Black holes science fact, fiction of fantasy Chris Done, University of Durham.
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Transcript of Black holes science fact, fiction of fantasy Chris Done, University of Durham.
Black holes science fact, fiction of fantasy
Chris Done, University of Durham
• Straight paths on curved space!!
• NOT a spooky, action at a distance force (Newtonian)
• Space(time) warped by mass(energy)
Gravity: warped spacetime
Gravity: warped spacetime• Matter tells space how to
curve, curvature tells matter how to move
• So light is affected too! • Lightbending – light travels in straight lines over curved
surface so path looks curved!• One of first tests of GR …
Gravity: warped spacetime
True position Apparent position
• More gravity, deeper hole in spacetime, higher velocity to escape - more mass or smaller size
• Black hole – escape velocity is faster than light so can’t get out!
• No change in curvature at Earths orbit – black holes don’t suck inexorably! Unlike bad SF movies…
Gravity: warped spacetime
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?
Black hole recipe: I• Take 1 massive star (at least
10 bigger than Sun)• Stars fuse 4H to He • Lose mass, gain energy via
Einstein’s E=mc2
• 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.
Chemistry!
Black hole recipe: I
• Take 1 massive star (at least 10x bigger than Sun)
• Stars fuse 4H to He • Lose mass, gain energy via
Einstein’s E=mc2
• Hydrogen bomb! in its stable life – outward pressure of hot gas (fusion) balanced by inward pull of gravity
• Cook until H all gone.
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!
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 C+He to O
• O core pulled…….
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!
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!
• Can’t go faster than c!
Black hole recipe: IV
• Hit this when Fe core is 1.4x mass of Sun
• e- + p+ > 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.
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?)
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
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
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
• Characteristic spectral lines
• Electron wave fits exactly only at certain distance=energy
Atomic lines
Ene
rgy
• Doppler shift!• Period and velocity
give distance and gravity strength
Doppler shift
Doppler ShiftAnd 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
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 troubleTrucks 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-owwThat'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
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
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
• In the centers of galaxies • Bright accretion discs (and
jets) powering intense activity from nucleus – AGN
• Can outshine host galaxy – quasi-stellar object - QSO
Supermassive black holes!
galaxy
quasar
star
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
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
• Differential velocity. friction gravity heat
• Thermal emission: L = AT4
• Temperature increases inwards as more gravitational energy and less area.
Spectra of accretion flow: disc
Log
Log
f
(
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
r
Newtonian gravity -1/r
Angular momentum, barrier 1/r2
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
r
Rest mass energy
Newtonian gravity -1/r
Extra GR -1/r3
Angular momentum, barrier 1/r2
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
r
Rest mass energy
Newtonian gravity -1/r
Extra GR -1/r3
Angular momentum, barrier 1/r2
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. • v<< c rest mass dominates • v~c then KE dominates.
Increasing energy increases response to gravity ie increases inertial mass and harder to increase speed!
Mass
vc
• 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. Can’t just go round (like fly-by-wire planes – need engines to keep it stable!)
• Origin of ‘black holes suck’ sci-fi ideas.
Spectra of accretion flow: disc
Log
Log
f
(
• 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
• a=0 Rlso = 3Rs horizon Rs
• a=1 (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 a=1
Spectra of accretion flow: disc
Log
Log
f
(
• Spinning black hole drags spacetime around with it
• Disc not rotating so fast with respect to spacetime so can get in closer
• a=0 Rlso = 3Rs horizon Rs
• a=1 (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 a=1
Spectra of accretion flow: disc
Log
Log
f
(
Speed limit c in SR• Travelling at constant speed c through spacetime!• ds2=c2dt2 –dx2
• Normally v<<c so all motion is through TIME• If v~c then more and more of speed goes through
space so less to go through time – time dilation!
ct
x
Speed limit c in SR• Travelling at constant speed c through spacetime!• ds2=c2dt2 –dx2
• Normally v<<c so all motion is through TIME• If v~c then more and more of speed goes through
space so less to go through time – time dilation!
ct
x
• 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 = AT4 so constant inner radius at last stable orbit L T4 as accretion rate changes
Galactic Binary systems
7 years
Gierlinski & Done 2003
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
Disc spectra: last stable orbit• Pick ONLY ones that look
like a disc! • L/LEdd T4
max (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
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 T4
max 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
• 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
Disc spectra: last stable orbit
• 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.
• Can’t go faster than c… 3Rs.
• GR gravity stronger….
Bright accretion discs!
• What happens at r=Rs=2GM/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)
• Can’t have fixed anything! So no sense to make a fixed radial grid…..
Event horizon
• No change in curvature at Earths orbit – black holes don’t suck inexorably! (Unlike bad SF movies… but there is something very odd close to the event horizon…..)
• But what happens at horizon? And below??
Gravity: warped spacetime
Curved spacetime: black holes• Black holes are just made up of curved spacetime!• No surface, no distinguishing features…
Event horizon
r
t
r
tr
t
r
t
• Horizon just the place where light can no longer get out
• Matter coming in can sail straight through…
rr=Rsr=0
• Below horizon spacetime itself is infalling!
• singularity at bottom – all matter crushed to infinite density in infinitesimal point
• NEED QUANTUM THEORY OF GRAVITY!
Gravity: warped spacetime