Luminosity and Colour of Stars Michael Balogh Stellar Evolution (PHYS 375)

The physics of stars A star begins simply as a roughly spherical ball of (mostly) hydrogen gas, responding only to gravity and it’s own pressure. To understand how this simple system behaves, however, requires an understanding of: 1.Fluid mechanics 2.Electromagnetism 3.Thermodynamics 4.Special relativity 5.Chemistry 6.Nuclear physics 7.Quantum mechanics X-ray ultraviolet infrared radio

Course Outline Part I (lectures 1-5)  Basic properties of stars and electromagnetic radiation  Stellar classification  Measurements of distance, masses, etc. Part II (lectures 6-13)  Chemical composition of stars (interpretation of spectra)  Stellar structure (interiors and atmospheres)  Energy production and transport Part III (lectures 14-22)  Stellar evolution (formation, evolution, and death)  White dwarfs, neutron stars, black holes

The nature of stars Stars have a variety of brightnesses and colours Betelgeuse is a red giant, and one of the largest stars known Rigel is one of the brightest stars in the sky; blue-white in colour Betelgeuse Rigel

Apparent brightness of stars Star name Relative brightness Distance (light years) Sirius18.5 Canopus Alpha Centauri Vega Arcturus Capella Star name Relative brightness Distance (light years) Proxima Centauri Alpha Centauri Barnard’s star Wolf Lalande The apparent brightness of stars depends on both: their intrinsic luminosity their distance from us Their colour is independent of distance The five brightest stars The five nearest stars

The Astronomical Unit Astronomical distance scale:  Basic unit is the Astronomical Unit (AU), defined as the semimajor axis of Earth’s orbit How do we measure this?  Relative distances of planets from sun can be determined from Kepler’s third law:  E.g. given P earth, P mars:  1AU = ×10 8 km

The “parallax” is the apparent shift in position of a nearby star, relative to background stars, as Earth moves around the Sun in it’s orbit This defines the unit 1 parsec = AU = 3.09×10 13 km ~ 3.26 light years Parallax 1 AU p d

Measuring Parallax The star with the largest parallax is Proxima Centauri, with p=0.772 arcsec. What is its distance? A star field with 1” seeing These small angles are very difficult to measure from the ground; the atmosphere tends to blur images on scales of ~1 arcsec. It is possible to measure parallax angles smaller than this, but only down to ~0.02 arcsec (corresponding to a distance of 1/0.02 = 50 pc).  Until recently, accurate parallaxes were only available for a few hundred very nearby stars.

Hipparcos The Hipparcos satellite (launched 1989) collected parallax data from space, over 3 years  120,000 stars with arcsec precision astrometry  More than 1 million stars with 0.03 arcsec precision  The distance limit corresponding to arcsec is 1 kpc (1000 pc).  Since the Earth is ~8 kpc from the Galactic centre it is clear that this method is only useful for stars in the immediate solar neighbourhood.

Parallax: summary 1.A fundamental, geometric measurement of distance 2.Can be measured directly 3.Limited to nearby stars 4.Is used to calibrate other, more indirect distance indicators. Ultimately even our estimates of distances to the most remote galaxies rests on a reliable measure of parallax to the nearest stars

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The electromagnetic spectrum The Earth’s atmosphere blocks most wavelengths of incident radiation very effectively. It is only transparent to visual light (obviously) and radio wavelengths. Observations at other wavelengths have to be made from space. U B V R I Different filters transmit light of different wavelengths. Common astronomy filters are named:

Blackbodies The energy radiated from a surface element dA is given by: Units of B (T): W/m 2 /m/sr

Blackbodies Energy quantization leads to a prediction for the spectrum of blackbody radiation: The energy radiated from a surface element dA is given by: Units of B (T): W/m 2 /m/sr

Planck’s law Calculate the luminosity of a spherical blackbody:  Each surface element dA emits radiation isotropically  Integrate over sphere (A) and all solid angles (  )

Properties of blackbody radiation 1.The wavelength at which radiation emission from a blackbody peaks decreases with increasing temperature, as given by Wien’s law: 2. The total energy emitted (luminosity) by a blackbody with area A increases with temperature (Stefan-Boltzmann equation) This defines the effective temperature of a star with radius R and luminosity L

Examples The sun has a luminosity L=3.826×10 26 W and a radius R=6.96×10 8 m. What is the effective temperature? At what wavelength is most of the energy radiated?

Example Why does the green sun look yellow?  The human eye does not detect all wavelengths of light equally

Examples Spica is one of the hottest stars in the sky, with an effective temperature K. The peak of its spectrum is therefore at 114 nm, in the far ultraviolet, well below the limit of human vision. We can still see it, however, because it emits some light at longer wavelengths

Apparent magnitudes The magnitude system expresses fluxes in a given waveband X, on a relative, logarithmic scale:  Note the negative sign means brighter objects have lower magnitudes  Scale is chosen so that a factor 100 in brightness corresponds to 5 magnitudes (historical)

The magnitude scale One common system is to measure relative to Vega  By definition, Vega has m=0 in all bands. Note this does not mean Vega is equally bright at all wavelengths!  Setting m ref =0 in the equation above gives: Colour is defined as the relative flux between two different wavebands, usually written as a difference in magnitudes

Apparent magnitudes ObjectApparent mag Sun-26.5 Full moon-12.5 Venus-4.0 Jupiter-3.0 Sirius-1.4 Polaris2.0 Eye limit6.0 Pluto15.0 Reasonable telescope limit (8-m telescope, 4 hour integration) 28 Deepest image ever taken (Hubble UDF) 29 The faintest (deepest) telescope image taken so far is the Hubble Ultra-Deep Field. At m=29, this reaches more than 1 billion times fainter than what we can see with the naked eye.