AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter...
Transcript of AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter...
![Page 1: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/1.jpg)
AS1001:Extra-Galactic Astronomy
Lecture 5: Dark Matter
Simon Driver Theatre [email protected]
http://www-star.st-and.ac.uk/~spd3
![Page 2: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/2.jpg)
Stars and Gas in Galaxies• Stars form from gas in galaxy• In the high-density regions the gas is
converted into Stars
– Elliptical: very little gas content– ~ all gas converted into stars =>
– Spiral: some gas content• most gas converted =>
– Irregular: lots of gas• little gas converted =>
![Page 3: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/3.jpg)
Distribution of Gas and Stars
STARLIGHT GAS (HI)
M82
NGC 3077
M81
![Page 4: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/4.jpg)
Dark Matter• However, we believe that GAS+STARS
only make up 10% of a galaxies total mass• The rest is in the form of DARK MATTER• We believe this because of the rotation
curves which imply more mass than we candetect in STARS+GAS
• Lets see why…
![Page 5: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/5.jpg)
Galaxy Rotation
• Galaxies form via collapse due to gravity• As they collapse the rotation increases
(conservation of angular momentum)
• Eventually, equilibrium is reached:
GRAVITATIONALFORCE = ROTATIONAL
FORCE
![Page 6: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/6.jpg)
Equilibrium• INWARD FORCE = GRAVITY
– M=Mass interior to radius r– m=Mass of a typical star
• OUTWARD FORCE = CENTRIPETAL
![Page 7: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/7.jpg)
The Virial Theorem• The Virial theorem applies when the galaxy is
in equilibrium and we can equate these twoForces:
• v = the velocity of rotation at radius r whichdepends only on the mass interior to r
mv
r
![Page 8: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/8.jpg)
The Mass of a Galaxy A star at the edge of a distant galaxy has a
velocity about the galaxy’s centre of 200km/s. Its distance from the centre of thegalaxy is 15 kpc. What is the mass of thegalaxy ?
![Page 9: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/9.jpg)
The Mass-to-light Ratio For the same galaxy if its absolute magnitude
is -20.5 mags what is its mass-to-light ratio ?
So the mass-to-light ratio (within the stellar disc) is:
![Page 10: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/10.jpg)
The Mass Distribution• Stars and gas are centrally concentrated• Hence if stars trace the mass then the mass
must also be centrally concentrated• Stars at large radii should see almost all the
mass, i.e.,
• If stars trace mass:A B
We need to measure v as a function of r => Rotation curve
![Page 11: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/11.jpg)
Measuring Rotation CurvesTake spectra at different locations in the galaxy
The two spectra are slightlyoffset and this differencegives a velocity difference between the centre and theedge of the galaxy
I
I
λΔλ
![Page 12: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/12.jpg)
Rotation Curves• As the stars and gas
are centrallyconcentrated weexpect: v ∼ r -0.5
• But by measuringrotation curves weobserve:
• A flat rotation curvebeyond the stellarpopulation
RADIUSV
ELOC
ITY
RADIUS
VELO
CITY B A
B A
=> Additional Mass Component
![Page 13: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/13.jpg)
A Universal Flat Rotation Curve
![Page 14: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/14.jpg)
Implication• At large radii:
• Hence:
• i.e., Mass is proportional to radius• Or:
• This is the equation for an isothermal sphereand implies a spherical halo of extra mass
![Page 15: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/15.jpg)
Our Working Galaxy Model
BULGEDARK MATTER HALO
STELLAR DISK
HI GAS DISK GLOBULAR CLUSTER
COMPANION
![Page 16: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/16.jpg)
Dark Matter in Galaxy Clusters• Pre-dates rotation curve observations and
analysis• Discovered by Fritz Zwicky (1930s)• Motions of galaxies within clusters suggests
clusters should not be bound: very largevelocities observed
• The fact that clusters are bound indicatesmore mass than present in luminous matter
• Dark matter required to keep cluster bound
![Page 17: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/17.jpg)
Conclusions• All spiral galaxies have flat rotation curves• Stars do not trace the mass• Stars are a minor mass component, about 10%• Some kind of DARK MATTER must exist• It must be distributed in a large outer halo
![Page 18: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/18.jpg)
DARK MATTER candidates• Normal (i.e., Baryonic)
– Ionised gas– Cold dust– Planets– White dwarfs– Black Holes– MACHOS (Massive Compact Halo Objects)
• Exotic (i.e., non-Baryonic)– WIMPS (Weakly Interacting Massive Particles)– Neutrinos (A wee bit of nothing that spins)
![Page 19: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/19.jpg)
Alternatively…• We do not have the correct theory of gravity• In the same way that Newtonian gravity
could not explain all observations (e.g.,Mercury’s orbit), General Relativity maynot be the whole story…
• We either need an observationalbreakthrough to “discover” dark matter, or aconvincing theoretical model
![Page 20: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/20.jpg)
Class Test Next Tuesday• 8 questions, each worth 5 marks, try all 8• 4 questions on The Galaxy• 4 questions on Galaxies & Cosmology
• G&C: first six lectures (I.e., inc this week)
![Page 21: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/21.jpg)
Lecture 1: Distances• Standard Candles:
• Period-Luminosity relation / Cepheidvariables•DON’T: remember formula•DO: understand calibration; importance of Cepheids•Calculate d given P, m•Calculate m given d, P
![Page 22: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/22.jpg)
Lecture 2: Galaxy Morphology• Hubble tuning fork; why not evolutionary
sequence• Galaxy types: Ellipticals, Spirals, Irregulars• Main features of each type. Components• Why are ellipticals red?• Understand: young & hot = blue
old & cool = redi.e., Bν(T*) ; L ~ T 4 (Keith’s course)
![Page 23: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/23.jpg)
Lecture 3: Galaxy Fundamentals
• How many stars? Assume FG = n*F*
F* = “Average star”Use:
• Formation scenarios. Observations for & against• Space density of galaxies: what d and V can we
see if we observe m = 14 and we know M = -20• How far apart are galaxies?• How are galaxies clustered? Soap suds, galaxies
found on the bubble surfaces: filaments & voids
![Page 24: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/24.jpg)
• Mass to Light ratios:
X = 1 for Sun; X ~10 for a galaxyGalaxy M/L ratios indicate dark matter
• Average density of Universe
![Page 25: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/25.jpg)
Lecture 4: Galaxy Spectra• Continuum; Absorption lines; Emission lines• 4000A break: blanket effect of absorption in
stellar atmospheres. Strong in ellipticals, weakerin spirals, absent in irregulars.
• Absorption lines: metals in stellar atmospheres => old stars => ellipticals, spiral bulges
• Emission lines: hot gas ionized by hot stars => young stars => spiral disks, irregulars
• Radial velocities:
![Page 26: AS1001:Extra-Galactic Astronomystar-spd3/Teaching/AS1001/eg5.pdf · Lecture 5: Dark Matter •Virial Equilibrium: Rotation = Gravity => circular orbits: •Calculate galactic masses](https://reader033.fdocuments.in/reader033/viewer/2022050405/5f824001454e5b48383e1b61/html5/thumbnails/26.jpg)
Lecture 5: Dark Matter• Virial Equilibrium: Rotation = Gravity
=> circular orbits:• Calculate galactic masses given v and r• Rotation curves: stars trace mass => v ~ 1/r0.5
Observe: v = constant => additional mass• v = const => ρ ~ 1/r2 => spherical isothermal halo• Dark matter in galaxy clusters: galaxies moving
too fast to stay bound• Conclusion: 90% of the Universe is made up of
dark matter… OR we have wrong theory of gravity