AIPS Data Analysis Training
Step-by-step recipe
Hiroshi Imai (Department of Physics, Faculty of Science, Kagoshima University, Japan)
今井裕（鹿児島大学理学部物理科学科）
Version 1 on 22 March 2004
Version 5 on 26 October 2005

Contents
1 Introduction
1.1 About this AIPS tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Goal of this AIPS tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Task, verb and adverbs in AIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Calling tasks and verbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 AIPS catalog ﬁles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 RUN ﬁle in AIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 How to start AIPS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Preparing data
2.1 Visibility data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Flag information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Expected ﬂags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Accidental ﬂags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Calibration data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Antenna gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 System noise temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Visibility phase calibration tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9
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10
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3 Loading UV data
11
3.1 File name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Time interval in the calibration (CL) tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 MSORT: Sorting the UV data into time-baseline order . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 INDXR: Creating an index (NX) table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Watching UV data
13
4.1 Extension tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Scans, source information and frequency setups . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2.1 About scans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2.2 About sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2.3 About frequency setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Quantity of the visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.4 Antenna information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.5 Visibility along frequency and among IFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.5.1 Printing Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.5.2 Total power spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.5.3 Cross-power spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.6 Visibility along time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.7 Estimating a coherence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2

5 Strategy of observation and calibration (1)16
5.1 Observation schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.1.1 Fringe ﬁnders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.1.2 Clock parameter calibrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.1.3 Maser fringe ﬁnders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.1.4 Phase/position-reference sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1.5 Bandpass calibrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 Step-by-step calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.3 Selecting a reference antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.4 Fringe search window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.5 Set a coherence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6 Fundamental calibration
20
6.1 Plotting calibration solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.2 Applying calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.2.1 SOURCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.2.2 CALSOUR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.2.3 INTREPOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.2.4 CUTOFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.3 Sampling bias correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.4 Amplitude calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.4.1 Making gain and system temperature tables . . . . . . . . . . . . . . . . . . . . . . . . 22
6.4.2 Creating amplitude calibration solution . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.4.3 Parallactic angle correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.5 Fringe ﬁtting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.5.1 Averaging spectral channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.5.2 Fundamental fringe ﬁtting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7 Self-calibration and hybrid mapping
26
7.1 Making a source image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7.1.1 Dirty beam, dirty map and CLEAN map . . . . . . . . . . . . . . . . . . . . . . . . . 26
7.1.2 Split a single source ﬁle from a multi-source UV data . . . . . . . . . . . . . . . . . . 26
7.1.3 Making a dirty beam and a dirty map . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7.1.4 Controlling AIPS TV Server . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7.2 Iterative process in hybrid mapping and self-calibration . . . . . . . . . . . . . . . . . . . . . 28
7.2.1 Selfcalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.2.2 Making a CLEANed image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.2.3 Checking image statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.2.4 End of iteration process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
8 Strategy on observation and calibration (2)31
8.1 Group delay estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
8.2 Bandpass calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
8.3 Velocity tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
8.4 Amplitude calibration with maser emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
9 Advanced calibration
33
9.1 Bandpass response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
9.2 Doppler tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
9.2.1 Deﬁning the source velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
9.2.2 Converting visibility data from in frequency to in velocity domain . . . . . . . . . . . 34
9.3 Template method using maser emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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10 Watching maser emission
36
10.1 Amplitude variation along time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
10.2 Amplitude and phase variation along velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
10.3 Amplitude against u-v distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
11 Maser calibration
39
11.1 Interactive data ﬂagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
11.2 Fringe ﬁtting using maser data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
11.3 Edit SN tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
11.4 Self-calibration using maser data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
12 Search for maser emission
42
12.1 Field of view of maser source data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
12.2 Long-time data integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
12.3 Fringe-rate mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
12.3.1 Wide ﬁeld mapping with relative fringe rates . . . . . . . . . . . . . . . . . . . . . . . 45
12.3.2 Estimating absolute coordinates of the maser source . . . . . . . . . . . . . . . . . . . 47
12.4 CLEAN image cubes having multiple wide ﬁelds . . . . . . . . . . . . . . . . . . . . . . . . . 47
12.5 Quick statistics of image cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
13 Creating ﬁnal image cubes
49
13.1 Final CLEANed image cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
13.2 Making full maser image in a single map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
14 Getting physical parameters51
14.1 Identiﬁcation of maser spots and features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
14.2 Gaussian ﬁtting to maser spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
15 Data backup
52
15.1 Back up AIPS UV data and images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
15.2 Backup only extension tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
16 Scientiﬁc analysis
53
16.1 Proper motion measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
16.1.1 Astrometric correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
16.1.2 Analysis of maser proper motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
16.2 What do maser sources trace? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
16.2.1 Internal and secular motions of maser features . . . . . . . . . . . . . . . . . . . . . . 56
16.2.2 Acceleration motions of maser features . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
16.2.3 Importance of multiple maser lines on the common reference frame . . . . . . . . . . . 58
17 Summary and future remarks
61
17.1 Phase-referencing technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
17.2 AIPS automatic pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
A Appendices65
A.1 Installation and setting AIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A.1.1 Disk space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A.1.2 Work permission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A.2 User environment for AIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.2.1 Commands in the login script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.2.2 Special variables for user . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.3 Updating AIPS version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.4 About this document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Chapter 1

Introduction
1.1

About this AIPS tutorial

This document is used for helping the tutorial in Astronomical Image Processing System (AIPS) data
reduction practice, which is planned for people who what to use AIPS for their actual scientiﬁc works.
Because an AIPS tutorial usually expected has a limited period, say shorter than ﬁve days in this tutorial,
people who attend the tutorial are strongly recommended to understand theoretical concepts of Very Long
Baseline Interferometry (VLBI), data correlation (delay tracking, fringe stopping, etc.) and output dataobtained from the correlators before or after the tutorial. A special course for beginners of VLBI as wellas radio astronomy may be provided by the author in Kagoshima University using AIPS automatic pipeline(e.g. [20]). To understand VLBI itself and theoretical concepts in detail, as well as individual functions in
AIPS programs, several suitable textbooks have already been published ([22, 23]; Prof. T. Sasao’s lecture
text; K. Wajima’s text [24]). This document describes connections between individual AIPS procedures andtheir suitable citations (shown in the Bibliography), which should be read during or after the AIPS tutorial.
Install of AIPS is also skipped in this tutorial except for the part which should be understood by computer
administrators who installs AIPS and give the users several permission (see section A.1).

1.2

Goal of this AIPS tutorial

Topics described in this document mainly focuses on practical matters in AIPS data reduction. Figure
1.1 presents a global ﬂow chart of the AIPS tutorial. At ﬁnal stage, procedures to obtain some scientiﬁc
information are described (in chapter 16). Thus this tutorial assumes full analysis of VLBI data with AIPS.
Most of the tutorial shall be based on practices using AIPS machines. Students shall read this document tounderstand purposes and fundamental functions of the individual AIPS procedures. How to input commands
shall be found in other documents (e.g. [24]). However, such documents often do not cover topics aboutdata reduction of spectral line (maser) source data, which are covered in this documents. Note that ﬁnal
AIPS outputs are not ﬁnal scientiﬁc results. More corrections are necessary, which are also described in 16.
In addition, note that there is no VLBI data prepared specially for this AIPS tutorial. Figures shown inthis documents are cited from many but diﬀerent VLBI projects of the author’s. The author, or tutor of thistutorial, is always using real VLBI data that have not only potential to be published in a speciﬁc scientiﬁcjournal but also diﬃculty and problems in data reduction. Through this tutorial, students shall understandhow to check or judge data quality and correct procedures in the data reduction.

1.3

Task, verb and adverbs in AIPS

1.3.1

Calling tasks and verbs

Task is an AIPS program, which is called by typing TASK ’ (task name) ’ at ﬁrst, then executed by typing
GO. Verb is an AIPS command, which is executed by directly typing its own verb name. The table 1.1 showsa list of the verbs. Adverb is an parameter, which is input by a user and called in some of tasks and verbs.

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CHAPTER 1. INTRODUCTION

6

A user, therefore, should note that the meaning of an adverb in one task is diﬀerent from that in the othertasks.
Input adverbs in a task or a verb can be checked by typing INP. Adverbs input in a task can be recordedby typing TPUT task name. Adverbs recorded by TPUT or set when executing the task can be called by typing
TGET [task name]. A combination of a task and its adverbs can be recorded by typing PUT [your speciﬁedname]. It can be called by typing GET [your speciﬁed name]. A task can be aborted by typing ABORT. HELP
and EXPLAIN show explanation of a task or an verb. Table 1.1 shows a list of the verbs. All tasks and verbs
can be recognized by typing only ﬁrst three characters or more of their own names.

1.3.2

AIPS catalog files

AIPS has AIPS catalog files (see also section 3.1), which are called by adverbs INDISK, IN2DISK, etc.,
GETN, GET2N, etc., and OUTDISK, GETO. These adverbs are used in diﬀerent purposes, in specifying a catalog
ﬁle as, e.g., input or output catalog ﬁle.
When a task is aborted by typing ABORT, status of the used catalog ﬁles should be checked by typing
UCAT (for UV ﬁles), MCAT (for image ﬁles) or PCAT (for all ﬁles). If a status ﬂag of a ﬁle is either WRITE or
READ, then the status should be cleared by typing GETN catalog number ; CLRSTAT. Otherwise any task andverb is invalid for the ﬁle having a status ﬂag.
An AIPS ﬁle is destroyed by typing ZAP. Header information of a AIPS ﬁle can be read by typing
IMHEADER. When removing only extension tables (see section 4.1), type EXTDEST.

1.4

RUN file in AIPSIn AIPS, a user speciﬁes tasks and inputs verbs and adverbs interactively. It is quite convenient, therefore,
to prepare a (electric) text ﬁle describing a sequence of input strings. The author does not recommend torecord the input strings in a notebook written by a pen or a pencil, because the strings in the notebook
are often diﬀerent from those actually input in AIPS and the notebook is often useless. On the other hand,
strings written in a text ﬁle are easily copied and pasted in the AIPS command-input window. This is helpful
to ﬁnd some problem just before executing AIPS tasks.
A RUN script describes such a sequence of strings in a grogram from, which is controlled by a grammar
similar to BASIC/FORTRAN language. Looping, case selection are valid in the RUN ﬁle. Special adverbs
can be deﬁned and speciﬁed by a user. Some RUN ﬁle has been developed as a pipeline script (see section
17.2).
A RUN ﬁle has a name such as [RUN ﬁlename].[user ID (hexadecimal)]. This should be put in the$RUNFIL directory or , unless $RUNFIL is speciﬁed, in $AIPS ROOT/$AIPS VERSION/RUN. This is called andexecuted by typing RUN [your RUN ﬁle].

1.5

How to start AIPS?

A user needs the following action items for smoothly starting AIPS.
• Not only your login account for an AIPS machine but also your AIPS ID number are necessary (contact
to the machine and AIPS administrator).
• If a user is using the machine without AIPS, type xhost + to add any machine to those having
permission for transporting working windows to the user’s machine.
• Login an AIPS machine, and set the environment DISPLAY. Not that some LINUX machine might has
to skip this step.
• Type the script described in chapter A.2.1. If a user wants to skip this step every time, follow theprocedure described in chapter A.2.1.
• Type aips tv=local. Note that the ﬁle aips should be symbolic-linked to the AIPS execution ﬁle
START AIPS in the AIPS home directory and the directory should be recognized in every location by
the user (by setting the user’s path).

CHAPTER 1. INTRODUCTION

Verb
ABORT
ALTDEF
ALTSWTCH
CELGAL
CLRMSG
CLRNAME
CLRNAME
CLRSTATDISMOUNT
EXIT
EXTDESTEXPLAIN
FREESPACGETGETHEAD
GETN
GETO
GO
HELP
EHEX
IMHEADERIMSTAT
INP
MCAT
MOUNT
PCAT
PRTHI
PRTMSGPUT
PUTHEADRENAMERESTORE
REWIND
RUN
SPY
TASK
TVAL
TVBOX
TVCLEAR
TVLABELTVINITTVMOVIE
UCAT
WAIT
ZAP

7

Table 1.1: AIPS verbs frequently used.
Function
Abort the task currently running.
Deﬁne velocity information in the header information.
Switch between velocity and frequency in the header information.
Convert between celestial and galactic coordinate in the header.
Clear messages in the memory.
Clear ﬁrst input ﬁle name information (INDISK, INNAME, INCLASS, INSEQ).
Clear ﬁrst output ﬁle name information (OUTDISK, OUTNAME, OUTCLASS, OUTSEQ).
Clear a status ﬂag of the AIPS ﬁle.
Dismount a tape drive (DAT, Exabyte, etc.) to unset a tape.
Exit AIPS.
Destroy an extension table in the AIPS ﬁle.
Show explanation of a task or a verb in more detail than HELP.
Show disk spaces.
Save a task/adverbs combination.
Get parameters from the header information.
Set an AIPS ﬁle in INDISK, INNAME, INCLASS, INSEQ by specifying an AIPS catalog number.
Set an AIPS ﬁle in OUTDISK, OUTNAME, OUTCLASS, OUTSEQ by specifying an AIPS catalog number.
Execute a task.
Show explanation of a task or a verb.
Show the current AIPS ID in a hexdecimal string.
Show a header of the AIPS ﬁle.
Perform image statistics in a selected box.
Show a list of adverbs input in the task.
Show a list of image AIPS ﬁles (catalog).
Mount a tape drive (DAT, Exabyte, etc.) to set a tape.
Show a list of all AIPS ﬁles (catalog).
Print a history of the AIPS ﬁle on a printer, a display or a ﬁle.
Print messages in the memory onto a printer, a display or a ﬁle.
Load a task/adverbs combination.
Put parameters to the header.
Rename an AIPS ﬁle.
Initialize tasks and adverbs.
Rewind the tape mounted.
Read a RUN ﬁle.
Show current task status.
Call a task.
Display an image on the TV Server.
Set a box on the TV Server.
Clear the TV Server.
Put labels on the TV Server.
Initialize the TV Server.
Display an image cube on the TV Server.
Show a list of UV AIPS ﬁles (catalog).
Wait the next task until ﬁnishing the task currently running.
Remove an AIPS ﬁle.

CHAPTER 1. INTRODUCTION

8Global flowchart for AIPS tutorial
For data analysis of maser sources

Introduction about AIPS
(Chapter 1)

Strategy on observationand calibration (2)(Chapter 8)

Preparing data
(Chapter 2)
FITS, flag, gain, Tsys

Loading UV data
(Chapeter 3)
FITLD/(MSORT)/INDXR

Advanced calibration(Chapeter 9)
BPASS/SETJY/CVEL/ (SPLIT/ACFIT)

Watching maser emission(Chapeter 10)
POSSM/VPLOT/UVPLTMaser calibration
Watching UV data
(Chapeter 5)
LISTR/DTSUM/PRTANPOSSM/VPLOT/UVPLT/COHER

Strategy on observationand calibration (1)(Chapeter 11)
IBLED/FRING/SPLIT/CALIB/IMAGR

Search for maser emission(Chapeter 12)
FRMAP/SPLIT/IMAGRTVMOVIE/IMEAN(Chapter 5)

Creating image cubes
Fundamental calibration(Chapter 13)
SPLIT/IMAGR/BLANK/SQASH(Chapeter 6)
UVFLG/ANTAB/APCALAVSPC/FRING

Getting physical parameters

Self-calibration andhybrid mapping

Data backup(Chapeter 7)
SPLIT/CALIB/IMAGRIMEAN/IMSTAT/PRTCC/TVALL(Chapter 14)
IMEAN/IMSTAT/JMFIT/SAD(Chapter 15)
TASAV/FITTP

Scinentific analysis
Lecture part
AIPS practiceData handling(Chapter 16)

Summary(Chapter 17)

Figure 1.1: Global ﬂow chart of the AIPS tutorial. Break lines indicate breaks of daily AIPS practice andlecture. The AIPS tutorial expects a ﬁve-day course. Grey parts will be skipped in the tutorial.

Chapter 2

Preparing data
Generally speaking, astronomical VLBI data reduction requires the following items from used telescopes anda VLBI correlator. Formats in ﬂag and calibration ﬁles that are read in AIPS are seen in the VLBA (aspen)
and the EVN (archive) homepages. They are used at the stage described in chapter 6.

2.1

Visibility data

To make data analysis with AIPS, visibility data are contained in FITS (Flexibility Image Transport System)
format. The data consists of not only complex visibilities but also the following items adopted in thecorrelation.
• Weights that indicate quality of the visibilities, which may be deﬁned on basis of tape playback andcorrelator performance.
• (u, v, w) values, but which may be directly used not for data analysis itself but for plotting data in
AIPS.
• Delays, delay rates and delay accelerations.
• Station coordinates and source coordinates with there references.
• Frequency and spectral channel setups.
• Scan information (time table of scans).

2.2

Flag information

Bad data, which are contaminated because of inappropriate operation, poor weather or system conditionand other reasons, severely aﬀect ﬁnal results in source images. The ﬂags are read in the AIPS task UVFLG.
The bad data that should be ﬂagged out are divided into two sorts as follows.

2.2.1

Expected flags

They can be made when making an observation schedule. In fact, NRAO’s SCHED has a function to generate
ﬂags in this case.
(1) Dead data that are generated, for example, during time when antennas are not tracking target sources
because of changing the target sources while data recording has already started. Antenna operation
limit also creates such invalid data. They can be expected on basis of antenna speciﬁcation andperformance.
(2) Visibilities that are located very close to IF band edges usually have poorer quality than those in otherband range. At some of frequency range may have artiﬁcial radio interferences.

9

CHAPTER 2. PREPARING DATA

2.2.2

10

Accidental flags

They are generated by operators by hand or operating system to operate antennas and backend during anobservation. There are major reasons to create such situations.
(1) Strong wind, snow, and thunders that makes antenna operation interrupted.
(2) Artiﬁcial accidents, e.g. wrong antenna operation and system troubles.

2.3

Calibration data

They are generated for each of telescopes or baselines to calibrate visibility amplitudes and phase. They areread in the AIPS task ANTAB. The following items are essential for this purpose.

2.3.1

Antenna gains

Ae
An antenna gain is deﬁned in AIPS as the degrees per ﬂux unit (K/Jy) DP F U = 2k
, where Ae is anBeﬀective aperture of the telescope kB Boltzman’s constant. Because the eﬀective aperture depends on antenna
elevation, this is usually described as a polynomial function. Coeﬃcients of the DPFU function can be
speciﬁed in the gain tables.

2.3.2

System noise temperatures

System noise temperature varies rapidly, especially at higher frequency because mainly of variation in weather
condition. In an advanced case, because of necessity, the temperatures are measured every 10 seconds. Thisis possible, for example in VERA system, by monitoring an electric power level toward a target source.
Sometimes, usually during the target sources are changed, an electric power levels should be measured
towards an absorber with its known temperature. The system temperature is measured as diﬀerence ofpower levels between towards the target and the absorber.

2.3.3

Visibility phase calibration tables

There are a few reason to insert phase calibration information. One of the most important reasons is phasecompensation for atmospheric phase ﬂuctuation. In VERA system, calibration tables to estimate diﬀerential
phase delay between dual beams are provided. Even in KVN that has no dual-beam system, other calibrationtables, for example which are provided by water vapor radio meters, may be eﬀective.

Chapter 3

Loading UV data
Figure 3.1 describes a ﬂow of AIPS tasks for data loading (FITLD) and for data transformation (MOSRT).
Adverbs input in each of the tasks can be seen by typing INP [task name] or HELP [task name]. Here, someof important tasks and adverbs are described.

3.1

File name

The name of an AIPS ﬁle, or a catalog ﬁle, consists of three parts: NAME, CLASS and SEQUENCE. NAME
usually speciﬁes what the ﬁle is, e.g. project code, source name. CLASS has only six characters and usuallyspeciﬁes which type the data is. The name of the task that ﬁnally produced the ﬁle is usually speciﬁed in
CLASS. SEQUENCE describes the order of similar kinds of ﬁles.
Note that all characters in a string are automatically capitalized when the string is bracketed with singlequotation marks (’) at the beginning and the end of the string. If the string does not have a single-quotation
mark after it, both of capital and lower-case characters are recognized.

3.2

Time interval in the calibration (CL) tables

Data calibration in AIPS (see chapter 5) is made by updating a calibration table (CL) see section 4.1, which
is a time/baseline series of complex gain factors. A time interval of the series should be short enough tocompensate visibility phase and amplitude variation. However, the time interval shorter shorter than theparameter period of the correlator output is meaningless. This time interval is speciﬁed in the adverb CLINTin unit of minute in the task FITLD. If the CL table is removed then created in the task INDXR, the adverb
APARM(3) speciﬁes the time interval. Usually CLINT1/60-5/60 (min).

3.3

MSORT: Sorting the UV data into time-baseline order

If the original FITS data do not have time-baseline order, this task should be executed. Sometimes MSORT
should be executed before concatenating multiple FITS ﬁles with the task DBCON otherwise MSORT consumes
extremely long time without successful execution.

3.4

INDXR: Creating an index (NX) table

An index (NX) table (see also section 4.1 maintains the information including scans, source coordinates,
frequency setups and so on. This table is necessary for executing other AIPS tasks. The ﬁrst three parametersin CPARM specify the maximum time gap between scans, the maximum scan length and the time interval of
the CL table.

11CHAPTER 3. LOADING UV DATA

12Block size
2880, 6250, 12880
bytes

FITS files

On DAT tape
Where isthe FITS?

MOUNT

FITLD
On DAT tape
Where isthe FITS?

DISMOUNT

MSORT
Sometimes necessary
DBCON for concatenating
multiple UV data
INDXR
MERGECAL

NX1

CL1(in new VLBA data)
concatenating attached
TY, GC and FG table

MSORTed files

Figure 3.1: Flow chart of the part that describes loading AIPS UV data.

Chapter 4

Watching UV data
4.1

Extension tables

AIPS UV data consists of visibilities, weights, (u, v, w) values and the extension tables. The existence of theextension tables can be checked with the verb IMHEAD (showing the ﬁle header). The list of the extension
tables are shown in the text [24]. The contents of them are displayed by using the tasks shown in table 4.1.
Table 4.1: AIPS extension tables and their displaying tasks.
Extension table
NX
AN
CL
SN
BP
TY
GC
PL
HI
CC
SU
FQ

4.2

Contents
Scans, source coordinate, frequency setups
Antenna parameters (coordinates, mounts, etc.)
Complex gain factors, delays and rates calibrated
Calibration solutions in amplitude, phase, delay and rate
Complex or total-power bandpass characteristics
System noise temperatures of antennas
Gains of antennas
Plot file
History table
CLEAN components in the image cube
Source information
Frequency setup

Task for display
INDXR
PRTAN
SNPLT, CLPLT
SNPLT, TBOUT (in file)
POSSM
SNPLT
SNPLT
LWPLA (in printer), TKPL (in TeK server)
PRTHI
PRTCC
???
???

Scans, source information and frequency setups

The task LISTR with setting OPTYPE=’SCAN’ displays them.
• When setting DOCRT=1 (or positive number), they appear in the terminal window inputting commands.
• When setting DOCRT=-1 without specifying OUTPRINT, they are printed out in a printer.
• When setting DOCRT=-1 with specifying OUTPRINT, they are recorded in the ﬁle speciﬁed in OUTPRINT.

4.2.1

About scans

The scans are displayed their time ranges in time order. In a maser source observation, the scans may
consists not only of scans towards the target maser source but also of scans towards the following sources.
(1) Fringe ﬁnders:
Bright continuum emission sources (QSOs) used for ﬁnding fringes in the ﬁrst step of data correlation.
These scans can also be used for obtaining complex bandpass characteristics (see caption 8 and section
9.1.

13

CHAPTER 4. WATCHING UV DATA

14(2) Clock parameter calibrators:
Continuum sources scanned every 30-90 minutes to monitor clock parameters (residual delays and delay
rates of individual antennas).
(3) Maser fringe ﬁnders:
Sometimes bight maser sources are observed at the beginning of the observation to check the frequency
setups. They are not used in data reduction.
(4) Phase-reference sources:
If the target maser sources are too weak to be detected within a coherence time (shorter than 5 minfor H2 O maser sources, see section 4.7), the phase-reference sources are scanned every period shorter
than the coherence time followed by the target maser sources.

4.2.2

About sources

In the output of the task LISTR, the source information consists of the source coordinates (J2000.0), Stokes
parameters (set to zero as defaults), the rest frequencies (set to the local frequencies as defaults) and theline-of-sight velocities (set to zero as defaults). Later, if necessary, they are speciﬁed by a user in the AIPS
task SETJY (see section 9.2.1).

4.2.3

About frequency setup

The frequency setup is a sequence of IF channels having local frequencies, band widths and frequency
resolutions of the spectral channels and upper-side or lower-side band information.

4.3

Quantity of the visibilities

The task DTSUM calculates and displays fractions of available visibilities in the individual baseline with respect
to the expected numbers of visibilities. This task is useful for ﬁnding which antenna has the largest numberof visibilities in the observation and is, therefore, suitable for a reference antenna (see section 5.3).

4.4

Antenna information

The task PRTAN presents antenna parameters contained in the AN table. The antenna coordinate (X, Y, Z)
on the Earth at the observation epoch, type of antenna mount (azimuth-elevation, equatorial, etc.), and an
axis oﬀset are displayed.

4.5

Visibility along frequency and among IFs

The task POSSM displays amplitudes and phases of visibilities along frequency. This is useful mainly forﬁnding maser emission in a number of spectral channels. Without any calibration, an integration period
set in the adverb SOLINT should be shorter than an expected coherence time (see section 4.7). If choosing
the all time range of the observation, a lot of spectra are generated from time to another. Therefore, it isappropriate to choose a time range in the adverb TIMERANGE.

4.5.1

Printing Spectra

When setting DOTV=1, the spectra are displayed on the AIPS TV server. When setting DOTV=-1, the spectra
are saved in the plot (PL) ﬁles. In the task LWPLA, they are printed out on a printer without specifying theadverb OUTFILE or plotted in PostScript ﬁles with specifying the adverb OUTFILE. When specifying OUTPRINTin the task POSSM, the spectra are save in the text ﬁle speciﬁed in the adverb OUTPRINT.
Without any antenna selection, visibilities in all baselines are plotted and so many time is consumed.
It is diﬃcult to check data in all of the baselines. It is convenient to select on antenna that have highest
sensitivity and most reliable performance as a reference antenna and to plots visibilities only in the baselines

CHAPTER 4. WATCHING UV DATA

15

including this reference antenna (see also section 5.3). This can be made by setting the adverb ANTENNAS tochoose only the reference antenna.
At this stage, only spectral-channels and frequency axes are available for the horizontal axis. To use theline-of-sight velocity axis, a user should deﬁne the system of the velocity, which is described in section 9.2.1.

4.5.2

Total power spectra

By setting APARM(8)=1, total power spectra from auto-correlation data are displayed. At this stage, maser
emission is found if the maser emission is enough bright. Usually, however, a maser emission peak is much
weaker than a slope of the bandpass characteristics and too weak to be identiﬁed. Nevertheless the total
power spectra are useful to ﬁnd artiﬁcial radio interference that should be ﬂagged out in data reduction. It
is also understood that how severely the IF band edges lose sensitivity or have poor quality of visibility.

4.5.3

Cross-power spectra

By setting APARM(8)=0, cross power spectra from cross-correlation data are displayed. There are two typesof integration, scalar average (APARM(1)=0 and vector average (APARM(1)=1). The former is useful to ﬁndmaser emission because this is similar to that made in total-power spectrum and even maser components
having big position oﬀsets can be detected.
The latter, on the other hand, has more information on the maser emission than the former. If maser
components have big position oﬀsets, they are weaken in the spectrum. By changing the adverbs SHIFT
R.A. oﬀset, Decl. oﬀset, the spectrum varies in which the maser components close to the shifted delaytracking center (R.A. oﬀset, Decl. oﬀset) appear without losing their visibility amplitudes. A coherencetime can be also roughly estimated by changing the adverbs SOLINT and by checking loss of the visibility
amplitudes.
Visibility phases in the spectral channels having maser emission have similar phases without their scattering. Therefore a user can see a smooth slope of the phases along frequency. In other word, detection ofsuch phase slope is indicative of maser emission detection.

4.6

Visibility along time

The task VPLOT displays amplitudes and phases of visibilities along time. Diﬀerent from POSSM, it is appropriate to set the adverb SOLINT to be much shorter than the coherence time for tracing amplitude and phasevariation in detail.
Because task VPLOT averages visibilities among frequency channels, the averaged visibilities have smaller
amplitudes at this stage because the visibilities before averaging have diﬀerent phases and then smearing
occurs. The removal of this smearing can be checked by comparing the VPLOT outputs between before andafter fringe-ﬁtting (see section 6.5.2).

4.7

Estimating a coherence time

A coherence time is a period for which visibilities can be integrated without reducing the visibility amplitude.
Coherence loss occurs because of phase ﬂuctuation due to the atmosphere and instability of the electric pathin the signal transportation system. A coherence time is inversely proportional to observed frequency,
empirically speaking 5–10 min at 5 GHz, 2–4 min at 22 GHz and 1–2 min at 43 GHz depending on weather
condition. The coherence time can be measured with the task COHER.

Chapter 5

Strategy of observation andcalibration (1)Here planning a VLBI observation and strategy of data calibration are described.
A visibility obtained in a VLBI observation ρobs
ij in a baseline between the telescopes i, and j usually has
a form of a normalized cross-correlation coeﬃcient and calibrated to be Vijcal by multiplying a complex gain
factor as follow,
Vijcalgij= gij e−φij ρobsij ,Tsys,i Tsys,jTsys,i Tsys,j
= 2kB
=
.
Ae,i Ae,jDP F Ui DP F Uj

(5.1)
(5.2)

where Ae and Tsys are an eﬀective aperture and a system noise temperature of the telescope, respectively,
kB Boltzman’s constant (see also equation of 15.1.6 of the text [24]). The amplitude of the gain factor is
obtained in the fundamental procedure (see sections 6.4.1 and 6.4.2) and self-calibration more precisely (seechapter 7).
To understand the contents of a phase part of the complex gain factor, the following equations that
describes a visibility phase, Δφ(ν, t), obtained in actual VLBI observation in one baseline in detail (see also
equations in chapter 12.5 of the text [23]) are useful.
Δφ(ν, t)φstr (ν)

2πν
(D + σD) · Δs(ν) + φstr (ν)
c+ 2π(ντ inst + σν LO Δt + ντ atm ) + φLO + φIF (ν) + 2πn2πν= arg [
B(σmap , ν) exp(−
D · σmap )dΩ ]
c
Ω



(5.3)
(5.4)

where
c: light velocity,
D, σD: True baseline vector and oﬀset of the adopted baseline vector from the true baseline vector,
Δs(ν): True radio source coordinate and oﬀset of the adopted source coordinate from the true source
coordinate,
φLO : Phase oﬀset caused by the local frequency standard and the mixer,
τ inst : Time-variable excess path delay caused by the electric transportation system (instrumental delay),Δt: Time oﬀset from the speciﬁc epoch,τ atm : Time-variable unknown excess path delay caused by the atmosphere towards the source,φIF (ν): Phase residual derived by the complex bandpass response in the IF channel,
2πn: 2π-n radians ambiguity in the phase,φstr (ν): Phase oﬀset caused by brightness distribution of the radio source, B(σmap , ν),σmap : Position oﬀset vector with respect to the speciﬁc celestial location, here equal to Δs(ν).

16CHAPTER 5. STRATEGY OF OBSERVATION AND CALIBRATION (1)17

At the ﬁnal stage, we need only information on the target source, B(σmap , ν) and Δs(ν). Note thata target source, especially a maser source has diﬀerent brightness distributions and position oﬀsets amongfrequency or line-of-sight velocity. In equation 5.3, a term including σD is ignored if it is suﬃciently small
with respect to Δs(ν). This situation, however, is not satisﬁed in high-precision diﬀerential astrometry
between two sources separated by as large as one arc degree.
Error terms in the second line of the right side of equation 5.3 should be removed out by data calibration.
τ inst and σν LO are usually called as ”clock parameters”; major parts of them are derived from the frequency
standards of VLBI stations. They are smooth functions of time and can be removed by fringe ﬁtting(see section 6.5.2). φIF is expected to be stable in the whole observation or within several hours and can beremoved by obtaining the visibilities of bright quasars after fringe ﬁtting (see section 9.1). τ atm is a functionof time and varies rapidly within a coherence time. It is removed by both fringe ﬁtting (see sections 6.5.2
and 11.2) and self-calibration (see chapter 7).

5.1

Observation schedule

To appropriately calibrate maser source data, calibrators should be appropriately observed. This means thatan observation schedule should be prepared with taking into account strategy of data calibration. There are
special notes on observations of maser sources as follows.

5.1.1

Fringe finders

Usually VLBI row data have big unknown clock parameters, clock oﬀsets (residual delays) and clock rateoﬀsets (residual delay rates) even if every clock of observation stations is being maintained by a hydrogenmaser frequency standard and a GPS time-keeping system. These oﬀsets sometimes achieve up to 1μs
and 100 mHz, respectively. Such oﬀsets severely smear fringe signals and prevent the data from coherent
integration for the whole observation.
Quasars suitable for ﬁnding fringes are selected as fringe ﬁnders. Their celestial coordinates shall be wellmeasured and they shall be so bright that they are detected within a coherence time even in most severe
situations expected in the observations. They are observed once or more for a coherence time or longer inthe observation.

5.1.2

Clock parameter calibrators

Usually, fringe ﬁnders are far away from the target sources of the observation on the sky plane. In actual,residual delays and delay rates contain not only clock parameters but also delay and rate residuals due tothe atmospheric excess path delays. Because the latter is diﬀerent among the sources located at diﬀerent
antenna elevation, continuum calibrators should be as close to the target sources as possible.
When target sources are bright continuum sources, themselves become clock parameter calibrators. On
the other hand, when target sources are maser sources, another continuum calibrators are necessary because
the maser sources themselves, they have maser emission in quite limited frequency range, cannot be used
to estimate (group) delay oﬀsets. The calibrators should be scanned every 30-90 min. At higher frequency
bands, shorter time interval (∼30 min) is adopted.

5.1.3

Maser fringe finders

Frequency setups that specify the number of IF channels, the local frequencies and band widths of the IF
channels, should be exactly set for maser source observations. Even only setting a wrong local frequency,
some parts or all of maser emission with narrow line spectrum in the limited range of Doppler frequency islost from the data. In particular, the Doppler frequency varies from one season to another due to the Earth’s
orbital motion and rotation.
This frequency shift is, of course, bigger at the higher frequency. The observer should carefully checkat which frequency the target maser sources are detected at the observation epoch. To check it during theobservation, a bright maser source which can be detected in the total-power spectrum in real-time is useful.
Therefore, for example, each of the VERA station has a real-time digital correlator to perform such a checkwith total-power spectra just before a VLBI observation starts.

CHAPTER 5. STRATEGY OF OBSERVATION AND CALIBRATION (1)

5.1.4

18

Phase/position-reference sources

If the target sources are too weak to be detected within a coherence time, continuum sources that are very
close to the target sources are scanned every period shorter than the coherence time followed by the target
sources. Such scans are performed by quickly nodding an antenna; the method is called as antenna-fastswitching phase-referencing. Fringe phases, delays and rates of the continuum sources are interpolated tothose of the target sources. Such continuum sources are called as phase-reference sources.
If the phase-reference source is a quasar, this is also used as position reference. On the contrary, when atarget source is bright enough to be detected and used for data calibration, a position-reference source with
faint emission is mapped in the opposite manner of that mentioned above. This method is calledas inverse
phase-referencing.

5.1.5

Bandpass calibrators

Each of IF channels has complex bandpass response, which derives bias in amplitudes and a small phase slope
along frequency. Information on complex bandpass response is necessary only when imaging continuum
sources with very high dynamic range or maser sources with very precise relative position accuracy (e.g. inposition errors smaller than 1/100 of angular resolution). The bandpass calibration may have to taken into
account when the VLBI system uses analog band ﬁlters. Even if using digital band ﬁlters such as the VERA
system, a receiver may have non-ﬂat bandpass response in wider bandwidths. In any case, at least bandpass
amplitude response should be calibrated. To obtain the bandpass response, amplitudes and phases are welldetermined in the individual frequency channels. Therefore, extremely bright continuum calibrators should
be observed.

5.2

Step-by-step calibration

VLBI data calibration with AIPS is a series of updates of the calibration table (CL), which contains thecomplex gain factors having amplitudes and phases. Because phases in the gain factors are interpolated
along frequency and time, they also have group delay residuals and phase drift rate residuals. Each of the
CL table updates is made with the task CLCAL by applying solution SN tables to create a new CL table froman old CL table. Row visibility data are never transformed; the calibrated visibility data are created byapplying the ﬁnest CL table to the row data. Therefore, disk spaces much larger than the size of row data
are consumed rapidly.

5.3

Selecting a reference antenna

Every visibility plot and calibration in AIPS is fundamentally antenna based, and all telescope performanceare evaluated with respect to the reference antenna. The reference antenna is chosen by a user with taking
into account sensitivity and reliability in the performance. To obtain a larger number of calibration solutions
with higher reliability, the reference antenna is a key in the data reduction.
There is another concern when choosing the reference antenna, baseline lengths. Generally speaking,an antenna close to the center of a VLBI array has an advantage to obtain a larger number of visibilities
because, taking into account the Earth’s rotation, this antenna observes radio sources with a larger numberof the array antennas in the same observation period. In addition, a radio source has a ﬁnite angular sizeand visibility amplitude of the source is reduced roughly proportional to baseline length. Thus this antenna
obtains visibilities with higher sensitivity.

5.4

Fringe search window

For maser data reduction, a user shall imagine a few types of the fringe search windows as shown in ﬁgure 5.1.
In the fringe ﬁtting described in fundamental calibration using continuum calibrators, a delay–rate window
should be adopted, while frequency–rate window should be adopted in the maser data calibration.

CHAPTER 5. STRATEGY OF OBSERVATION AND CALIBRATION (1)19

Figure 5.1: Fringe visibilities in fringe search windows. (a) search window in a time lag (τ ) versus parameter
period (t) plane; (b) same as (a) but in a time lag versus fringe frequency plane; (c) same as (a) but in a
spectral frequency versus parameter period plane; (d) same as (a) but in a spectral frequency versus fringe
frequency plane. For line sources, the obtained cross-power spectra have several spectral frequency peaks
corresponding to the Doppler velocities of the line components in the planes (c) and (d), and have several
fringe frequency peaks corresponding to the position oﬀsets from the correlation center position in the planes(b) and (d). For continuum sources with ﬂat power spectra, there are several time lag peaks in the planes (a)and (b). In the fringe search procedure, the planes (b) and (d) are used for the line and continuum sources,
respectively. These ﬁgures are cited from Reid (1995).

5.5

Set a coherence time

A coherence time shall be taken into account when making observation schedules and when making data
reduction. The coherence time can be estimated with the task COHER (see section 4.7).
Empirically, a coherence time described in famous books is slightly shorter than a period for which avisibility amplitude is reduced. Clock search described in chapter 6 can use the latter period. Therefore,scans of continuum calibrators are set to be slightly longer than the coherence time. On the other hand,phase-referencing and fringe ﬁtting that are performed to interpolate phases between scans should adopt asolution interval (the adverb SOLINT) shorter than the coherence time. Otherwise, removal of 2π-n radiansambiguity may fail.

Chapter 6

Fundamental calibration
Figure 6.1 describes a ﬂow of the fundamental calibration in AIPS. Each of the calibration procedures are
brieﬂy described in the following sections.

6.1

Plotting calibration solution

Calibration tasks such as ACCOR, APCAL, FRING CALIB generate solution (SN) tables. The solution tables canbe plotted with the task SNPLT. The calibration solutions in amplitude, phase, delay and rate are plottedagainst time by setting OPTYPE=’AMP’, ’PHAS’, ’DELA’ and ’RATE’, respectively. When setting DOTV=1, theplot is displayed on the AIPS TV Server, while setting DOTV=-1, the plot is saved in plot (PL) ﬁles in the
AIPS UV data. The PL ﬁles are printed out with the task LWPLA on a printer without specifying the adverb
OUTFILE or plotted in PostScript ﬁles with specifying the adverb OUTFILE.

6.2

Applying calibration

As described in section 6.2, data calibration is a series of updating the calibration (CL) table. The task
CLCAL makes updating a CL table. The following is an example of CLCAL inputs. A CL table that is newly
created can be applied several SN tables at the same time. The CL table can be applied many times without
removing previous application. Therefore, when previous applications were wrong, the CL is recommended
to be deleted.
Here some of important adverbs in CLCAL are described in detail.

6.2.1

SOURCEIt speciﬁes sources whose visibilities are calibrated. In most cases, all sources can be selected (SOURCE=’ ’).

6.2.2

CALSOUR

It speciﬁes sources whose solutions in the speciﬁc calibration task is applied. Combination of SOURCE andCALSOUR can change for the same CL table. This is convenient when the AIPS UV data several pairs of targetreference sources in antenna-fast-switching phase-referencing, which are speciﬁed in SOURCE and CALSOUR,
respectively. In this case, only scans of sources that speciﬁed in the latter adverb are passed in CLCAL without
incorrect data interpolation to other sources.

6.2.3

INTREPOL

It controls methods to interpolate calibration solutions provided by SN tables. If calibration solutions provided
have time intervals short enough to avoid any ambiguity in the interpolation, the default INTERPOL=’2PT’
can be adopted. In the antenna-fast-switching phase-referencing, INTERPOL=’AMBG’ is recommended to use
delay rate solutions and to avoid 2π-n radians ambiguity in phase interpolation. If calibration solutions

20

CHAPTER 6. FUNDAMENTAL CALIBRATION

21MSORTed data
band-edge flags
Flag file

FG1

UVFLG

SN1
ACCOR

SCHED

CLCAL

SNPLT/LWPLA
CL1+SN1 >> CL2xxxxxcal.vlba

CL2 >> CL3

VLOG

TECOR
TY1

gain/Tsys file

SNPLT/LWPLA

GC1

ANTAB

SNPLT/LWPLA

TY1+GC1 >> SN2

APCAL
gain_vlba.key

CLCAL

CL2+SN2 >> CL3

CLCOR

OPCODE='PANG' (parallactic angle correction)

Yes

AVSPC

SNPLT/LWPLA

32CH-averaged
data

NCHAN
> 64?
No
SN3

SN3
FRING
TACOP

SNPLT/LWPLAFRINGSNPLT/LWPLACLCAL CL4+SN3 >> CL5

Figure 6.1: Flow chart of the part that describes fundamental calibration.

CHAPTER 6. FUNDAMENTAL CALIBRATION

22

are temporarily sparse, in the case of amplitude calibration on basis of sparse data set of system noise
temperature, other interpolation methods may be adopted.

6.2.4

CUTOFFThe default (CUTOFF=0) means that all data points in the CL table are interpolated with the applied SN table.
Sometimes this default aﬀects the calibration result. If calibration solutions in a speciﬁc time range were
not obtained because of some bad reason, the data at this time range should be ﬂagged out. When setting
this adverb in unit of minute, an epoch without any calibration solution within this adverb criterion fromthe epoch is ﬁltered.

6.3

Sampling bias correction

From this point, the ﬂow of the fundamental calibration is described.
The task ACCOR makes this correction, which is described in other text in more detail. Because samplingbias usually occurs stably, a solution interval (SOLINT) is set relatively to a long period (10–60 min).

6.4

Amplitude calibration

6.4.1

Making gain and system temperature tables

To make amplitude calibration, information on gains and system noise temperatures of antennas are necessary
in a proper format for the AIPS task ANTAB to read them and to create a gain curve (GC) and system noise
temperature (TY) tables.
For VLBA data, these information is contained in the ﬁle named [project code]cal.vlba and put on thehost aspen (accessible from the VLBA web page). The ﬁle is extracted by using the task VLOG. To obtainantenna gain information, the ﬁle vlba gain.key is also necessary. This shall be attached in the cal.vlba
data mentioned above or the system noise temperature data named [project code].TSYS.
For other telescopes, a gain ﬁle should be prepared with a format shown as follows.
! JNET_gain.txt: gains for J-Net telescopes!
GAIN NOBEYA45 ALTAZDPFU = 0.362 FREQ=21530, 22630 POLY=GAIN KASHIM34 ALTAZDPFU = 0.115 FREQ=21530, 22630 POLY=GAIN MIZNAO10 ALTAZDPFU = 0.010 FREQ=21530, 22630 POLY=GAIN KAGOSIMA ALTAZDPFU = 0.005 FREQ=21530, 22630 POLY=GAIN MIZNAO20 ALTAZDPFU = 0.057 FREQ=21530, 22630 POLY=GAIN IRIKI
ALTAZ
DPFU = 0.061 FREQ=21530, 22630 POLY=GAIN OGASA20 ALTAZDPFU = 0.051 FREQ=21530, 22630 POLY=GAIN ISHIGAKI ALTAZDPFU = 0.048 FREQ=21530, 22630 POLY=!

1.000 /
1.000 /
1.000 /
1.000 /
1.000 /
1.000 /
1.000 /
1.000 /

where GAIN declares the gain information of the antenna speciﬁed after this string, DPFU is the degree per
ﬂux density, FREQ speciﬁes the frequency range (bottom and top) in which the gain information is valid.
Files of system noise temperatures also should be prepared with a format shown as follows.
!--- Tsys data ---------!
TSYS IRIKI
INDEX=’L1’ FT = 1.0 TIMEOFF=0 /357 17:33.1
224.1
357 18:06.3
246.8
357 18:56.8
206.3
/
!
TSYS OGASA20 INDEX=’L1’ FT = 1.0 TIMEOFF=0 /357 17:33.1
209.4

CHAPTER 6. FUNDAMENTAL CALIBRATION

23

357 18:06.3
249.1
357 18:56.8
214.3
/
!
TSYS ISHIGAKI INDEX=’L1’ FT = 1.0 TIMEOFF=0 /357 17:33.1
442.6
357 18:06.3
369.7
357 18:56.8
386.2
/
!
TSYS KASHIM34 INDEX=’L1’ FT = 1.0 TIMEOFF=0 /357 17:35.0
131.3
357 18:55.0
140.1/
where TSYS declares the gain information of the antenna speciﬁed after this string, INDEX describes a format for an array of circular polarization and IF channels. Here, L1 means IF1 Left circular polarization.
When having left and right circular polarization in each of four IF channels, INDEX is describes as follows,
INDEX=’L1’ ,’R1’,’L2’,’R2’,’L3’,’R3’,’L4’,’R4’. To understand the description in more detail, type
EXPLAIN ANTAB.

6.4.2

Creating amplitude calibration solution

Using the gain (GC) and system noise temperature (TY) tables created in the task ANTAB, a new solution (SN)table is created by the task APCAL. The performance of the task APCAL is described in other texts.

6.4.3

Parallactic angle correction

Some of recent VLBI systems are able to receive both of left-hand right-hand circular polarization signals
at the same time. Not only in such system but also the systems using azimuth-elevation mount antennas,
leakage of another circular polarization component should be taken into account. The leakage varies withparallactic angle of the receiver (rotation angle of the receiver with respect to the radio source) and aﬀects
visibilities, especially in VLBI polarimetry. The parallactic angle correction can be made in the task CLCOR
by seting the adverb OPTYPE=’PANG’. This task modiﬁes the speciﬁed CL table. It is appropriate to perform
this correction before fringe ﬁtting and further data calibration.

6.5

Fringe fitting

At this stage, only continuum calibrators are used in the fringe ﬁtting to solve clock parameters varying ona time scale of about one hour. In the solutions, average excess path delays due to the atmosphere towards
the sky close to the target (maser) sources are also included.

6.5.1

Averaging spectral channels

Usually VLBI data observing maser sources have a large number of spectral channels. For fringe ﬁtting, 16–64
spectral channels are suﬃcient and suitable for saving calculation time. The task AVSPC creates a channelaveraged data. In the task, the adverb AVOPTION=’SUBS’ is speciﬁed to average the spectral channels. The
adverb CHANNEL is the number of spectral channels averaged into one channel. For example, from data having
512 spectral channels, new data having 32 spectral channels are created when CHANNEL=16. At that time,
ﬂagging is also performed with an existing ﬂag (FG) table.

6.5.2

Fundamental fringe fitting

The task FRING performs fringe ﬁtting as mentioned above. At this stage, scans of only continuum calibrators
are used. Fringe ﬁtting using scans of maser emission is described in the section 11.2.

CHAPTER 6. FUNDAMENTAL CALIBRATION

SN 3 Lpol IF 1

0.1
Delay (Nano Seconds)

24

1L NOBEYA45

0.0
-0.1
10
5
20
10
0
0
-10
-20
18

2L KASHIM34

3L MIZNAO10

4L KAGOSIMA
20

22

1/00
1/02
TIME (HOURS)

1/04

1/06

1/08

Figure 6.2: Clock oﬀsets revealed in the fundamental fringe ﬁtting with the task FRING. The calibrator
JVAS0212+735 was observed at the 22.2 GHz band every 40 minutes. Because Nobeyama 45-m telescope isa reference antenna, delays of this telescope are always zero.
TASK ’FRING’
Calling the task FRING.
INDISK 1; GETN 100 Calling UV file in the AIPS catalog file.
CALSOUR ’NRAO530’ ’0212+735’
Calibrator sources
BCHAN 1Lowest channel number 0=>all
ECHAN 0Highest channel number
DOCALIB 2
Performing calibration with a CL table and weights.
GAINUSE 3
CL table to be applied.
FLAGVER 0
Latest FG table is applied.
DOBAND=-1
Bandpass (BP) table has not yet been created.
REFANT 1
Reference antenna.
SEARCH 2 0 Second priority antenna when without the reference antenna.
SOLINT 3
Solution interval, a little longer than a coherence time.
APARM
0Clear APARM.
APARM(7) 7Signal-to-noise ratio cutoff.
APARM(9) 1Second priority antenna is used when without the reference antenna.
DPARM(1) 0
3 baseline combinations to make closures.
DPARM(2) 0; DPARM(3) 0 Fringe search window is automatically set.
DPARM(4) 2Parameter period in the correlation in second.
SNVER
0
A new SN table is created.
INP; GOAt this stage, it is better to adopt a longer integration duration (solution period) to obtain mainly groupdelays (clock oﬀsets) with higher signal-to-noise ratios. Even if fringe phases are rapidly ﬂuctuated on ashorter time scale than a coherence time, group delays are more stable on a longer time scale within theirestimation uncertainty (1-3 nsec).
For example, suppose an uncertainty in the estimated clock oﬀset (group delay error) στ inst that derivesa phase drift along frequency. At the frequency ν separated by Δν from a reference frequency, a phase error
σφ is expected as follow,
σφ = Δνστ inst ∼ ν

D · σs,c(6.1)

CHAPTER 6. FUNDAMENTAL CALIBRATION

σs ∼c Δν inst
στ
.
D ν

25

(6.2)

By inserting, for example, D = 1000 km, c =3×105 km s−1 and Δν/ν =1/1000, an uncertainty of the
instrumental delay στ inst = 3 nsec derives a relative position error σs ∼ 180 μas.
On the other hand, phase ﬂuctuation on a shorter time scale can be compensated in the self-calibration
procedures described in the next chapter. At this stage only large phase drifts on a longer time scale arecompensated for removing 2π-n radians ambiguity in phase connection between successive short epochs.

Chapter 7

Self-calibration and hybrid mapping
The detail of the self-calibration and hybrid mapping is described in other books (e.g. [5]). Here concentrates
on how they are performed in AIPS. Figure 7.1 shows a ﬂow to perform the self-calibration and hybrid
mapping. Deﬁnition of self-calibration and hybrid-mapping are diﬀerent among the text books, here thehybrid-mapping is deﬁned as the whole procedures to obtain a CLEAN map and the self-calibration isdeﬁned as the procedure to obtain complex gain factors based on an assumed source model.

7.1

Making a source image

The ﬁrst step of the hybrid mapping is to provide a source brightness model. It is still ﬁne to assume asimple model (for example, one point Gaussian distribution). It is sometimes necessary to provide the model
on basis of the brightness distribution that is actually observed.

7.1.1

Dirty beam, dirty map and CLEAN map

A dirty beam is the VLBI synthesized beam that is directly calculated with (u, v) distribution and weights
of visibilities by inverse Fourier transformation. A dirty map is the map that is obtained by inverse Fouriertransformation of the visibilities without any CLEAN process. A dirty map is useful to judge the detectionand existence of a radio source or true peak components in the brightness distribution. The dirty map iscomposed of a true source brightness distribution convolved by the dirty beam. A CLEAN map is the map
obtained after deconvolution of the dirty image by the dirty beam in an iterative process (see, e.g., [5]).

7.1.2

Split a single source file from a multi-source UV data

It is convenient to split visibility data only of the target source from the original (multi-source) UV data.
The task SPLIT creates a new single-source ﬁle as follows.
INNAME’SPLIT’INDISK 1; GETN 100
SOURCES’LKHA234’ ’ ’
STOKES’ ’
BIF 1; EIF 0
BCHAN 1; ECHAN 0
DOCALIB2
GAINUSE9FLAGVER1
DOBAND1
BPVER
1
OUTDISK1OUTCLASS ’SPLIT ’
OUTSEQ
0DOUVCOMP
1

Call the task SPLIT.
Get the original (multi-source) UV data.
Target source split.
All Stokes types of data are passed.
All IF data are passed.
All channels are passed (except for the band edges).
Apply a CL table and weights.
CL table version to be applied.
Flag table version (including band edge flags).
Apply bandpass (BP) table.
BP table version to be applied.
Output UV file disk unit number.
Specifies the class name of the output single-source file.
A new sequence number is specified for the output file.
Compressed data are output.
26

CHAPTER 7. SELF-CALIBRATION AND HYBRID MAPPING

27

Data calibrated infundamental parts
hybrid mapping

SPLIT

for calibrator, GAINUSE=5
CL1

MULTI/INDXR
IMAGR

Dirty map

TVALL/IMSTAT/IMEAN
KNTR/LWPLATVALL/IMEAN

IMAGR

SN k

Image
Yes
dynamic range
CALIB
improved?
SOLMODE='P' (phase)
APARM(1)=3(phase closure)

No

SN k
CLCAL

CALIB

SOLTYPE='L1'
SOLMODE='A&P'(amplitude & phase)
APARM(1)=4(amplitude closure)

CLCAL CL k +SN k >> CL k+1

CL k +SN k >> CL k+1
IMAGR

TVALL/IMEAN

Yes

Image
dynamic range
improved?

No
IMAGR
TVALL/IMSTAT/IMEAN
KNTR/LWPLA

Final image cubes
Figure 7.1: Flow chart of the part that describes the hybrid mapping.

CHAPTER 7. SELF-CALIBRATION AND HYBRID MAPPINGAPARM 2 2 0
INP; GO

28

Averaging spectral channels but having multi-IF channels.

To create CL tables in the following self-calibration process, the tasks MULTI (to create a new multi-sourceﬁle) and INDXR (to create a new NX table) shall be performed.

7.1.3

Making a dirty beam and a dirty map

The task IMAGR creates a source image as well as a dirty beam. An example of adverb setting in the task
IMAGR is shown as follows.
TASK ’IMAGR’Call the task ’IMAGR’.
INDISK 1; GENT 101
Get a SPLITed file.
SOURCES ’LKHA234’ ’ ’
Source name made its images.
DOCALIB 2
Calibrate visibilities with a CL table and weights.
GAINUSE 2
CL table to be applied.
FLAGVER=-1; DOBAND=-1
No FG and BP tables are applied.
STOKES’I’
Stokes parameter I (intensity) map is created.
BCHAN 0; ECHAN 0
All channels are selected.
NCHAV 1; CHINC 1
It is unnecessary to average and skip spectral channels.
BIF 1; EIF 0
Select all IF channels.
OUTNAME’LKHA’
Output image name (name).
OUTDISK1
Output image disk drive #.
OUTSEQ
1
Output seq. no.
OUTVER
1
Version number of the CC table.
CLR2N
Clear IN2DISK, IN2NAME, IN2CLASS, IN2SEQ.
CELLSIZE .0002 .0002 (X,Y) grid size in arcsecond, smaller than 1/4 of the synthesized beam.
IMSIZE 512 512
Minimum image size
NFIELD
1
Only one field is selected.
FLDSIZE 512 512
Clean size of each field.
RASHIFT 0; DECSHIFT 0
No position shift of the field.
UVWTFN’NA’
Natural weight is specified at first.
NITER
0
No iteration because of making a dirty map.
DOTV=1
Display residuals on TV for interactive CLEAN control.
INP; GO

7.1.4

Controlling AIPS TV Server

The obtained image is shown on the AIPS TV Server with the verbs, TVAL (for single frequency channel) or
TVMOVIE (for multiple channels). The verb TVCLEAR clears one of the screen channels of the TV server. Moresimply, the task TVINIT clears all of the items displayed on the TV server. TVLABEL gives lavels (coordinate
information) for the image displayed on the TV server.

7.2

Iterative process in hybrid mapping and self-calibration

In the hybrid mapping, at the ﬁrst step, a user should provide a source model created from a simple
assumption of a source brightness distribution (one-point Gaussian distribution at the map origin) or froma rough image obtained by CLEANmapping. Such a source model is set in the task CALIB. The task CALIB
outputs a new solution (SN) table. Then a new CLEAN image with better quality is obtained from thevisibilities calibrated by this SN table in the task IMAGR. A CLEAN image newly obtained is again used as abetter source brightness model in the task CALIB. Thus the hybrid mapping is an iterative process followedby the tasks IMAGE, CALIB and CLCAL If a single source ﬁle, or an output of the task SPLIT is used in thisprocess, only SN tables are directly used in the task IMAGR (without applying the task CLCAL).

CHAPTER 7. SELF-CALIBRATION AND HYBRID MAPPINGSOLINT

CALIB

FLUX

1x
T(coh)T(coh): coherence time

-5σ

0.5

0.2

SOLTYPE=' 'SOLMODE='P'
APARM(1)=3

SOLTYPE='L1'
SOLMODE='A&P'
APARM(1)=4

29

IMAGR
σ: expected
noise levelon an image-20

Dyanamic range=I(peak)/noise

-50

0.1

-100
1

2

3

4

5 Iteration

1

2

3

4

5 Iteration

Figure 7.2: Variation of SOLINT, FLUX and other adverbs with iterations in the tasks CALIB (left) and IMAGR(right).

7.2.1

Selfcalibration

An example of adverb setting in the task CALIB is shown as follows.
TASK ’CALIB’
Call the task CALIB.
INDISK 1; GETN 101
Get SPLITed file.
CALSOUR ’LKHA234’ ’’Calibrator sources.
BCHAN 0; ECHAN 0
Select all spectral channels.
ANTENNAS
0
Select all antennas.
ANTUSE
2 0
Mean gain is calculated with antenna # 2.
UVRANGE0
Set all uv range for weight, useful for extended sources.
DOCALIB
2
Calibrate data with a CL table and weights.
GAINUSE4
CL table to be applied.
FLAGVER=-1; DOBAND=-1
No FG and BP tables applied.
IN2DISK 1; GET2N 102
Get an image file that was created in the task IMAGR.
INVERS
1
CC file version # in the image file.
NCOMP
20
Number of CLEAN comps to be used for source model.
OUTNAME’LkHa234
Output UV file name (name).
OUTCLASS’CALIB’
Output UV file name (class).
OUTSEQ0
A new sequence number is assigned.
OUTDISK1
Output UV file disk drive #.
REFANT
2
Reference antenna.
SOLINT
0.5
Solution interval in minute.
APARM(1)=3 3 and 4 ants make closures in pha. and amp./pha. calibrations, respectively.
APARM(7)7Signal-to-noise ratio cutoff.
’L1’ should be selected in amplitude/phase calibration.
SOLTYPE’L1’
SOLMODE’A&P’
Either ’P’ (phase only ) or ’A&P’ (amplitude/phase) is selected.
SNVER
0
A new SN table is generated.
INP; GOIf a multi-source ﬁle is used, the obtained SN table should be applied to the existing CL table with thetask CLCAL.

7.2.2

Making a CLEANed image

In making a CLEAN image with the task IMAGR, the following adverbs control the CLEAN performance.
NITER 1000

Number of CLEAN components picked up in maximum, or number of iterations.

CHAPTER 7. SELF-CALIBRATION AND HYBRID MAPPINGNMAP 1
CLBOX 0
GAIN 0.05
FLUX=-0.2

30

Number of maps containing the radio source emission.
No pixel coordinate of CLEAN boxes is specified for interactive setting.
Clean loop gain (0.01-0.2).
CLEAN stops when a Clean comp. is weaker than 0.2 Jy or has a negative value.

The coordinates of CLEAN boxes in which CLEAN components are picked up are interactively set on
the AIPS TV Server. Afterward, the adverbs CLBOX is set in the iterative process in the hybrid mapping inwhich a user knows where CLEAN components are expected to exist.

7.2.3

Checking image statistics(1) The verb TVBOX let a user put boxes on the image displayed on the AIPS TV Server. When quitting
the verb, pixel coordinates at bottom left and top right corners of the boxes are displayed. These
coordinates will be used in the image statistics.
(2) The task IMEAM displays results of the image statistics in a selected ﬁeld, maximum and minimum
intensities and the pixels providing these values, mean and r.m.s. levels of intensities. The statisticﬁeld is selected by the verb TVBOX and speciﬁed in the adverbs BLC (bottom left corner) and TRC (topright corner).
(3) The verb IMSTAT returns results of the image statistics in the speciﬁc adverbs.
(4) The task PRTCC prints a list of CLEAN components of the speciﬁed image (or image cube).

7.2.4

End of iteration process

The hybrid-mapping and self-calibration is an iterative process in which calibration solutions with the better
solutions and higher time resolution are gradually obtained from the better source brightness model. In theimaging (the task IMAGR), the adverb FLUX controls the quality of an obtained image, set to be larger absolutevalue to smaller absolute value. The value of the adverb reaches 3-5 times as big as a noise level calculatedwith noise theory and observation parameters. This control is meaningful when iterations of self-calibration
improve the calibrated data.
The quality of the self-calibration solutions are controlled by the adverb SOLINT, SOLMODE in the task
CALIB. The value of the adverb SOLINT is set from longer (but shorter than a coherence time) to shorter(equal to a parameter period if possible). The parameter of the adverb SOLMODE is set to ’P’ at the beginningand to ’A&P’ in the ﬁnal iteration stage. Variation in the adverbs values mentioned above is presented inﬁgure 7.2.
Result of every step of the iterations should be check using the tasks and verbs listed in section 7.2.3.
The dynamic range on an image, a peak intensity divided by r.m.s noise intensity, should be improved by
the iterations. If the improvement is saturated, then the iteration process stops.

Chapter 8Strategy on observation andcalibration (2)This chapter describes the importance of visibility calibration by watching every spectral channels especiallyfor spectral line or maser source data. Diﬀerent from images of continuum emission sources, the maser
sources consist of a number of maser spots that have diﬀerent locations and line-of-sight velocities. Thismeans that it is essential to make excess path delay calibration and amplitude calibration for individual
spectral channels. There are several diﬀerence in planning observations between for continuum and maser
sources. Here such diﬀerences are mainly discussed.

8.1

Group delay estimation

Because a maser source have emission in the limited number of spectral channels, even within which fringe
phases are quite diﬀerent, group delays or clock oﬀsets cannot be estimated with the maser emission. Therefore, another continuum calibrators are necessary to make clock oﬀset calibration (see also section 5.1.2).
Note that usually the continuum calibrators are far away from the target maser source and that excess pathdelays due to the atmosphere varies mainly with antenna elevation. Therefore, an accuracy of the groupdelay estimation towards the maser source is limited by the angular separation between the target and thecalibrators.

8.2

Bandpass calibration

To make maser astrometry with high precision or to get continuum source images with extremely highdynamic range image, bandpass calibration, especially for bandpass phase calibration, should be made using
very bright continuum calibrators (see also section 5.1.5). The data shall not be averaged along frequency
except for data having extremely high spectral resolution. At frequency bands of 22 GHz or higher, it is quitdiﬃcult to get the bandpass phase response unless suﬃcient time is consumed to scan the bright continuum
calibrators. For example, at 22 GHz including H2 O astronomical maser emission, only 10 or less continuum
calibrators can be used for this purpose. These calibrators still need big telescopes such as Nobeyama 45-m
telescopes. According to the author’s experience, such calibrators are scanned for as long as 40 minutes inJapanese VLBI Network (J-Net) observations. It is lucky if such bright calibrators can be used for clock
oﬀset calibration; in this case no extra time is necessary only for getting bandpass phase characteristics.
For these reasons, digital sampling just after down-converting the radio frequency signals and digitalﬁltering for base band channel data are essential. VERA has already introduced these systems, but theobtained data are not free from bandpass response problem because receivers and low-noise ampliﬁers still
have the bandpass responses in wide frequency widths.

31

CHAPTER 8. STRATEGY ON OBSERVATION AND CALIBRATION (2)

8.3

32

Velocity tracking

Suppose that individual maser spots having speciﬁc line-of-sight velocities with respect to the standard frame(e.g., the local stand of rest) generate maser emission at diﬀerent Doppler frequencies from time to anotherbecause of the Earth’s orbiting motion and rotation. A velocity vector of the Earth with respect to thetarget maser source varies by up to 1 km s−1 and 0.4 km s−1 per day due to them, respectively (see also,e.g., [19, 18]). Such velocity drifts are bigger than a velocity spacing of a spectral channel of VLBI data(typically 0.2 km s−1 ). In the maser data analysis, visibilities contained in the same Doppler velocity should
be collected in a velocity channel. Alternatively, fringe phases should be shifted as described in the texts([19, 18]).

8.4

Amplitude calibration with maser emission

Amplitude calibration described in the previous chapter is imperfect even if precise data of system noise
temperatures and antenna gains are provided. It is because the procedures mentioned above does not trace
the performance of antenna pointing. In the bigger telescopes with smaller beams, antenna pointing is
aﬀected by wind, sun light and weather condition. The observed ﬂux density of the sources rapidly changes
with time. When a maser source is bright enough to be detected within a short period (≤ 1 min) and its
size of maser feature distribution is compact (within several arcseconds), this can be used as an amplitude
calibrator. This method is called as the template method.
In the template method, a ”template” total-power spectrum is prepared from a telescope having goodsensitivity at an epoch when antenna parameters (gain and system noise temperature) are known. The
amplitude of the template spectrum is compared with those taken from other telescopes and at other epochs.
The relative accuracy of the amplitude calibration achieves a few percents. However, this method isinvalid when the maser source is variable during the observation (sometimes the ﬂux variation occurs). We
have a limited number of chances to perform the template method because we need bright maser emission(over 100 Jy) that can be detected with every telescope for a short period.

Chapter 9

Advanced calibration
This chapter describes further data calibration for obtaining maser image cubes (and high quality continuum
images). Figure 9.1 presents a ﬂow of the advanced calibration, from the data that are calibrated in thefundamental procedures described in previous chapters to making the data which can be used for creating
the ﬁnal image cubes.

9.1

Bandpass response

The task BPASS calculates bandpass response and creates a bandpass (BP) table. The performance of thetask BPASS is described in other texts. When setting the adverb BPASSPRM=1, bandpass amplitude response
is obtained from total-power spectra. There several notices in data reduction for maser sources especiallywhen obtaining complex bandpass response.
• A solution interval (SOLINT) is set to be longer than duration of the whole observation time for obtaining(time-constant) complex bandpass response with suﬃcient quality.
• Fringe ﬁtting and calibration should be completed before performing the task BPASS.
• Calibration for complex bandpass response is eﬀective when phase slopes of the response are well found.
• If quality of the obtained response is poor, the solution should be smoothed among frequency channels.
An example of the complex bandpass response is presented in ﬁgure 9.2. The phase slopes are quitesmooth and amplitude of the phase variation is smaller than 10 degrees except for the band edges. Thus
complex bandpass response is useful when the maser emission has a wide frequency (velocity) coverage.

9.2

Doppler tracking

Because a single narrow maser component detected is apparently moving along frequency during the observation as the Earth orbits the Sun and daily rotates. Calibration of visibilities for such Earth’s motion
is called as Doppler tracking. The principle of the Doppler tracking is described in the text ([19, 18]). In
AIPS all visibilities having the same line-of-sight velocity are collected in the same velocity channel after the
Doppler tracking.

9.2.1

Defining the source velocities

In the original FITS ﬁle and AIPS UV data, no velocity information is speciﬁed for sources. But a user knows
the correspondence between a Doppler frequency and a line-of-sight velocity of the maser source. In moreconvenient cases, especially when using NRAO’s SCHED for making an observation schedule, the user knowthat a center channel of each IF channel exactly corresponds to a source velocity speciﬁed in the SCHED
keyin ﬁle. The AIPS task SETJY sets such correspondence in a source (SU) table as follows.

33

CHAPTER 9. ADVANCED CALIBRATION

34

Data calibrated infundamental parts
Amplitude only or complex
BP1
POSSM/LWPLA

BPASS

Yes

Bandpass tables
are necessary?

APARM(8)=2
SETJY
CVEL

DOBAND=1
FLAGVER=1

CVEL output data
SPLIT
Yes
Maser total-power spectral
data with template

INDXR

NX1

Applying
template method?

SN4
ACFIT
TACOP

SNPLT/LWPLA
CLCAL

Apply either SN2 or SN4
and SN1, SN3 to create CL3(without TECOR)

Data calibrated inadvancing parts

Figure 9.1: Flow chart of the part that describes the advanced data calibration.
TASK’SETJY’Call the task SETJY.
SOURCES’LKHA234’
Sources to be modified.
BIF
1
Low IF # for flux density.
EIF
1
High IF # for flux density.
ZEROSP
0
Clear I,Q,U,V flux density.
OPTYPE’ ’
Clear function option type.
SYSVEL=-17.9
Velocity of the maser source (km/s).
RESTFREQ 2.223E+10, 5080000 Set a rest frequency of H2O maser emission (22,235,080,000 Hz).
VELTYP’LSR’
Set a velocity type to be "local standar of rest".
VELDEF’RADIO’Means velocity definition in "radio astromony frame".
APARM
127 0
New channel pixel to which SYSVEL referes.
INP; GO
Note that the task SETJY should be used for each of IF channels to set diﬀerent velocities for the IF
channels covering diﬀerent velocities. The contents of the modiﬁcation for the SU table is conﬁrmed in thetask LISTR (see section 4.2).

9.2.2

Converting visibility data from in frequency to in velocity domain

The task CVEL performs not only Doppler velocity tracking by modifying visibilities but also changing thechannel structure. In the output UV ﬁle of the task, frequency channels are converted to velocity channels.

CHAPTER 9. ADVANCED CALIBRATION

35

50
-50
1.2 IRIKI

OGASA20ISHIGAKI

IF 1(L)IF 1(L)

0.8
0.4
IF 1(L)
0.0
50-50
1.2 KASHIM34

Plot file version 1 created 08-FEB-2004 20:36:47
MULTI r03357b a.MSORT.1
Freq = 22.2270 GHz, Bw = 16.000 MH Bandpass table # 1
Lower frame: BP ampl Top frame: BP phase
Bandpass table spectrum Antenna: *Timerange: 00/00:00:01 to 999/00:00:00

0.8
0.4
IF 1(L)
0.0

Figure 9.2: Bandpass characteristics obtained in BPASS and plotted with POSSM (APARM(8)=2). Only Kashima
34-m antenna has a slope of bandpass phase because an analogue base band ﬁlter (VSOP terminal) is used.
Other VERA antennas have digital base band ﬁlters.
In the new channel system, a velocity channel speciﬁed in the adverb APARM(1) in the task SETJY has thevelocity speciﬁed in the adverb SYSVEL in the same task. The task CVEL is controlled as follows.
TASK ’CVEL’
INDISK 1; GETN 100
OUTNAME’j03153b’
OUTCLASS’CVEL’OUTSEQ
1
OUTDISK
1
SOURCES’LKHA234’
TIMERANG0FLAGVER0
DOBAND1
BPVER
1
INP; GO

Call the task CVEL.
Get a UV file.
Output UV file name (name)Output UV file name (class)
Output UV file name (seq. #)Output UV file disk unit #Source list to be shifted.
Specify all time range.
Apply the newest flag tabl.
Apply the BP table before maser data calibration.
Bandpass table version applied.

A user carefully check the CVEL result by watching messages shown in the message server while the task
is running. With wrong combination of the adverbs SYSVEL and APARM(1), large channel shifts occur andmany visibilities at one of the band edges are lost. After ﬁnishing the task CVEL, the task INDXR should beexecuted to make a new index (NX) table.

9.3

Template method using maser emission

The template spectrum and total-power spectral data are provided by the task SPLIT by setting the adverb
APARM(5)=2. The task ACFIT performs the template method. AIPS COOK BOOK chap. 9 describes thismethod in more detail. A user needs information on a sytem noise temperature and a degree per ﬂux density(DP F U = 2k/Aeﬀ ) of the telescope at the epoch, from which and when the template spectrum was taken.

Chapter 10

Watching maser emission
At this stage, reference velocity channels should be selected, which contain maser emission suitable forcalibration of the maser data. Such maser emission has so compact that visibility phase changes not by themaser structure but only by phase ﬂuctuation due to the atmosphere. At least brightness structure of themaser emission should be so simple that phase calibration is easy. Of course, the maser emission should bebright enough to calibrate the maser data with short calibration solution intervals. In practice, amplitude
information is also important to perform the channel selection. Such channel selection is performed with thetasks POSSM, VPLOT and UVPLT. The usage of the tasks POSSM and VPLOT are explained in sections 4.5 and
4.6, respectively.

10.1

Amplitude variation along time

Because visibility phases are severely ﬂuctuated by the atmosphere, it is risky to judge source brightness
structure with these phases. Instead visibility amplitudes are used for the judgment. Figure 10.1 shows time
variation of phases and amplitudes of the maser emission in the velocity reference channels. The temporary
variation in the amplitudes indicate an extended maser structure. The selected velocity channels, however,are more suitable for the reference channels than others because they have highest ﬂux densities.

10.2

Amplitude and phase variation along velocity

Cross-power spectra are also useful for judging source structure. Amplitude proﬁles of the spectra dramatically change with time. Individual amplitude peaks may correspond to individual maser features, whichhave diﬀerent sizes and locations. Because cross-power ﬂux density is aﬀected by source size and by blendof multiple features in the same velocity channel, ﬂux densities vary relatively among the amplitude peaks.
Velocity channels having large ﬂux densities, therefore, are suitable for the reference channels.
It is risky, however, to choose the velocity channel at the amplitude peak, in which another weakercomponents might exist and the source structure might be complicated. At this situation, slope of fringe
phases are useful to judge the source structure. If the phases are constant among several of the successive
velocity channels, the source structures in the velocity channels are almost same, which is expectable for acommon simple structure. Usually it is better to choose the velocity channels located slightly away from theamplitude peak to pick up one maser feature.

10.3

Amplitude against u-v distance

Flux density against u–v distance is obtained with the task UVPLT. This diagram indicates a source size andstructure. When the radio source is extended, the ﬂux density rapidly drops with u–v distance.

36

Phase (degree)

Amplitude (Jansky)

CHAPTER 10. WATCHING MASER EMISSION

80
60
40
20
0
100
0
-100
80
60
40
20
0
100
0
-100
80
60
40
20
0
100
0
-100

37

IF 1 CHAN 429 STK LLNOBEYA45 - KASHIM34 ( 1 - 2 )NOBEYA45 - MIZNAO10 ( 1 - 3 )NOBEYA45 - KAGOSIMA ( 1 - 4 )

20

22

1/00
1/02
TIME (HOURS)

1/04

1/06

Figure 10.1: Temporary variation in visibility amplitudes and phases that is obtained with the task VPLOT.
The reference channel candidates were selected in H2 O maser emission in LkHα234 observed with the J-Net.
Fringe phase is still scattered because of the atmospheric phase ﬂuctuation. On the other hand, visibility
amplitudes exhibit systematic temporary variation. It is expected that the maser emission in this diagram so
extended that the amplitudes increase only when projected baseline lengths shorten. The shortest baseline(Nobeyama-Kashima, 200 km) detected the highest ﬂux density of the maser emission, which is consistent
with the interpretation mentioned above.

CHAPTER 10. WATCHING MASER EMISSION

200
-200

38

200
-200
35 NOBE - MIZ

NOBE - KAS

80

25

40
15
0
200
-200

Timerange: 00/18:31:04 to 00/18:37:04
NOBE - KAG

25

15
420

430

440
Channels

450

460

200

200

-200

-200
60

200

NOBE - KAS

NOBE - MIZ

40
20

100

0
0
200
-200
35

Timerange: 00/20:58:05 to 00/21:04:05
NOBE - KAG

25
15
420

430

440
Channels

450

460

Figure 10.2: Variation of fringe amplitudes and phase along frequency, which are obtained from diﬀerent
baselines and epochs. There is an emission peak around the channel # 450, in which phase slope is ﬂat andamplitudes are large and stable.

Chapter 11

Maser calibration
This chapter describes how maser source data are calibrated with the selected reference velocity channels,
which is made in the previous chapter. The calibration solutions are applied to all of velocity channels andIF channels. Figure 11.1 shows a ﬂow of the maser calibration.

11.1

Interactive data flagging

Previously, amplitude calibration and fringe ﬁtting have used longer solution intervals that are close to acoherence time. In the self-calibration and fringe-ﬁtting in antenna-fast-switching phase-referencing, shorter
solution intervals shall be used. In such situations, bad data that usually appear in a short period (≤60 sec)
may generate strange calibration solutions and aﬀect ﬁnal images. Now such bad data should be removed
interactively. Although some of tasks can automatically remove such bad data (e.g., CLIPM), interactive
ﬂagging is still recommended. The task IBLED make the interactive ﬂagging.
It is expected that bad data appear in all velocity channels at the same time. It is convenient, therefore,
to ﬂag the bad data in the reference velocity channels then to apply the ﬂag to all velocity channels. To
perform it, at ﬁrst, the reference velocity channels are split from the AIPS UV data by the task SPLIT. The
SPLITed (single source) ﬁle is converted to be a multi-source ﬁle by the task MULTI, and a new NX tableshould be created by the task INDXR. This SPLITed ﬁle is used by IBLED to specify all velocity channels, or
BCHAN=0; ECHAN=0. When a ﬂag (FG) table newly created is copied to the original AIPS UV data, the ﬂag
information in the FG table can be applied to all velocity channels.
The author has ﬂagged visibilities in Stokes parameter I in all baseline data in the task IBLED for VLBA,EVN and J-Net data. Visibility data in the task IBLED are averaged in a period shorter than a coherencetime but the period is still long enough to have suﬃcient signal-to-noise ratios (≥20).

11.2

Fringe fitting using maser data

At this stage, only residual delay rates and phases are calculated with the reference velocity channels by thetask FRING. To perform it, the adverb DPARM(2)=-1 is speciﬁed to switch delay calculation oﬀ. The adverb
SOLINT is still set to be a duration close to a coherence time. Note that BIF and EIF are never speciﬁed tokeep the same number of IF channels in the SN table newly created as that in the AIPS UV data. Only the
IF channel containing the reference velocity channels, of course, has good solution.
The solutions are displayed by the task SNPLT and by specifying OPTYPE=’rate’. It is recommended tocheck whether the uncertainty of the rate solutions is within the value that can solve 2π-n radians ambiguityin phase connection. The fringe rate criterion σνf in unit of Hz is calculated as follow,
1,(11.1)
5ΔT
where ΔT is the solution interval of the fringe ﬁtting in unit of second. This equation means that a phasedrift less than 1/5 rotation is permitted.
σνf ≤

39

CHAPTER 11. MASER CALIBRATION

40

Data calibrated in advancing parts
Finding reference velocity channels
POSSM/VPLOT/UVPLTSPLIT/MULTI/INDXR
Data in the reference velocity channels
FG1 (new)

IBLED

Flagging ALL velocity channels

TACOP

SN4
For reference channels
DPARM(2)=-1 (no delay solution)FRING

SNPLT/LWPLASNCOR Copy 1 IF solutions to all IF channels
CLCAL

CL5+SN4 >> CL6

SPLIT

Hybrid mapping
for reference velocity
channels of maser emission
TACOP
Copy all SN tables

SNCOR Copy 1 IF solutions to all IF channels
CLCAL

Apply all above SN tables

Fully calibrated data
Figure 11.1: Flow chart of the part that describes calibration using reference velocity channels in maser
emission data.

11.3

Edit SN tables

If there are solutions poorly determined in the SN table, they can be ﬂagged out interactively by the task
SNEDT on the AIPS TV Server. In particular, fringe ﬁtting solutions should be carefully taken care because
bad solutions may introduce 2π-n radians ambiguity in phase interpolation.
Usually there are several IF channels that cover diﬀerent velocity ranges, while the reference velocity
channels are included only in one of the IF channels. In this case, solutions obtained in this IF channel
should be copied to other IF channels. This can be made by the task SNCOR with setting the adverbs
OPCODE=’CPSN’ and SNCORPRM= [IF channel containing true solutions].

11.4

Self-calibration using maser data

At this stage, the reference velocity channels are split for self-calibration. To keep the ﬁle structure that has
the same number of IF channels and Stokes types, when performing the task SPLIT only the adverbs BCHAN
and ECHAN are modiﬁed (see also section 7.1.2). Even if an IF channel containing the reference velocity

CHAPTER 11. MASER CALIBRATION41

SN 4 Lpol IF 1

Rate (mHz)

0.000
10
0
-10
-20
20
0
-20
-40
-60
50
0
-50

1L NOBEYA45

2L KASHIM34

3L MIZNAO10

4L KAGOSIMA
18

20

22

1/00
1/02
TIME (HOURS)

1/04

1/06

Figure 11.2: Fringe-ﬁtting solutions (rate residuals) that are obtained with the LkHα234 H2 O maser emission
in the selected velocity channels.

channels is used in self-calibration and hybrid mapping, all IF channels should be split at this stage.
The self-calibration process in the remaining parts is the same as that described in sections 7.1.3 and7.2.1. There are two important notes as follows.
(1) In the task IMAGR, the adverbs BIF and EIF should be speciﬁed to select only one IF channel containing
the maser emission. On the other hand, in the task CALIB, all IF channels should be speciﬁed. As
results many solution failures occurs at IF channels without maser emission. This does not matter formaser data calibration. Instead, solutions in the IF channels containing the maser emission should bechecked with the task SNPLT.
(2) All SN tables are necessary to update the existing CL table in step-by-step. All of the SN should copied
to the original (multi-source) UV data, edited with the task SNCOR in the same procedure as that
described in section 11.3, and applied with the task CLCAL.
(3) If the tasks MULTI and INDXR are not used in the previous step, the task IMAGR uses an SN table that iscreated in a previous step to use the task CALIB. In this case, only ﬁnal SN table is used for calibrating
the original visibility data without any update of CL tables.

Chapter 12

Search for maser emission
In practice, maser emission, especially H2 O maser emission is found in a huge sky area and in a wide velocity
coverage. Sometimes it covers up to 10 arcseconds and quite huge for VLBI imaging. There are as many as1000 spectral channels having maser emission. In these case, it is impossible for one CLEAN image cube tocover the whole maser emission region with over (104 ×104 ) grids. From the beginning, it is quite diﬃcult
to look for such maser emission in CLEAN image cubes. Here, how maser emission is looked for in the widesky ﬁeld is described.
Sometimes it is forgotten that VLBI images lose their absolute coordinates after fringe ﬁtting and selfcalibration. Here how the absolute coordinate is estimated is also described.

12.1

Field of view of maser source data

Field size of maser distribution is the most severe factor of all the data reduction procedures. It is a goodidea to estimate the size of ﬁeld of view for the data before choosing the methods of maser emission search.
The complex visibility V (u, v, w), which is obtained after cross correlation with delay tracking and fringe
rotation from a two element interferometer with a baseline vector (u, v, w) when observing the source withbrightness distribution B(ξ, η), is described as follows, ∞ ∞V (u, v, w) =
−∞





dξdη
A(ξ, η)B(ξ, η) exp −2πj uξ + vη + w( 1 − ξ 2 − η 2 − 1) 
, (12.1)
1 − ξ 2 − η2−∞where (u, v, w) has a unit of wavelength of the observed radiation and is deﬁned with respect to the celestial
position in the correlation processing, (ξ, η) is position oﬀset from the above assumed position, A(ξ, η) is thegeometric mean of the beam pattern of the telescope assuming the telescopes accurately turned to the above
assumed position (see also Eq. 3.13 of text [23]). Here there are three criteria to determine the ﬁeld of view.
For astronomical masers, ’bandwidth smearing’ can be ignored because of narrow frequency spacing of eachmaser component.
I. We usually obtain simultaneously the real and imaginary parts of the visibility shown in Eq. 12.1 andcalculate visibility amplitudes and phases. The obtained visibilities are time-averaged for a parameter(accumulation) period (0.1–10 s) with delay tracking and fringe rotation using one set of the tracking
parameters (e.g., geometrical delay). The fringe phase, therefore, is smeared and fringe amplitude is
reduced because the tracking parameters should change during the parameter period with the Earth’s
rotation. Thus, ’the time average smearing’ gives the limit on the ﬁled of view under the criterion
shown approximately as follows,
1 rad ≥ Δφ  2πΔτ ωe Dλ · Δθ,(12.2)

where Δφ is a phase shift during a parameter period, Δτ duration of the parameter period, ωe angularvelocity of the Earth’s rotation, Dλ projected baseline length in unit of wavelength, Δθ the ﬁeld of42

CHAPTER 12. SEARCH FOR MASER EMISSION

43

Figure 12.1: Geometrical relationship between a source underobservation B(ξ, η) and an interferometer or one antenna pairof an array. The spacing vector
Dλ of the telescopes has components (u, v, w). The ﬁgure iscited from ﬁgure 3.2 of the text
[23].

Figure 12.2: Image volume and its relation to the sky brightness along the one image coordinate l(ξ or η). n
shows the direction of the map center. The direction is called as ’a phase-tracking center’ when phase shifting
is made to shift the map center. (Left) Three-dimensional transformation of the analytic visibility function
maps the sky brightness onto a unit sphere. The dots represent these sources. (Middle) Convolution with adirty beam results in sidelobes, shown as dashed lines. The direction of the dashed lines rotate as the Earthrotates. (Right) The two-dimensional image is recovered by projection onto the tangent plane indicated byvertical dashed line. The separation between two sources is more signiﬁcantly diﬀerent on the tangent planefrom that on the unit sphere at point with larger distance from the direction n.

CHAPTER 12. SEARCH FOR MASER EMISSION

44

view. This equation means that the observation with the longer baseline corresponds to the smallerﬁeld of view. The ﬁeld of view is,Δθ[as] ≤ 14.2

λ[cm].
Δτ [s] D[1000km](12.3)For example, the ﬁeld of view of about 7is obtained when the baseline length is 3000 km, the observed
wavelength is 1.35 cm (H2 O 22 GHz water maser) and the parameter period is 1. If the ﬁeld size ofmaser distribution or separation between the reference and target source is larger than the ﬁeld limit,
we must perform the data correlation separately assuming the source positions at several celestial points
or at both the reference and target sources. The output data, therefore, increases with the number ofthe correlation positions.
II. The ﬁeld of view of the single CLEAN map is limited more severely. The image synthesis is made on
the single plane, while the actual source brightness distribution is on the sphere of the sky. The eﬀect
on imaging by the position discrepancy between the two planes is shown in Fig. 12.2. The shape of
the image or the brightest point of the source should be changed at edge of the wide ﬁeld map.
Thus, ’the polyhedron imaging’ has the limit on the ﬁled of view under the criterion shown approximately as follows,(Dλ · σ)2 ≤ a,

(12.4)

where, Dλ is a baseline vector of the telescope pair, σ is position oﬀset from the map center, and a is
a factor to determine the criterion, usually 1/20 or 1/25. In conclusion, the limit of ﬁeld of view for’the polyhedron imaging’, in unit of radian, is given as follows,
Δθ ≤



λ/D/5 ≈ θsyn /5,(12.5)

where θsyn is a synthesized beam of the interferometer. For example, when the synthesis beam is 1
mas, the ﬁeld of view of the single plane map is limited to about 2.8.
III. Of course, a primary beam of a telescope absolutely gives a limit on ﬁeld of view.

12.2

Long-time data integration

After full calibration that has been mentioned above, coherent integration for the whole observation time
gets possible. The task POSSM makes cross-power spectra performed such long-time integration. Figure12.3 shows cross-power spectra with an integration duration of as long as 12 hours. H2 O maser components
weaker than 1 Jy are now detected. If setting the adverb NPLOT=0, data in all baselines speciﬁed are averaged
to make a cross-power spectrum of the VLBI array.
Note that scalar and vector averages (setting the adverb APARM(1)=1 and =0, respectively) provide different cross-power spectra. The former is similar to that obtained in total-power spectra in which most of
all maser emission is detected. Therefore the former is used to ﬁnd faint maser emission. The latter, on theother hand, is aﬀected by array conﬁguration and the source structure. The latter is used, for example, toestimate rough location of faint maser emission that cannot be detected in the fringe-rate mapping mentioned
in the next section.

12.3

Fringe-rate mapping

Fringe-rate mapping method has been described in detail in these documents ([27, 19, 18]). Fringe phases
enable us to make synthesized images that performs inverse Fourier transform of visibilities. The fringe
phases, however, are aﬀected by many factors and themselves have 2π-n radians ambiguity problems. In
early VLBI observations, fringe rates have been used as major observable parameters. Nowadays, fringe rates
are still important to make rough maps with wide ﬁelds of as large as several tens of arcseconds. Because

CHAPTER 12. SEARCH FOR MASER EMISSION

100

200
0

45

-100
NOBE - MIZ

NOBE - KAS

40

40

20

20

0

IF 1(LL)

0

200

200

-200
40 NOBE - KAG-200

IF 1(LL)

KASH - MIZ

30
30
20

20

10

10
0

IF 1(LL)
200

0
400

600
Channels800

IF 1(LL)
200

400

600
Channels

800

Figure 12.3: Cross power spectra of the LkHα234 H2 O masers that are obtained by integration for the wholeobservation time (12 hours). Bars on the top of the spectrum of Nobeyama–Kaashima baseline indicate
detection velocity ranges of the H2 O maser emission, in which clear phase slopes are seen.

fringe rates do not have any ambiguity, they are also used to estimate absolute coordinates of the target
sources after applying clock parameter calibration.
A fringe rate spectrum is obtained by Fourier transform of a cross-correlation function against time in a
spectral channel (see [19, 18]). A relative fringe frequency, a relative fringe rate multiplied by the observed
frequency νf is expressed as follows,Δνf  u̇Δα cos δ + v̇Δδ.

(12.6)

where (u̇, v̇) are the time-variation rate of a baseline vector. Thus a fringe frequency is a linear function ofsource coordinates; one line is drawn on the fringe-rate map as shown in ﬁgure 12.4. Because (u̇, v̇) varies
more slowly than the baseline vector (u, v), wide-ﬁeld mapping is possible.
Note, however, that the fringe-rate mapping is unavailable for sources very close to the celestial equator(|δ| ≤10◦) because most of the lines shown above are almost parallel to the north–south direction and it isquite diﬃcult to identify the location of maser spots.

12.3.1

Wide field mapping with relative fringe rates

Fringe-rate mapping has been used to make mainly maps of H2 O masers having very wide ﬁelds of maser
spots distribution (e.g. W3OH, Orion KL, W49N, etc.) and CH3 OH masers whose observations could use
only a few telescopes that have the receiving systems covering the special frequency band (e.g. 6.7 GHz). The
accuracy of such kind of position estimation is limited by the phase (rate) ﬂuctuation due to the atmosphereand empirically achieved around 100 times as poor as the synthesized beam size of the VLBI array.
The task FRMAP performs the fringe-rate mapping as follows.

CHAPTER 12. SEARCH FOR MASER EMISSION

46

1.0
0.8

Decl. offset or ΔY (arcsec)

0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

R.A. offset or ΔX/cosδ (arcsec)

Figure 12.4: A fringe-rate map for a group of selected velocity channels containing H2 O maser emission in
LkHα234. Two red circles indicate the locations of the H2 O maser spots. Each of the lines were obtained byintegrating the visibility data for 15 minutes. 10 lines were omitted in the iterative process in identiﬁcationof maser spots.

TASK ’FRMAP’
Call the task FRMAPINDISK 1; GETN 100
Get UV data used for the mapping.
SOURCES ’LKHA234’
Maser source nameUVRANG0
UV range limit is useful when making wide-field maps.
TIMERANG 0
Time range to be selected, useful for precisely getting maser data.
STOKES ’I’
Stokes parameter ’I’ is used for the mapping.
BIF 1
IF number including maser emission.
BCHAN 440; ECHAN 446
Begin and end of velocity channels plotted.
CHANNEL=-1
No channel for phase reference in the mapping is specified.
ANTENNAS m1
Antennas with high sensitivity are specified.
BASELINE 0
All baselines with ANTENNAS.
DOCALIB
2
Calibrate with a CL table and weights.
GAINUSE 9
CL table version to be applied.
FLAGVER 0
Flag table version.
DOBAND
1
Apply a BP table.

CHAPTER 12. SEARCH FOR MASER EMISSION

47

BPVER
1
BP table version to be applied.
APARM(1) 2
Pre-average interval in second, similar to a parameter period.
APARM(3) 5
Number of spectral channels to be averaged.
APARM(4) 50; APARM(5) 100
R.A. and decl. steps of a map grid to find maser emission (mas).
APARM(6) 2000; APARM(7) 1000
Half widths of a map on the sky in unit of mas.
BPARM(1) 10
Threshold (in sigmas) in detection maxima in fringe spectrum.
BPARM(2) 70
Time interval between beginnings of interval of averaging (min).
BPARM(3) 15Interval of averaging in unit of minute.
DOTV
1
Plot a fringe-rate map on the AIPS TV Server.
INP; GO
There are special notes for the adverbs in the task FRMAP to work appropriately.
• CHANNEL: The task FRMAP works appropriately even before full data calibration has not made yet. In
this case, this adverb sets a phase-referencing channel, whose phases are subtracted from all spectral
channels before obtaining fringe-rate spectrum.
• TIMERANGE: Because data are picked up uniformly along time by following the adverbs BPARM(2),BPARM(3), specifying this adverb enables us to get more visibility data from the selected source.
• BPARM(1): Smaller number for a wider ﬁeld, larger number for quicker processing.
• BPARM(2), BPARM(3): Because less than 11 fringe-rate spectra are available in each of baselines, theseadverbs should be set appropriately.
• BPAEM(6): Minimum number of lines that cross the same point, or a maser spot location, on the sky.
The input value is multiplied by the number of lines per baseline and by the number of baselines. To
ﬁnd fainter maser emission, a smaller number (say 0.2) is suitable.

12.3.2Estimating absolute coordinates of the maser source

Absolute coordinates of maser sources are quite important information especially to make image cubes having
a velocity range over several tens of kilometers.
For example, suppose maser spots that are found in diﬀerent Doppler frequency channels separated by up
to Δν. If the absolute source coordinate has a position uncertainty Δs, an uncertainty of relative positions
among the maser spots σs is derived from the following equations,νD · ΔsD · σs∼ Δν,cc

σs ∼ ΔsΔνν

(12.7)

By inserting, for example, Δs ∼ 100 mas, Δν/ν ∼ 1/1000 (corresponding to a Doppler velocity of 300 km s−1 ),an error of 10 μas in the relative maser spot position is derived.
Estimation of the absolute coordinate is made after fundamental calibration (see section 6) with continuum calibrators but before fringe ﬁtting with the target maser source. This means that the calibration (CL)table used here shall be obtained by applying a solution (SN) table as obtained in section 6.5. The accuracyof such kind of position estimation is limited by the phase (rate) ﬂuctuation due to the atmosphere andempirically achieved around 100 times as poor as the synthesized beam size of the VLBI array.

12.4

CLEAN image cubes having multiple wide fields

To make image cubes of maser sources, the UV data that are calibrated using the data in reference velocity
channels of maser emission are at ﬁrst split to a single source ﬁle using the task SPLIT with applying thelatest CL table and FG, BP (if not applied yet) tables that are already prepared (see section 7.1.2). An image
cube consists three channel axes, R.A. and decl. oﬀsets and velocity or frequency channels.
The task IMAGR has been explained in more detail in section 7.2.2. Here, the adverbs in the task, which
are essential for creating maser image cubes with multiple ﬁelds, are described as follows.

CHAPTER 12. SEARCH FOR MASER EMISSION48

DOCALIB=-1; DOBAND=-1
Not applied any CL or BP table, which is already applied.
BCHAN k1; ECHAN k2
Making image cubes covering channels from k1 to k2.
NCHAV 1
Every velocity channel is mapped independently.
CHINC 1All channels without skipped channels are used.
BIF m1; EIF m1 The IF channel m1 is selected.
NFIELD
5
Multiple fields including maser emission are CLEANed at the same time.
DO3DIMAG 0
If pos. offsets are large, using different tangent points are recommended.
FLDSIZE 1024
Wider field (1024 x 1024 pixels) for looking for maser emission.
RASHIFT 0, -.07, .28, .08, -.07
R.A. shifts for the individual fields (arcsec).
DECSHIFT 0, .13, .25, .13, -.13
Decl. shifts for the individual fields (arcsec).
UVTAPER 0
If the source is extended, (Gaussian taper may be necessary (kilo-lambda).
UVRANGE 0
If necessary long (U, V) distance having poor data quality is no used.
UVWTFN ’NA’
To get a sharp beam, uniform weight (UF) is recommended.
NBOXES 0; CLBOX 0 Search CLEAN components in the whole maps.
OVERLAP 1
Restore CLEAN components in overlapped fields.
DOTV=-1
Automatic imaging without human interaction makes the process fast.
After looking for true maser spots, a user can compress the mapping ﬁelds and velocity channel ranges
to save ﬁle size and time for model ﬁtting (see section 14.2).

12.5

Quick statistics of image cubes

Here the task IMEAN is useful to quickly ﬁnd maser emission (see section 7.2.3). When setting the adverbs
DOCRT=1 and OUTPRINT=[output text ﬁle name], all results in the task are printed out to the speciﬁed ﬁle.
By using the keyword ”Maximum”, a user quickly ﬁnd the peak intensity in the image cube. Because animage cube is usually made the statistical analysis channel by channel, a simple RUN script shown as follow
is easy to quickly make such procedures.
proc pkfnd
dowait=1
scalar xg,yg,xmg,ymg,ix,iy,nx,ny,nedge,nover,px,py,bvel,evel,iv
nx=xg/xmg; ny=yg/ymg
task ’imean’
docat=-1;dotv=-1;docrt=-1
for iv=bvel to evel
for ix=1 to nx
for iy=1 to ny
px=xmg*(ix-1)+1-noverif(px < nedge) then px=nedge; end
py=ymg*(iy-1)+1-noverif(py < nedge) then py=nedge; end
blc px, py, iv
px=xmg*ix+noverif(px > xg-nedge) then px=xg-nedge; end
py=ymg*iy+noverif(py > yg-nedge) then py=yg-nedge; end
trc px, py, iv
go imeanend
end
return;finish
In the above script, a user speciﬁes newly deﬁned adverbs, XY, YG, XMG, YMG, NEDGE, NOVER, BVEL, EVEL. To
ﬁnd more than one maser spots in a velocity channel, sub-ﬁelds are speciﬁed, in which only one maser spotwith the maximum intensity is picked up.

Chapter 13

Creating final image cubes
After full calibration procedures, one can ﬁnally get image cubes and use them for scientiﬁc purposes. For
high-precision astrometry, more careful corrections for the image cubes should be performed. Of course,
backups for the data and image cubes ﬁnally obtained shall be performed. Figure 13.1 presents a ﬂow ofsuch ﬁnal procedures.

13.1

Final CLEANed image cubes

After searching for true maser spots in wide ﬁelds, as shown in section 12.3 or 12.4, only ﬁelds and velocity
channels close to the true maser spots found are created.

13.2

Making full maser image in a single map

Maser source data usually has a form of a image cube (X-oﬀset, Y-oﬀset, V-oﬀset). To show all of maser
spots found in diﬀerent velocity channels into a two-dimensional map (example, see ﬁgure 13.2), the following
sequence is useful.
(1) Use the verb IMSTAT to ﬁnd a rms noise level for each of velocity channels.
(2) Use the task BLANK to set intensities of pixels without true maser emission to zero. At this stage, imageﬁles for the individual velocity channels are obtained.
(3) Use the task SUMIM to sum image ﬁles for the individual velocity channels into one map.
The task SQASH is also used to compress the ﬁle of the BLANK output into one map, but the obtained
map may by noise. It is because noise is not appropriately omitted in the task BLANK in velocity channels
in which bright maser emission creates bright side lobes. It is diﬃcult to omit only the side lobes without
deleting fainter true emission in other velocity channels.

49

CHAPTER 13. CREATING FINAL IMAGE CUBES

50

Fully calibrated data

FRMAP

Maser emission
with wide distribution?

Yes

SPLIT
SPLIT

IMAGR
Trial image cubes

IMAGR

Final image cubes

BLANK/SQASH/IMSTATSUMIN/KNTR/CNTR

Final CLEANed
image cubes

TASAV/FITTP
PRTHI

Figure 13.1: Flow chart of thepart that describes creating image cubes and ﬁnal processing in
AIPS and VLBI analysis.

Image cube editing

Backuped files

JMFIT/SAD

Image cube analysis

Scientific data analysis

150

100

Decl. offset (mas)

50

0

-50

-100

-150

Center at RA 21 41 57.37200 DEC 65 53 08.2390
Cont peak flux = 1.0591E+03 JY/BEAM*channel
Levs = 1.059E+03 * (0.050, 0.080, 0.128, 0.205,
0.328, 0.524, 0.839, 1.342, 2.147, 3.436, 5.498,
8.796, 14.07, 22.52, 36.03)
200

150

100

50
0
R.A. offset (mas)

-50

-100

Figure 13.2: Full map of the LkHα234 H2 O masers, which was made by a sequence of the tasks and verbs
IMSTAT, BLANK, SUMIM and KNTR. The brightest maser feature at the map origin has a peak intensity of
78 Jy/beam and sidelobes. There are weak maser features have peak intensities less than 4 Jy/beam, which
can still be seen in the map because diﬀerent blank cutoﬀs (but uniﬁed at a 6-σ noise level) in the task BLANK
were set in the individual velocity channels.

Chapter 14

Getting physical parameters
14.1

Identification of maser spots and features

Deﬁnitions of a maser spot and a maser feature are described in the papers [10, 15]. The maser spot is asingle velocity component of the maser emission. A maser feature is a group of the maser spots with similar
positions and velocities (within a few mas) and a few kilometers per second, respectively). These deﬁnitions
are important to identify true maser emission. True maser spots should be detected at almost the same
location among successive velocity channels. A group of such maser spots is deﬁned as a maser feature z andcalculated its location and velocity in the next process.

14.2

Gaussian fitting to maser spots

Gaussian bright distribution models for maser spots are calculated with the task JMFIT. According to author’s
experience a large fraction of time has been consumed in this part. Because the task JMFIT requests suitableﬁtting boxes (the adverbs BLC and TRC and assumptions of the number of Gaussian components (the adverb
NGAUSS, as well as the adverb GPOS specifying their locations).
At present the task SAD (Search And Destroy) automatically performs the identiﬁcation of Gaussiancomponents and their ﬁtting.

51

Chapter 15

Data backup
Here how to make data backup is described. The calibrated visibility data can be fully saved on DAT tapes
or FITS ﬁles. However, because the visibility data themselves are quite huge, there is an idea to save only
the necessary parts used for quickly recovering the calibrated visibilities and image cubes. It is also a goodidea to save the created image cubes for quickly using speciﬁc scientiﬁc purposes or for shipping them toother collaborators or scientists.

15.1

Back up AIPS UV data and images

All of the AIPS UV data and image ﬁles are saved on DAT tapes or FITS ﬁles on hard disk drives with thetask FITTP. It takes long time, however, to save on DAT tapes for the present huge data.

15.2

Backup only extension tables

The task TASAV splits only extension tables from the original visibility data. Only the extension tables areneeded to make the backup copies, which can be quickly applied to the original visibility data by copying
with the task TACOP.

52

Chapter 16

Scientific analysis
Although distributions of maser features only on the sky plane and the line-of-sight velocity are impressive,proper motions of the maser features provide great advantage in scientiﬁcally interpreting the observational
results with small amount of assumptions and often without ambiguity in the interpretation. Therefore, thistext concentrates on actual steps for the proper motion measurements.

16.1

Proper motion measurement

16.1.1

Astrometric correction

The obtained maps of a maser source is usually deformed by several factors that shall vary with observing
epochs. Therefore maser maps obtained at the diﬀerent epochs are deformed in diﬀerent amount. The
astrometric correction recovers such bending eﬀects as follows. The correction includes scale correction andaxis rotation.
The scale correction should be performed along the line-of-sight velocity because the phase-referencetechnique using reference velocity channels gives the similar phase drift due to the clock delay oﬀset if themaser spot in the reference channel has a position oﬀset with respect to the tracking center in the data
correlation. This correction Δθ(v) is performed for the maser spot with the LOS velocity v using thefollowing equation,v − vrefθref ,(16.1)cwhere vref is the line-of-sight velocity of the phase-referenced maser spot and c is a speed of light, θ ref isa position oﬀset of the phase-referenced maser spot with respect to the phase tracking center in the data
correlation.
Axis rotation occurs when conversion of the coordinate epoch is performed from the standard epoch (e.g.
J2000) to the observing epoch in the data correlation. The coordinate conversion introduces negligible axis
rotation only in the tiny ﬁeld very close to the phase(delay) tracking center (≤1). The rotation of thecoordinate system strongly depends on the source position with respect to the North or South Pole.
The ﬁrst step of the astrometric correction is the coordinate conversion of the phase-referenced maser
feature from the original coordinate system (J2000.0) to the one at the observing session. It is easier toconvert the source coordinate into the Cartesian coordinates and then rotate the coordinate system. The
conversion from the spherical coordinate (α, δ) to the Cartesian coordinate x=(x, y, z) is described as follows,Δθ =x= cos δ cos α(16.2)yz= cos δ sin α= sin δ.

(16.3)(16.4)

Here, the coordinate rotation matrixes around x-, y- and z-axis are denoted as Rx (θ), Ry (θ) and Ry (θ),
respectively, where θ is the rotation angle in the counter-clockwise direction. Then the coordinate rotationfrom x to x by precession and nutation is described as follows,53

CHAPTER 16. SCIENTIFIC ANALYSIS

54x
N (Δψ, Δ)==P (zA , θA , ζA ) =N (Δψ, Δ)P (zA , θA , ζA )xRx (− − Δ)Rz (−Δψ)Rx ()(16.5)(16.6)Rz (−zA )Ry (θA )Rz (−ζA ),(16.7)

where zA , θA , ζA are the precession angles, Δψ, Δ are the nutation angles.
The coordinate conversion for annual aberration from x (x , y  , z  ) to x”(x”, y”, z”) is approximately
performed as follows,x”= {x + πγ cos l + κ sin l} /ρ”y” = {y + (πγ sin l − κ cos l) cos } /ρ”z” = {z  + (πγ sin l − κ cos l) sin } /ρ”ρ” =x”2 + y”2 + z”2 ,(16.8)(16.9)(16.10)(16.11)

where γ, κ, , l are the parameters of the Solar position with respect to the Earth. If the source is looked atnear the Sun (within a few ten degrees), we should consider the relativistic defraction. In this dissertation,
this factor is ignored because the maser source W3 IRS5 is on the northern sky.
In the second step, the coordinates of the maser features around the phase-referenced maser spots inthe spherical coordinate system at the observing session should be determined. The relation between therelative positions in the Cartesian (xm , ym ) and the spherical coordinates (αm = α0 + Δαm , δm ) is describedas follows,xm=cos δm sin Δαm(16.12)ym=cos δ0 sin δm − sin δ0 cos δm cos Δαm ,(16.13)where (α0 , δ0 ) is the coordinate of the phase-referenced maser spot. In this dissertation, this conversion was
performed by using the inverted form of Eq. 16.12 changed with some approximations.
In the third, the newly speciﬁed maser coordinates should be inverted again to the coordinates at J2000.0
and converted to the Cartesian coordinates.
In the recent version of AIPS, the task UVFIX exactly performs the axis rotation described above but for
the visibility data. The task recalculates the visibilities as if the data were correlated at the speciﬁed antenna
coordinates and the source positions. This task shall be applied before the fundamental calibration (see section
6) or calibration with maser data (see section 11). Otherwise, the maser spots in the phase-reference velocity
channel may have a position oﬀset from the map origin.
Deﬁnition of position and velocity of maser feature
It is very important problem to deﬁne the positions and line-of-sight velocities of the maser features consistingof many adjacent maser spots. Usually measurements of maser positions and velocities as well as their time
variation are made on the basis of positions and velocities of the maser features because the maser feature,
which is actually a physical feature (cloud), is a fundamental unit of the gas kinematics. The deﬁning
methods are diﬀerent from one investigator to another. Someone deﬁned the maser feature position andvelocity from the three-dimensional (x-y position and velocity) ﬂux-averaged position for the included maser
spots. On the other hand, the author have deﬁned the maser feature position and velocity from the intensity
peak in position and velocity.

16.1.2Analysis of maser proper motions

It is quit diﬃcult to trace motions of individual maser spots from one epoch to another because it is still
unclear whether a motion of each of the maser spots having the same velocity traces a true motion of thephysical object. At present, proper motions of maser features may be well measured. If one can obtainmaser feature distributions observed at multiple epochs, they are superposed somehow without any precise

CHAPTER 16. SCIENTIFIC ANALYSIS

55

4
4
4

16

16

16

20

20

20

29

33

29

33
41

Relative radial velocity

26

Relative decl. offset

Relative R.A. offset

26
26
29
33
41

47

41

47
50

47

50

51

51

940

960

1 km s-1

2 mas

2 mas
980 1000 1020

JD-2450000

5150

940 960

980 1000 1020

JD-2450000

940 960

980 1000 1020

JD-2450000

Figure 16.1: Sample of measured proper motions and the Doppler velocity drifts of maser features that had
been detected in ﬁve epochs (Imai et al. 2003b). Solid lines in plots of proper motions show ﬁt lines assuming
constant velocity motions. The solid lines in the plots of the Doppler velocity drift show ﬁt lines assuming
constant acceleration motions.

CHAPTER 16. SCIENTIFIC ANALYSIS

56

common coordinate systems. Then position drifts of the individual masers with time are elucidated. They
are so called relative proper motions of maser features.
There are two methods to superpose the multiple maps. The ﬁrst, a reference maser feature may be
selected, which has been detected at every epoch and does not change its internal structure. Figure 16.1
shows examples of relative proper motions measured for the RT Vir H2 O masers [13] in this method. Thismethod well works for the relative proper motions, but sometimes collapses. If there are many maser futures
located in a tiny sky ﬁeld and velocity range, it is diﬃcult to trace one feature between the observing epochs.
Figure 16.1 also shows a few misidentiﬁcations of maser proper motions. Therefore, objective analysis issometimes necessary. For example, one prepare many types of shifts of the maser maps and evaluate inwhich type maser features are best coincided each other between the observing epochs. Even if a reference
maser feature is unambiguously selected, an accuracy of the proper motion measurements is limited bytemporal change of the internal structure of the reference feature.
To improve an accuracy of proper motion measurement, multiple reference maser features are used to
calculate mean positions of the them. The mean positions are used for superposing the maser maps. Note thatboth of the methods mentioned above are lost true motions of the reference feature an the mean positions,
respectively. Phase-referencing VLBI observations that provide extragalactic reference radio sources may
recover such lost information (see section 17.1.

16.2

What do maser sources trace?

Because maser emission occurs in the special physical condition and geometry in a molecular clump, maser
emission traces tiny volumes in interstellar gas clouds associated with outﬂows from young stellar objects andmass-loss ﬂows from Mira-type pulsating stars (see, e.g., Elitzur 1992 [9]). It has been improved, however,
the apparent motions of maser clumps, or maser features, trace true kinematics of the gas clouds mentioned
above. Even if a limited number of maser features detected, their proper motions provide us great informationon the 3-D gas kinematics by adding line-of-sight velocities of the masers, which is not able to be revealedin thermal-line emission having widespread distribution.

16.2.1

Internal and secular motions of maser features

Figure 16.3 gives examples of maser proper motions. Because observations of H2 O and SiO masers provide
us angular resolution ﬁner than 1 mas, Many these maser sources (but less than 30 sources) have beenmeasured their proper motions so far.
Usually, without extragalactic reference sources, maser proper motions are relatively measured with respect to one or a group of maser feature positions. Proper motions of the W3 IRS5 H2 O masers are inthis case. (see the left side of ﬁgure 16.3. Such relative astrometry has been done so far because absolutecoordinates of the H2 O masers are lost in the self-calibration procedure (see chapter 7) or obtained with avery poor accuracy (see section 12.3). Note that, even if the position accuracy is poorer, measurements ofabsolute coordinates of maser sources are important for scientiﬁc analysis. In the case of the W3 IRS5 H2 O
masers, driving sources of outﬂows found in this regions were identiﬁed to be two of radio continuum sources
observed in other observations, which also measured absolute coordinates of the continuum sources ([3]).
With extragalactic reference sources, maser positions are measured with respect to those of the reference
sources. When the reference sources have accurate absolute coordinates, the absolute coordinates of themasers are also accurately measured at the same time. In such measurements, apparent motions of themasers consist of (1) internal motions of the maser source, (2) secular motions of the maser source due to,e.g., the Galactic rotation, (3) an annual parallax of the maser source. The right side of ﬁgure ?? shows
the motions of the IRAS 19134+2131 H2 O masers, which trace the Galactic rotation and (marginally) theinternal motions.

16.2.2

Acceleration motions of maser features

So far, proper motions of maser features have been ﬁt to straight lines, which assume constant velocity motions. Taking into account, for example, the dynamics of stellar pulsation and orbital motions, accelerations
may be detected especially in the kinematics of H2 O and SiO masers.

CHAPTER 16. SCIENTIFIC ANALYSIS

1755

57

568

415

5.4 AU

5.4 AU

7.2 AU
566

1753

413
564

1751

411

Relative Decl. offset (mas)

1749
802
800
2000

798

562

409
796 -353

-355

-357

-359

560
-319 -321 -323 -325 -327
-11
7.2 AU
-12

1000
-13
-14

0

-15
12
-854

-1000

11

10

9

8

5.4 AU

-2000

-855

3600 AU

1997 March 26
1997 October 8
1997 March 26

-856

-3000
2000

1000

0

-1000

-2000

-3000

Relative R.A. offset (mas)
-2074

-248

-249

-250

-2367
5.4 AU

7.2 AU

-2076

-2586

5.4 AU

-2369
-2588

-2078
-2371

-2590

-2080
-2082
238

-857
-247

236

234

232

-2373
-481
230

-483

-485

-2592
-487
-704

-706

-708

-710

Figure 16.2: Sub-arcmillimeter structures of individual H2 O maser features and their time variation thatfound in the W3 IRS5 region (Imai et al. 2002b). Each of maser features, masing gas clumps, consists ofmaser spots, which have successive line-of-sight velocities and positions extended within a few of astronomical
units. The pattern of spot distributions are stable within a speciﬁc period (shorter than a few months), andsuccessively vary with time. Time gaps longer than this period in monitoring observations make us diﬃcult
to identify the same maser feature from one observing epoch to another.

CHAPTER 16. SCIENTIFIC ANALYSIS

2000 AUMe

Decl. offset (mas)

20 km s-1

58

20

4 January 2003(a)(b)
500 AU at 16 kpc

0
20

0

-20

-40

-60

-80

-100

-120

-140

R.A. offset (mas)

Mf

20

(a)

(b)

10

Md2

Md1 Mc

+

B

+A

Ma
Mb

10

200 AU at 16 kpc

200 AU at 16 kpc

0
10

0

-10

-20

-130

-140
0

Figure 16.3: Water maser proper motions. Left: Water maser
features and compact radio continuum sources in W3 IRS5
(Imai et al.(2003). Arrows indicate locations and proper motionsof maser features. The arrow length indicates the magnitude of
the proper motion per year (×325), respectively. The radio continuum sources, which were mapped by Claussen et al. (1994),
are shown as contours. Two plus marks A and B indicate thelocations of driving sources of the outﬂows in W3 IRS5, whichwere estimated by Imai et al.(2000b). Right: Position drifts ofwater masers in IRAS 19134+2131. The maser feature positions
were measured with respect to the extragalactic reference source
J1925+2106, 2◦.5 away from IRAS 19134+2131. The Galactic rotation from the top to the bottom is seen. The internal expansion
motions are also identiﬁed.
Figure 16.4 shows an example of detected acceleration motions in H2 O masers in the semiregular variable
RT Virginis ([13]). The maser kinematics generally expresses a spherical expansion from the central star.
This also traces transportation of shocks driven by stellar pulsation. In fact, one of the maser features
exhibits acceleration on the sky. This acceleration motion is evident even if the maser proper motion ismeasured with respect to that of a reference maser feature. Such acceleration motions were discovered in
SiO masers as well (e.g., [6]). If relative position accuracy of maser features achieve 10 μas, such acceleration
stuﬀ is expected to be in the scope of scientiﬁc analysis.
Even in a maser system, it has been diﬃcult to compare the locations among diﬀerent species of maser
emission (OH, H2 O, SiO). For example, a Mira variable star has SiO, H2 O and OH (1612 MHz) masers in its
circumstellar envelop, which are located at short to far distances from the star. It is interesting but diﬃcult
to trace a gas clump in the envelope moving from the SiO region by way of the H2 O region towards the
OH maser region within a decade. Superposition of maser maps with an accuracy comparable to such gas
clumps (smaller than a few astronomical units) is crucial.

16.2.3

Importance of multiple maser lines on the common reference frame

Physical conditions and locations of astronomical masers still have unclear parts. It is because their tiny
volumes and diﬀerent behaviors from those found in thermal-line observations make us diﬃcult to compare theissues mentioned above with those of thermal lines that are relatively well understand. One of the diﬃculties
comes from uncertainty in absolute coordinates of the thermal and maser lines, which are necessary tocompare the expected physical conditions and to discuss the physical links between these lines.
There is another example to explain the importance of the map superposition. Figure 16.5 shows morphologies and kinematics of the W43A H2 O and OH (1612 MHz) masers in the OH/IR star W43A ([14]).
In particular, the H2 O maser kinematics is well understood, which is well ﬁt by a precessing bipolar jet

CHAPTER 16. SCIENTIFIC ANALYSIS

50

59

(a)

May 11
May 31
June 19
July 13 32
August 1

1

33
Decl. offset (mas)-50

Decl. offset (mas)

0

37
0

-1

-100

-50

-100

49
48

-2

31

30

46

-3

10 AU at 220 pc
0

42
45

31

32
10 km s-1

47

(b)

1

0

-1

-2

-10

-11

R.A. offset (mas)-150

R.A. offset (mas)Figure 16.4: Water maser proper motions in the semiregular variable RT Virginis (Imai et al. 2003). Left:
The 3-D velocity ﬁeld of water maser features. A 3-D velocity vector of a feature is indicated by a cone. The
mean velocity vector of the maser features was subtracted from each of the observed velocity vectors. The
plus symbols indicate the locations of the star, estimated by the model ﬁtting using proper motions exhibiting
both expansion and infall (pink) and only expansion (green). Right: Spatial structures of maser features andtheir time variation in the two selected ﬁelds. Each of the ﬁlled circles shows a velocity component (maserspot). Radial velocities of spots change by 0.056 km s−1 from one spot to the adjacent spot. (a): Maser
features around the map origin. A position-reference feature is spatially ﬁxed at the map origin to makemeasurements of maser proper motions, but will move from south to north so that it expands with respect
to the star. (b): Maser features exhibiting acceleration motions. The maser feature on a black line shows aclear constant acceleration motion and the development of its V-shaped structure. The maser feature had
kept its brightness peak close to the crease of the V-shaped structure.
(see ﬁgure 16.6) and a location of the dynamical center is well estimated in the H2 O maser maps. It is
still unclear, however, whether the dynamical center of the H2 O masers coincides with that of an expansion
traced by the OH masers because absolute coordinates of these masers are still unclear (now in investigation).
Phase-referencing VLBI observations using a common position reference source may achieve an accuracy ofabsolute positions better than a few mas (see section 17.1. This accuracy may solve this issues and make us
understand the true character of W43A (a single star or a binary system).

North-South Offset (milliarcsecond)

CHAPTER 16. SCIENTIFIC ANALYSIS

60

OH maser
LSR velocity

Proper Motion
100 km s-1(June - October 1994)

042 - 44 km s-1
38 - 42 km s-1
25 - 30 km s-1

H2O maser
LSR velocity-200

0500 AU at 2.6 kpc

x(October 1994)
119 - 126 km s-1
114 - 117 km s-1-3 - 0 km s-1-8 - -7 km s-1-50 - -46 km s-1-57 - -50 km s-1

-200

-400

-600

East-West Offset (milliarcsecond)
Figure 16.5: H2 O and 1612-MHz OH masers in W43A (Imai et al. 2002a) observed in 1994. Although
the relative positions between the H2 O and OH masers are still under investigation in more detail, it was
conﬁrmed that they are almost the same as those shown in this ﬁgure. Dotted lines show spatial alignmentsof maser features in the red-shifted and blue-shifted H2 O maser clusters. A broken line shows the directionof the jet. Arrows indicate proper motions of the H2 O masers. The OH masers are well modeled by aspherically-expanding ﬂow with an expanding velocity of ∼9 km s−1 and a radius of ∼500 AU.

North-south offset (AU)

500

250

Precessing jet model (2002.3)
Precessing jet model (1994.8)
0

-250

-500

Maser spot (Oct. 1994)
Maser spot (Apr. 2002)
1000

500

0

-500

-1000

East-west offset (AU)Figure 16.6: The W43A H2 O masers observed in 1994 and 2002 with the VLBA and a precessing jet model
shown in dotted lines. The length of the jet has increased by ∼700 AU since the year 1994. The modeled
patterns were obtained from the following parameter values; a constant jet velocity of ±150 km s−1 , an
inclination of 39◦ with respect to the sky plane, a position angle of 65◦, a precession opening angle of 5◦, anda precession period of 55 years. These values are improved from those obtained previously. It is assumed
that only the direction of the bipolar ejection of material is varying continuously with time.

Chapter 17

Summary and future remarks
17.1

Phase-referencing technique

The author believes that the phrase phase-referencing in VLBI has been originally used for every observationand data reduction technique, in which all visibilities are calibrated using fringe phases in some part of thesame VLBI data or another VLBI data. Recently, the phrase phase-referencing technique is used mainly
for an observation and data reduction technique that uses extragalactic continuum sources as position andfringe-phase reference. The detail of the phase-referencing technique is described in the texts ([8, 1]).
Recently, a major fraction of VLBI observations adopt the phase-referencing technique to detect radiosources, which can be detected not within a coherence time (≤5 min) but for the whole observation time(∼10 hrs). In this case, the reference source should be bright enough to be detected within the coherence
time. There is an opposite case in which a position-reference source is detected by brighter target sources.
In this case, the target source positions are determined with respect to the position-reference source. The
authors has revealed that the phase-reference technique is valid for a source pairs separated by up to 3◦atthe 22 GHz band (e.g. [11]).
The phase-referencing technique is supported in AIPS, especially the tasks CLCAL, which interpolate
visibility phases of target sources by solving 2π-n radians ambiguity with fringe rates. The task UVFIX
precisely recalculates visibilities as if data correlation is made with source coordinates and station coordinates
newly speciﬁed. The task TECOR applies calibration for total electron contents (TEC). The task CLCOR
permits insertion of artiﬁcial excess path delays or phase oﬀsets to recover the excess path delays due to theatmosphere, which cannot be modeled in the data correlation. Usages of these tasks may be described inauthor’s future text.

17.2

AIPS automatic pipeline

Reduction of VLBI data, especially for spectral line sources, is a hard work. Comparing with data reductionof other observational instruments, this is a big disadvantage in astronomy and few people have tackled tosuch a ”masochistic work” in the world [8]. This situation has recently changed by automatically running
AIPS using ”pipelines”. A pipeline is a sequence of AIPS tasks and modules to control a pass of the tasks.
The grammar of a pipeline script is quite simple such as program languages of FORTRAN, BASIC andso on. For example, data reduction of the TX Cam SiO masers (up to 75 observing epochs) [6] has been
automatically made using Diamond’s pipeline script. Based on this script, EVN automatic pipeline has also
been developed [20]. The EVN pipeline has been released not only for personal data reduction but also forproviding several services for EVN users.
Very likely, pipelines for VERA/J-Net are indispensable, which have to release observational results
every few days because observations will be done in almost the same rate and their scientiﬁc goals shouldbe achieved within one decade. These should be supposed taking into account that at least a few years havebeen consumed to publishing a scientiﬁc paper since a few of VLBI observations were made.
The AIPS pipeline has several functions useful not only to VLBI users but also to VLBI network operatorsand organizers as follows.
• Creating fundamental extension tables (SN, CL, FG, BP, TY, GC) for users.
61

CHAPTER 17. SUMMARY AND FUTURE REMARKS62• Making fundamental plots for data checking.
• Checking data quality and reliability of the VLBI network.
• Quick looking preliminary images of targets and calibrators.
• Introducing VLBI images to VLBI beginners (e.g. bachelor students).
• Automatic data reduction (in advanced use).
Programming of the AIPS pipeline scripts should be one of the most important topics in the AIPS
tutorial, which will be described in the author’s text. Some of the ﬁgures are obtained by segment of such
pipelines.

Bibliography[1] Beasley, A. J., Conway, J. E. 1995, in Very Long Baseline Interferometry and the VLBA, ed. J. A. Zens,
P. J. Diamond, P. J. Napier (ASP: San Francisco), chap. 17[2] Bridle, A. H., Schwab, F. R. 1999, in Synthesized Imaging in Radio Astronomy II, ed. G. B. Taylor,
C. L. Carilli, R. A. Perley (ASP: San Francisco), chap. 18[3] Claussen, M. J., Gaume, R. A., Johnston, K. J., Wilson, T. L. 1994, ApJL, 424, L41[4] Cotton, W. D. 1999, in Synthesized Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L. Carilli,
R. A. Perley (ASP: San Francisco), chap. 17[5] Cotton, W. D. 1995, in Very Long Baseline Interferometry and the VLBA, ed. J. A. Zens, P. J. Diamond,
P. J. Napier (ASP: San Francisco), chap. 10[6] Diamond, P. J., Kemball, A. J. 2003, ApJ 599, 1372
[7] Diamond, P. J., 1995, in Very Long Baseline Interferometry and the VLBA, ed. J. A. Zens, P. J. Diamond, P. J. Napier (ASP: San Francisco), chap. 12[8] Diamond, P. J. 1989, in Very Long Baseline Interferometry, ed. M. Felli, R. E. Spencer (Dordrecht:
Kluwer), p. 231[9] Elitzur, M. 1992a, in Astronomical Masers (Dordrecht: Kluwer)–. 1992b, ARA&Ap, 30, 75[10] Gwinn, C. R., 1994, ApJ, 429, 241[11] Imai, H., Morris, M., Sahai, R., Hachisuka, K., Azzollini, F. J. R. 2004, A&Ap, in press[12] Imai, H., Horiuchi, S., Deguchi, S., Kameya, O. 2003, ApJ, 595, 285[13] Imai, H., Shibata, K.M., Marvel, K.B., Diamond, P.J., Sasao, T., Miyoshi, M., Inoue, M., Migenes, V.,
Murata, Y. 2003, ApJ, 590, 460[14] Imai, H., Obara, K., Diamond, P. J., Omodaka, T., & Sasao, T. 2002a, Nature, 417, 829[15] Imai, H., Deguchi, S., Sasao, T. 2002b, ApJ, 567, 971[16] Imai, H., Kameya, O., Sasao, T., Miyoshi, M., Deguchi, S., Horiuchi, S., Asaki, Y. 2000, ApJ, 538, 751[17] Moran, J. M. Dhawan, V. 1995, in Very Long Baseline Interferometry and the VLBA, ed. J. A. Zens,
P. J. Diamond, P. J. Napier (ASP: San Francisco), chap. 9[18] Reid, M. J. 1999, in Synthesized Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L. Carilli,
R. A. Perley (ASP: San Francisco), chap. 24[19] Reid, M. J. 1995, in Very Long Baseline Interferometry and the VLBA, ed. J. A. Zens, P. J. Diamond,
P. J. Napier (ASP: San Francisco), chap. 11[20] Reynolds, C., Paragi, Z., Garrett, M. A. 2002, in URSI General Assembly, Commission J(http://www.evlbi.org/pipeline/user expts.html)
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BIBLIOGRAPHY

64[21] Rupen, N. P. 1999, in Synthesized Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L. Carilli,
R. A. Perley (ASP: San Francisco), chap. 12[22] Taylor, G. B., Carilli, C. L., Perley, R. A. 2001, Synthesized Imaging in Radio Astronomy II (ASP: San
Francisco)[23] Thompson, A. R., Moran, J. M., Swenson, G. W., Jr. 2001 in Interferometry and Synthesis in Radio
Astronomy, 2nd edition (John Wiley & Sons: New York)[24] Wajima, K. 2003, in Radio Interferometry Summer School 2003, chap. 15 (in Japanese)—. 2004, translated in English.
[25] Walker, R. C. 1999, in Synthesized Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L. Carilli,
R. A. Perley (ASP: San Francisco), chap. 22[26] Walker, R. C. 1995, in Very Long Baseline Interferometry and the VLBA, ed. J. A. Zens, P. J. Diamond,
P. J. Napier (ASP: San Francisco), chap. 13[27] Walker, C. R. 1981, AJ, 86, 1323

Appendix A

AppendicesA.1

Installation and setting AIPS

Instruction of AIPS installation is described in the NRAO’s AIPS home page, http://www.aoc.nrao.edu/aips/ .
Therefore, the installation instruction is not described in this document. Some of special remarks are described as follows.

A.1.1

Disk space

A working disk space is recommended to be larger than 10 Gbytes per observation. Here one observation
corresponds to data that consists of scans of one target source and calibrators for obtaining images or image
cubes of the target source in one observing epoch, usually during shorter than 24 hours. Because spectralline (mainly maser) data have a large number of spectral channels and short parameter periods (see [2]),the data size easily gets huge. For example, the author is always getting VLBA data with a size as large
as 15 Gbytes because the data are obtained from 10 antennas and have 1024 spectral channels. Therefore,
DAT tape drives, with which DDS3 or DDS4 tapes are available, are necessary to put FITS data to harddisk drive (HDD) even if the ﬁles in HDD are compressed into 1/3 of the original size. Even VERA andKVN with smaller number of telescopes do not change such a situation because all of users may have data ofmultiple observations. Data size limit of 2 Gbytes also should be ﬁxed by install the latest LINUX or UNIX
operating system and by compiling AIPS programs in C and FORTRAN, which does not appear the data
size limit.

A.1.2

Work permission

The administrator of your computer in your institutes should edit /etc/services to put the following lines.
sssin
ssslockmsgservtekserv
aipsmt0
aipsmt1
aipsmt2
aipsmt3
aipsmt4
aipsmt5
aipsmt6
aipsmt7

5000/tcp
5002/tcp
5008/tcp
5009/tcp
5010/tcp
5011/tcp
5012/tcp
5013/tcp
5014/tcp
5015/tcp
5016/tcp
5017/tcp

SSSIN
SSSLOCKMSGSERVTEKSERVAIPSMT0
AIPSMT1
AIPSMT2
AIPSMT3
AIPSMT4
AIPSMT5
AIPSMT6
AIPSMT7# AIPS TV server# AIPS TV Lock
# AIPS Message Server# AIPS TekServer# AIPS remote FITS disk access# AIPS remote tape 1# AIPS remote tape 2

In addition, the administrator should permit AIPS user putting RUN ﬁles (see sections 1.4 and 17.2) inthe directory $AIPS ROOT/RUN or $AIPS ROOT/$AIPS VERSION/RUN, and HELP ﬁles (see section 17.2) in the
directory $AIPS ROOT/$AIPS VERSION/HELP.

65

APPENDIX A. APPENDICES

A.2

66

User environment for AIPS

It is convenient for a user to set the following environments and commands because the user may always
have to type them before starting AIPS.

A.2.1

Commands in the login script

Add the following script either in .login or .cshrc (in c-shell environment), .bashrc (in bash-shell environment).
• In the case of c-shell environment:

source [AIPS root directory]/LOGIN.CSH;$CDTST• In the case of bash-shell environment:

source [AIPS root directory]/LOGIN.SH;$CDTST

These enables the user to the default variables speciﬁed in AIPS. A user has to type them when he/shewants to touch AIPS programs themselves (e.g. when updating AIPS).

A.2.2

Special variables for user

For example, a user may want to specify a directory to put PostScript ﬁles created by AIPS. In this case, it
is recommended to specify a directory to do it. The following command or script in the login script can set
the directory.
• In the case of c-shell environment:

setenv [New variable name] [Your speciﬁed directory]• In the case of bash-shell environment:

A.3

export [New variable name]=[Your speciﬁed directory]

Updating AIPS version

Updating AIPS version is essential for smoothly operating AIPS. Some of AIPS tasks may have severe bugs.
There may be many problems just after installing newer version of AIPS. To update the AIPS version, auser should perform the following procedures.
• Log in as an AIPS administrator, or a login user to install/update AIPS.
• Type the scripted described in chapter A.2.1.
• Move to the home directory of the AIPS administrator. The script named do diary.[host name].
• Type source do diary.[host name].
• Move to $UPDATE and look at the ﬁle named UPD[date]. [time]. The date and time are the epoch when
AIPS was updated by using the above script. This output ﬁle is a log ﬁle to record what parts were
updated in AIPS.
• In AIPS, type RUN NEWPARAM.

A.4

About this document• 22 March 2004: 1st version.
• 25 March 2004: 2nd version, many modiﬁcations and additions.
• 5 May 2004: 3rd version, updating chapter 1 and appendix.
• 4 June 2004: 4rd version, improving several ﬁgures.
• 26 October 2005: 5rd version, improving several ﬁgures and documents.