October 24, 2016
Astronomy 122
Prof. J. Brau

• The Sun
• Measuring the Stars

The Sun


Main sequence star
150,000,000 kilometers from Earth

8 light-minutes
5 billion (5 x 10⁹) years old
696,000 kilometer radius
speed of light is 300,000 km/second

Spectral class G2V
Solar constant: 1400 Watts/m²
Knowing solar constant (Brightness) and the distance to the Sun
. . . allow us to determine: Absolute magnitude: +4.8
defined as apparent magnitude at distance of 10 pc

Central temperature 15,000,000 K

• highest temperature and pressure at the center
Surface temperature 6,000 K
Estimated eventual lifetime : 10 x 10⁹ years ( 5 billion more)
Most abundant elements: hydrogen and helium

also most abundant elements of all main-sequence stars



Thermonuclear Fusion

Provides energy

hydrogen "burns" -> helium

proton-proton chain

• 4(¹H) -> ⁴He + energy + 2 neutrinos + 2 positrons
• a fraction of the mass of initial particles is converted to energy (E=mc²)


Thermonuclear fusion is also responsible for virtually all the starlight we see.



Note: initial energy of Sun came from gravity as the matter collapsed and heated until fusion "turned on"


Hydrostatic equilibrium

balance of force of gravity and outward gas pressure

(core compresses and heats until balance is achieved)

Most of the Sun's energy is generated within 1/4 of the Sun's radius

• The core

Most of the Sun's mass is contained within 60% of its visible radius


Thermal equilibrium

Heat produced in the core is balanced by flow from the surface

Heat is transferred from the core to the surface by:

Radiation - from core to bottom of the convection zone

Convection - from the bottom of the convection zone to the surface

No significant heat transfer from conduction

Heat/energy generated at the core (by thermonuclear fusion) makes its way to the surface after tens of thousands of years

Neutrinos produced as a by-product of fusion in the core pass out in a couple of seconds

• neutrinos carry no charge
• neutrinos have very little mass
• neutrinos interact very little, which results in their passing directly through and out of the Sun once they are produced



Sun's Atmosphere

Photosphere - Produces visible surface - 6000 K

absorption lines of photosphere and lower chromosphere reveal presence of some 67 elements
Ten most common elements in the solar atmosphere
• Hydrogen (91.2 % of atoms)
• Helium (8.7% of atoms)
• Oxygen (0.078%)
• Carbon (0.043%)
• Nitrogen (0.0088%)
• Silicon (0.0045%)
• Magnesium (0.0038%)
• Neon (0.0035%)
• Iron (0.0030%)
• Sulfur (0.0015%)

Chromosphere - Diffuse - emission lines

Corona - millions of km thick
. . . 1-2 million K; best seen during solar eclipse

Granules - photosphere - due to convection

Spicules - chromosphere - jets of surging gas

Supergranules

Coronal Hole - seen in x-ray image of Sun

hole in the Sun's corona

Sunspots - cool (4000K) dark regions on the Sun's surface


• intense magnetic fields
• reveal differential rotation
  • 25 day period at equator
  • 35 day period near the poles
• solar cycle
  • Sunspot maximum every 11 years
  • Magnetic polarity reverses every 11 years -> 22 year cycle
  • Sunspot data
• magnetic dynamo model

Prominences -huge arching columns of cool gas above the photosphere

Solar Flares - violent explosions on the solar surface associated with complex sunspot groups

Coronal mass ejection - Giant magnetic bubbles of ionized gas that separate from the Sun's atmosphere and escape into interplanetary space

NASA movie

Solar activity such as flares and sunspot number can dramatically affect conditions on Earth.

Measuring the Stars


Stellar Parallax - method to measure the distance of closest stars
• d (parsecs) = 1/ p (in arc seconds)
• 1 parsec = 3.26 light-years
Closest other star to the Sun is about 4 light-years (1.3 parsecs) away

• a little more than 1 parsec
• Alpha Centauri complex
Distance scale can be extended with Spectroscopic Parallax
• Spectroscopic Parallax uses Spectral Class, Brightness, Inverse-square Law, and Main Sequence relationship of Luminosity and Spectral Class

Motion

transverse (proper motion) measured directly, after correcting for parallax, for nearby stars

radial measured through Doppler effect

true space motion is the combination of proper motion and radial motion

Brightness

measure of the amount of light reaching the Earth

also called Apparent Magnitude

Luminosity

measure of the total amount of energy or light emitted by star

also called Absolute Magnitude

Absolute Magnitude is what the Apparent Magnitude would be if the star were 10 parsecs away

Brightness (or apparent magnitude) decreases as the inverse-square law

NOTE
Luminosity and Absolute Magnitude measure the same property in different units
Brightness and Apparent Magnitude measure the same property in different units
Also will see reference to Apparent Brightness, and Absolute Brightness

Magnitude Scale

Defined by Greeks to classify star brightness

• Brightest stars were called Magnitude 1
• Stars barely visible to naked eye called Magnitude 6

5 units = 100 x brightness (or luminosity) change

1 unit = 2.5 x change

Brightest star (Sirius) Magnitude -1.5

The larger the magnitude, the fainter the star

Magnitude 6 stars - barely visible to the naked eye

Magnitude 30 - visibility limit of Space Telescope

Comparison of Luminosity and Absolute Magnitude

Temperature and Color

Blackbody theory relates the color of a star to its surface temperature

• red -> 3,000 K
• orange -> 4,000 K
• yellow -> 6,000 K
• white -> 10,000 K
• blue -> 20,000 K

Filters

• V (visible)
• B (blue)
• U (ultraviolet)

Detailed Spectra

spectral classes (spectral type)

O B A F G K M

• O is hottest and most massive
• M is coldest and least massive

Hertzsprung-Russell Diagram

Absolute Magnitude vs. Spectral Type

or Luminosity vs. Temperature (reverse order)

Main Sequence (generates energy through thermonuclear fusion in core)

Giants (once were main-sequence stars)

White dwarfs (once were main-sequence stars)

The cosmic distance scale can be extended with Spectroscopic Parallax

• Spectroscopic Parallax uses Spectral Class, Brightness, Inverse-square Law, and Main Sequence relationship of Luminosity and Spectral Class

Luminosity Class

90% of the stars are main sequence stars

• We can distiguish the non-main-sequence stars based on the width of spectral lines
  • large stars are less dense in the absorbing atmosphere, and therefore have narrower lines







Stellar Mass

Binary stars

Most stars are in a multiple star system (binary, triple, ...)

Stars move in elliptic orbits about a common "center of mass"

Types of binaries

• Visual binary
• Spectroscopic binary
• Eclipsing binary

Measuring orbits of binary reveals mass

• Conclusion -> Luminosity proportional to (Mass)³ for massive main-sequence stars
  and proportional to (Mass)⁴ for more common main-sequence stars
• Consequently -> Lifetime inversely proportional to (Mass)² for the most massive stars
  Or, for massive stars, - approximate




Stellar Lifetime


15 solar mass star has lifetime of only 15 million years, roughly 1/1000 of the lifetime of a star like the Sun




Stellar Size

Betelgeuse is large enough, and close enough, to have it's size resolved directly

its radius is about 600 times that of the Sun





Most stars are too distant, or too small, to measure the size directly

Combining Luminosity with Temperature gives Stellar Size

The total luminosity is the area of the star times its surface temperature to the fourth power (Blackbody theory)

OR -> Luminosity ~ Area x Temp⁴

or -> Luminosity ~ Radius² x Temp⁴

and this implies Radius ~ √ Luminosity  / Temp²

this maps out lines on the HR diagram of specific radii of the stars

• Stars above the main sequence are giants
  • The red giants are giant stars with surface temperatures making them red (about 3000-4000 K)
• Stars below the main sequence are dwarf
  • The white dwarf are very hot, small stars

Very important conclusion from "measuring the stars"


The evolution and properties of a main sequence star is predominantly determined by the mass of the star

Star clusters

Open (or galactic) clusters

• loosely packed, groups of younger stars

Globular clusters

• tightly packed, groups of the oldest stars known
  • older than 10,000,000,000 years
• age determined from "turn-off" point in H-R diagram