maglimit3.pdf

Limiting magnitude areas - telescopic and naked-eye - for northern hemisphere observers

[email protected] Rev. 8/6/2006

Go to: 44 Northern NELM Fields 34 Northern TLM Fields Extinction correction factors Bortle Dark-Sky Scale (External link)Schaefer TLM Calculator (External link) Sky Quality Meter (External link) NELM to B Calculator TLM and NELM area database forCartes du Ciel Excel worksheet

Quick start for finding Telescopic Limiting Magnitude ("TLM")

The following is a basic procedure. Alternative, but more labor intensive methods, are detailed in the section titled"Discussion".

Before you go into the field:

From Table 1 determine which open cluster will transit or be at a 60 degree or higher altitude above your localhorizon during your planned observing frame.

1.

Table 1 - Clark and RASC Charted Open Cluster Telescopic Limiting Magnitude AreasCat_Id_________ J2000_Position Con HR_HD Comments___________________________________________________

NGC225 J004342.00+614648.0 Cas Clark note: 20 stars mag 9+

NGC1647 J044554.00+190636.0 Tau Clark note: 25 stars mag 8 to 13; OMeara10

NGC2129 J060106.00+231836.0 Gem Clark note: about 50 stars

NGC2422 J073636.00-142848.0 Pup

RASC M67 TLMA J085006.00-115300.0 Cnc Northwest quadrant of M67; mag range: 10.6-21.3; coordinates per HEARSAC

NGC6494 J175700.00-185848.0 Sgr

NGC6823 J194309.60+231724.0 Vul Clark note: 30 stars mag 11+

NGC6910 J202307.20+404612.0 Cyg Clark note: 40 stars mag 10+

NGC7031 J210712.00+505248.0 Cep 50 stars mag 11+

NGC7235 J221224.00+571536.0 Cep about 25 stars

Sources:

Clark, R.N., 1990. Star Clusters for Finding Your Limiting Magnitude. Appendix C in Visual Astronomy of the Deep Sky, Cambridge UniversityPress and Sky Publishing http://www.clarkvision.com/visastro/

RASC. 2005. RASC Observing Handbook (Annual) http://www.rasc.ca/handbook/obsform.pdf

Go to a local university library and obtain R.N. Clark's chart of that open cluster(s) from Appendix C of his bookVisual Astronomy of the Deep Sky. Alternatively, go online and prepare a facsimile chart using Jean Mermilliod'sWebda Open Cluster Database. From the Webda homepage, click Navigation | Enter the NGC designation in theDisplay the Page box | Select Query - From cluster chart (plotted). Once plotted, the chart will look like Figure 19.

2.

Make one copy of your open cluster chart for a range of eyepieces in your equipment. Label each chart copy withan the eyepiece focal length.

3.

A paint program or a copier with a reversing feature can be used to make single or double reversed copies of yourcharts that will be easier to use at the eyepiece.

4.

Using an online Schaefer TLM Calculator prepare a table of predicted telescopic limiting magnitudes in the form ofTable 2 for your telescope and your personal characteristics:

5.

Table 2 - Sample table of predicted telescopic limiting magnitudes for a 10 inch Newtonian telescope at the zenith -assumes 50 year old expert observer on stars with color index = 0Eyepiece Power NELM 5.1 5.6 6.1 6.6 7.1 7.6

17mm 68x 14.3 14.7 15.1 15.4 15.9 16.4

10mm 114x 14.9 15.3 15.6 15.8 16.2 16.7

6mm 200x 15.3 15.7 15.9 16.1 16.5 17.0

6mm 2x Barlow 488x 16.0 16.2 16.2 16.3 16.7 17.2

Bortle 6 5 4 3 2 1

Optionally, graph Table 2 in the following forms:

Limiting magnitude areas - telescopic and n... http://fisherka.csolutionshosting.net/astronot...

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Figure 1 - Effect of applying increasing magnificationto a 10 inch telescope on TLM under a mag 6.1 sky

Figure 2 - Schaefer TLM curves for a 10 inch telescope -various sky brightnesses and constant observer and starcharacteristics

To aid in preparing these estimates, an Excel worksheet is provided that incorporates a Schaefer limiting magnitudecalculator.

Determine which naked-eye limiting magnitude ("NELM") field, listed in Table 6, will be nearest your zenith and youropen cluster TLM field.

6.

Go to the Nine Planets website or the International Meteor Organization website and printout the NELM finder chartfor your naked-eye limiting magnitude area and the star count table that you will use to estimate sky brightness.

7.

On the observing night, do the following:

Estimate and record the naked-eye sky brightness near your TLM field (Table 1) from the NELM area you identifiedfrom in Table 6.

1.

Estimate and record the number of degrees from your zenith your naked-eye limiting magnitude field.2.

Estimate and record the number of degrees from your zenith to the open cluster from which you will take a TLMreading with your telescope.

3.

Using your telescope and your charts of the open cluster that are labeled and paired with your eyepieces, start withthe lowest magnification. Circle and letter the faintest stars visible on the chart. "X"-mark stars that are not visible."S"-mark those stars you cannot separate because they are too close together. Record the faintest star visible onyour chart for that eyepiece. Then repeat, working your way down to your shorter focal-length, higher magnificationeyepieces.

4.

After the observing night, reduce your data:

Go back online to the Webda database chart. Confirm the photometry of your limiting magnitude decision stars. Ifthe limiting magnitude stars you circled are not O, B or A, you may need to reevaluate their true Johnson V bandlimiting magnitude using a Schaefer TLM Calculator.

1.

Table 3 - Table for recording measurements

Observation_Id__________________ ________1________ ________2________ ________3________ ________4________ ________5________

Date UTC

Op description

Telescope description

Observer description

Eyepiece fl

NELM Area

NELM Area Zenith Distance

TLM Cluster

TLM Cluster Zenith Distance

Extinction factor

Star Chart Id

Webda Id

Chart V-band magnitude

Color index

Spectral class

Notes

Magnification

Adjusted NELM magnitude

Adjusted V-band magnitude

Adjust your readings for extinction using Table 5.2.

Discussion


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What

Amateur astronomers uses the phrase "finding the limiting magnitude" in several contexts to describe the quality ofthe night sky or the performance of their instrument. Depending on the context of use, these questions are aboutthe apparent brightness of an object, asked by using the phrase "finding your limiting magnitude" may refer to:

Finding the limiting visual magnitude at the zenith using your naked eye;1.

Finding the limiting visual magnitude in any area of the sky off-zenith;2.

Finding the telescopic limiting magnitude of your telescope or binoculars; or,3.

Finding the photographic limiting magnitude of your telescope coupled with a digital or film camera.4.

Answers to these questions are given in terms of the apparent brightness of stellar point objects or of extendedobjects like galaxies or the night sky visible in the eyepiece. The answer to "what's your limiting magnitude ?"might be expressed by amateur astronomers in terms of:

The magnitude of a stellar point source in the modified Pogson magnitudescale;

1.

The integrated magnitude of an extended object in the Pogson magnitudescale;

2.

The surface brightness of an extended object in terms of "B" - magnitudesper square arcsecond (MPSAS); or,

3.

The surface brightness of an extended object in terms of the photographic"Ba" scale - candelas per square foot.

4.

A NELM to B Calculator to convert between the NELM (V) magnitude system forstellar objects to the MPSAS (B) system for sky brightness is provided.

Figure 3 - Conversion betweenNELM and MPSAS (B)

Why

Amateur astronomer asks to the question "what's your limiting magnitude ?" in order to:

Communicate the condition of parts of the night sky to other amateurs;1.

Record the condition of the night sky for their observing records;2.

Predict the visibility of objects either for visual observing or astrophotography;3.

Measure the performance of their eyes without telescopic assistance; or,4.

Measure the performance of their telescopes when employed as an aid to enhance or extend human vision.5.

The ability to measure the performance of one's eyes and of one'stelescopes under varying night sky conditions is a basic amateurastronomy skill. It's part of getting know your new scope.

Because performance of the telescope depends on the background skybrightness, the beginning step for measuring the performance of yourtelescope is to find the naked-eye-limiting magnitude of the sky near yourobject-of-interest. NELM is an indirect estimate of sky brightness.

Figure 4 - Effect of applied magnificationand background sky brightness onlimiting magnitude for a 30" telescope

How

General dark-sky scale

For most North American amateurs, their night skies typically have variations in sky brightness due to lightpollution.

Figure 5 - All sky photograph atSanta Monica National Resource

Figure 6 - All sky photograph atBryce Canyon National Park

Figure 7 - All sky photograph atNatural Bridges National Monument


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Area - false color coded for skybrightness - heavy light pollution(single reversal image)

southeastern Utah - false colorcoded for sky brightness - partiallight pollution (single reversalimage)

southwestern Utah - false colorcoded for sky brightness - no lightpollution (single reversal image)

Source and photo credits: Night Sky Team, Canyonlands National Park, U.S. National Park Service. 200_. All SkyNight website. http://www.nps.gov/cany/nature/allskyimages.htm accessed Aug. 2006

In part because of these common light pollution variations in North American night skies, in 2001, John Bortledeveloped the Bortle Dark Sky Scale:

Table 4 - Bortle Dark Sky ScaleClass_________________________ Description

Class 9 - Inner city sky Naked-eye limiting magnitude is 4.0 or less

Class 8 - City sky M31 and M44 visible on good nights at zenith; NELM 4.5 at zenith

Class 7 - Suburban/urban transition Milky Way invisible; NELM 5.0

Class 6 - Bright suburban sky M33 visible in binos only; NELM 5.5

Class 5 - Suburban sky Milky Way weak visible; NELM 5.6-6.0

Class 4 - Rural/suburban transition Milky Way visible w/o detail; NELM 6.1-6.5

Class 3 - Rural sky Light pollution evident at horizon; NELM 6.6-7.0

Class 2 - Typical dark sky site Zodical light visible with color; NELM 7.1-7.5

Class 1 - Excellent dark sky site NELM 7.6

Source: Bortle, John. 2006. Bortle Dark-Sky Scale. (Web article). Sky & Telescope. http://skyandtelescope.com/resources/darksky/article_81_1.asp

The Bortle scale is very useful for communicating the general nature of totally or partially light polluted skies,but it is not used as a parameter in determining telescopic limiting magnitude performance.

The human eye's response to a star's color index effects the visual determination of NELM and TLM

Naked-eye limiting magnitude and telescopic limiting magnitude are measured byobserving stars. A star's MK spectral class, as measured through its color index(B-V), effects your measurement of NELM or TLM. The eye has many morefaint-light sensitive rods that are used for dark-adapted scotopic vision than light-adapted photopic cones (120M rods v. 6-7M cones). Furthermore, the morenumerous rods are more efficient than cones in the blue-white wavelength around507nm. As a result, brain interprets light from blue and white stars as beingbrighter than a photometer measuring in the V-band would report. Conversely,red color index stars are reported to the brain by the human eye as fainter thanwould be measured by a photometer. This is also known as the Purkinje effect. Asthe brightness of a scene decreases, the brighntess of red colors decreases fasterthan the brightness of blue colors.

External content link toHyperphysics figure of theefficiency of dark-adaptedscotopic vision vs. photopicdaylight vision in thehuman eye.

The eye over reports the V-band magnitude of an O,B and A star. Statedconversely, the brightness of red color K and M stars is underreported by the eye.The one-magnitude range of this effect shown in Figure 8 explains why for twostars shown on charts with the same apparent V-band brightness, one star maybe invisible to the eye while the other is not. Rough compensating factors for astars color index are shown in Figure 8.

Best practices when measuring NELM and TLM includes trying to use, wheneverpossible, stars of a similar spectral class, e.g. - O,B and A stars, in order to obviatethe eye's differing sensitivity to color. When making measurements determine thespectral class of the star that defines, in particular, your TLM measurement, soyou are not up to a magnitude off. When selecting stellar fields by which you willmeasure TLM, try to use fields with an relative abundance of O,B and A stars.

Figure 8 - Effect of stellarcolor index on the limitingmagnitude of a 10"telescope

Naked-eye limiting magnitude

Visual determination of NELM ("NELM")

To visually determine naked-eye limiting magnitudes or telescopic limiting magnitudes is less a questionabout "how" and is more of question about "where" to look. Visual determination of naked-eye limitingmagnitude and telescopic limiting magnitude involves finding a suitable pre-measured star field as closeto the zenith, in the case of determining a night sky's zenithal limiting magnitude ("ZLM"), or as close tothe object-of-interest as possible. When measured off-zenith near and object-of-interest, ZLM is calledNELM.


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To make the measurement for the naked-eye, one needs a wide stellar field with pre-determined standardmagnitudes where the stars are in the range of 2 to 6.5 magnitudes and have narrow step intervalsbetween stars. If the minimum interval of available steps between stars in the limiting field is 0.3 or 0.4magnitudes, which is the maximum accuracy for your estimate. The International Meteor Organization("IMO") has pre-measured the magnitudes of star fields suitable for northern hemisphere observers. TheInternational Meteor Organization limiting magnitude fields have very finely 0.1 magnitude stepped fields- the best visual accuracy available.

Figure 9 - Plot IMO NELM AreaOverview Chart 3

Figure 10 - IMO Limiting MagnitudeArea 13 (Lyr-Her) Chart

Figure 11 - Author's wide-area NELMchart for the Orion-Tau region

Table 6 is a consolidated list of naked-eye limiting magnitude fields for north hemisphere observers andincludes a description of the naked-eye limiting magnitude fields of the IMO and from other majorsources. However, the IMO's limiting magnitude field charts are a simpler and easier way to view thelocation of these fields.

Use of these NELM fields is self-explanatory. Print and download the charts and limiting magnitude tables.The Nine Planets website has a complete list of charts of the IMO fields along with tables showing themagnitude of stars by count for each field. The Nine Planets website is recommended over the IMOwebsite for printing hardcopies of IMO limiting magnitudes charts and tables. After assembling the chartsand tables into an observing book and becoming familiar with main fields applicable to your favoredobserving points, stepping out of your car and looking up to determine the ZLM or NELM on a particularnight becomes second nature.

Visual determination of ZLM and NELM has an accuracy of about 0.2 magnitudes for average observers -assuming that the available minimum stellar magnitude steps in your limiting magnitude field are 0.1 or0.2 magnitudes. A magnitude field that has steps of 0.5 or 1.0 magnitudes cannot accurately measuremagnitudes in smaller steps.

The traditional method of finding ZLM or NELM from a star chart suffers from this accuracy limitation.Rarely does a star field align itself near your local zenith that has a sufficient number of steps betweenstellar magnitudes to permit an accurate measurement of ZLM.

Figure 12 - Wide-area NELM Chart generated with Cartes du Ciel - similar to McBeath-LMA05

The better method is to find the NELM in highly plotted International Meteor Organization limitingmagnitude areas and then adjust the off-zenith but more accurate NELM reading for atmosphericextinction. Adjusted (or reduced) for atmospheric extinction, your off-axis NELM yields an estimate ofZLM.

As a supplemental aid in finding the IMO NELM areas in a planetarium program, markers for the IMOLimiting Magnitude Areas have been ported to a Cartes du Ciel compatible external database -tlmnelm.zip (8kb).

Photoelectric determination of NELM

Visual determination of ZLM has been largely supplanted in modern amateur practice by a consumerdevice - Welch and Tekatch's Sky Quality Meter. The Sky Quality Meter is small hand-held device thatexamines a 60 degree cone of the sky around the zenith and that reliably reports an "average" brightnessfor that area of the celestial sphere.

The Sky Quality Meter reports in the B (MPSAS) scale, not the magnitude scale. See Figure 3, above.Equations to convert magnitudes NELM (V) to MPSAS (B) and B back to V are given in the Math Appendix,or use the provided NELM to B Calculator


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The Sky Quality Meter does not completely replace the older and less accurate method of visualdetermination of NELM. The Sky Quality Meter is designed to measure a set cone of the sky around thezenith. It cannot be used off zenith or describe small areas near the horizon. Many of dark skies nowavailable to northern hemisphere observers are compromised by light pollution. One part of the horizonmay have a 4.5 magnitude sky and opposite side a 6.2 magnitude hole. The Sky Quality Meter cannotaccurately estimate such skies.

For skies with significant light pollution caused variations in sky brightness, the visual NELM method willremain the method of choice for amateurs.

Adjust the NELM measurement for extinction

Raw chart and catalogue values, such as those plotted from the Tycho-2 catalogue and the HipparcosMission, need to be adjusted for atmospheric extinction.

A simple table of extinction correcting values is provided in Table 5, below. Depending on the distance toyour local zenith to your NELM limiting magnitude area, stars will be fainter than the catalogue valuelisted above due to atmospheric extinction. In general, add the Table 5 correction value to your NELMmeasurement.

Telescopic limiting magnitude

To determine your visual telescopic limiting magnitude, you need to find a star field that contains a goodselection of stars near your telescope's limit. To select a good star field, you first need some prediction orestimate of what the limit will be. Predicting telescopic limiting magnitude cannot be divorced from thequestions of the background brightness of the night sky or the from the magnification applied by the observer.

Pre-estimating your TLM in order to select a good star field

Historically, TLM has been estimated using variations onthe Steavenson-Sigdwick light-grasp model:

TLM = Background Sky Brightness + Light Grasp ofthe Eye + Light Grasp of the Telescope {Eq. 1}

TLM = 6.5 - 5*Log10(eye pupil size_in) +5*Log10(Telescope Aperture_in) {Eq. 2},assuming a 6.5 ZLM and simplifying for an assumed0.3 inch eye pupil

TLM = 9.1 + 5*Log10(D) {Eq. 3},where D is the aperture of the scope in inches.

Figure 13 - A traditional Steavenson-typemodel of TLM - a mag 6.5 sky withoutconsideration of magnification - aperture toTLM

There are many published variations of this light grasprule based on measuring the eye pupil and telescopeaperture in meters, centimeters or millimeters:

TLM = 16 + 5*Log10(D_m) {Eq. 4},same as Eq. 3 in meters (after Kitchin 2003 at 168)

TLM = 7.5 + 5*Log10(D_cm) {Eq. 5},same as Eq. 3 in centimeters

TLM = 1.8 + 5*Log10(D_mm) {Eq. 6},same as Eq. 3 in millimeters.

Figure 14 - A traditional Steavenson-typemodel of TLM - a mag 6.5 sky withoutconsideration of magnification - TLM toaperture

The simple light-grasp model does not account for the application of magnification and it assumes auniform sky brightness of 6.5 mags. Astronomers of the late 1800s and early 1900s realized theinadequacy of the model. Referring to Steavenson's data from the late 1800s, Sidgwick noted that, "thesecurves do not agree well with the results of observations, yielding results which are consistently high byabout 1.5 mag through the aperture range from 2 to 20inch." Sidgwick (1971 3d at 27).

The "missing" 1.5 magnitudes results from the application of increasing magnification from the lowestuseable (3.7x per inch of aperture) to extreme magnification (75x per inch of aperture). The sametelescope applied at a higher magnification sees "deeper" than the same telescope used at a lower


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magnification, as shown Figure 1, above, for a 10 inch telescope and in the following graph for variousaperture sizes:

Figure 15 - Schaefer TLM curves for various apertures -at one sky brightness (NELM 6.6) and constant observer and star characteristics

The simple light grasp model does not consider the response of the human eye to faint light.

Spurred by the need to spot planes and ships against the horizon at dusk, World War II advanced researchinto the ability of the human eye to see faint stellar and extended objects against backgrounds of varyingbrightness. Knoll (1946), Hecht (1947) and Weaver (1947) characterized the response of the human eyeto stellar points against bright backgrounds. (Blackwell (1946) examined the eye's ability to see extendedobjects (patches) against varying levels of brightness. Here, we are only concerned with stellar points.)

Figure 16 - Ability of the human eye to see stellar points against varying sky brightness backgrounds perWeaver (1947)

Between 1940 and the 1990s, a new problem arose for the modern amateur that Sidgwick andSteavenson did not face - light pollution. Between the 1940 and 1999, the United States populationincreased from 131.7 hundred million in 1940, to 248.7 hundred million persons in 1990 and to 272.9million persons in 1999. The average density of United States residents increased from 16.9 persons persquare mile in 1880, to 44.2 persons per square mile in 1940, to 70.3 persons per square mile in 1990,and to 77.1 persons per square mile in 1999 - a 74% increase over 1940. (U.S. Statistical Abstract of theUnited States, 2006 online edition). Electric lighting came into widespread use in this era of increasingdensity. Population density is correlated with light pollution.

Increasing light pollution spurred professional research to characterize the background brightness of thesky as population encroached on major observatory sites. Garstang (1989). The best skies aroundobservatories have a sky brightness of about 21 or 22 MPSAS. Cinzano (2001a, 2001b) expandedGarstang's light-pollution sky-brightness model into space-based satellite imagery of the Earth at night.This led to many of the tools that amateur astronomers use everyday to predict whether the sky will begood for a particular night, including the ClearSky Clock, the Meteorological Service of Canada's NorthAmerican Seeing Forecast and the International Dark Sky Society Dark Sky Map.

In the late 1980s and early 1990s, then NASA/JPL research Bradley E. Schaefer synthesized thesedevelopments into a new model for telescopic limiting magnitude - one that considered appliedmagnification, light-grasp (aperture), the physiological ability of the human eye to see faint point sources,and background sky brightness. Schaefer (1990). This improved model predicting telescopic limitingmagnitudes is called the Schaefer TLM algorithm or in this note - "Schaefer curves".

The Schaefer TLM algorithm is mathematically ponderous. Schaefer algorithm models star brightnessbased on the product of a series of corrective factors:

I* = L * F_b * F_c * F_t * F_p * F_a * F_r * F_sc * F_c * F_s from Schaefer (1990) {Eq. 7} (see MathAppendix).

Fortunately, you do not have to know how it works or what the algorithm means. Online Schaefer TLMcalculators, based on code that Schaefer published in Sky & Telescope in 1989, will perform thecomputation for you:

Bogan's Schaefer TLM Calculator

Catskill's Astro Club Mirror Schaefer TLM Calculator

Additionally, this author has ported the Schaefer algorithm to Visual Basic for Applications (VBA) code foruse within Microsoft Excel spreadsheets.

Using a modern Schaefer TLM online calculator, gather your telescope's or binocular's predictedperformance in a table similar to Table 2, above.

Using the modern Schaefer TLM model, you can graph your scope's expected performance either for one


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expected NELM sky brightness, as shown in Figure 1, above, or in a broader form that records expectedtelescope performance for varying sky brightnesses, as shown in Figure 2, above. The following chartsalso show this broader form of graphic presentation. They were prepared for an amateur 30" aperturetelescope and binoculars from data organized as shown in Table 2 and plotted using a spreadsheetprogram. The charts show the effect of both background sky brightness and applied magnification on thelimiting magnitude of a telescope.

Figure 17 - Effect of light pollution on binocularlimiting magnitude - all factors except lightpollution held constant

Figure 18 - Effect of applied magnification andbackground sky brightness on limiting magnitude fora 30" telescope

Telescopic limiting magnitude usually refers to the faintest stellar point observable using averted vision atthe highest applied magnification useable on the telescope. But in modern practice, each TLMmeasurement is limited to and paired with the stated ZLM sky brightness under which the TLMmeasurement was made.

To practically apply these techniques, using a 10" scope as a working example, if you are going to darksky site and reasonably know it will be a magnitude 6.1 sky, and you usually use at most a 6mm eyepieceat 200x, then Figure 1 and Table 2, above, indicate that you need to find an open cluster or othertelescopic limiting magnitude field that at least maps down to magnitude 15.9. If you are going to sitewith variable brightness that may be anything between magnitude 5.1 to magnitude 6.6, referring to thebroader TLM chart form like Figure 2, above, will give you the needed TLM estimate.

Now that you know who deep the field needs to be, you can start looking for a suitable TLM field to use onyour observing night.

Selecting a good stellar field to measure TLM

To make the visual measurement of telescopic limiting magnitude, one needs a stellar field that:

Will comfortably fit in the true-field-of-field of an eyepiece;

Has a pre-determined standard magnitudes where the stars are in the range of 9 to 16 magnitudesdepending on the aperture of your telescope or binocular;

Generally has O,B,A type stars of a similar color index;

Have tight interval steps between the stars of a similar color index. Ideally, you would want 0.1 to0.2 magnitude interval steps between the available O,B and A stars in the measuring field; and,

The available stars need to be spaced far enough apart that they do not merge and their brightnessintegrates together in the eyepiece.

Few stellar fields meet all these requirements. Often the available step intervals between stars aregreater than 0.5 magnitudes. This means the maximum visual accuracy that you can obtain using thatTLM field cannot be lower that 0.5 magnitudes. The human eye sees stars with a red color index(G,K,M,N,S) fainter than stars with a whiter color index (O,B,A,F). If you field has mixed spectral types,care needs to be taken that you have not overestimated the faintest star magnitude because it is a redcolor index star.

For pre-measured visual TLM fields, there are three primary sources: 1) 9 open clusters measured by R.N.Clark in Appendix C to his 1990 book Visual Astronomy of the Deep Sky (plus a 10th cluster, M67, chartedin the RASC's Observer's Handbook), 2) ZLM charts generated by planetarium software, and 3) Landolt's24 photometry star fields spaced along the celestial equator.

Finding TLM using Clark open cluster stellar fields

Table 7 is a list of telescopic limiting magnitude areas. The NGC objects in the list are Clark's 9charted open clusters with a 10th plot for M67 in the Royal Astronomical Society of Canada's annualObserver's Handbook. This amateur author has also charted NGC1647 in detail to magnitude 13 foruse with smaller scopes.

Clark's charted open clusters generally go down to magnitude 15 or 16. For persons living in ruralareas travel to a major university that will have a copy of Clark's out-of-print text is not practical.However, facsimiles of Clark's open cluster charts can be prepared using Jean Mermilliod's onlineWebda Open Cluster Database at the University of Vienna. The Webda interface quickly plots a


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cluster chart by a limiting magnitude cut-off value for any open cluster with an NGC number.

From the Webda homepage, click Navigation | Enter the NGC designation in the Display the Page box| Select Query - From cluster chart (plotted).

reasonable facsimiles of Clark's open cluster charts can be prepared using Jean Mermilliod's onlineWebda Open Cluster Database at the University of Vienna. The Webda interface quickly plots acluster chart by a limiting magnitude cut-off value for any open cluster with an NGC number.

From the Webda homepage, click Navigation | Enter the NGC designation in the Display the Page box| Select Query - From cluster chart (plotted).

Figure 19 - Webda plot of open cluster NGC6910 tomag. 14 in Cyg Figure 20 - Author's chart for open cluster

NGC1647

A paint program can be used to single or double reverse such charts so they are easier to use at theeyepiece:

Figure 21 - Double reversed Webda plot of opencluster NGC6910 Figure 22 - Double reversed chart for open

cluster NGC1647

Finding TLM using planetarium program generated ZLM charts of stellar fields

The traditional method of finding TLM is to use a star chart. Modern planetarium programs extendthis tradition by allowing the easy generation of user prepared charts. Cartes du Ciel is one suchprogram.

Figure 23 - Plot of 1.5 ° TFOV around alf Her tomagnitude 15 prepared from Cartes du Ciel Figure 24 - Plot of 1.5 ° TFOV around alf Her to

magnitude 14 from Simbad "Query & Plot" utility

There are three limitations of the traditional charting method in the modern planetarium programage.

First, you must have the Hubble GST and Tycho-2 or the USNO A2 catalogues installed in yourplanetarium program to generate charts down to a limit of magnitude 15. These catalogues are noteasily downloaded since they can exceed 500mb in size.

Second, in the post-2000 era of low-cost DOBs with apertures larger than 10 inches, amateurtelescopes now frequently reach below magnitude 15 at their highest useable magnification. Evenwith the USNO A2 reduced catalogue installed, you may not be able to generate charts that reach asufficient depth.


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Third, even where you can generate a chart, rarely will there be a sufficient number of stars in thefield of the appropriate 0.1 or 0.2 magnitude intervals within the O,A and B spectral classes andaround your predicted TLM.

The zenith chart method has the attraction in that a TLM measuring field can always be generated inor near the zenithal hole. You do not have to wait for a charted open cluster to transit at a sufficientaltitude.

Even if you do not have a planetarium program, useable zenith TLM measuring charts can begenerated using the CDS Strasburg Simbad web application. Figure 24 is a sample chart generatedusing Simbad:

Use Togo's online coordinate conversion calculator to determine the right ascension anddeclination near for your local zenith - altitude 90 degrees and an azimuth of 0 degrees.

Use a chart to find a bright star in a constellation near the zenith.

Enter the name of the bright star in the CDS Strasburg Simbad web application, e.g. - iot Her.

When the Simbad Query Result screen displays, under the section labeled "Plot and ImageTools", use "Query and Plot" to plot a chart equal to the size of your TFOV. Simbad providesoptions for limiting the display to stars only.

Right-click the Simbad generated chart to download the chart to your local computer.

While connected to the Simbad chart, you can click on any star to get more information.

Finding TLM using stellar fields in Landolt photometry areas and Skiff's LONEOS catalogue

For smaller scope owners whose limiting magnitude is between 9 and 12magnitudes, Landolt's 24 pre-measured photometry fields provide anotheroption for measuring TLM. In the 1970s, Landolt performed photo-electricmeasurements on 226 stars in charts 24 areas spaced at about 15 degreeintervals along the celestial equator. Unlike open clusters, Landolt fieldsare just collections of fortuitously optically aligned stars. Initially, Landolt'sphotometry fields ranged from magnitude 9 to 12. In the 1990s,approximately another 500 stars were measured in those same fields,extending some fields down to magnitude 16. Online catalogues of stars inthe Landolt fields are available through databases at CDS-Simbad (1973,1983 and 1993) and at the University of Hawaii.

Landolt fields suffer from limitations similar to planetarium programgenerated zenithal charts. Most Landolt fields do not contain a sufficientnumber of O,B and A stars of a close intervals to make accurate TLMmeasurements.

Figure 25 - LandoltPhotometry Areas in Virto Oph on the celestialequator using Cartes duCiel

The depth and charting clarity of Landolt fields can be improved and supplemented with 34,000stars in Brian Skiff's (Lowell Observatory) LONEOS photometry catalogue. This catalogue compilesabout 34,000 stars with known photometry from around magnitude 12 to 19 for use in the LowellObservatory Near-Earth Object Search (LONEOS). Skiff's catalogue incorporates Landolt's photometrystars. A Cartes du Ciel external catalogue of Skiff's catalogue is available for download from Cartes.

Table 7 provides a list of 24 of Landolt's stellar photometry fields from his1973 paper. Where the brightest central star of Landolt's field is a star witha Henry Draper catalogue designation, the HD number is also listed inTable 7.

To use the Landolt fields, download and print a hardcopy of Landolt'slengthy 1973 paper which includes photographs and star designations foreach of the fields.

As a supplemental aid in finding the Landolt areas in a planetariumprogram, markers for the Landolt celestial equator photometry fields havebeen ported to a Cartes du Ciel compatible external database -tlmnelm.zip (8kb). The Landolt area markers can be supplemented byadding Skiff's LONEOS catalogue of 34,000 stars to Cartes du Ciel. Onceloaded, charts similar to Figure 26 can be generated.

Figure 26 - Plot ofLandolt Area SA-105using Cartes du Ciel

Even if not used as TLM fields, intermediate amateurs interested in astrophotography andphotometry should become familiar with Landolt's fields. They are used to calibrate the photometryreadings in your CCD camera software.


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Adjust the TLM measurement for extinction

As with NELM measurements, apply the simple table of extinction correcting values in Table 5, below,to adjust the catalogue value of the star's apparent brightness for extinction.

Rough correction of NELM and TLM readings for atmospheric extinction

An International Comet Quarterly table (Green 1992) provides rough TLM and NELM correcting values foratmospheric extinction based on the kilometers of the observing point above sea level:

Table 5 "Average" Atmospheric Extinction in Magnitudes for Various Elevations Above Sea Level (h, in km)(Excerpts from Green 1992)

z h = 0 h = 0.5 h = 1 h = 2 h = 3 01 0.28 0.24 0.21 0.16 0.13 10 0.29 0.24 0.21 0.16 0.13 20 0.30 0.25 0.22 0.17 0.14 30 0.32 0.28 0.24 0.19 0.15 40 0.37 0.31 0.27 0.21 0.17 45 0.40 0.34 0.29 0.23 0.19 50 0.44 0.37 0.32 0.25 0.21 55 0.49 0.42 0.36 0.28 0.23 60 0.56 0.48 0.41 0.32 0.26 62 0.60 0.51 0.44 0.34 0.28 64 0.64 0.54 0.47 0.37 0.30 66 0.69 0.59 0.51 0.39 0.32 68 0.75 0.64 0.55 0.43 0.35 70 0.82 0.70 0.60 0.47 0.39 72 0.91 0.77 0.66 0.52 0.43 74 1.02 0.86 0.74 0.58 0.48 76 1.15 0.98 0.84 0.66 0.54 78 1.34 1.13 0.98 0.76 0.63 80 1.59 1.34 1.16 0.91 0.74

Green, Daniel. July 1992. Correcting for Atmospheric Extinction. International Comet Quarterly. 14:55 << http://cfa-www.harvard.edu/cfa/ps/icq/ICQExtinct.html >>

The "z" value is the degrees from zenith to the celestial object. So z=80 is 10 degrees altitude above thelocal horizon.

For example, if the "V" band catalogue magnitude of your comparison star is 7.5, the star is located 30degrees above the horizon (or 60 degrees from the zenith), the observer is at sea level, then the truezenithal brightness of the comet is v7.5 and its apparent brightness is v6.9 (7.5-0.56).

Practical measurement of telescope/binocular performance using NELM and TLMreadings

The evolution of the modern Schaefer TLM algorithm along with increased light pollution variations in sky brightnessexperienced by modern amateurs, suggests three methods for examining the telescopic limiting magnitude of atelescope and of comparing telescope performance against TLM model predictions.

The first traditional method, shown in Figure 1 above, involves using the highest useable magnification under thebest possible dark sky to measure the faintest possible star.

The second method, also shown in Figure 1 above, involves using a range of eyepieces under a single skybrightness condition to see if the overall performance of the telescope follows the predicted Schaefer curve.

The third method, shown in Figure 2 above, involves accruing TLM data in a variety of sky brightness conditions tosee if the telescope performs as predicted as shown in the various Schaefer curves in Figure 2.

This third option is well-suited to the modern urban-suburban amateur.

To aid in recording TLM & NELM measurements, an Excel worksheet is provided that incorporates a Schaefer limitingmagnitude calculator.

Naked-Eye Limiting Magnitude Areas


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Obtain NELM charts and tables from:

International Meteor Organization (IMO) Visual Limiting Magnitude Areas http://www.imo.net/visual/major/observation/lm

McBeath Limiting Magnitude Areas http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1991JBAA..101..213M

Table 6 - Naked-Eye Limiting Magnitude (NELM) Areas (N=44) for Northern Hemisphere ObserversCat_Id_________________ J2000_Position Con Comments_______________________________________________________

McBeath-LMA02 J005645.21+382957.6 And Coords per NASA HEASARC; marker is mu. And

IMO-LMA18 J011018.74+420453.3 And mu. And-gam And-phi And; coords per NASA HEASARC; marker is 44 And

IMO-LMA29 J022252.31-733844.9 Hyi gam Hyi-alf Hyi-bet Hyi; coords per NASA HEASARC; marker is kap Hyi

McBeath-LMA01 J023148.00+891536.0 UMi Marker is alf UMi

RASC Polar LMA J023148.00+891536.0 UMi Marker is Polaris.

IMO-LMA02 J034511.63+423442.8 Per bet Per-del Per-zet Per; coords per NASA HEASARC; marker is nu. Per

McBeath-LMA08 J035801.77-133030.7 Eri Coords per NASA HEASARC; marker is gam Eri

IMO-LMA20 J045403.01+662033.6 Cam 42 Cam-bet Cam-gam Cam; coords per NASA HEASARC; marker is alf Cam

McBeath-LMA03 J050157.60+434912.0 Aur Marker is eps Aur

IMO-LMA08 J050305.75+213523.9 Tau alf Tau-bet Tau-zet Tau; coords per NASA HEASARC; marker is iot Tau

IMO-LMA22 J051255.90-161219.7 Lep bet Lep-bet Ori-53 Eri; coords per NASA HEASARC; marker is mu. Lep

IMO-LMA17 J055129.40+390854.5 Aur eps Aur-tet Aur-del Aur; coords per NASA HEASARC; marker is nu. Aur

McBeath-LMA09 J064651.09-142533.5 CMa Coords per NASA HEASARC; marker is 11 CMa

IMO-LMA04 J072543.60+274753.1 Gem alf Gem-eps Gem-bet Gem; coords per NASA HEASARC; marker is iot Gem

IMO-LMA28 J091202.54-645146.2 Car bet Car-eps Car-iota Car; coords per NASA HEASARC; marker is NGC2808

IMO-LMA03 J095059.36+590219.4 UMa 23 UMa-tet UMa-bet Uma; Coords per NASA HEASARC; marker is ups Uma

IMO-LMA09 J101042.93+154215.8 Leo alf Leo-bet Leo-gam Leo-del Leo; coords per NASA HEASARC; marker is 33 Leo

McBeath-LMA10 J113300.12-315127.4 Hya Coords per NASA HEASARC; marker is ksi Hya

IMO-LMA23 J122033.64-221257.2 Crv del Crv-gam Crv-eps Crv-bet Crv; coords per NASA HEASARC; marker is zet Crv

IMO-LMA19 J123328.94+694717.7 UMi kap Dra-alf Dra-bet UMi; coords per NASA HEASARC; marker is kap Dra

IMO-LMA27 J124743.26-594119.6 Cru bet Cen-alf Cru-gam Cru; coords per NASA HEASARC; marker is bet Cru

McBeath-LMA04 J125602.40+381912.0 CVn Marker is alf02 CVn

IMO-LMA16 J131814.51+494055.4 CVn alf CVn-eps UMa-eta UMa; coords per NASA HEASARC; marker is 21 CVn

IMO-LMA10 J132318.89-045527.9 Vir alf Vir-zet Vir-gam Vir; coords per NASA HEASARC; marker is 65 Vir

IMO-LMA11 J144500.00+270412.0 Boo alf CrB-gam Boo-alf Boo; marker is eps Boo

McBeath-LMA11 J145909.68-420615.1 Cen Coords per NASA HEASARC; marker is kap Cen

IMO-LMA26 J151738.89-633637.7 Cir gam TrA-alf TrA-eta Ara-alf Cen; coords per NASA HEASARC; marker is eps Cir

IMO-LMA24 J153531.58-144722.3 Lib bet Lib-gam Lib-sigma Lib-alf Lib; coords per NASA HEASARC; marker is gam Lib

IMO-LMA12 J154938.40-032548.0 Ser alf Ser-bet Lib-del Oph; marker is mu. Ser or 36 Ser

McBeath-LMA05 J163130.57+333049.2 Lyn Coords per NASA HEASARC; marker is 31 Lyn

IMO-LMA15 J164914.40+455848.0 Her bet Dra-tau Her-pi Her; marker is 52 Her

IMO-LMA25 J165009.81-341735.6 Sco alf Sco-eps Sco-khi Lup; coords per NASA HEASARC; marker is eps Sco

McBeath-LMA06 J170136.36+333405.8 Her Coords per NASA HEASARC; marker is 59 Her

IMO-LMA13 J181951.71+360352.4 Lyr bet Lyr-zet Lyr-tet Her-nu Her; coords per NASA HEASARC; marker is kap Lyr

IMO-LMA01 J182559.14+653348.5 Dra khi Dra-zet Dra-del Dra-ksi Dra; coords per NASA HEASARC; marker is 42 Dra

McBeath-LMA12 J191001.76-392026.9 CrA Coords per NASA HEASARC; marker is bet CrA

IMO-LMA05 J193404.80+072248.0 Aql zet Aql-gam Aql-del Aql; marker is mu. Aql

IMO-LMA14 J201747.20+380158.5 Cyg eps Cyg-eta Cyg-gam Cyg; coords per NASA HEASARC; marker is 34 Cyg

McBeath-LMA07 J205710.42+411001.7 Cyg Coords per NASA HEASARC; marker is nu. Cyg

McBeath-LMA14 J210846.85-885723.4 Oct Coords per NASA HEASARC; marker is sig Oct

IMO-LMA30 J212626.61-652158.3 Pav alf Tuc-alf Pav-eps Pav; coords per NASA HEASARC; marker is gam Pav

IMO-LMA07 J214526.93+610714.9 Cep alf Cep-bet Cep-del Cep; coords per NASA HEASARC; marker is nu. Cep

McBeath-LMA13 J225738.40-293712.0 PsA Marker is alf PsA

IMO-LMA21 J230926.80-211020.7 Aqr alf PsA-98 Aqr-del Aqr; coords per NASA HEASARC; marker is 88 Aqr

IMO-LMA06 J235229.29+190713.0 Peg alf And-gam Peg-alf Peg; coords per NASA HEASARC; marker is phi Peg

Other sources referenced in Table 6:


Telescopic Limiting Magnitude Areas

Obtain or generate TLM charts from:

Webda Open Cluster Database


12 de 16 24-09-2014 16:11

Landolt, A. 1973. UBV photoelectric sequences in the celestial equator selected areas 92-115.

Clark, R.N., 1990. Star Clusters for Finding Your Limiting Magnitude. Appendix C in Visual Astronomy of theDeep Sky

Table 7 - Telescopic Limiting Magnitude Areas (N=34) for Northern Hemisphere ObserversSmall Scope Fields: N=24; Large scope fields: N=10Cat_Id_________ J2000_Position Con HR_HD Comments___________________________________________________

NGC225 J004342.00+614648.0 Cas Clark note: 20 stars mag 9+

SA92 J005501.20+004720.4 Psc HD005319 Mag range: 10-13; N=12; Landolt1992 adds 41 stars to mag 16; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

SA93 J015450.16+004658.8 Psc Mag range: 9-12; N=29; Central star is BD+00 307. HD col is central star othername; common name is Landolt central star id; either is region marker; Bayer orFlamsteed, if present, is bright star adjacent to field.

SA94 J025556.16+003057.6 Cet Mag range: 6-13; N=31; Landolt1992 adds 7 stars to mag 14; Central star isBD-00 617. HD col is central star other name; common name is Landolt centralstar id; either is region marker; Bayer or Flamsteed, if present, is bright staradjacent to field.

SA95 J035415.12+001720.4 Eri HD024537 Mag range: 8-13; N=26; Landolt1992 adds 44 stars to mag 16; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

NGC1647 J044554.00+190636.0 Tau Clark note: 25 stars mag 8 to 13; OMeara10

SA96 J045250.40+000701.2 Ori HD031073 Mag range: 6-12; N=34; Landolt1992 adds 6 stars to mag 13; HR1574 is v5.97star in field.HD col is central star other name; common name is Landolt centralstar id; either is region marker; Bayer or Flamsteed, if present, is bright staradjacent to field.

SA97 J055725.92+000140.8 Ori HD040210 Mag range: 7-12; N=30; Landolt1992 adds 7 stars to mag 14; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

NGC2129 J060106.00+231836.0 Gem Clark note: about 50 stars

SA98 J065209.60-001742.0 Mon HD050209 Mag range: 8-13; N=30; Landolt1992 adds 46 stars to mag 18; HR2530, v5.78, isbright star in field. HD col is central star other name; common name is Landoltcentral star id; either is region marker; Bayer or Flamsteed, if present, is brightstar adjacent to field; manually corrected declination plotting sign error.

NGC2422 J073636.00-142848.0 Pup

SA99 J075440.80-003722.8 Mon HD064605 Mag range: 8-12; N=29; HD col is central star other name; common name isLandolt central star id; either is region marker; Bayer or Flamsteed, if present, isbright star adjacent to field; manual correction of coordinate sign

RASC M67TLMA

J085006.00-115300.0 Cnc Northwest quadrant of M67; mag range: 10.6-21.3; coordinates per HEARSAC

SA100 J085357.60-003643.2 Hya HD076082 Mag range: 8-14; N=31; Landolt1992 adds 6 stars to mag 13; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field; manually correcteddeclination plotting sign error.

SA101 J095638.40-002739.6 Sex HD086135 Mag range: 8-12; N=31; Landolt1992 adds 35 stars to mag 16; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field; manually correcteddeclination plotting sign error.

SA102 J105524.00-004846.8 Leo HD094616 Mag range: 8-12; N=29; HR4245, v6.3, is bright star in field. HD col is central starother name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field; manually correcteddeclination plotting sign error.

SA103 J115500.00-003321.6 Vir HD103486 Mag range: 8-12; N=28; HD col is central star other name; common name isLandolt central star id; either is region marker; Bayer or Flamsteed, if present, isbright star adjacent to field; manual correction of coordinate sign

SA104 J124304.80-003216.8 Vir HD110572 Mag range:8-12; N=21; Landolt1992 adds 34 stars to mag 16; galaxy in FOV isprobably NGC4632; HD col is central star other name; common name is Landoltcentral star id; either is region marker; Bayer or Flamsteed, if present, is brightstar adjacent to field; manually corrected declination plotting sign error.

SA105 J133745.60-003730.0 Vir HD118579 Mag range: 7-12; N=47; HD col is central star other name; common name isLandolt central star id; either is region marker; Bayer or Flamsteed, if present, isbright star adjacent to field; manual correction of coordinate sign

SA106 J144138.40-002558.8 Vir Mag range: 8-14; N=31; central star is BD+00 3224; galaxy NGC5719, Bmag 13.1is in field; HD col is central star other name; common name is Landolt central starid; either is region marker; Bayer or Flamsteed, if present, is bright star adjacentto field.

SA107 J153900.00-001839.6 Ser HD139590 Mag range: 6-12; N=32; Landolt1992 adds 28 stars to mag 16; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field; manually correcteddeclination plotting sign error.

SA108 J163719.20-002446.8 Oph HD149845 Mag range: 8-13; N=33; HD col is central star other name; common name isLandolt central star id; either is region marker; Bayer or Flamsteed, if present, isbright star adjacent to field; manual correction of coordinate sign


13 de 16 24-09-2014 16:11

SA109 J174450.40-000802.4 Oph HD161304 Mag range: 9-14; N=17; Landolt1992 adds 7 stars to mag 14; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field; manually correcteddeclination plotting sign error.

NGC6494 J175700.00-185848.0 Sgr

SA110 J184216.80+000918.0 Aql HD172829 Mag range: 7-12; N=17; Landolt1992 adds 39 stars to mag 16; HD172651, v7.4,is bright star in field. HD col is central star other name; common name is Landoltcentral star id; either is region marker; Bayer or Flamsteed, if present, is brightstar adjacent to field.

SA111 J193821.60+002042.0 Aql HD185297 Mag range: 7-13; N=20; Landolt1992 adds 8 stars to mag 13; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

NGC6823 J194309.60+231724.0 Vul Clark note: 30 stars mag 11+

NGC6910 J202307.20+404612.0 Cyg Clark note: 40 stars mag 10+

SA112 J204221.60+002642.0 Aqu HD197232 Mag range: 9-12; N=20; Landolt1992 adds 7 stars to mag 12; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

NGC7031 J210712.00+505248.0 Cep 50 stars mag 11+

SA113 J214226.40+002642.0 Aqu HD206488 Mag range: 7-12; N=18; Landolt1992 adds 42 stars to mag 15; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

NGC7235 J221224.00+571536.0 Cep about 25 stars

SA114 J224221.60+004612.0 Aqu HD215044 Mag range: 7-12; N=26; Landolt1992 adds 9 stars to mag 12; HD215129, v. 6.9,is bright star near in field; galaxy PGC0069505, Bmag 15.5, is 1 deg s.w. ofcentral star. HD col is central star other name; common name is Landolt centralstar id; either is region marker; Bayer or Flamsteed, if present, is bright staradjacent to field.

SA115 J234314.40+005414.4 Psc HD222733 Mag range: 8-13; N=19; Landolt1992 adds 7 stars to mag 12; HD col is centralstar other name; common name is Landolt central star id; either is region marker;Bayer or Flamsteed, if present, is bright star adjacent to field.

Sources:

Clark, R.N., 1990. Star Clusters for Finding Your Limiting Magnitude. Appendix C in Visual Astronomy of the Deep Sky, Cambridge UniversityPress and Sky Publishing http://www.clarkvision.com/visastro/

Webda Open Cluster Database http://www.univie.ac.at/webda/

Landolt, A. 1973. UBV photoelectric sequences in the celestial equator selected areas 92-115. 1973AJ.....78..959L; CDS Cat. VI/191996yCat.6019....0L http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?1973AJ.....78..959L

Landolt1992: Landolt, A. Jul. 1992. UBVRI photometric standard stars in the magnitude range 11.5-16.0 around the celestial equator.1992AJ....104..340L ; CDS Cat. II/183A/ http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992AJ....104..340L

CFHT Table of Landolt Standard Stars on the Celestial Equator http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/


Math appendix

Convert MPSAS (B) to NELM (V)

B_mpsas = 21.58 - 5 log(10^(1.586-NELM/5)-1) {Eq. 8} per Olof Carlin (1990)

Convert NELM (V) to MPSAS (B)

NELM=7.93-5*log(10^(4.316-(Bmpsas/5))+1) {Eq. 9} per Olof Carlin (1990)

In order to be visible, an extended object, like a galaxy or nebula, has to have a surface brightness brighterthan the background sky brightness. A list of the brightness of approximately 600 deep sky objects in both themagnitude and MPSAS scales is available in Clark's Visual Astronomy of the Deep Sky. Clark lists the MPSASand integrated magnitude for 616 common DSOs in Appendix E to the Visual Astronomy, available online athttp://www.clarkvision.com/visastro/appendix-e.html.

Schaefer's algorithm

I* = L * F_b * F_c * F_t * F_p * F_a * F_r * F_sc * F_c * F_s {Eq. 7, above}

- from Schaefer (1990), where

L = is the response of the human eye to lightF_b = transforms the binocular eye perception equation of Knoll (1946) and Hecht (1947) to monocular viewing


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F_e = extinction factorF_t = transmission factor of the telescopeF_p = correction factor for the observer's exit pupil size based on the observer's ageF_m = correction factor for the dimming of the image resulting from magnificationF_r = extended object size correction factorF_sc = correction factor for the Stiles-Crawford effect in the human eyeF_c = correction factor for the color of the star observedF_s = correction factor for the experience of observer

Acknowledgements

Centre de Données astronomiques de Strasbourg - Simbad: This note has made use of the SIMBADdatabase, operated at CDS, Strasbourg, France.

Centre de Données astronomiques de Strasbourg - Catalogue Service: This note has made use ofcatalogues redistributed through the CDS Astronomer's Catalogue Service, operated at CDS, Strasbourg, France.

NASA Astrophysics Data System/Computation Facility at the Harvard-Smithsonian Center forAstrophysics - NASA ADS Abstract Services: This note has made use of NASA's Astrophysics Data System.

Webda: This note has made use of the WEBDA database, operated at the Institute for Astronomy of the Universityof Vienna.

References

Blackwell, H. R. Nov. 1946. Constant thresholds of the human eye. 1946JOSA...36..624B http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1946JOSA...36..624B

Bortle, John. 2006. Bortle Dark-Sky Scale. (Web article). Sky & Telescope. http://skytonight.com/resources/darksky/3304011.html?page=1&c=y

Clark, R.N., 1990. Star Clusters for Finding Your Limiting Magnitude. Appendix C in Visual Astronomy of the DeepSky, Cambridge University Press and Sky Publishing.http://www.clarkvision.com/visastro/

Cinzano, P. et al. 2001a. Naked-eye star visibility and limiting magnitude mapped from DMSP-OLS satellite data .2001MNRAS.323...34C http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001MNRAS.323...34C

Cinzano, P. et al. 2001b. The first World Atlas of the artificial night sky brightness. 2001MNRAS.328..689Chttp://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001MNRAS.328..689C

Garstang, R. H. 1986. Model for Artificial Night-Sky Illumination. 1986PASP...98..364G http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986PASP...98..364G

Garstang, R. H. 1989. Night-sky brightness at observatories and sites.1989PASP..101..306Ghttp://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1989PASP..101..306G

Garstang, R.H May. 1999. Vision thresholds revisited (abstract). American Astronomical Society, 194th AAS Meeting,#09.16 http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999AAS...194.0916G

Garstang, R.H. April 1999. New Formula for Optimum Magnification and Telescopic Limiting Magnitude. Journal ofthe Royal Astronomical Society of Canada. 93:80 http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999AAS...194.0916G

Garstang, R. H. 2000. Limiting visual magnitude and night sky brightness. Memorie della Societa AstronomiaItaliana 71:83 http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2000MmSAI..71...83G

Green, Daniel. July 1992. Correcting for Atmospheric Extinction. International Comet Quarterly. 14:55 http://cfa-www.harvard.edu/cfa/ps/icq/ICQExtinct.html

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Kitchen, C. (2003 2d). Telescopes and Techniques. Springer.

Knoll, H. A. et al. Aug. 1946. Visual thresholds of steady point sources of light in fields of brightness from dark todaylight. 1946JOSA...36..480K http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1946JOSA...36..480K

Landolt, A. 1973. UBV photoelectric sequences in the celestial equator selected areas 92-115. 1973AJ.....78..959L;CDS Cat. VI/19 1996yCat.6019....0L http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?1973AJ.....78..959L

Landolt, A. Jul. 1992. UBVRI photometric standard stars in the magnitude range 11.5-16.0 around the celestial


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Mermilliod, J., Paunzen, E. 200_. Webda Open Cluster Database.http://www.univie.ac.at/webda/

McBeath, A. 1991. Visual limiting magnitude determination charts. 1991JBAA..101..213M http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1991JBAA..101..213M

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