1. High Energy Astrophysics emp@mssl.ucl.ac.uk http://www.mssl.ucl.ac.uk/
Accretion
High Energy Astrophysics

2. loss rotational energy
Introduction
Mechanisms of high energy radiation
X-ray sources
Supernova remnants
Pulsars
We have studied mechanisms of emission of high-energy radiation and discussed sources of X-rays such as supernova remnants and pulsars.
In the case of SNRs, emission is generally thermal and is produced in the cooling of material ejected in the explosion and interacting with the interstellar medium (ISM). Synchrotron emission is also observed from SNRs.
For pulsars, the loss of rotational energy by the spinning neutron star as it slows down produces much of the observed energy. Also, the energy produced from the magnetic dipole effect is comparable to rotational losses.
thermal
synchrotron
loss rotational energy
magnetic dipole

3. Accretion onto a compact object
Principal mechanism for producing high-energy radiation
Most efficient of energy production known in the Universe.
Gravitational potential energy released for body mass M and radius R when mass m accreted
However the principal mechanism for producing high-energy radiation is that of the accretion of material onto a compact object.
The process is defined by the equation shown.
This shows the gravitational potential energy released (Eacc) by the accretion of a mass m onto a body of mass M and radius R (G is the gravitational constant).

4. Example - neutron star Accreting mass m=1kg onto a neutron star:
neutron star mass = 1 solar mass
R = 10 km
=> ~10 m Joules,
ie approx 10 Joules per kg of
accreted matter - as electromagnetic radiation m R 16
To illustrate the amount of energy released by the process of accretion, we take the example of a typical neutron star and accrete 1kg of matter onto it. Assuming m comes from infinity with no energy, then the equation given on the previous slide applies. Using R=10km for the neutron star radius and a mass of 1 solar mass, we find that for every kilogram accreted by the neutron star, 1e16 Joules of energy are released.
Energy released eventually as electromagnetic radiation. 16 M

5. Efficiency of accretion
Compare this to nuclear fusion H => He releases ~ mc ~ 6 x m Joules - 20x smaller (for ns) 2 14
So energy released proportional to M/R ie the more compact a body is, the more efficient accretion will be.
We compare the energy released by a kg of matter by the nuclear fusion process with that of accretion onto a neutron star and find that accretion (using the previous example) is 20 times more efficient.
The previous equation for the gravitational potential energy released by accretion shows that the energy released is proportional to the ratio of mass to radius (M/R) of the accreting body, ie the more compact the body, the higher the accretion efficiency.

6. Accretion onto white dwarfs
For white dwarfs, M~1 solar mass and R~10,000km so nuclear burning more efficient by factor of ~50.
Accretion still important process however - nuclear burning on surface => nova outburst accretion important for much of lifetime
Compactness is thus an important parameter when considering the efficiency of accretion compared to other processes. For example, for a white dwarf with a mass of 1 solar mass and a radius of 10,000km, nuclear burning is 50 times more efficient than accretion. However, this does not mean that accretion does not occur on white dwarfs…
Nuclear burning occurs on the surface of a white dwarf and the process tends to run away producing an event of great brightness but short duration - such an event is called a nova outburst.
For much of a white dwarf’s lifetime however, no nuclear burning occurs but it does accrete material from its surroundings. In white dwarf binary systems, the white dwarf primary accretes matter from a companion star - these are known as cataclysmic variables and are quite common in the Galaxy.

7. Origin of accreted matter
Given M/R, luminosity produced depends on accretion rate, m.
Where does accreted matter come from? ISM? No - too small Companion? Yes. . .
The luminosity produced by a body with a given compactness depends on its accretion rate, mdot.
The source of the accreted material is probably NOT the ISM as the luminosity produced would not be observable. In Galactic binary systems, the presence of a companion provides the source of matter for accretion.

8. Accretion onto AGN 9
Active Galactic Nuclei, M ~ 10 solar mass - very compact, very efficient (cf nuclear) - accretes surrounding gas and stars
Active Galactic Nuclei, the cores of distant galaxies, contain supermassive black holes with masses typically of around a billion solar masses or more. Thus they are very compact and very efficient producers of energy and their fuel is the gas and stars which surround them.

9. Fuelling a neutron star
Mass = 1 solar mass observed luminosity = J/s (in X-rays)
Accretion produces ~ J/kg
m = / kg/s ~ 3 x kg/year ~ 10 solar masses per year 31 16
Looking at a neutron star again now, and we are going to calculate the mass accretion rate required to produce the observed luminosity.
Substituting as shown we find that 1e-8 solar masses are required every year to produce the luminosities observed (assuming of course that this is all due to accretion).
If a neutron star is accreting matter from an early-type companion then this figure compares favourably with the expected mass loss from the mass loss in the stellar wind, which is in the region of 1e-6 to 1e-5 solar masses per year. . 31 16 22 -8

10. The Eddington Luminosity
There is a limit to which luminosity can be produced by a given object, known as the Eddington luminosity.
Effectively this is when the inward gravitational force on matter is balanced by the outward transfer of momentum by radiation.

11. Note that R is now negligible wrt r
Eddington Luminosity
Outgoing photons from M scatter material (electrons and protons) accreting.
Accretion rate controlled by momentum transferred from radiation to mass M m r F F
grav
rad
Note that R is now negligible wrt r
At high luminosities, the accretion rate may be controlled by the outward momentum transferred from the radiation to the accreting material.
Consider spherically symmetric accretion onto a body of mass M of a particle of mass m at a distance r. (note that r is now much larger than the radius f the body, R).
Outgoing photons from M scatter off of the incoming material via Thomson scattering.

12. Scattering L = accretion luminosity
Scattering cross-section will be Thomson cross-section s ; so no. scatterings per sec:
no. photons crossing at r per second -2 -1
photons m s e

13. Momentum transferred from photon to particle:
Momentum gained by particle per second = force exerted by photons on particles hn
e-, p

14. radiation pressure = gravitational pull
Eddington Limit
radiation pressure = gravitational pull
At this point accretion stops, effectively imposing a ‘limit’ on the luminosity of a given body.
The Eddington limit defines the luminosity for a given mass M at which the outward pressure of radiation is balanced by inward gravitational attraction. At greater luminosities, accretion would be halted so that if all of the luminosity of the source were derived from accretion, it would effectively be switched off.
So the Eddington luminosity is:

15. Assumptions made
Accretion flow steady + spherically symmetric: eg. in supernovae, L exceeded by many orders of magnitude.
Material fully ionized and mostly hydrogen: heavies cause problems and may reduce ionized fraction - but OK for X-ray sources
Edd
We have assumed throughout these derivations that the accretion flow is steady and spherically-symmetric.
Steady flow : In supernovae the flow is not steady and the Eddington luminosity may be exceeded by many orders of magnitude,
Spherically symmetric: If accretion occurs over only a fraction of a star’s surface then the Eddington luminosity L_Edd may be expressed as fL_Edd where f is the fraction over which accretion occurs. (And this applies to only simple geometries).
Material mostly Hydrogen: This is a good approximation in most astrophysical situations.
Gas fully ionized: Adding just a small fraction of heavy elements can invalidate the assumption that the gas is fully ionized. However for X-ray sources, the most abundant ions can usually be stripped of their electrons by a very small fraction of the X-ray luminosity.

16. Electrostatic forces between e- and p binds them so act as a pair.
What should we use for m?
Electrostatic forces between e- and p binds them so act as a pair.
Thus:
M Joule/sec
The attractive electrostatic Coulomb force between electrons and protons means that as they move out the electrons drag the protons with them. In effect, the radiation pushes out electron-proton pairs against the gravitational force which is acting on mass m~m(proton) at a distance r.
M Joule/sec
Joule/sec

17. Black Holes
Black hole does not have hard surface - so what do we use for R?
Use efficiency parameter, h
at a maximum h = 0.42, typically h = 0.1
solar mass bh as efficient as neutron star .
then
The problem with black holes is that the matter falling onto a black hole does not have a hard surface to accrete upon - the energy carried by the matter may just become part of the total mass of the black hole without being radiated. The uncertainty in this case is parameterized by h and is believed to be about 0.1 for black holes in general.
For a solar mass neutron star, h~0.15 thus despite the extra compactness of stellar mass black hole, it may be no more efficient than a typical neutron star at converting gravitational potential energy into radiation via accretion.

18. Emitted Spectrum define temperature T such that hn~kT
define ‘effective’ BB temp T
thermal temperature, T such that:
rad
rad b
To characterize the emitted continuum spectrum we define three effective temperatures, the radiation, blackbody and thermal temperatures.
Radiation temperature defined such that energy of a typical photon hn is of the order of kT_rad.
Blackbody temperature is the temperature the source would have if it were to radiate the given power as a blackbody spectrum.
Thermal temperature is temperature accreted material would reach if its gravitational potential energy were turned entirely into thermal energy. th
=>

19. Accretion temperatures
Flow optically-thick:
Flow optically-thin:
If the accretion flow is optically-thick, the radiation reaches thermail equilibrium with the accreted material before leaking out to the observer, and the radiation temperature is similar to the blackbody temperature.
If the accretion flow is optically-thin, the accretion energy is converted directly into radiation which escapes without further interaction and the radiation temperature is thus similar to the thermal temperature.

20. Accretion energies In general, For a neutron star, assuming
Recalling of course that any system cannot radiate a given flux less than the blackbody temperature, we find that the radiation temperature must be greater than (or equal to) to blackbody temp, but less than (or equal to) the thermal temperature.

21. Neutron star spectrum Thus expect photon energies in range:
similarly for a stellar mass black hole
For white dwarf, L ~10 J/s, M~M , R=5x10 m,
=> optical, UV, X-ray sources 26
acc
Sun 6

22. Accretion modes in binaries
ie. binary systems which contain a compact star, either white dwarf, neutron star or black hole.
(1) Roche Lobe overflow
(2) Stellar wind
- correspond to different types of X-ray binaries
1. In the course of its evolution, one of the stars in a binary has expanded, or the binary separation has become sufficiently narrow, that the gravitational pull of the companion can remove the outer layers of the envelope. This is known as Roche lobe overflow.
2. Much of the mass of one of the stars may be ejected in the form of a stellar wind, and some of this material will be captured gravitationally by the companion.

23. Roche Lobe Overflow Compact star M and normal star M
normal star expanded or binary separation decreased => normal star feeds compact 1 2 CM M M + 2 1 a

24. Roche equipotentials Sections in the orbital plane M M + + + v L 1 CM2 + + + v
Consider a binary system with a compact star of mass M and a normal companion (M2) orbiting their common centre of mass CM. The gravitational field’s equipotential surfaces will be spheres at small distances from the masses and at large distances (centred on CM).
The most important feature from the point of view of accretion is the critical surface at which the equipotentials of the two stars touch.The volume contained within this surface surrounding each star is called the Roche Lobe.
The lobes join at the inner Lagrangian point L1. Material inside one lobe in the vicinity of this point finds it much easier to pass through it into the other lobe than to escape the critical surface altogether. This is what is known as Roche Lobe overflow. L 1

25. Accretion disk structure
The accretion disk (AD) can be considered as rings or annuli of blackbody emission.
Dissipation rate, D(R) R
It is assumed that the disk is geometrically-thin and optically-thick in the z-direction. Thus each annular element of the disk radiates roughly as a blackbody with a temperature T(R) , where :
Sigma x T^4(R) = D(R)
Where D(R) is the dissipation rate and sigma x T^4 is the blackbody flux.
R_* is the radius of the black hole (or compact object).
Dissipation through the disk is independent of the viscosity in the disk – and the dissipation rate is the energy flux through the faces of the thin disk. Thus if the disk is optically-thick in the z-direction, we are justified in assuming that the dissipation rate is equivalent to the blackbody emission.
= blackbody flux

26. Disk temperature Thus temperature as a function of radius T(R): When
Substituting the blackbody flux equation into the dissipation equation gives the temperature of the disk as a function of radius. At radii larger than the radius of the compact body, the temperature is given by the equation shown. Note that the temperature decreases with radius with a power –0.75.

27. Accretion disk formation
Matter circulates around the compact object:
ang mom outwards
matter inwards

28. Matter sinks deeper into gravity of compact object
Material transferred has high angular momentum so must lose it before accreting => disk forms
Gas loses ang mom through collisions, shocks, viscosity and magnetic fields: kinetic energy converted into heat and radiated.
Matter sinks deeper into gravity of compact object
A consequence of this process is that the material transferred has high angular momentum for the orbital motion of the binary, so it cannot accrete directly onto the compact object, and an accretion disk forms.
In the disk, the gas loses angular momentum by dissipative processes (collisions, shocks, viscosity), the energy of the ordered motion is converted into heat and this is radiate away. The matter seeks deeper into the gravitational potential of the compact object.
The matter originally forms a ring around the star, but the conservation of angular momentum implies that angular momentum is transferred outwards so that the outer parts of the disk expand to form a ring.
Assuming that the disk is in Keplerian motion, then the differential rotation in the disk implies that viscosity in the disk is significant.

29. Magnetic fields in ADs
Magnetic “flux tube”

30. Mag field characteristics
Magnetic loops rise out of the plane of the disk at any angle – the global field geometry is “tangled”
The field lines confine and carry plasma across the disk
Reconnection and snapping of the loops releases energy into the disk atmosphere – mostly in X-rays
The magnetic field also transfers angular momentum out of the disk system
The footpoints of the magnetic loops are anchored in the accretion disk material. Because the disk is Keplerian and material rotates at an angular velocity which depends on the distance to the centre of the disk, the loops can become stretched and tangled if both feet do not form at the same radial distance. Eventually, differentially-rotating loops will snap and reconnect, which releases huge amounts of energy, mostly in X-rays.
Plasma is trapped by the loops and confined, and transfers angular momentum out of the disk system, which further assists the material as it falls towards the compact object and is accreted.

31. Disk Luminosity
Energy of particle with mass m in circular orbit at R (=surface of compact object)
Gas particles start at large distances with negligible energy, thus 1 2 1 2 GM R 1 2
mv = m = E 2
acc
How much luminosity is produced in the disk?
We assume that a particle with mass m which has zero negligible energy at infinity falls into the disk. The energy of the oarticle in a circular orbit at R (where R is the surface of the compact star) is given by the equation shown. This is what the particle is left with at R, ie it has lost the rest of its gravitational potential energy which it had at infinity in the disk.
The gas particles start at large distances from the star with negligible energy then the luminosity of the system is given by the expression shown where Mdot is the accretion rate.
Thus half of the available energy is radiated while the matter in the disk spirals inwards. . MM 2R 1 2
L = G = L
disk
acc

32. Disk structure
The other half of the accretion luminosity is released very close to the star.
X-ray UV optical
bulge
The diagram illustrates a cross-section through a binary star accretion disk. Half of the accretion luminosity is released in the disk - the other half very close to the compact star.
The disk is generally assumed to be geometrically-thin although X-ray observations of X-ray binaries indicate that the disk either bulges or flares up at the the outer edges. Such activity is seen in dipping low-mass X-ray binaries (LMXRBs). This may be due to radiation torques warping the disk, to tidal forces exerted by the secondary or due to the impact of the accreting material on the edge of the disk.
The disk is optically-thick throughout except at the very inner edges which are probably optically-thin and emit bremsstrahlung radiation.
Once the material has fallen low along the disk near the surface of the star, it may heat this surface or fall into the black hole.
Hot, optically-thin inner region; emits bremsstrahlung
Outer regions are cool, optically-thick and emit blackbody radiation

33. Stellar Wind Model
Early-type stars have intense and highly supersonic winds. Mass loss rates to solar masses per year.
For compact star - early star binary, compact star accretes if -6 -5
Early type stars have both intense and highly supersonic winds. If a compact star (black hole, neutron star or white dwarf) is in a binary with an early-type star of this type, it can accrete from the star if the conditions of the equation are met.
R is the distance from the compact object, eg a neutron star
v(ns) is the neutron star velocity
M is the neutron star mass
v(w) is the velocity of the wind outwards (typically a few thousand km/s)
GMm r 1 2
m(v + v ) 2 2
> w ns

34. matter collects in wake
Thus :
2GM
v + v r =
acc 2 2 w ns r
acc
The wind velocity is generally of the order of a few thousand km/s while the neutron star moves at about 200 km/s. The speed of sound in the gas is about 10km/s, thus a bow shock forms around the neutron star and this forms at r(acc). Capture will occur within a cylindrical region with its axis along the relative wind direction. Matter collects behind the neutron star in its orbital motion, in a wake or a stream.
It is not clear whether a disk always forms in this case.
Cygnus X-1 is a well-known example of an accreting binary of this type.
bow shock
matter collects in wake

35. Stellar wind model cont.
Process much less efficient than Roche lobe overflow, but mass loss rates high enough to explain observed luminosities.
10 solar masses per year is required to produce X-ray luminosities of J/s. -8 31

36. Magnetic neutron stars
For neutron star with strong mag field, disk disrupted in inner parts.
This is where most radiation is produced.
Compact object spinning => X-ray pulsator
Material is channeled along field lines and falls onto star at magnetic poles
If the neutron star (or white dwarf) has a strong magnetic field, then the field is disrupted in the inner parts. The material is channeled along the magnetic field lines and falls onto the star at the magnetic poles. This is where most of the radiation is produced.
The compact object is usually spinning, thus if the magnetic axis is offset from the rotation axis, the system is observed to be an X-ray pulsator.

37. ‘Spin-up pulsars’
Primary accretes material with angular momentum => primary spins-up (rather than spin-down as observed in pulsars)
Rate of spin-up consistent with neutron star primary (white dwarf would be slower)
Cen X-3 ‘classical’ X-ray pulsator
The accretion of angular momentum from incoming material makes these X-ray pulsators spin-up, rather than spin-down as observed in radio pulsars.
The rate of spin-up seen in X-ray pulsators (and their observed levels of luminosity) are consistent with the presence of a neutron star primary rather than a white dwarf, since the rate of white dwarf spin-up would be slower.

38. Types of X-ray Binaries
Group I Group II
Luminous (early, Optically faint (blue)
massive opt countpart) opt counterpart
(high-mass systems) (low-mass systems)
hard X-ray spectra soft X-ray spectra
(T>100 million K) (T~30-80 million K)
often pulsating non-pulsating
X-ray eclipses no X-ray eclipses
Galactic plane Gal. Centre + bulge
Population I older, population II
The luminosities for X-ray binaries are typically in the range of 7e28 to 1e31 J/s - the upper limit being roughly the Eddington limit for a 1 solar mass neutron star.
At lower luminosities (~1e26 J/s) the compact object is probably a white dwarf ie the primary in a cataclysmic variable system.