View source for BRC Optical Ground-Based Follow-Up

=Big Picture=

Optical data can be incredibly helpful in weeding out garbage from our YSO selection. Remember that Spitzer is phenomenally efficient, and with just a few seconds can reach objects at the edge of the Universe. Recall the discussion in the CG4 paper, and just at a gut level how much nicer the SEDs look if we have optical data too. Recall the stuff on the [[Resolution]] page (specifically example 4) and how much high spatial resolution matters. High spatial resolution optical imaging may allow us to determine that some of these objects are actually resolved galaxies. Once we add optical photometry to the SEDs, the shape of the SEDs may allow us to determine that some of these objects are actually AGN and not YSOs.

The Las Cumbres (LCOGT) Faulkes Telescope on Haleakala (specifially JD Armstrong) has kindly offered to help us get optical ground-based follow-up observations. We need to plan coherently (professionally!) for these observations to ensure we get the best quality data in the least amount of time possible. ("Ooops we screwed up" will not generally get you additional telescope time.)

=Planning Observations=

In order to plan for ground-based follow-up of our targets, we have many things to consider. These are the same issues, in more or less the same order, that I would consider before writing a proposal to any telescope for anything; this isn't fabricated just for you!
*'''Are the objects visible''' (ever) from the observatory(ies) to which we have access? 
**Ex 1: the CG4 object from last year is a Southern Hemisphere object, so unless you have access to a Southern Hemisphere telescope, that's not possible. 
**Ex 2: the BRC objects are Northern Hemisphere (both of them). When are they visible from the LCOGT telescope in Hawaii? See airmasses calculation below to help in answering that question.
*What '''filters''' are available at the telescope? And, '''which are best suited''' to the science we want to accomplish?
**JD says that they have currently: Sloan u,g,r,i, Halpha, and PannStarrs z,y. 
**Any constraints on the Wien side of the SED will help us, so anything optical is scientifically helpful.
**I have no experience with z and y. 
**While young stars are often bright in Halpha (and you know that from Ogura's papers), pretty much everything is fainter in narrow band filters (such as Halpha) than broad-band filters (such as the Sloan filters). So, anything will take much longer to detect to sufficient signal-to-noise in Halpha than in the other filters.  It will take less time for us to get measurements in the broadband filters.
**I have some experience with the Sloan filters, so I know (for example) how to convert them into the right units for addition to the SEDs. Recall the shape of a stellar SED. Assuming all of our targets are really stars, will they be brighter at u or i?
**JD says that he is willing to do two filters for us. Which two would you do? I vote for r and i. Do you understand why?
*What is the '''spatial extent''' of '''sources on the sky''' that we care about?
**We don't have a final list of sources yet. But recall that a single IRAC field of view is 5 arcminutes on a side, and the region that we care most about (with four IRAC bands) is basically a single IRAC field of view. There are serendipitously obtained patches of just 2 bands offset from the main field; each of those patches is also basically a single IRAC field of view, so basically also 5 arcmin on a side. The centers of the serendipitously obtained fields are both a little more than 5 arcminutes offset from the center of the main field.
*What is the '''spatial extent''' of a single pointing of the ground-based telescope?
**In this case, 9 arcmin. So with a single pointing, we can obtain essentially the entire region with 4-band IRAC coverage in one of our fields, even if the fields are rotated nearly 45 degrees with respect to each other. So, great! No need to tile a large region with the LCOGT telescope.
*What is the '''surface density''' of the sources in our field of view, and what is the '''spatial resolution''' of the optical telescope?
**Recall the [[Resolution]] discussion to understand why this matters.
**The spatial resolution of IRAC is ~1.2-1.5 arcsec. There may be sources spaced closer together than that, but we wouldn't be able to tell based on the IRAC data.
**The spatial resolution of the LCOGT telescope is 1.1 arcsec, and is seeing-limited. So, if we have a bad weather night, then the resolution will be worse, but seems to commonly be comparable to IRAC. So we're good here too.
*What are the '''total integration times''' we need?
**JD says "magnitude 19 is easily within reach."
**What are the brightnesses we expect from our targets? Ah, this is the meat of it! More below.
*How many '''dithers''' will be needed?
**Typically, one does at least 3 dithers in order to clean out cosmic rays, but if the exposures are very short, just one can be sufficient. It depends on how much our total integration time works out to be.
*What kinds of '''calibrators''' do we need?
**We need to find (stable) objects of known brightnesses in r and i bands (preferably comparable brightnesses to our targets), at a comparable airmass to our targets, and plan to observe them (request time to observe them) before and after our science targets.
**JD says that there are some Faulkes archives of standards from which we can pick; I hope he can help with this.
*'''Who''' will actually do the observing? (and from where?)
**No one is going to Hawaii!
**JD says that both queue and internet-based remote observing is possible. TBD.
*In '''what format''' will we get the data back? On what '''timescale'''?
**The images will arrive back to us in FITS format, flatfielded and bias subtracted but nothing else -- no coordinates, not calibrated, nothing else. We will need to take care of all of that in some fashion.
**Timescale? Presumably immediately, or within a few days of the observations.
*Who will '''process''' the data (and how)?
**You guys will have to lead this!
**My thought was to sidestep the coordinates issue, use the IRAC images in essence as finding charts (though 2MASS might be better choices) to find the subset of sources in which we are interested (surviving best YSO candidates and calibrators in those fields), and have you guys do APT photometry on those targets. Once we have measurements in total counts (or counts/sec), we can solve for extinction and color corrections and calibrate the measured photometry (as opposed to calibrating the images themselves).
*What will we do with the data when we have it?
**See the CG4 paper for examples!


==Hourly almanac (airmasses) for our targets==

calculated for Hawaii.

 *** Hourly airmass for brc27 ***
 Epoch 2000.00: RA   7 04 00.0, dec -11 22 55
 Epoch 2011.87: RA   7 04 33.4, dec -11 24 01
 At midnight: UT date 2011 Nov 16, Moon 0.72 illum,  31 degr from obj
  Local      UT      LMST      HA     secz   par.angl. SunAlt MoonAlt 
  18 00     4 00    21 18    -9 47   (down)   -71.1     -4.8    ... 
  19 00     5 00    22 18    -8 47   (down)   -73.4     ...     ... 
  20 00     6 00    23 18    -7 47   (down)   -73.5     ...     ... 
  21 00     7 00     0 18    -6 46   (down)   -72.2     ...     ... 
  22 00     8 00     1 18    -5 46  (v.low)   -69.9     ...     -1.6
  23 00     9 00     2 18    -4 46    4.439   -66.3     ...     11.5
   0 00    10 00     3 19    -3 46    2.261   -61.0     ...     24.8
   1 00    11 00     4 19    -2 46    1.602   -52.8     ...     38.4
   2 00    12 00     5 19    -1 46    1.318   -40.0     ...     52.1
   3 00    13 00     6 19    -0 45    1.195   -19.8     ...     65.9
   4 00    14 00     7 19     0 15    1.172     6.7     ...     79.6
   5 00    15 00     8 19     1 15    1.240    30.7     ...     84.8
   6 00    16 00     9 20     2 15    1.430    47.0     -7.7    71.6
 At midnight: UT date 2011 Dec 16, Moon 0.67 illum,  51 degr from obj
  Local      UT      LMST      HA     secz   par.angl. SunAlt MoonAlt
  18 00     4 00    23 16    -7 49   (down)   -73.5     -4.0    ... 
  19 00     5 00     0 16    -6 48   (down)   -72.3    -17.1    ... 
  20 00     6 00     1 16    -5 48  (v.low)   -70.0     ...     ... 
  21 00     7 00     2 16    -4 48    4.599   -66.5     ...     ... 
  22 00     8 00     3 17    -3 48    2.297   -61.2     ...     ... 
  23 00     9 00     4 17    -2 48    1.616   -53.2     ...      2.1
   0 00    10 00     5 17    -1 48    1.324   -40.5     ...     15.7
   1 00    11 00     6 17    -0 47    1.197   -20.6     ...     29.4
   2 00    12 00     7 17     0 13    1.171     5.7     ...     42.9
   3 00    13 00     8 17     1 13    1.236    30.0     ...     56.0
   4 00    14 00     9 18     2 13    1.420    46.6     ...     67.7
   5 00    15 00    10 18     3 13    1.830    57.0     ...     74.2
   6 00    16 00    11 18     4 13    2.884    63.7    -11.5    69.5


 *** Hourly airmass for brc34 ***
 Epoch 2000.00: RA  21 33 30.0, dec +58 04 32
 Epoch 2011.62: RA  21 33 50.9, dec +58 07 39
 At midnight: UT date 2011 Aug 16, Moon 0.93 illum,  61 degr from obj
  Local      UT      LMST      HA     secz   par.angl. SunAlt MoonAlt
  19 00     5 00    16 15    -5 19    2.653   -87.8     -3.0    ... 
  20 00     6 00    17 15    -4 19    1.997  -100.9    -16.4    -1.4
  21 00     7 00    18 15    -3 18    1.639  -115.3     ...     12.4
  22 00     8 00    19 16    -2 18    1.434  -131.9     ...     26.2
  23 00     9 00    20 16    -1 18    1.322  -151.3     ...     39.8
   0 00    10 00    21 16    -0 18    1.277  -173.2     ...     52.9
   1 00    11 00    22 16     0 42    1.288   164.1     ...     64.6
   2 00    12 00    23 16     1 42    1.359   143.1     ...     71.8
   3 00    13 00     0 16     2 43    1.504   124.9     ...     69.1
   4 00    14 00     1 17     3 43    1.760   109.2     ...     59.1
   5 00    15 00     2 17     4 43    2.212    95.4    -14.8    46.5
   6 00    16 00     3 17     5 43    3.080    82.7     -1.4    33.2
 At midnight: UT date 2011 Sep 16, Moon 0.86 illum,  66 degr from obj
  Local      UT      LMST      HA     secz   par.angl. SunAlt MoonAlt
  19 00     5 00    18 17    -3 17    1.631  -115.8     -9.2    ... 
  20 00     6 00    19 17    -2 16    1.430  -132.5     ...     ... 
  21 00     7 00    20 18    -1 16    1.320  -151.9     ...      6.6
  22 00     8 00    21 18    -0 16    1.276  -173.9     ...     20.0
  23 00     9 00    22 18     0 44    1.289   163.4     ...     33.6
   0 00    10 00    23 18     1 44    1.362   142.5     ...     47.4
   1 00    11 00     0 18     2 44    1.510   124.3     ...     61.3
   2 00    12 00     1 18     3 45    1.771   108.8     ...     75.2
   3 00    13 00     2 19     4 45    2.232    95.0     ...     87.5
   4 00    14 00     3 19     5 45    3.119    82.3     ...     76.4
   5 00    15 00     4 19     6 45    5.239    70.0    -17.1    62.6
   6 00    16 00     5 19     7 45   14.754    57.7     -3.1    48.8
 At midnight: UT date 2011 Oct 16, Moon 0.84 illum,  79 degr from obj
  Local      UT      LMST      HA     secz   par.angl. SunAlt MoonAlt
  18 00     4 00    19 15    -2 18    1.435  -131.9     -1.2    ... 
  19 00     5 00    20 16    -1 18    1.323  -151.2    -15.2    ... 
  20 00     6 00    21 16    -0 18    1.277  -173.2     ...     ... 
  21 00     7 00    22 16     0 42    1.288   164.2     ...      4.2
  22 00     8 00    23 16     1 42    1.358   143.1     ...     17.1
  23 00     9 00     0 16     2 42    1.503   124.9     ...     30.3
   0 00    10 00     1 16     3 43    1.759   109.3     ...     43.6
   1 00    11 00     2 17     4 43    2.211    95.5     ...     57.2
   2 00    12 00     3 17     5 43    3.076    82.7     ...     70.8
   3 00    13 00     4 17     6 43    5.122    70.4     ...     84.0
   4 00    14 00     5 17     7 43   13.931    58.1     ...     81.2
   5 00    15 00     6 17     8 43   (down)    45.4     ...     67.7
   6 00    16 00     7 17     9 44   (down)    32.1     -4.8    54.1

=Brightness Estimations For Our Targets=

We know some information about our targets, but we need to make some educated guesses and assumptions in order to get some estimates of how bright our targets are likely to be at the optical bandpasses.

We have JHK and IRAC-1 for most if not all of our 'interesting' targets. Of the data we have, these bandpasses are closest to the optical, and least likely to be affected by any excess due to a circumstellar disk.  We need to use this information to get an educated guess as to the distribution of brightnesses we will expect for our targets in the optical.

We have no good and simple way of estimating any extinction (reddening, or Av). So, we will assume no reddening. This is not necessarily a good assumption, but it's all we can do at this time.

Most of our stars will probably end up being late K stars or early M stars. The mass function is such that there are more M stars than K stars, but our brightness limits are such that we probably only reach to early M stars, which cuts off the mass function effect.

Conceptually, the process we need to follow is:
#Take the observed distribution of brightnesses for our 'interesting' targets.
#Assume that they are all really stars, and have minimal or no Av.
#Get an estimate of where the photosphere is based on the NIR.
#Extrapolate a guess at the expected brightness of the photosphere in the optical. 

I can think of two different ways we can do this. One is conceptually harder and easier to implement in Excel ("option 1" below); the other is conceptually easier but harder to implement in Excel ("option 2" below).

==Option 1==

As you know, young stars can have a LOT going on. They have circumstellar disks, reddening, accretion... it is tough to get a really good, solid empirical estimate of what truly plain disk-free young stars actually look like, what colors they really have. There are a few different estimates in the literature, and they are unevenly good, and sometimes even internally inconsistent. My own favorite list kinda falls apart at about M2 (and later). I have copied it below. These are not quite just main sequence colors because these stars have not yet completely settled onto the main sequence, but you could also start from a distribution of main sequence colors if you needed to.

You can use the brightness at just one band (say, J), hope that that band is minimally affected by any of the other things that are going on, assume that all of the stars that we have are about K7, read off the V-J color below for that type, and shift the distribution of J accordingly. How does this change if you assume they are all a different type? Or use a different band to extrapolate to V?

 SpTy    code	Mv    Ic   U-V   V-Ic  U-B   V-R   V-J   V-H   V-K   R-I
 B0   V 1.0   -4.00 -3.74 -1.38 -0.30 -0.31 -0.12 -0.70 -0.31 -0.83 -0.18
 B1   V 1.1   -3.08 -2.86 -1.23 -0.26 -0.31 -0.11 -0.61 -0.31 -0.74 -0.15
 B2   V 1.2   -2.40 -2.21 -1.08 -0.23 -0.31 -0.10 -0.55 -0.31 -0.66 -0.13
 B3   V 1.3   -1.60 -1.44 -0.94 -0.19 -0.31 -0.09 -0.45 -0.31 -0.56 -0.10
 B4   V 1.4   -1.39 -1.26 -0.84 -0.18 -0.31 -0.08 -0.30 -0.31 -0.49 -0.09
 B5   V 1.5   -1.20 -1.10 -0.72 -0.16 -0.31 -0.07 -0.35 -0.31 -0.42 -0.09
 B6   V 1.6   -0.80 -0.71 -0.61 -0.14 -0.31 -0.07 -0.30 -0.31 -0.36 -0.07
 B7   V 1.7   -0.51 -0.43 -0.50 -0.12 -0.31 -0.06 -0.25 -0.31 -0.29 -0.06
 B8   V 1.8   -0.20 -0.05 -0.40 -0.09 -0.31 -0.04 -0.17 -0.31 -0.24 -0.05
 B9   V 1.9    0.27  0.35 -0.17 -0.04 -0.11 -0.03 -0.09 -0.16 -0.13 -0.01
 A0   V 2.0    0.60  0.60  0.00  0.00  0.00 -0.02 -0.01  0.00  0.00  0.02
 A1   V 2.1    1.00  0.98  0.05  0.02  0.02  0.01  0.06  0.06  0.07  0.03
 A2   V 2.2    1.30  1.25  0.10  0.07  0.04  0.03  0.11  0.13  0.14  0.04
 A3   V 2.3    1.50  1.42  0.15  0.11  0.06  0.03  0.18  0.21  0.22  0.05
 A4   V 2.4    1.70  1.59  0.20  0.14  0.08  0.04  0.25  0.28  0.30  0.07
 A5   V 2.5    1.90  1.76  0.24  0.17  0.10  0.09  0.27  0.36  0.38  0.08
 A6   V 2.6    2.05  1.84  0.26  0.20  0.10  0.10  0.31  0.41  0.44  0.10
 A7   V 2.7    2.20  1.93  0.28  0.22  0.09  0.11  0.35  0.47  0.50  0.11
 A8   V 2.8    2.40  2.08  0.30  0.27  0.07  0.13  0.43  0.54  0.57  0.14
 A9   V 2.9    2.55  2.18  0.32  0.33  0.05  0.16  0.50  0.61  0.64  0.16
 F0   V 3.0    2.70  2.28  0.34  0.37  0.03  0.19  0.58  0.67  0.70  0.18
 F1   V 3.1    2.92  2.48  0.36  0.40  0.03  0.22  0.63  0.73  0.76  0.19
 F2   V 3.2    3.15  2.69  0.37  0.43  0.02  0.23  0.68  0.79  0.82  0.20
 F3   V 3.3    3.27  2.79  0.38  0.45  0.01  0.24  0.72  0.87  0.91  0.21
 F4   V 3.4    3.38  2.87  0.39  0.47  0.00  0.25  0.75  0.97  1.01  0.22
 F5   V 3.5    3.50  2.96  0.40  0.50 -0.02  0.26  0.79  1.06  1.10  0.24
 F6   V 3.6    3.67  3.09  0.44  0.53 -0.02  0.28  0.85  1.17  1.21  0.25
 F7   V 3.7    3.83  3.21  0.49  0.56 -0.01  0.30  0.90  1.27  1.32  0.26
 F8   V 3.8    4.00  3.34  0.54  0.59  0.02  0.31  0.96  1.30  1.35  0.28
 F9   V 3.9    4.20  3.51  0.59  0.61  0.04  0.32  0.99  1.33  1.38  0.29
 G0   V 4.0    4.40  3.69  0.64  0.63  0.04  0.33  1.03  1.36  1.41  0.30
 G1   V 4.1    4.55  3.83  0.64  0.65  0.04  0.34  1.08  1.39  1.44  0.31
 G2   V 4.2    4.70  3.97  0.64  0.67  0.04  0.35  1.09  1.41  1.46  0.32
 G3   V 4.3    4.83  4.09  0.71  0.68  0.08  0.35  1.11  1.44  1.49  0.33
 G4   V 4.4    4.97  4.22  0.79  0.69  0.15  0.36  1.15  1.47  1.53  0.34
 G5   V 4.5    5.10  4.34  0.86  0.71  0.20  0.36  1.16  1.52  1.58  0.35
 G6   V 4.6    5.20  4.43  0.90  0.73  0.22  0.37  1.18  1.58  1.64  0.36
 G7   V 4.7    5.38  4.59  0.95  0.75  0.24  0.38  1.22  1.66  1.72  0.37
 G8   V 4.8    5.50  4.69  1.00  0.77  0.27  0.39  1.26  1.69  1.76  0.38
 G9   V 4.9    5.70  4.87  1.13  0.83  0.35  0.44  1.30  1.73  1.80  0.39
 K0   V 5.0    5.90  5.02  1.27  0.88  0.45  0.47  1.41  1.88  1.96  0.41
 K1   V 5.1    6.10  5.17  1.44  0.93  0.59  0.50  1.53  2.00  2.09  0.43
 K2   V 5.2    6.40  5.47  1.52  0.95  0.63  0.53  1.60  2.13  2.22  0.45
 K3   V 5.3    6.60  5.54  1.80  1.06  0.83  0.57  1.79  2.33  2.42  0.49
 K4   V 5.4    7.00  5.85  2.01  1.15  0.94  0.62  1.91  2.53  2.63  0.53
 K5   V 5.5    7.40  6.08  2.22  1.32  1.06  0.70  2.13  2.74  2.85  0.62
 K6   V 5.6    7.75  6.37  2.43  1.38  1.16  0.73  2.24  2.88  3.00  0.66
 K7   V 5.7    8.10  6.65  2.54  1.45  1.18  0.76  2.52  3.03  3.16  0.69
 K8   V 5.8    8.55  6.85  2.64  1.70  1.20  0.86  2.66  3.18  3.32  0.84
 M0   V 6.0    8.86  7.06  2.65  1.80  1.22  0.89  2.80  3.48  3.65  0.91
 M0.5 V 6.05   9.14  7.26  2.66  1.88  1.24  0.92  2.91  3.58  3.76  0.96
 M1   V 6.1    9.41  7.45  2.67  1.96  1.26  0.94  3.02  3.67  3.87  1.02
 M1.5 V 6.15   9.79  7.74  2.68  2.05  1.27  0.97  3.14  3.79  3.99  1.08
 M2   V 6.2   10.16  8.00  2.70  2.16  1.27  1.00  3.28  3.91  4.11  1.16
 M2.5 V 6.25  10.70  8.39  2.73  2.31  1.27  1.05  3.53  4.16  4.38  1.26
 M3   V 6.3   11.18  8.71  2.75  2.47  1.28  1.10  3.84  4.40  4.65  1.37
 M3.5 V 6.35  12.00  9.34  2.77  2.66  1.28  1.16  4.08  4.69  4.95  1.50
 M4   V 6.4   12.71  9.85  2.89  2.86  1.29  1.23  4.39  4.98  5.26  1.63
 M4.5 V 6.45  13.20 10.18  2.98  3.02  1.27  1.36  4.78  5.39  5.69  1.66
 M5   V 6.5   14.69 11.30  3.07  3.39  1.28  1.48  5.22  5.80  6.12  1.91
 M5.5 V 6.55  15.75 11.99  3.10  3.76  1.29  1.70  5.78  6.37  6.71  2.06
 M6   V 6.6   16.49 12.48  3.35  4.01  1.30  1.80  6.26  6.93  7.30  2.17
 M6.5 V 6.65  17.14 12.82  3.48  4.32  1.32  2.03  6.63  6.93  7.30  2.30
 M7   V 6.7   17.76 13.22  3.60  4.54  1.33  2.15  7.03  6.93  7.30  2.41
 M8   V 6.8   18.26 13.60  3.85  4.66  1.33  2.15  7.61  6.93  7.30  2.51
 M8.5 V 6.85  18.13 13.56  3.98  4.67  1.33  2.15  7.63  6.93  7.30  2.52
 M9   V 6.9   19.29 14.93  4.10  4.68  1.33  2.15  7.65  6.93  7.30  2.53
 SpTy    code	Mv    Ic   U-V   V-Ic  U-B    V-R   V-J   V-H   V-K   R-I

You should look at the distribution of V values you derive.  How faint do we have to go in order to catch 50% of our targets of interest? 80%? 90%? All of them?  How sensitive is this value to your choice of type or color to leverage?

This is pretty easy to implement in Excel. It's just one column more of calculation, and if you code it up right, you can make absolute cell references, such that you can change one single cell value to play with the effects of the assumption of the type, and another single cell value to play with the color offset (e.g., which band you choose to leverage from). BUT you are depending that whatever known color from which you are leveraging is uncontaminated (from Av, disk, accretion, variability, or just plain errors).

V is Johnson V, not Sloan r or i.  V is bluer than either Sloan r or i, so if our estimates of V are any good, getting to a V of x will almost certainly get to an r or i of x.

We're assuming no reddening. That's almost certainly going to affect what fraction of stars we actually do detect.

==Option 2==

Look again at the SEDs that were included as part of the CG4 paper. Note that for the stars for which we did not have a spectral type, we just assumed a type of M0. I have a model grid that includes M0 stars. It's really hard to make really good models, especially for the late type stars, because of the complicated chemistry and quantum mechanics (molecules, line emission) involved.  The models I have are a hybrid of the best available over a wide range of masses -- they are called Kurucz-Lejeune models (because Dr. Lejeune took Dr. Kurucz's models and updated them slightly). (Note that above, it was hard to get a guess at a plain photosphere from empirical observations of real young late-type stars; here it's hard to get a guess at a plain photosphere from the perspective of calculating models.)

What we did in the CG4 paper was normalize the model to the energy at K (if available), or other NIR bands if K was not available. We can do the same thing for our BRC SEDs. One can then use the model to read off a guess at what the expected energies are at the central wavelengths of the two Sloan bands (r and i). Then you have to back out the expected magnitude by "undoing" the calculation you did to get it into an SED in the first place : log lambdaFlambda (erg/s/cm^2) -> lambdaFlambda (erg/s/cm^2) -> Flambda (erg/s/cm^3) -> Flambda (Jy) -> magnitude (mag). 

[http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/A%2bAS/125/229 Here is the original full grid of models]. Note that you can get them for "a large range of stellar parameters : Teff=50,000K to K, logg=5.50 to -1.02 and
[M/H]=-5.0 to +1.0." (the latter is metallicity, in case that wasn't clear-- it's also written [Fe/H]).

Here is a 'standard' M0 model in log lambdaFlambda (erg/sec/cm^2).  [[file:justm0model.txt]] Note that there are a lot of points here because it is a model and is designed to provide a well-sampled spectral energy distribution. Watch your units!  You can then use this to get a guess at r and i.

Just like you did above, you should look at the distribution of r and i values you derive.  How faint do we have to go in order to catch 50% of our targets of interest? 80%? 90%? All of them?  You don't really have the machinery to do this, but in theory you can pick your own model to experiment with, and you can also experiment with different values of Av. 

This is harder to implement in Excel. You'll have to take a spreadsheet in which you calculated SEDs, figure out how to normalize the model to K, make a plot, check that normalizing at K is the best thing to do (or is it better to normalize at a different band?).  Then interpolate the expected energy at the r and i bands, and back out a magnitude at the two bands. 

Here, you are no longer depending that whatever single band from which you are leveraging is uncontaminated (from Av, disk, accretion, variability, or just plain errors) because you will make a plot to check on the model fit and see if normalizing at a different band is better.

Here, you are explicitly estimating Sloan r and i, not just V.  BUT you do have to be careful to keep track of whether you are working with Vega magnitudes or AB mags. Most Sloan folks work in AB mags instead.  [[Central wavelengths and zero points]] is our local repository of central wavelengths and zero points. For AB mags, instead of a Vega zero point, you always use a flat reference spectrum, so the zero point is 3631 Jy for all bands.

We're still assuming no reddening. That's still almost certainly going to affect what fraction of stars we actually do detect. We can redden the model and check, but I am worried that this will be a lot of trouble for you, for not a lot of gain.  In some cases, the combination of even just J, H, and K will clearly indicate some degree of reddening (e.g., the model will be a poor fit).