White dwarfs, black holes, dark matter · The discovery of white dwarfs: SiriusB 1844 Friedrich Wilhelm Bessel 1844 The motion of Sirius Sirius A and B Frank Verbunt ( Dept. Astronomy

Frank Verbunt

White dwarfs, black holesand dark matter

Quantum mechanics and

General Relativity

Wageningen 26 March 2015

Outlinediscovery white dwarfs

quantum-mechanics:pressure

gravity and pressure:maximum mass

discovery neutron stars

general relativity theory

general relativity tests

black holes

the Universe

dark matter & energy

Frank Verbunt ( Dept. Astronomy Nijmegen) White dwarfs, black holes, dark matter March 26, 2015 1 / 37

The discovery of white dwarfs: Sirius B 1844

Friedrich WilhelmBessel 1844

The motion ofSirius

Sirius A and B


Why are white dwarfs different?

From light to densitythe amount of light emittedby a star increases with thearea of its surface and withits surface temperature

Sirius B has (almost) thesame temperature asSirius A

but emits only 0.0001 asmuch lighthence: its

I surface area is 0.0001,I radius 0.01,I density 106

times that of Sirius A

More accuratelySirius A: a normal star

massa 2 × that of Sun

radius 1,7 × that of Sun

density 0,4 × that of Sun

(density Sun: 1.4 × water)

Sirius B: white dwarf

mass 1,0 × that of Sun

radius is 0,0084 × that ofSun

density 1.7 × 106 that of Sun


The simile of the Swiss village

Mayor Heisenberg

hotel rooms have

minimum size

Policeman Pauli

maximum 2 persons in

each room

Average priceLow-season: freechoice of rooms.High-season: manyrooms full; averageprice high


Quantum-mechanics: ‘rooms for velocity’

Chandrasekhar

application to whitedwarfs

Heisenberg uncertainty relation, Pauliexclusion principle

p is momentum = mass × velocityh is side of cube ( Planck constant)

electron: 0,00072 m/s proton: 0,000 000 4 m/s


Velocity and pressure; stellar structure

Pressurea particle collides: force:mass × velocity =momentum

many particles: pressureideal gas: higher pressurewhen

I temperature higher: highervelocities

I density higher: moreparticles

at very high densitypresseure depends only ondensity

‘degenerate pressure’

Equilibrium in stargravity pulls star in

pressure-difference pushesout

star settles at equilibrium

ordinary star: pressure ofideal gas

without source of energy starcools and constracts

white dwarf: degeneratepressure

size unaffected by cooling


Maximum mass of white dwarf

White dwarfs of increasing massa low-mass white dwarf is fullynon-relativistically degenerate(v � c)a heavier white dwarf

I is smallerI has a relativistically

degenerate center (v ' c)

the heavier the white dwarf, the(fractionally) larger therelativistic center

until at Mch the whole dwarf isrelativistically degenerate

Maximum mass of white dwarfwhen a white dwarf massexceeds Mch

I central pressure increasesI gravity increases faster

no equilibrium betweenpressure difference andgravity possible

gravity wins: the white dwarfcollapses

hence Mch is maximum mass


From neutron to the prediction of neutron stars

1932 Chadwick discoversneutron

1934 Baade & Zwicky predictneutron star

radius compared to that ofwhite dwarf scales as massof electron to that of neutron:Rns

Rwd=

me

mn× 25/3 '

1580

14 mile diameter

too small to detect . . .

formation = supernova

LA Times 19 jan 1934⇒


Crab pulsar in visible light: 30 rotations/s


Philosopher George Berkeley criticises Newton

Berkeley 1685-1753in an empty universe rotationand distance are not defined:hence they do not exist. ‘noabsolute space’

example: bucket of waterI in space with stars: water

rises along edge inrotating bucket

I in empty space: waterdoes not rise

I (Newton: water rises inboth cases: ‘absolutespace’)

picture of merry-go-round:‘Mach principle’ inspirationfor Einstein


SRT: Special Relativity - Theory: velocity of light

low velocitiesvelocity ball w.r.t. cyclist:20 + 30 = 50 km/h

high velocitiesvelocity light w.r.t. cyclist:200 000 + 300 000 , 500 000 km/sbut 300 000 km/s! how can this be?velocity = distance / time:something wrong with distanceand/or time


General Relativity - Theory: heavy and inert mass

a heavy mass is strongly attracted by gravity, e.g. from Earth; a lowmass less so

it takes more effort to bring a heavy mass into motion than a lightmass: the inert mass of a heavy object is bigger

as a result a low-mass object falls equally fast as a heavy one: heavymass = inert mass. Accidentally? Newton: yes. Einstein: no!


GRT-: simple axioms, complicated mathematics

AxiomsSRT: velocity of light thesame for all observers atconstant velocities

ART: velocity of light thesame for all observers ataccelerating velocities

acceleration = gravity

Einstein 1915re-writes physics

horrendously complicatedmathematics

needs help from Hilbert. . .

General relativityComplicated mathematicalequation can only be solved intwo very simple cases

1. spherical mass inotherwise empty universe(classical tests of GRT)

Schwarzschild solved thiscase analytically!Consequence: black hole

2. homogeneous andisotropic universe

Nowadays: fastest computerssolve other problems numerically(e.g. two masses)


GRT: the field equations of Einstein 1915

distribution of mass = curvature of space-time


GRT-: differences with Newton’s gravity

Distances in GRTin empty space thecircumference of a circle isO = 2πr

near a massa the circumferenceof a circle is O < 2πr

to draw this we must draw ahollow

Consequences: 1long axis of ellipse advances(Einstein 1915: Mercury)


GRT: the classical tests

Consequences: 2light follows curved orbit nearmass (Eddington 1919: solareclipse)

this made Einstein famous

Consequences: 3distances in direction ofmass are longer (Shapiro1964: Venus 0.0002 s)


GRT: binary neutron stars and stronger tests

neutron-star binary: orbital period 8 hr

rotation long axis ellipse: as much in one day as Mercury in a century!

orbit shrinks due to emission of gravitational radiation



2 effects determine masses of neutron stars; 3rd effect tests GRT

PSR1913+16 PSR J0737−3039



The accurracy of the pulsar as a clock allows unprecented accurracy indetermining the orbit (period, eccentricity, masses of the neutron stars).

PSR1913+16 PSR J0737−3039,valid on 6 July 1984 30 May 2004pulse-period P 0.059030002593481(7)s 0.022699378599624(1)sderivative P 8.62713(8) × 10−18ss−1 1.75993(5) × 10−18ss−1

2nd derivative | P | < 2 × 10−29s s−1

orbital period Pb 0.322997448930(4)d 0.10225156248(5)dderivative Pb −2.4184(9) × 10−12 −1.252(17) × 10−12

eccentricity e 0.6171338(4) 0.0877775(9)periastron-motion ω 4.226595(5)◦yr−1 16.89947(68)◦/yrmass pulsar M1 1.4414(2)M� 1.3381(7)M�mass companion M2 1.3867(2)M� 1.2489(7)M�


GRT: strong effects and the black hole

deeper depression for larger mass

when the ratio radous / mass becomes too small, the bottom dropsout: the distance to the edge (the ‘horizon’) is infinite

we call this a black hole

to understand this we consider first the Newtonian dark star


Gravitation according to Newton: the dark stsr

Michel 1784, Laplace 1795the escape velocity vescdepends on ratiomass/radius

vesc =

√2GM

R

vesc for Sun: 440 km/s

when we compress the Sunto radius 3 km vesc is equal tothe velocity of light

Propertiesa particle of light that moves upis decelerated and falls back:light cannot reach us

the star for us is dark:astre occlu

a dark star is stable

one can travel there . . . andreturn in a finite time

clocks near the surface tick atthe same rate as clocks far away


Gravity according to Einstein: the black hole

the radius Rs of the horizonequals the radius of the darkstar

classical testslight is bent already outside thehorizon

nothing can pass the horizonfrom inside, not even light

a dark star inescapablycollapses

one can travel there . . . but thencannot return

the traveller sees his clock ticknormally but for a farawayobserver the clocks slow downnear the horizon and thetraveller hovers just outside it


Gravity according to Einstein: the black hole

classical testslight is bent already outside thehorizon

nothing can pass the horizonfrom inside, not even light

a dark star inescapablycollapses

one can travel there . . . but thencannot return

the traveller sees his clock ticknormally but for a farawayobserver the clocks slow downnear the horizon and thetraveller hovers just outside it


GRT: the universe

The Universe‘Copernican principle’: the Sunhas no special position in theUniverse‘extended Copernican principle’:there are no special positions inthe Universe

homogeneous: mass-densitythe same everywhere

isotropic: the same in alldirections

complicated equationsbecomes very simple

2nd-order differentialequation: 2 constants

Einstein 1915Solution for homogeneousUniverse

expands or shrinks

but stars do not move fromus

the Universe is static

mathematical trick:‘cosmological constant’

1921: Friedman: static, butnot stable

Einstein ignores this


Nebulae beyond the stars: M81 en M82


Spiral galaxies

Voorbeeld van diverse bulgedisk verhoudingenin edge-on stelsels


Vesto Slipher discovers that galaxies move away from us

first measurement 1912: Andromeda nebula moves towards us:vr = −300 km/s. Most other galaxies move away: V.M. Slipher , 1917,Proceedings of the American Philosophical Society, vol. 56, p.403-409


The expanding Universe

Einstein & Lemaître ±1933 Lemaître1925 Einstein static but notstable

I the Universe expandsI according to GRTI and measured by SlipherI velocity proportional to

distance

Einstein not impressed. . .

discovery later claimed byHubble


The expanding Universe: the Big Bang

Lemaîtrethe Universe expands

was smaller in the past

its temperature was higher

its density was higher

The Universe started as anexploding primordial atom

George Gamow 1904-1968the inital Universe was hotand dense

therefore: nuclear fusion; allelements made in first 3minutes

Alpher, Bethe, Gamow 1948

as the Universe expands itbecomes transparent

radiation and matter coolindependently

radiation now 5 á 50 K

(in fact: 3 K)


Cluster Abell 1185


Dark matter in clusters of galaxies

Zwicky 1933/37: Coma clustervelocities v ' 700 km/s

size R = 0.8 Mpc

mass in galaxies too small toconfine cluster: most massinvisible

Coma cluster of galaxies


Dark matter in clusters of galaxies

Confirmation 1curved stripes in galaxyclusters

gravity lense: mass in clusterdeforms and amplifies imageof faraway galaxy

from this derive mass incluster

agrees with kinematic mass

Confirmation 2hot X-ray emitting gas

confinement requires largemass

agrees with kinematic mass

Cluster of galaxies


3 K background radiation

Discovery

from all directions

3 K + dipole=direction ownmotion

COBE / WMAP


3 K background radiation: fluctuations: 9 yr WMAP

variation across sky ∼< 1 : 105: how does one side know about the other?


3 K background radiation: fluctuations: 4 yr Planck


Dark matter and dark energy

Dark matter fractionsolar system: negligible

10 pc (globular cluster):negligible

103 pc (solar environment):30 %

104 pc (galaxy): 64-84 %

107 pc (cluster of galaxies):70 %

Dark matter naturenot baryonic

primordial black holes (?)

new type of particles (?)

Het standaard-model

voor elk deeltje eensupersymmetrisch deeltje


Dark energy

Discovery of dark energywhite dwarf collapse startsfusion

leading to explosion =supernova Ia

all equally bright

brightness known: distanceknown

faraway supernovae indicatepush: dark energy

also indicated by details ofcosmic background radiation

supernova 1994D


Ordinary matter, dark matter and dark energy

WMAP and Planckat largest scales: 109 pc

dark energy 72.1±2.5%

dark matter 23.3±2.3%

baryons 4.6±0.2%


White dwarfs, black holes, dark matter · The discovery of white dwarfs: SiriusB 1844 Friedrich Wilhelm Bessel 1844 The motion of Sirius Sirius A and B Frank Verbunt ( Dept. Astronomy

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