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A Manual of Time Estimator
Last Update: 27^{th} July 2020
A Manual of Time Estimator
This page is designed to explain the usage of the time estimators for line observations.
There are two types of time estimators: one is for position switching observations, the other is for OnTheFly observations.
Applicants who aim to observe multiline and/or multitargets are requested to estimate the observing time for all the lines and targets.
After the time estimation, applicants should append (i.e., copy and paste) the results after the Science and Technical Justification.
For position switch observations:
Time Estimator for PSW
For OnTheFly observations:
Time Estimator for OTF
Since the time estimator uses JavaScript, please enable JavaScript.
If JavaScript is forbidden in your browser, the message will be printed on "* Messages:" field.
The meaning of each parameter of Time Estimator for Position Switch (PSW) Observations is explained in this section.
If parameters you input are wrong, the error message will pop up.
The time estimator for PSW consists of 10 parameters:

1. Receiver
Single beam
2Beam (FOREST Beam1 and Beam3)
Choose the number of beams of the receiver.
Except for OnOn observations with FOREST receiver, your choice is only "Single beam".
If you intend to observe OnOn observations with FOREST receiver, you must check whether your target is compact enough compared to the beam separation of FOREST Beam1 and Beam3 (70 arcsec).

2. Polarization (Default: Double)
Single
Double
Choose the polarization you want to obtain.
Some receivers can obtain the righthand circular polarization (RHCP) and the lefthand circular polarization (LHCP), or horizontal (H) and vertical (V) polarizations simultaneously if your array setup of the backend permits.
You can quickly check the details of each receiver at Capability of the 45m Telescope for this season section in the status report.
Note that H40 receiver can only obtain LHCP (i.e., your choice is only "Single" for H40).

3. Tsys (K)
Input the typical system temperature read from figures presented in
Capability of the 45m Telescope for this season section in the status report.
The system temperature shown in
the status report was measured at the elevation of 70 degrees in winter, which should be the same as input by the user here (T
_{sys input}).
The input system temperature is not directly used to calculate the observing time.
Since the atmosphere strongly affects the system temperature, it is important to correct the system temperature to estimate the realistic observing time.
The correction of the system temperature due to elevation and optical depth of the Earth atmosphere is as follows:
Throughout Semester 2020 (DecemberApril),
T_{sys obs}=T_{sys input} exp[τ_{Mean}*sec EL_{max}τ_{Winter}*sec(20 deg.)]
where EL
_{max} is the maximum elevation of the targets.
You can estimate the maximum elevation of targets in Fig. 1 in
Target section.
The optical depth of the Earth atmosphere at Nobeyama is determined based on measurements by NRO.
Table 1 illustrates the optical depth of the Earth atmosphere at Nobeyama:
Table 1: Optical Depth of the Earth Atmosphere at Nobeyama
Observing Frequency (GHz) 
Optical Depth of the Earth Atmosphere in Winter τ_{Winter} 
Mean Optical Depth of the Earth Atmosphere τ_{Mean} 
2046 
0.070 
0.100 
4671.5 
Not Available^{*)} 
Not Available^{*)} 
71.5112 
0.090 
0.180 
112116 
0.220 
0.310 
*) No receiver covers this frequency range.

4. Trms (Ta*) (K) required
Provide 1 σ noise temperature in
T
_{A}
^{*} in the unit of Kelvin.

5. Total number of different ON points (>1 for mapping; =1 for using 2Beam)
Indicate the number of ON positions of your targets.

6. Integ. time of one scan (sec) (typically 20 sec, or shorter)
Give integration time of one scan in the unit of second.
The integration time of one scan is limited by the stability of the sky and the receiver.
NRO recommends the integration time of one scan of 20 seconds or shorter.

7. Number of ONs per OFF (2Beam: blank)
Provide the number of ON positions at the interval of OFFsource observations.
The sky condition and baseline stability limit the interval between OFFsource observations.
Generally saying, the interval between OFFsource observations under a clear sky is about 11.5 minutes.
Therefore, the number of ON position at the interval of OFFsource observations is 13 taking into account the telescope slewing time.

8. Maximum Elevation of the Target (deg)
Describe the maximum elevation of targets.
You can estimate the maximum elevation of targets in Fig. 1 in Target section.
Note that the observable elevation range of the telescope is 1180 degrees.
If your target reaches higher than 80 degrees, please input 80 for this field.

9. Frequency (GHz)
Indicate the frequency of the target line.
This value is used for the correction of system temperature.
The frequency range is limited to 2046 GHz and 71.5116 GHz which are covered by the receivers mounted on the Nobeyama 45m telescope.

10. Resolution
Frequency resolution (kHz)
Velocity resolution (km/s)
Specify desired frequency or velocity resolution.
In the process of calculating observing time, the program performs a conversion from velocity resolution to frequency resolution.
In this conversion, it assumes that the observing frequency specified in field 9 can be approximated to rest a frequency of the target line.
Therefore, if you want to observe highz objects (> ~10000 km s
^{1}), you must choose frequency resolution mode or calculate velocity resolution regarding the Doppler effect.
By clicking the "Calc" button, the calculation will be performed, and a summary of input parameters and results are shown at the bottom of the page unless the parameter(s) is/are false.
The meaning of the results is as follows:

Scan number for one ONpoint_sm =
The number of scans for one ONpoint when the observation will be done.

Tsys_obs_sm = (K)
Expected system temperature at the maximum elevation of the target.

Total obs. time_sm = (min)
The total observing time to achieve the required rms noise level in the unit of minutes.

Total obs. time_sm = (hr)
Same as above but in the unit of hours.

Version =
A version of the time estimator.
Note that
1. "Total obs. time" includes OFF integration and telescope slewing time, and NOT includes the overheads for pointing and tuning.
You must multiply the overhead factor of 1.3 to Total obs. time_sm to obtain final total observing time.
2. Scan number = (Number of Beams) * (Number of Sequences: onoff or onon is one sequence), NOT includes polarization.
The resultant "Scan number for one ONpoint" is a number of scans to be observed for one beam (polarization).
Therefore, if you intend to obtain two polarizations simultaneously, you need to include two polarizations in one "Device Table" when you make observing scripts.
Please copy and paste the input parameters and the results at the end of Science and Technical Justifications.
You can get correct display by enclosing these text with \begin{verbatim*} and \end{verbatim*} in LaTeX file.
Since the time estimator uses JavaScript, please enable JavaScript.
If JavaScript is forbidden in your browser, the message will be printed on "* Messages:" field.
The explanation for Time Estimator for OTF Observations is described in this section.
For detailed information about OnTheFly observations, applicants should refer to OTF Observations with the 45m telescope.
Especially in choosing observing parameters, refer to Determining Parameters and Sensitivities.
In order to calculate the observing time for OTF, there are 15 parameters to be filled:

1. Receiver
Single
FOREST
Select the receiver which you want to use.
"Single" means OnTheFly observation with a single beam receiver.

2. Polarization (Default: Double)
Single
Double
Specify the number of polarizations to obtain.
You can easily consult which receiver can obtain double (Horizontal and Vertical, or Righthand circular polarization and Lefthand circular polarization) polarizations at
Capability of the 45m Telescope for this season section in the Status Report page.
Note that H40 receiver can only obtain LHCP (i.e., your choice is only "Single" for H40).

3. Frequency (GHz)
Fill the frequency of targets taking into account the effect of the Doppler shift.
This value is used for the correction of the system temperature.
The frequency range is limited to 2046 GHz and 71.5116 GHz which are covered by the receivers mounted on the Nobeyama 45m telescope.

4. Maximum Elevation of the Target (deg)
Describe the maximum elevation of targets.
This value is used in order to correct atmospheric effects on the system temperature.
You can estimate the maximum elevation of targets in Fig. 1 in Target section.
Note that the observable elevation range of the telescope is 1180 degrees.
If your target reaches higher than 80 degrees, please input 80 for this field.

5. Length of mapping area along the Scans (arcsec)
Indicate the length of the mapping area along with the scans in arcsec.
Note that to overlap the scans of four beams of FOREST, the length of the mapping area along the scans is 50'' larger than the length you want to map.
In case of choosing a dump time of 0.04 second in field 8, the size of the mapping area is limited to 30 arcmin. ≤ size ≤ 60 arcmin.

6. Length of mapping area perpendicular to the scans (arcsec)
Indicate the length of the mapping area perpendicular to the scans in arcsec.
As the reason described above, the length of the mapping area perpendicular to the scans is 50'' larger than the length you want to map for FOREST.

7. Time for one scan (sec)
Fill in the time for one scan.
The time for one scan can be determined by the conditions explained in
Scan Pattern and Observation Parameters at the OTF page.
The observatory allows users the integration time of one scan between 10 and 30 seconds and recommends 20 seconds.
If scan speed is beyond the threshold at high EL, please arrange the parameters "5. Length of mapping area along the scans" and "7.Time for One scan".

8. Dump Time (sec)
Choose data dump time from 0.1 sec and 0.04 sec.
Note that data dump time does not affect the sensitivity.

9. Number of ONs per OFF
Describe the number of ONs per OFF.
Typically, this number is 1 or 2 (mainly depending on the baseline stability).

10. Separation between the scans (arcsec)
Indicate a separation between the scans in arcsecond.
Spacings between scan rows should be smaller than the Nyquist sampling rate (1/2 of the HPBW).
Taking the antenna jitters etc. into account, oversampling is recommended (about 1/3 of the HPBW).

11. Map grid (arcsec)
Input map grid in arcsec.
It is recommended to set the map grid is larger than or equals to scan separations.
For the Nyquist sampling, this value must be smaller than 1/2 of the HPBW of the beam of the Nobeyama 45m telescope.

12. OFFpoint separation (arcmin)
Provide the separation of OFFpoint from the centre of the map in arcminutes.

13. Tsys (K)
Input the typical system temperature read from figures presented in
Capability of the 45m Telescope for this season section in the status report.
The system temperature shown in
the status report was measured at the elevation of 70 degrees in winter, which should be the same as input by the user here (T
_{sys input}).
The input system temperature is not directly used to calculate the observing time.
Since the atmosphere strongly affects the system temperature, it is important to correct the system temperature to estimate the realistic observing time.
The correction of the system temperature due to elevation and optical depth of the Earth atmosphere is as follows:
Throughout Semester 2020 (DecemberApril),
T_{sys obs}=T_{sys input} exp[τ_{Mean}*sec EL_{max}τ_{Winter}*sec(20 deg.)]
where EL
_{max} is the maximum elevation of the targets.
You can estimate the maximum elevation of targets in Fig. 1 in
Target section.
The optical depth of the Earth atmosphere in Nobeyama is determined based on measurements by NRO.
Following table illustrates the optical depth of the Earth atmosphere at Nobeyama:
Table 1: Optical Depth of the Earth Atmosphere at Nobeyama
Observing Frequency (GHz) 
Optical Depth of the Earth Atmosphere in Winter τ_{Winter} 
Mean Optical Depth of the Earth Atmosphere τ_{Mean} 
2046 
0.070 
0.100 
4671.5 
Not Available^{*)} 
Not Available^{*)} 
71.5112 
0.090 
0.180 
112116 
0.220 
0.310 
*) No receiver covers this frequency range.

14. Resolution
Frequency Resolution (kHz)
Velocity Resolution (km/s)
Indicate the frequency resolution in kHz or the velocity resolution in km/s.
In the process of calculating observing time, the program automatically converts velocity resolution to frequency resolution.
In the conversion, it assumes that the observing frequency specified in field 3 can be approximated to a rest frequency of the target line.
Therefore, if you want to observe highz objects (>∼10000 km s
^{1}), you must choose a frequency resolution mode or calculate a velocity resolution regarding the Doppler effect.

15. Convolution function
Bessel*Gauss
Sinc*Gauss
Gauss
Pillbox
Spheroidal
Provide the convolution function on making a map.
The details can be found at
Convolution in "Make Map" on the OTF page.
When you click "calc" button, the observing time will be calculated with your input parameters, and a summary of input parameters and results are shown at the bottom of the page.
The meaning of the results is as follows:

1.theta [deg] = 0.0
An initial rotation angle of a rotator.
The initial rotation angle set to be 0.0 for all OTF observations.

2.Beam overlapped area = [''] * ['']
The beam overlapped area for observations with FOREST.
Since other receivers are all single beam, there is no meaning for these receivers.
The scans of 4 beams must be overlapped due to the limitation of the use of FOREST.
Thus, the beam overlapped area is (Length of mapping area along with the scans  50'')*(Length of mapping area perpendicular to the scans  50'').

3.vscan is [''/sec] ( per 0.1s sample or per 0.04s sample)
A scan speed of the Nobeyama 45m telescope in case that data dump time is 0.1 or 0.04 second.
The value of (scan speed[''/sec]) x (dump time 0.1 or 0.04 [sec] must be smaller than 1/2 of the HPBW.
NRO recommends that this value should be smaller than 1/3  1/4 of the HPBW.

4.Nrow =
A number of scans to map.

5.tapp [sec] = , ttran [sec] = , ttranoff [sec] =
Time to accelerate the telescope for each scan, to transit the telescope to next scan and transit to OFFpoint.
tapp and ttran will be used to make observing scripts.
When ttran [sec] = 99 is indicated, the scan speed is beyond the threshold at high EL.
Arrange the parameters "5. Length of mapping area along the scans" and "7.Time for One scan”.

6.tOFF = [sec] > [sec]
An observing time for OFFpoint per one sequence.
tOFF will also be used for making observing scripts.

7.tOH = [sec]
An overhead time per one scan row.

8.ttot(ON) [min] =
An expected total ONsource time per one observing script.

9.ttot(OBS) [min]/[hour] =
An expected total observing time per one observing script.
ttot(OBS) does not include the overheads for pointing and tuning.
You must multiply the overhead factor of 1.3 to ttot(OBS) to obtain final total observing time (For FOREST, the overhead factor is 1.4).

10.eta(ON/OBS) =
The ONsource efficiency.
This value is derived by calculating ttot(ON)/ttot(OBS)

11.tcell(ON) [sec] =
An ONsource time per one map grid per one observing script.

12.tcell(OFF) [sec] =
An OFFsource time per one map grid per one observing script.

13.Tsys_inp [K] =
The system temperature input by the user.

14.Tsys_obs_sm[K] =
An expected system temperature at the maximum elevation of the target.

15.dTa*_sm[K] =
An expected noise temperature per one observing script for each map grid in
T_{A}^{*} [K] which could be achieved.
For FOREST, this value indicates the noise temperature for the area in which four beams overlap.
Applicants should use this value to calculate the total observing time.

16.Version =
A version of the time estimator.
The total observing time for your OTF observation can be calculated using "9. ttot(OBS)" and "15. dTa*_sm".
Assume the rms noise which you are going to achieve is T_{rms},
number of observing script to achieve T_{rms} (N) can be calculated as
N=(T_{rms}/dT_{a}*_{sm})^{2}.
Therefore, the total onsource time can be written as
Nt_{tot(OBS)}.
Finally, multiplying the overhead factor (f), you can get the total observing time T_{obs}.
The overhead factor is 1.3 except for FOREST whose overhead factor is 1.4.
T_{obs}= fNt_{tot(OBS)}.
Please copy and paste the input parameters and the results at the end of Science and Technical Justifications.
You can get correct display by enclosing these text with \begin{verbatim*} and \end{verbatim*} in LaTeX file.
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A Manual of Time Estimator