airy disks

Examples of airy disks in the following topics:

• Limits of Resolution and Circular Aperatures

  • For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the Airy disc, as shown in .
  • Computer-generated image of an Airy disk.
  • The gray scale intensities have been adjusted to enhance the brightness of the outer rings of the Airy pattern.

• Magnification and Resolution

  • These are called Airy disks.
  • The resolving power of a microscope is taken as the ability to distinguish between two closely spaced Airy disks (or, in other words, the ability of the microscope to distinctly reveal adjacent structural detail).

• Vertical Structure

  • We have assumed that the disk is thin.
  • The pressure gradient in the disk must resist the vertical component of gravity.
  • This is essentially assuming that the disk is isothermal vertically.
  • The relative thickness of the disk remains nearly constant with radius if only internal heating is important in a vertically isothermal disk.
  • To go further we need an estimate of the density of the disk.

• Emission

  • If we assume that the energy is radiated through the surface we find that the flux per unit area is half this value (two surfaces) and that the total luminosity of the disk is
  • If one assumes that the disk radiates locally as a blackbody, the spectrum is simply the sum of the various blackbodies (the so-called multi-temperature disk model).

• Accretion Disks

  • Understanding the production of ejecta is beyond our scope, but examining the transport of angular momentum through a rotating disk of material is not once we add an additional ingredient to our analysis, viscosity.
  • Around this radius, the accretion flow must make a transition between a spherical inflow and a disk.
  • Unfortunately, natural estimates for the microscopic viscosity of astrophysical gas are too small by many orders of magnitude to account for the structure of accretion disks.
  • It is likely that accretion disks are turbulent magnifying the effects of small-scale viscosity to larger scales.

• Problems

  • This is a simplified model for an accretion disk.
  • Let's divide the accretion disk into a series of rings each of mass $M$.
  • What and where is the peak temperature of the disk?
  • What and where is the minimum temperature of the disk?
  • Sketch the spectrum from the accretion disk on a log-log plot.

• Modelling the Stress

  • where the inequality holds because the turbulent velocity is limited by the sound speed, and the size of the eddies is limited by the thickness of the disk.
  • The disk gets thinner as the value of $\alpha$ increases and gets fatter as the infall velocity approaches the orbital velocity.
  • We can combine the $\alpha$-prescription with vertical radiative transfer to obtain an estimate of the central density and temperature of the disk.
  • Essentially, the thickness of the disk in this case is constant except near the inner edge where it becomes thinner.
  • The situation for the cold accretion disk is somewhat uglier but no more complicated.

• Kirby-Bauer Disk Susceptibility Test

  • Kirby-Bauer antibiotic testing (also called KB testing or disk diffusion antibiotic sensitivity testing) uses antibiotic-containing wafers or disks to test whether particular bacteria are susceptible to specific antibiotics.
  • A larger zone of inhibition around an antibiotic-containing disk indicates that the bacteria are more sensitive to the antibiotic in the disk.

• Angular Momentum Transport

  • where $r_I$ is the inner radius of the disk.
  • Therefore, there is a torque acting in the disk
  • The viscous torque is the product of the viscous stress in the tangential direction, the area upon which the stress acts (the half-height of the disk is $h$) and the radius.
  • For example we can now determine the energy generated per unit area of the disk

• The Importance of Motivation

  • ., cramped cubicle vs. airy, open office); internal motivations include thoughts and emotions (e.g., boredom with performing the same task over and over vs. excitement at being given a wide variety of project types).