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Lecture 8, Introduction to Black Hole Astrophysics (PHYS480) Hsiang-Yi Karen Yang, NTHU, 4/20/2021 • HW4 Will Be Posted on Ilms and Course Website Today

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Lecture 8, Introduction to Black Hole Astrophysics (PHYS480) Hsiang-Yi Karen Yang, NTHU, 4/20/2021 • HW4 Will Be Posted on Ilms and Course Website Today Lecture 8, Introduction to Black Hole Astrophysics (PHYS480) Hsiang-Yi Karen Yang, NTHU, 4/20/2021 • HW4 will be posted on iLMS and course website today. Due date: 4/27/2021 • Please search for black hole news for the oral presentation and paste the news link here: https://docs.google.com/spreadsheets/d/1_aYyMj1wf_uGheZ7zp_hvthmy4mdmPwI xFDdZOMG-nc/edit?usp=sharing • For the oral presentations, I will compile the scores and comments from the audience and send to you after the presentation • Please start forming a team of 3 people for the final report. Choose a team leader and enter your names on iLMS -> 小組專區 § Your feedback and comments would be valuable for improvements of this course! § Link to the course evaluation form: https://qrgo.page.link/9f6cE § Or scan the QR code here: § The Eddington limit – the maximum luminosity a body can achieve due to the competition between radiation pressure force and gravity § Accretion properties depend on angular momentum and mass accretion rates § When no angular momentum -> spherical Bondi accretion; when there is angular momentum -> accretion disks § Solution of the angular momentum problem: outward angular momentum transport due to viscosity in shear flows, which allows mass to flow inward § Three types (slim, thin, and thick) of accretion disks depending on the mass accretion rate § X-ray binaries exhibit state transitions between X-ray hard and soft spectra, corresponding to transitions between thin and thick accretion disks due to varying accretion rates �̇ �̇ = !" �̇ #$$ § Radiatively less efficient than thin disks § Radiation pressure driven winds Slim disk § Only occur in rare cases (�̇ ≳ 1) § Radiatively efficient § Spectrum well described by Thin disk superposition of black-body radiation § Quasars, disk-dominated X-ray (0.01 ≲ �̇ ≲ 1) binaries § Radiatively inefficient § Accretion is hot – corona Thick disk § Spectrum described by nonthermal (�̇ ≲ 0.01) processes § Sgr A*, low-luminosity AGN, corona- dominated X-ray binaries § Measuring BH masses § Four methods § Mass distribution of BHs § Open questions and future prospects § Measuring BH spins § Three methods § Spin distribution of BHs § Open questions and future prospects 232 6 Evidence for Black Holes Beaming and collimation is also compatible with the observation of “achromatic” breaks, the name given to the simultaneous steepening in the light curve at all ener- gies. The radiation emitted by a plasma moving at relativistic speeds is beamed into an angle θ 1/Γ in the direction of motion. If Γ is very high only a small portion of the jet’s∼ section is visible. But in the internal/external shock model the outflow decelerates in the external shocks. As the bulk Lorentz factor decreases and the jets advances a larger fraction of the emitting region becomes visible. As long as θ < θjet beamed emission cannot be observationally distinguished form spherical. But even- tually when Γ < 1/θjet the whole section of the jet becomes visible. An observer now receives less radiation than she/he would do if the radiation were spherically symmetric because the observed section increases only because the jet is advancing. So the light curve begins to decays faster. The jet opening angle can be calculated from the time of the break. For long GRBs θjet 5◦–10◦ whereas θjet 5◦–25◦ for short GRBs, although the latter estimate is more∼ uncertain due to poor∼ statistics. Gamma-ray bursts with chromatics breaks and very late breaks (which could imply large jet opening angles) have been observed. In the classical fireball model the outflows are matter (not magnetically) dom- inated; recall from Chap. 5 that a low magnetization is essential for shocks to develop. Electrons accelerated at the internal shocks radiate the prompt emission through synchrotron radiation in the locally amplified magnetic field, and perhaps also synchrotron-self Compton and inverse Compton scattering of thermal photons. The afterglow radiation is synchrotron emission from electrons accelerated at the external shocks. If the jet is powered by the rotational energy of the black hole it is likely that the magnetization remains high and magnetic energy is dissipated by reconnection, instabilities, or other mechanisms different from shocks. Although the baryon load (if any) of GRB jets is unknown radiation of hadronic origin has been also considered, recently in particular to explain the GeV emission from some GRBs detected with Fermi-LAT. Gamma-ray bursts jets with a content of relativistic protons should be sources of neutrinos created in proton-photon interactions. Inter- estingly, neutrino bursts could be expected even in the absence of a burst of radiation if the jets cannot make it through the stellar envelope in a collapsar. These are called “choked” gamma-ray bursts. Short gamma-ray bursts and their progenitors must be as well sources of gravitational radiation. § Use the orbital parameters of stars to determine the mass of the central object 6.2 Evidence§ forNewtonian Stellar-Mass gravity: Black Holes !!" !"$ � = = 6.2.1 Dynamical Arguments# %&# § Complications that need to be taken into account: It is possible to derive§ Mass from of Kepler’sthe companion laws anstar expression (due to orbits that around relates the the center masses of ofmass; important for smbhs) 6.2 Evidence for Stellar-Mass Black Holes 233 the two components§ ofInclination a binary systemof orbits and (because the inclination Doppler’s angle effect of only the orbitaltraces velocities plane. along the line of sight) This is known as the§ massThe mass function functionand (Week is given 5): by 3 3 3 3 V Porb M sin i M sin i f(M) ∗ . (6.2) = 2πG = (M M )2 = (1 q)2 + ∗ + Fig. 6.4 Definition of the parameters in the binary mass function. The angle i gives the inclination of the plane of the orbit with respect to the plane of the sky (perpendicular to the line of sight). The velocity V is the component along the line of sight of the orbital velocity of M measured where indicated ∗ ∗ Here M and M are the masses of the compact object and the donor star, respec- ∗ tively, q M/M is the mass ratio, i is the inclination angle of the orbit, Porb is the orbital period,= and∗ V is the semi-amplitude of the donor star’s line-of-sight velocity. The definitions of i and∗ V are made clear in Fig. 6.4. The mass function is an∗ interesting quantity because its value can be calculated from parameters (Porb and V )measurablefromthelightcurveofthedonorstar. If i and M are independently∗ known the value of M follows directly from that of f .Forourpurpose,however,itisenoughtonoticethatthemassfunctionsetsan∗ absolute lower limit to the mass of the compact object: f(M) M, (6.3) ≤ where the equal corresponds to i 90◦ and q 0. The upper limit for the mass of aneutronstarisuncertain,mainlybecauseoftherelativelypoorknowledgeabout= → the equation of state of matter at extremely high densities. It is presently thought to be somewhere in the range MNS 2.9–3.2 M (e.g. Rhoades and Ruffini 1974; Kalogera and Baym 1996), and up to∼ a 20–25 %& larger if the star is rotating rapidly (Friedman and Ipser 1987;Cooketal.∼1994). A value of f larger than this consti- tutes a piece of dynamical evidence for the presence of a black hole. There are more than 20 stellar-mass black hole candidates in binary systems iden- tified on dynamical grounds (e.g. Remillard and McClintock 2006;Casares2010; Özel et al. 2010). In some cases f<MNS,butindependentconstraintsoni or M ∗ allow to assure that M>MNS.Thefirsttobediscoveredandperhapsthemostex- amined galactic black hole candidate is Cygnus X-1. This is a binary system formed by a compact object and a massive O-type donor star. According to the latest es- timates by Orosz et al. (2011)themassofthecompactobjectinCygnusX-1is M (14.81 0.98)M , far beyond any upper limit for the mass of a neutron star. Aside= a few± other exceptions,& however, most galactic black hole candidates have been found in low-mass binaries—particularly in those classified as “X-ray tran- sients” or “X-ray novae”. These systems spend most of their lives in quiescence 33 1 (X-ray luminosity LX ! 10 erg s− )untilsometypeofinstabilityintheaccretion disk triggers a sudden increase in the accretion rate. Then they enter in outburst, § This is how we knew Cygnus X-1 and Sgr A* are BHs § This method provides the most precise mass measurements, but it can only be applied to really nearby systems § smbhs: dozens in the Milky Way Galaxy + a few in nearby galaxies § SMBHs: one in the Milky Way and <~20 nearby galaxies § For SMBHs in other galaxies, it is impossible to resolve motions of individual stars § But for relatively nearby galaxies where the sphere of influence (the region where BH’s gravity is dominant) can be resolved, motions of stars/gas can be measured by the smearing of spectral lines due to Doppler’s effect § Velocity dispersion (s) = standard deviation of the velocity distribution Acknowledgments N.J.M., C.-P.M, K.G. and J.R.G. are supported by the Na- tional Science Foundation. C.-P.M. is supported by NASA and by the Miller In- stitute for Basic Research in Science, University of California, Berkeley. S.A.W. is supported by NASA through the Hubble Fellowship. Data presented here were obtained using Gemini Observatory, W.M. Keck Observatory, and Mc- Donald Observatory. The Gemini Observatory is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the National Science Foundation on behalf of the Gemini partnership. The W. M. Keck Observatory is operated as a scientific partnership among the Cal- ifornia Institute of Technology, the University of California, and NASA. The McDonald Observatory is operated by the University of Texas at Austin.
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