Extragalactic Astronomy ASTR 5630
Popular in Course
Popular in Astronomy
This 12 page Class Notes was uploaded by Willie Cummings on Monday September 21, 2015. The Class Notes belongs to ASTR 5630 at University of Virginia taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/209717/astr-5630-university-of-virginia in Astronomy at University of Virginia.
Reviews for Extragalactic Astronomy
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/21/15
Whittle EXTRAGALACTIC ASTRONOMY titans PDFs 6 STELLAR DVNAMICSI DISKS Index Questions Images References Prim Next M 1 Introduction a Scope of these Leclures Tnts snoteo ts mature extenstve and can be ntgnty sopntstteated Fortunatety for us We don t reaty need and don t nave tnettrne for a detailed treatrnent tnstead my arn th oeto a present tne maortnemes tn proad outhne a extract some trnportartt anatyttc resutts a devetop our tntutttve understandtng of eadn topte a oonnea eadn topteto our opservattonat knowtedge of gaaxtes Stnee tne snoteo ts so Wetghty tt ts sensote to spread tt out a ott Topte 5 eonstders dtsk dynarntes and tne formatton of bars and sptras Toptee Topte t2 eonstders dynarntcat trtetton encounters opte ts dtseussesnow btadlt notes can affect ga Etytne end We th have covered almost an of ElampT wntte ornttttrtg much of the detatt and rnergers axy stru an re So tets now pegtn thn dtsk dynarntcs Tne pan for thtstoptctakesusthrough a number of tnteresttng tnernes epicycles penurbattons of srnpte orwtar orptts resonances Wnen eptcydes Syn rontze thn tne pasmge of dtsk patterns density waves a SeW39COHSaem response to coherent eptcydtc rnott instabil ies when otsks begm to dump up under se frgravtty amplmcation when thts dumpmg grows to form bars and sptras Next Prev M 2 Epicycles a Overview D9lt stars have approxtrnatew ctrcutar orots wth smaH oewattons a orwta rot aong guiding center deferent radtung angutar vetoctyng a sma er eMpttca epicycle angutar vetoctty K retrograde oonsoer gramtycentntugat oaance amp oo servauon of AM o oonstoer star mdmg center GO and gwe t at g a Mch raotaty outwards o oonsermng AM mrv Smoe H ceases a my and centnm ga forces Foenmga Dlt vf r X r393 He Fgw fa s rnore slowlythan r2 at arge raon Fgw gt Foenmga and the star gets puHed back inwar s o as t fa s n r decreases so v tncreases a but now Few under AM cons torn it e and th rnovest mga gt Fgw and the star moves star omrd retatwe to the so outmrds agam a the cycte repeats and we have a smat retrograde epicycle Wages An equwaent oesc ptton oonsoers the conohstoroe m a rotatmg frame nerat g and K are dtfferent so orotts don t dose However when observedfromframe rotatmg at 7 A K a orotts are closedeuipses oentereo on gmdmg center At thts pomt ets one y anttctpate the retevance of eptcyctestor sptra arrns o For eptcycte phases whtch vary Syaemauca y wth raows a nested eMpttca orptts may oowo m a sptrat pattern inematic densit y wave m tum perturbed by the spra oenstty pattern a 0 KS thts es the strnpte eptcyoes are rnootn Se froonsts tent sohmon ts a density wave gas reponse causes Show and star torrnatton a wstpte sptra arrnst trnages Now et s return to the eptcyctes and oenve thetr onaraoensttcs Constoer a sm ooth axtsymrnetnc atteneo rnass oratnoutton wtth potentta ltIgter Smce we have no aztrnutha forces AM ts conserved and we have 5 u B 1 7 2 R R4 6R39 If b Vertical z Motions Take rst the z mOUOn aboutthe ptahe 0 shoe the dtsx S symmethc about po then the zrforoe at 20 5 zero 53 oonsder We empty expand the Home hnea yfor max 2 sma mOUOn above and betow the ptane 7 M 6 7 3 7 2 54 2 e 7 a Thts gwes Stmpte Harmomc Mottoh SHMJ wth frequencyu Where 12 32 BAH zt Zcos1t 1110 65 For MHky Way may hear the Sun 12 4 7r 3 o whtch gues a vemca OSaHaUOn pehod 27F u 55 X107 yr1l8 ctrcutar pertod n 0 Radial Molions Ftrs t oomstderthe ctrcutar gmdmg orbtt Rcona t has radms Rg ctrwtar vetoaty vC and angutar vetoatyng dehhed by However rrouce that m can a so be wrrtterr as 5 L2 SE where gt63 Rz 252 quot 7 68 R 7 8R 39 39 ew m TD form Typwca y Den has a rmmrnum Hang aeep y at sma R and s ow y at arge Rrrnages1 Tm Hm r 39 39 At the rmmrnurn m Dew We recover the arw ar gmdmg orbn of radms Rg 25 7 7 33 392 33 Vi 69 6R 1 0 ath R BBL R9 Other orbrts Wm osaHaIe m radms about Rg Consrder the poterma 21R R9 x 76 e 7162 e5 7 7 BR Rq39 23R Rf Tm gwes SHM aboutthe gmdmg radms A 32 7N2 510 6R2 R quot Mt Xcoslct 5H wrm frequencm Where 621 z 645 SL2 d z H e3a39 PM 6R2 R a 6R R R3 1112 RE d Azimulhal Motion Smce LZ R92 19 R20 cona Changes m R yrerd changesm I reca I dot L 21 21 72 177 9 177 RA R9 9 R9 513 lntegratlon glVeS 232 X 9 sinltmt ngt 514 R9 29 e Tnus t tollowstne guldlrlg center wltn smal arnplltuoe SHM superposed aklrlg tne yams 1n tnetorwaro olreolon wltn orlglrl on tne guldlrlg center we nave 112 73Xsin0 at1wbo 515 tne osaHaIlorl of frequencyl 1stne Ems as n x but out of pnase by 90 Taken together and settlrlg tne 1n1t1al pnase U 0 we nave o x x oosm o yr20K gtlt SlrlU elliptical eplcycle wltn radlalazlmuthal ax1s ratlo K l 20 eplcydlc rnot1on 1sretrograde w rt orblt of Ptolernys were prograoe for stars of sarne 1 veloclty eHlpSOld 0R l 09 K l 20 a however at glverl R veloclty eHlpSOld 0R l 09 20 l K a for llteplenan n lx R52 we get K dosed eHlpSe centered at tne eHlpse focus as ratlo 21 of Ptolernys were 1 1 ardes o For at rotatlorl curven lx Rquot we gem sort2 n for solo bod rotatlorl 2 ns we gem 2 2 1n general lt K lt 20 so K gt n and eplcycle completed belore rotatlorl o Here 1s a model of srnall amphtude eplcychc rnot1on near tne am e Values Near the Solar Neighborhood lt 1s useful to rerexpress and 2 1n terrns of Oon s constants A and El a brlef derlvatlorl and rellew of Oort s oonstants can befound nere Oort s A expresses local shear 1t1s derlved from raolal velootles v l o A sn2l wnere llongltuoe Va 1R11S2 if 77 i 515a Ru 2 Ifll n AlsM p542 Oort s El expresses local voniciiy 1e local rotatlorl V x v 1t1s derlved from proper rnot1ons v l o A oos2l El 1 V 1V 1 19 2x2 7 J 7 7 i i 515m B 9Rr1R 2R11RRRD Rn Oment bea es umatefor Oort s E15712 4 0 6 kmskpc Together these gwe 20 A B e 1 72 ll srtBA s B 7432 no 37 km kpc 5 W 6170 a Star m the sotar netghborhood make 1 3 eptcychc excurstons per orbt a From dw9lt mass modets We ha e a Home aw shown here a for pewhar vetoaty 0R oz 30 kms We ha eptcyde Stzesrvo m1 kpc vemcal exwrsons 011 500 SHM mtght not be qmte Vahd for vemca molten a for the Sun W 7 kmsz dtrewon ghmg the excurstons shown here Note the sun passesthrough the dtsk mane every Myr Smhar penod 86Myr there 5 evtdence that speaes exttnctton Udal perturbattonsto the Oort doud may Next Prev Top 3 Resonances a Rotating Patterns and cratenng has a be responstb e Smuta on m hyrh m as these can have the shape of sptra and bar patterns these patterns are nether stamenary nor move wtth the dts stars vetoaty p the mterac uon of these patterns thh the eptcydtc motton can ead to resonances b Corotation Resonance CR Ftrs t oonstder a star Whtdw orbts at the pattern speed We havennp or nymso such stars experience a persistant nonaxisymmetric perturbation their response can build up epicycle phase rotates technically this is a resonance to azimuthal epicycle perturbation with natural frequency 0 c Lindblad Resonances lLR OLR 0 Consider stars which complete exactly 1 epicycle between the passage of each arm 0 their interaction with the spiral arm is resonant epicyclic amplitude is amplified and wave propagation is strongly modified where do such resonances occur in the galaxy the angular frequency of the star wrt the pattern is Up 9 there are two cases ve if gt Hp star moves past arms ve if Qp gt U arms move past stars angular frequency of encountering each arm in an m armed spiral is mmp 0 so condition for resonance is m p H or Dip zixlm notice that Hp 12 H is a special case of a two armed spiral with 9p lt 91 there are two classes of resonance p H m Inner Lindblad Resonance Hp Q 2 H m Outer Lindblad Resonance to establish the radii of these resonances one needs to know the pattern speed the rotation curve VCR which gives 2R and KR depending on VCR and Qp there may be 01 resonances images note there can be 012 inner Lindblad resonances d Importance of Resonances Resonances are important for several reasons density waves can only survive inbetween the lLR and OLR the forcing function must be slower than H to sustain the wave density waves cannot pass an lLR they are absorbed like waves on a beach important in allowingpreventing propagation across the disk through the center orbit shapes change across the resonances forcing belowabove natural frequency yields inout phase response outside lLR x1 orbits parallel to bar inside lLR x2 orbits perpendicular to bar outside CR orbits again perpendicular cf near nuclear orthogonal bars are common gt cf bars don39t extend beyond CR stop close to it gt bars probably rotate with pattern speed Hp RCR expect stellar rings to form at CR and OLR inner and outer rings do seem to correspond to expected CROLR locations gas driven inwards to lLR and outwards to lLR expect and find gas ringsdisksstarformation near lLR gas only runs into arm at R lt CR expect dust lanes and star formation ridges to fade out close to OR note that for the Milky Way estimates are for m2 lLR at 8ka OR at NMkpc and cm at 20kpci with ID 15 kmlskpc Nexll Prev Topl 4 Density Waves a Kinematic Density Waves ln generali orbits are not closed A4172 epicydes per orbit Howeveri oonsider aframe which rotates at 29 a v2 K a at 29 we with the guide oenter witnessiust the epicycle with no orbital rnotion a now go sower y is afteri eplcycle star moved through half an orbit after seoond epicycle back to start a orbit is closed in thisframe s orbit is ellipse with so at center s in general Us flKm will close after rn radia oscillationsl imagesl Now oonsider set of orbits whose epicydic phases vary monotonically with radius ie PA of ellipses rotates with increasing smple orbit crowding will generate atwo arm spiral pattern viewgraph roughlyi if 27 v2 KN constfor all radii then pattern lixed in rotating frame in floflrfotatlflg frarnei pattern rotates at a v2 K pattern speed for observed mm mg a v2 K isfarly ooflS LanL so pattern is quite long lived for mat rotation curvei howeveri pattern speed does vary slowly with R so spiral winds up but sower than material windup by factor 2p l 2 0 3 some improvement but still not adequate I Howeven 39 m 439quot h 7 h Ari this is a result ffofn deflsty wave theory to whidn we now turn b LinShu QSSS Density Wave Theory i Motivalion and Sketch of Approach The generation of kinematic spiras asslmeS axisymmetrie potentia Howeveri orbit crowding yields a nonaxisymmem39c spiral perturbation ar and gas orbits modilied bythe spira perturbation Their new orbits define a new surface densty and assooated potentia 39 utlofl The analyss is difficult Lin amp Shu 1954i 1955 and much subsequent work radius Look for 0888 Quas Stationary Sprial Structure a ien R N oons Study response of epicyclesto periodicforcing function asthey pass the spira arms This is recast aswaves propagating in a differentialy rotating disk Anaytic methods only Workfortlgh y wound spirals WKEI methods Derive a dispersion relation w fllt giving phase veloot Hlt and group velocity dw l dk wsfreouencyi k wavenum er difficulties are enoountered near the lLRi OLR OK but they are tractable ii Resulls QSSS solutions are found with Up dwdk gtlt 12H independent of R pitch angles 39l391quotR const yielding logarithmic spirals waves sustained if forcing frequency ml p QR is slower than KR this occurs between lLR and OLR note this region is larger for m2 than m4 so two spirals most common waves are absorbed at lLR wave response is reduced for disks with higher velocity dispersion probably need a quotcoldquot component to be continually replenished response of gas is nonlinear collisionsshocks above threshold images k2FIH2w2gt1 I where spiral potential is lIRquotfvquot F COSKR m with w forcing frequency 2 m p gas runs into itself cf traffic jams expect narrow gas features as observed predict velocity streaming in vicinity of arms calculations when tweaked seem to fit well cf Hl study of M81 images explains the fundamental correlation between BulgeDisk ratio and Pitch angle in Spirals Roberts Roberts amp Shu 1975 show geometry of density wave and strength of shock depend on a galaxy masssize Vrot and b central concentration This explains a correlation of pitch angle with BD ratio b at given stage pitch angle increases with lower luminosity gals c absence of dwarf spirals since in low mass galaxies the spiral shock is weakerabsent leading to dwarf irregulars iii Remaining Problems with 0888 despite much theoretical effort still unclear if LinShu QSSS important for real galaxies astrophysical complexities cold gas only 24 of volume hot gas won39t respond something else here unclear whether strength of many observed arms can be achieved passage through arms increases dispersion and therefore Q this will quench the arms and halt the process unclear whether creation of new cold component is sufficient to maintain process Careful study of 50 galaxies Kormendy amp Norman reveal few which may need 0888 0 Many galaxies have other causes of density waves eg tides bars ovals see below 0 Many most galaxies are flocculent with no obvious global spiral pattern 0 Yet other galaxies eg late Sc have large solid body rotation region coherent material arms can exist here no need for density wave c Alternative Sources of Global Density Waves There are two other obvious sources of density waves both m2 i Tides tidal field of passing neighbor creates a strong m2 perturbation early simulations eg Toomre amp Toomre 1972 nicely show strong outer arms arms did not however go to center viewgraph later simulations Toomre 1981 included selfgravity and did better images nowadays many simulations reveal a strong deep m2 spiral note however these spirals are transient ii Bars and Oval Distortions s e anotner s r rrne oerturbatronsr rrnagesr Sanders amp Huntley r 975 found a Weak oar generates strong sorra arrns Howeverr neeos viscosity re orssoatron vrscosrty stops the arm formatron eed a a rernorrng bar and orssroatron to form the oonousron sorrar arrns onlyn Next Prev Top 5 Disk lnstabilities and Their Amplification a Local Disk Stability Toomre39s 0 Parameter 7 Suor rnstaorrrtres togetner wrtn orrterentrar rotation may generate sorra structure o rnstaorrrtres can arrse from a oornoetrtron between granty causrng overoense regronsto corraose serrar orsoersr n Wnrcn rnnrortst corraose r momentum Wnrcn rnnrortstne corraose nsfor rnsaorrrtres oltr Wnere 2 ar wReeeez ere v5 rstne sound speed and X rstne total surface densty Lets look orretry at tne oerrvatron i Jeans Analysis Consroer overdense regron raorus R rn a nonrotating dl9lt o tne oorraose trrne lstcorr N R r v Wnere v N grantatrona verocrty N e M r R V R GM rR R3 GMJV R r e 2 2 rs surface densrty so t00H N tne trrne for stars to escape tne regron rs teSC N R r o 0 rs orsoe so collapse occurs lftcorr lt teSC r e 2 lt R r 0 a Tne crrtrca srzetorstability due to orsoersron rstneretore RJ lt02 r e E a New oonsroer a rotating disk tne rotar angurar verocrty rs Oort s oonstant El tne regron rsstable rf Foenmga gt Fgww rntnrscase RE2 6 Rm gt e X r 52 gt Tne crrtrcal srzeiorstability due to rotatron rstnerefore thedlsklsunmablelntherange RJ lt R lt Rm Rm 0 Cornornrng tnese and refore tne disk rs locally stable rf RJ gt re 0262 gt GilEr or care recallthaIElK2I4Uand 172nsoElA 8 Tnenna oorldltlorl ford19lt staolllty 1stneretore O E was GE gt 1 ii 0 from Disk Dispersion Helalions oonsdertnetlrne developrnentol Wave penurbatlorlslrl adlsk 6 1x exp 1 k rrLtt 518a 7 2nGElklFS2k IR Stars 51 Wnere vs Sound speed and F 1s a reduc tlon taoor see am 62d tne dlsk 1s unstable 1m lt0 for al K snce exp 71 Mt exp Tt Wltn W real Tnls yleldsfor staolllty E KVSWGE gt 1 0513 E ag88662 gt1 Factors Wnlcn prornote gravltatlorlal 1nstaolllty are low stellar veloot dlsperslon 0R nlgn surface rnass denslty X low eplcycllcfrequencles Note even for OgtLd19lts may all be vulnerable to global lns tabllltles rnodes Solar nelgnoornood 0R80 WW 1 E5o M p62 1K86 krnlskpc e glve o14 and sotne MW dlsk 1s locally staple near tne sun b Swing Ampli cation Some arwms tanoes allow a powerful arnpllncatlon of splral patterns eg Toomre1981 i The Swing Ampli er lf We nave a leading splral densty wave tnen dltterentlal rotatlorl W111 gradualy rotate 1t lrlto atrailing splra Wave 1 1rnagesl tne rotatlorl of tne pattern 1sretrograde tnetlrnesoaletorrotatlon1sllt a eplcydlc motlon approxlrnately lollows tne arrn a long penurbatlorl duratlorl so eplcyde arnpllned che emerglng tralhrlg pattern 1s strongly amplilied arnpllncatlon gain depends on O and Arad1a wavelengtn of patern 1rnagosl maxlm wnenA15 H wnere Am 4 7r 3 X l 52 snortestA normally staplllzed by rotatlorl for A gt 2 AW less effectwe staplllzed by rotatlorl lust d1sllt rlOlSe nas al A present 5 AW arnpllned l 1rnagesl asusud 2 This swing amplification is thought to be very important ii Feedback for the Amplifier For this to work we need a source of leading spiral waves however these are not normally generated in a rotating disk Instead look for feedback trailing waves converted into leading waves 0 waves reflected from outer edge experience 180 phase shift trailing leading unlikely to operate in real galaxies edges too soft o trailing waves passing through the center emerge as leading waves images this can only occur when we have no ILR which blocks wave passage Swing amplification with feedback is probably very important in maintaining strong sprial structure c Bar Instability and its Suppression NBody simulations of disks seem to form bars remarkably easily Indeed it is difficult to devise stable disk models even with O gt 1 Reality of this bar instability has been verified using analytic methods Here is an NBody simulation showing bar formation image multiarm spirals form first then two arms then a bar the bar lasts until the end of the simulation the instability can be suppressed with high dispersion as for spiral density waves Swing Amplification helps explain the instability recall leading waves are strongly amplified into trailing ones nothing happens unless there is a source of leading waves trailing waves pass through center and emerge as leading hence feedback keeps the amplifier going bar grows quickly recall waves cannot pass an ILR where Q lb 2 52 so for feedback to work need 2b gt H 52 everywhere simulations verify this and quotconfirmquot central tunneling as a source of feedback E uivaIent description involves epicyclic response to forcing function if Rb lt H2 then the forcing frequency is greater than the epicyclic frequency response is out of phase by7r feeds x1 orbits which extend along the bar gt bar can grow by accululating stars in x1 orbits However if ILR exists I Qb lt m2 response is in phase favours x2 orbits which are perpendicular to the bar weakens the bar Likewise outside corotation Q 9b lt m2 x1 orbits again suppressed while x2 orbits reinforced explains why bars rarely extend beyond CR Early work Hohl 1971 Ostriker amp Peebles 1973 noted the severity of the bar instability as usual increasing stellar dispersion can calm the instability they found disks were stabilized against bar formation for KEO KErot gt 5
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'