ASTR EXAM 2 Cheat Sheet PDF

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Summary

THE SUN is powered through nuclear energy nuclear potential energy 10 billion yrs. Luminosity total energy radiated calculated from fraction of energy that reaches Earth constant: energy that reaches Earth (1400 luminosity: 4 x 1026 watts 6 x 108 meters (109x wider than 2 x 1030 kilograms mass of ba...

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THE SUN

-Sun is powered through nuclear energy (E=mc2) nuclear potential energy ~ 10 billion yrs. Luminosity -luminosity: total energy radiated by Sun; calculated from fraction of energy that reaches Earth -solar constant: Sun’s energy that reaches Earth (1400 W/m2) -total luminosity: 4 x 1026 watts -radius: 6.9 x 108 meters (109x wider than Earth’s) -mass: 2 x 1030 kilograms (300,000x mass of Earth’s) -2 balances: 1) gravitational equilibrium: between&the&outward&& &&&&&&&&&&&push&of&internal&gas&pressure&and&the&inward&pull&of&& &&&&&&&&&&&gravity& &&&&&&& & &&&&&&&2)&energy&balance:& rate&at&which&fusion&releases&& &&&&&&&&&&&&energy&in&the&Sun’s&core&and&the&rate&at&which&the&& &&&&&&&&&&&&Sun’s&surface&radiates&this&energy&into&space& -core: most inner part of Sun; where nuclear fusion takes place (15 million Kelvin) -nuclear fusion: combining two nuclei into larger one -proton-proton chain: fusing 4 hydrogen nuclei into 1 helium nucleus w/ two protons and neutrons. Also releases gamma rays, neutrinos & positrons as result& -chromosphere:&middle&layer&of&the&solar&atmosphere&and&the& region&that&radiates&most&of&the&Sun’s&ultraviolet&light -photosphere:&outer&layer&of&the&atmosphere,&visible&surface&of &Sun & & -granulation:&rising&hot&gas&cells & -corona:&outermost&layer&of&this&atmosphere;&high&temperature&(1& million&Kelvin)&&&emits&most&X&rays;&low&density& -convection&zone:&where&energy&generated&in&the&solar&core&travels& upward,&transported&by&the&rising&of&hot&gas&and&falling&of&cool&gas& -radiation&zone:&energy&moves&outward&primarily&in&the&form&of& photons&of&light& -radiative&diffusion:&photons&take&long&time&to&make&outward& progress&b/c&they&constantly&deflect&off&things&and&stray&from&a& straight&path& -sunspots:&blotches&on&Sun’s&surface&that&look&darker&(4000&K)& & -strong&magnetic&fields&that&come&in&pairs&and&twist& & -lines&closer&when&field&is&stronger,&further&when&weaker & & -solar&prominences:&gas&trapped&under&giant&loops&& & -sunspot&cycle:&cycle&of&sun&spots&rising/falling& & -solar&cycle&lasts&about&11&yrs.&Before&N/S&switch& -solar&flares:&emit&bursts&of&UV&light&and&X&rays&at&speed&of&light& -solar&wind:&stream&of&charged&particles&continually&blown&outward& in&all&directions&from&the&Sun& -coronal holes: regions of corona nearly devoid of hot gas -eruptive prominences aren’t as dangerous as solar flares -Maunder minimum: historical data indicating most minimal sun spot activity (1650-1700)

STARS& -apparent brightness obeys inverse square law (i.e. if Sun was viewed from twice Earth’s distance, it would be dimmer by 2 2=4) -apparent brightness = star’s luminosity / 4d2pi -measuring stellar distance using trigonometric parallax: d = 1/p -d= distance in parsecs; p= parallax angle in arc seconds -1 parsec = 3.26 light years -dimmest stars: 10-4LSun ; brightest stars: 10 6LSun -apparent magnitude (m): how bright a star appears in sky -the smaller the magnitude, the brighter (1 brighter than 2)

-absolute magnitude (M): magnitude at 10 parsecs away -MSun = 4.83 ß we compare everything to Sun -distance modulus: difference btwn. apparent & absolute mag. m – M à Luminosity = n(M2-M1 ) where n=2.512 (light ratio) -spectral type: way&of&classifying&a&star&by&the&lines&that&appear&in& its&spectrum;&it&is&related&to&surface&temperature& & -OBAFGKM&from&hottest&(UV)&to&coolest&(infrared)& & -hottest&has&less&&&weak&lines;&coolest&has&opposite& -binary&star&systems:&star&system&containing&two&stars& & -visual&binary:&can&be&seen&distinctly&as&they&orbit& & -spectroscopic&binary:&identified&through&Doppler&shifts&& in&spectral&lines&(alternating&blue&&&redshifts)&& -eclipsing&binary:&orbit&in&our&line&of&sight;&when&neither& is&eclipsed,&we&see&both&lights.&When&one&eclipses,& brightness&drops&b/c&other&star&is&slightly&covered& -the&more&unequal&the&masses&are,&the&more&the¢er&mass& shifts&towards&the&bigger/massive+star& -measuring/estimating&stellar&masses:& & M1&+&M2&=&aau 3&/&Py2& & -rearranging&Law&of&Torques:&m1m2&=&r1r2&à&&& &&&&&m1&=&m2&(r2&/&r1)&& & & & -P&=&binary&system&period&(yrs.)&;&a&=&avg.&separation&(AU)& & m&–&M&=&5logd&–&5&(for&finding&distance)& 4& -Stefan-Boltzman&Law:&F&=&σT -&F&=& energy &per&;&T&=&temperature&;&σ&=&constant&(5.7&×& −8 2 4 10 &watt/(m &×&K ))& -calculating&stellar&radii:& 2 4 & Luminosity&=&R T -H-R&Diagram:&plots&stars&as&points,&with&stellar&luminosity&on&yaxis&and&spectral&type&(surface&temp.)&on&x-axis& & -temperatures&decrease+from&right&to&left& & -luminosity&ticks&each&increase&tenfold& & -main&sequence:&prominent&streak&running&from&upper&& left&to&lower&right&of&diagram& -supergiants:&large&and&bright& -giants:&smaller&in&radius&and&luminosity,&but&brighter&& than&main&sequence&stars&of&same&spectral&type)& -white&dwarfs:&small&in&radius,&high&temperature&& -stellar&luminosity&classes:& & I.&supergiants& & V.&main&sequence& & II.&bright&giants& & VI.&sub&dwarfs& & III.&giants& & VII.&white&dwarfs& & IV.&subgiants& -main-sequence&lifetime:&The&length&of&time&for&which&a&star&of&a& particular&mass&can&shine&by&fusing&hydrogen&into&helium&in&its&core& & -higher&mass&=&longer&lifetimes& -stellar&motion&is&a&combination&or&radial&(directly&towards/away)& and&traverse&(perpendicular&to&Earth)&direction& -even&if&they&don’t&seem&to&shift,&they&could&be&exhibiting& radial&motion&(blue/redshift)& & -calculating&traverse&velocity:&Vt&=&4.74μd& & μ&=&arc&sec./yr,&;&d&=&distance&(km)& 2 2 2 & -space&velocity:&Vspace &=&VT &+&VR &

EXAMPLE PROBLEMS: 1) Trigonometric Parallax Sirius, the brightest star in our night sky, has a measured parallax angle of 0.379″. Find its distance in parsecs and lightyears. Formula: d = 1 / p 1. d = 1 / 0.379 = 2.64 parsecs 2. 2.64 parsecs x 3.26 light years/parsec = 8.60 light years 2) Comparing Modern Magnitudes The Sun has an absolute magnitude of about 4.8. Polaris, the North Star, has an absolute magnitude of −3.6. How much more luminous is Polaris than the Sun? Formula: L= n(M 2-M1) 1. L = 2.512(4.8-(-3.6)) = 2.5128.4 = 2500 2. Polaris is 2,500x brighter than the Sun

3) Distance Modulus a.

b.

Star A has an apparent magnitude of 2.0 (brighter) and an absolute magnitude of 6.0 (dimmer). Find the difference of the two distances. 1. m – M = 2.0 – 6.0 = -4.0 2. nm-M = 2.512-4.0 = .025 = .025 / 1 3. Assign b1 and b2 d1 = x b1 = .025 d2 = 10 pc b2 = 1 2 2 4. b1 = d2 à .025 = 10 à x = 1.58 pc 2 2 1 x b2 d1 Star A has an apparent magnitude of 4 .0 (dimmer) and an absolute magnitude of -3.0 (brighter). Find the difference of the two distances. 1. m – M = 4.0 – (-3.0 ) = 7.0 2. nm-M = 2.5127.0 = 637.157 / 1 3. Assign b1 and b2 d1 = x b1 = 1 d2 = 10 pc b2 = 631.157 1 = 102 à x = 251 pc 4. b1 = d2 2 à 2 631.157 x2 b2 d1

4) Measuring Stellar Mass a.

5)

Preset 14 has an average separation of .12156 AU and a period of .02667 years. The radii are r1 = 4, r2 = 1.25 3 2 Formula: M1 + M2 = aau / Py 3 1. M1 + M2 = .12156 / .026672 = 2.52 2. m1m2 = r1r2 à m1 = m2 (r2 / r1) à m1 = m2 (1.25/4) 3. m2 (1.25/4) + m2 = 2.52 à m2 = 1.92 4. m1 = m2 (1.25/4) à m1 = 1.92 (1.25/4) = .60

Measuring Stellar Radii a. Star A is the same size as the Sun, but is 3x hotter. How much more luminous is Star A? Formula: L = R2T4 1. Lstar = R2T4 à 34 = 81 Lsun = R 2T4 14 b.

Spica is 3.9x hotter than the Sun, with LSpica = 12,100LSun. Determine the radius. 1. Lstar = R2T4 à 12100 = R2 3.94 Lsun = R 2T4 1 R2 14 2 2. 12100 = R (231) à 7.2 = R R2...