Galaxies Astro 530 Prof. Jeff Kenney

Transcription

1 Galaxies Astro 530 Prof. Jeff Kenney CLASS 8 February 7, 2018 Spiral Structure (Part 2) 1

2 Spiral structure in galaxies something interesjng that happens in a disk can reveal physical condijons in that disk can transfer angular momentum outwards otherwise doesn't greatly affect formajon & evolujon of galaxy

3 there are different types of spiral structure, but spiral structure requires: differen'al rota'on (for all) gas (for all but,dal arms) 3

4 Why low mass galaxies have weak spiral structure V rot (km/s) RotaJon curves of high & low mass galaxies 10 r (kpc) High mass disk (spiral galaxy) Large V max and flat at large r Low mass disk (dwarf galaxy) small V max and close to solid body rotajon 50 Ω = V rot /r (km/s/kpc) 10 Angular speed curves of high & low mass galaxies 10 r (kpc) High mass disk (spiral galaxy) Lots of differen;al rota;on (Ω varies a lot with radius) - > strong spiral arms low mass disk (dwarf galaxy) li>le differen;al rota;on (Ω nearly constant with radius) - > weak spiral arms

5 Gas needed for (most) spiral structure In order to have structures in a disk, the stuff making up the structure needs to have sufficiently small random mojons. If random mojons are too large, the stuff doesn t stay in the structure. Gas can have small random mojons. It is collisional and can therefore dissipate energy & dynamically cool (reduce mojons). Stars are collisionless. They can be dynamically heated (increase mojons) but not cooled.

6 S0 galaxies: Disk galaxies without gas & therefore no spiral structure

7 how long does spiral structure last in disk with only stars a]er gas removed? Unsharp Masked D99 Subaru D100 D100 in Coma cluster ongoing ram pressure stripping of gas no gas or star formajon in outer disk stripped~200 Myr ago - - sjll strong spiral structure in stellar disk (arm- interarm contrast ~2:1) HST Cramer+2018 D99 ram pressure stripped dust tail D99 in Coma cluster no gas or dust or ongoing star formajon star formajon stopped ~500 Myr ago due (probably) to ram pressure stripping; very weak spiral structure in stellar disk remains but will conjnue to fade (arm- interarm contrast ~1.05:1) 7

8 3 types of spiral structure physically 3 different things happening although common physical elements 1. Grand design spirals (density waves) 2. Flocculent spirals (stochasjc) 3. Tidal material spiral arms Can have mul,ple types of spiral structure within 1 galaxy Cri,cal common elements: differen'al rota'on (for all), gas (for all but,dal arms) 8

9 major merger simula;on: watch development of spiral features

10 M51 Outer arm Jdal? Tidal arms can drive strong density waves & be connected to density wave arms inner arms grand design 10

11 Grand design Spiral arms Spiral- shaped regions of enhanced density and enhanced star formajon Two effects make grand design Spiral arms 1. traffic jams of stars & gas in arms 2. Star formajon triggered in arms

12 Two effects make Grand design Spiral arms 1. traffic jams of stars & gas in arms Stars in arms now DON T STAY in arm, they pass through arm Arm is region of extra mass & density à extra gravity in arm causes stars to slow down a wave caused by disturbance to disk à arms are density waves

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14 V rot (km/s) Density wave palern Stars & gas Density wave as rotajng palern Ω = V rot /r (km/s/kpc) r CR r (kpc) NOTE - - in reality: Palern exists over limited range in radius Palern speed may vary Stars & gas differenjal rotajon with radius or Jme Can have more than Density wave palern one palern in galaxy Solid body rotajon stars & gas orbit faster than palern (road crew analogy) r CR r (kpc) stars & gas orbit slower than palern (traffic cop analogy) r CR = corotajon radius orbital speed of stars & gas match palern speed

15 I ll come back to discuss SDWs but first I want to discuss the other effect 15

16 Two effects make Grand design Spiral arms 2. Star formajon triggered in arms Gas cloud compressed when it enters density wave, triggering star formajon. The most massive young stars are blue and very luminous, AND they explode as Supernovae shortly a]er they form, before they get far from spiral arm. So luminous massive stars seen near arm, not between arms.

17 Density wave spiral arms rotajon blue stars downstream side of arm dust on upstream (leading) side of arm blue stars downstream from dust in spiral arms of grand design spiral galaxy M51 17

18 spiral density wave in gas with star formajon

19 Star formajon in density wave spiral arms OB stars explode as supernovae within a few 10 6 yr a]er formajon, leading to excess of young blue massive stars near spiral arm 19

20 arm of young stars NGC 2903 arm of old stars (density wave) star formajon offset from old stellar spiral arm 20

21 How spiral structure affects star formajon Star formajon rate /Area (Hα) flocculent grand design Arm Class Spiral arms have very li>le influence on large- scale star forma;on rates, but they do organize the pa>ern of star forma;on in a galaxy Doesn t affect rates in gas- rich inner disks probably since molecular gas there is already forming stars as fast as it can Might have bigger effect on SF in HI- dominated outer galaxy, since arms could make more dense molecular gas than would otherwise form (Elmegreen 2011) Elmegreen & Elmegreen

22 arms don t affect global SFRs much what do they do? they can redistribute angular momentum I will talk about this when we discuss BARS

23 back to SDWs 23

24 Arm- interarm contrast in grand design spirals Arm- interarm contrast in near- infrared (~old stars) in M51 is ~2:1-3:1 (large effect!) Rix & Rieke 1993 Spitzer 3.6µm image of M51 Lots of extra mass & gravitajonal force in arms 24

25 KinemaJcs of spiral density waves HI kinemajcs of Grand Design Spiral NGC 4321 SDWs cause perturbajons to Velocity field Observed perturbajon depends on distance from line- of- nodes Azimuthal streaming mojons observed along l- o- n (major axis) Radial streaming mojons observed perpendicular to l- o- n (minor axis) Chung etal

26 Compare to velocity field in Flocculent spiral NGC 4414 only weak kinemajc disturbances in arms HST HI intensity HI velocity field Hα image NIR image smooth component subtracted Thornley & Mundy 1997 While some weak stellar arms (density wave?) are seen in NIR image (arm enhancement ~30% above interarm), most of the star formajon (Hα) and HI is not associated with these arms & there are only small perturbajons to velocity field due to these arms à Most of spiral structure is stochasjc 26

27 spiral arms induce streaming (non- circular) mojons M51 CO velocity M51 Hα velocity M51 CO intensity M51 Hα intensity Shely+2007

28 Spiral arm streaming mojons in spiral density wave (deviajons from circular mojon) gas density model radial velocity CO data 2 spiral arms gas density radial velocity azimuthal velocity azimuthal velocity gas density must average over spiral arm streaming mojons to get good circular speed curve Shely+2007

29 How trailing arm perturbs orbit to strengthen itself Trailing spiral arm with extra mass True orbit perturbed by arm density Arm center Par to arm ~azimuthal Circular orbit Perp to arm ~radial NUCLEUS ParJcle is pulled outwards by extra mass of spiral arm. this slows it down in azimuthal (rotajonal) direcjon. It starts to fall back (radially) near the peak of the arm. Extra mass of arm keeps the orbit near arm for extra Jme, reinforcing arm. This works for trailing arm but not leading one, most effec,ve at certain pitch angle. Works for flocculent arms as well as density wave arms; for gas & stars. 29

30 Under what condijons does perturbajon to stellar orbit reinforce SDW? a.) arm is trailing b.) perturbing frequency < epicyclic frequency If periodic pull of spiral (perturbing frequency m Ω P - Ω ) is faster than natural in- out (radial) frequency of star on its orbit (epicyclic frequency κ), the stars cannot respond fast enough to reinforce spiral, so wave dies out 30

31 What is the orbit of the Sun in the Milky Way? 31

32 What is the orbit of the Sun in the Milky Way? at first ignore star- star collisions i.e., assume a spajally smooth & Jme- independent gravitajonal potenjal Φ Gravita;onal poten;al Φ(x) of star cluster or galaxy x this part! cumula,ve gravita,onal effect of all the more distant stars? Smooth part doesn t change (much) over Jme individual star- star gravita,onal encounter Steep parts due to individual stars move around as stars move The total potenjal is the sum of a smoothly varying shallow potenjal well due to the average effect of many distant stars, plus a steep potenjal well near each star. In some (but not all!) cases the steep potenjal well near each star can be ignored.

33 Point mass (Kepler potenjal) φ = - GM/r F = GMm/r 2 [NOTE: F~r - 2 ] v c = [GM/r] 1/2 Can have bound or unbound orbit bound orbits are ellipjcal with period T φ = T r = 2π [a 3 /GM] - 1/2 equal periods! closed orbit a = semi- major axis Get this by solving equajon of mojon Bound orbits are ellipses with gravitajonal center at one focus r 1 r a r 2 r p r 1 - =r a = apocenter radius r 2 =r p = pericenter radius center of ellipse is not at center of mass CM is one focus of ellipse

34 what is the radial distribujon of mass most opposite from a point source yet sjll physically stable? A. density ρ(r) ~ r - 1 B. density ρ(r) ~ r - 2 C. constant density D. density ρ(r) ~ r 1 E. density ρ(r) ~ r n

35 what are orbits like inside a Constant Density Sphere? sphere with radius r sph density ρ c examine orbits that are completely inside the sphere the central regions of some galaxies are not too different from constant density

36 Constant density sphere (spherical harmonic oscillator potenjal) φ(r) = - 2πGρ c (r sph2 - r 2 /3) r < r sph φ(r) = - 4πGρ c r sph3 /3r r > r sph sphere with radius r sph & density ρ inside sphere (r<r sph ), potenjal has the form: φ = - 1/2 W 2 r 2 + constant F = mω 2 r [NOTE: F~r ] spring constant v c = [4πGρ c /3] 1/2 r T φ = 2 T r = [3π/Gρ c ] 1/2 radial period is exactly ½ the azimuthal period! - > closed orbit Bound orbits are ellipses with gravitajonal center at ellipse center r 2 r p r 1 r a center of ellipse is center of mass

37 azimuthal period T φ Jme it takes for one full azimuthal cycle φ = 0 - > 2π radial period T r Jme it takes for one full radial cycle r = r 1 - > r 2 - > r 1 r 1 r 2 point mass T φ = T r constant density sphere T φ = 2 T r

38 mass distribujons ρ(r) in Galaxies are in between point sources & constant density spheres e.g. isochrone potenjal φ = - GM / (b + [b 2 +r 2 ] - 1/2 ) approaches constant potenjal as r- >0 approaches point mass as r >> b In general: T φ = β T r 1 < β < 2 star completes radial oscilla,on before moving 2π in azimuth In most cases β = 2π /Δϕ is irrajonal then orbit is not closed Bound orbits are roseles

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40 Rosele orbit

41 For orbit in plane of disk star oscillates in radius as it orbits κ = epicyclic frequency = 2π /T r = frequency of in- &- out (radial) mojon Ω = angular frequency = 2π /T φ = frequency of angular mojon For Sun in Milky Way: κ o /Ω o = 1.3 Sun makes 1.3 radial oscillajons for every complete orbit around GalacJc Center orbit not closed orbit is rosele T φ = 2π /Ω o = 240 Myr ( galacjc year ) T r = 2π /κ o = 170 Myr

42 epicyclic frequency = κ = 2π /T r frequency of in- &- out (radial) mojon κ 2 (R) = 2 V/R (V/R + dv/dr) Point mass (Kepler potenjal) V(R)~R - 1/2 κ = Ω 2 extreme cases: depends on: mass distribujon or rotajon curve & its gradient Constant density sphere V(R)~R κ = 2Ω in general Ω < κ < 2Ω

43 For orbit perpendicular to plane of disk star oscillates verjcally as it orbits ν = verjcal epicyclic frequency = frequency of up- &- down (verjcal) mojon For Sun in Milky Way: ν o /Ω o = 2.7 Sun makes 2.7 verjcal oscillajons for every complete orbit around GalacJc Center orbit not closed orbit is rosele T z = 2π /ν o = 87 Myr ν o [4πGρ o ] 1/2 for (nearly) constant density disk ρ o = density at disk midplane In general ν o depends on disk mass density and ver,cal mass distribu,on of disk

44 Orbit of star in disk of milky way showing verjcal mojon

45 How is this orbit wrong? (for Sun in Milky Way?)

46 How is this orbit wrong? (for Sun in Milky Way?) 1. Most orbits not closed 2. Sun makes ~2.7 verjcal oscillajons for every full (azimuthal) orbit, not 4

47 Under what condijons does perturbajon to stellar orbit reinforce SDW? PerturbaJon to stellar orbit reinforces SDW if: a.) arm is trailing b.) m Ω P - Ω < κ m = number of arms perturbing frequency < epicyclic frequency If periodic pull of spiral (perturbing frequency m Ω P - Ω is faster than natural in- out frequency κ, the stars cannot respond fast enough to reinforce spiral, so wave dies out There is a spiral arm pitch angle where this reinforcement is a maximum i.e. gravitajonal instability has maximum growth rate and this is the pitch angle that will form 47

48 Where in galaxy does perturbajon to stellar orbit reinforce SDW? perturbing frequency < epicyclic frequency m Ω P - Ω < κ inside CR, Ω>Ω P m(ω- Ω P ) < κ Ω- Ω P < κ/m - Ω P < κ/m Ω ConJnuous spiral wave can propagate only between ILR2 where Ω P = Ω-κ/m and OLR where Ω P = Ω+κ/m Ω P > Ω - κ/m outside CR, Ω<Ω P m(ω P - Ω) < κ Ω P - Ω < κ/m Ω P < Ω + κ/m ILR1 ILR2 48

49 M101

50 Hidden spiral modes in galaxies: evidence of m=2,3,4 spiral modes in galaxies M101 Sky- enhanced view Three- fold Symmetric image Two- fold Symmetric image Two- fold AnJ- Symmetric image Two- fold Symmetric Image with resonance LocaJons (I4:1, CR, OLR) Elmegreen etal 1992 Three- fold Symmetric Image with resonance LocaJons (I3:1, O3:1) 50

51 M51

52 Hidden spiral modes in galaxies: evidence of m=2,3,4 spiral modes in galaxies M51 Sky- enhanced view Three- fold Symmetric image Two- fold Symmetric image Two- fold AnJ- Symmetric image Two- fold Symmetric Image with resonance LocaJons (I4:1, CR, OLR) Elmegreen etal 1992 Three- fold Symmetric Image with resonance LocaJons (I3:1, O3:1) 52

53 How does disk respond when you kick it? Studying how waves propagate in disks tells us about physical condijons in disks which are otherwise unobservable Modes of ringing bell Seismology: Earthquake waves & earth s interior Helioseismology: Sun s waves & sun s interior

54 Preceding is for stars & stellar orbits what about gas? Simple spiral palerns made from oval gas orbits Gas orbits can t cross (gas is collisional) Gas doesn t follow epicycles like stars But gas can have streamlines (gas version of orbit) which reinforce spiral palern True gas streamlines generally not so simple may also have shocks 54

55 Another important condijon for the existence of spiral structure: Is disk dynamically cold enough for structure to form? 55

56 Is disk dynamically cold enough for structure to form? Toomre stability parameter Q: Fight of gravity vs. pressure & centrifugal forces from rota,on σ R = radial velocity dispersion κ = epicyclic frequency Σ = mass surface density If Q < 1 gravity wins, ~ structure can form Spiral arms Dense (star- forming?) gas clouds c s = sound speed σ = velocity dispersion Ω = angular frequency Σ = mass surface density 56

57 Disk stars can reinforce a spiral wave and help it grow only if random mojons are small enough not to take them outside spiral arms Structure can form in disk only if Q<1.5 If Q<1.5 in gas & stars, can have SDWs and flocculent arms If Q<1.5 in gas but Q>1.5 in stars, might get flocculent arms but no SDWs in stars If no gas à Q>1.5 in stars a]er a while, get SO galaxy with no arms 57