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.