Measuring Stellar Distances Stellar Parallax few hundred pc Absolute & Apparent Magnitudes distance Spectroscopic Parallax Cepheid variables

Stellar Distances Light Years – distance light travels 1 yr. Astronomical Units AU – distance Earth - Sun. Parsec – based on parallax. Meters.

Hold up pencil Blink eyes Pencil moves against backdrop. Look at post. Blink eyes. Stellar Parallax

Parallax Method Clip 11 min ldqPwwhttps:// ldqPww

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

Near vs. Distant Star Parallax

Measure Parallax Angle 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) (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 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 LY / 3.26 = 1.34 pc. p = 1/d1/1.34 pc arc-sec

Ex 2: The nearest star has a parallax of 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 qbCkhttp:// qbCk

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. Absolute & Apparent Magnitudes

Apparent and Absolute Mag’s ~ first 4 min P8Veb_AlJ0http:// P8Veb_AlJ0

m = 1 defined as 100x brighter than m = 6 magnitude increase of 5 = increase brightness of factor 100x. Each step of 1 mag = changes brightness of Star by Apparent mag depends on luminosity & distance. Negative values appear brighter. Sun =

Ex 3: A 2 magnitude difference is an apparent brightness difference of 2.51 x 2.51 = ~16 ~40 To find brightness b using apparent magnitude; raise 2.51 to power  m (mag). (2.511) 2 = What difference in brightness is 3 magnitudes? 4 magnitudes?

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 10 4.

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 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 W/m 2. The peak is 600 nm. a. Find the surface temperature. b. If the temperature implies a luminosity of 1 x W, what is the star’s distance in LY?

4.8 x 10 3 K use Wein’s displacement. d = 2.8 x 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.

Find the period. This gives the luminosity (use graph). Measure the apparent brightness (done with telescope). Determine d from the L & brightness. Cepheid Variables Method

When Cepheid’s are close enough to use stellar parallax to measure distance, then the absolute magnitude can be found from: Where did this period-luminosity relation come from?

IB Set Cepheid Variables.