Midterm 3 Flashcards
What would we discover looking at the stars in the night sky?
We could see stars had different apparent brightness
- most stars appear white
- some appear color (red, blue, yellow)
Apparent magnitude
The brightness of a star as it looks in the night sky
Determining brightness of a star terms
- Luminosity
- flux
- magnitude
All three are related
Luminosity
The entire light output from a star
- this is measured in units of Watts, like a light bulb
- we don’t measure this one directly
The total energy output of a star in units of watts
Flux
More related to what we measure with an electronic camera at the telescope
- measured as photons/second or counts/second
- or it can be in terms of watts/m^2
A linear measure of the brightness of a star in units of photons/second
Magnitude
Apparent magnitude is how bright a star appears to our eye
-our eye doesn’t respond to light linearly
Star’s generating energy for light
We know that stars generate their own energy
-this energy leaves the star’s surface and is radiated into space
luminosity: L=4piR^2oT^4
- R=radius of the star and T= surface temp.
- Therefore two things effect the amount of light a star gives off: Radius and temp.
What two things effect the amount of light a star gives off?
Radius and temperature
Apparent magnitude scale
symbolized by “m”
- system given to us by Hipparchus
- BRIGHTEST stars in sky are 1st magnitude
- FAINTEST stars visible to the unaided eye are 6th magnitude
- 1st to 6th is 100 times brightness
- this is a logarithmic or power law scale just like the response of the human eye
- each step in magnitude a 2.512 times brighter
Magnitude difference and brightness ratio
Magnitude difference
-1 (1st to 2nd magnitude) = 2.512 brightness ratio
- 2 (1st to 3rd, 2nd to 4th) = (2.512)^2 = 6.31
- 3 (1st to 4th) = (2.512)^3 = 15.85
- 10 (1st to 11th) = (2.512)^10 = 10,000 (could not see with human eye but use telescope)
Some stars are brighter than 1st magnitude
Brightest star has a magnitude of -1.44 (Sirius A)
Others
- Canopus (-.62)
- Arcturus (-.05)
- Alpha Centauri (-.01)
- Vega (+.03)
- Capella (+.08)
- Rigel (+.18)
What is the brightest star
Sirius (sun and moon are more tho)
Other objects on magnitude scale
Sun = -26.7 Full moon = -12.6 eye limit = +6.0 Pluto = +14.0 Faintest Object HST = +30
Intro to measuring distance to stars
As light moves further form the star it is spread over larger areas
- means one of the most important things we can learn about any astronomical object is it’s distance
- NOTHING can prepare people for the distances to the stars
- however distance is one of the most important quantities we need to measure
Nearest star (Alpha Centauri) - is 40 trillion kilometers away
How do we measure distance? (Parallax)
Uses simple geometry
-when you change positions the background of a given object changes? - use to determine distance of nearby object
When the earth moves in its orbit, its motion causes some stars to appear to move with respect to the more distant stars
- why we can’t determine the distance to the nearby stars
- called STELLAR PARALLAX
Stellar parallax
The shift in a stars position based on the motion of the Earth
p = r/d r= 1 A.U.
definition: if p = 1 arc sec then d = 1 parsec
- 1 parsec = 206,265 A.U.
- 1 parsec = 3.26 lightyears
Distance equation
Parallax equation now becomes: d=1/p
p=.1 arcsec
d=1/p = 1/.1 = 10 parsecs
Bernard’s star
p=.545 arcsec
d=1/.545 = 1.83 parsecs
Proxima Centauri (closest) p=.772 arcsec d=1/.772 = 1.3 parsecs
Difficulties with parallax
The best we can do from normal earth based telescopes is .01 arctics
- this is a distance of 100 parsecs or 326 lightyears (not very far)
- to improve distance measurements we moved into space
- 1989 ESA launched HIPPARCOS
- –could measure angles of .002 arcsec - this moves us out to about 500 parsecs or 1630 lightyears
- –HIPPARCOS has measured distances of 20,000 nearby stars
- US Naval observatory Interferometer can match this from ground
How to measure distances beyond 500 parsecs?
500 parsecs is relatively small area of space
- now use indirect methods of distance determination
- new spacecraft - GAIA will push further with parallax
Distance effect apparent magnitude?
Intrinsic brightness of the object
-distance to the object
Ex. Sirius A - m=-1.44, 8.61 ly Canopus - m=-.62, 313 ly Alpha Centauri m=-.05, 4.4 ly Rigel - m=+.18, 773 ly
THEREFORE BRIGHTEST STARS IN THE NIGHT TIME SKY ARE NOT ALWAYS THE INTRINSICALLY BRIGHTEST STARS
Nearby stars distance and brightness
For nearby stars we know
- distance from parallax
- apparent magnitude
We can define the apparent brightness in terms of the output of the object and the distance to that object
Flux = L/4pid^2
Absolute magnitude
The true brightness of an object based on a logarithmic scale
m1-m2 is the diff. btwn magnitudes measured at 2 diff. distances
m1-m2 = 5 * log(d/D)
“M” represents absolute magnitude
-we pick the distance of 10 parsecs to be the distance associated with M (D=10pc)
Absolute Magnitude equation
m - M = 5 * log(d/10)
OR m - M = 5log(d) - 5
m - M also called DISTANCE MODULUS
Ex. of absolute magnitude
- Sun = +4.8
- Faintest stars = +20.0
- Giant elliptical galaxies -23
- Supernova 1987 A = -15.5
Distance with apparent and absolute magnitudes
if we know both apparent and absolute magnitudes we can find the distance
- to do this we MUST have known absolute magnitude
- objects with known absolute magnitude are called standard candles