Rodrigo Nemmen IAG USP Event Horizon Telescope: Towards Imaging a Black Hole Credit: Warner, Paramount

Credit: Warner, Paramount R. Nemmen

R. Nemmen

http://eventhorizontelescope.org/

Black holes have event horizons: only absorb light and matter 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 R. Nemmen

photon sphere Schwarzschild radius light rays Rph = 3GM c2 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 RS = 2GM c2 AAACB3icbZDLSsNAFIYn9VbrLdqlm2ARXEhJiqAboehCN0K99AJtDJPJpB06mYSZSSGEPIBP4VZX7sStj+HCd3GaZqGtPwx8nP8czpzfjSgR0jS/tNLS8srqWnm9srG5tb2j7+51RBhzhNsopCHvuVBgShhuSyIp7kUcw8CluOuOL6d+d4K5ICF7kEmE7QAOGfEJglKVHL1659yfD3wOUdq4uslS9NjIHL1m1s1cxiJYBdRAoZajfw+8EMUBZhJRKETfMiNpp5BLgijOKoNY4AiiMRzivkIGAyyOvQmJRI52mt+RGYfK9Aw/5OoxaeTV38MpDIRIAld1BlCOxLw3Lf7n9WPpn9kpYVEsMUOzRX5MDRka01AMj3CMJE0UQMSJ+raBRlCFIlV0FZWHNX/9InQadcusW7cnteZFkUwZ7IMDcAQscAqa4Bq0QBsgkIBn8AJetSftTXvXPmatJa2YqYI/0j5/AAUimPM= AAACB3icbZDLSsNAFIYn9VbrLdqlm2ARXEhJiqAboehCN0K99AJtDJPJpB06mYSZSSGEPIBP4VZX7sStj+HCd3GaZqGtPwx8nP8czpzfjSgR0jS/tNLS8srqWnm9srG5tb2j7+51RBhzhNsopCHvuVBgShhuSyIp7kUcw8CluOuOL6d+d4K5ICF7kEmE7QAOGfEJglKVHL1659yfD3wOUdq4uslS9NjIHL1m1s1cxiJYBdRAoZajfw+8EMUBZhJRKETfMiNpp5BLgijOKoNY4AiiMRzivkIGAyyOvQmJRI52mt+RGYfK9Aw/5OoxaeTV38MpDIRIAld1BlCOxLw3Lf7n9WPpn9kpYVEsMUOzRX5MDRka01AMj3CMJE0UQMSJ+raBRlCFIlV0FZWHNX/9InQadcusW7cnteZFkUwZ7IMDcAQscAqa4Bq0QBsgkIBn8AJetSftTXvXPmatJa2YqYI/0j5/AAUimPM= AAACB3icbZDLSsNAFIYn9VbrLdqlm2ARXEhJiqAboehCN0K99AJtDJPJpB06mYSZSSGEPIBP4VZX7sStj+HCd3GaZqGtPwx8nP8czpzfjSgR0jS/tNLS8srqWnm9srG5tb2j7+51RBhzhNsopCHvuVBgShhuSyIp7kUcw8CluOuOL6d+d4K5ICF7kEmE7QAOGfEJglKVHL1659yfD3wOUdq4uslS9NjIHL1m1s1cxiJYBdRAoZajfw+8EMUBZhJRKETfMiNpp5BLgijOKoNY4AiiMRzivkIGAyyOvQmJRI52mt+RGYfK9Aw/5OoxaeTV38MpDIRIAld1BlCOxLw3Lf7n9WPpn9kpYVEsMUOzRX5MDRka01AMj3CMJE0UQMSJ+raBRlCFIlV0FZWHNX/9InQadcusW7cnteZFkUwZ7IMDcAQscAqa4Bq0QBsgkIBn8AJetSftTXvXPmatJa2YqYI/0j5/AAUimPM= AAACB3icbZDLSsNAFIYn9VbrLdqlm2ARXEhJiqAboehCN0K99AJtDJPJpB06mYSZSSGEPIBP4VZX7sStj+HCd3GaZqGtPwx8nP8czpzfjSgR0jS/tNLS8srqWnm9srG5tb2j7+51RBhzhNsopCHvuVBgShhuSyIp7kUcw8CluOuOL6d+d4K5ICF7kEmE7QAOGfEJglKVHL1659yfD3wOUdq4uslS9NjIHL1m1s1cxiJYBdRAoZajfw+8EMUBZhJRKETfMiNpp5BLgijOKoNY4AiiMRzivkIGAyyOvQmJRI52mt+RGYfK9Aw/5OoxaeTV38MpDIRIAld1BlCOxLw3Lf7n9WPpn9kpYVEsMUOzRX5MDRka01AMj3CMJE0UQMSJ+raBRlCFIlV0FZWHNX/9InQadcusW7cnteZFkUwZ7IMDcAQscAqa4Bq0QBsgkIBn8AJetSftTXvXPmatJa2YqYI/0j5/AAUimPM= https://www.codeproject.com/Articles/994466/Ray-Tracing-a-Black-Hole-in-Csharp

R. Nemmen R = 3 p 3M Apparent boundary Weakly dependent on spin and inclination Bardeen 1973 R = 9/2M(a Nonspinning Spinning (a = 1) Black hole casts apparent shadow on light from surrounding accretion flow

R. Nemmen Bardeen 1973; Luminet 1979 Black hole Accretion disk

Black hole casts apparent shadow on light from surrounding accretion flow R. Nemmen Weakly dependent on spin and inclination Black hole Accretion disk Bardeen 1973; Luminet 1979 R = 3 p 3M Shadow size Schwarzschild

Thorne, Warner, Paramount

Luminet 1979 1979A&A....75..228L

Supermassive 106-1010 solar masses one in every galactic nucleus 5-30 solar masses ~107 per galaxy Stellar black holes ~1 Mpc ~100 kpc Active galactic nuclei Quasars Radio galaxies black holes Gamma- ray bursts Microquasars 1 pc = 3×1013 km

Supermassive 106-1010 solar masses one in every galactic nucleus 5-30 solar masses ~107 per galaxy Stellar black holes Active galactic nuclei black holes Microquasars d = 20 Mpc ⟨M⟩ = 108 Msun θshadow = Rshadow/d ~10-7 arcsec 0.4 mm (Moon) d = 1 kpc ⟨M⟩ = 10 Msun θshadow = Rshadow/d ~10-9 arcsec 1000 nm (Moon)

Journey to Sagittarius A*: Supermassive black hole at the center of our Galaxy Credit: ESO

Credit: ESO

10 light-days = 260 billion km Sgr A* black hole mass = 4✕106 solar masses Ghez, Schödel, Genzel et al.

Sagittarius A*: Mass and distance

Solar System Sagittarius A* Mass = 4×106 MSun d = 8.4 kpc Rshadow=0.4 a.u. θshadow = 5×10-5 arcseconds

Need an Earth-size telescope to resolve Sgr A*’s event horizon ✓ = 2.5 ⇥ 105 ✓ d ◆ arcsec angular resolution wavelength diameter observatory Rayleigh criterium

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T(l,m) • V(u,v), the complex visibility function, is the 2D Fourier transform of T(l,m), the sky brightness distribution (for incoherent source, small field of view, far field, etc.) [for derivation from van Cittert-Zernike theorem, see TMS Ch. 14] ! • mathematically u,v are E-W, N-S spatial frequencies [wavelengths]" l,m are E-W, N-S angles in the tangent plane [radians]" (recall ) T(l,m) van Cittert-Zernike theorem, see TMS Ch. 14] al frequencies [wavelengths]" s in the tangent plane [radians]" ) 19 Interferometry basics visibility sky brightness Visibility and Sky Brightness • V(u,v), the complex visibility function, is the 2D Fourier trans sky brightness distribution (for incoherent source, small field [for derivation from van Cittert-Zernike theorem, see T ! • mathematically u,v are E-W, N-S spatial frequencies [wavelengths]" l,m are E-W, N-S angles in the tangent plane [radians]" (recall ) Visibility and Sky • V(u,v), the complex visibility fun sky brightness distribution (for i [for derivation from van Citt ! • mathematically u,v are E-W, N-S spatial freque l,m are E-W, N-S angles in the (recall ) Interferometer observes 2D components u,v of Fourier transform of sky brightness

An Example of (u,v) plane Sampling 3 configurations of SMA antennas, ν = 345 GHz, dec = +22 deg 38 An Example of (u,v) plane Sampling 3 configurations of SMA antennas, ν = 345 GHz, dec = +22 deg

Inner and Outer (u,v) Boundaries V(u,v) amplitude V(u,v) phase T(l,m) 40

Inner and Outer (u,v) Boundaries V(u,v) amplitude V(u,v) phase T(l,m) V(u,v) amplitude V(u,v) phase T(l,m) 40

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Observations: Apr 5-14 2017 64 GB/s data writing rate during obs. ~few Petabytes/night 5 nights: ~20 Petabytes

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South Pole data: only after winter (Oct 2017)

Sagittarius A* Solar System M87 radio galaxy Milky Way d = 8.4 kpc d = 18 Mpc M = 4×106 MSun M = 6×109 MSun

No. 1, 2000 FALCKE, M Early black hole shadow predictions Optically thin gas around the BH in Sgr A* Falcke+2000 Flux (arbitrary units) Distance (GM/c2) Free-falling gas a = 0.998

Chi-Kwan Chan 1.3 mm

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Theoretical preparations

Virtual laboratory of numerical relativistic astrophysics Gravity: general relativity Fluid dynamics Electrodynamics

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 ds2 = ↵2dt2 + ij(dxi + p = ( 1)⇢✏ ;l s the stress energy tensor. In a coordinate basis, ffiffiffiffiffiffiffi À g p Tt Á ¼ À @i ffiffiffiffiffiffiffi À g p Ti À Á þ ffiffiffiffiffiffiffi À g 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 FlF À 1 4 glFF :

R (M) z (M) magnetic field black hole log ρ winds jet accretion flow

Shiokawa GRMHD simulations: “Weather forecast” around black holes

Black hole appearance: Ray tracing in curved spacetimes 1. Photon generation: synchrotron and bremsstrahlung

2. Photon propagation: Solve geodesic equation Black hole appearance: Ray tracing in curved spacetimes Geodesic equation Radiative transfer 3. GEODESIC INTEGRATION General relativistic radiative transfer differs from conven- ional radiative transfer in Minkowski space in that photon tra- ectories are no longer trivial; photons move along geodesics. Tracking geodesics is a significant computational expense in grmonty. The governing equations for a photon trajectory are dxα dλ = kα (11) which defines λ, the affine parameter, the geodesic equation dkα dλ = −Γα µν kµkν, (12) and the definition of the connection coefficients With ε = 0.04, grmonty integrates ∼16,700 geodesics s−1 on a single core of an Intel Xeon model E5430. If we use fourth- order Runge–Kutta exclusively so that the error in E, l, and Q is ∼1000 times smaller, then the speed is ∼ 6200 geodesics s−1. If we use the Runge–Kutta Prince–Dorman method in GSL with ε = 0.04 the fraction error is ∼ 10−10 and the speed is ∼1700 geodesics s−1. These results can be compared to the publicly available integral-based geokerr code of Dexter & Agol (2009), whose geodesics are shown as the (more accurate) solid lines in Figure 1. If we use geokerr to sample each geodesic the same number of times as grmonty (∼180), then on the same machine geokerr runs at ∼1000 geodesics s−1. It is possible that other implementations of an integral-of-motion- based geodesic tracker could be faster. If only the initial and final states of the photon are required, we find that geokerr computes ∼77,000 geodesics s−1. The adaptive Runge–Kutta Cash–Karp integrator in GSL computes ∼34,500 geodesics s−1 with fractional error ∼10−3. 4. ABSORPTION grmonty treats absorption deterministically. We begin with the radiative transfer equation written in the covariant form 1 C d dλ Iν ν3 = jν ν2 − (ναν,a ) Iν ν3 . (15) (see Mihalas & Mihalas 1984). Here Iν is specific intensity and for example, i Since Iν/ν3 along each ray emission) where is the different parentheses is with second-o τ and then set Since the com rest-mass ene opacity at the be reused as th Our treatm determines w

3. Solve radiative transfer equation: absorption Geodesic equation Radiative transfer 3. GEODESIC INTEGRATION General relativistic radiative transfer differs from conven- ional radiative transfer in Minkowski space in that photon tra- ectories are no longer trivial; photons move along geodesics. Tracking geodesics is a significant computational expense in grmonty. The governing equations for a photon trajectory are dxα dλ = kα (11) which defines λ, the affine parameter, the geodesic equation dkα dλ = −Γα µν kµkν, (12) and the definition of the connection coefficients Black hole appearance: Ray tracing in curved spacetimes publicly available integral-based geokerr code of Dexter Agol (2009), whose geodesics are shown as the (more accura solid lines in Figure 1. If we use geokerr to sample ea geodesic the same number of times as grmonty (∼180), th on the same machine geokerr runs at ∼1000 geodesics s−1 is possible that other implementations of an integral-of-moti based geodesic tracker could be faster. If only the initial and final states of the photon are requir we find that geokerr computes ∼77,000 geodesics s−1. T adaptive Runge–Kutta Cash–Karp integrator in GSL compu ∼34,500 geodesics s−1 with fractional error ∼10−3. 4. ABSORPTION grmonty treats absorption deterministically. We begin w the radiative transfer equation written in the covariant form 1 C d dλ Iν ν3 = jν ν2 − (ναν,a ) Iν ν3 . ( absorption absorption

4. Count photons that leave: Image or spectra Black hole appearance: Ray tracing in curved spacetimes E1 E2 E4 Energy Number of photons Spectra Image

Impact of inclination angle on black hole shadow Ray tracing/radiative transfer: BHOSS (Younsi+2018) Fluid dynamics: BHAC (Porth+2017)

Impact of B, black hole spin, electron thermodynamics ⊵ Ray tracing/radiative transfer: GRAY Fluid dynamics: HARM3D Chan+2015a,b

Ray tracing: RAPTOR (Bronzwaer+2018) Fluid dynamics: BHAC (Porth+2017) Credits: Davelaar, Moscibrodzka, Bronzwaer & Falcke

https://twitter.com/hfalcke/status/851176340971806721

Moscibrodzka

Falcke et al. 2000; Broderick et al. 2014 Expectativa da primeira imagem de um buraco negro: Silhueta do horizonte de eventos

Earth’s direction Opposite direction Special relativistic effect: aberration (Doppler boosting) v ≈ c

Earth’s direction: brighter Opposite direction: dimmer Special relativistic effect: aberration (Doppler boosting)

Effect of gravitational lensing

What will we learn?

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Spin and orientation of black hole Simulation 1 Nonrotating black hole viewed from 30 degrees above accretion disk plane Simulation 2 Nonrotating black hole viewed from 10 degrees above accretion disk plane Simulation 3 Rapidly spinning black hole viewed from 10 degrees above accretion disk plane 48 SCIENTIFIC AMERICAN 55 microarcseconds Broderick & Loeb 2009 accretion disk plane Simulation 1 Nonrotating BH, orientation 10° Simulation 2 Kerr BH, orientation 10° accretion disk event horizon

How do black holes produce jets? Spin, magnetic fields, accretion flow?

Chan et al. 2015 ApJ 150 100 50 0 -50 -100 -150 Relative right ascension (µas) 150 100 -50 a=0.7 SANE, const T e,funnel 150 100 50 0 -50 -100 -150 Relative right ascension (µas) -150 -100 -50 Relative 150 100 50 0 -50 -100 -150 Relative right ascension (µas) 150 100 -50 0 50 100 150 a=0.9 SANE, const T e,funnel 150 100 50 0 -50 -100 -150 Relative right ascension (µas) -150 -100 -50 0 50 100 150 Relative declination (µas) ∆PA=140°, FWHM=42.98µas 100 150 100 150 s) ∆PA=0°, FWHM=40.88µas 150 100 50 0 -50 -100 -150 Relative right ascension (µas) -150 -100 -50 Relative a=0.9 SANE, const T e,funnel 150 -150 -100 -50 Relative 150 100 50 0 -50 -100 -150 Relative right ascension (µas) -150 -100 -50 0 50 100 150 Relative declination (µas) a=0.0 MAD, const θ e,funnel 150 -150 -100 -50 0 50 100 150 Relative declination (µas) 100 150 s) 100 150 s) Near-horizon jet production and accretion flow Jet-dominated, strong B Disk-dominated, weak B

Prolate horizon Oblate horizon Superspinning (naked singularity?) Quadrupole deviations from GR? Validity of Kerr metric Broderick et al. 2014; Bambi & Freese 2009 Kerr metric predicts circular horizon shadow

Polarimetric imaging

IAG-related work

Gustavo Soares PhD Artur Vemado Msc Henrique Gubolin Msc Fabio Cafardo PhD Raniere Menezes PhD Ivan Almeida Msc Rodrigo Nemmen Apply to join my group Roberta Pereira undergrad (IC) blackholegroup.org +Caio Salgado, IC +Edson Ponciano, IC

Brasil + Argentina collaboration PI: Lepine Collaborators: Z. Abraham (radio) R. Nemmen (BH physics)

Event Horizon Telescope in a nutshell Network of radio telescopes, mm- wavelengths Goals: Direct image of event horizons Test general relativity (strong field) Probe black hole “gastrophysics” First observation with full array: April 2017 Work in progress… R. Nemmen Rodrigo Nemmen IAG USP

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Relative right ascension 50 0 50 00 013) 244003 H The first picture of a black hole E v e n t H o r i z o n Telescope attains the impossible BURACO NEGRO NO CENTRO DE M87 FAZ DENÚNCIAS GRAVES CONTRA O PT 2017 EXCLUSIVO

Github Twitter Web E-mail Bitbucket Facebook Group figshare rodrigo.nemmen@iag.usp.br rodrigonemmen.com @nemmen rsnemmen facebook.com/rodrigonemmen nemmen blackholegroup.org bit.ly/2fax2cT