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Black holes science fact, fiction of fantasy Chris Done, University of Durham Gravity: warped spacetime • Straight paths on curved space!! • NOT a spooky, action at a distance force (Newtonian) • Space(time) warped by mass(energy) Gravity: warped spacetime • Matter tells space how to curve, curvature tells matter how to move 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 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 can’t get out! • No change in curvature at Earths orbit – black holes don’t suck inexorably! Unlike bad SF movies… 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 + 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 Energy Atomic lines Doppler shift • Doppler shift! • Period and velocity give distance and gravity strength Doppler Shift Susan cruisin' down the freeway seventy-eight, And assuming the policeman is doing standing in range His gun tells him all go speedracing, go speedracing about the frequency change She justSusan's likes towalking, drive fast, it's notHer thatspeed she's racing late (nodays tail-gating, Then walking are doneno tail gat Goes overlight a hilltop what surprise (toofar, latelightspeed's sister, you're for itthe now They're yearsand away, anda that's pretty theinlimit, Blue and red flashing lights right in front of her eyes Nee nee nah nah big speedlimit Now Susan'splenty standing sidefrom of her But there's we by canthe learn thecar, light of a star (split it with a show methere's your licence, you're prism, little lines in it)in big trouble Trucks blowing right by her but she's notthat's going far By looking at the spectrum at the light glowing (wavelengths of (they're stillmeasured cruisin', Susan's losin') its Doppler Shift will tell us if it's emission, with precision) She's beenorcaught by a doo speed trap, and now she can hear, coming going Doo here comes the physics, now, That's the Doppler Shiftyou're - you in seeforit,itit's true Doppler Shift - to the red Sound the Doppler Shift right in her ear Eeee-oww or theof blue That's Doppler Shift - you've heard it I know, Doppler Shift - first it's Whenthe a star is approaching and it's coming our way Its spectrum then it's bluer, low won't you hear what I say And when a star's retreating seems The cop's gunAnd shoots out only measures radar Andits thefrequency beam bounces back off waygood out of range the scientist change Well Susan's that's acar redshift, If the star is moving away 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 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 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 = AsT4 • Temperature increases inwards as more gravitational energy and less area. Log n f(n) Spectra of accretion flow: disc Log n 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 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 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 Speed limit c in SR • Space-time curved by mass-energy • All forms of energy gravitate!! Mass • 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! c v • 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’ scifi ideas. Log n f(n) Spectra of accretion flow: disc Log n • 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 Log n f(n) Spectra of accretion flow: disc Log n • 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 Log n f(n) Spectra of accretion flow: disc Log n 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 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 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 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 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 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 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. • Can’t go faster than c… 3Rs. • GR gravity stronger…. Event horizon • 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….. Gravity: warped spacetime • 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?? Curved spacetime: black holes • Black holes are just made up of curved spacetime! • No surface, no distinguishing features… Event horizon • Horizon just the place where light can no longer get out • Matter coming in can sail straight through… r=0 r=Rs r t r 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!