From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Sun Sep 07 2003 - 12:54:09 PDT
As you know, the 1st epoch of the spring 2004 HST search will be done
with a very large gap, ~ 200 days, between new and refs. This means
that some fraction of candidates will be old Type Ia's, whose value for
follow-up is dubious. In addition, we have the issue of trying to
suppress Type II's for all searches.
I asked Peter to run Type Ia and Type II simulations with a 180 gap,
and generating the detected SN counts in r, i, and z for ACS on HST. I
have used the results to calculate S/N values using the expected search
exposure times, using 4/5 orbit in z and 1/5 orbit in r or i. These S/N
values were used to insert noise into the color measurements. I also
used a scatter of 0.1 in the redshifts, assuming that most of the
redshifts will come from photo-z's. I required S/N > 6 in z for an
object to be considered a candidate. I then experimented with a range
of linear color cuts of the form color_cut = a*z + b for z > 1.2 to see
whether Type II's or old Type Ia's can be suppressed using the color
information. Again, remember that all cuts are made using the measured
(noisy) values in order to simulate the information actually available
from the search.
As a baseline, out of all the candidates with phot-z > 1.2, the
simulation finds that 61% will be good Type Ia's, 19% will be Type II's,
and 20% will be late Ia's.
Now, whenever a cut is made, some good Type Ia's will be lost. The
fraction of good Ia's retained relative to the total number of Ia's is
the "efficiency". Of the Ia's that pass the cuts, the fraction which
are late is the "late fraction". Without cuts the late fraction is 24%.
Likewise, I define the "Type II fraction" as the number of Type II's
that pass the cuts, relative to the sample of good Ia's plus the number
of Type II's. (Here one could have constructed alternative indicators
of Type II contamination by including the late Ia's or excluding the
Type II's from the denominator.) Without cuts the Type II fraction is
also 24%.
What I find is that for i-z the Type II fraction runs at about 23% for
any color cut that gives a reasonable efficiency. This is because for a
fraction of Type II's, color at a single epoch doesn't tell you much.
For r-i the Type II fraction decreases as the efficiency increases, and
so is never better than the limiting no-cut value of 24% Thus, for
candidates with z_phot > 1.2, color cuts don't help in rejecting Type II's.
As for rejecting late Type Ia's, recall that the baseline late fraction
is 24% for 100% efficiency. Making a color cut of course leads to a
loss of efficiency, so I tried to balance efficiency and late
fraction. When there is no noise included, most late Ia's can be
rejected while retaining very high efficiency. (Indeed, my observation
of this situation in Peter's simulation is what motiviated the present
investigation.) When noise was included, I found that r-i was not
effective in eliminating late Type Ia's. This is probably because there
is little flux in r-band to work with for z > 1.2. For noisy i-z,
there is a shallow minimum in late fraction over efficiency when the
efficiency is about 80%. Here the late fraction is about 16%.
In this case one has thrown out 20% of the good Ia's in order to
achieve a reduction from 24% to 16% in the fraction of late objects you
would follow. This can be a successful strategy when there are SNe to
spare, however, when there are no spare SNe, as in our HDFN search, an
80% efficiency is too low. At 90% efficiency, using i-z the late
fraction is 19%; at 95% efficiency the late fraction is 21% for i-z.
The bottom line is that some of these populations overlap a lot in
color-redshift space when the color and redshift uncertainties are
considered, so they can't be effectively separated.
The big danger is that these results are model-dependent. One could
choose a color cut based on the models which then leads to a poor
efficiency for real data. Also, the uncertainties play a key part and
thus must be well known. Moreover, there appears to be little gain in
applying a color cut since Type II's can't be rejected very well and
the gains in cutting late Ia's are modest. If a color cut is to be
used, i-z is better than r-z; from this, I would not expect V-z to help
at all.
Note that these cuts may help much more at lower redshift where the
S/N of the color measurements is better and where there is a larger
fraction of observable Type II's (according to the models). This would
matter if we want to work at lower redshift to increase the search
yield, or in understanding what can be done when we don't have photo-z's.
Overall, for the 1st epoch search we are likely to have about 40%
contamination from undesirable objects, even if we have photo-z's. Our
follow-up plan should be conceived to try to detect such objects using
changes in color and/or brightness as well as color and brightness
themselves.
- Greg
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