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This is not possible. Studies have shown that a minimum of 90 quanta incident upon the fully dark adapted human eye is the threshold of detectability (with optimum target size and flash duration). This corresponds to a magnitude of 7.6 for a Vega type star just detectable with a fully wide 7mm iris. Which becomes magnitude 13.4 for a 4" aperture. If he is detecting magnitude 16, that is 11x fainter than the limit and corresponds to about 8 quanta incident on the eye. About 10% of those actually get through to be detected by the rod cells, so in fact statistically even less than 1 quanta is getting "detected"! Thats just not possible because a minimum of 5-9 quanta are needed for the retina to respond. Thats the way it is physiologically "wired", for optimum dark signal/noise. If the retina responded to single quanta the background would be too noisy for effective imaging in the brain, and this guy would have been stumbling around in the dark.
Mike Linnolt
Alas, this is wrong, too, mainly since it ignores using high magnifications which makes the background darker. Even the naked-eye limit from 'true-dark' sites is in the early 8s, around V=8.2 plus or minus a couple tenths.
No, I don't believe the mag. 16 with 10cm aperture either. At high power, something like 150x or so with this aperture, the V limit will be between 14.5 and 15. Seeing has to be good, of course, to get this faint, probably 1" fwhm or better.
Maybe Hasegawa was using B magnitudes (which will be numerically larger than V magnitudes) for this reckoning. On the other hand, Mike's seemingly conservative numbers might result from an incorrect transformation from photon-quanta to V magnitudes, or more likely, the definition of what constitutes threshold detectability. The latter goes down considerably with experience, typically being in the 5-10 percent rate for the best (most patient in this case) observers. If you insist on seeing something 50 percent or even 100 percent of the time viewing it, then sure, the limit is much brighter. That's not what Hasegawa-san would have been doing, for sure.
\Brian
> This is not possible. Studies have shown that a minimum of 90 quanta > incident upon the fully dark adapted human eye is the threshold of > detectability (with optimum target size and flash duration).These values may be dependent on experiments. I know there exist physiological description that the threshold is much lower, even corresponding to a few detected photons in a single retinal cell.
> This corresponds to a magnitude of 7.6 for a Vega type star just detectable > with a fully wide 7mm iris. Which becomes magnitude 13.4 for a 4" > aperture.Won't observers be surprised to hear this limiting magnitude for a 10 cm (4 inch) aperture? I had years-long experience with this aperture, but the limiting magnitude 13.5 was a "usually detectable" value under moderate conditions (in moderate citylight). I once had an experience to catch the outburst of EY Cyg in rise. According to the reports to the AAVSO, the object was recorded below 14.0 (in average) on the same night. I remember that the object looked "conspicuously brighter than usual". The quoated value more looks like to me a safe limit.
> About 10% of those actually get through to be detected by the rod cells, > so in fact statistically even less than 1 quanta is getting "detected"!In what time, in 1 second? The time-constant of the eye response may not be always 1 sec or similar length. Furthermore, there is always Poissonian fluctuations of photon detections. It is possible, even at this mean photon rate, one may detect a packet arrival of photons in a reasonable waiting time. The observer may have succeeded in training the detection neural network to distinguish the increased occcurence of such events against the background.
Regards, Taichi Kato(vsnet-chat 6009)
> No, I don't believe the mag. 16 with 10cm aperture either. At high > power, something like 150x or so with this aperture, the V limit will be > between 14.5 and 15. Seeing has to be good, of course, to get this faint, > probably 1" fwhm or better.I agree that this value is reasonable under good conditions. The magnitude 13.5 is too bright.
> Maybe Hasegawa was using B magnitudes (which will be numerically > larger than V magnitudes) for this reckoning.No, at the time of these observations, Hasegawa-san used V-magnitude sequences, either from literature or from "photographic V" determinations. I just remember that Hasegawa-san was also very inclined to blazar observations (with the same 10 cm telescope). His limiting magnitude played the most important role in such faint objects as OJ 287, 3C 279, 4C 29.45 etc. He positively recorded these objects at around 15 or sometimes fainter (I even saw a report of 16.2 or possibly below this). The values are not inconsistent with the modern knowledge, and were not inconsistent with the quasi-simultaneous photographic observations (the object was sometimes undetected by a 30cm photographic instrument, but was positively recorded by a 10cm visual observation).
Regards, Taichi Kato(vsnet-chat 6010)
Doubtful. There have been some reports of people seeing 8th magnitude stars, but for the vast majority of observers, I believe the quoted figure is accurate and not conservative. Those exceptional observers likely had unusually large pupil diameters, rather than more sensitive retinas. My own limit is just about 13.5 with a 4" aperture under dark skies, and hardly ever have I known anyone to go much better than that.
The studies were done under optimum dark-room conditions with targets size <10 arcmins, which would correspond to the best seeing at highest magnifications described.
The studies used a 60% detection rate as the threshold of detectability. Yes, fainter objects may be detected at 5-10% rate, but at that level, would you consider it a safe observation? Its hard to reproduce the observed location of an object that appears so infrequently, resulting in a low confidence of correct identification. Personally, if I cannot see my target at least 50% of the time, I wont bother estimating it.
Mike Linnolt
The 90 quanta is incident on the eye externally. 10% will get thru to be detected by the rod cells. A single photon can produce a measurable cell membrane hyperpolarization, but thats done by using patch-clamping techniques in vitro on isolated cells. In vivo, it takes 5-9 quanta to produce a measurable retinal response.
I would say 13.5 at 50% detectability under good dark skies, not in the city.
The optimum time constant of the retina is around 100ms. Longer "integrations" dont help much because of temporal summation (Bloch's Law). You can try to wait for a rare string of photon hits, but those will be infrequent. When it happens, the object may appear briefly but then vanish again for a much longer period. In a realistic star field, it will be very difficult to positively identify a faint object below your limit if seeing it just 5% of the time... Observations made like this should be highly suspect.
Certainly, even if one makes a dubious positive observation at a 5% rate or less, its accuracy would be much lower than the normal +/-0.1 for visual.
Mike Linnolt
>> The studies used a 60% detection rate as the threshold of detectability.
QED. You're basically quoting the venerable lab stuff that was done 50+ years ago by Blackwell. It's still good, but needs to be put in the astro-viewing context. Roger Clark and Brad Schaefer have done a lot of work in this area that you should read. Try these for starters:
Brad Schaefer 1989, "How faint can you see?", Sky & Telescope, volume 77,
page 332 (March 1989).
Brad Schaefer 1989, "Your telescope's limiting magnitude", Sky & Telescope,
volume 78, page 522 (November 1989).
Brad Schaefer 1990, "Telescopic limiting magnitudes", Publ. Astron. Soc.
Pacific, volume 102, page 212.
Roger Clark 1994, "How faint can you see?", Sky & Telescope, volume 87, part
4, page 106 (April 1994).
Roger Clark 1990, "Visual Astronomy of the Deep Sky", Cambridge University
Press
Once you get to Roger's book, which is out-of-print and maybe hard
to find in libraries, skip to Mel Bartels Web site:
http://www.efn.org/~mbartels/aa/visual.html
...where you can find excellent discussion about visual thresholds and so forth, and where you can find out the errors Roger made in his book (which he admits to). This page contains Roger's threshold vs detection- probability table from the 1994 S&T article. The 50 percent detection limit for 10cm (4-inches) aperture is indeed 13.7, as Mike quoted. My 14.5-to-15 figure also indeed corresponds to 10 percent by his table.
There's a link at Bartels' site to the very long exchange about this problem between he, Nils Olof Carlin, Harald Lang, and Roger Clark. The math gets very serious in that one. Likewise there's a link to my not-so-long description of how-dark-is-dark re best observing sites. Not included are my brief notes about the Heber Curtis mag limit tests from Lick in the early 1900s nor about Dave Nash's double-blind test at the Nebraska Star Party some years ago. Both the latter indicate reasonable limits of V=8.2 or so for typical eyes (Nash says his vision is not particularly sharp).
If you look at the papers cited in my sky-brightness article, the ones from the 1950s cited near the beginning should convince you that the range of retinal sensitivity is very small among normal individuals. This and the pupil-diameter frankly have rather little to do with visual thresholds, instead physio- and psychological factors weigh heavily. Basically, the experienced old observers with 4-5mm pupils see just as faint as younger folks with 7-8mm pupils. And of course telescopically pupil size doesn't enter into it at all (you want to use exit pupils of 1mm or smaller).
I agree that the photographic V sequences around the active galaxies could be problematic (the ones from Asiago that were commonly used have large scatter and scale errors). Also I have trouble with quoting magnitudes for variable objects, when you don't actually have reliable contemporaneous V-band photometry. It is much better to use fields with stable ordinary stars. The one produced by Arne Henden around M57 that we published in the September 2001 issue of Sky & Telescope (page 102) is widely used by northern deep-sky observers, but there are plenty of others all over the sky. (I can supply some if you want to compare with V-based AAVSO charts.)
\Brian
My experience was in Kyoto light-polluted sky. Magnitude 13.5 was relatively easily achieved.
This is one of illustrative examples. Even before the CCD era, we preferrably used V-magnitude sequences, which are presently proven to be correct at least to the accuracy of measuring the sequences. Well before the AAVSO adopted correct V sequences, we had correct V sequences for many variable stars. The late Prof. Huruhata was pioneering in determining these V magnitudes.
There was a proposed method, at least among us, to record (or remember) the number of positive photon (packet) detection events at the variable and comparison star within certain time, and regard the difference just as Pogson's step value, or use them for interpolation method. From this description of the proposed method, it may have been possible that observers actually recognized the time fraction of postive detections. If the expected location of the variable is more frequently detected than the background, wouldn't it be reasonable to positively record the detection? (We are naturally, perhaps unknowingly, applying the same technique to CCD photometry). Yes, these "observations" should have been incorrect to a certain statistical limit, but they more exactly decribe what was recognized, rather than completely discarding infrequent detections.
Regards, Taichi Kato(vsnet-chat 6017)
Not all visual observers are in persuit of 0.1 mag accuracy. Some people are in persuit of 0.01 mag, and others are satisfied with 1 mag accuracy.
By the way, what time bins should we adopt to calculate the entire observing time? (Just because I don't have a correct photon number V-mag conversions on the retina) If you refer to 100ms time-constant for the time bins, 100s corresponds to 1000 bins. Then you can expect 50 detections for a 5% rate. The 1-sigma statistical error of 50 detections is 7 = sqrt(50), indicating that the relative error is 7/50, corresponding to ~0.15 mag. For 1% detections, the error becomes ~0.3 mag, wouldn't it be reasonably small?? If this estimate is true, the required observing time is extremely reasonable for actual visual observation. [As the first approximation, I neglected contributions from the sky background, but would be easily estimated in the same way].
Regards, Taichi Kato(vsnet-chat 6018)
Well, I really have doubts about these tests. Personally, I cant seem to do much better than about 6.8 from Mauna Kea, and I think my sensitivity is pretty good even though my acuity is about 20/30, which is probably the limiting factor. But, I can estimate down to about 16.3 with my 37cm under ideal conditions, since I can then focus precisely, which is right at my 50% threshold as I calculated, so I feel pretty good about this. Most observers I personally met are about that same level. It seems to me some kind of bias is going on in selecting particularly sensitive individuals for these tests, or they are not being 100% honest?
This seems odd. One of the key factors in naked eye, and it is in the formula I used to derive it as well, is the aperture of the eye. The difference between 4.5mm and 7.5mm is 1.1 magnitudes. But there may be some compensatory effect going on with the older eyes, that is as the pupil size decreases slowly, the retina develops a lower throshold of signal detection? Dont know if anyone has studied this in detail.
Mike Linnolt
[here are my two notes with results about naked-eye magnitude limits, which have posted around the Net for about as long as there's been the Web. Note that these results are entirely consistent with the limit Mike Linnolt gave, but simply apply to lower detection probabilties. They are also consistent with other personal anecdotal experience. For instance, several times at the Texas Star Party, I would get different folks oriented with the sequence in eastern Coma mentioned below, and giving them general directions and not saying anything about magnitudes, have them try to spot progressively fainter stars. Even the relatively inexperienced observers, people you wouldn't think of as being hot-shot deep-sky observers, typically start having problems only once you got close to V=8.0. Similarly, observing the same region very casually at a dark site in southeastern Arizona, a friend pointed out a star I hadn't mentioned---one he didn't know the location of and certainly didn't know the magnitude of, but which I did: V=8.1. It's a star I know the location of, but have never been able to see. Anyway, on to Dave Nash and Heber Curtis... ]
In re naked-eye magnitude limits, here is a post I made to the sci.astro.amateur newsgroup several years ago. At that time, the Hipparcos/Tycho photometry had not been published, so the observer not only did not know where the stars were but also could not have known their correct V magnitudes, since they had not been measured, and traditional astrometric catalogues contained values up to 0.5 mag. in error.
A couple of months ago, in the s.a.a. thread of discussion comparing the merits of sky quality and darkness of the Texas Star Party versus the Nebraska Star Party, Dave Nash claimed to have seen some mag. 8 stars from NSP last August. The test was "blind" in the sense that he made a sketch of a small area of the sky without looking at an atlas to select stars. (As will be seen, however, Dave is far from being blind.) The region is near the head of Draco, the asterism sometimes called the "lozenge". Upon comparing with the Tirion "Sky Atlas 2000", he was surprised to find that the most difficult stars were marked with the smallest symbols on the chart, corresponding to roughly mag. 8.
At my request, Dave supplied IDs for the specific stars involved. Only the brightest star involved had any reliable published photometry, so I was curious to find out just how bright these stars really were. I promised to observe them photoelectrically at the first opportunity. I was able to do so about 3 o'clock this morning, and the results are summarized below.
For the record, I used the Lowell 53cm photometric telescope, Stromgren b and y filters, and a 29" diaphragm. I observed Dave's stars together with nine primary and secondary Stromgren standards, whose colors extended beyond the range of colors of Dave's stars. The y filter observations are transformed to standard Johnson V magnitudes, as is usual in this sort of work. The Stromgren y filter has the same central wavelength as a V filter, but is only ~200A wide, instead of ~1000A wide. For what it's worth, my several hundred observations of Landolt equatorial standards show that I match his V system systematically to within a couple thousandths of a magnitude over the color range -0.28 < B-V < 1.75. As a further historical aside, the original primary standards for the UBV system were measured on the same 53cm telescope in the mid-1950s by Harold Johnson and Daniel Harris. This morning the rms errors of the linear fits to V magnitude and b-y color were +/-0.009 and 0.008 mag., respectively. I would have preferred to use more standards, but these nine were entirely adequate for the purpose at hand.
During the course of a general survey of mag. 6-8 stars, I had previously measured the two brighter stars three and two times each, respectively. This morning's results agree with those observations well within their mutual errors, so I am confident that the single observations of the fainter stars are reliable to within about 0.015 mag. or better.
Name RA (2000) Dec V b-y spec SAO HD BD
HD 160520* 17 37 14 +55 44.5 7.027 0.710 K0 7.2(GC) 7.18 7.4
.006 .003
HD 162131 17 46 30 +53 34.7 7.609 0.088 A2 7.5(AGK1) 7.34 7.5
.005 .001
HD 163010 17 50 31 +57 26.6 8.01 0.01 B9 7.5(AGK1) 7.9 7.7
HD 161353 17 42 13 +52 03.4 8.06 0.58 K0 7.8(AGK1) 8.1 7.9
HD 161179 17 41 23 +51 28.3 8.15 0.77 K2 8.0(AGK1) 8.1 7.9
* for HD 160520, Kornilov et al. (1991) give: V = 7.050, B-V = 1.158, from
four observations.
The table lists the stars along with 0'.1-precision positions. The new
magnitudes and colors come next. For the two multiply-observed stars, I give
the rms scatter of the data on the second line of each entry. For the fainter
three stars, I give the results to just two decimals. The spectral types are
listed directly from the HD catalogue, which is the only source of types for
these particular stars. My b-y colors combined with the spectral types show
that the sample consists of two early-A type stars (probably dwarfs) and three
garden-variety K-giants.
The final three columns are "visual" magnitudes from three sources: the SAO star catalogue, the HD catalogue, and the BD. The original source for the SAO magnitudes is given in each case. As you can see, the magnitudes in the early catalogues aren't _so_ bad, but nevertheless usually report the stars to be brighter than they really are, and scatter around "truth" by up to half a magnitude.
In summary, Dave saw three mag. 8 stars from Merritt Reservoir, which shows not only that NSP has a great site, but that Dave is a skilled visual observer and also probably has acute (sharp) vision. He probably can see similarly faint from similarly-good sites, such as TSP, or other high and dry dark places. I've been observing from "perfect" sites in the desert Southwest US and Chile for twenty years and haven't been able to go fainter than about V=7.8, so my hat's off to ya, pal!
[posted to the 'amastro' list]
This second note deals with Heber D. Curtis' observations of some faint stars from Lick at the turn of the (last) Century. In this case, the stars were selected ahead of time, and a large black mask attached to a telescope (the 12-inch refractor at Lick). The mask contained a hole through which Curtis viewed from the observing floor, and swept across the star location in search of it. This isn't a good test of finding faint stars at unkown locations, but as with the Nash test the star magnitudes were very poorly determined, so he could not know how faint he was seeing on the now standard scale.
For some years Brent Archinal and I have wondered about the naked-eye limiting magnitudes determined by Heber Cutis at Lick Observatory at the turn of the Century. He claimed to see down below mag. 8, but we wondered what the modern standard V magnitudes of those stars were. I've dug out the relevant publication (1901 Lick Obs. Bulletin, 2, 67), and have looked up the stars (fortunately a short and well-identified list). The names are given below along with V and B-V from the Hipparcos/Tycho catalogues, and the magnitude Curtis gave for the same stars. I use the H/T data for convenience; they ought to be reliable to within a couple percent, and comparison with data collected in SIMBAD from ordinary sources suggest these numbers are fine for the present purpose. Curtis's comments are also shown for most of the stars.
As can be seen, the faintest star he saw reliably is V = 8.44, and two others below V=8.0 and one at 7.98 were seen as well. As might be expected, he did rather better overall on the near-overhead field around T UMa than on the T Vir field, several degrees south of the Equator (Lick is at about latitude +37.4). Just that alone tells you a lot about observing other than close to the meridian.
These in essence reproduce the results of Dave Nash at the Nebraska Star Party several years ago, when he did a double-blind test using stars in the head of Draco, and saw down to about V=8.2. On winter and spring nights at our Anderson Mesa site, I use a star in Coma at V=7.8 as a transparency test, and usually see it.
group near T Vir
Star V B-V Curtis remarks
HD 106384 6.56 0.28 6.52 [FG Vir, sl var]
HD 107830 7.19 0.43 7.20 seen easily
HD 105654 7.23 0.40 7.31 seen quite easily
HD 106515 7.34 0.82 7.42 seen easily
HD 106622 7.47 0.93 8.1 seen without difficulty on last two nights
HD 106579 8.44 0.44 8.3 seen with considerable difficulty; perhaps
one-fifth of trials failed
group near T UMa
HD 110275 7.98 0.24 8.1 seen; one or two failures
HD 110408 8.08 0.53 8.2 seen
HD 110104 8.21 1.12 8.3 seen with difficulty
BD+60 1415 8.98 1.35 8.5 glimpsed at intervals; very doubtful
(vsnet-chat 6021)
That's because you're at 13K feet on MK. Unless you're using supplemental oxygen, you're going to lose a magnitude or two. Personally, the sky atop MK doesn't look much different to me than a good dark sky at sea level. The O2 shortage will do that.
If everyone's eyes could be calibrated to a formula like that we wouldn't be having all these discussions about visual observing! :->
The experience level of the observer is a major factor. The last two summers I've worked with *totally* inexperienced observers. Some of them have difficulty picking out a 10th mag star in an 8" scope - at first. Pretty soon it's easy, second nature, and they can work fainter and fainter. Even an experienced observer has to keep in practice - the best planetary observer I ever knew used to say, "The more you look, the more you see".
Still, I do wonder a bit about 16th mag obs with a 4" scope. As someone else says, maybe the comps used were photographic magnitudes, and the stars were brighter visually. 14.5 - 15 I don't think I'd question, using a high-quality refractor under a dark sky.
Jim B.
Yes, it seems some observers on some occaisons may be seeing stars in the eighth magnitude or less. There is some room for variation in individual perceptions, even though studies have shown the variation in retinal sensitivity is small. Pupil size, exceptional acuity and technique may play more of a role for such gifted individuals.
But, as far as taking scientifically useful data for variable stars goes, what is the point of these extraordinary cases? The vast majority of observers who will submit their observations to VSNET or AAVSO will have a NELM around 7.6 at 50% detection. I dont think it is a good idea to suggest observers should strive to make estimates at 5% detection just to go deeper.
I have done quite a bit of faint estimations. While sometimes I do detect stars at 5-10%, they seem to "pop" into view infrequently, I do not believe an accurate estimate can be made. In fact, at this low detection rate, I commonly see a fainter comp star appear brighter than a brighter comp star! You just cannot make a reliable comparison based on these "pops" or flashes of view you get. The error on the estimate is probably going to be worse than 0.5 mag at these low detection rates. Why corrupt the database with such poor values?
I feel strongly that estimates submitted for archiving should be made at no less than 50% detection. Trying to go deeper is fine for testing your scope, sky or techniques, or friendly competition at a star party, but it has no place in serious data gathering.
Mike Linnolt
Although it will not be very meaningful to suggest naked-eye observers to strive for this, it will be meaningful to observers who are working with the largest possible instrument.
If you feel insufficient statistics, you probably need to increase the watching time to make a better time-average. An instantanenous watch at such faint stars can be misleading.
People have been inventing a method (although it is difficult to explain by words) to more meaningfully treat with these low frequency detections. As I showed yesterday, the statitical limiting accuracy at this detection rate is not so poor as expected. Such a method is comparable to an effort by Sebastian to get accurate V estimates with human eyes. Someone would not want to believe an accurate estimate can be made in Sebastian's method, too. But the reality is not. A slight difference between Sebastian's and Hasegawa-san's methods is that the latter apparently needs more mental concentration. Hasegawa-san sometimes expressed an extreme degree of exhaustion.
> The error on the estimate is probably > going to be worse than 0.5 mag at these low detection rates. Why corrupt > the database with such poor values?Should we not report observations whose errors may exceed 0.5 mag? There seem to be a comparable or larger scatter at least in some objects.
Regards, Taichi Kato
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