Tension and Systematics in the Gold06 SnIa Dataset
Abstract
The Gold06 SnIa dataset recently released in astroph/0611572 consists of five distinct subsets defined by the group or instrument that discovered and analyzed the corresponding data. These subsets are: the SNLS subset (47 SnIa), the HST subset (30 SnIa), the HZSST subset (41 SnIa), the SCP subset (26 SnIa) and the Low Redshift (LR) subset (38 SnIa). These subsets sum up to the 182 SnIa of the Gold06 dataset. We use MonteCarlo simulations to study the statistical consistency of each one of the above subsets with the full Gold06 dataset. In particular, we compare the best fit parameters obtained by subtracting each one of the above subsets from the Gold06 dataset (subset truncation), with the corresponding best fit parameters obtained by subtracting the same number of randomly selected SnIa from the same redshift range of the Gold06 dataset (random truncation). We find that the probability for is large for the Gold06 minus SCP (Gold06SCP) truncation but is less than for the Gold06SNLS, Gold06HZSST and Gold06HST truncations. This result implies that the Gold06 dataset is not statistically homogeneous. By comparing the values of the best fit for each subset truncation we find that the tension among subsets is such that the SNLS and HST subsets are statistically consistent with each other and ‘pull’ towards CDM while the HZSST subset is statistically distinct and strongly ‘pulls’ towards a varying crossing the line from below . We also isolate six SnIa that are mostly responsible for this behavior of the HZSST subset.
pacs:
98.80.Es,98.65.Dx,98.62.SbI Introduction
Current cosmological observations show strong evidence that we live in a spatially flat universe Spergel:2003cb with low matter density Tegmark:2003ud that is currently undergoing accelerated cosmic expansion. The most direct indication for the current accelerating expansion comes from the accumulating type Ia supernovae (SnIa) data hzsst ; scp ; lr ; snobs ; Astier:2005qq ; Riess:2004nr ; Riess:2006fw which provide a detailed form of the recent expansion history of the universe.
This accelerating expansion has been attributed to a dark energy component with negative pressure which can induce repulsive gravity and thus cause accelerated expansion (for recent reviews see Padmanabhan:2006cj ; Copeland:2006wr ; Perivolaropoulos:2006ce ; Alcaniz:2006ay ; Sahni:2006pa ; Uzan:2006mf ; Polarski:2006ut ) The simplest and most obvious candidate for this dark energy is the cosmological constant Sahni:1999gb with equation of state . This model however raises theoretical problems related to the fine tuned value required for the cosmological constant. These difficulties have lead to a large variety of proposed models where the dark energy component evolves with time usually due to an evolving scalar field (quintessence) which may be minimally quintess or nonminimally modgrav coupled to gravity. Alternatively, more general modified gravity theoriesNojiri:2006ri have also been proposed based on theoriesChiba:2003ir ; Nojiri:2003ft ; Nojiri:2006be (for a debate on the issue see Amendola:2006kh ), braneworldsAref'eva:2005fu ; Lazkoz:2006gp ; Bogdanos:2006dt ; Cai:2005qm , GaussBonnet dark energyNojiri:2005vv , holographic dark energyZhang:2005yz etc. The main prediction of the dynamical models is the evolution of the dark energy density parameter . Combining this prediction with the prior assumption for the matter density parameter , the predicted expansion history is obtained as
(1) 
The dark energy density parameter is usually expressed as
(2) 
where is related to by Saini:1999ba ; Nesseris:2004wj ; Huterer:2000mj
(3) 
If the dark energy can be described as an ideal fluid with conserved energy momentum tensor then the above parameter is identical with the equation of state parameter of dark energy
(4) 
Independently of its physical origin, the parameter is an observable derived from (with prior knowledge of ) and is usually used to compare theoretical model predictions with observations.
The two most reliable and robust SnIa datasets existing at present are the Gold dataset Riess:2006fw (hereafter Gold06) and the Supernova Legacy Survey (SNLS) Astier:2005qq dataset. The Gold dataset compiled by Riess et. al. is a set of 182 supernova data from various sources analyzed in a consistent and robust manner with reduced calibration errors arising from systematics. It contains 119 points from previously published data Riess:2004nr (hereafter Gold04) plus 16 points with discovered recently by the Hubble Space Telescope (HST). It also incorporates 47 points () from the first year release of the SNLS dataset Astier:2005qq out of a total of 73 distant SnIa. Some supernovae were excludedRiess:2006fw due to highly uncertain color measurements, high extinction and a redshift cut or , to avoid the influence of a possible local “Hubble Bubble”, so as to define a highconfidence subsample. In addition, a single algorithm (MLCS2k2) was applied to estimate all the SnIa distances (including those originating from SNLS) thus attempting to minimize the nonuniformities of the dataset.
The total of 182 SnIa included in the Gold06 dataset can be grouped into five subsets according to the search teams/instruments that discovered them. These subsets are shown in Table I. A detailed table of all the data used in our analysis and their subset origin is shown in the Appendix. Notice that the early data of the Gold06 dataset were obtained mainly in the 90’s and consist of the High z Supernova Search Team (HZSST) subset, the Supernova Cosmology Project (SCP) subset and the Low Redshift (LR) subset.
The above observations provide the apparent magnitude of the supernovae at peak brightness after implementing correction for galactic extinction, Kcorrection and light curve widthluminosity correction. The resulting apparent magnitude is related to the luminosity distance through
(5) 
where in a flat cosmological model
(6) 
is the Hubble free luminosity distance (), are theoretical model parameters and is the magnitude zero point offset and depends on the absolute magnitude and on the present Hubble parameter as
(7)  
The parameter is the absolute magnitude which is assumed to be constant after the above mentioned corrections have been implemented in .
Subsets  Total  Redshift Range  Years of discovery  Ref. 

SNLS  47  20032004  Astier:2005qq  
HST  30  19972005  Riess:2006fw  
HZSST  41  19952001  hzsst  
SCP  26  19952000  scp  
LR  38  19902000  lr 
The data points of the Gold06 dataset are given after the corrections have been implemented, in terms of the distance modulus
(8) 
The theoretical model parameters are determined by minimizing the quantity
(9) 
where and are the errors due to flux uncertainties and peculiar velocity dispersion respectively. These errors are assumed to be gaussian and uncorrelated. The theoretical distance modulus is defined as
(10) 
where
(11) 
and also depends on the parameters used in the parametrization of in equation (6).
The parametrization used in our analysis is the CPL parametrization Chevallier:2000qy ; Linder:2002et
(12)  
(13) 
with a prior of the matter density parameter (as in Ref. Riess:2006fw ), assuming flatness, according to the methods described in detail in Ref. Lazkoz:2005sp ; Nesseris:2005ur .
The previous version of the Gold sample Riess:2004nr (Gold04) had been shown to be in mild () tension with the SNLS dataset Nesseris:2005ur ; Jassal:2005qc . While the Gold04 mildly favored an evolving dark energy equation of state parameter (crossing the phantom divide line w=1) over the cosmological constant (CDM) at almost level Alam:2004jy ; Wang:2006ts ; Daly:2006ax ; Huterer:2004ch ; Shafieloo:2005nd ; Lazkoz:2005sp , the SNLS data had shown no such trend and provided Nesseris:2005ur a best fit very close to (CDM). The trend towards phantom divide crossing can not be explained in the context of minimally coupled quintessence and could be viewed as an indication for more exotic modelsGannouji:2006jm ; Guo:2006pc ; Kujat:2006vj ; Zhang:2006at ; Nesseris:2006hp ; Briscese:2006xu ; Kahya:2006hc ; McInnes:2005vp . This mild tension could have been attributed to systematic errors due eg to the different algorithm used in the analysis of the two datasets. The new version of the Gold sample however, (Gold06) involves an improved uniform analysis and incorporates a large part of the SNLS sample. Thus there could have been an anticipation that the mild tension with SNLS would be ameliorated or even disappear. As shown in Fig. 1 however, this anticipation has not been fulfilled (see also Alam:2006kj ; Gong:2006gs ).
The mild (almost ) tension between the Gold04 and the SNLS samples (Figs. 1a and 1b) has not decreased by using the Gold06 sample (Fig. 1c)! The investigation of the origin of this tension and the statistical uniformity of the Gold06 dataset consist the main focus of the present paper.
Ii Tension in the Gold06 Dataset
The 182 SnIa included in the Gold06 dataset originate mainly from the search teams/instruments shown in Table I. The low redshift subset (LR) is a mixture of various early SnIa by different groups and instruments but we consider it as a single subset because otherwise we would have to increase the number of subsets beyond a reasonable number.
In order to investigate the statistical uniformity of the Gold06 dataset and also the origin of the tension with the SNLS, we have decomposed the Gold06 dataset into the subsamples of Table I and constructed new datasets by subtracting each one (or two) of the subsets from the full Gold06 dataset. We thus obtained the following six subset truncations:
We did not consider the subset with low redshift truncation because the subset is not uniform and also because subtracting it can not be associated with a corresponding random truncation in the same low redshift range (the range is spanned completely by the LR subset). We then addressed the following two questions:

How do the best fit values for each of the six truncations compare with the corresponding best fit value of the full Gold06 dataset?

How do the best fit values for each of the six truncations compare with the corresponding best fit value of a random truncation of the full Gold06 dataset made in the same redshift range as that of the subtracted subset?
The answer to the first question is provided in Fig. 2 where we show the best fit values for each one of the above six truncations. Notice that the two multiple truncations: (point 1) and (point 6) correspond to more extreme best fit values of . The best fit of the Gold06 dataset along with its and contours is also shown in Fig. 2 (point 0).
The following comments can be made on the basis of Fig. 2:

The truncation leaves the best fit of the Gold06 dataset practically unchanged

No single subset truncation is able to shift the best fit values beyond the contours of the Gold06 dataset.

All the subset truncations (except ) systematically shift the best fit along the major axis of the ellipse. In particular for and the best fit is left mainly under the influence of and is shifted along the major axis, away from CDM towards an evolving crossing the line (, ). On the other hand for the best fit is left under the influence of and and is shifted towards CDM. This implies that the subsets and favor CDM while the subset favors an evolving crossing the phantom divide . This result is further amplified by the behavior of the multiple truncations (further shifted towards CDM) and (strongly shifted towards a varying crossing the phantom divide at a level more than (see Fig. 2)).
Based on the above comments we conclude that the answer to the first question stated above can be summarized as follows: The best fit values for each of the four single set truncations 25 do not differ more than from the best fit corresponding values of the Gold06 dataset but they show distinct trends which are characteristic for each one of the truncations.
A separate question (related to the second question stated above) is the question of statistical consistency between each subset truncation and the full Gold06 dataset. To address this question we compare the best fit value of for each subset truncation with a large number (500) of corresponding random truncations of the Gold06 dataset. The random truncations involve random subtractions of the same number of SnIa and in the same redshift range as the subset truncation. These random truncations can be used to obtain the range for the
Dataset  (MC)  

expected values of the best fit of the randomly truncated Gold06 dataset.
If the best fit values of the subset truncation is within the range of the best fit values of the random truncation then the considered subset truncation is a typical truncation representative of the Gold06 dataset and statistically consistent with it. If on the other hand differs by or more from the mean best fit values of the random truncation then the considered subset truncation is not a typical truncation and is systematically different from the full dataset. We have implemented the above comparison for the six subset truncations referred above and the results are shown in Table II and in Fig. 3.
The following comments can be made on the basis of Table II and Fig. 3:

The is a typical, statistically consistent subset of the Gold06 dataset because its truncation does not significantly alter the statistical properties of the Gold06 dataset. In particular the best fit value of the truncation differs only by from the corresponding mean random truncation best fit which involves random subtraction of the same number of SnIa from the same redshift range as the SCP subset.

The other five subsets considered in Fig. 3 are not typical subsets of the Gold06 dataset. The best fit values of the truncations considered in Fig. 3 differ by more than from the mean best fit values of the corresponding random truncations.

An extreme case is the truncation whose best fit values are away from the corresponding mean best fit values of a random truncation! This implies that the combination of the which is left over from the truncation strongly favors an evolving and is statistically inconsistent with the Gold06 dataset. This result is consistent with Fig. 2 which also shows that best fit of the truncation is about away from the Gold06 best fit!

The and subsets are statistically very similar to each other (with a trend towards CDM) even though they are both significantly different (more that ) from the corresponding random truncations of Gold06 (see also Fig. 2).

Both Figs 2 and 3 indicate that the trend towards CDM increases for more recent ( and ) data while earlier data ( and ) seem to favor and evolving .
The above results can also be verified by considering the ‘pure’ Gold06 dataset which does not include the 47 SnIa of SNLS. This dataset (Gold06p) consists of 135 SnIa and is essentially a filtered version of the Gold04 dataset with the addition of the 16 SnIa with discovered recently by the HST. The best fit parameter values for the Gold06p dataset are somewhat shifted in the direction of varying compared to the full Gold06 (compare Figs. 2 and 4) as expected since SNLS favors CDM. As shown in Fig. 4 and Table III, the effect of each subset truncation in this case is more prominent due to the smaller number of points in the Gold06p dataset.
Dataset  (MC)  

For example, the truncation shifts the best fit parameter values of the Gold06p by about in the direction of CDM (and beyond it) while the shift with respect to the random truncations of Gold06p is (Fig. 5). The corresponding shifts with respect to the Gold06 dataset were about and respectively (Figs. 2 and 3).
Iii DiscussionConclusion
The fact that more recent SnIa data (HST and SNLS) seem to favor CDM significantly more than earlier data (HZSST) makes it possible that earlier data may be more prone to systematic errors. It is therefore interesting to identify a small subset of SnIa from the HZSST data that is mostly responsible for the trend of HZSST towards an evolving . We have isolated the group of SnIa in the HZSST subset whose distance modulus differs by more than from the CDM predictions (). The group which consists of just six SnIa is also significantly responsible for the trend of the HZSST subset towards an evolving . These SnIa are: (SN99Q2, SN00ee, SN00ec, SN99S, SN01fo, SN99fv). The shifted best fit parameter values due to these six SnIa data truncation are shown in Fig. 6a superposed on a MonteCarlo simulation of corresponding random 6 point truncations to the HZSST subset. We anticipate that the possible systematic errors that lead to the distinct behavior of the HZSST subset are maximal for these six SnIa and it may be easier to identify them and correct them in this set of six SnIa. Alternatively these 6 SnIa could be discarded from the Gold06 dataset as outliers in an effort to improve its statistical uniformity and bring it to line with the more recent data.
A visual display of the six datapoints (points in red) compared to other datapoints is shown in Fig. 6b where we show the distance modulus relative to CDM () of the Gold06 data in the redshift range of the HZSST subset. In the same plot we show (thick dashed line) the distance modulus corresponding to the best fit values obtained from the Gold06p data (dashed line) indicating that all of the six red datapoints strongly favor the best fit over CDM.
In conclusion we have demonstrated that despite the careful filtering and the improved calibration, the Gold06 dataset is plagued with statistical inhomogeneities which are possibly due to systematic errors. Given the fact that the more recent data (SNLS and HST) are statistically consistent with each other and homogeneous, it is highly probable that the possible source of systematic errors lies within the earlier data and in particular in the HZSST subset.
Numerical Analysis: The mathematica files and the datafile used in the numerical analysis of this work may be found at http://leandros.physics.uoi.gr/gold06/gold06.htm or may be sent by email upon request.
Acknowledgements
This work was supported by the European Research and Training Network MRTPNCT2006 0358631 (UniverseNet). SN acknowledges support from the Greek State Scholarships Foundation (I.K.Y.).
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Iv Appendix
SN 
Subsample  

SN03D1au 
0.504  42.61  0.17  SNLS 
SN03D1aw  0.582  43.07  0.17  SNLS 
SN03D1ax  0.496  42.36  0.17  SNLS 
SN03D1cm  0.870  44.28  0.34  SNLS 
SN03D1co  0.679  43.58  0.19  SNLS 
SN03D1fc  0.331  41.13  0.17  SNLS 
SN03D1fl  0.688  43.23  0.17  SNLS 
SN03D1fq  0.800  43.67  0.19  SNLS 
SN03D3af  0.532  42.78  0.18  SNLS 
SN03D3aw  0.449  42.05  0.17  SNLS 
SN03D3ay  0.371  41.67  0.17  SNLS 
SN03D3bh  0.249  40.76  0.17  SNLS 
SN03D3cc  0.463  42.27  0.17  SNLS 
SN03D3cd  0.461  42.22  0.17  SNLS 
SN03D4ag  0.285  40.92  0.17  SNLS 
SN03D4at  0.633  43.32  0.18  SNLS 
SN03D4cx  0.949  43.69  0.32  SNLS 
SN03D4cz  0.695  43.21  0.19  SNLS 
SN03D4dh  0.627  42.93  0.17  SNLS 
SN03D4di  0.905  43.89  0.30  SNLS 
SN03D4dy  0.604  42.70  0.17  SNLS 
SN03D4fd  0.791  43.54  0.18  SNLS 
SN03D4gg  0.592  42.75  0.19  SNLS 
SN03D4gl  0.571  42.65  0.18  SNLS 
SN04D1ag  0.557  42.70  0.17  SNLS 
SN04D2cf  0.369  41.67  0.17  SNLS 
SN04D2fp  0.415  41.96  0.17  SNLS 
SN04D2fs  0.357  41.63  0.17  SNLS 
SN04D2gb  0.430  41.96  0.17  SNLS 
SN04D2gp  0.707  43.42  0.21  SNLS 
SN04D3co  0.620  43.21  0.18  SNLS 
SN04D3cy  0.643  43.21  0.18  SNLS 
SN04D3df  0.470  42.45  0.17  SNLS 
SN04D3do  0.610  42.98  0.17  SNLS 
SN04D3ez  0.263  40.87  0.17  SNLS 
SN04D3fk  0.358  41.66  0.17  SNLS 
SN04D3fq  0.730  43.47  0.18  SNLS 
SN04D3hn  0.552  42.65  0.17  SNLS 
SN04D3kr  0.337  41.44  0.17  SNLS 
SN04D3lu  0.822  43.73  0.27  SNLS 
SN04D3ml  0.950  44.14  0.31  SNLS 
SN04D3nh  0.340  41.51  0.17  SNLS 
SN04D3oe  0.756  43.64  0.17  SNLS 
SN04D4an  0.613  43.15  0.18  SNLS 
SN04D4bq  0.550  42.67  0.17  SNLS 
SN04D4dm  0.811  44.13  0.31  SNLS 
SN04D4dw  0.961  44.18  0.33  SNLS 
1997ff  1.755  45.35  0.35  HST 
2002dc  0.475  42.24  0.20  HST 
2002dd  0.950  43.98  0.34  HST 
2003eq  0.840  43.67  0.21  HST 
2003es  0.954  44.30  0.27  HST 
2003eb  0.900  43.64  0.25  HST 
six outliers of the HZSST subset are denoted by a .
SN 
Subsample  

2003XX  0.935  43.97  0.29  HST 
2003bd  0.670  43.19  0.24  HST 
2002kd  0.735  43.14  0.19  HST 
2003be  0.640  43.01  0.25  HST 
2003dy  1.340  44.92  0.31  HST 
2002ki  1.140  44.71  0.29  HST 
2002hp  1.305  44.51  0.30  HST 
2002fw  1.300  45.06  0.20  HST 
HST04Pat  0.970  44.67  0.36  HST 
HST04Mcg  1.370  45.23  0.25  HST 
HST05Fer  1.020  43.99  0.27  HST 
HST05Koe  1.230  45.17  0.23  HST 
HST04Gre  1.140  44.44  0.31  HST 
HST04Omb  0.975  44.21  0.26  HST 
HST05Lan  1.230  44.97  0.20  HST 
HST04Tha  0.954  43.85  0.27  HST 
HST04Rak  0.740  43.38  0.22  HST 
HST04Yow  0.460  42.23  0.32  HST 
HST04Man  0.854  43.96  0.29  HST 
HST05Spo  0.839  43.45  0.20  HST 
HST04Eag  1.020  44.52  0.19  HST 
HST05Gab  1.120  44.67  0.18  HST 
HST05Str  1.010  44.77  0.19  HST 
HST04Sas  1.390  44.90  0.19  HST 
SN95K  0.478  42.48  0.23  HZSST 
SN96E  0.425  41.69  0.40  HZSST 
SN96H  0.620  43.11  0.28  HZSST 
SN96I  0.570  42.80  0.25  HZSST 
SN96J  0.300  41.01  0.25  HZSST 
SN96K  0.380  42.02  0.22  HZSST 
SN96U  0.430  42.33  0.34  HZSST 
SN97as  0.508  42.19  0.35  HZSST 
SN97bb  0.518  42.83  0.31  HZSST 
SN97bj  0.334  40.92  0.30  HZSST 
SN97ce  0.440  42.07  0.19  HZSST 
SN97cj  0.500  42.73  0.20  HZSST 
SN98ac  0.460  41.81  0.40  HZSST 
SN98M  0.630  43.26  0.37  HZSST 
SN98J  0.828  43.59  0.61  HZSST 
SN99Q2  0.459  42.67  0.22  HZSST 
SN99U2  0.511  42.83  0.21  HZSST 
SN99S  0.474  42.81  0.22  HZSST 
SN99N  0.537  42.85  0.41  HZSST 
SN99fn  0.477  42.38  0.21  HZSST 
SN99ff  0.455  42.29  0.28  HZSST 
SN99fj  0.815  43.75  0.33  HZSST 
SN99fm  0.949  44.00  0.24  HZSST 
SN99fk  1.056  44.35  0.23  HZSST 
SN99fw  0.278  41.01  0.41  HZSST 
SN99fv  1.199  44.19  0.34  HZSST 
SN00ec  0.470  42.76  0.21  HZSST 
SN00dz  0.500  42.74  0.24  HZSST 
SN00eg  0.540  41.96  0.41  HZSST 
TABLE IV continued
SN 
Subsample  

SN00ee 
0.470  42.73  0.23  HZSST 
SN00eh  0.490  42.40  0.25  HZSST 
SN01jh  0.884  44.22  0.19  HZSST 
SN01hu  0.882  43.89  0.30  HZSST 
SN01iy  0.570  42.87  0.31  HZSST 
SN01jp  0.528  42.76  0.25  HZSST 
SN01fo  0.771  43.12  0.17  HZSST 
SN01hs  0.832  43.55  0.29  HZSST 
SN01hx  0.798  43.88  0.31  HZSST 
SN01hy  0.811  43.97  0.35  HZSST 
SN01jf  0.815  44.09  0.28  HZSST 
SN01jm  0.977  43.91  0.26  HZSST 
SN95aw  0.400  42.04  0.19  SCP 
SN95ax  0.615  42.85  0.23  SCP 
SN95ay  0.480  42.37  0.20  SCP 
SN95az  0.450  42.13  0.21  SCP 
SN95ba  0.388  42.07  0.19  SCP 
SN96ci  0.495  42.25  0.19  SCP 
SN96cl  0.828  43.96  0.46  SCP 
SN97eq  0.538  42.66  0.18  SCP 
SN97ek  0.860  44.03  0.30  SCP 
SN97ez  0.778  43.81  0.35  SCP 
SN97F  0.580  43.04  0.21  SCP 
SN97H  0.526  42.56  0.18  SCP 
SN97I  0.172  39.79  0.18  SCP 
SN97N  0.180  39.98  0.18  SCP 
SN97P  0.472  42.46  0.19  SCP 
SN97Q  0.430  41.99  0.18  SCP 
SN97R  0.657  43.27  0.20  SCP 
SN97ac  0.320  41.45  0.18  SCP 
SN97af  0.579  42.86  0.19  SCP 
SN97ai  0.450  42.10  0.23  SCP 
SN97aj  0.581  42.63  0.19  SCP 
SN97am  0.416  42.10  0.19  SCP 
SN97ap  0.830  43.85  0.19  SCP 
SN98ba  0.430  42.36  0.25  SCP 
SN98bi  0.740  43.35  0.30  SCP 
SN00fr  0.543  42.67  0.19  SCP 
TABLE IV continued
SN 
Subsample  

SN92bs  0.063  37.67  0.19  LR 
SN94M  0.024  35.09  0.22  LR 
SN94T  0.036  36.01  0.21  LR 
SN97dg  0.029  36.13  0.21  LR 
SN00bk  0.026  35.35  0.23  LR 
SN98cs  0.032  36.08  0.20  LR 
SN00cf  0.036  36.39  0.19  LR 
SN98dx  0.053  36.95  0.19  LR 
SN99gp  0.026  35.57  0.21  LR 
SN99X  0.025  35.40  0.22  LR 
SN99cc  0.031  35.84  0.21  LR 
SN94Q  0.029  35.70  0.21  LR 
SN95ac  0.049  36.55  0.20  LR 
SN96bl  0.034  36.19  0.20  LR 
SN90O  0.030  35.90  0.21  LR 
SN96C  0.027  35.90  0.21  LR 
SN96ab  0.124  39.19  0.22  LR 
SN99ef  0.038  36.67  0.19  LR 
SN92J  0.046  36.35  0.21  LR 
SN92bk  0.058  37.13  0.19  LR 
SN92bp  0.079  37.94  0.18  LR 
SN92br  0.088  38.07  0.28  LR 
SN93H  0.025  35.09  0.22  LR 
SN93ah  0.028  35.53  0.22  LR 
SN90T  0.040  36.38  0.20  LR 
SN90af  0.050  36.84  0.22  LR 
SN91U  0.033  35.53  0.21  LR 
SN91S  0.056  37.31  0.19  LR 
SN92P  0.026  35.63  0.22  LR 
SN92bg  0.036  36.17  0.20  LR 
SN92bl  0.043  36.52  0.19  LR 
SN92bh  0.045  36.99  0.18  LR 
SN92au  0.061  37.31  0.22  LR 
SN92ae  0.075  37.77  0.19  LR 
SN92aq  0.101  38.70  0.20  LR 
SN93ag  0.050  37.07  0.19  LR 
SN93O  0.052  37.16  0.18  LR 
SN93B  0.071  37.78  0.19  LR 