1	Astro 1050 Fri. Oct. 17, 2003 Today: Extra Credit Articles Homework Chapter 8, Properties of Stars
2	Homework #5 Q1 At what wavelength does the spectrum of a 10000 K type A star peak? Use Wien’s Law: λ = 3000000 nm/T, so 300 nm. Q2 The neutral atom of the most common form of hydrogen consists of a proton and an electron. Q3 Fusion of very light elements to make heavier ones releases energy, as does fission of very heavy elements to make lighter ones. The most "energetically favorable" and stable element from which neither fission nor fusion can release energy is IRON Q5 In the two page spread you can find the solar flare energy in terms of nuclear weapons (up to a billion H-bombs), and determine that yes, the traitor dies like the dog he is! Q6 1 kg of mass transformed into energy: E = mc² so E=1 kg x (3x10⁸m/s)² = 9x10¹⁶ J
3	Homework #5 Q7 1 kg of H fused into He. How much energy is liberated? Use E = mc², but must determine how much mass is converted. We learned in class that 4.3 ´ 10^-12 J released for each He produced. He masses 6.645 ´ 10^-27kg, so we have 1.5x10²⁶ He in a kg, each producing the above energy. Multiply the energy per He times number of He = 1.5x10²⁶ x 4.3 ´ 10^-12 J = 6.4x10¹⁴ J Q9 Sunspot brightness, use E = σT⁴ (T1/T2)⁴ = (5800/4200)⁴ = 3.6 times brighter
4	Measuring a and P of binaries Two types of binary stars Visual binaries: See separate stars a large, P long Can’t directly measure component of a along line of sight Spectroscopic binaries: See Doppler shifts in spectra a small, P short Can’t directly measure component of a in plane of sky If star is visual and spectroscopic binary get get full set of information and then get M
5	Masses and the HR Diagram Main Sequence position: M: 0.5 M_Sun G: 1 M_Sun B: 40 M_sun Luminosity Class Must be controlled by something else
6	The Mass-Luminosity Relationship L = M^3.5
7	Eclipsing Binary Stars System seen “edge-on” Stars pass in front of each other Brightness drops when either is hidden Used to measure: size of stars (relative to orbit) relative “surface brightness” area hidden is same for both eclipses drop bigger when hotter star hidden tells us system is edge on useful for spectroscopic binaries
8	Starting Ch.9: Interstellar Medium Since stars die, new ones must somehow be born They must be made out of material like star: H, He, plus a little heavier elements Three types of interstellar “nebulae” or clouds Emission nebulae -- Glow with emission lines Reflection nebulae -- Reflect starlight Dark nebulae -- seen in silhouette
9	Emission nebulae The red glow is Hydrogen Balmer a (Ha ) emission Could be from hot gas but – relative strength of emission lines not always right Can also get fluorescence: UV photon from bright star boosts electron to high level (or ionizes it) Emission lines created as electron cascades back down through H energy levels The “horse” is a dark cloud in front of the glowing gas.
10	Reflection nebulae – The Pleiades Cluster of new stars Visible to unaided eye in western Taurus Stars form in clusters – most of which slowly spread apart. Reflection nebula is reflected sunlight Can see stellar-like spectra with absorption lines Blue light scattered more efficiently than red Pleiades didn’t form here – just moving through this cloud of dust.
11	Dark Nebula
12	Spectral Measurements Use spectra of stars Ignore broad (“high pressure” stellar lines Very narrow (low pressure) lines from interstellar gas This one Ca II = Ca⁺¹ Stronger in more distant stars Stronger when looking through interstellar gas clouds Hydrogen hard to measure remember Balmer rules
13	Measurements at other Wavelengths Infrared “Cirrus” really slightly warm dust X-Rays of hot gas near exploded stars (supernova) Radio observations of “Molecular Clouds” Called that because cool and dense enough for molecules to form H₂ also hard to detect CO common and easy to detect Densest have 1000 atoms/cm³ T as low as 10 K Location of star formation
14	Collapse of Molecular Clouds Barely stable against collapse: Imagine slightly compressing cloud Gravity goes up because material is packed more tightly (R in 1/R² is smaller) Tends to make cloud want to collapse Pressure goes up because material is packed more tightly (P µ rT) and r higher Tends to make cloud want to expand For smaller clouds Pressure wins (stable) For larger clouds Gravity wins (collapse) As it collapses and becomes denser, smaller and smaller parts become unstable Shock wave can trigger collapse
15	What will a forming star look like in HR diagram? Temperature changes relatively simple Starts out large and relatively cool Must be on red side of diagram It heats up as it contracts Must towards the blue Luminosity more complicated because it depends on T and R Not much energy to start with Luminosity must start out low Collapse releases grav. energy Luminosity will rise Fusion begins, releases more energy Luminosity at a peak Collapse slows, only have fusion now Luminosity declines Finally stabilizes on the main sequence
16	How does mass affect collapse? More massive protostars have stronger gravity Collapse speed will be much faster Fast collapse and short lifetime means massive stars reach end of lifetime while low mass stars in cloud are just forming Supernova shocks may come from earlier generation of stars Sequential Star Formation Energy from supernova and other effects eventually disrupts cloud – prevents further collapse.
17	Observations of collapse Young cluster “NGC 2264” Few million years old High mass stars have reached main sequence Lower mass stars are still approaching main sequence T Tauri stars Naming of classes of stars: Usually named after first star in class: T Tauri Stars with letters (RR Lyrae) are typically “variable” stars Earlier stages hidden by dust
18	More details of stellar structure and energy generation Alternatives to the proton-proton chain Fusion of Helium to heavier elements Proton-proton reaction slow because: Need two rare events at once High energy collision of 2 protons Conversion of p Þn during collision
19	The CNO Cycle Gives way around need for p ®n during the collision Still must happen later – but don’t need to rare events simultaneously Trade off is need for higher energy collisions (T>16 million K) Add p to some nucleus where new one is still “stable” Wait for p ® n while that nucleus just “sits around” The net effect is still 4 ¹H ® ⁴He C just acts like a “catalyst”
20	Heavy Element Fusion Triple Alpha process ⁴He + ⁴He ® ⁸Be + g ⁸Be + ⁴He ® ¹²C + g Similar type reactions create heavy elements above 600 Million K Plot to left gives: x: # of neutrons y: # of protons Right one – add neutron Up one – add proton Diagonal – p ® n or reverse Jumps: add ⁴He or more
21	Models of Stellar Structure Divide star into thin shells,calculate how following vary from shell to shell (i.e. as function of radius r) P (Pressure) T (Temperature) r (Density) To do this also need to find: M (Mass) contained within any r L (Luminosity) generated within any r P example:
22	Numerical Stellar Models
23	Why don’t stars collapse? Limiting case: Assume no nuclear fusion so only energy source is gravity. Star is “almost” in hydrostatic equilibrium Star radiates energy: If nothing else happened T would drop, P would drop, star would shrink. Star does shrink, but in doing so gravitational energy is converted to heat, preventing T from continuing to drop. In fact, since star is now more compact, gravity is stronger and it actually needs higher P (so higher T) to prevent catastrophic collapse As star shrinks, ½ of gravitational energy goes into heating up star, ½ gets radiated away Rate at which it radiates energy, so rate at which it shrinks, is limited by how “insulating” intermediate layers are
24	Why do we get steady fusion rates? Strange counterintuitive result: As star radiates away thermal energy it actually heats up (because as it shrinks gravity supplies even more energy) Star continues to shrink till it gets hot enough inside for fusion (rather than gravity) to balance energy being radiated away. Nuclear thermostat If fusion reactions took place in a “box” with fixed walls: Fusion Þ more energy Þhigher T Þ more fusion (explosion) If fusion reactions take place in sun with “soft gravity walls”: If fusion rate is too high T tries to go up but star expands and actually ends up cooling off – slowing down fusion. (steady rate)
25	Mass-Luminosity relationship L µ M^3.5Why? Higher mass means higher internal pressure Higher pressure goes with higher temperature Higher temperature means heat leaks out faster Star shrinks until T inside is high enough for fusion rate (which is very sensitive to temperature) to balance heat leak rate
26	Lifetime on Main Sequence L µ M^3.5T µ fuel / L = M/M^{3.5 =} M^-2.5 Example: M=2 M_Sun L = 11.3 L_SunT =1/5.7 T_Sun
27	How about a 0.5 solar mass star? M = 0.5 M_sun Time = Luminosity =
28	How about a 0.5 solar mass star? M = 0.5 M_sun Time = 5.7 times solar lifetime Luminosity = 0.09 solar luminosity
29	Width of Main Sequence – and Stellar Aging As star converts H to He you have more massive nuclei Pressure related to number of nuclei Gravity related to mass of nuclei Pressure would tend to drop unless something else happens Temperature must rise (slightly) to compensate Luminosity must rise (slightly) as heat leaks out faster
30	Orion Nebula: A Star-Forming Region Red light = Hydrogen emission Blue light = reflection nebula Dark lanes = dust Astronomy Picture of the Day: http://antwrp.gsfc.nasa.gov/apod
31	Protoplanetary Disks in the Orion Nebula Dusty disk seen in silhouette Central star visible at long wavelengths
32	Herbig-Haro objects: The angular momentum problem As clouds try to collapse angular momentum makes them spin faster A disk forms around the protostar Material is ejected along the rotation axis
33	Herbig-Haro 34 in Orion Jet along the axis visible as red Lobes at each end where jets run into surrounding gas clouds
34	Motion of Herbig-Haro 34 in Orion Can actually see the knots in the jet move with time In time jets, UV photons, supernova, will disrupt the stellar nursery