Study Guide for Test #3

Dr. J. R. Webb

Stellar Astronomy

 

 

Chapter 17.  The Nature of Stars.

 

• Apparent magnitude (m)– How bright an object appears to be to an observer.
•  If  the change in magnitude, DM , is 1, then the difference in brightness DB, is 2.512.  In general,  DB = (2.512)^DM (e.g. DM = 5,  DB = (2.512)⁵ = 100)
• Absolute Magnitude (M) -  The magnitude a star would be if it were exactly 10 parsecs away.    M = m –5log(d) +5, where d is the distance in parsecs.

(Note:  The Sun’s apparent magnitude from Earth is –26.5, its apparent brightness would be +4.8 if it were 10 parsecs from Earth, thus its absolute magnitude is +4.8.

• stellar parallax -The distance d(parsecs)  = 1./parallax angle  in arc seconds.

Closest other star – proxima Centauri – p = 0”.75 ~ 20 parsecs.

• Luminosity – The energy output per unit time.

 

• Color Indices – U – B = m_u – m_v, and is called the U-B color index.  It measures the amount of ultraviolet light relative to the amount of Blue light emitted by a star.  B-V = m_b – m_v is the B-V color index.   (Note: you can use either apparent magnitudes m, or absolute magnitudes M to compute the color index, since they are differences, the distance cancels out.)  A graph of B-V versus temperature allows one to determine the temperature of a star by measuring just the m_b and m_v.

 

• Spectral Types – Originally Harvard astronomers classified stellar spectra into categories A through Q, but upon further study, realized that when they spectra arranged according to temperature, the classes became:

O             B                 A              F                G                     K                    M

Hot                                                                                                             Cool

A stars spectrum is included in one of these categories based on the presence, absence, and strength of various spectral lines.  (example:  The Balmer lines of hydrogen or the H and K lines of Calcuim). (See Figure 19-10 and Box 19-4)

 

• Strengths of Absorption lines:  See Figure 19-11.  You MUST understand this table.  Line strength means, how visible or how dark the lines are compared to the rest of the spectrum.  Spectral type is the

 

• The Hertzsprung-Russell Diagram (H-R diagram)  IMPORTANT!!! – Plot absolute magnitude versus color index (or temperature or spectral type).  Every phase of a stars evolution can be traced on this diagram.

 

Key Parts of the H-R Diagram

1.  Main sequence – stars converting H to He, in hydrostatic equilibrium.  Middle age of star.  Luminosity class V, also called dwarfs.
2.  White Dwarf region – cores of dying stars. (no luminosity class)
3.  Sub Giants – highly evolved low mass stars.  Luminosity class IV.
4.  Giants – highly evolved stars.  Luminosity Class III.
5. Bright Giants – Highly evolved massive stars.  Luminosity Class II.
6. Super Giants – Highly evolved massive stars.  Luminosity class I.

 

• Main Sequence is a Mass relationship – massive stars, upper left, less massive stars as you go toward lowert right-hand side of HR diagram.
• Stellar Radius – Larger stars are brighter for a given temperature, thus occur higher on the H-R diagram than smaller stars. (e.g. White Dwarfs versus Supergiants.)
• Binary Stars – used to determine stellar masses by applying Kepler’s 3rd Law. (refer to chapter 3,   P² = [ (4p²)/G(M₁+M₂)]a³ where P is sidereal period and a is the semimajor axis.).
1. Optical Doubles – two stars that appear to be physically connected but are really far apart.
2. visual binaries – can be seen as two distinct stars from Earth.
3. spectroscopic binaries – star systems where stars are to close together to be resolved from Earth, but can be detected by their spectral lines that shift as the stars orbit each other (Doppler shifts).
4. Eclipsing binaries – When the stars orbital plane is parallel to the line of sight, thus we see the stars “eclipse” each other.
5. What we get from Binaries: relative masses of stars from radial velocity curve, relative sizes of stars and relative brightnesses from eclipses.

 

• Main Sequence Lifetimes – Low mass. Later spectral types, G, K M, live longer than more massive O,B or A stars.  Hot stars have more fuel, but burn hotter and use their fuel much faster than low mass stars.

 

Chapter 18.  The Birth of Stars.

 

GRAVITY VERSUS INTERNAL PRESSURE!!!

 

• Gravity – depends solely on the mass of the star.
• Internal Pressure –
1. Temperature (gas and radiation pressure)
2. Rotation
3. Magnetic Fields

 

• Regions of Star Formation –

1.      Cold regions in interstellar space – HI regions – l = 21-cm line due to the spin-flip of the electron in the hydrogen atom.

2. H₂ regions , molecular hydrogen only forms in very cold regions but radiates very little.  Fortunately, tracer CO radiates at l = 2.6 –mm and ratio is:  H₂/CO = 10,000/1
3.  Dark Nebula – cold dark regions usually embedded in HII regions.
4. Bok Globules – small, round nebula r ~ 1-2 ly, M ~ 20-200 M_o, T ~ 5-15K

 

• The Big Picture of Star Formation –

1.      A cloud of gas collapses by mutual gravitational attraction.

2.      Inner regions cool and further collapse –Dark nebula

3.      Internal temperatures and pressures rise and fight collapse.  This process is a balance between gravity, cooling by radiation which tends to keep internal  temp and pressure low, and heating due to gravitational collapse.  Cloud fragments into smaller pieces..

4.      Since cooling can never be efficient enough to reduce the internal pressure enough according to current theories, “Something” causes further collapse.

1. Shock waves from other, newly formed stars
2. Shock waves from supernova explosions
3. Shock waves from galactic spiral arms.

 

5.      Further collapse forms small, round Bok Globules.

 

6.      Globules collapse further and form proto-stars.

 

7.      After 1000’s of years, T_surface = 2000-3000K, M ~ 1M_solar, R ~ 20 R_solar, L ~ 100L_solar.  Star now appears on the Birthline on the H-R diagram.

 

8.      Cocoon nebula.

 

9.      Masses of stars:  80 M_solar > M_star > 0.08M_solar.

 

10.  Problems with Star formation- How does a single, isolated star not in a spiral galaxy form?  No shocks around?

 

 

Chapter 19 & 20  Stellar Evolution:    Stellar Evolution: The Death of Stars.

·        Low mass Stars (3-4 M_solar)

 

a.       Core composition changes from H to He

b.      He fuses to Carbon at 100,000,000 K.

c.       As H is depleted in core, core collapses and heats up a H shell around core begins to burn and envelope expands – Red Giant stage.

d.      Core continues to collapse until T ~ 100,000,000K.  Helium burns explosive (Helium flash) because of quantum degeneracy (all He is at same temp).

e.       Outer layers are blown off into interstellar space (planetary nebula) and hot, solid carbon core becomes a White Dwarf.

 

• High Mass Stars (over 3-4 M_Solar)

 

a.       Core composition changes from H to He

b.      He burning takes off smoothly due to high gravitational pressure.  So star has a core burning He to Carbon, and a shell buring H to He, and a H envelope.

c.       Onion Skin Model

·        H to He

·        He to Carbon

·        Carbon to Magnesium and Neon

·        Neon to Magnesium and oxygen

·        Oxygen to silicon

·        Silicon to iron

d.      At this point Iron burning is an endothermic reaction, it doesn’t release energy as the previous reaction, but saps the energy of the core!  This causes immediate core collapse.  As outer layers crash onto the core, the envelope material is blown off and a supernova results!

e.       If core mass is less than 1.4 M_solar the the core remnant is a white dwarf.

f.        If core mass is greater than 1.4 M_solar, neutron star.

g.       If core mass exceeds abut 3 M_solar, then core remnant is a black hole!