Friday, May 10, 2019

About Surface Brightness

About Surface Brightness

                                                                   Martin Lewicki

First published in the Bulletin of the Astronomical Society of South Australia
May 2005


Astronomers use a brightness scale called magnitude to indicate how bright a star appears to the eye. The magnitude scale has been in use since the time of Hipparchus (about 130 BCE). The brightest stars were binned as “magnitude 1” with progressively fainter stars binned down in stages to naked eye limit at “magnitude 6”. After the invention of the telescope stars fainter than naked-eye limit were further scaled down beyond magnitude 6 to as faint as modern telescopes can detect at around magnitude 30!  Put simply, a brighter magnitude was a smaller number than a fainter magnitude with a lager number. To make astronomical object listings more complete astronomers also determined magnitudes for non-stellar objects such as nebulae and clusters. When a deep sky object is given a “magnitude” it means that if its light were concentrated to a stellar point it would shine with the same brightness as a star of that same magnitude. This is known as its integrated magnitude. It would then seem reasonable to assume that deep sky objects with brighter magnitudes should consistently be easier to visually detect than those with fainter magnitudes. Yet even a novice soon discovers that many deep sky objects of the same magnitude do not always look the same brightness. Furthermore, sometimes an object of the same magnitude as another may not even be visible while the other still is! What’s happening here?

The discrepancy arises due to the varying sizes of deep sky objects in the sky. For stars, their light is always concentrated into a point so that there is a direct relationship between a star’s brightness and the magnitude scale. But deep sky objects vary in size so their light may be spread more or less over different size areas making them more or less visible for a given magnitude. Their visibility depends therefore on their surface brightness rather than their total brightness or integrated magnitude. You can see surface brightness in action when you aim a torch-light at a surface and move it inward then outwards. While the surface brightness of the circle of light dims as it enlarges and brightens when it contracts, the total amount of light remains constant.

Surface brightness of an object is measured as magnitude per square arc minute. For example the galaxy NGC 55 at magnitude 8 spreads its light over about 180 square arc minutes. This gives it a surface brightness of about magnitude 13 per square arc minute. The planetary nebula NGC 3132 in Vela is also at magnitude 8 but has its light concentrated into a much smaller area about 1.3 square arc minutes. This results in a surface brightness just under magnitude 8 per square arc minute — almost the same as its “stellar” magnitude. This makes NGC 3132 much easier visually detect than NGC 55.
                              

Another example is the “Silver Coin Galaxy” NGC 253 in Sculptor at magnitude 7.6. The Silver Coin is easily picked up with pair of binoculars when near zenith whereas under the same circumstances the enigmatic galaxy Centaurus A at a much brighter magnitude 6.7 is somewhat more difficult. The reason again is surface brightness. NGC 253 has its light concentrated in 160 square arc minutes giving it a surface brightness of magnitude 12.7 per square arc minute, while the light of Centaurus A is thinly spread out over a much larger 550 square arc minutes giving it a surface brightness of magnitude 13.5 per square arc minute. No wonder the Silver Coin is easier to visually detect! Using surface brightness magnitude therefore is a more practical way to estimate the degree of visibility of extended deep sky objects than using integrated magnitude.







 NGC 253 The “Silver Coin Galaxy” ( left) at magnitude 7.6 is paradoxically easier to visually
 detect than the “brighter” Centaurus A right) at magnitude 6.7
Images: Paul Haese


Most deep sky objects however vary their light distribution across their surfaces and produce variations in visibility for a given surface brightness whereas listed surface brightness magnitudes are the average brightness across the object. Surface brightness is therefore an approximate guide to visibility. For example, galaxies with bright cores will be easier to visually detect than the same size and surface brightness galaxies with a more even light distribution.  The Seyfert galaxy M77 in Cetus is a good example. Its 8.9 magnitudes is spread out to a surface brightness of 12.8 magnitude per square arcminute. But it has a bright nucleus that concentrates more of its light making it more star like and more easily visible.

While catalogues also give surface brightness for open star clusters too they are not often that useful. Stars in open clusters vary greatly in distribution, number and brightness of stars and the eye tends to focus on individual stars than the overall light distribution. IC 2602, the bright  “Southern Pleiades” for example has a listed surface brightness of magnitude 11.6, hardly an indication of its true visibility! Here IC 2602 has several bright stars ranging from magnitude 2.7 to 5 spread over 7,800 square degrees — plenty of room to dilute its 1.9 magnitudes. Surface brightness is more useful for globular clusters and for open clusters if they are distant and begin to resemble nebulae. 


Most planetarium software now include surface brightness magnitudes as well as the integrated magnitudes in their deep sky listings. Other listings such as those in the Bright Star Atlas 2000 (Tirion) provide only integrated magnitudes and object sizes in arc minutes. But these two factors will enable you to calculate surface brightness yourself (see side-box). Serious deep sky observers may use other criteria such as surface brightness per square arc second to determine visibility especially when using large apertures and high magnifications.

Armed with surface brightness listings I have found that with my Meade ETX90 (Maksutov 90mm), I can on a good night from my suburban backyard pick up deep sky objects to as faint as a surface brightness magnitude 13.5 per square arc minute. Of course this appears to fly in the face of the magnitude limit for a 90mm telescope (magnitude 11.0 for stars at my observing site). But then, when you are looking at an extended deep sky object in the eyepiece the eye is recording photons over a larger area of the retina and your amazing brain software is capable of integrating these hits to inform you that “there is something there”.

***
 

 

Calculating Surface Brightness
 
Get the magnitude and dimensions in arc minutes of the object from a catalogue. Calculate its area in square arc minutes

Circular object
A=pi*r*r (where r is radius)

Elliptical object
A=pi*(a/2*b/2) where a & b are the major and minor axes of the ellipse
Rectangular object

A=a*b  (where a & b are length and breadth).

Example: Omega Centauri mag 3.7 dimension 36’
A=3.142*17*17 = 907.9
SB= mag+2.5*log10(A) = 11.1
Surface brightness = mag 11.1 /sq arcmin



Friday, March 22, 2019

How Bright is that Meteor - In Light Bulbs?






Rick Scott and Joe Ormon


How Bright is that Meteor - In Light Bulbs?

Martin Lewicki


Astronomy Educator Adelaide Planetarium. Astronomical Society of South Australia
Published in the Bulletin of the Astronomical society of South Australia May 2019

It was a question posed by a school student in the Adelaide Planetarium. I really had no idea. Just how many light bulbs worth of light does a particular “shooting star” emit? To work this out is a complicated process involving the meteor mass, composition, velocity,  angle of entry and atmospheric physics that had me rattling my brain for months. But there is also a simple rule-of-thumb I derived that can give a quick good-enough approximate answer in a few moments by consulting a look-up table.

Casual star gazers are well aware of these streaking particles of dust or rock incinerating in our upper atmosphere, sometimes putting on a meteor shower when Earth ploughs through a swarm of them. These remnants of early solar system formation, debris of asteroid collisions and particles left behind by visiting comets collide with the Earth’s atmosphere as it moves around the Sun at 30 kilometers per second. Meteors can plunge into our atmosphere anything from 11 km/sec to 70 km/sec heating up to thousands of degrees emitting a portion of its energy as light that we see as a “shooting star”.

After reading through a few (sometimes impenetrable) documents on what happens as a meteor burns up I was frustrated that there was nothing on how much light a typical meteor emits in user-friendly terms nor how to calculate it. What I was looking for was the lumen output of the meteor during incineration. This could be easily converted to light bulb brightness units. For example, a typical household light bulb emits 800 lumens (60W old fashion incandescent equivalent).  If you are star gazing and a meteor streaks across the sky overhead and reaches a maximum magnitude of say -3 (somewhat brighter than Jupiter) how many light bulbs worth of light is that meteor emitting?

An internet search found at least two pieces of program code both in BASIC. An old one from Sky and Telescope, January 1987 issue METEOR.BAS[1] and a more recent one from the Australian Space Academy METFLITE.BAS [2]. Both give somewhat different results for the same meteoroid input parameters but at least provide a guide. They work best for meteoroids less than 1 kilogram. Readers familiar with BASIC programming may download and try for themselves with the links at the end of this article. I will present an real meteor sighting as an example.

Both programs require an input of mass, density, velocity and zenith distance angle of entry. The programs then chew through the complex algorithms that models what happens as the meteor plunges into the atmosphere.  The results are a timeline table in steps of fraction seconds of the meteor flight ending its career as height, velocity, deceleration, mass loss and visual magnitude.  All this I was hoping will give me the info I needed. But the best these programs delivered was the meteor’s visual magnitude and energy in watts.

An attempt to derive lumens from visual magnitude had me juggling all manner conversions such as calculating the Sun’s magnitude knowing its lumen output from far enough away (light years) to match the magnitude of a meteor at a typical 70 to 100 kilometers altitude. I even thought of using a lux meter or a Sky Quality Meter to measure a standard 5mm LED light from one meter to fix a reading then have someone walk away with it to the other side of the oval at night, far enough until the LED visually matched the appearance of a choice first magnitude star in the sky that night.  I had a bee in my bonnet about solving this. Finally a direct conversion of magnitude to lumens turned up on the internet. The requisite formula is (for the math mined):

                                                  Lux = 10^((-14.18-Vm)/2.5) [3]

Lux is the amount of light received from the meteor at ground level. This gives us lumens once we know the meteor distance and its visual magnitude Vm. I added this as extra lines of code to the Sky and Telescope BASIC [4] program and finally got my meteoric LIGHT BULBS!

Here is an example of a meteor I observed in December. It was moving from the Gemini/Orion direction from the north-east in late evening. It was very slow and gradually built up in brightness greater than Jupiter but less than Venus. After several seconds it culminated in brightness almost overhead. Total time was around 5 or 6 seconds. I estimate magnitude about -3.0. Perhaps it was an early Geminid which are known for their slow burn[5]. After several attempts inputting experimental mass, density, speed and zenith distances into my modified Sky and Telescope METEOR.BAS code I received an output that seemed to match my observation. The meteor was an 8 gram rocky type with a density of 2500 kilograms per cubic meter, a velocity of 35 kilometers per second and entering zenith angle of 65 degrees. 

The program begins output (Table 1) when the meteor reaches magnitude 0.1 at three seconds into flight and continues to magnitude -3.1 about 5 seconds into flight when it glows with the light of more than 3000 light globes before it rapidly extinguishes.  This presumes a maximum brightness achieved near zenith as it was for my observation. If the meteor peaks at an angle lower than at zenith, then it is further away and is further dimmed due to atmospheric extinction. This means its intrinsic brightness must be greater than the same magnitude meteor at zenith. Readers can find approximate corrected values to the intrinsic brightness for zenith angles other than zero in Table 2.

It turns out those meteors less than 1 kilogram burn up at a height between 70 and 100 kilometers. Those in the range of a few tens of grams consistently reach peak magnitude around 75km. Armed with this knowledge it is possible to adopt a generic meteor model that relates magnitude to lumens directly, that is to light bulbs, without complex calculations but with less accuracy.  This is also provided by Table 2. Simply look up observed magnitude, its zenith angle (or altitude above horizon) and read off the light bulb value. Of course the mass, density and other properties of the meteor are not available in this simplified method but it should satisfy an audience at a dark sky site or in a planetarium wondering “how bright is that meteor really?”  Thanks to Andrew Cool for helpful discussions and program code assistance.


What are Lux and Lumens?
These are SI metric system standards referring to light received and light emitted. 1 lux is 1 lumen of light spread over 1 square meter at a distance of 1 meter from the source.  Its total emission in all directions like a globe will therefore be 4 x pi or 12.57 lumens, or 1 candela. 1 candela is about the brightness of a standard household candle as in “candle power”.  How bright a light source appears to an observer of course depends on its distance squared.  Double the distance is four times fainter, halve the distance is four times brighter.  If my 8 gram, magnitude -3.1 stony meteor shining at 3000 light bulbs was brought down to earth only 1.4 meters away it would glare at 120,000 lux or magnitude -26.7  --- as bright as the midday sun!

Links and References:

1. Sky and Telescope METEOR.BAS https://www.skyandtelescope.com/astronomy-resources/basic-programs-from-sky-telescope/    See note 4 for author’s modified code.

2.  Australian Space Academy: METFLITE.BAS for original code http://www.spaceacademy.net.au/watch/debris/metflite.htm

4. Download the programs for QBasic and BBC Basic. QBasic versions include code lines for light bulbs output. Link: http://www.adelaideobservatory.org/darkskysa/program files/ 

5. Readers may wonder if I saw an Iridium flare. Note this is near midnight when any Iridium satellite is deep within the Earth shadow and is not capable of catching any sunlight, especially from overhead!



TABLE 1

OUTPUT OF METEOR.BAS {MODIFIED SKY AND TELESCOPE CODE)

INITIAL MASS (KG) 0.008
DENSITY (KG PER CUBIC METER) 2500
SPEED AT ENTRY (KM/S) 35
ZENITH ANGLE (DEG) 65

 TIME  HEIGHT   SPEED    DECEL   MASS   VISUAL  POWER   LUMENS     LAMPS
  (S)   (KM)     (KM/S)  (M/S/S)   (%)    MAG    WATTS            (800-LM)
 3.71    95.1    35.0      11     95.6   -0.1   2.5E+03  2.4E+05     304  
 3.82    93.5    35.0      14     94.4   -0.4   3.2E+03  3.1E+05     387  
 3.93    91.9    35.0      18     92.8   -0.7   4.0E+03  3.9E+05     492  
 4.04    90.2    35.0      23     90.8   -0.9   5.1E+03  5.0E+05     623  
 4.15    88.6    35.0      30     88.3   -1.2   6.4E+03  6.3E+05     786  
 4.26    87.0    35.0      40     85.2   -1.5   8.0E+03  7.9E+05     985  
 4.37    85.4    35.0      52     81.3   -1.8   1.0E+04  9.8E+05    1226  
 4.48    83.7    35.0      68     76.4   -2.1   1.2E+04  1.2E+06    1511  
 4.59    82.1    35.0      89     70.5   -2.3   1.5E+04  1.5E+06    1839  
 4.70    80.5    35.0     118     63.3   -2.6   1.8E+04  1.8E+06    2199  
 4.81    78.9    34.9     159     54.8   -2.8   2.1E+04  2.1E+06    2567  
 4.92    77.2    34.9     217     45.1   -3.0   2.4E+04  2.3E+06    2896  
 5.03    75.6    34.9     304     34.4   -3.1   2.5E+04  2.5E+06    3107  
 5.14    74.0    34.8     440     23.3   -3.1   2.5E+04  2.5E+06    3088  
 5.25    72.4    34.8     679     13.0   -3.0   2.2E+04  2.2E+06    2699  
 5.36    70.8    34.7    1179      4.9   -2.7   1.5E+04  1.5E+06    1840  
 5.47    69.2    34.5    2833      0.6   -1.6   5.2E+03  5.1E+05     637

Time;
in seconds. Height; altitude overhead. Speed; kilometers per second  Decel; deceleration meters per second per second. Mass; percent remaining mass. Visual mag; visual magnitude at zenith. Power; energy in watts. Lumens; intrinsic amount of light emitted in the visual range. Lamps; equivalent light output in 800-lumen light bulbs.


TABLE 2
 
                        GENERIC METEOR AT ~75KM HEIGHT
                           VERY APPROXIMATE VALUES
                        METEOR ASSUMED LESS THAN 1 KG
                       (INCLUDES ATMOSPHERIC EXTINCTION)

                           METEOR LIGHT BULBS (800-LM)

                           ALTITUDE(ABOVE HORIZON)         
       90°       75°       60°       45°       30°       15°       10°
                                 ZENITH DIST
               15°       30°       45°       60°       75°       80°
----------- ---------------------------------------------------------------
MAG    BULBS ---->
-6     55000    61307      85067     125400    440000    3119994   10214339
-5     20000    22293      30933     45600     160000    1134543   3714305
-4     9000     10032      13920     20520     72000     510545    1671437
-3     3000     3344       4640      6840      24000     170182    557146
-2     1500     1672       2320      3420      12000     85091     278573
-1     500      557        773       1140      4000      28364     92858
 0     200      223        309       456       1600      11345     37143
 1     90       100        139       205       720       5105      16714
 2     30       33         46        68        240       1702      5571
 3     10       11         15        23        80        567       1857
 4     5        6          8         11        40        284       929
 5     2        2          3         5         16        113       371
 6     1        1          2         2         8         57        186

In the above table read the visual magnitude in the left column then zenith distance (or the complementary altitude) in top rows to find a ball-park intrinsic light bulb luminousity of a meteor.  Bright meteors at zenith distances of 75° or more may require a meteor larger than 1kg so the brightness figures are wildly uncertain here but are included for the sake of completion. Example: You observe a meteor at magnitude 2.5 (typical) at a zenith angle 45 degrees. This meteor burns with the light of between 68 and 23 light bulbs. Rough interpolation for magnitude 2.5 suggests around 50 or so light bulbs.