Lecture 6: Measuring Stars-Magnitudes, Motion, and Spectral Types

"It is a capital mistake to theorize before one has data."
A. Conan Doyle, Scandal in Bohemia

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Date: February 9, 1995
Reading Assignment: pp. 390-400

Description : Magnitudes, Motion, and Classification of Stars

Objectives

be able to describe and apply the concept of stellar parallax as a way of determining the distance to a star

be able to distinguish between radial and transverse velocities

be able to describe how radial motion is measured

be able to describe how proper motion is measured

be able to describe how proper motion is related to transverse velocity

be able to describe one direct method of determining the size of stars

be able to describe one indirect method of determining the size of stars

be able to distinguish and describe apparent and absolute magnitude

be able to describe what color index is and how it is used

be able to list the spectral classes of stars

Lecture Outline

Slide # 1: Measuring Stars - I

Magnitudes, Motion, and Spectral Types

Slide # 2: The Sun

the solar atmosphere and photosphere

corona, chromosphere

sunspots, solar cycle, magnetic fields, activity

the solar interior

computer models of the solar interior

observations of the solar interior

Slide # 3: How do you "model" a star?

laws of physics

computer simulations

matches to observed data

Slide # 4: Star Modeling- Laws of Physics

hydrostatic equilibrium

energy transport

energy generation

mass continuity

Slide # 5: Testing the Solar Models

Helioseismology

Solar Neutrino Astronomy

Slide # 6: Measuring Stars

distance

luminosity and brightness

motion- radial and transverse velocity

diameters

color index

Spectral Types

Slide # 7: Distances to Stars

distances to astronomical objects cannot easily be determined

often many steps on the "distance ladder" must be used

the first step is parallax

Slide # 8: Measuring Distances

How do you measure how far it is to a distant object?

Slide # 9: Measuring Distances (GRAPHICS)

How would you measure the distance across a large river?

Slide # 10: Triangulation (GRAPHICS)

Construct a right triangle across from a fixed reference point

Slide # 11: Triangulation (GRAPHICS) Slide # 12: Triangulation (GRAPHICS)

By using trignometry or similar triangles, you can calculate the distance acro

Slide # 13: Triangulation of Objects in Space?

Celestial objects are much farther away

We must

Use as very large baselines in our triangle

Be able to measure very small angles

Slide # 14: Large Baselines : Earth (GRAPHICS) Slide # 15: Large Baselines : Earth (GRAPHICS) Slide # 16: Large Baselines : Earth (GRAPHICS) Slide # 17: Views from the Observers (GRAPHICS) Slide # 18: View from the Observers (GRAPHICS)

The two observers see the object in two different positions

The shift is due to PARALLAX

Slide # 19: Large Baselines : Earth's Orbit (GRAPHICS)

A very large baseline is need to measure the parallax of stars

Slide # 20: Parallax

simple geometry to determine distance

only works for nearby stars

Slide # 21: Parsecs and Arcseconds

Parsec

206265 AU's

about 3.26 light years

Arcsecond

1/3600 degrees

1/60 arcminutes

Slide # 22: Parallax (GRAPHICS)

the formula

Slide # 23: Parallax Example (GRAPHICS)

What is the distance of a star with a parallax of 0.2 Arcseconds?

Slide # 24: How Bright are the Stars?

depends on distance and luminosity

Slide # 25: Apparent Brightness (GRAPHICS)

street lights and the Moon

Slide # 26: Luminosity (GRAPHICS)

street light at the distance of the Moon

Slide # 27: Brightness of Stars

luminosity or absolute brightness

amount of energy created by the star

independent of distance

brightness or apparent brightness

how a star appears from Earth

depends on luminosity and distance

Slide # 28: Magnitudes

measures brightness and luminosity of stars

absolute magnitude

apparent magnitude

very old system

invented by Hipparchus in 2nd century BC

Slide # 29: Apparent Magnitudes (GRAPHICS)

small numbers are brighter stars

Slide # 30: Small Numbers are Brighter? (GRAPHICS)

ranking of brightness

Slide # 31: Apparent Magnitudes (GRAPHICS)

objects we see in the night sky

Slide # 32: Facts about Magnitudes

small is bright

5 magnitudes = 100 in brightness

magnitudes add - brightness multiplies

Slide # 33: Absolute vs Apparent

Apparent magnitude

what you see from Earth

measures apparent brightness

Absolute magnitude

magnitude of a star IF it were 10pc away

measure of luminosity or absolute brightness

Slide # 34: Constellation Corner (GRAPHICS)

Constellation De Jour

Slide # 35: Orion (GRAPHICS)

Feb 15 - 9pm - S - 4.0

Slide # 36: Orion (GRAPHICS)

Feb 15 - 9pm - S - 4.0

Slide # 37: Orion (GRAPHICS)

Feb 15 - 9pm - S - 5.0

Slide # 38: Temperature and Color (GRAPHICS)

stars are thermal emitters

Wien's law and Stephan's law apply

temperature and energy flux can be calculated

Slide # 39: The Planck Curve

The position of the peak and the area under the curve depend on Temperature

Slide # 40: Stellar Magnitudes

close stars appear brighter than far stars

inverse square laws

large stars appear brighter than small stars

luminosity - size relationship

hot stars appear brighter than cool stars

Stephan's law

Slide # 41: Stellar Spectra (GRAPHICS)

The position of the peak and the area under the curve depend on temperature, d

Slide # 42: Color Index

hot stars emit more blue light than cool stars

color index is the ratio of blue/red

temperature is related to color index

Slide # 43: Stellar Spectra (GRAPHICS)

red filters and blue filters

the 60,000K curve has the bluest color index and highest temperature

Slide # 44: Orion Revisited (GRAPHICS)

star have visible color differences

Slide # 45: Wien's Law (GRAPHICS)

Peak Wavelength in cm

T in Kelvin

Slide # 46: Line Intensity (GRAPHICS)

temperature determines line intensity

Slide # 47: Spectral Classes (GRAPHICS)

stars are classified by their spectra

line intensity changes with temperature

Slide # 48: Stephan's Law (GRAPHICS)

sigma is

Stephan-Boltzmann constant

5.67 x 10-5 erg/s/cm2/K4

Slide # 49: Luminosity and Size (GRAPHICS)

the total luminosity is related to temperature and surface area

Slide # 50: Measuring Stellar Diameters

indirect method

measure temperature

measure distance

measure brightness

calculate luminosity from brightness and distance

calculate radius from luminosity and temperature

direct method

speckle interferometery

interferometery

Slide # 51: Space Motion (GRAPHICS)

stars are moving through space

motion can be divided into radial and transverse

Slide # 52: Radial Motion (GRAPHICS)

motion directly toward or away from observer

Slide # 53: Doppler

Blue Shift

higher frequencies, shorter wavelength

the observer moves toward the source

the source moves toward the observer

Red Shift

lower frequencies, longer wavelengths

the observer moves away from the source

the source moves away the observer

Slide # 54: Doppler Effect (GRAPHICS)

the change in wavelength is proportional to velocity

Slide # 55: Radial Motion (GRAPHICS)

measured by using the Doppler shift

Slide # 56: Transverse Motion (GRAPHICS)

motion in the plane of the sky

Slide # 57: Transverse Motion

angular motion

observed change in position

transverse velocity

actual motion in the sky

related to angular motion and distance

Slide # 58: Proper Motion (GRAPHICS)

change in apparent position of stars due to motion

Slide # 59: Measuring Transverse Velocity

measure distance to star

parallax

measure change in angular position due to motion

proper motion

calculate transverse velocity

Slide # 60: Transverse Velocity (GRAPHICS)

the Formula