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Introduction to Stars

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Stellar Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert d to A.U. by using trigonometry To calculate p for star with d given in lightyears, use d=1/p but convert ly to pc. Remember: 1 degree = 3600” Note: p is half the angle the star moves in half a year

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Our Stellar Neighborhood

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Scale Model If the Sun = a golf ball, then –Earth = a grain of sand –The Earth orbits the Sun at a distance of one meter –Proxima Centauri lies 270 kilometers (170 miles) away –Barnard’s Star lies 370 kilometers (230 miles) away –Less than 100 stars lie within 1000 kilometers (600 miles) The Universe is almost empty! Hipparcos satellite measured distances to nearly 1 million stars in the range of 330 ly almost all of the stars in our Galaxy are more distant

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Luminosity and Brightness Luminosity L is the total power (energy per unit time) radiated by the star, actual brightness of star, cf. 100 W lightbulb Apparent brightness B is how bright it appears from Earth –Determined by the amount of light per unit area reaching Earth –B L / d 2 Just by looking, we cannot tell if a star is close and dim or far away and bright

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Brightness: simplified 100 W light bulb will look 9 times dimmer from 3m away than from 1m away. A 25W light bulb will look four times dimmer than a 100W light bulb if at the same distance! If they appear equally bright, we can conclude that the 100W lightbulb is twice as far away!

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Same with stars… Sirius (white) will look 9 times dimmer from 3 lightyears away than from 1 lightyear away. Vega (also white) is as bright as Sirius, but appears to be 9 times dimmer. Vega must be three times farther away (Sirius 9 ly, Vega 27 ly)

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Distance Determination Method is (L)Understand how bright an object is (L) appears (B)Observe how bright an object appears (B) Calculate how far the object is away: B L / d 2 So L/B d 2 or d √L/B

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Homework: Luminosity and Distance Distance and brightness can be used to find the luminosity: L d 2 B So luminosity and brightness can be used to find Distance of two stars 1 and 2: d 2 1 / d 2 2 = L 1 / L 2 ( since B 1 = B 2 ) i.e. d 1 = (L 1 / L 2 ) 1/2 d 2

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Homework: Example Question Two stars -- A and B, of luminosities 0.5 and 2.5 times the luminosity of the Sun, respectively -- are observed to have the same apparent brightness. Which one is more distant? Star A Star B Same distance

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Homework: Example Question Two stars -- A and B, of luminosities 0.5 and 2.5 times the luminosity of the Sun, respectively -- are observed to have the same apparent brightness. How much farther away is it than the other? L A /d 2 A = B A =B B = L B /d 2 B d B = √L B /L A d A Star B is √5=2.24 times as far as star A

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The Magnitude Scale A measure of the apparent brightness Logarithmic scale Notation: 1 m.4 (smaller brighter) Originally six groupings –1 st magnitude the brightest –6 th magnitude is 100x dimmer So a difference of 5mag is a difference of brightness of 100 Factor 2.512=100 1/5 for each mag.

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Absolute Magnitude The absolute magnitude is the apparent magnitude a star would have at a distance of 10 pc. Notation example: 2 M.8 It is a measure of a star’s actual or intrinsic brightness called luminosity Example: Sirius: 1 M.4, Sun 4 M.8 –Sirius is intrinsically brighter than the Sun

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Finding the absolute Magnitude To figure out absolute magnitude, we need to know the distance to the star Then do the following Gedankenexperiment: –In your mind, put the star from its actual position to a position 10 pc away –If a star is actually closer than 10pc, its absolute magnitude will be a bigger number, i.e. it is intrinsically dimmer than it appears –If a star is farther than 10pc, its absolute magnitude will be a smaller number, i.e. it is intrinsically brighter than it appears

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