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Exposure Time Estimation for WFPC2 Images of Extended Targets
-J. Biretta, 16 March 1995, v1.0 (v1.01 07 August 1995)
We describe how to estimate exposure times for extended targets. In section (1) we show how to derive count rates using both analytic formulae and SYNPHOT for extended targets with stellar, non-thermal, and emission line spectra. In section (2) we use these count rates to derive signal-to-noise ratios and exposure times. Section (3) discusses exposure splitting to eliminate cosmic rays.
Contents:
1) Estimation of the detected count rate for the target.
A) Objects with Stellar Spectra
i) WFPC Handbook Equation 6.1,
ii) SYNPHOT black body approximation, and
iii) SYNPHOT Gunn-Stryker Atlas
B) Objects with Non-thermal Spectra Using SYNPHOT
C) Objects with Emission Line Spectra Using SYNPHOT
2) Estimation of signal-to-noise ratios and exposure times for target.
A) Detailed Signal-to-Noise Ratio (SNR) Calculation.
B) Exposure Time Estimation.
3) Cosmic Rays and Exposure Splitting.
Appendix: Bruzual-Persson-Gunn-Stryker Spectrophotometric Atlas.
1) Estimation of the detected count rate for the target.
We consider extended targets with stellar, non-thermal, and emissiom line spectra. Herein "Handbook" refers to the WFPC2 Instrument Handbook v.2.0.
A) Count rate estimation for stellar spectra.
i) Using WFP2 Handbook Equation 6.1.
This is perhaps the quickest method of count rate estimation, and will be sufficient for most purposes. Equation 6.1 is:
s = 2.5x1011 * t * integral{QT d(lambda)/(lambda)} * 10[-0.4(V+AB)] [eqn 1]
Where t = exposure time,
integral{} is tabulated as the second column of
Handbook Table 6.2
V = V magnitude of target per pixel
AB is tabulated in Handbook Table 6.1
Note that the magnitude per pixel is just the magnitude per square arcsecond + 5 for the WFC, and + 6.7 for the PC. For the example, a target with V=22 per square arcsecond has V=27 per WFC pixel and V=29.6 per PC pixel. Consider an E galaxy with V=22 per square arcsecond observed in the WFC with the F814W filter. From Handbook Table 6.1 we see AB=-0.85. Hence the count rate is:
R = s / t = 2.5x1011 * 0.0182 * 10[-0.4(22+5-0.85)] R = 0.158 electron sec-1 pixel-1.
ii) Using SYNPHOT with a blackbody approximation.
SYNPHOT in the STSDAS package can be used to make a more detailed estimation of the target count rate. It will be more detailed in that the actual CCD can be specified, and the actual response curves of the CCD and filter are used.
For the observation mode (or "obsmode") we input "wfpc2,2,f555w" for the obsmode, to indicate wfpc2, camera 3 meaning CCD WF3, and the filter f555w.
For the target spectrum (or "spectrum") we use a 4300 degree Kelvin blackbody which roughly approximates a K3III star or E galaxy. We input "rn(bb(4300),band(v),27.0,vegamag" which means to use a 4300 degree blackbody which is normalized to V=27 per WFC pixel (V=22 per square arcsecond) in a system where Vega is defined to have magnitude zero.
The output form in set to "counts" which here means detected electrons.
In detail the input dialog looks like this:
>cl
cl>stsdas
st>hst_calib
hs>synphot
epar calcphot
Image Reduction and Analysis Facility
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f814w Instrument observation mode
spectrum= rn(bb(4300),band(v),27.0,vegamag) Synthetic spectrum to calculate
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
After typing the input parameters as shown above (using
Mode = band(wfpc2,3,f814w)
Pivot Equiv Gaussian
Wavelength FWHM
7939.227 1487.07 band(wfpc2,3,f814w)
Spectrum: rn(bb(4300),band(v),27.0,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 0.176201
The result indicates that the target will have a countrate R = 0.176 electrons sec-1 pixel-1. This is slightly larger than the above value.
iii) Count rate estimation using SYNPHOT with Gunn-Stryker Spectrophotometic Atlas.
We repeat the above example using SYNPHOT. For the observation mode (or "obsmode") we input "wfpc2,3,f814w" for the obsmode, to indicate wfpc2, camera 3 meaning CCD WF3, and the filter f814w.
For the target spectrum we use our knowledge that an E galaxy spectrum is similar to a K3III star. Looking in the paper by Gunn and Stryker, Ap.J. Supp. 52, 121 (1983), we locate a K3III star in column 3 of their Table 1. (Or see Appendix 1 below.) We find that their star ID=143 has such a spectrum. Hence we input to SYNPHOT the following specification for the "spectrum":
rn(crgridbpgs$bpgs_143.tab,band(v),27,vegamag)
Which tells synphot to use ID number 143 from the Gunn-Stryker Atlas, and to renormalize it to a magnitude of V=27 per WFC pixel, in a system where Vega has magnitude zero. We note that the actual spectra being used are from the Bruzual-Persson-Gunn-Stryker, where the original spectra are extended into the UV and IR.
Again, the output form in set to "counts" which here means detected electrons.
In detail the SYNPHOT input dialog looks like this:
>cl
cl>stsdas
st>hst_calib
hs>synphot
epar calcphot
Image Reduction and Analysis Facility
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f814w Instrument observation mode
spectrum= rn(crgridbpgs$bpgs_143.tab,band(v),27.,vegamag) Synthetic spectrum
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
After typing the input parameters as shown above (using
Mode = band(wfpc2,3,f814w)
Pivot Equiv Gaussian
Wavelength FWHM
7939.246 1487.093 band(wfpc2,3,f814w)
Spectrum: rn(crgridbpgs$bpgs_143.tab,band(v),27.,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 0.189248
The result indicates that the target will have a countrate R = 0.189 electrons sec-1 pixel-1. This is slightly larger than the above value.
B) Objects with Non-thermal Spectra.
Consider a knot in a synchroton jet where the emission has a powerlaw spectrum of form:
F(nu) = F(nu,0) * nu(alpha)
where alpha is the spectral index and the flux has units of ergs sec-1 cm-2 Hz-1. SYNPHOT allows powerlaws to be defined in terms of wavelength, hence we rewrite this as:
F(lambda) = F(lambda,0) * lambda(alpha+2).
If this knot is say 1 arcsec in area on the sky and is known to have a total magnitude V=16 with spectral index -1.5, we may synthesize its spectrum per PC pixel in SYNPHOT using the commands:
rn(pl(5000,0.5),band(v),22.7,vegamag)
where pl(5000,0.5) denotes a powerlaw in wavelength with index alpha+2 = -1.5+2 = 0.5, and fiducial wavelength 5000 Angstroms. This powerlaw spectrum is then renormalized to v=22.7. = 16 + 6.7 per PC pixel. (Note the fiducial wavelenth is unimportant in this example.)
For an observation in say F814W in the PC we would specify SYNPHOT inputs:
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,1,f814w Instrument observation mode
spectrum= rn(pl(5000,0.5),band(v),22.7,vegamag) Synthetic spectrum to calculate
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
And obtain output:
Mode = band(wfpc2,1,f814w)
Pivot Equiv Gaussian
Wavelength FWHM
7952.232 1502.978 band(wfpc2,1,f814w)
Spectrum: rn(pl(5000,0.5),band(v),22.7,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 4.704958
Hence this knot will give R=4.70 electrons sec.-1 pixel-1 in the PC.
An alternate situation is one in which the region has a flux F(nu) at some frequency, instead of a magnitude. Consider the same 1 arcsec square area with a total flux F(nu)=0.0012 Jy at 5000 Angstroms, or 0.0012*(0.0462) = 2.54e-6 Jy per PC pixel. This spectrum can be modeled by a command such as:
rn(pl(5000,0.5),gauss(5500,100),2.54e-6,jy)
which tells SYNPHOT to normalize the spectrum such the flux F(nu) = 2.54e-6 Jy per PC pixel at 5500 Angstroms. The normalization at 5500 Angstroms is imposed by specifying the Gaussian function gauss(5500,100). Hence inputs to SYNPHOT are:
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,1,f814w Instrument observation mode
spectrum= rn(pl(5000,0.5),gauss(5500,100),2.54e-6,jy) Synthetic spectrum to
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
and the output is:
Mode = band(wfpc2,1,f814w)
Pivot Equiv Gaussian
Wavelength FWHM
7952.232 1502.978 band(wfpc2,1,f814w)
Spectrum: rn(pl(5000,0.5),gauss(5500,100),2.54e-6,jy)
VZERO (COUNTS s^-1 hstarea^-1)
0. 3.948181
so that the count rate is R = 3.95 electrons sec-1 pixel-1.
C) Objects with Emission Line Spectra.
A typical situation will be one in which the observer has a total flux of the form:
F(lambda) in erg sec-1 cm-2 Angstroms-1
for the line, a line width W in Angstroms, and size for the emission region in square arcseconds. Such a spectrum may be synthesized in SYNPHOT by specifying a spectrum:
unit([F(lambda)],flam)*box([lambda],[w])
which tells SYNPHOT to generate a constant spectrum of [F(lambda)] and multiply it by a box of height unity, full width [w], centered at [lambda]. One problem which can occur here, is that the default wavelength table in SYNPHOT is too coarse to properly handle narrow lines. Hence is it necessary to first define a new wavelength table using the GENWAVE command as follows:
PACKAGE = synphot
TASK = genwave
output = new_wave Wavelength set table name
minwave = 1000. Minimum of wavelength range (Angstroms)
maxwave = 12000. Maximum of wavelength range (Angstroms)
dwave = 1. Wavelength interval (Angstroms/pixel)
(dveloci= INDEF) Velocity interval (km/s/pixel)
(wavecol= WAVELENGTH) Wavelength set table column name
(mode = a)
This will generate an new wavelength table on disk with name new_wave.tab which runs between 1000 and 12000 Angstroms in 1 Angstrom steps. Next one runs CALCPHOT. Assuming the target has say:
F(lambda) = 1.4 x 10-12 erg sec-1 cm-2 Angstrom-1 at 6563 Angstroms w = 15 Angstroms area = 5 arcsec2
And we want the count rate per WFC (WF3) pixel in F702W. We first compute the flux per WFC pixel as:
F(lambda) * (0.10)2 / area = 1.4 x 10-12 * (0.10)2 / 5 = 2.8 x 10-15
Then we use CALCPHOT:
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f702w Instrument observation mode
spectrum= unit(2.8e-15,flam)*box(6563,15) Synthetic spectrum to calcu
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= new_wave) Wavelength table name
(refdata= ) Reference data
(mode = h)
with output:
Mode = band(wfpc2,3,f702w)
Pivot Equiv Gaussian
Wavelength FWHM
6902.879 1363.456 band(wfpc2,3,f702w)
Spectrum: unit(2.8e-15,flam)*box(6563,15)
VZERO (COUNTS s^-1 hstarea^-1)
0. 100.3481
Which indicates a count rate R = 100 electrons sec-1 pixel-1.
2) Estimation of signal-to-noise ratio and exposure time.
The second part of exposure time estimation involves taking account of the various noise sources, estimating the signal- to-noise ratio (SNR), and finally computing the exposure time.
In section (A) below we outline a generalized SNR calculation including photon noise, read noise, dark noise, and sky noise. Section (B) presents a similar calculation for exposure time. Proposers interested only in rough exposure time estimates should go directly to section (B) equations 13 to 15.
We note that this calculation is nearly identical to that for stellar targets, except that it is performed per detector pixel and hence [sharpness] is effectively unity.
A) Detailed Signal-to-Noise Ratio (SNR) Calculation.
There are several noise sources, which we now consider - photon noise of the target, and three sources of "background" noise: read noise of the CCD, noise from the dark current, and photon noise from the sky.
i) Target photon noise. The noise due to the target is simply:
n(target) = sqrt(R * t) [eqn 2]
where R is the target count rate, and t is the exposure time.
ii) CCD read noise. This is independent of exposure time and is approximately 5.3 electrons for the 7 electrons per DN gains setting (default), and 7.5 electrons for the 14 gain setting. These values will be sufficiently accurate for most purposes; specific values for each CCD can be found in Handbook Table 4.3. Assuming the default gain setting of 7, we have:
n(read) = 5.3 [eqn 3]
Note that images read out in "area" mode, that is, with 2x2 on-chip summation, will have half as much read noise per 0.1x0.1 arcsec. sky area on the WFC (or 0.046x0.046 arcsec. area on PC1).
iii) Dark current. The dark current acts as an additional source of "photons" with a corresponding noise. The dark current count depends on both the exposure time and camera overheads times, and is roughly:
d = DCR * (t+44) = 0.003 * (t+44)
at the standard CCD operating temperature of -88 (-90 nominal) degrees C. (See Handbook Table 4.4 for values at other CCD temperatures.) Note DCR = dark count rate in electrons sec-1. The noise will be just the square root of these counts:
n(dark) = sqrt(0.003 * (t+60)) [eqn 4]
iv) Noise from Sky Counts. The counts contributed by sky glow depend on the target location in the sky. See Handbook Table 6.3. For example, a target near the ecliptic pole suffers a sky glow of V=23.3 mag. per square arcsecond, or converting to WFC pixels by adding 5 magnitudes (or 6.7 for PC), the sky brightness is 23.3+5=28.3 mag. per WFC pixel. For targets near the ecliptic, the sky brightens by about 1 magnitude. Using Handbook Equation 6.1 and Tables 6.1 and 6.1, the sky contributes a count rate:
SCR = 2.5x1011 * integral{QT d(lambda)/(lambda)} * 10[-0.4(V+AB)]
For example, in F555W at the ecliptic pole we have:
SCR = 2.5x1011 * 0.029 * 10[-0.4(28.3+0)]
= 0.0347
where SCR = the Sky Count Rate per pixel, integral{QT d(lambda)/(lambda)} = 0.029 is from Table 6.2 for the F555W filter, V=28.3 mag from above, and AB=0 for the sky from Table 6.1. For convenience, we have tabulated values of the Sky Count Rate (SCR) in Table 1 for most broadband filters.
Table 1. Sky Count Rates (SCR, electrons per sec. per pixel) for targets at the ecliptic pole. For targets near ecliptic plane, multiply by 2.5. Filter WFC PC ------- ------ ------ F336W 0.0006 0.0001 F439W 0.0034 0.0007 F547M 0.0146 0.0029 F555W 0.035 0.0068 F569W 0.027 0.0054 F606W 0.059 0.0122 F622W 0.039 0.0081 F675W 0.037 0.0077 F702W 0.055 0.0011 F785LP 0.016 0.0033 F791W 0.032 0.0066 F814W 0.036 0.0075 F850LP 0.0079 0.0016
The noise contributed by the sky is again merely the square root of the total counts, or:
n(sky) = sqrt(SCR * t) [eqn 5]
Both the read noise, the dark noise, and the sky noise all act effectively as background noises per pixel, and maybe summed as:
n(background) = sqrt( n(read)2 + n(dark)2 + n(sky)2 ) [eqn 6]
= sqrt( 5.32 + 0.003*(t+44) + SCR*t ) [eqn 7]
Since we are computing the signal-to-noise ratio per detector pixel for an extended target, no correction is needed for the PSF size. The total noise, combining the target photon noise and the total background noises, is thus:
n(total) = sqrt( n(photon)2 + n(background)2 ) [eqn 8]
and the signal-to-noise ratio per detector pixel is:
SNR = r * t / n(total) [eqn 9].
Combining equations 2 through 9, the signal to noise ratio is thus:
R*t
SNR = ----------------------------------------------------- [eqn 10]
sqrt( R*t + n(read)2 + DCR*(t+44) + SCR*t )
where R = target count rate (electrons sec-1 pixel-1; from section 1 above),
t = exposure time (sec.),
n(read) = read noise (electrons pixel-1; Handbook Table 4.3),
DCR = dark count rate (electrons sec-1 pixel-1; Handbook Table 4.4),
SCR = sky count rate (electrons sec-1 pixel-1; above Table 1),
Using typical values n(read)=5.3 and DCR=0.003 this may be simplified to:
R*t
SNR = ------------------------------------ [eqn 11]
sqrt( 28.2 + (0.003 + SCR + R)*t )
where SNR is the signal-to-noise ratio per detector pixel for the
WFC and PC, respectively,
R = target count rate (electrons sec-1 pixel-1; from section 1 above),
t = exposure time (sec.), and
SCR = sky count rate (electrons sec-1 pixel-1; above Table 1).
B) Exposure Time Estimation.
Since we are really interested in knowing the exposure time, t, it is useful to solve the quadratic equation [eqn 10]. We find:
1
t = ----- ( B + sqrt[ B2 + 4 * A * Y ] ) [eqn 12]
2*Y
where:
A = n(read)2 + 44 * DCR
B = DCR + SCR + R
Y = ( R/SNR )2
and t = exposure time (sec.),
SNR = desired signal-to-noise ratio per pixel,
R = target count rate (electrons sec-1 pixel-1; from section 1 above),
n(read) = read noise (electrons pixel-1; Handbook Table 4.3),
DCR = dark count rate (electrons sec-1 pixel-1; Handbook Table 4.4),
SCR = sky count rate (electrons sec-1 pixel-1; above Table 1),
We note that A is in effect the square of the time-independent noise, while B*t is the square of the Poisson noise.
Using typical values n(read)=5.3 and DCR=0.003 we find:
A = 28.2, B = 0.003 + SCR + R [eqn 13]
For example, if we want a signal-to-noise ratio (SNR)=30 per pixel for the target in section (1.A.i.) with R=0.158 counts sec.-1 pixel-1 in the WFC and filter F814W, we have:
A = 28.2 B = 0.003 + 0.036 + 0.158 = 0.197 Y = ( 0.158/30 )2 = 0.0000277
and an exposure time:
1
t = ----------- ( 0.197 + sqrt[ 0.1972 + 4 * 28.2 * 0.0000277] )
2*0.0000277
t = 7250 sec.
3) Cosmic Rays and Exposure Splitting
An additional consideration when choosing exposures is the cosmic ray flux on the detector. Cosmic rays corrupt approximately 20 pixels per second on each CCD. These artifacts can be removed by spliting exposures into two or more sub-exposures, so as to allow removal of corrupted pixels in the combined image.
The impact of cosmic rays, and the recommended spliting, depends on the science goals. Programs seeking to image a small target (a few arcseconds in size) will tend to be relatively robust against cosmic rays. Whereas programs searching for faint objects over a wide area are more susceptible to cosmic ray artifacts. Below we give rough guidelines for the number of sub-exposures required for a given total exposure.
We also note that splitting exposures will increase the total noise as sqrt(number of sub-exposures) if the read noise dominates. The read noise will dominate in cases where A >> B*t in equations 13 to 15 above. In these cases some iteration maybe needed to determine the correct total exposure and number of sub-exposures to produce a desired signal-to-noise ratio. Splitting will have little impact on the noise if the observation is limited by Poisson noise from the target or sky (A << B*t).
Table 2. Recommended Number of Sub-Exposures
Total Exposure Recommended Number of Sub-Exposures
Time (sec.)
Robust Programs Search Programs
-------------- --------------- ---------------
0-300 2 3
300-600 2 4
600-1600 3 4
1600-5000 3 5
5000-10000 4 6
>10000 one exp. per orbit one exp. per orbit
These values were estimated under the assumption that a 1% probability of irrecoverable damage to a 1 arcsec. square target was acceptable for "robust programs." But only 0.01 corrupted pixels per CCD was acceptible in the combined image for "search programs."
We note that the telescope scheduling software automatically splits all exposures longer that 600 sec. into two sub-exposures, unless CR-SPLIT=NO is specified.
Example: For the 7250 sec. exposure estimated above of a nebula say 1" in size, we would want 4 sub-exposures per Table 2 above. (We would consider this a "robust" program, since we are interested only in a small region of the detector where the nebula is.) Considering the allowed WFPC2 exposure times, we might request four 1900 sec. exposures. We note that A << B*t (28 << 1428), so that Poisson noise dominates, and hence no compensation is needed for splitting the exposure.
In general, it will be advantageous to dither the pointing of the split exposures by integral pixels, so as to aid in removal of hot pixels. For the PC a dither of POS TARG 0.501, 0.501 arcsec. is recommended, and on the WFC we recommend 0.498, 0.498 arcsec., as these are nearly ingegral pixel dithers in all four CCDs. See memos elsewhere on dithering.
Appendix
Appendix 1. Directory of Stars in Bruzual-Persson-Gunn-Stryker Spectrophotometric Atlas.
ID STAR NAME SP T AV V U-B B-V V-R R-I V-K 1 9 SGR O5 1.120 4.794 -1.150 -0.337 -0.397 -0.437 -0.930 2 9 SGE O8F 1.010 5.264 -1.114 -0.323 -0.385 -0.475 -0.930 3 HR 8023 O6 1.140 4.829 -1.083 -0.313 -0.393 -0.472 -0.930 4 -1 935 B1V 0.218 4.961 -0.955 -0.263 -0.342 -0.398 -0.810 5 60 CYG B1V 0.170 5.277 -0.911 -0.269 -0.369 -0.435 -0.850 6 102 HER B2V 0.250 4.007 -0.831 -0.245 -0.360 -0.447 -0.740 7 ETA HYA B3V 0.030 4.134 -0.684 -0.201 -0.312 -0.347 -0.610 8 IOTA HER B3V 0.075 3.685 -0.665 -0.203 -0.323 -0.380 -0.610 9 HR 7899 B4V 0.070 5.831 -0.652 -0.195 -0.340 -0.386 -0.570 10 38 OPH A1V 0.510 5.351 -0.490 -0.139 -0.293 -0.330 -0.380 11 HR 7174 B6V -0.060 5.977 -0.287 -0.107 -0.255 -0.306 -0.280 12 9 VUL B7V -0.080 5.147 -0.283 -0.099 -0.254 -0.273 -0.240 13 HD 189689 B9V 0.090 7.203 -0.228 -0.081 -0.251 -0.250 -0.180 14 THETA VIR A0V 0.030 4.278 0.150 -0.026 -0.210 -0.222 -0.060 15 NU CAP B9V -0.060 4.843 0.052 -0.020 -0.211 -0.213 -0.040 16 HR 6169 A2V 0.067 6.373 0.177 -0.017 -0.203 -0.246 -0.040 17 HD 190849A A1V 0.300 6.825 0.113 0.009 -0.219 -0.215 0.020 18 69 HER A2V 0.032 4.561 0.167 0.000 -0.203 -0.235 0.000 19 HD 190849B A3V 0.300 7.271 0.180 0.057 -0.194 -0.196 0.150 20 58 AQL A0V 0.056 5.534 0.193 0.057 -0.170 -0.168 0.150 21 78 HER B9V -0.290 5.972 0.215 0.036 -0.170 -0.190 0.100 22 HR 6570 A7V 0.039 6.001 0.262 0.107 -0.165 -0.209 0.290 23 HD 187754 A2V 0.110 8.365 0.343 0.125 -0.131 -0.114 0.360 24 THETA1 SER A5V 0.026 4.554 0.225 0.143 -0.120 -0.153 0.400 25 PRAESEPE 276 0.007 7.558 0.317 0.159 -0.091 -0.132 0.420 26 PRAESEPE 114 0.007 8.223 0.255 0.175 -0.074 -0.117 0.460 27 PRAESEPE 154 0.086 8.399 0.207 0.219 -0.065 -0.093 0.560 28 HD 190192 A5V 0.155 8.507 0.216 0.231 -0.048 -0.083 0.610 29 PRAESEPE 226 0.086 8.801 0.180 0.275 -0.012 -0.052 0.720 30 PRAESEPE 37 0.086 8.906 0.155 0.306 0.010 -0.053 0.810 31 HD 191177 F4V 0.099 8.731 0.220 0.309 0.035 -0.047 0.840 32 PRAESEPE 332 0.086 9.617 0.079 0.389 0.070 -0.008 1.010 33 BD+293891 F6V 0.092 9.085 0.114 0.398 0.098 0.000 1.040 34 PRAESEPE 222 0.086 10.016 0.089 0.430 0.096 0.031 1.110 35 HD 35296 F8V 0.010 4.833 0.100 0.489 0.157 0.059 1.210 36 BD+263780 G0V 0.045 8.433 0.088 0.503 0.164 0.053 1.240 37 HD 148816 F9V 0.028 7.257 -0.030 0.509 0.179 0.093 1.260 38 HD 155675 F8V 0.051 8.427 0.042 0.508 0.186 0.090 1.260 39 PRAESEPE 418 0.087 10.482 0.144 0.527 0.160 0.059 1.270 40 HYAD 1 0.027 7.345 0.196 0.530 0.169 0.066 1.270 41 HD 122693 F8V 0.040 7.999 0.207 0.511 0.194 0.043 1.250 42 HD 154417 F8V 0.017 5.941 0.131 0.538 0.181 0.058 1.290 43 HYAD 2 0.027 7.715 0.223 0.579 0.194 0.072 1.380 44 HD 227547 G5V 0.062 9.843 0.230 0.589 0.201 0.089 1.400 45 HD 154760 G2V 0.041 8.639 0.204 0.586 0.211 0.096 1.390 46 HD 190605 G2V 0.027 7.639 0.283 0.593 0.204 0.078 1.400 47 HYAD 15 0.027 8.014 0.285 0.620 0.223 0.105 1.470 48 HD 139777A K0V 0.010 6.637 0.204 0.631 0.244 0.094 1.490 49 HD 136274 G8V 0.020 7.849 0.410 0.672 0.283 0.123 1.550 50 HYAD 26 0.028 8.559 0.407 0.710 0.259 0.115 1.620 51 HD 150205 G5V 0.021 7.468 0.383 0.700 0.257 0.141 1.620 52 HYAD 21 0.028 9.060 0.536 0.766 0.282 0.152 1.780 53 +02 3001 G8V 0.017 7.448 0.470 0.789 0.365 0.175 1.840 54 HD 190571 G8V 0.017 7.430 0.587 0.816 0.338 0.200 1.950 55 HYAD 183 0.027 9.636 0.778 0.887 0.390 0.216 2.150 56 HD 190470 K3V 0.013 7.820 0.810 0.895 0.389 0.202 2.170 57 HD 154712 K4V 0.016 8.623 0.987 0.967 0.491 0.268 2.390 58 HYAD 185 0.027 9.410 0.999 1.074 0.548 0.341 2.680 59 +38 2457 K8V 0.012 9.773 1.170 1.057 0.555 0.272 2.600 60 HYAD 173 0.027 10.389 1.302 1.202 0.650 0.407 3.030 61 GL 40 M0V 0.008 8.860 1.305 1.269 0.756 0.475 3.260 62 HYAD 189 0.027 11.027 1.387 1.319 0.749 0.488 3.400 63 HD 151288 K7V 0.007 8.031 1.344 1.350 0.764 0.504 3.520 64 HD 157881 K7V 0.005 7.508 1.370 1.332 0.791 0.525 3.470 65 HD 132683 M0V 0.009 9.347 1.378 1.342 0.829 0.524 3.500 66 GL 15A M0V 0.005 8.030 1.331 1.514 1.057 0.812 4.030 67 GL 49 M2V 0.005 9.458 1.336 1.443 1.056 0.832 4.160 68 GL 109 M4V 0.005 10.490 1.380 1.501 1.233 1.044 4.620 69 GL 15B M6V 0.004 11.002 1.574 1.707 1.463 1.221 5.040 70 GL 83.1 M8V 0.005 12.235 1.450 1.704 1.674 1.404 5.580 71 GL 65 M5V 0.009 11.999 1.223 1.768 2.082 1.741 6.670 72 HR 7567 B1IV 0.640 5.142 -0.861 -0.249 -0.380 -0.443 -0.780 73 HR 7591 B2III 0.130 5.835 -0.844 -0.249 -0.343 -0.407 -0.780 74 20 AQL B3IV 0.670 4.471 -0.542 -0.156 -0.306 -0.340 -0.440 75 HR 7467 B3III 0.130 6.481 -0.569 -0.182 -0.318 -0.372 -0.540 76 IOTA LYR B7IV 0.030 5.390 -0.417 -0.132 -0.282 -0.308 -0.380 77 HR 7346 B7III -0.050 6.431 -0.288 -0.108 -0.269 -0.297 -0.280 78 59 HER A3III 0.067 5.357 0.200 -0.045 -0.239 -0.238 -0.100 79 HR 6642 A0IV 0.090 6.031 0.066 -0.041 -0.249 -0.268 -0.080 80 11 SGE B9IV -0.040 5.832 0.033 -0.027 -0.228 -0.264 -0.060 81 60 HER A3IV 0.041 4.780 0.227 0.085 -0.156 -0.186 0.240 82 HD 192285 A4IV 0.174 7.963 0.239 0.124 -0.144 -0.142 0.360 83 ALPHA OPH A5III 0.014 2.035 0.239 0.152 -0.108 -0.149 0.420 84 HD 165475B A5IV 0.085 7.478 0.317 0.229 -0.078 -0.123 0.590 85 HD 165475 A5IV 0.071 7.072 0.256 0.245 0.001 -0.026 0.650 86 XI SER F0IV 0.015 3.487 0.257 0.240 -0.040 -0.081 0.640 87 HD 5132 F0IV 0.064 7.559 0.182 0.287 -0.003 -0.082 0.740 88 HD 508 A9IV 0.124 8.115 0.279 0.305 0.001 -0.049 0.810 89 HD 210875 F0IV 0.149 8.523 0.302 0.317 -0.020 -0.050 0.860 90 RHO CAP F2IV 0.025 4.709 0.137 0.339 0.049 -0.017 0.930 91 HD 7331 F7IV 0.080 7.156 0.125 0.427 0.083 -0.004 1.090 92 BD+630013 F5IV 0.159 8.664 0.096 0.444 0.082 0.011 1.140 93 HD 13391 G2IV 0.095 8.531 0.180 0.546 0.194 0.049 1.300 94 HD 154962 G8IV 0.031 6.228 0.365 0.644 0.226 0.110 1.500 95 HD 192344 G4IV 0.059 7.671 0.368 0.646 0.218 0.113 1.500 96 HR 6516 G6IV 0.021 5.270 0.375 0.651 0.217 0.077 1.510 97 HR 7670 G6IV 0.026 5.718 0.478 0.672 0.229 0.079 1.510 98 HD 128428 G3IV 0.055 7.647 0.503 0.715 0.262 0.121 1.650 99 31 AQL G8IV 0.019 5.128 0.482 0.732 0.273 0.093 1.660 100 -02 4018 G5IV 0.080 8.595 0.583 0.791 0.353 0.153 1.850 101 M67 F143? 0.144 11.203 0.624 0.807 0.343 0.156 1.890 102 HD 11004 G5IV 0.073 7.951 0.532 0.825 0.389 0.242 1.970 103 HD 173399A G5IV 0.048 7.196 0.613 0.808 0.331 0.213 1.920 104 HD 56176 G7IV 0.031 6.233 0.629 0.857 0.364 0.230 2.010 105 HD 227693 G5IV 0.125 9.043 0.740 0.868 0.352 0.207 2.030 106 HD 199580 K2IV 0.052 7.136 0.835 0.881 0.385 0.206 2.080 107 HD 152306 G8III 0.090 6.923 0.695 0.880 0.355 0.169 2.060 108 PRAESEPE 212 0.084 6.451 0.837 0.894 0.361 0.208 2.100 109 THETA1 TAU G8III 0.027 3.694 0.872 0.904 0.366 0.219 2.120 110 HD 170527 G5IV 0.040 6.713 0.789 0.918 0.390 0.233 2.160 111 HD 136366 K0III 0.072 6.090 0.930 0.931 0.373 0.243 2.200 112 HD 191615 G8IV 0.061 7.708 0.890 0.947 0.422 0.258 2.210 113 HD 124679 K0III 0.045 5.112 0.893 0.946 0.383 0.221 2.210 114 HD 131111 K0III 0.049 5.336 0.939 0.956 0.428 0.282 2.250 115 HD 113439 K0III 0.070 7.143 1.045 0.957 0.421 0.206 2.230 116 HD 4744 G8IV 0.055 7.498 0.876 0.989 0.472 0.290 2.350 117 HD 7010 K0IV 0.071 8.006 0.904 0.994 0.453 0.270 2.320 118 46 L MI K0III 0.025 3.672 1.033 0.991 0.447 0.263 2.320 119 91 AQR K0III 0.031 4.130 1.123 1.010 0.440 0.253 2.360 120 M67 F141 0.145 10.196 1.144 1.007 0.431 0.226 2.350 121 HR 8924A K3III 0.073 6.104 1.253 1.015 0.417 0.229 2.350 122 HD 140301 K0IV 0.031 6.269 1.164 1.016 0.438 0.280 2.380 123 HD 95272 K0III 0.030 3.964 1.107 1.041 0.453 0.292 2.440 124 HD 72184 K2III 0.061 5.670 1.245 1.051 0.431 0.266 2.450 125 HD 119425 K2III 0.046 5.179 1.167 1.042 0.441 0.254 2.420 126 HD 106760 K1III 0.040 4.850 1.196 1.074 0.473 0.277 2.510 127 PSI U MA K1III 0.018 2.861 1.244 1.081 0.479 0.289 2.520 128 PHI SER K1III 0.054 5.448 1.308 1.067 0.400 0.242 2.480 129 HD 136514 K3III 0.065 5.303 1.442 1.105 0.461 0.289 2.570 130 MU AQL K3III 0.050 4.355 1.366 1.123 0.484 0.266 2.600 131 HR 5227 K2IIIP 0.067 6.168 1.364 1.146 0.511 0.293 2.650 132 HD 154759 K3III 0.122 8.093 1.413 1.172 0.543 0.288 2.720 133 20 CYG K3III 0.064 4.931 1.690 1.198 0.473 0.292 2.760 134 ALPH SER K2III 0.015 2.508 1.360 1.097 0.469 0.297 2.550 135 MU LEO K2III 0.026 3.733 1.520 1.172 0.520 0.301 2.730 136 +1 3131 K0III 0.076 6.402 1.203 1.143 0.520 0.312 2.660 137 M67 F170 0.144 9.415 1.662 1.237 0.585 0.340 2.870 138 18 LIB A K2IIIP 0.060 5.726 1.525 1.189 0.519 0.352 2.600 139 +28 2165 K1IV 0.073 9.557 1.642 1.259 0.614 0.358 2.950 140 NGC 188 1_69 0.100 12.229 1.544 1.232 0.568 0.383 2.900 141 +30 2344 K3III 0.077 10.239 1.691 1.263 0.630 0.373 2.950 142 HD 83618 K3III 0.037 3.741 1.550 1.262 0.602 0.387 2.960 143 HD 158885 K3III 0.144 7.025 1.522 1.260 0.600 0.420 2.970 144 HD 166780 K5III 0.138 7.188 1.791 1.323 0.652 0.422 3.120 145 HD 148513 K4III 0.074 5.260 1.939 1.386 0.591 0.426 3.310 146 M67 T626 0.144 9.107 1.858 1.391 0.672 0.433 3.310 147 HD 127227 K5III 0.084 7.298 1.999 1.389 0.739 0.481 3.320 148 M67 IV-202 0.146 8.533 2.070 1.463 0.777 0.512 3.480 149 HD 50778 K4III 0.044 3.888 1.846 1.384 0.707 0.523 3.310 150 HD 62721 K5III 0.067 4.650 1.868 1.393 0.730 0.529 3.340 151 HD 116870 M0III 0.069 5.097 1.896 1.413 0.776 0.571 3.410 152 HD 60522 M0III 0.049 3.844 2.037 1.482 0.803 0.602 3.680 153 -1 3113 K5III 0.125 8.161 2.334 1.609 0.860 0.609 3.790 154 +2 2884 K5III 0.090 6.623 2.046 1.434 0.838 0.629 3.550 155 -2 3873 M0III 0.096 6.906 2.135 1.549 1.060 0.850 4.320 156 HD 104216 M2III 0.097 5.972 1.935 1.523 1.037 0.872 4.300 157 HD 142804 M1III 0.121 6.386 2.309 1.694 1.023 0.907 4.280 158 HD 30959 M3III 0.065 4.469 2.142 1.705 1.297 1.064 4.860 159 HD 151658 M2III 0.194 7.212 2.305 1.770 1.361 1.119 5.000 160 -2 4025 M2III 0.120 8.843 2.038 1.643 1.420 1.195 5.180 161 -01 3097 M2III 0.125 9.038 2.058 1.612 1.510 1.279 5.300 162 TX DRA 0.112 7.049 1.885 1.547 1.525 1.339 5.400 163 Z CYG M8III 0.305 8.246 1.881 1.569 1.615 1.358 5.540 164 +01 3133 M5III 0.120 8.944 1.713 1.498 1.774 1.506 5.820 165 -2 3886 M5III 0.102 9.021 1.615 1.544 1.927 1.583 6.060 166 W HER M6III 0.115 10.578 0.818 1.099 2.562 1.959 7.000 167 TY DRA M8 0.144 8.777 1.267 1.564 2.347 1.969 6.740 168 SW VIR M7III 0.087 6.948 1.009 1.674 2.779 2.110 7.350 169 RZ HER M6III 0.310 12.767 0.126 1.380 3.068 2.397 7.000 170 R LEO 0.110 8.861 0.315 1.918 3.672 2.789 7.000 171 AW CYG N 0.324 8.215 2.614 3.790 1.650 0.956 7.000 172 WZ CAS N 0.327 6.535 3.579 2.636 1.397 1.073 7.000 173 69 CYG B0IB 0.442 5.511 -1.028 -0.234 -0.370 -0.395 -0.600 174 HR 7699 B5IB 1.051 5.167 -0.585 -0.190 -0.320 -0.376 -0.450 175 HR 8020 B8IA 1.333 4.395 -0.552 0.027 -0.153 -0.196 0.160