8. Galactic rotation 8.3 Rotation from HI and CO clouds

ASTR112 The GalaxyLecture 5

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8. Galactic rotation 8.3 Rotation from HI and CO clouds 8.4 Best rotation curve from combined data9. Mass model of the Galaxy


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Galactic rotation from HI and CO clouds

For disk objects in a differentially rotating galaxy,

The radial velocity, VR is amaximum at point P along agiven line of sight, when α = 0 and Rmin = R0 sinl.

lR

lV

sin)(

sincos

OO

OR


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At point P one obtains

lVlRR

lV

lV

RR

RR

sin(max))sin(

sin(max)

sin(max)

ORO

OR

OR

min

min

Procedure:For a number of longitudes l, find VR (max) for 21-cmradiation from HI clouds along that line of sight, andhence obtain Θ(R). This works for R<R0 only.


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HI cloud radial velocities along a given line of sight


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HI radial velocities are a maximum in thisdirection for gas at position A, where thevelocity is about 70 km/s. The cloud at A

has a galactic orbital radius of R0sinl


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• For R>R0 (directions 90º < l < 270º) there is no maximum in radial velocity.• But for R>R0 we can use CO in dense molecular clouds. These are often associated with star-forming regions, and there are ways to estimate distances to stars and hence to the CO• Then obtain the outer parts of the galactic rotation curve from

• Note that when distance d to a cloud is known, then both angle α and orbital radius R are also known

cos/)sin()(OR

lVR


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Rotation curve for the Galaxy

• The best rotation curve Θ(R) for the Galaxy comes from combining radial velocity data for stars, HI clouds and CO in dense molecular clouds• Result: Θ varies little with radius, though there are dips at around R = 3 kpc and 10 kpc• Mean velocity of galactic orbits is Θ ~ 220 km/s• This “flat” rotation curve is a major surprise• Expected result, if galactic mass is from stars, is Θ ∝ R -½


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Galactic rotation curve Θ(R) based mainly on CO.The “flat” (i.e. nearly constant) curve is evidence

for extra mass in the form of dark matter in the Galaxy


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Rotation curve for the Galaxy, based mainly on HI clouds


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The galactic rotation curve

R (kpc) Θ (km/s) P (106 yr) ω (rad/Myr)1 220 28 0.222 205 60 0.103 195 95 0.0664 215 110 0.0555 220 140 0.0457 225 190 0.0338.5 (R0) 220 240 0.02610 210 290 0.02112 225 330 0.01914 235 370 0.01716 235 420 0.015


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Mass model for the Galaxy

(a) Models with essentially all the mass in the centre of the Galaxy.

M mass of GalaxyP orbital period for stars at radius R; P = 2πR/ΘΘ(R) orbital velocity G gravitational constant


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For central mass or point mass models

2

12

1

3

2

24

RR

GM

RGM

P

Θ ∝ R-½ is not observed, showing that theGalaxy must move under the gravitational influence of a distributed mass.


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(b) Models with a uniform star density everywhere

RG

GRR

GM

RM

2

1

2

122

1

3

34

34

34

This model predicts Θ∝R and ω=Θ/R= constant,(solid body rotation) which is also quite differentfrom the observed rotation curve.


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The discrepancy between the observed galactic rotation curve and those predicted by two verysimple mass models of the Galaxy.


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The real mass distribution

The real mass distribution must be intermediatebetween a central mass concentration and auniformly distributed mass. That is the mass isdistributed throughout the Galaxy, but the density is decreasing outwards.

The fundamental problem: The density from the masses of all the observed stars plus ISM also decreases outwards, but far more rapidly than can account for a flat rotation curve.


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The rotation curve that would be produced by bulge and disk stars is not enough to produce the flat curve actually observed. A large dark matter halo must also be invoked.


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Mass model of the Galaxy (M. Schmidt, 1965)Radius surface density mass inside cylinder R (kpc) σ (M⊙ /pc2) of radius R (109 M⊙)

1. 1097 113. 646 315. 421 578.5 181 9810. 114 11112. 66 12314. 42 13116. 28 138


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Maarten Schmidt’s mass model of 1965 was a fairly early attempt. It had a total galactic mass inside a radius of 18 kpc of 1.43 × 1011 M⊙

More recent models give several times this mass, orabout 3.4 × 1011 M⊙

Of this mass, dark matter in the halo may account formore than 2 × 1011 M⊙ while the remainder is

observable mass in the form of stars or ISM.


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The nature of dark matter?

This is one of the big unsolved problems ofastronomy.

The dark matter in the Galaxy and other galaxiesmay be:• lots of very low mass and low luminosity stars, such as red dwarfs, brown dwarfs or white dwarfs• numerous black holes• some form of matter, possibly as subatomic particles which are so far unknown to science


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End of lecture 5End of lecture 5

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8. Galactic rotation 8.3 Rotation from HI and CO clouds