ASTRO&310:&& &&&&Galac/c&&&Extragalac/c ...disrupted&Sagitarius&dwarf&galaxy,& currently&merging&with&the&Milky&Way& 31 Simulaon&of& /dal&disrup/on& of&Sagitarius& dwarf&galaxy&...

ASTRO 310: Galac/c & Extragalac/c Astronomy

Prof. Jeff Kenney

Class 15 October 24, 2018 Tidal Interac/ons for Galaxies & Star Clusters

/mescales of Local Group a small loose group of galaxies

calculate /mescales ..but now “par/cles” are galaxies not stars! N = 3 (# of large galaxies) R = 0.5 Mpc n = 10 gal Mpc-‐3 σ  = 200 km/s

tcross = 2x109 yr < tH so group should be virialized trelax = 109 yr < tH so 2-‐body encounters have changed orbits tcoll = 1010 yr ~ tH so collisions & mergers important in groups all $mescales short so galaxy-‐galaxy gravita$onal encounters (both direct collisions & near misses) important in galaxy groups

Tidal forces

Gravita/onal force ac/ng on extended body

If we subtract the force at the center of mass, we get the differen$al gravita$onal force = $dal force To observer at center, the near & far sides are experiencing accelera/ons which differ from its own

Tidal disrup/on of dwarf galaxy companion of M31

Tidal arms

NGC 205

Interac/ng pair of large

spiral galaxies

Tidal arms

Tidal tails of halo globular cluster

Palomar 5

6

Palomar 5 Op/cal image

Stellar /dal tails extend from Pal 5

The outer parts of Pal 5 are being /dally disrupted by gravita/onal force of MW as Pal 5 orbits MW

effects of /dal interac/ons

•  removal of outer par/cles by $dal stripping

•  add KE to unstripped par/cles by $dal hea$ng

•  trigger forma/on of bars and 2-‐arm spirals (both m=2 modes) in disks of galaxies

Tidal forces

Gravita/onal force ac/ng on extended body


examine gravita/onal force exerted by companion galaxy M (~point source) on 3 stars within extended galaxy m

M

companion galaxy M

extended galaxy m

aN aC aF R

r r

gravita)onal accelera)on on 3 stars: NEAR aN = GM/(R-‐r)2 CENTER aC = GM/R2 FAR aF = GM/(R+r)2

view of differen/al accelera/on (/dal accelera/on) across extended galaxy

M

companion galaxy M

extended galaxy m

ΔaN ΔaF R

r r

)dal accelera)on on 2 stars: NEAR ΔaN = aN -‐ aC ≅ + aC (2r/R) = +2GMr/R3 FAR ΔaF = aF -‐ aC ≅ -‐ aC (2r/R) = -‐ 2GMr/R3

toward companion

away from companion

Q: Why does the earth orbit the Sun, but the /dal force on the earth is greater from the Moon?

Tidal force falls off as R-‐3

•  Gravita/onal force on earth from Sun greater than from Moon (since Gravita/onal force falls off as R-‐2 ) … but…

•  Tidal force on earth from Moon greater than from Sun (since Tidal force falls off as R-‐3)

QUESTION •  The water /des on the 2 sides of the earth are the same size, but the /dal arms in interac/ng galaxies are generally different sizes – WHY?

Lunar /des on earth

r R

r/R<<1 for earth-‐moon system (r/R = 1/30) so the 2 /dal bulges on the earth are symmetric

actual photo of earth & moon taken by OSIRIS-‐REX spacecran

Tidal arms in interac/ng galaxy

pair Arp84

r/R~1 for these interac/ng galaxies so the 2 /dal arms of the northern galaxy are NOT symmetric

R r

QUESTION & ANSWER

•  The water /des on the 2 sides of the earth are the same size, but the /dal arms in interac/ng galaxies are generally different sizes – WHY?

•  In many galaxy interac/ons r/R~1 NOT r/R<<1 (i.e., distance at closest approach is comparable to galaxy size) so 2 /dal tails are produced but they are not symmetric

Tidal stripping

Radial distribu/on of starlight in globular cluster M92

Sharp trunca/on at “/dal radius” due to /dal interac/on with Milky Way Galaxy

Tidal radius

when is material /dally stripped from object m?

r R

M m

Tidal radius can a mass hold it itself together by self-‐gravity against 5dal force across it exerted by the gravity from another body?

•  Is not where the gravita/onal force from m and M are equal

•  Is where gravita/onal force from m ( Fm ) is equal to the difference in gravita$onal force from M at center and ‘edge’ of m ( ΔFMce )

ΔFMce Fm

r/dal

m M


r R

M m

masses must be orbi/ng but first we will ignore that fact


r R

M m

masses must be orbi/ng but first we will ignore that fact

When is material /dally stripped from an object?

1. Rough approxima/on: ignore the fact that the masses M and m must be orbi/ng each other. i.e., ignore centrifugal forces r/dal = (m/2M)1/3R

stuff at distance r from center of m will be stripped if r>r/dal


1. Rough approxima/on: ignore the fact that the masses M and m must be orbi/ng each other. i.e., ignore centrifugal forces r/dal = (m/2M)1/3R Q: When are /dal impacts on m large?


1. Rough approxima/on: ignore the fact that the masses M and m must be orbi/ng each other. i.e., ignore centrifugal forces r/dal = (m/2M)1/3R Q: When are /dal impacts on m large? A: when r/dal is small -‐> when R small, m small, M large -‐> close interac$on & big difference in mass



2. Beter approxima/on: take into account centrifugal force associated with circular orbit of m around M r/dal = (m/3M+m)1/3R [deriva/on given in S&G, with r/dal -‐> rJ , R -‐> D ]



2. Beter approxima/on: take into account centrifugal force associated with circular orbit of m around M r/dal = (m/3M+m)1/3R [deriva/on given in S&G, with r/dal -‐> rJ , R -‐> D ]

3. No approxima/on: the orbits of most galaxies and star clusters are not circular. Solu/on is complex. Effects largely determined by distance of closest approach. Get rough solu/on by using #2, with R= distance of closest approach

Interes/ng behaviors of /dal radius 5dal stripping as runaway process… •  mass m of stripped objects drops as it gets stripped, so /dal radius r/dal shrinks – could be runaway process r/dal = (m/2M)1/3R

is it stripped or not?? … for elongated orbit … •  /dal radius shrinks as object gets closer to center (R gets smaller), so more stuff stripped …

•  but /dal radius expands as object gets further from center (R gets larger), so stuff can get re-‐captured !!

changes in /dal radius on elongated orbits

R R

R

rt

rt

rt

orbit direc/on large /dal radius rt when far away (large R)

/dal radius becomes large again aner closest approach when R gets large again – may recapture stars lost at closest approach!

smallest /dal radius rt at closest approach (smallest R)

Structure of /dal tails

•  Direc/on of 2 /dal arms rela/ve to orbital mo/on of main body: arms roughly fall along orbit of main body (WHY…?)

•  Inner tail (closer to central body) is the leading tail – par/cles orbit faster Outer tail is trailing tail – par/cles orbit slower (this is as expected -‐-‐ the orbital /me is faster closer to the central body)

To central body (Milky Way)

Some halo globular clusters originate from the /dally disrupted Sagitarius dwarf galaxy, currently merging with the Milky Way

31

Simula/on of /dal disrup/on of Sagitarius dwarf galaxy

Simula/on of /dal disrup/on of Sagitarius dwarf galaxy

interes/ng behaviors seen in this simula/on: 1.  /dal interac/on triggers bar and spiral arms (both m=2 structures, like /des) in large galaxy

2.  small galaxy originally in circular orbit – outer parts /dally stripped, inner core sinks to center. this sinking process is like mass segrega/on – massive thing sinks to center, less massive par/cles (stars) move outwards

bars in galaxies

something interes/ng that happens in a disk can drive some stars out of disk plane to make par/cular type of bulge (pseudobulge) cause large gravita/onal torques which drive material radially inward or outward drive secular evolu$on of disk galaxies

Classic barred spiral NGC 1300

37

NGC 1300 HST

Dust lanes along leading edges of stellar bar (generally true) Not much star forma/on along bar (not always true) Spiral arms emerge from bar ends (not always true)

Bars exist in spirals, S0s, dwarf irregulars

38

NGC 4608, barred S0

NGC 5020, barred spiral

LMC , barred irregular (Sm)

don’t need gas to have bar (unlike spiral arms) -‐-‐ stellar orbits can support a bar in some dwarfs the bar is

offset from galaxy center

>50% of spirals & S0s have bars

What are bars? Descrip5on of morphology:

•  Elongated linear feature of extra stellar mass density

•  In disk plane: bars elongated ~2.5:1 -‐ 5:1

•  Perpendicular to disk plane: most stars near disk plane but at some radii in some bars stars get far from disk to make peanut-‐shaped bulge

39

Stellar orbits in bars

40

RCR Corota/on radius

Many stellar orbits highly elongated in direc/on of bar. Such stars make up the bar. Athanassoula (1992) models

Unlike stars in density wave spiral arm, stars in a bar STAY IN THE BAR

Figure shows some of the closed orbits in a simple model of a barred galaxy. These closed orbits are only a subset of all the stellar orbits, but there are enough stars on similar orbits in many real galaxies to make a bar.

stellar bars have large m=2 component

41

Meaning of m=2: Azimuthal distribu/on of something (e.g. light, mass) described by I(θ) = I0cos(mθ), where m=2 as you go around once, you encounter 2 peaks & 2 troughs

θ

θlight intensity

bar

Tidal forces

External gravita/onal force ac/ng on extended body


Tidal forces have dominant m=2 component

Bars can be triggered by /dal interac/on or minor merger

/dal interac/ons have strong m=2 component, so ideal for triggering m=2 bars or spiral arms

43

NOTE: the bars in these galaxies are not necessarily caused by this /dal encounter!

Does this galaxy have a bar?

45 NGC 253 in op/cal

Bars easier to see in NIR

46 NGC 253 in NIR (2MASS)

Bars easier to see in NIR dust ex/nc/on at op/cal λs can hide bars

47

NGC 253 in op/cal NGC 253 in NIR (2MASS)

Bar frequency higher in NIR studies than op/cal studies, since the underlying stellar mass distribu/on is traced beter in NIR.

Stellar bar does not appear to extend above the dust in disk, indica/ng that the stellar bar is NGC 253 is a THIN DISK component

ASTRO 310: Galac/c & Extragalac/c Astronomy

Prof. Jeff Kenney

Basics on the Forma)on of the Elements these slides won’t be covered in class. please review before

Lecture 16 (Mon Oct 29)!

Lunar /des on earth

r/R<<1 for earth-‐moon system (r/R = 1/30) so the 2 /dal bulges on the earth are symmetric

r

R

ASTRO&310:&& &&&&Galac/c&&&Extragalac/c ...disrupted&Sagitarius&dwarf&galaxy,& currently&merging&with&the&Milky&Way& 31 Simulaon&of& /dal&disrup/on& of&Sagitarius& dwarf&galaxy&...

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