A Study of the Mundy Debris Disk
'science' investigation of mark's simulations of mapping the
debris disk. bjb. 2001sep07
what i did:
1 - restrict myself to 345 GHz, since that is where the model
was really calculated anyway (see lee's model description).
2 - retrieve the necessary files from mark's website:
DEBRIS.1.345.MODEL2 - the model
DEBRIS.1.345.1.CVM2 - 12 m INT; 12 m TP
DEBRIS.2.345.1.CVM2 - 12 m INT; 12 m TP; 7 m INT
DEBRIS.3.345.1.CVM2 - 12 m INT; 7 m INT; 7 m TP
FLUXSCALE - the 'sault weighting' correction map
note that you don't need all 3 different '*.MODEL2' files,
because they are identical.
3 - convolve the model image with the appropriate gaussian beam
(task CONVL in AIPS, with BMAJ=1;BMIN=.91;BPA=83.39).
4 - make the 'sault weighting' correction to the convolved model
image (task COMB in AIPS, with OPCOD='MULT'; APARM=1,0; input map
# 1 is the result from step 3 above; input map # 2 is the
FLUXSCALE image).
5 - fix the 'flux density scale'. because mark fudged the flux
density in the model, i need to make a correction for that.
mark at one point stated that the multiplication factor was 10000,
but it seems to me that that's not right. for example, consider
the central pixel value (the max in the images, due to the stellar
emission). in the original input model, the value of this pixel
is 240.2 uJy/pixel. in mark's input model, the value of this
pixel is 9.30 mJy/pixel. the ratio of these two is 38.7, not
10000. but, the problem here is in the resampling, since the
original input model had pixel size of 16.67 masec/pixel, and
mark's has 143.2 masec/pixel, or, a factor of 100 larger pixels.
what happens if you convolve both the original model and mark's
model with the beam of the reconstructed images and compare?
since this beam size (1.0 X 0.91 asec) is much larger than either
pixel size, the differing pixel size in the two inputs to the
convolution shouldn't matter. in the original model (convolved),
the central pixel value goes to 0.5447 uJy/pixel. in mark's model
(convolved), the central pixel value goes to 214.4 uJy/pixel. now,
multiply these by pixels/beam: ( pi*bmaj*bmin/[4*ln2] / pixsiz )^2,
and the convolved original has a max of 2.085 mJy/bm, and mark's
convolved has a max of 11.12 mJy/bm. so, it looks to me like you
only have to divide the reconstructed images (and mark's convolved
model) by a factor of 11.12/2.085 = 5.33. use COMB in AIPS to do
this.
this is a *serious* confusion, and is a problem with the way that
mark did his simulations. why not just take the flux density as
given by the model? why does he have to scale it at all?
harumph...
6 - make 'fidelity' images
i don't know what is the 'standard' for definition of fidelity any more,
so i did the simple thing of:
reconstruction - model
fidelity image = ------------------------
model
these are the 3 contour/gray scale plots that i made (and sent to al).
7 - qualititative assessment of the reconstructed images.
the first thing to say is that the reconstructed images all look
pretty good, to first order. in all 3 of them, you can see the
inner gap, inner rings, middle gap, outer ring, and both
'condensations' (and associated debris pileups). of the 3
simulations, the 2nd is the best, however. you can see that
it gets the stuff in the inner portion of the disk much better
than the other 2. also, the 'junk' at the upper left is of
smaller amplitude.
8 - quantitative assessment of the reconstructed images.
a - star flux density & hence effective temperature
this is impossible to do, because of the poor resolution. too
much disk dust is included in that central pixel, and so any
derived flux density is *much* too high. the star flux density
is of order 240 uJy, whereas we've got roughly 2 mJy (factor of
10 too high) in that central beam.
b - disk geometry factors
i - disk diameter & inclination
i took cuts in the vertical and horizontal directions to estimate
these. the 'size' in either dimension is the number of pixels
between points where the flux density went to 1 uJy/bm. this is
cheating (and not strictly the right way to do it in any case),
but i didn't want to go to the full trouble of ellipse fitting,
and it will be close enough, IMHO.
1 - 'y-size' = 109 pixels = 15.61 asec
'x-size' = 156 pixels = 22.34 asec
2 - 'y-size' = 109 pixels = 15.61 asec
'x-size' = 152 pixels = 21.77 asec
3 - 'y-size' = 107 pixels = 15.32 asec
'x-size' = 177 pixels = 25.35 asec
but, remember that these are convolved effective sizes, so the
roughly 1" beam has to be 'deconvolved' out of them. to first
order, this beam convolution increases the size on either side
of the center by 2" or so, so subtract 4" from the above sizes,
giving:
1 - 'y-size' = 11.61 asec = 140 AU
'x-size' = 18.34 asec = 220 AU
-> inclination ~ 40 deg.
2 - 'y-size' = 11.61 asec = 140 AU
'x-size' = 17.77 asec = 210 AU
-> inclination ~ 42 deg.
3 - 'y-size' = 11.32 asec = 130 AU
'x-size' = 21.35 asec = 260 AU
-> inclination ~ 30 deg.
the sizes should be 140 AU and 200 AU. so, simulations 1 & 2
did pretty well here (though #2 is again better), but sim 3 is
pretty far off.
c - total disk dust mass
not yet done.
d - size of 'holes' & gaps, etc...
not yet done.