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Estimating Lunar Phase Requirements (1Mar94)
(from CTIO, NOAO Newsletter No. 37, 1 March 1994)

When you wrote your telescope time request, did you carefully work out
the lunar phase requirement? Or did you think to yourself, "I'm working
on galaxies, I must need dark time!" and then put down "5" for your
"number of days from new moon." One of the reasons why you did things
in this way, as most of us do, was that there is no better way easily
available.  This brief note proposes to help you in this regard.

Some convenient data on Tololo sky brightness as a function of lunar
phase can be found in another Newsletter article by Alistair Walker
(1987) Although Alistair insists that these data should not be
over-interpreted, they are in fact consistent at the 20% level with
data on lunar disk brightness as a function of phase (e.g. Russell
1916, Minnaert 1961).  For convenience the Walker (1987) numbers are
reproduced below:

                            Table I
         Sky Brightness as a Function of Lunar Phase

Days from          Sky Brightness (mag/arcsec2)
New Moon         U       B        V        R       I
    0          22.0    22.7     21.8     20.9    19.9
    3          21.5    22.4     21.7     20.8    19.9
    7          19.9    21.6     21.4     20.6    19.7
   10          18.5    20.7     20.7     20.3    19.5
   14          17.0    19.5     20.0     19.9    19.2

What do these show? First of all, the contrast between full moon and no
moon is greatest at U and least at I.  At U, the ratio is a factor of
100, while at I, it is a factor of 2.  Extrapolation to the infrared
shows that even at the J band the full moon contributes no more than a
couple of percent to the night sky brightness.  Furthermore, because
the moon brightness peaks so sharply around full moon, the sky
brightness is very much less only a few days away.

Let's take as a criterion for desirable sky brightness that the moon
degrade your signal to noise by 10% - that is, that it increase total
photon counts by 20%.  Note that sky brightness varies during the
night, seasonally, and even with solar cycle, and just at random by
factors substantially greater than this.  Consider several different
cases:

                           CCD Imaging

For routine faint-object photometry, the relevant area of sky is
roughly the area under the core of the PSF - which one can
conservatively take as 1 square arcsecond.  Using the numbers from the
table, one can calculate a variety of examples:

1a)  Faint stars, BVRI = 24.  At these magnitudes the star itself
     contributes relatively little to the total brightness, so one need
     only ask at what point the night sky brightness is increased 20% by
     the moon.  This happens first at the shortest wavelength - B in this
     example. Walker's numbers indicate that even at three days from new
     moon the effect should be significant (defined as 20%), but a
     comparison with lunar disk observations suggests that one can go
     three days safely and probably four days - especially if one recalls
     that at that phase the moon is not present most of the night.  Also,
     if you are doing BVRI, only the B is affected - so your actual loss
     of efficiency is more like 2% than 20%.

     At six days from new moon, the B sky brightness is roughly double,
     and that at V ~20% higher.  Your overall efficiency, with the moon
     around less than half the night, is reduced by about 15% for a program
     involving equal dark BVRI exposures.

1b)  Not so faint stars.  At BVRI = 22, the star is already significantly
     brighter than sky at B, and roughly equal to sky at V.  Thus the
     effect of the moon is substantially reduced, and one can go about
     six days from new moon before the total B counts increase by 20%.
     At BVRI = 20, one can safely work past quarter moon.  If one is also
     doing U = 20, one is still restricted to times before quarter moon.
     Again, this is taking the worst-case filter; a multi-filter program
     can usually go to lunar phase one or two days brighter without serious
     loss of efficiency.

1c)  Aperture photometry.  If one's program is of isolated objects, then
     PSF fitting is not appropriate, and it is necessary to repeat the
     calculation for a larger aperture (synthesized) on the sky.  Use of
     a 10 arcsec aperture is equivalent to shifting the calculations above
     by 4.7 magnitudes.  (A 5 arcsec aperture shifts them by 3.2 mag.)
     This would indicate that aperture photometry at UBVRI = 15 can
     be done to roughly quarter moon.

1d)  Galaxy photometry.  This is really just another form of aperture
     photometry, but the easiest way to visualize it is recognizing that
     for most programs, the average surface brightness within the
     measurement aperture is fainter than sky - hence the lunar phase
     requirements are similar to those for example 1a.

In summary, then, for most imaging programs gray or dark time is
necessary.  But really prime dark time is needed for only the most
demanding cases.

                          CCD Spectroscopy

For visible-wavelength spectroscopy, the appropriate sky area is
normally the slit width times the height of the extraction window.
This depends on the instrumental set-up and the seeing, but is usually
a few square arcseconds.  If the slit is sufficiently narrow, one needs
to correct for light loss from the object.  Another consideration is
that the V and R sky brightness values are due in large part to a small
number of airglow lines, so that the situation in between these lines
is in reality much more like that at B for spectroscopy.  Here are some
examples:

2a)  CS/CCD observations of V = 20.  Assume a slit width of 1.5 arcsec
     and window length of 3 arcsec.  Then carry out the calculation at
     B = 20.  The dark sky is contributing roughly 30% of the total counts.
     When one goes through the numbers, the total counts increase by 20%
     about six days from new moon.

     For V = 18 one can work slightly past quarter moon.

     For work on the 1.5-m the slit dimensions are larger, and the
     magnitudes given above need to be made brighter by perhaps 1.5 mag.

2b)  Echelle observations of V = 18.  Echelle slits tend to be narrower,
     but given that there may be loss of light from the object, the situation
     is not much different than for the Cass spectrograph at the same
     magnitude level. (Obviously, exposure times are longer - but the
     proportional effect of moonlight is the same.)

2c)  Echelle observations of U = 16.  If you weren't working in the
     ultraviolet, you could probably work right through full moon - but if
     you need to work at U you have to work at quarter moon or darker.
     The limiting magnitude for work at full moon at U is roughly 13.5.
     Note, though, that you still can't work very close to the moon, and
     if this is a potential problem you should specify dates when the moon
     is unacceptably close to your main object or objects.

2d)  Argus observations of V = 20.  The area under an Argus fiber is
     somewhat less than that used for the spectrograph calculations; light
     loss missing the fiber may or may not be greater.  (Light loss in the
     fiber doesn't count, since sky photons are also lost in the same
     proportion.) To the accuracy of these calculations, the differences
     aren't significant; the conclusions are that for V = 20 (if you can
     find the objects) you need darker than quarter moon, for V = 18
     quarter moon is acceptable, and for V = 16 even full moon is OK.
     (Conditions are undoubtedly somewhat more restrictive if you are
     working down at the blue limit of Argus.)

                            IR Observing

As noted above, the moon has no significant effect on the observations
themselves.  But it is often necessary to acquire the program objects
visually.  This is normally done in the red with a CCD TV.  Since most
of the telescope time is not spent on acquisition (one hopes), a
greater than 10% loss of sensitivity is acceptable.  If one sets this
to be a factor of two increase in the R counts, then for extremely
faint objects one cannot work within three days of full moon; once the
objects get brighter than about R = 20 even full moon should be
acceptable.

Of course, these data apply only when the moon is relatively distant
from the object; when the moon is 30d away (and especially if moonlight
reaches the telescope optics!) things are much worse.  If this is
potentially a problem, work out the dates when the moon will be within
30d of your main program objects and indicate those on the proposal as
dates to avoid, for this reason.

                           Summary Table

It is suggested that you use this to help you in preparing your
proposal - and if you feel you need more restrictive lunar phase than
given here, you should provide a detailed explanation of the reasons
why.  Note that there are undoubtedly many cases not covered by the
table, but it shouldn't be too hard to work out the relevant
conditions.  It is important to realize that these are fairly
conservative numbers (10% loss of signal to noise in the bluest filter)
and it is thus practical to schedule many proposals - especially those
involving many nights - to include somewhat brighter time.

                             Table II
                   Acceptable Days from New Moon

                        BVRI         UBVRI        4-m      4-m
                        Phot.        Phot.         UV      Vis.
Magnitude               PSF fit      PSF fit      Spect.   Spect.
   14                    14           14            13        14
   16                    14           12             9        14
   18                    11            8             6         8
   20                     8            6             5         6
   22                     6            5             4         5
   24                     5            4             4         5
                                                                                                             References

1) Minnaert, M. 1961 in Planets and Satellites, ed. G.P. Kuiper and B.M.
   Middlehurst (U. of Chicago: Chicago) 213.
2) Russell, H.N. 1916 Ap. J., 43, 103.
3) Walker, A. 1987 NOAO Newsletter, 10, 16.

Jay Elias

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