Black holes science fact, fiction of fantasy

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Black holes science fact, fiction of fantasy

• Chris Done, University of Durham

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Gravity warped spacetime

• Straight paths on curved space!!
• NOT a spooky, action at a distance force
  (Newtonian)
• Space(time) warped by mass(energy)

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Gravity warped spacetime

• Matter tells space how to curve, curvature tells
  matter how to move

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Gravity warped spacetime

• So light is affected too!
• Lightbending light travels in straight lines
  over curved surface so path looks curved!
• One of first tests of GR

True position
Apparent position
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Gravity warped spacetime

• More gravity, deeper hole in spacetime, higher
  velocity to escape - more mass or smaller size
• Black hole escape velocity is faster than light
  so cant get out!
• No change in curvature at Earths orbit black
  holes dont suck inexorably! Unlike bad SF movies

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Gravity warped spacetime

• Utterly extreme. Need mass of earth squashed down
  to 1cm! Or mass of sun squashed into size of
  London.
• Impossible!!!!!!!!?
• How to get such extreme compression?

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Black hole recipe I

• Take 1 massive star (at least 10 bigger than Sun)
• Stars fuse 4H to He
• Lose mass, gain energy via Einsteins Emc2
• Hydrogen bomb! in its stable life outward
  pressure of hot gas (fusion) balanced by inward
  pull of gravity
• Cook until all hydrogen fuel eventually
  exhausted.

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Chemistry!
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Black hole recipe I

• Take 1 massive star (at least 10x bigger than
  Sun)
• Stars fuse 4H to He
• Lose mass, gain energy via Einsteins Emc2
• Hydrogen bomb! in its stable life outward
  pressure of hot gas (fusion) balanced by inward
  pull of gravity
• Cook until H all gone.

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Black hole recipe II

• Run out of H but gravity never runs out
  contracts core so higher temperatures
• then fuse higher atomic number elements
• Builds up all the chemical elements of the
  periodic table!

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Chemistry!

• He core pulled in by gravity, temperature
  increases. If high enough fuse 3He to C
• C core pulled in by gravity temperature
  increases. If high enough fuse CHe to O
• O core pulled.

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Black hole recipe II

• Builds up all the chemical elements of the
  periodic table!
• But get less and less energy!
• Iron is crossover between fusion and fission! No
  more energy!
• Iron core builds up as iron ash sinks down from
  layers above. pulled in by gravity but no other
  energy!

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Black hole recipe III

• Fe core pulled in by gravity. How far can
  material be compressed?
• Electron degeneracy pressure wave-particle
  duality in quantum mechanics. Smaller box,
  smaller wavelength, higher energy, faster!
• Cant go faster than c!

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Black hole recipe IV

• Hit this when Fe core is 1.4x mass of Sun
• e- p gt n n
• Neutrons have higher mass, shorter wavelength so
  fit in MUCH smaller box! Floor drops away.
• Dramatic supernovae explosion!
• Neutron star core left held up by degenerate
  neutrons.
• mass of sun, size of London.

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A digression..

• Outer layers blasted across interstellar space
• Contains all heavy elements needed for life (C,
  N, O, Fe etc)
• Where slams into molecular gas then triggers next
  generation of stars/planets(/life?)

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Black hole recipe V

• But core being hit by infalling layers from above
• Neutrons get squashed into smaller and smaller
  box, going faster and faster
• Hit c at 1.4-3x mass of sun (depends on rotation
  rate)
• no known state of matter can hold up complete
  collapse
• Event horizon only factor of 3 smaller than a
  neutron star

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Observing black holes?

• How to test this ?
• The thing about a black hole, its main
  distinguishing feature is its black! And the
  thing about space, your basic space colour is its
  black! So how are you supposed to see them ? Red
  Dwarf

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Disc Accretion

• Single particles orbit
• Gravitational orbits - inner ones faster
• Continuous ring of gas - Frictional viscosity
  dissipates energy as material can fall inwards
• BRIGHT accretion discs glowing X-ray hot

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Atomic lines

• Characteristic spectral lines
• Electron wave fits exactly only at certain
  distanceenergy

Energy
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Doppler shift

• Doppler shift!
• Period and velocity give distance and gravity
  strength

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Doppler Shift
Susan cruisin' down the freeway doing
seventy-eight, go speedracing, go speedracing
She just likes to drive fast, it's not that
she's late (no tail-gating, no tail gating) Goes
over a hilltop and what a surprise (too late
sister, you're in for it now) Blue and red
flashing lights right in front of her eyes Nee
nee nah nah Now Susan's standing by the side of
her car, show me your licence, you're in big
trouble Trucks blowing right by her but she's not
going far (they're still cruisin', Susan's
losin') She's been caught by a speed trap, and
now she can hear, here comes the physics, you're
in for it now, Sound of the Doppler Shift right
in her ear Eeee-oww That's the Doppler Shift -
you've heard it I know, Doppler Shift - first
it's high then it's low The good cop's gun
shoots out only radar And the beam bounces back
off bad Susan's car
And assuming the policeman is standing in range
His gun tells him all about the frequency change
Then Susan's walking, walking Her speed racing
days are done They're light years away, and
that's pretty far, lightspeed's the limit, the
big speedlimit But there's plenty we can learn
from the light of a star (split it with a prism,
there's little lines in it) By looking at the
spectrum at the light that's glowing (wavelengths
of emission, measured with precision) its Doppler
Shift will tell us if it's coming or going Doo
doo That's the Doppler Shift - you see it, it's
true Doppler Shift - to the red or the blue When
a star is approaching and it's coming our way Its
spectrum seems bluer, won't you hear what I say
And when a star's retreating way out of range And
the scientist measures its frequency change Well
that's a redshift, If the star is moving away
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By gravity all they possess!

• Gravitational effect on nearby stars
• Stars in GC get to within a lightday, but this is
  2000x event horizon. Not probing the REALLY
  curved BH spacetime.
• Hard to detect

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By gravity all they possess!

• Gravitational effect on nearby stars
• Stars in GC get to within a lightday, but this is
  2000x event horizon. Not probing the REALLY
  curved BH spacetime.
• Hard to detect

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Supermassive black holes!

• In the centers of galaxies
• Bright accretion discs (and jets) powering
  intense activity from nucleus AGN
• Can outshine host galaxy quasi-stellar object -
  QSO

galaxy
quasar
star
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Conclusions

• black holes ultimate test of Einstein General
  Relativity
• Can form astrophysically from death of massive
  stars
• Most stars are in binaries X-ray bright
  accretion
• Measure mass from binary orbit BH or NS
• Supermassive black hole in centre of our Galaxy
• And in most other galaxies too accretion of
  material again gives X-rays, powers activity seen
  from Quasars

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Disc Accretion

• Single particles orbit
• Gravitational orbits - inner ones faster
• Continuous ring of gas - Frictional viscosity
  dissipates energy as material can fall inwards
• BRIGHT accretion discs glowing X-ray hot

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Spectra of accretion flow disc

• Differential velocity. friction gravity ? heat
• Thermal emission L AsT4
• Temperature increases inwards as more
  gravitational energy and less area.

Log n f(n)
Log n
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Behaviour of maximum

• Newtonian orbits
• Gravity attractive wants to be closer in.
• but if closer then rotate faster due to angular
  momentum conservation
• Bigger outward centrifugal force!
• Balance inward gravity with outward angular
  momentum to get stable orbit
• Can always orbit closer

energy
Angular momentum, barrier ?1/r2
r
Newtonian gravity ? -1/r
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Behaviour of maximum

• Extra terms in GR potential
• (Rest mass energy)
• Term which is ve so adds to gravitational
  potential and makes it stronger
• Gravity will always dominate if get to small
  enough r!

energy
Angular momentum, barrier ?1/r2
Rest mass energy
r
Newtonian gravity ? -1/r
Extra GR ?-1/r3
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Behaviour of maximum

• Extra terms in GR potential
• (Rest mass energy)
• Term which is ve so adds to gravitational
  potential and makes it stronger
• Gravity will always dominate if get to small
  enough r!
• Last stable orbit gravity so strong that no
  friendly angular momentum barrier to stop you
  falling down

energy
Angular momentum, barrier ?1/r2
Rest mass energy
r
Newtonian gravity ? -1/r
Extra GR ?-1/r3
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Speed limit c in SR

• Space-time curved by mass-energy
• All forms of energy gravitate!!
• Increase v ie KE so increase response to gravity.
  
• vltlt c rest mass dominates
• vc then KE dominates. Increasing energy
  increases response to gravity ie increases
  inertial mass and harder to increase speed!

Mass
v
c
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Spectra of accretion flow disc

• How far in can the disc go? Obviously stops at
  event horizon! But GR gravity is stronger than
  Newtonian there is a point where stable orbits
  no longer possible. Cant just go round (like
  fly-by-wire planes need engines to keep it
  stable!)
• Origin of black holes suck sci-fi ideas.

Log n f(n)
Log n
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Spectra of accretion flow disc

• This point depends on SPIN
• Spinning black hole drags spacetime around with
  it
• Disc not rotating so fast with respect to
  spacetime so can get in closer
• a0 Rlso 3Rs horizon Rs
• a1 (maximal Kerr) Rlso 0.5 Rs
  horizon 0.5 Rs
• Can get in closer to spinning black hole. More
  energy to dissipate over smaller area disc
  temperature 3x higher for same luminosity for a1
  

Log n f(n)
Log n
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Spectra of accretion flow disc

• Spinning black hole drags spacetime around with
  it
• Disc not rotating so fast with respect to
  spacetime so can get in closer
• a0 Rlso 3Rs horizon Rs
• a1 (maximal Kerr) Rlso 0.5 Rs
  horizon 0.5 Rs
• Spinning black hole has more energy to dissipate
  over smaller area disc temperature 3x higher for
  same luminosity for a1

Log n f(n)
Log n
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Speed limit c in SR

• Travelling at constant speed c through spacetime!
• ds2c2dt2 dx2
• Normally vltltc so all motion is through TIME
• If vc then more and more of speed goes through
  space so less to go through time time dilation!

censored!
ct
x
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Speed limit c in SR

• Travelling at constant speed c through spacetime!
• ds2c2dt2 dx2
• Normally vltltc so all motion is through TIME
• If vc then more and more of speed goes through
  space so less to go through time time dilation!

ct
x
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Galactic Binary systems

• Huge amounts of data
• See accretion rate vary on timescales of
  days-years
• Observational template of accretion flow as a
  function of L onto 10 M? BH
• Thermal disc L AsT4 so constant inner radius
  at last stable orbit L? T4 as accretion rate
  changes

7 years
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Disc spectra last stable orbit

• Pick ONLY ones that look like a disc!
• L/LEdd ?T4max (Ebisawa et al 1993 Kubota et al
  1999 2001)
• Constant radius over factor 10-50 change in
  luminosity
• Last stable orbit!!! Looks like Einstein GR
  (Gregory, Whisker, Beckwith Done 2004)
• Proportionality constant gives Rms i.e. a as
  know M
• Consistent with low to moderate spin not maximal

Gierlinski Done 2003
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Disc spectra last stable orbit

• Pick ONLY ones that look like a disc!
• L/LEdd ?T4max (Ebisawa et al 1993 Kubota et al
  1999 2001)
• Constant radius over factor 10-50 change in
  luminosity
• Last stable orbit!!! Looks like Einstein GR
  (Gregory, Whisker, Beckwith Done 2004)
• Proportionality constant gives Rms i.e. a as
  know M
• Consistent with low to moderate spin not maximal
• Matches theoretical spin from supernovae collapse

Gierlinski Done 2003
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Conclusions

• GR black holes event horizon, last stable orbit
• Can form astrophysically from death of massive
  stars
• Where these accrete then get observational tests
  of GR in strong field from X-ray emitting gas
  lighting up regions of strong spacetime curvature
  
• Simple disc spectra luminosity can change by
  factor 50 with L ?T4max implies constant size
  scale
• Consistent with GR prediction of last stable
  orbit for low/moderate spin black holes
• Corrections to GR from proper gravity must be
  smallish
• ASTROPHYSICS ? PHYSICS

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Disc spectra last stable orbit

• Pick ONLY ones that look like a disc!
• L/LEdd ?T4max (Ebisawa et al 1993 Kubota et al
  1999 2001)
• Constant radius over factor 10-50 change in
  luminosity
• Last stable orbit!!! Looks like Einstein GR
  (Gregory, Whisker, Beckwith Done 2004)
• Proportionality constant gives Rms i.e. a as
  know M
• Consistent with low to moderate spin not maximal

Gierlinski Done 2003
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Bright accretion discs!

• Huge gravitational potential energy of infalling
  material so gas heated to X ray temperatures and
  very luminous.
• Bright accretion disc GR gravity stronger than
  Newton. Last stable orbit at 6Rs.
• Newton orbit closer in by going round faster.
• Cant go faster than c 3Rs.
• GR gravity stronger.

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Event horizon

• What happens at rRs2GM/c2?
• Speed is distance/time ? c at Rs no matter where
  dropped from or how fast it was hurled towards
  the hole
• So must be infinite accelerations (could drop
  from rest just above horizon and would still be
  at c at Rs)
• Cant have fixed anything! So no sense to make a
  fixed radial grid..

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Gravity warped spacetime

• No change in curvature at Earths orbit black
  holes dont suck inexorably! (Unlike bad SF
  movies but there is something very odd close to
  the event horizon..)
• But what happens at horizon? And below??

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Curved spacetime black holes

• Black holes are just made up of curved spacetime!
• No surface, no distinguishing features

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Event horizon

• Horizon just the place where light can no longer
  get out
• Matter coming in can sail straight through

rRs
r0
r
t
r
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Gravity warped spacetime

• Below horizon spacetime itself is infalling!
• singularity at bottom all matter crushed to
  infinite density in infinitesimal point
• NEED QUANTUM THEORY OF GRAVITY!