!
Self-gravitující disk s nulovou disperzí rychlostí
d Ti       1    ôRĽxR d£ve
-+ — {- + -} = 0
dt        R   ČR 06
d Vr Č Vr V0 Ô Vr Ve2 Ô Q> - +Vr- +----=--
dt dR R   dQ       R dR
ôyq ô\q Ve d Ve vR v0 1 d <l> -+vR-+--+ -=---
dt ÔR        R   d Q        R R ÔQ
d2®    1 1 d2® d2Q>
-+--+--+-        = 4 n G £(R, 9, t) ô(z)
d R2   R ÔR     R2 d 6    d z2
Počáteční rovnovážný stav: Lineární porucha:
E = £o (R) £ = So (R) + £i (R,6,t)
O = O0(R,z) O = 0>0(R,z) + $i(R,G,z,t)
vR=0 vR=vR1(R,e,t)
ve = V(R) = R Í1(R) > 0 ve = V(R) + vei(R,9,t)
■
Linearizace rovnic s poruchou
d £i          0Li    1   0R£oVri Ho^vei -+ íl -+--+--= 0
ôt 09     R 0R R ČO
0 Vri 0 Vri ô <Di
-+ íl--2 íl vei =--
0t 09 dR
ô Vei       ^ vei 10 G>i
-+Í1-+2 B vri =---
0t 09 R 09
02<J>!      1 0 0»!     1 02<D1 02€>!
-+--+--+-= 4nGZl ô(z)
0 R2    R 0 R     R2 0 9    0 z2
Elementární řešení (vlnové módy): Hustotní vlna spirálního tvaru
Ľi = £*(R) exp [i(cot - m9)] = L'(R) exp [i(a>t - mO + F(R))] £*(R) komplexní:      L*(R) = L(R) exp [ i F(R) ]
F(R): „fázový faktor" {phase factor),
„tvarová funkce" {shape function)
podobně pro <Di, vR1 a vei:
Oi=0* (R) exp[i(ot-m8)] Vri=Vri*(R) exp[i(ot-m9)] v6i= v61* (R) exp[i(ot - mQ)]
Frekvence vlny:
CO = COr + ÍG>i
oscilující módy:    | coR | » | coi |
tlumené: rostoucí: neutrální:
coi>0
coi<0 {overstability)
O)!=0
nestabilní módy:
- COi » I COr I
f vn* t: J, •     &s[i»e- FC It) - «.et)]
Hi
w fe, v. - *
2-7
■ <t> = *o
AO,—r
% 30 <
I
o ill
£ 'o
5
_     a s
So
Sb
RSA TYPE
Sc
Figure 6-12. Measured pitch angle as a function of Hubble for 113 galaxies (Kennicutt Reprinted by permission of The Astronomical Journal.
99
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pa
/
AUCH t M ESQ
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R sie „
• K*9tALMf'S£?A*A€£ Se>vS£&we# n»99 + Fa) »Co***
/^ŕ** a ft) -       » 2<r
✓is —- >©, *r*#0
# ítA^řA'uui' vínové ď/sio
XAM£NA
2-44
to the sun
<gt= receding    0=approaching
Figure 6-6. The appearance of leading and trailing arms. Galaxy A has leading arms, while galaxy B has trailing arms, but both exhibit the same pattern on the sky and the same radial velocity field.
To Ihc sun
Figure 0-7. Distinguishing near and far sides of a disk galaxy. The dots represent objects such as novae or globular clusters. There is an obscuring dust layer in the central plane of the disk which is shown as a line in the side view at left. In tne observer's view, at right, objects behind the dust layer are fainter and are shown as open circles.
__
2-4X
£4 + l4
ssJÖSSjS"*'
• O t STÉKÁN i X£L/\6£
t
?
9t
/ť^ ; 4T 4*tťýň,§ť se £4
Z? <"*4 * & * U/S.
2. * Ufr
p*= s. hr    C w)
O f SIC S NENVLOtŕOV
H víta ť:
i
t.
9C 9£
4
2-4h
7*fXlA& ' Af£fT£LVtS
xiCk)*
9€ s (iSL(lC)
in f SI
l/vy
2
o
^/kcrfl
1 2 trailing
Figure 6-14. (a) The dispersion relation for tightly wound disturbances in gaseous [eq. (6-40), dashed ,Iines] and stellar [eq. (6-^6), solid lines] disks. The curves shown are (bottom to top) Q = 1, 1.5, and 2. Since only [a| and \k\ are shown, there is no distinction between leading and trailing waves, or waves inside and outside corotation. (b) Dispersion relation in the form of wavenumber versus radius for an m = 2 tightly wound wave in a stellar Mestel disk with Q = 1.5. The radial scale is in units of the corotation radius rcRt       only waves inside corotation are shown. The inner Lindblad resonance is at r = 0.293rcR. The direction of the group velocity is shown by-arrows.
0.4 0.8 1.2
Wavelength, X/Xcrjj
Figure 4 The Lin-Shu-Kalnajs dispersion relation for iixisynimctric density waves of lo frequency (u = VK and modest radial wavelength /. in a thin, rotating disk of stars endov with Q times the minimum random motions required by Equation (3).
Lindblad resonance Corotation
X/X,
Ftc. 6 — Dispersion relation .\( v ) for tlrnsity waves (Lin aiul Shu). The arrows show the direct ion of propagation of the waves. Q measures tilt" velocity clispfrsion.