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High Energy Astrophysics > 6: X-RAY BINARIES > Flashcards

6: X-RAY BINARIES Flashcards

1
Q

How many stars are in binaries?

A

Half of them.

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2
Q

A small fraction of binaries have a companion that is a compact object. What are three examples of this?

A

White Dwarf, Neutron Star, Black Hole

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3
Q

Why are the compact objects in a binary system called X-ray binaries?

A

They are strong X-ray sources.

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4
Q

How and why do XRBs form? What are the 3 sources after the formation that emit X-rays?

A

They occur if the binary orbit is close enough to the normal star. The material from the normal star flows onto the compact object, forms an accretion disk, boundary layer, and hot spots - which emit X-rays.

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5
Q

What is the most efficient power source in the Universe?

A

Accretion of material onto compact objects.

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6
Q

What is the equation for converting PE into KE?

A

(1/2)mv^2 = (GMm)/r

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7
Q

What is KE converted to on the star surface?

A

Heat and then radiation.

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8
Q

What is the equation for the radiated luminosity if all the KE goes to radiation? HINT: η is the efficiency of conversion of potential energy into radiation.

A

L = ηmc (where m has a dot on the top)

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9
Q

Can all of the PE of the material right down to the object’s surface be extracted?

A

No. Usually, the PE of the last stable orbit of matter around the compact object is what is relevant.

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10
Q

What would happen if matter fell in directly and why doesn’t this happen?

A

There would be no heat release. Conservation of angular momentum prevents direct infall.

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11
Q

What is the equation for mass m in orbit around M and because the Virial theorem applies, what equation is produced?

A

A1: KE ~ (mv^2)/r^2.
A2: KE = (GMm)/2r = - (PE)/2

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12
Q

How does a disk form?

A

Conservation of angular momentum allows collapse along the rotation axis of in-falling material.

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13
Q

Why do viscous forces arise in the disk?

A

Because of the material moving at different radii along with different speeds (Kepler’s law).

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14
Q

Why do the viscous forces cause radiation?

A

There is a transfer of angular momentum outwards, which allows inner material to fall inwards. This provides frictional, dissipative forces to heat material which then radiates.

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15
Q

What is the equation for energy release and efficiency, considering viscous forces?

A

A1: −PE/2 = (GMm)/2r where r is last stable orbit
A2: Efficiency, η = (GM)/2rc^2

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16
Q

What is the equation for the Schwarzschild radius and what value of η does this produce?

A

A1: rS = (2GM)/c^2 ≈ 3(M/M.) km
A2: 1/12 (0.06)

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17
Q

What is a Kerr BH and what is its η value?

A

It is the most efficient energy source known in the Universe.

0.426

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18
Q

What happens if the luminosity, L, is too great?

A

The radiation pressure blows away in-falling material, which is an ionised plasma of equal numbers of electrons and protons.

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19
Q

When does the Eddington limiting luminosity occur?

A

When the luminosity is large enough that these forces balance f_rad = f_grav and where L = L_edd.

20
Q

What happens when the Eddington limiting luminosity is exceeded?

A

Material is pushed away and accretion halts.

21
Q

What is the Eddington luminosity equation?

A

LEdd =(4πGMmpc)/σ_T = 1.3 × 10^31 (M/M.) W

22
Q

What were the luminosities of early X-ray sources for M = 1M.?

A

< Ledd
~

23
Q

What is the equation for the peak of BB spectrum?

A

hν_peak ≈ 3kT (in flux per unit frequency)
λ_peak ≈(hc)/5kT (in flux per unit wavelength)

24
Q

What is the average temperature and energy for an X-ray?

A

T ≈ 2 × 107 K
E ≈ (kT)/e ≈ 1.7 keV

25
Q

What are the two classes of XRB and what differentiates them?

A
  1. Low-mass XRB (LMXRB) where the donor star is a slowly evolving low mass (less than or equal to 1.4 solar masses)
  2. High-mass XRB (HMXRB) where the donor is a young massive (larger or equal than 10 solar masses) star with strong winds
26
Q

Where are the two different classes of XRBs expected to be found?

A

LMXRB - May have moved away from birthplace
HMXRB - star-forming regions (e.g. spiral arms)

27
Q

What do HMXRBs require to form?

A

They require 2 stars with masses large enough to eventually go supernova. After the first supernova, an HMXRB is created. After the second supernova, a binary consisting of 2 compact objects will be formed.

28
Q

If the compact object in HMXRB is NS, what will it possess?

A

It will have a strong B field that can influence accretion.

29
Q

For a dipole magnetic field, what is B proportional to?

A

1/r^3

30
Q

What is the equation of B(r) if Bs is the field at the surface of a star of radius r*?

A

B(r) = Bs (r*/r)^3

31
Q

What is the outward magnetic pressure for an ordered field (field lines aren’t tangled)?

A

Pr ≈ uB = (B^2)/2µ0

32
Q

What is the equation for the inwards ram pressure exerted by in-falling material?

A

P_ram = ρv^2

33
Q

What is the Alfvén radius?

A

When ram pressure is balanced by magnetic pressure.
ρv^2 =(B_s)^2/2µ0 x (r∗/rm)^6

34
Q

What is the Alfvén radius, r_m?

A

Look at notes.

35
Q

What value is the Alfven radius?

A

1.2 x 10^3 km -> 120 r_*

36
Q

What are the conditions in the vicinity of the Alfvén radius?

A

Magnetically dominated + accreting material is funnelled along field lines

37
Q

What does the in-falling material form?

A

X-ray emitting hotspots at magnetic poles.

38
Q

What is an x-ray pulsar?

A

Because the magnetic axis of the NS isn’t aligned with the rotation axis of the binary, the observer sees pulsed X-ray emission.

39
Q

Old pulsars spin down due to magnetic dipole emission. How can they be sped up again?

A

Via accretion. They can be spun up for very short periods.

40
Q

How do LMXRBs cause spin-up of the NS or WD?

A

Accretion occurs gradually over a long time, and if the companion is a NS (or a WD) accretion can impart significant angular momentum spinning up the NS.

41
Q

What happens if at the Alfvén radius, the disk rotates faster than the star?

A

The disk exerts a torque leading to spin-up.

42
Q

What is a millisecond pulsar?

A

They are spun up in a binary system and are old objects. They have much lower magnetic fields and therefore much slower decays of their periods.

43
Q

Are all pulsars with periods of milliseconds, millisecond pulsars?

A

No. Young isolated pulsars (like the Crab) may have periods of milliseconds but due to their high magnetic fields, their periods will decay rapidly.

44
Q

How do you tell the difference between an X-ray pulsar and a stellar mass BH?

A

A1: If x-rays are bright and pulsed it’s an x-ray pulsar
A2: if x-rays are bright but not pulsed, it could be stellar mass BH

45
Q

How are black hole candidates determined and why?

A

The mass of the unseen compact object can be inferred from the orbit of a companion normal star. For a few dozen XRBs in the Galaxy, the compact object mass is greater than the maximum theoretical limit of ~ 3 solar masses for NS. Many show flickering behaviour which isn’t regular like a pulsar.

High Energy Astrophysics (11 decks)

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