What's the rationale behind the false colours in solar observation photographs? Images from SOHO, SDO and other sun observatories are often coloured differently for different wavelengths or temperatures:


http://www.nasa.gov/mission_pages/sunearth/science/Sun-Wavelength-Chart.html has statements like "This light is emitted from the upper transition region and the chromosphere and are typically colorized in red."

How is the convention of which temperature or wavelength gets which colour established?

Is it simply so that scientists can immediately tell what temperature or wavelength a picture shows, or are the colours optimized to show particular features?

And why is there a white ring or circle in the sunshade in some SOHO imagery, and why different sizes compared to the disc in the two photos above?
Some of the images shown in your question are not colored or colorized, it is not a false color; it's the real color. The calculations that are made to produce the false colors that are used on colorized image datasets are shown in the aia_lct.pro file, where the exact RGB values are provided.

Where a false color is chosen it is done so (for SDO and some other images) using the AIA Standard Color Tables (which are generated in the aia_lct.pro file). 

Information on the "VSO's Guide to SDO Data Analysis" (.PDF), on page 46, describes use of the subroutines in the sdo/aia/idl/calibration/aia_colors.pro source code file from http://www.heliodocs.com/ or view "Installing Solarsoft" for ready to run versions and more info.

See Section 6.6.1 "Using AIA Standard Scaling and Colors" for additional information about the aia_colors.pro function. The Introduction of that Guide contains additional information and links about the SDO mission.



Here is the Description of the colors NASA uses for different wavelengths (using the AIA Standard Color Tables):


  view-source:https://sdo.gsfc.nasa.gov/data/aiahmi/

&lt;h4&gt;Telescopes&lt;/h4&gt;
&lt;select name="telescope" id="telescope" class="form-control"&gt;
    &lt;option value="aia_0171"&gt;AIA 171 (gold)&lt;/option&gt;
    &lt;option value="aia_0193"&gt;AIA 193 (bronze)&lt;/option&gt;
    &lt;option value="aia_0304"&gt;AIA 304 (red)&lt;/option&gt;
    &lt;option value="aia_0211"&gt;AIA 211 (purple)&lt;/option&gt;
    &lt;option value="aia_0131"&gt;AIA 131 (teal)&lt;/option&gt;
    &lt;option value="aia_0335"&gt;AIA 335 (blue)&lt;/option&gt;
    &lt;option value="aia_0094"&gt;AIA 094 (green)&lt;/option&gt;
    &lt;option value="aia_1600"&gt;AIA 1600 (yellow/green)&lt;/option&gt;
    &lt;option value="aia_1700"&gt;AIA 1700 (pink)&lt;/option&gt;
    &lt;option value="hmib"&gt;HMI Magnetogram (gray)&lt;/option&gt;
    &lt;option value="hmibc"&gt;HMI Colorized Magnetogram (colorized)&lt;/option&gt;
    &lt;option value="hmii"&gt;HMI Intensitygram (gray)&lt;/option&gt;
    &lt;option value="hmiic"&gt;HMI Intensitygram (orange)&lt;/option&gt;
    &lt;option value="hmiihi"&gt;HMI Intensitygram High Cadence (orange)&lt;/option&gt;
    &lt;option value="hmiif"&gt;HMI Intensitygram Flat (orange)&lt;/option&gt;
    &lt;option value="hmid"&gt;HMI Dopplergram (gray)&lt;/option&gt;
    &lt;option value="COMP211193171"&gt;AIA Composite 211, 193, 171&lt;/option&gt;
    &lt;option value="COMP304211171"&gt;AIA Composite 304, 211, 171&lt;/option&gt;
    &lt;option value="COMP094335193"&gt;AIA Composite 094, 335, 193&lt;/option&gt;
    &lt;option value="COMPHMI171"&gt;Composite AIA 171, HMI Magnetogram&lt;/option&gt;
&lt;/select&gt;



Here is a webpage showing the images in your question in various sizes, including a 48 hour movie for each.



The full Electromagnetic Spectrum:



The Visible Spectrum, including Fraunhofer Line Letters and Wavelength Numbers:



The Fraunhofer lines are typical spectral absorption lines. Absorption lines are dark lines, narrow regions of decreased intensity, that are the result of photons being absorbed as light passes from the source to the detector. In the Sun, Fraunhofer lines are a result of gas in the photosphere, the outer region of the sun. The photosphere gas is colder than the inner regions and absorbs light emitted from those regions.

Here is the wavelength's frequency for each Element of interest:







Each Filter accepts a narrow band which has a specific use and specific properties. Filters are more expensive when the bandwidth is very narrow, single frequency Filters are unnecessary and unaffordable.

Different frequency ranges of the spectrum are used to resolve different aspects of the object being observed, similarly different bandwidths are used to further enhance those features.

Listing the bandwidths for every filter and the expected results would be exhaustive, one website that gives such info for each of their filters is Daystar where their filter comparison page indeed confirms that the Sun can be viewed in black and white using a monochrome sensor. It's when you want to combine multiple channels that use of color becomes necessary.

Here is an example of the differences between bandwidths for the Hydrogen Alpha Filter (a deep-red visible spectral line in the Balmer series with a wavelength of 656.28 nm):


Filters with 0.8 ångström bandwidths will reveal prominences in high contrast
Filters with 0.7 ångström bandwidths will reveal prominences in high contrast and occasionally, surface texture. Prominences are generally larger with .7Å filters than in narrower bandwidths
Filters with 0.6 ångström bandwidths will reveal some surface contrast as well as prominences.  A .6Å filter can be a good compromise for those having a difficult decision
Filters with 0.5 ångström bandwidths will reveal better surface contrast as well as great prominences
Filters with 0.4 ångström bandwidths will reveal excellent surface contrast as well as fine chromosphere detail
Filters with 0.3 ångström bandwidths will reveal superior surface contrast above any other filter. Views are generally somewhat dimmer.  Expect "Pencil-Thin" details on surface and prominence features


It is bandwidth that is used to derive contrast, not coloring.



The SDO (Solar Dynamics Observatory) is a sun-pointing semi-autonomous spacecraft that allows nearly continuous observations of the Sun. Unlike the human eye which uses rods and cones, the SDO uses 3 instruments: 


The AIA (Atmospheric Imaging Assembly) images the solar atmosphere in multiple wavelengths to link changes in the surface to interior changes. Data includes images of the Sun in 10 wavelengths every 10 seconds. 
The EVE (Extreme Ultraviolet Variability Experiment) measures the Sun's extreme ultraviolet irradiance with improved spectral resolution, "temporal cadence", accuracy, and precision over preceding measurements made by TIMED SEE, SOHO, and SORCE XPS. 
The HMI (Helioseismic and Magnetic Imager) studies solar variability and characterizes the Sun's interior and the various components of magnetic activity. HMI produces data to determine the interior sources and mechanisms of solar variability and how the physical processes inside the Sun are related to surface magnetic field and activity. 
The Magellan craft used Synthetic Aperture Radar uses radio waves and not visible light to image map objects. Magellan synthetic aperture radar mosaics from the first cycle of Magellan mapping are mapped onto a rectangular latitude-longitude grid to create this image. Data gaps are filled with Pioneer Venus Orbiter altimetric data, or a constant mid-range value. Simulated color is used to enhance small-scale structure. The simulated hues are based on color images recorded by the Soviet Venera 13 and 14 spacecraft. The image was produced by the Solar System Visualization project and the Magellan science team at the JPL Multimission Image Processing Laboratory. 

Similarly SDO data outside the visible spectrum is colorized to allow invisible portions of the electromagnetic spectrum (and Magnetometer recordings) to be visualized by the human eye in a readily digestible image rather than serving the general public a large dataset of numbers.
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 700 nm. In terms of frequency, this corresponds to a band in the vicinity of 430–770 THz.

The spectrum does not, however, contain all the colors that the human eyes and brain can distinguish. Unsaturated colors such as pink, or purple variations such as magenta, are absent, for example, because they can be made only by a mix of multiple wavelengths. Colors containing only one wavelength are also called pure colors or spectral colors.



  Q: How is the convention of which temperature or wavelength gets which colour established?
  
  Is it simply so that scientists can immediately tell what temperature or wavelength a picture shows, or are the colours optimized to show particular features?


The colors are not optimized to show particular features or provide contrast. The aia_lct.pro file is where the exact RGB values are calculated, see top of this answer.


  Q: And why is there a white ring or circle in the sunshade in some SOHO imagery, and why different sizes compared to the disc in the two photos above?


The coronagraph blocks out the Sun with an occulting disk to reveal the much fainter structures in the Sun's atmosphere. Sometimes multiple images are combined to remove the disk and provide a unoccluded image.

The Large Angle and Spectrometric Coronagraph (LASCO) in the Solar and Heliospheric Observatory (SOHO) doesn't use the latest technology, sometimes there are disturbances in the images.

There are two kinds of disturbances that repeatedly occur:


Blackouts and Whiteouts, in broken lines, circle-like shapes, or over the whole picture. They are caused by the electronics box. There has never been a firmware update, since it was judged as too sensitive changing the flight-software.
Black and white pixels, occurring in patterns, without pattern or alone. Those "missing blocks" are telemetry dropouts, caused by radio interference or a disturbance in the data transfer to Goddard Space Flight Center.




[The section below might benefit from some more editing if the OP requests it.]




  AIA 193
  
  This channel highlights the outer atmosphere of the Sun - called the corona - as well as hot flare plasma. Hot active regions, solar flares, and coronal mass ejections will appear bright here. The dark areas - called coronal holes - are places where very little radiation is emitted, yet are the main source of solar wind particles.
  
  Where: Corona and hot flare plasma
  
  Wavelength: 193 angstroms (0.0000000193 m) = Extreme Ultraviolet
  
  Primary ions seen: 11 times ionized iron (Fe XII)
  
  Characteristic temperature: 1.25 million K (2.25 million F)





  AIA 304
  
  This channel is especially good at showing areas where cooler dense plumes of plasma (filaments and prominences) are located above the visible surface of the Sun. Many of these features either can't be seen or appear as dark lines in the other channels. The bright areas show places where the plasma has a high density.
  
  Where: Upper chromosphere and lower transition region
  
  Wavelength: 304 angstroms (0.0000000304 m) = Extreme Ultraviolet
  
  Primary ions seen: singly ionized helium (He II)
  
  Characteristic temperature: 50,000 K (90,000 F)





  AIA 171
  
  This channel is especially good at showing coronal loops - the arcs extending off of the Sun where plasma moves along magnetic field lines. The brightest spots seen here are locations where the magnetic field near the surface is exceptionally strong.
  
  Where: Quiet corona and upper transition region
  
  Wavelength: 171 angstroms (0.0000000171 m) = Extreme Ultraviolet
  
  Primary ions seen: 8 times ionized iron (Fe IX)
  
  Characteristic temperature: 1 million K (1.8 million F)





  AIA 211
  
  This channel (as well as AIA 335) highlights the active region of the outer atmosphere of the Sun - the corona. Active regions, solar flares, and coronal mass ejections will appear bright here. The dark areas - called coronal holes - are places where very little radiation is emitted, yet are the main source of solar wind particles.
  
  Where: Active regions of the corona
  
  Wavelength: 211 angstroms (0.0000000211 m) = Extreme Ultraviolet
  
  Primary ions seen: 13 times ionized iron (Fe XIV)
  
  Characteristic temperature: 2 million K (3.6 million F)





  AIA 131
  
  This channel (as well as AIA 094) is designed to study solar flares. It measures extremely hot temperatures around 10 million K (18 million F), as well as cool plasmas around 400,000 K (720,000 F). It can take images every 2 seconds (instead of 10) in a reduced field of view in order to look at flares in more detail.
  
  Where: Flaring regions of the corona
  
  Wavelength: 131 angstroms (0.0000000131 m) = Extreme Ultraviolet
  
  Primary ions seen: 20 and 7 times ionized iron (Fe VIII, Fe XXI)
  
  Characteristic temperatures: 10 million K (18 million F)





  AIA 335
  
  This channel (as well as AIA 211) highlights the active region of the outer atmosphere of the Sun - the corona. Active regions, solar flares, and coronal mass ejections will appear bright here. The dark areas - or coronal holes - are places where very little radiation is emitted, yet are the main source of solar wind particles.
  
  Where: Active regions of the corona
  
  Wavelength: 335 angstroms (0.0000000335 m) = Extreme Ultraviolet
  
  Primary ions seen: 15 times ionized iron (Fe XVI)
  
  Characteristic temperature: 2.8 million K (5 million F)





  AIA 094
  
  This channel (as well as AIA 131) is designed to study solar flares. It measures extremely hot temperatures around 6 million Kelvin (10.8 million F). It can take images every 2 seconds (instead of 10) in a reduced field of view in order to look at flares in more detail.
  
  Where: Flaring regions of the corona
  
  Wavelength: 94 angstroms (0.0000000094 m) = Extreme Ultraviolet/soft X-rays
  
  Primary ions seen: 17 times ionized iron (Fe XVIII)
  
  Characteristic temperature: 6 million K (10.8 million F)





  AIA 1600
  
  This channel (as well as AIA 1700) often shows a web-like pattern of bright areas that highlight places where bundles of magnetic fields lines are concentrated. However, small areas with a lot of field lines will appear black, usually near sunspots and active regions.
  
  Where: Transition region and upper photosphere
  
  Wavelength: 1600 angstroms (0.00000016 m) = Far Ultraviolet
  
  Primary ions seen: thrice ionized carbon (C IV) and Continuum
  
  Characteristic temperatures: 6,000 K (11,000 F), and 100,000 K (180,000 F)





  AIA 1700
  
  This channel (as well as AIA 1600) often shows a web-like pattern of bright areas that highlight places where bundles of magnetic fields lines are concentrated. However, small areas with a lot of field lines will appear black, usually near sunspots and active regions.
  
  Where: Temperature minimum and photosphere
  
  Wavelength: 1700 angstroms (0.00000017 m) = Far Ultraviolet
  
  Primary ions seen: Continuum
  
  Characteristic temperature: 6,000 K (11,000 F)





  AIA Composite 211, 193, 171
  
  This image combines three images with different, but very similar, temperatures. The colors are assigned differently than in the single images. Here AIA 211 is red, AIA 193 is green, and AIA 171 is blue. Each highlights a different part of the corona.





  AIA Composite 304, 211, 171
  
  This image combines three images with quite different temperatures. The colors are assigned differently than in the single images. Here AIA 304 is red (showing the chromosphere), AIA 211 is green (corona), and AIA 171 is dark blue (corona).





  AIA Composite 094, 335, 193
  
  This image combines three images with different temperatures. Each image is assigned a color, and they are not the same used in the single images. Here AIA 094 is red, AIA 335 is green, and AIA 193 is blue. Each highlights a different part of the corona.





  [Webpage had no Info Popup for: AIA 171 &amp; HMIB]





  HMI Magnetogram
  
  This image comes from HMI, another instrument on SDO. It shows the magnetic field directions near the surface of the Sun. White and black areas indicate opposite magnetic polarities, with white showing north (outward) polarity and black showing south (inward) polarity.
  
  Where: Photosphere
  
  Wavelength: 6173 angstroms (0.0000006173 m) = Visible (orange)
  
  Primary ions seen: Neutral iron (Fe I)
  
  Characteristic temperature: 6,000 K (11,000 F)





  HMI Colorized Magnetogram
  
  This image comes from HMI, another instrument on SDO. It shows the magnetic field directions near the surface of the Sun. White and black areas indicate opposite magnetic polarities, with white showing north (outward) polarity and black showing south (inward) polarity.
  
  Where: Photosphere
  
  Wavelength: 6173 angstroms (0.0000006173 m) = Visible (orange)
  
  Primary ions seen: Neutral iron (Fe I)
  
  Characteristic temperature: 6,000 K (11,000 F)





  [Webpage had no Info Popup for: HMI Intensitygram - colored]





  [Webpage had no Info Popup for: HMI Intensitygram - Flattened]





  [Webpage had no Info Popup for: HMI Intensitygram]





  [Webpage had no Info Popup for: HMI Dopplergram]





  [Webpage had no Info Popup for: HMI Intensitygram - High Cadence]





  EVE/ESP and EVE/MEGS-P
  
  This plot shows time series of 5 strong EUV emission lines, showing how bright the flare is emitting at these various emissions. Also shown is a Dark value, which is a detector that is blocked from seeing the Sun, which shows energetic particles from the Sun that can penetrate the EVE instrument and cause false counts. This Dark diode will increase during solar storms.
  
  Where: Solar Irradiance (full Sun)