urn:nasa:pds:uranus_occ_u149_irtf_320cm:data:2200nm_ring_four_egress_sqw
1.0
Diffraction square well model fit to the occultation profile of u149 (2MASS 20462044-1838345) by Uranus Ring four.
1.14.0.0
Product_Ancillary
French, Richard G.; McGhee-French, Colleen A.; Gordon, Mitchell K.
2020
model fit uranus rings
model fit uranus alpha
Input data and results of non-linear least squares fits of a diffraction square well model to the occultation profile of u149 (2MASS 20462044-1838345) by Uranus Ring four.
2021-04-05
1.0
Initial version
Science
Derived
Input data and results of non-linear least squares fits of a diffraction square well model (sqw) to the occultation profile of star u149 (2MASS 20462044-1838345) by Uranus Ring four. The square-well model is described in Elliot et al. (1984). In addition to this label file, this product consists of seven files describing the sqw as applied to the specified occultation. Those files are a single .pdf file containing plots showing the observations of an individual Uranus ring occultation profile and the best-fitting diffraction square-well model, for the given occultation event; a .txt file that contains a description of the observations being fitted, the conditions of the non-linear least squares fit, and the results of the fit; five .tab table files. The five table files are *_p.tab which contains time series observations of a single ring occultation, and corresponding model results; *_i.tab which contains intermediate model results; *_c.tab file which contains the composite convolution function c(t) for the model; the *_s.tab file which contains the strip brightness distribution of the occulted star; and the *_h.tab file which contains the impulse response of the detector. Note that some of these files will contain only a single line of data if none of the relevant model parameters are being fitted for a given individual ring profile.
Ring-Moon Systems
Ring Occultation Profile
Earth-based Observations of Uranus System Stellar Occultations
Observing Campaign
urn:nasa:pds:context:investigation:observing_campaign.earth-based-uranus-stellar-occultations
ancillary_to_investigation
Uranus Rings
Uranian Ring System
Ring
urn:nasa:pds:context:target:ring.uranus.rings
ancillary_to_target
four Ring of Uranus
Ring
The four ring of Uranus.
Center of motion: Uranus;
LID of central body: urn:nasa:pds:context:target:planet.uranus;
NAIF ID of central body: 799.
urn:nasa:pds:context:target:ring.uranus.four_ring
ancillary_to_target
SPK
ura111.bsp
SPK
vgr2.ura111.bsp
SPK
earthstns_itrf93_040916.bsp
BPC
earth_720101_031229.bpc
LSK
naif0012.tls
These kernel files were used in the generation of the products in the parent bundle. Some or all of them may not have been used directly in the generation of this product.
urn:nasa:pds:uranus_occ_support:document:earth-based-uranus-stellar-occultations-user-guide
ancillary_to_document
The User Guide for Earth-based Uranus Stellar Occultations.
urn:nasa:pds:uranus_occ_u149_irtf_320cm:data:2200nm_wavelengths
ancillary_to_data
Wavelengths and relative weights used in the calculation of diffraction pattern for square-well models of the individual ring profiles.
urn:nasa:pds:uranus_occ_u149_irtf_320cm:data:2200nm_counts-v-time_occult::1.0
ancillary_to_data
Normalized counts vs. time for the entire occcultion.
urn:nasa:pds:uranus_occ_u149_irtf_320cm:browse:2200nm_obs_geom
ancillary_to_document
Diagram of the Uranus system showing the occultation track.
urn:nasa:pds:uranus_occ_u149_irtf_320cm:browse:2200nm_earth
ancillary_to_document
Diagram of the view of the Earth from Uranus at mid-occultation Time.
urn:nasa:pds:uranus_occ_u149_irtf_320cm:browse:2200nm_alt
ancillary_to_document
Plot of the altitude (in degrees) of Uranus and the sun relative to the horizon over the duration of the occulation.
urn:nasa:pds:uranus_occ_u149_irtf_320cm:browse:2200nm_ring_sqw_gallery
ancillary_to_document
Gallery of square-well diffraction model fits to individual ring profiles.
Elliot et al. (1984). "Structure of the Uranian rings. I. Square-well model and particle-size constraints" Astron J. 89, 1587-1603. http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1984AJ.....89.1587E&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf
u149_irtf_320cm_2200nm_ring_four_egress_sqw.pdf
plots
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These plots show the observations of an individual Uranus ring occultation profile and the best-fitting diffraction square-well (sqw) model, for the specified occultation event.
upper left panel:
Comparison of observed count rate (black) as a function of time
(lower x axis), the best-fitting diffraction square well model (blue),
and the corresponding square well itself (red). The full and zero
stellar intensity levels are shown as dashed lines. The time-series data and the
best-fitting model are included in the corresponding ring model *.tab
file with a name given by
event_obs_tel_wl_ring_name_direction_sqw_p.tab
(ex: u17b_saao_188cm_2220nm_ring_six_ingress_sqw_p.tab)
upper right panel:
Same as upper left panel, but normalized to units of the flux of the
unocculted star, so that the upper free-space baseline is 1.0 and 0.0
represents a complete loss of the stellar signal.
lower left panel:
The model diffraction pattern (blue) for the square well itself (red),
averaged over the filter bandbass and (possibly) at a higher time
resolution than the observations themselves that are shown in the upper left
panel. Especially for data sets with rather low time resolution, it is
necessary to subdivide the observed time per bit (dt) into a
higher-resolution "mesh." The number of mesh points (m) is always an odd
integer. Then, when computing the best-fitting square well model to the
actual data, the (possibly) higher-resolution model profile is summed over
m points. Frequently, this summing converts a smooth- and
continuous-looking diffraction pattern into a jagged pattern, reflecting
the fact that the integration time dt is often longer than the time
scale of variation of the diffraction pattern of the ring. The time-series
model at the subdivided time resolution dt/m is included in the
corresponding ring model *.tab file with a name given by
event_obs_tel_wl_ring_name_direction_sqw_p.tab
(ex: u17b_saao_188cm_2220nm_ring_six_ingress_sqw_i.tab)
Also included in the lower left panel is a curve representing the
occultation star convolution kernel (the strip-brightness distribution of
the star), shown as a purple curve centered at the mid-point of the
geometric square well model. The time-series stellar convolution kernel is
contained in the corresponding ring model *.tab file with a name given by
event_obs_tel_wl_ring_name_direction_sqw_s.tab
(ex: u17b_saao_188cm_2220nm_ring_six_ingress_sqw_s.tab)
For IR data with an instrumental time constant included in the square-well
diffraction model, the corresponding time constant convolution kernel is
included in the lower left planel plot as a green line, and in the
the corresponding ring model *.tab file with a name given by
event_obs_tel_wl_ring_name_direction_sqw_h.tab
(ex: u17b_saao_188cm_2220nm_ring_six_ingress_sqw_h.tab)
When both a finite star (i.e., not a point source) and a non-zero
instrumental time constant are included in the square-well model, the
correspoinding joint convolution kernel from these two separate sources of
model smoothing is shown as an orange curve, and included in the
the corresponding ring model *.tab file with a name given by
event_obs_tel_wl_ring_name_direction_sqw_c.tab
(ex: u17b_saao_188cm_2220nm_ring_six_ingress_sqw_c.tab)
lower right panel:
Same as lower left panel, but normalized to units of the flux of the
unocculted star, so that the upper free-space baseline is 1.0 and 0.0
represents a complete loss of the stellar signal.
0
PDF
u149_irtf_320cm_2200nm_ring_four_egress_sqw.txt
summary
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This file provides details of the diffraction square-well model fitted to the observations of an individual Uranus ring, for the given occultation occultation event.
The first part of the file describes the IDL program that performed the fit
of the square-well (sqw) model to the data.
The occultation event, observatory, telescope, instrument, ring, and occultation
direction are defined.
DATA FILE INFORMATION documents the source data file and the specific subset
of data to be fitted in this sqw model.
EVENT INFORMATION provides additional information about the specific ring
event and event geometry.
SQUARE WELL MODEL INFORMATION specifies the number of mesh points m into
which each observed time bin is subsampled to provide higher time resolution
for the calculation of the square well diffraction pattern, before then
coadding the subsampled model to the time resolution of the data being
fitted.
SQUARE WELL MODEL FIT RESULTS contain the results of the non-linear
least-squares fit of the sqw model to the data, including post-fit
residuals, the initial and final parameter values, and their errors,
calculated assuming that all data points have equal weight. Parameters that
are fitted have an asterisk (*) preceding the corresponding Initial Value.
The correlation matrix is also shown, with obvious two-letter abbreviations
for the fitted variable names. Note that the underlying model is performed
in the time domain, but for convenience the corresponding length dimensions
for the square-well width, star diameter, equivalent width, and equivalent
depth are also shown. See Elliot et al. 1984 for further details.
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u149_irtf_320cm_2200nm_ring_four_egress_sqw_c.tab
composite-convolution
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This file contains the composite convolution function c(t) for the diffraction square well model fitted to the data. See Elliot et al. (1984) for details, and Table 1 for definitions of the fitted parameters.
0
39
UTF-8 Text
Provides the column headers, separated by commas, for the data table.
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69
The composite convolution function c(t) for the diffraction square well model fitted to the data. Columns 3 to the end contain partial derivatives of the model function C with respect to fittable parameters, as defined below. If a particular parameter is not being fitted for a specific model, the partial derivative with respect to that parameter is set to -9.9999900000E+99.
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C Time
1
1
ASCII_Real
17
Seconds
Time, relative to the square well model mid-time, of the calculated convolution function, in seconds.
C
2
19
ASCII_Real
18
Model composite convolution function, (Elliot et al. (1984), eq. 10).
dC/dTC
3
38
ASCII_Real
18
s*(-1)
Partial derivative dC/d(t_c), where C is the model composite convolution function and and t_c is the time constant of the detector. dC/dTC is given in inverse seconds. (Elliot et al. (1984), Table 1). Refer to the details of the fitted model function to determine whether the time constant is for a single- or double-pole filter - see also Eq. 9, Elliot et al. (1984).
-9.9999900000E+99
dC/dSTAR
4
57
ASCII_Real
18
s*(-1)
Partial derivative dC/dT_star, where C is the model composite convolution function and and T_star is the star diameter in seconds. dC/dSTAR is given in inverse seconds. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dC/dLIMB
5
76
ASCII_Real
18
Partial derivative dC/db, where C is the model composite convolution function and b is the limb darkening parameter (Elliot et al. (1984), Table 1.)
-9.9999900000E+99
u149_irtf_320cm_2200nm_ring_four_egress_sqw_h.tab
impulse-response
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This file contains the impulse response of the detector h(t) for the diffraction square well model fitted to the data.
0
19
UTF-8 Text
Provides the column headers, separated by commas, for the data table.
19
1
The impulse response of the detector h(t) for the diffraction square well model fitted to the data. See Elliot et al. (1984) for details,and Table 1 for definitions of the fitted parameters. Column 3 contains the partial derivatives of the model function H with respect to fittable parameters, as defined below. If a particular parameter is not being fitted for a specific model, the partial derivative with respect to that parameter is set to -9.9999900000E+99.
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3
0
57
H_TIME
1
1
ASCII_Real
17
s
Time, relative to the square well model mid-time, of the calculated convolution function, in seconds.
H
2
19
ASCII_Real
18
Impulse response of the detector h(t) (Elliot et al. (1984), eq. 9).
dH/dTC
3
38
ASCII_Real
18
s*(-1)
Partial derivative dH/dt_c, where t_c is the star diameter in seconds. dH/dTC is given in inverse seconds. (Elliot et al. (1984), Table 1). Refer to the details of the fitted model function to determine whether the time constant is for a single- or double-pole filter.
-9.9999900000E+99
u149_irtf_320cm_2200nm_ring_four_egress_sqw_i.tab
intermediate-model
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Intermediate model results for a diffraction square well model fit to the data.
0
60
UTF-8 Text
Provides the column headers, separated by commas, for the data table.
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4911
Intermediate model results for a diffraction square well model fit to the data. See Elliot et al. (1984) for details,and Table 1 for definitions of the fitted parameters. Columns 3 to the end contain partial derivatives of the model function I with respect to fittable parameters, as defined below. If a particular parameter is not being fitted for a specific model, the partial derivative with respect to that parameter is set to -9.9999900000E+99.
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I TIME
1
1
ASCII_Real
17
s
Time from the start of the time series data file used for the fit, for the middle of each calculation bin. The duration of each calculation bin is either equal to dt/n_mesh, where n_mesh is an odd number greater than or equal to 1, representing the sub-sampling of the observation integration time. See Elliot et al. (1984) Eq. 13. n_mesh is given by the time interval between successive TSEC values in the data being fitted (see the *_p.tab file corresponding to this *_i.tab file) divided by the time interval between successive I_TIME values in this file.
I BAR
2
19
ASCII_Real
18
Model value for the normalized signal for each time bin = Pbar(t) Eq. 7 Elliot et al. (1984).
dI/dT0
3
38
ASCII_Real
18
s*(-1)
Partial derivative dI/dt0, where I is the model function and t0 is the midtime of the square well model. dI/dT0 is given in inverse seconds. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dI/dW
4
57
ASCII_Real
18
s*(-1)
Partial derivative dI/dW, where I is the model function and W is the duration of the square well in seconds. dI/dW is given in inverse seconds. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dI/dV
5
76
ASCII_Real
18
s/km
Partial derivative dI/dv_perp, where I is the model function and v_perp is the component of the sky plane velocity of the star perpendicular to the local elliptical ring edge measured in km/sec. dI/dV is given is s/km. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dI/dF
6
95
ASCII_Real
18
Partial derivative dI/df_0, where I is the model function and f_0 is the fractional transmission. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dI/dEW
7
114
ASCII_Real
18
s*(-1)
Partial derivative dI/dE_0, where I is the model function and E_0 is the equivalent width in seconds. dI/dEW is given in inverse seconds. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dI/dED
8
133
ASCII_Real
18
Seconds
Partial derivative dI/dA_0, where I is the model function and A_0 is the equivalent depth in seconds. dI/dED is given in inverse seconds. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
u149_irtf_320cm_2200nm_ring_four_egress_sqw_p.tab
model-results
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Time series observations of a single ring occultation, and corresponding model results for a diffraction square well model fit to the data.
0
123
UTF-8 Text
Provides the column headers, separated by commas, for the data table.
123
24
Time series observations of a single ring occultation, and corresponding model results for a diffraction square well model fit to the data. See Elliot et al. (1984) for details,and Table 1 for definitions of the fitted parameters. Columns 4 to the end contain partial derivatives of the model function P with respect to fittable parameters, as defined below. If a particular parameter is not being fitted for a specific model, the partial derivative with respect to that parameter is set to -9.9999900000E+99.
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15
0
285
TSEC
1
1
ASCII_Real
17
s
Time in seconds from the start of the time series data file used for the fit, for the middle of each time bin.
DATA
2
19
ASCII_Real
18
Observed counts per second, for each time bin.
P
3
38
ASCII_Real
18
counts/s
P gives the model value for the recorded signal for each time bin. In Eq. 13, Elliot et al. (1984), P corresponds to n(t_i), where t_i is the time of the bin.
dP/dT0
4
57
ASCII_Real
18
counts/(s*2)
Partial derivative dP/dt0, where P is the model and t0 is the midtime of the square well model. dP/dT0 is given in counts/s^2. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dP/dW
5
76
ASCII_Real
18
Seconds
Partial derivative dP/dW, where P is the model and W is the duration of the square well in seconds. dP/dW is given in counts/s^2. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dP/dV
6
95
ASCII_Real
18
km*(-1)
Partial derivative dP/dv_perp, where P is the model and vperp is the component of the sky plane velocity of the star perpendicular to the local elliptical ring edge measured in km/sec. dP/dv_perp is given in inverse kilometers. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dP/dSTAR_CTS
7
114
ASCII_Real
18
dP/dSTAR_CTS: Partial derivative dP/dnbar_star, where P is the model and nbar_star is unocculted star level in counts/second. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dP/dBASE
8
133
ASCII_Real
18
dP/dBASE: Partical derivative dP/dnbar_b, where P is the model and nbar_b is the free-space background count rate in counts per second (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dP/dF
9
152
ASCII_Real
18
counts/s
Partial derivative dP/df_0, where P is the model and f_0 is the fractional transmission. dP/dF is given in counts/second. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dP/dSTAR
10
171
ASCII_Real
18
s*(-2)
Partial derivative dP/dT_star, where P is the model and T_star is the star diameter in seconds. dP/dSTAR is given in inverse seconds squared. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dP/dSLOPE
11
190
ASCII_Real
18
s
Partial derivative dP/d_ndot_b, where P is the model and n_dot_b is the background slope in counts/sec^2. dP/dSLOPE is given is seconds. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dP/dEW
12
209
ASCII_Real
18
s*(-2)
Partial derivative dP/dE_0, where P is the model and E_0 is the equivalent width in seconds. dP/dEW is given in inverse seconds squared. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dP/dED
13
228
ASCII_Real
18
s*(-2)
Partial derivative dP/dA_0, where P is the model and A_0 is the equivalent depth in seconds. dP/dED is given in inverse seconds squared. (Elliot et al. (1984), Table 1)
-9.9999900000E+99
dP/dLIMB
14
247
ASCII_Real
18
s*(-2)
Partial derivative dP/db, where P is the model and b is the limb darkening parameter. dP/dLIMB is given in inverse seconds squared. (Elliot et al. dP/dLIMB (1984), Table 1).
-9.9999900000E+99
dP/dTC
15
266
ASCII_Real
18
s*(-2)
Partial derivative dP/t_c, where P is the model and t_c is the time constant of the detector. dP/dEW is given in inverse seconds squared. (Elliot et al. (1984), Table 1) Refer to the details of the fitted model function to determine whether the time constant is for a single- or double-pole filter - see also Eq. 9, Elliot et al. (1984).
-9.9999900000E+99
u149_irtf_320cm_2200nm_ring_four_egress_sqw_s.tab
strip-brightness
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This file contains the strip brightness distribution of the occulted star s(t) for the diffraction square well model fitted to the data.
0
31
UTF-8 Text
Provides the column headers, separated by commas, for the data table.
31
35
the strip brightness distribution of the occulted star s(t) for the diffraction square well model fitted to the data. See Elliot et al. (1984) for details,and Table 1 for definitions of the fitted parameters. Columns 3 to the end contain partial derivatives of the model function S with respect to fittable parameters, as defined below. If a particular parameter is not being fitted for a specific model, the partial derivative with respect to that parameter is set to -9.9999900000E+99.
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4
0
76
S_TIME
1
1
ASCII_Real
17
s
Time, relative to the square well model mid-time, of the calculated convolution function, in seconds.
S
2
19
ASCII_Real
18
Model strip brightness distribution of the occulted star s(t) (Elliot et al. (1984), eq. 8)
dS/dSTAR
3
38
ASCII_Real
18
s*(-1)
Partial derivative dS/dT_star, where S is the model strip brightness distribution of the occulted star s(t) and T_star is the star diameter in seconds. dS/dSTAR is given in inverse seconds. (Elliot et al. (1984), Table 1).
-9.9999900000E+99
dS/dLIMB
4
57
ASCII_Real
18
Partial derivative dS/db, where S is the model strip brightness distribution of the occulted star s(t) and b is the limb darkening parameter (Elliot et al. (1984), Table 1)
-9.9999900000E+99