# Hubble Space Telescope 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.

```

#### 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

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 to advance to the next line) as above, we type ":go" and SYNPHOT returns this output:

```   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

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 to advance to the next line) as above, we type ":go" and SYNPHOT returns this output:

```   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

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

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

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

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.),
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),
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
```