* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 12
Chinese astronomy wikipedia , lookup
Theoretical astronomy wikipedia , lookup
Astronomical unit wikipedia , lookup
Dyson sphere wikipedia , lookup
Star of Bethlehem wikipedia , lookup
Stellar evolution wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Star formation wikipedia , lookup
Star catalogue wikipedia , lookup
Observational astronomy wikipedia , lookup
Corona Borealis wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Canis Minor wikipedia , lookup
Auriga (constellation) wikipedia , lookup
Canis Major wikipedia , lookup
Aries (constellation) wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
Corona Australis wikipedia , lookup
Perseus (constellation) wikipedia , lookup
Cosmic distance ladder wikipedia , lookup
The magnitude system ASTR320 Monday October 10, 2016 What we measure: apparent brightness How bright a star appears to be in the sky depends on: • How bright it actually is – Luminosity • and its distance from us, d. • We call this the “apparent brightness”: 𝐿 𝑏= 4𝜋𝑑 2 • This is a measure of the radiant flux produced by the star. What we want to know: luminosity • Luminosity, the total light given off by a star – Units of energy: photons / sec, or in erg / sec • Intrinsic property of the star (does not depend on distance) • WARNING: The definitions of things like "luminosity", "flux", "flux density", etc. used by astronomers are not the same as those used in other disciplines (e.g., our "luminosity" is called "flux" in other sciences) Luminosity • Note that we have not yet said which wavelengths or energies of the individual photons or light. • For today we’re discussing bolometric quantities – i.e., summed over all frequencies. • Practically this is a very hard thing to measure, since it requires measuring the entire EM spectrum of a source, which is impossible with a single type detector. • Bolometric fluxes have to be inferred by knowledge of the physics producing the luminous source for which you have partial information, or pieced together from observations at all parts of the EM spectrum. • In astronomy we usually use fluxes at specific energies. Luminosity • Because fνδν = fλδλ, and ν = c / λ, 𝜈 𝑓𝜈 = 𝜆 𝑓 𝜆 • The functions fν(ν) and fλ(λ) are referred to as the spectral energy distribution (SED) of the source. • When referring to bolometric fluxes, it is common to use units of Janskys (Jy) (borrowed from radio astronomy): – 1 Jy = 10-26 W m-2 Hz-1. – 1 Jy = 10-23 erg sec-1 cm-2 Hz-1. The magnitude system • Astronomers quantify the intensity of light produced by a source with the unit magnitudes • Magnitudes are a logarithmic representation of the spectral flux density of a source. – Allows for easy comparison of sources with immense ranges in flux density. – The magnitude system, let’s be honest, is not readily intuitive. History of the magnitude system • The system was devised by Greek astronomer Hipparchus, ca. 150 BC, to catalog the brightness of stars. – Brightest stars were placed in the first magnitude class, next brightest were second magnitude, etc. – Based on how bright a star appears to the unaided eye. • Ptolemy also used them in his Almagest – Catalog of ~1000 naked eye stars. – 6 "magnitude" classes: • 1 = brightest • 6 = faintest Magnitudes of some familiar objects • Here’s where it gets messy: • Bright stars have smaller magnitudes than faint stars! • This has confused/frustrated/enraged many an astronomer… History of the magnitude system • Revisions have been made in last few centuries. – Extend scale to < 1 mag to place Sun, Moon, bright planets on same scale. – Once the telescope was invented, extend scale to > 6 mag. • 1850: N. R. Pogson (British astronomer) notices that, because eyes work logarithmically, the classical magnitude scale corresponds roughly to set ratios of brightness between successive magnitudes. • Also notes that mag 6 is about 100x fainter than mag 1. • Since Δm = 5 appears to be 100x ratio in brightness, and 1 5 100 = 2.5119, Pogson formalized scale so that ratios between successive magnitudes are exactly 2.5119. Magnitudes in context: ColorMagnitude Diagram (CMD) Magnitude: definition • Take two stars, one is 100x (5 magnitudes) brighter than the other. • Remember: the brighter star has a smaller magnitude. • Compare their fluxes: (𝑚2 −𝑚1 ) 𝐹1 = 100 5 = 2.5119(𝑚2−𝑚1) 𝐹2 • Note that the above equation also shows that fractions of magnitudes are possible for stars with brightnesses in between two integer magnitudes. Apparent Magnitude • The apparent brightness of a star observed from the Earth is called the apparent magnitude. The apparent magnitude is a measure of the star's flux received by us. • This is the quantity we actually measure with a telescope. Magnitude: definition • Take the logarithm of (𝑚2 −𝑚1 ) 𝐹1 = 100 5 𝐹2 • To derive a more useful equation: 𝐹2 𝑚2 − 𝑚1 = −2.5 log10 ( ) 𝐹1 • That can be used to compare the apparent magnitude, m, of two sources. Absolute magnitude • By definition: if a star is 10 parsecs from Earth, then its apparent magnitude would be equal to its absolute magnitude, M. • The absolute magnitude is a measure of the star's luminosity---the total amount of energy radiated by the star every second. Absolute magnitude • If you measure a star's apparent magnitude and know its absolute magnitude, you can find the star's distance (using the inverse square law of brightness). • If you know a star's apparent magnitude and distance, you can find the star's luminosity. • The luminosity is an intrinsic property of the star, not based on how far away it is. • A star's luminosity tells you about the internal physics of the star and is a much more important quantity than the apparent brightness. Absolute magnitude • We can relate the absolute and apparent magnitude by using the definition of absolute magnitude (the magnitude of a star if it were at a distance of 10 pc) 2 (𝑚−𝑀) 𝐹10 𝑑 5 100 = = 𝐹 10 𝑝𝑐 • Where F is the flux measured at d, in parsecs. • And F10 is the flux measured at d=10 pc. • Take the logarithm to get: 𝑀 = 𝑚 − 5 log10 𝑑 + 5 • (If d is in pc) Distance modulus • Rewrite this equation: 𝑀 = 𝑚 − 5 log10 𝑑 + 5 • As the distance modulus, µ: 𝜇 = 𝑚 − 𝑀 = 5 log10 𝑑 − 5 • The distance is the difference between the apparent, m, and the absolute magnitude, M, of a source. • This is a very useful quantity! Magnitudes in context: ColorMagnitude Diagram (CMD) Example: Distance modulus 𝜇 = 𝑚 − 𝑀 = 5 log10 𝑑 − 5