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Black hole primer for undergraduate students (physics/astronomy)

Black hole primer for undergraduate students (physics/astronomy)

Lecture: black hole primer for undergraduate students and first year grad students in physics and astronomy. Prepared and taught by Prof. Rodrigo Nemmen at IAG USP.

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.

Rodrigo Nemmen

July 27, 2017
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  1. A general relativity primer Einstein’s field equation Stress-energy Ricci curvature

    Metric Ricci scalar spacetime curvature 㱺 = constant × matter-energy Newtonian analogue Solution to field equation gives For a free particle: Geodesic equation metric Poisson equation
  2. What is a black hole? Remarkable prediction of general relativity

    Normal object Black hole surface event horizon singularity
  3. Event horizon: one-way membrane, matter/ energy can fall in, but

    nothing gets out Black hole event horizon singularity Region inside event horizon causally cut-off from outside RS = 2GM c2 = 2.95 ✓ M M ◆ km Radius of event horizon: Schwarzschild radius
  4. What is a black hole? Once inside, nothing escapes Massive,

    compact astronomical object: gravity so strong that it traps all that fall inside the event horizon
  5. What is a black hole? Once inside, nothing escapes Massive,

    compact astronomical object: gravity so strong that it traps all that fall inside the event horizon
  6. What is a black hole? Once inside, nothing escapes Massive,

    compact astronomical object: gravity so strong that it traps all that fall inside the event horizon
  7. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
  8. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes Sogro Sogra
  9. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
  10. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
  11. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
  12. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
  13. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes Chuck Norris
  14. Massive, compact astronomical object: gravity so strong that it traps

    all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
  15. sun MERCURY Radii of objects not to scale 100x deeper

    Mercury depth gravity well To black hole, very VERY far down
  16. sun VENUS MERCURY EARTH 6,379 KM To sun, far down

    Radii of objects not to scale 100x deeper Mercury depth gravity well To black hole, very VERY far down
  17. ç depth gravity well ç Black holes have deep, relativistic

    gravity wells ç BLACK HOLE sun 106x deeper
  18. ç depth gravity well ç Black holes have deep, relativistic

    gravity wells ç BLACK HOLE sun 106x deeper
  19. Classical vs quantum black holes Credit: BBC Black holes from

    general relativity are classical objects Quantum BHs: need quantum gravity theory Quantum BHs have weird properties: Hawking radiation Information paradox Will not talk about them
  20. Classical vs quantum black holes Credit: BBC Black holes from

    general relativity are classical objects Quantum BHs: need quantum gravity theory Quantum BHs have weird properties: Hawking radiation Information paradox Will not talk about them
  21. surprise them showing places where we see BHs all around

    us! how can it be? how can they shine? hang-on! Luo+16 Chandra Deep Field South 81 days of exposure
  22. How massive can a black hole be? BHs with M

    ≳ 3 Msun form naturally by gravitational collapse of massive stars No other stable equilibrium available at these masses
  23. How massive can a black hole be? BHs with M

    ≳ 3 Msun form naturally by gravitational collapse of massive stars No other stable equilibrium available at these masses Open question: Do low-mass BHs form naturally?
  24. Two populations of black holes Supermassive 106-1010 solar masses one

    in every galactic nucleus 5-60 solar masses ~107 per galaxy Stellar
  25. Two populations of black holes Supermassive 106-1010 solar masses one

    in every galactic nucleus 5-60 solar masses ~107 per galaxy Stellar Open question: Do intermediate-mass BHs exist? How massive are the initial seeds of supermassive BHs?
  26. XRBs show dramatic state transitions, whose origin is unknown X-ray

    binaries, M~5-20Msun, 107 objects per galaxy visible light Credit: NASA GSFC; Britannica
  27. M81 NGC 1097 M87 One supermassive BH in every galactic

    nuclei, M~106-1010Msun visible light Credit: NASA, HST, CXC
  28. M81 NGC 1097 M87 One supermassive BH in every galactic

    nuclei, M~106-1010Msun Do dwarf galaxies host supermassive BHs? visible light Credit: NASA, HST, CXC
  29. Criteria used to identify astrophysical BHs Must be compact: radius

    < few Rs Must be massive: M > several Msun, too massive to be a neutron star (Mns,crit ≤ Msun) These are strong reasons for BH candidates It is possible to empirically prove the existence of event horizons Prove that BHs have event horizons (soon: Event Horizon Telescope, LIGO) How do we know they are black holes?
  30. Black holes are the most perfect macroscopic objects in the

    universe A black hole has no-hair (no-hair theorem) Made only of spacetime warpage Mass M Spin: angular momentum J Charge Q J = a GM2/c 0  |a|  1 RS = 2GM c2
  31. Fg = Fc ) GMm r2 = mv2 r Measuring

    mass in astronomy Test particle in circular orbit M m v Best mass estimates are dynamical ) M = v2r G Alternatively, Kepler’s third law P2 r3 = 4⇡2 G(M + m) ) M ⇡ 4⇡2r3 GP2
  32. Fg = Fc ) GMm r2 = mv2 r Measuring

    mass in astronomy Test particle in circular orbit M m v Fc=Fg Best mass estimates are dynamical ) M = v2r G Alternatively, Kepler’s third law P2 r3 = 4⇡2 G(M + m) ) M ⇡ 4⇡2r3 GP2
  33. Exercise Suppose a star is measured in a circular orbit

    with P=15 years and r=1000 au. Compute M. M m Kepler’s third law ) M ⇡ 4⇡2r3 GP2 r 1 au = 1.5E11 m G = 6.67E-11 N m2/kg2 Msun = 2E30 kg
  34. Black hole spin generates spacetime whirlwind (non-Newtonian effect) Huge energy

    stored in rotating spacetime black hole Credit: Thorne
  35. Credit: ESO Black holes surrounded by accretion disks, release enormous

    amounts of light How efficient is the release of light?
  36. Credit: ESO Black holes surrounded by accretion disks, release enormous

    amounts of light How efficient is the release of light?
  37. Credit: ESO Black holes surrounded by accretion disks, release enormous

    amounts of light Credit: NatGeo v → c near the horizon How efficient is the release of light?
  38. Energy released: U = GMm R L = ˙ U

    = GM ˙ m R Luminosity:
  39. Energy released: U = GMm R L = ˙ U

    = GM ˙ m R Luminosity: ) L = ⌘ ˙ mc2
  40. Energy released: U = GMm R L = ˙ U

    = GM ˙ m R Luminosity: ) L = ⌘ ˙ mc2 ⌘ / M/R Radiative efficiency:
  41. Energy released: U = GMm R L = ˙ U

    = GM ˙ m R Luminosity: For black holes: η ~ 10-40% ) L = ⌘ ˙ mc2 ⌘ / M/R Radiative efficiency:
  42. Sugar (sucrose) C12 H22 O11 1g ! 4 kcal= 16.2

    kJ = 1e23 eV ⌘ = E mc2 = 1.6 ⇥ 1011erg 9 ⇥ 1020erg = 2 ⇥ 10 10 R. Nemmen
  43. Sugar (sucrose) C12 H22 O11 1g ! 4 kcal= 16.2

    kJ = 1e23 eV ⌘ = E mc2 = 1.6 ⇥ 1011erg 9 ⇥ 1020erg = 2 ⇥ 10 10 R. Nemmen
  44. Itaipu Dam − 14 GW ⌘ = mgh mc2 =

    10 14 ✓ h 100 m ◆
  45. Itaipu Dam − 14 GW ⌘ = mgh mc2 =

    10 14 ✓ h 100 m ◆
  46. Credit: ESO Radiative efficiency: Black holes surrounded by accretion disks,

    release enormous amounts of light ⌘ rad = Erad out Egas in = 10 40% 100x more efficient than nuclear fusion! Most efficient radiators in the universe Radiate across all eletromagnetic spectrum!
  47. Credit: ESO Radiative efficiency: Black holes surrounded by accretion disks,

    release enormous amounts of light ⌘ rad = Erad out Egas in = 10 40% 100x more efficient than nuclear fusion! Most efficient radiators in the universe Radiate across all eletromagnetic spectrum!
  48. Gamma-ray bursts 3C 31 4 I.F. Mirabel Fig. 1.2 The

    British journal Nature announced on July 16, 1992 the discovery of a microquasar in the Galactic center region [22]. The image shows the synchrotron emission at a radio wavelength of 6 cm produced by relativistic particles jets ejected from some tens of kilometers to light years Black hole binaries (microquasars) ~1 pc 1E1740.7-2942 ~1 Mpc ~100 kpc Active galactic nuclei ~10-4 pc? Tidal disruption events
  49. How are relativistic jets produced by black holes? Conjecture: from

    spinning black holes Growing evidence that this is correct Theory/simulations Observations (?)
  50. https://www.youtube.com/watch?v=9MHuhcFQsBg Penrose process: Spinning black hole has free energy that

    can be extracted Rotational energy of spacetime (frame dragging) Thought experiment by Penrose that demonstrates the principle, probably not important in astrophysics But magnetized accretion disks is promising Penrose 1969 Ruffini & Wilson 1975; Blandford & Znajek 1977
  51. https://www.youtube.com/watch?v=9MHuhcFQsBg Penrose process: Spinning black hole has free energy that

    can be extracted Rotational energy of spacetime (frame dragging) Thought experiment by Penrose that demonstrates the principle, probably not important in astrophysics But magnetized accretion disks is promising Penrose 1969 Ruffini & Wilson 1975; Blandford & Znajek 1977
  52. Toy model for jet production from black hole: rotation +

    accretion + B Semenov+04, Science possibilities remain to be better explored in future simula- tions of accretion flows. Interestingly enough, s is similar to the dispersion of s values obtained in the hydrodynamic RIAF simulations of Yuan, Wu & Bu (2012); Bu et al. (2013) for a range of initial conditions. Range of black hole spins and/or magnetic flux threading the horizon – If powerful jets are produced via the BZ mecha- nism then the two fundamental parameters that regulate the jet power are the black hole spin a and the magnetic flux h threading the horizon, besides the mass (Blandford & Znajek 1977; Semenov, Dyadechkin & Punsly 2004): Pjet / ⇠ ✓ a h M ◆2 ; (9) i.e., a and h are degenerate to some extent (cf. Jet power Blandford & Znajek 77; Komissarov+; Nemmen+07; Tchekhovskoy+ spin magnetic flux Blandford-Znajek mechanism: magnetic flux tube spinning black hole ergosphere ⇠ a2 ˙ Mc2 ⊵
  53. Toy model for jet production from black hole: rotation +

    accretion + B Semenov+04, Science possibilities remain to be better explored in future simula- tions of accretion flows. Interestingly enough, s is similar to the dispersion of s values obtained in the hydrodynamic RIAF simulations of Yuan, Wu & Bu (2012); Bu et al. (2013) for a range of initial conditions. Range of black hole spins and/or magnetic flux threading the horizon – If powerful jets are produced via the BZ mecha- nism then the two fundamental parameters that regulate the jet power are the black hole spin a and the magnetic flux h threading the horizon, besides the mass (Blandford & Znajek 1977; Semenov, Dyadechkin & Punsly 2004): Pjet / ⇠ ✓ a h M ◆2 ; (9) i.e., a and h are degenerate to some extent (cf. Jet power Blandford & Znajek 77; Komissarov+; Nemmen+07; Tchekhovskoy+ spin magnetic flux Blandford-Znajek mechanism: ⇠ a2 ˙ Mc2 ⊵
  54. Gustavo Soares PhD Artur Vemado undergrad (IC) Henrique Gubolin Msc

    Fabio Cafardo PhD Raniere Menezes PhD Ivan Almeida Msc http://rodrigonemmen.com/group/ Rodrigo Nemmen Apply to join my group Roberta Pereira undergrad (IC)
  55. “Weather forecast for black holes” Virtual laboratory of numerical relativistic

    astrophysics Gravity: general relativity Gas (plasma) Electromagnetic fields
  56. Required physics: Fluid dynamics + electrodynamics Plus: equation of state

    D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ Fluid dynamics conservation equations Mass Momentum Energy D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ r · Frad r · q D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ r · Frad r · q D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ Maxwell equations
  57. Equations of general relativistic magnetohydrodynamics Plus: equation of state ideal

    MHD condition Kerr metric Conservation of Particle number Energy-momentum r⌫(⇢u⌫) = 0 r⌫Tµ⌫ = 0 r⌫ ⇤ Fµ⌫ = 0 r⌫Fµ⌫ = Jµ Maxwell equations r⌫ ⇤ Fµ⌫ = 0 r⌫Fµ⌫ = Jµ Fµ⌫u⌫ = 0 ds 2 = ↵ 2 dt 2 + ij( dx i + p = ( 1)⇢✏ ;l s the stress energy tensor. In a coordinate basis, ffiffiffiffiffiffiffi Àg p Tt  Á ¼ À@i ffiffiffiffiffiffiffi Àg p Ti  À Á þ ffiffiffiffiffiffiffi Àg p T  À ; ð4Þ notes a spatial index and À  is the connection. rgy momentum equations have been written with dex down for a reason. Symmetries of the metric conserved currents. In the Kerr metric, for exam- xisymmetry and stationary nature of the metric o conserved angular momentum and energy cur- eneral, for metrics with an ignorable coordinate rce terms on the right-hand side of the evolution or Tt l vanish. These source terms do not vanish quation is written with both indices up. ss energy tensor for a system containing only a id and an electromagnetic field is the sum of a Tl fluid ¼ ð þ u þ pÞulu þ pgl ð5Þ The rest of M and are not n MHD. Maxwell’s by taking the Here FÃ l ¼ 1 2 tensor (MTW which can be The comp blul ¼ 0. Fol where i denotes a spatial index and À  is the The energy momentum equations have bee the free index down for a reason. Symmetrie give rise to conserved currents. In the Kerr me ple, the axisymmetry and stationary nature give rise to conserved angular momentum a rents. In general, for metrics with an ignora xl the source terms on the right-hand side o equation for Tt l vanish. These source terms when the equation is written with both indices The stress energy tensor for a system con perfect fluid and an electromagnetic field is fluid part, Tl fluid ¼ ð þ u þ pÞulu þ pgl (here u  internal energy and p  press electromagnetic part, Tl EM ¼ Fl F À 1 4 glF F :
  58. 256 x 256 x 64 r θ 3D computational mesh

    4×106 resolution elements Need to evolve to t>15000 M (4 yrs for a 109 BH) Global, general relativistic MHD (GRMHD) simulations of gas around spinning BHs HARM code + MPI + 3D = HARMPI Gammie+03; Tchekhovskoy
  59. We are starting to treat the radiation from these systems

    y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
  60. We are starting to treat the radiation from these systems

    y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
  61. y x Units of GM/c2 phd, Gustavo soares Work in

    progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
  62. y x Units of GM/c2 phd, Gustavo soares Work in

    progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
  63. y x Units of GM/c2 Work in progress Preliminar result:

    Null geodesics in x-y plane around Kerr black hole
  64. Chan+15a,b ApJ radio 10 GHz 1.3mm IR 2.1μm X-rays Future:

    Radiative transfer and GPU- accelerated ray tracing in BH spacetimes ptg
  65. Chan+15a,b ApJ radio 10 GHz 1.3mm IR 2.1μm X-rays Future:

    Radiative transfer and GPU- accelerated ray tracing in BH spacetimes ptg
  66. Remarkable connection between central black holes and host galaxies: the

    M-σ relation MBH = 2 ⇥ 108M ✓ 200 km s 1 ◆5.6 Woo+13; McConnell & Ma 13; Heckman & Best ARA&A 14 1010 109 108 107 106 60 80 100 200 300 400 Elliptical/classical bulge Pseudobulge AGN Quiescent 9.0 6 7 8 9 10 M BH /M Velocity dispersion/km s–1 log 10 (M BH /M ) M a b Figure 9 nualreviews.org sonal use only. mass central black hole host galaxy propriety: σbulge (km/s) Fundamental link between BH growth and galaxy evolution
  67. 10 Mpc Fabian 12 ARAA; Tombesi+15 Nature; Cheung+16 Nature; Vogelsberger+14

    Nature Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) “BH explosions” in the simulation
  68. 10 Mpc Fabian 12 ARAA; Tombesi+15 Nature; Cheung+16 Nature; Vogelsberger+14

    Nature Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) “BH explosions” in the simulation
  69. PI: S. Doeleman (MIT/Haystack) idéia original: H. Falcke (Radboud) Attaining

    the impossible: first image of an event horizon just around the corner Credit: Science Magazine
  70. PI: S. Doeleman (MIT/Haystack) idéia original: H. Falcke (Radboud) Attaining

    the impossible: first image of an event horizon just around the corner Credit: Science Magazine
  71. Summary: Black holes Black holes: collapsed objects from which nothing

    can escape (once inside) Astrophysical labs of general relativity, fluid dynamics and electrodynamics that can’t be found on Earth Brightest systems in the universe Important for galaxy formation/evolution Open questions in the field Very soon: first image of event horizon LIGO is opening new observational windows If you are interested in doing research in these topics, please talk to me
  72. Github Twitter Web E-mail Bitbucket Facebook Blog figshare [email protected] http://rodrigonemmen.com

    @nemmen rsnemmen http://facebook.com/rodrigonemmen nemmen http://astropython.blogspot.com http://bit.ly/2fax2cT