Hi Jacek,
There are two differences that I see. The first is that I was plotting
the ratio DR(n)/DR(1) while you are plotting (DR(n)-DR(1))/DR(1). That
accounts for your first 4 vs 5 discrepancy. The second difference is
in how you define the ratio for the total. You are combining the two
sizes as a weighted sum to account (I think) for the initial factor of
20 difference between the sizes of the deep and time-dep. But that is
already accounted for in your formula for the deep size. So the effect
is to wrongly deweight the time-dep size.
With those fixed, we agree.
Jacek Becla wrote:
Hi Tim,
Thanks. I tried to fiddle with a spreadsheet for a while, but couldn't
get exactly the same plot. Deep db: you have x5 after 10 years, and I
ended up with x4.39. Total: you have x6, and I ended up with x5.04.
See attached. Can you spot the different? What functions did you use?
Jacek
Tim Axelrod wrote:
Hi Jacek,
I have created a simple model for how the size of the object database
will grow between data releases (DR). Here are my assumptions:
1. Data releases occur every 6 months
2. We meet our SRD requirements of 100 visits per field per year
3. The database is split into two parts. The first, dominated by
galaxies, contains the static information for every object detected
at that point in the survey, mostly generated by combining the
information in image stacks. I'll call this the 'deep database'
The second, dominated by stars, contains the time dependent
information for objects bright enough to be usefully detected in
individual exposures. I'll call this the 'time dependent database'.
4. An object record in the deep database is about 100 bytes: 6
band magnitude + errors; data quality flags; shape information.
5. An object record in the time dependent database is about 10
bytes: 1 band magnitude + error + data quality flags.
6. For the first DR, the limiting magnitude for the time dependent
database is 24.5 (where it remains), while the limiting magnitude for
the deep database is already at about 26.1 from stacking 20 R band
images. So at DR1, there are already about 20 times more objects in
the deep database than in the time dependent.
Consider first the growth of the deep database. The limiting flux
to fixed signal-to-noise will decrease as 1/sqrt(n_exp), where n_exp
is the number of exposures effectively stacked and used for
detection. I assume that measurement occurs in all bands, but
detection occurs only in the R band. The SRD calls for 40 R band
exposures per field per year, or 20 additional for every DR. The
limiting magnitude increases as 1.25*log (20DR), and we go
progressively fainter in the galaxy brightness distribution. I've
taken the galaxy data here from the Subaru Deep Field, which gives
the slope of the cumulative brightness distribution to be
d(logN)/d(mag) = 0.45 in the region of interest. The size of the
deep database then grows as 100 * (20DR)**(0.45 * 1.25)
The time dependent database grows strictly linearly with the number
of observations in all bands, which is 50 per DR, so it goes as 10 *
(50 DR).
Taking account of the factor of 20 difference in number of objects at
DR1, two attached plots show the growth of the deep database size,
and the growth of both together. The roughly square root growth of
the deep data dominates the first half of the survey, but is then
overtaken in the second half by the linear growth of the time
dependent database. In spite of my many assumptions, which are
unlikely to be right in detail, I think the overall behavior is about
right.
Let me know if you see an error or need more information.
Cheers,
Tim
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