Measuring Stellar Distances Stellar Parallax few hundred pc

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Measuring Stellar Distances • Stellar Parallax few hundred pc • Absolute & Apparent Magnitudes

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

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.

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

Parallax Method Clip 11 min • https: //www. youtube. com/watch? v=XUQAI ldq. Pww

Earth’s motion in orbit causes parallax. 1 AU Sun

Earth’s motion in orbit causes parallax. 1 AU Sun

Near vs. Distant Star Parallax

Near vs. Distant Star Parallax

Measure Parallax Angles are very small – measured in arc seconds.

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

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

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.

1 pc. = distance when p is 1 arc sec.

Stellar distance d = 1/p p = 1/d d (dist) – #parsecs p (parallax

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

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

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

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

Starlight beginning thru parallax • http: //www. youtube. com/watch? v=jjmj. EDY qb. Ck

Absolute & Apparent Magnitudes • Greeks classified stars - Apparent mag (m) – bright

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

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

• 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).

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

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

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

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

Using M and m to determine distance

Relate apparent to absolute magnitude and distance. M = absolute magnitude m = apparent

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.

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

Arcturus prb

Hwk. • Read Hamper 337 - 340 • Do 10, 12 starting on pg

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

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

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 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 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

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.

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

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

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

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

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 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

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

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

• 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.

IB Set Cepheid Variables.