Gamma Rays X Rays Review: Electromagnetic Radiation Increasing energy 10-15 m 103 m 10-9 m 10-6 m 10-4 m 10-2 m Increasing wavelength • EM radiation consists of regularly varying electric magnetic fields which can transport energy over vast distances. • Physicists often speak of the “particle-wave duality” of EM radiation. • Light can be considered as either particles (photons) or as waves, depending on how it is measured • Includes all of the above varieties -- the only distinction between (for example) X-rays and radio waves is the wavelength.

Wavelength  • Wavelengthis the distance between two identical points on a wave. (It is referred to by the Greek letter  [lambda])

Frequency time unit of time • Frequency is the number of wave cycles per unit of time that are registered at a given point in space. (referred to by Greek letter  [nu]) • It is inversely proportional to wavelength.

Wavelength andFrequency Relation  = v/ • Wavelength is proportional to the wave velocity, v. • Wavelength is inversely proportional to frequency. • eg. AM radio wave has a long wavelength (~200 m), therefore it has a low frequency (~KHz range). • In the case of EM radiation in a vacuum, the equation becomes c Where c is the speed of light (3 x 108 m/s)

Light as a Particle: Photons E = h • Photons are little “packets” of energy. • Each photon’s energy is proportional to its frequency. • Specifically, each photon’s energy is Energy = (Planck’s constant) x (frequency of photon)

The Planck function • Every opaque object (a human, a planet, a star) radiates a characteristic spectrum of EM radiation • spectrum (intensity of radiation as a function of wavelength) depends only on the object’s temperature • This type of spectrum is called blackbody radiation ultraviolet visible infrared radio Intensity (W/m2) 0.1 1.0 10 100 1000 10000

Temperature dependence of blackbody radiation • As temperature of an object increases: • Peak of black body spectrum (Planck function) moves to shorter wavelengths (higher energies) • Each unit area of object emits more energy (more photons) at all wavelengths

Wien’s Displacement Law • Can calculate where the peak of the blackbody spectrum will lie for a given temperature from Wien’s Law: 5000/T Where  is in microns (10-6 m) and T is in degrees Kelvin (recall that human vision ranges from 400 to 700 nm, or 0.4 to 0.7 microns)

Colors of Stars • The color of a star provides a strong indication of its temperature • If a star is much cooler than 5,000 K, its spectrum peaks in the IR and it looks reddish • It gives off more red light than blue light • If a star is much hotter than 15,000 K, its spectrum peaks in the UV, and it looks blueish • It gives off more blue light than red light

Betelguese and Rigel in Orion Betelgeuse: 3,000 K (a red supergiant) Rigel: 30,000 K (a blue supergiant)

Blackbody curves for stars at temperatures of Betelgeuse and Rigel

Luminosities of stars • The sum of all the light emitted over all wavelengths is called a star’s luminosity • luminosity can be measured in watts • measure of star’s intrinsic brightness, as opposed to what we happen to see from Earth • The hotter the star, the more light it gives off at all wavelengths, through each unit area of its surface • luminosity is proportional to T4 so even a small increase in temperature makes a big increase in luminosity

Consider 2 stars of different T’s but with the same diameter

What about large & small stars of the same temperature? • Luminosity goes like R2 where R is the radius of the star • If two stars are at the same temperature but have different luminosities, then the more luminous star must be larger

How do we know that Betelgeuse is much, much bigger than Rigel? • Rigel is about 10 times hotter than Betelgeuse • Rigel gives off 104 (=10,000) times more energy per unit surface area than Betelgeuse • But the two stars have about the same total luminosity • therefore Betelguese must be about 102 (=100) times larger in radius than Rigel

So far we haven’t considered stellar distances... • Two otherwise identical stars (same radius, same temperature => same luminosity) will still appear vastly different in brightness if their distances from Earth are different • Reason: intensity of light inversely proportional to the square of the distance the light has to travel • Light wave fronts from point sources are like the surfaces of expanding spheres

Stellar brightness differences as a tool rather than as a liability • If one can somehow determine that 2 stars are identical, then their relative brightnesses translate to relative distances • Example: the Sun and alpha Centauri • spectra look very similar => temperatures, radii almost identical (T follows from Planck function, radius can be deduced by other means) => luminosities about the same • difference in apparent magnitudes translates to relative distances • Can check using the parallax distance to alpha Cen

The Hertsprung-Russell Diagram

Deducing Temperatures and Luminosities of Stars (and other objects…)