26.02.2018 Accretion power in astrophysics HIGH-ENERGY ...
Transcript of 26.02.2018 Accretion power in astrophysics HIGH-ENERGY ...
HIGH-ENERGY ASTROPHYSICS
26.02.2018
Accretion power in astrophysics
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Textbook
โข Accretion power in astrophysics - Frank, King and Raine http://qxyang.lamost.org/uploads/books/Accretion_Power_in_Astrophysics.pdf
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Goals
โข Eddington limit with derivation
โข Bondi accretion (Spherical symmetry):โ Accretion radius
โ Supersonic accretion
โข Wind accretion vs Roche Lobe overflow
โข Accretion disk properties: temperature and typical spectrum
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Introductionโข Accretion luminosity and
role of compactness.
โข Eddington luminosity
โ Balance radiation with gravitation
โ Assume ionized hydrogen
โ Discuss deviations
โข Typical temperatures:
โ Temperature if radiation were a black body
โ Temperature if gravitational energy were all converted into heat
โข Perform these calculations as in book
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Bondi accretionโข Spherical accretion
โข Solution with sonic point
โข Bernoulli eq.
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Accretion radiusโข Accretion radius:
โ Radius at which gravitational pull equals the sonic speed of medium (thermal motion)
โข Efficiency of spherical accretion is low.
โข For X-ray binaries, we need to have others mechanisms.
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Inefficiently radiating flow?โข Density of the flow is
๐ =แถ๐
4๐๐2๐ฃ= ๐๐๐๐
๐
๐๐๐๐
โ3/2
โข Density near a stellar black hole reach 1022๐๐โ3 like the Earth atmosphere, near a supermassive (106 โ 109) ๐๐ ๐ข๐ black-hole ?
โข Matter falls on a free-fall time scale
๐ก๐๐ =๐ ๐๐๐
32
๐บ๐ 1/2~๐บ๐
๐๐๐๐๐๐ต๐ป
3/2
~10โ5๐
๐๐ ๐๐
๐๐๐๐
๐๐ต๐ป
3/2s
โข Accretion flow could be heated at the temperature in the GeV range
๐~๐๐ฃ๐๐2 ~
๐บ๐๐
๐~mc2
โข However, emission can be produced oly if the time scale of energy loss is lower than the free-fall time scale
๐ก๐ต๐~ 10โ5๐
1020 ๐๐โ3
โ1
๐
โข For very low accretion rate, particles cannot interact and there is no emission.
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Galactic centerโข Density of medium is around
102๐๐โ3
โข Temperature from X-rays around 0.1-1 keV
โข From motion of stars, we derive a mass of 4 ร 106๐๐ ๐ข๐ and the closest star orbits at 1000 gravitational radii
โข Variability occurs on time scales of 10 min, comparable to a Keplerian orbit around the BH
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Sgr A*โข We can use the accretion radius and the
free-fall time scale (Exercise) to derive an accretion rate corresponding to a luminosity of 1041 erg/s (efficiency 0.1), at 8 kpc, this would be way too high for observations (10โ10erg/s/cm2)
โข We think of a very inefficient way of producing X-rays from accreting material: radio, flares in IR, in X-ray and TeV gamma-rays -> particles do not interact while falling!
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Observationsโข Quiescent and flaring
periods
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F. Yusef-Zadeh M. Et al.ApJ 144, 1 (2012)
Galactic center as an emitterโข Letโs focus on IR and X-ray flare, which are
correlatedโข Electrons are heated up at the energy of
protons, which fall onto the central object at ~GeV energy giving rise to IR-range photons
๐๐ ๐ฆ๐๐โ = 0.05๐ต
1๐บ
๐ธ
1๐บ๐๐
2eV
โข These photons can Inverse Compton on the same population of electrons in the hard X-ray range
๐๐ผ๐ถ =๐ธ๐๐๐
2
๐๐ ๐ฆ๐๐โ
= 100๐๐ ๐ข๐๐โ0.01๐๐
๐ธ๐1๐บ๐๐
2
๐๐๐
โข We know the peak energy, but what about the intensities? We need to know the magnetic field and radiation densities
โข Letโs estimate the radiation field as the observed luminosity in a dimension close to the Schwarschild radius
๐๐๐๐ =๐ฟ
4๐๐2= 1012.5๐ฟ36
๐
10๐บ๐
2 ๐๐
๐๐3
โข X-ray is comparable or smaller than IR, then the energy density of magnetic field should be similar
๐๐ต =๐ต2
8๐= 1012.5
๐ต
10 ๐บ
2 ๐๐
๐๐3
Value of B-field? (~10 G)
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TeV and radio emissionsโข TeV and radio emissions cannot
be straightforwardly interpreted and are probably due to ifferent populations of electron and or radiation processes
โข They are not variable, therefore they could be roduced at larger distances
โข Very active research of Sgr A* and its surroundings
โข For instance echo of past activity on molecular clouds
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Wind accretionโข Early-type stars have a strong
wind, powered by absorption of lines in the UV. Mass loss rate is 10โ10 โ 10โ6๐๐ ๐ข๐/๐ฆ๐
โข if a compact object is embedded, it can accrete. Bondi-Hoyle accretion
โข Wind speeds is ๐ฃ๐ค๐๐๐ ๐ =
๐ฃโ 1 โ๐ โ
๐
โ๐ฝwith terminal
velocity of ~1000 km/sโข A strong tidal tail is formed, but
when accretion s possible?
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Manousakis et al. (2014)
Wind accretionโข In stedy state, accretion radius is
๐๐๐๐ =2๐บ๐
๐๐ 2
โข With a mass accretion rateแถ๐ = ๐๐๐๐๐
2 ๐๐๐๐ โข In a binary system, the medium
velocity is not the sound speed, but the wind speed plus the orbital motion
โข ๐ฃ๐๐๐ = 2๐บ๐/๐ with a the binary separation
โข We must substitute to ๐๐ 2 the
value ๐ฃ๐ค๐๐๐2 + ๐ฃ๐๐๐
2 ~๐บ๐
๐+
๐ฃ๐ค๐๐๐,โ2
โข Considering the density ๐๐ค๐๐๐ =แถ๐๐ค๐๐๐
4๐๐2๐ฃ๐ค๐๐๐2 , we can derive
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Beyond a simple theory
โข Acrretion from close binaries: Vela X-1, Cyg X-1
โข We need to consider several other aspects, such as the photionization of the wind, which decellerates wind
โข Possible to form a small and possibly intermittent accreiton disk.
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Useful parametrizationโข We use a frame rotating with
the system and account for Coriol force to obtain the effective potential
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โข The solution of this equation is not straightforward, but we obtain the potentials of the previous figure. A good parametrization (๐ =
๐2
๐1)
Exercisesโข Derive the free-fall time scale.โข Derive the energy gained by a free falling
proton on a body of 1 Solar mass and radius R. Compute it it for the Schwartschild radius.
โข Compute the temperature of a fluid of protons fallen onto the surface of a star for Solar mass, Solar radius, Earth radius, neutron star radius (10 km), and Scharschild radius.
โข Get an estimate of the accretion radius for a one solar mass star in the ISM (T~10000 K).
โข Estimate the mass accretion rate and accretion luminosity for one solar mass with the above radii
โข Compute the temperature of a black-body emitting all the gravitational energy as a black-body for the previous cases.
โข Estimate the sonic point radius and speed as function of the value at infinity (use Bernoulli equation). Can we use the adiabatic approximation ? (gamma=5/3)
โข Get the temperature radial dependency at any radius from a central object for a mass accretion rate แถ๐ . Is temperature higher far or close to the central object? Waht is the luminosity?
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Roche Lobe overflow
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โข Matter can inflow from inner lagrangian point
โข It posseses a sizeable angular momentum
Formation of an accretion diskโข When streaming from the inner
Lagrangian point, particles have an angular momentum.
โข Gas speed is dominated by the orbital motion (~1000 km/s) while the sound speed is ~10 km/s
โข The stream will intersect itself in different ellipses and create shocks. It will settle at the first stable orbit which conserves initial angular momentum, the circularization radius, obtained from equating the angular momentum at the Lagrangian point to a circular orbit
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๐ = ๐1 +๐2, 4๐๐3 = ๐บ๐๐2
Thin accretion disk
โข H<<R, radiation pressure negligeable, strictly valid only for ๐ฟ โช ๐ฟ๐ธ๐๐
โข Gas pressure must support disk vertically against gravitation
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Thin diskโข Remember that sound
speed is ๐๐ 2 โ
๐
๐
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โข Is the flow supersonic or subsonic?
โข ๐ฃ = 1.2 ร 1010๐/
๐๐ ๐๐ ๐ 6cm/s
โข Like in Bondi accretion, but matter remains very long in orbit, so efficient emission !!
Thin disk/2
โข Radial acceleration due to pressure, negligeable as compared to gravitation
โข Radial speed is very low, almost Keplerian motion
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โข แถ๐ = โ2๐ ๐ ๐ฃ๐ with sigma the surface density
โข Vertical density scales exponentially due to assumption that the pressure balances gravity
โข ๐น๐ง โ๐บ๐
๐ 2๐ง
๐ โ ๐ง
โข ๐ ๐ง โ exp(โ๐ง
๐ป)
Thin disks/3โข Since angular speed is
๐ =๐บ๐
๐ 3
1
2, there is
differential motion and thus, possibly shear visccosity.
โข Angular momentun decreases with decreasing radius (write equation)
โข Accretion disks are pumps of angular momentum
โข Force due to viscosity is
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Torque
โข This torque need to balance the loss of angular momentum
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Temperature profileโข We need to equate the
dissipation torque to thermal emission at each radius
โข 2๐๐๐ต๐4 = ๐ท(๐ )
โข Why the 2?
โข ๐ ๐ โ ๐ โ3
4
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Accretion disk spectrumโข Disk emits as a suprposion of
black bodiesโข In reality other factors also
need to included, such as metallicity, viscous parameter, preseence of an atmosphere, properties of the compact object etc.
โข Pivot temperature is the inner disk temperature
๐~5 ๐9โ1
4eV
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โข Spectrum of AGN in the UV, of X-ray binaries in X-rays
Dissipationโข Disk dissipate
half of potentl energy of the accretion flow.
โข From virial theorem
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