Galaxies

Black-Hole in M87, 2019 (2021, 2023, 2024 Updates)

		M87 and its black-hole (also see "Space Fact"). An image of this black-hole is presented to the world by the Event Horizon Telescope(s) (EHT) in April, 2019. However, close examination reveals that the image is a shadow (actually a silhouette) formed by dark object against radio frequency background, and the whole picture is in false colors. It is stitched together with missing data filled in by some sort of educated guessing, a.k.a. "Bayesian Inference".
Figure 05-02r1 M87, Black-Hole [view large image]	Figure 05-02r2 M87 BH Parms	The following shows the theoretical base and processing involved in the imaging.

• The Advent in Radio Telescopes - Optical telescope observes light with wavelengths in the range of 7 - 4.5 x 10^-5 cm. Since the largest aperture "A" of optical telescope is about 1000 cm, the corresponding resolution is limited to r_es ~ 2x10⁵x(/A) arc-sec (as) ~ 0.01 as. On the contrary, modern array of radio telescopes with baseline b ~ 10⁹ cm (~ diameter of the Earth), can achieve resolution r_es ~ 2x10⁵x(/b) as ~ 20x10^-6as for radio wavelength ~ 0.1 cm. Thus, the technique known as Very Long Baseline Interferometry (VLBI), is now available to image the black-hole in M87. Actually, such resolution is barely enough to view the structure of the accretion disk (usually makes of gas, dust and other stellar debris which do not emit light spontaneously), it would not be enough to see the details closer to the black-hole (see data in Figure 05-02-r2).



	EM Wave Interference - The quality of the image depends on the interference pattern of the radio wave. The focus becomes increasingly shaper with longer baseline b as shown in Figure 05-02s1(a), which plots 3 patterns from different ratio of b/ for only one source. Diagrams (b), and (c) display progressively more complicated patterns (in 2-D) as more sources are involved.
Figure 05-02s1 Interference [view large image]

• Very Long Baseline Interferometry (VLBI) - This is the observational technique employed by the Event Horizon Telescope(s) (EHT) to take a picture of the black-hole.
  
  
  • Figure 05-02s2(a) shows the setup of one baseline (2 radio telescopes) and a formula for the path difference, which is essentially equivalent to the one in double slit experiment.
  • Figure 05-02s2(b,c) shows the hookup of 3 telescopes. It requires a correlator to process the data (labeled by very accurate time stemps) shipped over and eventually produces the image.
  • Figure 05-02s3(a) shows the variation of the incident angle driven by the rotation of the Earth. There are 8 major radio telescopes in the EHT. The measurements were taken in April 5, 6, 10 and 11, 2017 (see "Imaging the Central Supermassive Black Hole").

  		Figure 05-02s3(b) shows the paths of measurements against the center of the black-hole. Further apart of the telescopic pair corresponds to longer baseline and hence better resolution up to 25 as. The path length is in unit of G or 109 . There are lot of empty space in between the paths, meaning a lot of missing data to complete the imaging. These voids are filled up by an algorithm developed by Dr. Katie Bouman (see her TED Talk).
  Figure 05-02s2 Interferometry [view large image]	Figure 05-02s3 VLBI [view large image][see video]	Figure 05-02s3(c) shows the input to the correlator in complicated wave pattern and the black-hole output. The video shows the imaging process.

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• The appearance and luminosity (in false colors) of the M87 black-hole environment is determined by many effects -
  
  
  • Gravitational Lensing - A massive object would bend light rays passing through its vicinity, something like focusing of light rays by optical lens.
  • Warped Space - The shadow is caused by the gravitational bending and capture of light by the event horizon. For accreting black holes embedded in a geometrically thick, optically thin emission region (i.e., thick and transparent disk), the combination of an event horizon and light bending leads to the appearance of a dark "shadow" together with a bright emission ring. Its shape can appear as a "crescent" because of fast rotation and relativistic beaming.
  • Synchrotron Radiation - It is the emission of EM wave in the direction of the relativistic motion of charged particles as shown in Figure 05-02t. As its light is polarized, observation of the polarized and total intensities in the video of Figure 05-02t shows that most of the radiation comes from synchrotron emission in the direction of the object's motion.
  • Doppler (relativistic) Beaming - The relativistic motion between source and observer changes the frequency of light - blue shifted for approaching while red shift by receding (causing the luminosity to increase or decrease respectively).
  • Aberration - It is the change in an object's apparent direction caused by the relative transverse motion of the observer. It causes most of the photons to be emitted along the object's direction of motion. The effect is similar to the changing direction of rain drops as observed in a moving car.
  • Time Dilation - The light is red shifted as the consequence of special relativity and accounts for a change in observed luminosity.
  
  By taking into consideration of these effects, a formula is derived for the observed luminosity S_o of a spherical plasma in terms of the intrinisic luminosity S_e (mostly in the form of synchrotron radiation) and the Doppler factor D :
  S_o = S_eD^p, where
  

  Figure 05-02t Black-hole Imaging [view large image], [see video]

  Using the simulation in Figure 05-02t as example:
  For the face-on case, = 90^o D = (1 - v²/c²)^1/2, indicating that S₀ << S_e, the luminosity is reduced by the effects.
  For the edge-on case, = 0^o D = [(1 + v/c)/(1 - v/c)]^1/2, indicating that S₀ > S_e, the luminosity is enhanced by the effect.
  
  The animation accompanied with Figure 05-02t shows the appearance of a spherical bright spot in the accretion flow around a black-hole, which is not spinning (a = 0) and at a distance of about 6 time the Schwarzschild radius R_s = 2GM/c² = 2x10¹⁵ cm. The upper right panel shows no gravitational lensing effects. The left panel shows the lensing, starting with face-on and then decreasing in inclination to edge-on (with respect to our line of sight). On the lower right, the graphs show the change in linearly polarized emission and total emission corresponding to the motion in the left panel.
  
  
• Black-hole Jet - A prominent feature of M87 is a narrow, one-sided jet emanating from its center and extending for thousands of light years. Such appearance can be explained by the above example of edge-on synchrotron source. For the approaching (toward

  Earth) case, D = [(1 + v/c)/(1 - v/c)]1/2 which implies enhanced luminosity. For edge-on receding source v is replaced by -v so that D = [(1 - v/c)/(1 + v/c)]1/2 which implies reduced luminosity. However, even the approaching jet is absent in the M87 black-hole image because it is highly sensitive to observing wavelength as shown in the simulation images of Figure 05-02u and the accompanied video. The brightness of the jet becomes un-noticeable at the observational wavelength of 0.1 cm (see Figure 05-02u).

  Figure 05-02u Black-hole Jet [view large image], [see video]

  The video simulates the black-hole in different wavelength/frequency. It shows the accretion disk becomes more transparent with decreasing wavelength. At around 0.1 cm, the accretion disk becomes completely transparent and reveals the black-hole silhouette.

	moves around because the environment around the black hole changes on a scale of several weeks. Strong magnetic fields stir the accretion disk and produce hotter spots that then orbit the black hole. See "The first-ever image of a black hole is now a movie".
Figure 05-02w M87 Black Hole, 2009-2017 [view large image]	In 2018, a separate team reported evidence of a blob of hot gas circling SgrA*, the Milky Way’s central black hole, over the course of around 1 hour. Because M87* is more than 1,000 times the size of SgrA*, the dynamics around M87* take longer to unfold.

The 2017 EHT observation of synchrotron polarization is published in "The Astrophysical Journal Letters" on March, 2021 (see "First M87 Event Horizon Telescope Results. VII. Polarization of the Ring"). That's a long long letter for the professionals, here is just an attempt to understand the link between the observed polarization pattern and the magnetic field.


• The observed polarization pattern is shown in Figure 05-02x,a for 4 days in one week. The polarization fraction is relatively low.

  It indicates that the emission occurs inside a magnetized plasma with lot of scrambling (reducing the degree of polarization). The pictures also show that the pattern varies in one day. Therefore, the maximum size of the emitting region would be no more than : R ~ c x (seconds in one day) = (3x1010 cm/sec) x (86400 sec) ~ 2.6x1015 cm, which is a little bit larger than the Schwarzschild radius of the M87 black hole Rs ~ 2x1015 cm ~ 100 AU.

  Figure 05-02x M87 Magnetic Field [view large image]

  1 AU = 1.5x1013 cm (distance from Sun to Earth)

• Figure 05-02y provides a video to show the formation of the polarization as observed on Earth.
  1. The source of the synchrotron radiation comes from the plasma rotating around the black hole in a disk.

  In cylinderical coordinate, the magnetic field has a r-component on the disk beside the dominant field along the z-axis (Figure 05-02x,e). This r-component is dragging along with the rotation producing a B component (as shown in purple, Figure 05-02x,c). It is the electrons spiraling around the B that produce the synchrotron radiation. The B-polarization is in the direction of the B field, with the E-polarization at right angle (see Figure 05-02x,c or the video in Figure 05-02y).

  Figure 05-02y M87 Polarization [image, video]

  The magnetic fields with the corresponding polarization patterns are shown in Figure 05-02x,b.

• The observed polarization maps are compared to a gallery of 72,000 snapshot images from numerical simulations probing 120 different models of the accretion flow and jet. It suggests that the surroundings of M87 are best described by a model called Magnetically Arrested Disk (MAD). Figure 05-02x,d shows the MAD model as viewed from within the plane of the accretion disk around a black hole. Poloidal magnetic field lines pile up close to the black hole, pushing back on the infalling matter. Note that the field has a radial component which is important as it is dragged along by rotation of the plasma generating a magnetic field component in the direction. It is this B field that produces the observed polarization pattern as mentioned above.


• In another model known as "Magnetohydrodynamics (MHD)", similar B component is also developed from the poloidal magnetic field (Figure 05-02x,e). It is the Lorentz force (Figure 05-02x,c) that holds the plasma together providing ultimately the source for the radiation and polarization.

		be a black hole (see Figure 05-02z1). However, there is no jet in the 300 GHz radio image of the M87 black hole taken by EHT in 2019 and its supposedly refined image in 2021. The disappearance can be explained by weak synchrotron (non-thermal) emission at the higher frequency of 300 GHz (see Figure 05-02z2). The jet re-appears in the 2023 radio image at 100 GHz from the Global Millimetre VLBI Array (GMVA). It shows the twisted helix close to the black hole from the accretion disk. Thus, it requires lower frequency to see the non-thermal jet; while higher frequency shows the jet by thermal radiation.
Figure 05-02z1 M87 Jet [view large image]	Figure 05-02z2 Radiation Types [view large image]	There is no jet ~ 300 GHz because both types of emission are weak near that point. (see video in Figure 05-02u, and the "Formation of Jet").

		Figure 05-02z4 shows the helically shaped magnetic field composing 2 components, e.g., Bz and B along the z and directions respectively. The thermal component moves along the z-axis collimated in the confined direction in a narrow beam. While only the lighter mass electrons can be bended over into the direction emitting the non-thermal radiation (see synchrotron in Figure 05-02z5).
Figure 05-02z3 Thermal Emission from New-Born Stars [view large image]	Figure 05-02z4 Magnetic Field

Synchrotron radiation is emitted by charged particles, usually electrons, moving at relativistic speeds in magnetic fields. In a magnetic field a charged particle is forced to circle around the field line in a helical path. An accelerating charged particle emits electromagnetic radiation that is radiated along the direction in which the particle is moving. A large population of relativistic particles moving in a magnetic field will radiate over a wide range of frequencies and has a high degree of polarization (Figure 05-02z5).

Figure 05-02z5 Synchrotron Radiation [view large image]

		A moving charged particle in a magnetic field would be reflected by the Lorentz force F = q (vxB), where q is the charge, v is the velocity, and B is the magnetic induction. The magnetic field can in turn be generated by current loop. In a region with uniform magnetic field, the curvilinear path of the charged particle becomes a circle as shown partially in Figures 05-02z6,7 and if the velocity has a component in the direction of the magnetic filed then the trajectory will be a helix as in the jets of many astronomical objects such as quasars or black holes; we can further identify the accretion disk to be the current loop generating the magnetic field.
Figure 05-02z6 Synchrotron Polarization [view large image]	Figure 05-02z7 Synchrotron Spectrum [view large image]

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