DOUBLE STAR NOTES :
RESOLUTION & MAGNITUDE LIMITS

NOTE: This Section Still Requires Expanding!!!

INTRODUCTION : PRECEPTS of RESOULTION

Close Pairs

1) Resolving the closest pairs below about 1 or 2 arcsec can require the combination of aperture, moderate to high magnification and good seeing. This is also around the threshold of moderate seeing, meaning that in unfavourable conditions, these pairs may not be clearly split.

2) For the closest pairs, resolution is assumes a number of provisos being meet. These include;

a. Both stars are equally 6.0v (visual) magnitude.
b. Both stars are solar-like yellow stars
c. Aperture is large enough to split the pair cleanly.
d. Optics are clean, freshly coated if reflectors, and have optical qualities better than about 1/8th wave.

3) Close pairs which are brighter than 6th magnitude become more difficult to resolve because of the overwhelming light of the components. This often requires either the light be reduced via an aperture stop — limiting the telescopes aperture or using neutral density filters.

4) Close pairs which are fainter in magnitude are also more difficult to resolve, and are much more problematic when nearing the faintest magnitude limit of the telescope.

5) Close pairs with increasing differences in magnitude (Δm) also become far more difficult to resolve, as the light of the primary star often overwhelms the nearby companion. For each magnitude in difference rises almost exponentially, roughly doubling in resolution for every two magnitudes.

6) Close pairs have commonly a transition phase from an apparent single star to seeing the pair cleanly resolved. As all stars through telescopes are not real pinpoints but are seen as Airy Disks — a central bright spot encircled by a number of much fainter rings — the two stars can appear elongated, joined or merged together. Clean separation is defined by dark space existing between the components.

7) Close pairs on the Dawes Limit, may or may not be cleanly resolved. The empirical Dawes Limit is a result of a large sample of various sizes of telescopes, each being tested for their ability to split pairs by average observers through the Earth’s atmosphere. It is defined by the simple equation;

Res (arcsec) = 11.58 / D (cm) or

Res (arcsec) = 4.54 / D (inches)

Where;
Res = Resolution in arcsec
D = Aperture in either centimetres or inches.

I.e. 7.5cm (3-inch) is 1.52 arcsec, 10.5cm (4-inch) is 1.14 arcsec, 20cm (8-inch) is 0.57 arcsec, while 30cm (12.5-inch) is limited to 0.38 arcsec.

8) Resolution of Close Pairs also has the Theoretical Limit. This is based on the criteria from optical theory, and is made on the diameter of the third outer ring of the observed Airy disk. This limit is 20.9% bigger than the resolution of the Dawes Limit. I.e. 20cm sees 0.57 arcsec, but the Airy disk covers more like 0.69 arcsec. It is unlikely that an observer — regardless of the observing conditions — could exceed this limit. This limit can be calculated by the simple equation;

TRes (arcsec) = 13.84 / A (cm) or

TRes (arcsec) = 5.43 / A (inches)

Where;
TRes = Theoretical Resolution is in arcsec
D = Aperture in either centimetres or inches.

I.e. 7.5cm (3-inch) is 1.84 arcsec, 10.5cm (4-inch) is 1.31 arcsec, 20cm (8-inch) is 0.69 arcsec, while 30cm (12.5-inch) is limited to 0.46 arcsec

Standard Pairs

1) All standard pairs (and wider pairs) usually are easy to resolve regardless of the conditions. Resolution is not necessarily limited by the atmospheric seeing, and these can be typically resolved using optimum telescope magnifications — sometimes called moderate magnifications.

2) Resolution of all standard pairs can be achieved in small telescopes but usually not so in binoculars

3) Problems may occur with very bright stars or those having significant differences in magnitude.

Wide Pairs

1) Wide pairs (and wider pairs) usually are always easy to resolve regardless of the conditions. Resolution is not limited at all by seeing, and these can be resolved using low telescope magnifications.

2) If both stars are viewed in dark skies and above about 10th magnitude, wide pairs are readily visible in binoculars. In city skies this may be limited to about 7th magnitude.

3) Most wide pairs are generally more spectacular in low magnifications because they can include the general field stars — especially when they reside in places in the Milky Way.

MAGNITUDE LIMITS

1) The other observational constraint on observing stars is the theoretical magnitude visible for the aperture used.

2) Magnitude limits or limiting magnitude are difficult quantities to ascertain because of many other influencing factors. This includes things such as the observing conditions (transparency), light pollution, the observer’s eyesight, magnification or atmospheric seeing.

3) Based on the average observer, a practical simple calculation is based on either Observed or Theoretical magnitudes;

m(v) = 2.7 + 5× log ( D (cm) / 10 )

Where;
m(v) = Observed Magnitude Limit.
D = Aperture in centimetres.

Where;
m(v) = Observed Magnitude Limit.
D = Aperture in centimetres

These determined limits are only a guide. Strong colours like deep red variables and luminous blue stars can likely be seen below the stated threshold limit. Colour contrasts for stars at the lower end of the range is likely to disappear at these particular lower magnitudes. Furthermore seeing and transparency conditions, dust or smoke, and proximity to urban skies through light pollution can drastically change the telescope magnitude limits. On the best nights, it is probably possible to get 0.5 magnitudes lower than the limit. It is also quite possible that with experience and tricks like averted vision may extend these to lower limits.

Observations and assumptions from which the table was constructed may be inapplicable to other conditions.;

1) Atmospheric seeing can render small instruments able to see fainter objects than larger ones.
2) Most telescopes and all observers are not ‘normal’
3) Magnification and eyepiece type will affect the outcome.
4) Direct or averted vision
5) Type of telescope (loss of light in 2-degree spectrum)
6) Bright field objects affect dark adaptation

Last Update : 20th September 2016

Southern Astronomical Delights © (2011)

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