Last Update: 1st August 2017

# A Manual of Time Estimator

This page is designed to explain the usage of the time estimators for line observations. There are two time estimators: one is for position switching observations, the other is for On-The-Fly observations. Applicants who aim to observe multi-line and/or multi-targets are requested to estimate the observing time for all the lines and targets and append (i.e., copy and paste) the results after the Science and Technical Justification. Note that NRO requests applicants who wish to carry out continuum observations to estimate the observing time by themselves. The estimation procedure is shown in Observing Plan for Continuum Observations.

## Links to the Time Estimators

For position switch observations:
Time Estimator for PSW

For On-The-Fly observations:
Time Estimator for OTF

## A Manual of Time Estimator for Position Switching Observations

Since the time estimator uses JavaScript, please enable JavaScript. If JavaScript is forbidden in your browser, the message will be printed on "* Messsages:" 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:
• Single beam
2-Beam (FOREST Beam1 and Beam3)

Choose the number of beams of the receiver.
Except for On-On observations with FOREST receiver, your choice is only "Single beam". If you intend to observe On-On 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
• Single
Double

Choose the polarisation you want to obtain.
Some receivers can obtain the right-hand circular polarisation (RHCP) and the left-hand circular polarisation (LHCP), or horizontal (H) and vertical (V) polarisations simultaneously if your array setup of the backend permits (You can easily check details of each receiver at Capability of the 45-m 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 45-m 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 (Tsys input). The system temperature varies with the season mainly due to humidity. Thus this value is not directly used to calculate the observing time. Since the atmosphere strongly affects on 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:

For Semester A (December-February),

Tsys obs=Tsys input exp[τSemester A{sec ELmax-sec (20 deg.)}]

For Semester B (March-May),
Tsys obs=Tsys input exp[τSemester B*sec ELmaxSemester A*sec(20 deg.)]

where ELmax 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 Semester A τSemester A
Optical Depth of
the Earth Atmosphere
in Semester B τSemester B
20--46 0.070 0.150
46--71 Not Available*) Not Available*)
71--112 0.090 0.350
112--116 0.220 0.500
*) No receiver covers this frequency range.

• 4. Trms (Ta*) (K) required
• Provide 1 σ noise temperature in TA* in the unit of Kelvin.

• 5. Total number of different ON points (>1 for mapping; =1 for using 2-Beam)
• 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 (2-Beam: blank)
• Provide the number of ON positions at the interval of OFF-source observations.
The interval between OFF-source observations is determined by the sky condition and the baseline stability. Generally saying, the interval between OFF-source observations under a clear sky is about 1--1.5 minutes. Therefore, the number of ON position at the interval of OFF-source observations is 1--3 taking into account for the telescope movement.

• 8. Maximum Elevation of the Target (deg)
• Describe the maximum elevation of targets.
Note that the observable elevation range of the telescope is 11--80 degrees. If your target reaches higher than 80 degrees, please input 80 for this field.

• 9. Frequency (GHz)
• Indicate the frequency of targets.
This value is used for the correction of system temperature. The frequency range is limited to 20--116 GHz which is covered by the receivers mounted on the Nobeyama 45-m 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 assuming that the observing frequency specified in the field 8 can be approximated to rest frequency of the target line. Therefore, if you want to observe high-z objects (> ~10000 km s-1), you must choose frequency resolution mode or calculate velocity resolution regarding the Doppler effect.

By clicking "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:

First four items are estimations for Semester A (from December to March).

• Scan number for one ON-point_sa =
• The number of scans for one ON-point when the observation will be done in Semester A.
• Tsys_obs_sa = (K)
• Expected system temperature at the maximum elevation of the target in Semester A.
• Total obs. time_sa = (min)
• The total observing time for Semester A to achieve the required rms noise level in the unit of minutes.
• Total obs. time_sa = (hr)
• Same as above but in the unit of hours.

Following items are estimations for Semester B (from March to May).
• Scan number for one ON-point_sb =
• The number of scans for one ON-point in case of the observation in Semester B.
• Tsys_obs_sb = (K)
• Expected system temperature at the maximum elevation of the target in Semester B.
• Total obs. time_sb = (min)
• Total observing time in Semester B to achiesve the required rms noise level in the unit of minutes.
• Total obs. time_sb = (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_sa (or Total obs. time_sb) to obtain final total observing time.

2. Scan number = (Number of Beams) * (Number of Sequences: on-off or on-on is one sequence), NOT includes polarization.
The resultant "Scan number for one ON-point" is a number of scans to be observed for one beam (polarisation). Therefore, if you intend to obtain two polarisations simultaneously, you need to include two polarisations in one "Device Table" when you make observing scripts.

Please copy and paste the input parameters and the results on 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.

## A Manual of Time Estimator for On-The-Fly Observations

Since the time estimator uses JavaScript, please enable JavaScript. If JavaScript is forbidden in your browser, the message will be printed on "* Messsages:" field.

The explanation for Time Estimator for OTF Observations is described in this section. For detailed information about On-The-Fly observations, applicants should refer to A Guide to OTF Observations with 45-m. Especially on choosing observing parameters, refer to Determining Parameters and Sensitivities.

In order to calculate the observing time for OTF, there are 14 parameters to be filled:
• Single
FOREST

Select the receiver which you want to use. "Single" means On-The-Fly observation with a single beam receiver.

• 2. Polarization
• Single
Double

Specify the number of polarisations to obtain. You can easily consult which receiver can obtain double (Horizontal and Vertical, or Right-hand circular polarisation and Left-hand circular polarisation) polarisations at Capability of the 45-m 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 20--116 GHz which is covered by the receivers mounted on the Nobeyama 45-m 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.

• 5. Length of mapping area along the Scans (arcsec)
• Indicate the length of mapping area along the scans in arcsec.
Note that to overlap the scans of four beams of FOREST, the length of mapping area along the scans is 50" larger than the length you want to map.

• 6. Length of mapping area perpendicular to the scans (arcsec)
• Indicate the length of mapping area perpendicular to the scans in arcsec.
As the reason described above, the length of 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 Hints on Choosing Parameters at the OTF page.

• 8. 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).

• 9. 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. Taking the antenna jitters etc. into account, oversampling is recommended (about 1/3 of the HPBW).

• 10. 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 45-m telescope.

• 11. OFF-point separation (arcmin)
• Provide the separation of OFF-point from the centre of the map in arcminutes.

• 12. Tsys (K)
• Input the typical system temperature read from figures presented in Capability of the 45-m 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 (Tsys input).

The system temperature varies with the season mainly due to humidity. Thus Tsys input is not directly used to calculate the observing time. Since the atmosphere strongly affects on the system temperature, it is important to correct the system temperatrue 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:

For Semester A (December-February),

Tsys obs=Tsys input exp[τSemester A{sec ELmax-sec (20 deg.)}]

For Semester B (March-May),
Tsys obs=Tsys input exp[τSemester B*sec ELmaxSemester A*sec(20 deg.)]

where ELmax 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 Semester A τSemester A
Optical Depth of the Earth Atmosphere
in Semester B τSemester B
20--46 0.070 0.150
46--71 Not Available*) Not Available*)
71--112 0.090 0.350
111--116 0.220 0.500
*) No receiver covers this frequency range.

• 13. 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 assuming that the observing frequency specified in the field 3 can be approximated to a rest frequency of the target line. Therefore, if you want to observe high-z objects (> ~10000 km s-1), you must choose a frequency resolution mode or calculate a velocity resolution regarding the Doppler effect.

• 14. 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" in 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] = Not available (Note theta = 0)
• An initial rotation angle of a rotator. The initial rotation angle set to be 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. In the 2017--2018 observing season, 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 the scans - 50")*(Length of mapping area perpendicular to the scans - 50").
• 3.vscan is ["/sec] ( per 0.1s sample)
• A scan speed of the Nobeyama 45-m telescope in case that data dump time is 0.1 second.
NRO recommends that (scan speed ["/sec]) x (dump time 0.1[sec]) should not 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 accerelate the telescope for each scan, to transit the telescope to next scan and transit to OFF-point. tapp and ttran will be used to make observing scripts.
• 6.tOFF = [sec] -> [sec]
• An observing time for OFF-point 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 ON-source 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 1.3 to ttot(OBS) to obtain final total observing time (For FOREST, the overhead factor is 1.4).
• 10.eta(ON/OBS) =
• The ON-source efficiency.
This value is derived by calculating ttot(ON)/ttot(OBS)
• 11.tcell(ON) [sec] =
• An ON-source time per one map grid per one observing script.
• 12.tcell(OFF) [sec] =
• An OFF-source time per one map grid per one observing script.
• 13.Tsys_inp [K] =
• The system temperature input by the user.
• 14.Tsys_obs_sa[K] =
• An expected system temperature at the maximum elevation of the target in Semester A.
• 15.dTa*_sb[K] =
• An expected noise temperature per one observing script for each map grid in TA* [K] which could be achieved in Semester A.
For FOREST, this value indicates the noise temperature for the area which four beams overlap. Applicants should use this value to calculate the total observing time.
• 16.Tsys_obs_sb[K] =
• An expected system temperature at the maximum elevation of the target in Semester B.
• 17.dTa*_sb [K] =
• Same as 15. but for Semester B.
• 18.Version =
• A version of the time estimator

The total observing time for your OTF observation can be calculated using 9. ttot(OBS), 15. dTa*_sa, and 17. dTa*_sb. Assume the rms noise which you are going to achieve is Trms, number of observing script to achieve Trms (N) can be calculated as


Nsa=(Trms/dTa*sa)2 (for Semester A),
Nsb=(Trms/dTa*sa)2 (for Semester B).

Therefore, the total on-source time can be written as

Nsattot(OBS) (for Semester A),
Nsbttot(OBS) (for Semester B).

Finally, multiplying the overhead factor (F), you can get the total observing time Tobs. The overhead factor is 1.3 except for FOREST whose overhead factor is 1.4.

Tobs sa= FNsattot(OBS) (for Semester A),
Tobs sb= FNsbttot(OBS) (for Semester B).


Please copy and paste the input parameters and the results on 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.