Measuring Stellar Distances Stellar Parallax few hundred pc
- Slides: 44
Measuring Stellar Distances • Stellar Parallax few hundred pc • Absolute & Apparent Magnitudes • Spectroscopic Parallax • Cepheid variables distance
Stellar Distances • Light Years – distance light travels 1 yr. • Astronomical Units AU – distance Earth - Sun. • Parsec – based on parallax. • Meters.
Stellar Parallax • Hold up pencil • Blink eyes • Pencil moves against backdrop. • Look at post. • Blink eyes.
Parallax Method Clip 11 min • https: //www. youtube. com/watch? v=XUQAI ldq. Pww
Earth’s motion in orbit causes parallax. 1 AU Sun
Near vs. Distant Star Parallax
Measure Parallax Angles are very small – measured in arc seconds.
Angular Measurements Angular measure of object is expressed in degrees, arc-minutes or arc-seconds. 360 o in circle 1° = 1/360 of a circle or 60 minutes of arc. 1 arcminute = 1' = 1/60 of a degree or 60 sec of arc. 1 arcsecond = 1" = 1/60 of an arcminute = 1/3600 of a degree.
Distance - Parcsec (pc): distance at which an object would have a parallax angle (p) of one arc second. Equals approximately 3. 26 light years (ly) or about 206, 265 astronomical units – AU. AU – distance Earth to Sun. (1. 5 x 1011 m)
1 pc. = distance when p is 1 arc sec.
Stellar distance d = 1/p p = 1/d d (dist) – #parsecs p (parallax angle) – #arc-seconds.
Ex 1: The nearest star to Earth is Alpha Centauri, which is at a distance of 4. 37 ly. Calculate the parallax angle that was measured to obtain that distance. • 4. 37 LY / 3. 26 = 1. 34 pc. • p = 1/d • 0. 746 arc-sec 1/1. 34 pc
Ex 2: The nearest star has a parallax of 0. 760 arc sec. What is this in parsecs? • d = 1/p • d = 1/ 0. 76 = 1. 3 pc.
Why can’t stellar parallax be used to measure very distant stars? • Angle gets too small. Few hundred pc upper limit.
Starlight beginning thru parallax • http: //www. youtube. com/watch? v=jjmj. EDY qb. Ck
Absolute & Apparent Magnitudes • Greeks classified stars - Apparent mag (m) – bright = 1 dim = 6. Greater than 6 need telescope to see. • Now we can see further stars so stars can have neg magnitudes.
Apparent and Absolute Mag’s ~ first 4 min • http: //www. youtube. com/watch? v=9 P 8 Veb_Al. J 0
• m = 1 defined as 100 x brighter than m = 6 • magnitude increase of 5 = increase brightness of factor 100 x. • Each step of 1 mag = changes brightness of Star by 2. 511 • Apparent mag depends on luminosity & distance. • Negative values appear brighter. Sun = -26. 8.
To find brightness b using apparent magnitude; raise 2. 51 to power Dm (mag). Ex 3: A 2 magnitude difference is an apparent brightness difference of 2. 51 x 2. 51 = (2. 511)2 = 6. 25. What difference in brightness is 3 magnitudes? 4 magnitudes? • ~16 • ~40
If 2 stars have magnitudes of m 1 and m 2, and apparent brightness of b 1 & b 2 This relationship holds true:
Ex 4: If the apparent magnitude of A & B are m= 9. 5 and -1. 5 respectively, find the ratio of their apparent brightness. = 2. 49 x 104.
Absolute Magnitude – M If all stars were moved to 10 pc from us – what would the apparent magnitude be? Will the apparent magnitude of most stars increase or decrease if we bring them to 10 pc? Most would decrease – they will be brighter & become more negative. A few will increase it they are being moved further away.
Using M and m to determine distance
Relate apparent to absolute magnitude and distance. M = absolute magnitude m = apparent magnitude d = distance in pc.
Ex 4: Alpha Centauri has an apparent magnitude of 0. 10 & is 1. 34 pc away. Calculate its absolute magnitude, M. = 4. 5
Arcturus prb
Hwk. • Read Hamper 337 - 340 • Do 10, 12 starting on pg 340. • Do handout IB Stellar Distance 1 ques 1.
Spectroscopic Parallax • Uses apparent brightness b, and luminosity or apparent/absolute magnitude to determine distance. • Need to know spectral class (MS, WD, ) of star, & surface temp. & use HR diagram.
Spectroscopic Parallax Uses Luminosity & Apparent Brightness • Use Wein’s Displacement to find surface T.
Use spectral dark lines to find composition which gives spectral class. Usually main sequence.
• Use H-R temp. to find luminosity (main sequence) or absolute magnitude.
Use apparent brightness (W/m 2) to calculate distance (m). L in Watts. Or use apparent & absolute magnitude to calculate distance (pc). Assumes star is on main sequence.
Ex 5: A study of a star suggests it is a main sequence star. Its apparent brightness is 1 x 10 -12 W/m 2. The peak l is 600 nm. a. Find the surface temperature. b. If the temperature implies a luminosity of 1 x 10 26 W, what is the star’s distance in LY?
4. 8 x 103 K use Wein’s displacement. d = 2. 8 x 1018 m = 300 LY
Beyond 10 Mpc, it’s hard to distinguish a bright far star from a dimmer closer star. A “standard candle” is a star of known L in a cluster. We can then compare it with other stars in the same galaxy or cluster to determine the luminosity of other stars.
Cepheid Variables – luminosity varies over time. Star expands & contracts. The outer layers undergo variations in Temp and surface area.
Apparent brightness vs. time (days) Use to find period. Period relates to luminosity/absolute mag M.
The luminosity or Absolute Magnitude changes with the period in days. • Can use the period to find L, then use Cepheid as standard candle to find L for other stars in galaxy.
Cepheid Variables If Cepheid Variables close enough to measure d using stellar parallax, then can use apparent brightness to find absolute magnitude.
Cepheid Variables Method • Find the period. • This gives the luminosity • (use graph). • Measure the apparent brightness (done with telescope). • Determine d from the L & brightness.
• Where did this period-luminosity relation come from? When Cepheid’s are close enough to use stellar parallax to measure distance, then the absolute magnitude can be found from:
IB Set Cepheid Variables.
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