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"# Two lectures on quasar lensing and microlensing\n",
"\n",
"R. W. Schmidt\n",
"\n",
"Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg,\n",
"Mönchhofstrasse 12-14,\n",
"D-69120 Heidelberg,\n",
"Germany\n",
"\n",
"Email: rschmidt@uni-heidelberg.de"
]
},
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"metadata": {},
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"## Abstract\n",
"\n",
"This contribution is a summary of two lectures I gave at the Jena meeting in September 2019. The topic of the first lecture was quasar lensing, the topic of the second was Microlensing. This text thus features a collection of topics from quasar lensing and planetary microlensing. My goal was to choose rather the intuitive than the mathematically rigorous explanation. For some of the diagrams I include the python code to generate them. All programs contained in this article are free software: you can redistribute them and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation."
]
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"## 1. Quasars and quasar lensing\n",
"\n",
"\n",
"### 1.1 The quasar engine\n",
"\n",
"According to the current understanding, quasars are the bright centres\n",
"of galaxies. The large fluxes from these pointlike sources can be\n",
"detected up to high redshift. This led people in the 80s to construct\n",
"models where the gravitational energy of material in a disc\n",
"surrounding a supermassive black hole is radiated away as\n",
"electromagnetic radiation. The potential energy released by the\n",
"accretion of a particle of mass $m$ down to the surface of a body of mass\n",
"$M$ and radius $R$ is \n",
"\n",
"$$\\Delta E_{acc}= G M m / R~~ (1)$$\n",
"\n",
"Working this out for a neutron star with a radius $R\\approx 10$km and\n",
"$M\\approx M_{sun}$ yields\n",
"\n",
"$$\\frac{\\Delta E_{acc}}{m} \\approx 10^{16} J/kg~~(2) $$\n",
"\n",
"Frank, King & Raine (2002) show that this value is larger than the yield for\n",
"nuclear fusion ($\\Delta E_{fusion}/m \\approx 0.007 c^2 \\approx 6\\times\n",
"10^{14} J/kg$). They stress that for black holes this calculation is\n",
"more complicated because there is no surface and find $\\approx 0.06\n",
"c^2$ using the correct general-relativistic treatment.\n",
"\n",
"[Shakura & Sunyaev (1973)](https://ui.adsabs.harvard.edu/abs/1973A%26A....24..337S/abstract)\n",
"showed that it is possible to construct a simple\n",
"thin-disc model of the viscous material in the accretion disc that is\n",
"inspiraling and radiates away the liberated\n",
"energy. At the same time, there is also a transport of angular\n",
"momentum outwards. The luminosity emitted by a Shakura-Sunyaev disc\n",
"is\n",
"\n",
"$$L=\\frac{G \\dot{m} M}{2 R} = \\frac{1}{2} L_{acc}~~ (3)$$\n",
"\n",
"where the $L_{acc}$ is the accreting potential energy of the disc.\n",
"\n",
"Modelling the emission using black-body radiation leads to the relation\n",
"that the closer one gets to the central object the more the maximum of\n",
"the emission moves to shorter wavelengths:\n",
"\n",
"$$r_{\\lambda} \\propto \\lambda^{4/3}~~ (4)$$\n",
"\n",
"One can also express this using the temperatures $T$: \n",
"\n",
"$$T=T_\\lambda \\left(\\frac{r}{r_\\lambda}\\right)^{-3/4} ~~ (5)$$\n",
"\n",
"($T_\\lambda = (3 G M \\dot{m}/ 8 \\pi r_\\lambda^3 \\sigma)^{1/4}$,\n",
"$\\sigma$=Stefan-Boltzmann constant).\n",
"With $R\\approx 10^4 km$, $\\dot{m}\\approx 10^{16} g/s$ and $M\\approx M_{sun}$ we find\n",
"for UV radiation $T_\\lambda\\approx 4\\times10^4$ K . When reducing the radius by a factor\n",
"$\\sim 10^4$, the temperature will increase by factor 1000.\n",
"\n",
"The (black-body) luminosity emitted at a particular radius should only depend on the temperature $T$, but is also proportional to the mass accretion rate: $L\\propto \\dot{m}$. Considering the Eddington luminosity at which the radiation would completely halt spherical accretion, \n",
"\n",
"$$L_{edd}= 4 \\pi G M m_p c/\\sigma_T,~~(6)$$\n",
"\n",
"($m_p$: proton mass, $\\sigma_T$: Thompson cross section)\n",
"a black hole mass-radius-luminosity relation can be derived (e.g., [Kochanek 2004](https://ui.adsabs.harvard.edu/abs/2004ApJ...605...58K/abstract)):\n",
"\n",
"$$M \\propto r_\\lambda^{3/2} ~(L/L_{edd})^{-1/2}.~~(7)$$\n",
"\n",
"__To keep in mind__:\n",
"The relations governing the accretion disk are testable using quasar lensing, especially *quasar microlensing*.\n",
"\n",
"* We need to show that the emission region has different sizes $r_\\lambda$ for emission at different wavelengths (equation 4).\n",
"\n",
"* Furthermore, this radius $r_\\lambda$ should obey relation (7) when the luminosity (assuming, e.g., Eddington luminosity) or the black hole mass can be measured.\n",
"\n",
"We shall see that there is evidence for both relations in the data."
]
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""
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"source": [
"###### Fig.1 : Artistic impression of the accretion disc surrounding a black hole. Perpendicular to the disc, emerging jets are illustrated. Image credit: NASA/CXC/SAO."
]
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"### 1.2 Multiple imaging of quasars\n",
"\n",
"In a gravitational lens situation, light rays from the source are\n",
"deflected by a massive object close to the line-of-sight. Very close\n",
"to the deflection mass (or even inside the deflecting mass for transparent/extended\n",
"lenses such as galaxies), the source can be imaged multiple times. \n",
"This effect is called __strong lensing__ and occurs once\n",
"the source crosses an imaginary line called the caustic.\n",
"\n",
"In Figure 2 (code cell 1) it is shown how the images of a background object can be constructed using the lens equation\n",
"\n",
"$$\\beta = \\theta - \\frac{d_{ds}}{d_d} \\hat{\\alpha} ~~ (8) $$\n",
"\n",
"with the quantities (angles with respect to the lens centre)\n",
"\n",
"$\\theta$: image position\n",
"\n",
"$\\hat{\\alpha}$: deflection angle, often it is defined: $\\alpha = \\frac{d_{ds}}{d_d} \\hat{\\alpha}$\n",
"\n",
"$\\beta$: source position\n",
"\n",
"$d_s$: (angular diameter) distance observer -- source\n",
"\n",
"$d_{ds}$: (angular diameter) distance lens -- source\n",
"\n",
"In the case depicted in Fig. 2, the deflection angle is constant (a so-called isothermal sphere). There are three aspects relevant for observations:\n",
"\n",
"* __Image multiplicity__: If the source is inside the region marked by the blue lines, two images can be observed (with the exception of the special symmetrical case where observer, lens and source are aligned).\n",
"\n",
"* __Magnification__: In the figure, only the radial extent of the source is shown, where no magnification occurs for this lens because of the constant deflection angle:\n",
"$$\\mu_r = \\frac{d \\theta}{d \\beta}=1 ~~ (9).$$\n",
"The magnification in the tangential direction is proportional to the ratio of image position and source position, relative to the centre of the lens:\n",
"$$\\mu_t = \\frac{\\theta}{\\beta} ~~ (10).$$\n",
"\n",
"* __Parity__: The image further away from the lens is imaged without parity change ('R'), but the inner image is mirror-inverted ('Я') because the light rays connect to the source via the other side of the lens.\n"
]
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"([], )"
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\n",
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