Nobeyama Radio Polarimeters (NoRP) Analysis Manual ver. 0.4

T. Yokoyama

October 25, 2000

1 Introduction

This is a manual for analysis of the data obtained by Nobeyama Radio Polarimeter (NoRP; Nakajima et al. 1985) and Toyokawa Radio Polarimeter (TYKW; Torii et al. 1979; Shibasaki et al. 1979).

For any questions and requests, please send an e-mail to

     nsro-service@solar.nro.nao.ac.jp

The latest information on NoRP is updated on NSRO Web site. The URL is

      http://solar.nro.nao.ac.jp/norp/

1.1 What’s New

Change from ver 0.3

• Add new procedures for spectrum fitting

• Add new procedures for deriving spectrum from assumed physical variables

• Event list

• Daily averaged fluxes (after removing the flaring data)

2 How to setup

(1) Installation of the SolarSoftware.

Install the SolarSoftware (SSW). If this was not installed, please contact your system manager. The primary distribution site for SolarSoftware is: http://www.lmsal.com/solarsoft/

(2) Setup of your personal environment

Include the followings in your environment setup file (~/.cshrc).

setenv␣SSW␣SSW-directory^{1}

      setenv␣SSW\_INSTR␣``norp''
      setenv␣NORP␣/archive/pub/norp
      source␣${SSW}/gen/setup/setup.ssw
      source␣${NORP}/setup/setup.norp

1/sgi1/ssw in NSRO

3 Analysis

3.1 Start Analysis

The NoRP IDL procedures described in this section all depend on the SolarSoftware (SSW). When you start the analysis, start up the SSW/IDL as follows:

unix% sswidl <CR>

3.2 Database

3.2.1 Event List

There is a data base for the events (’evx’ data) from January 1990 to May 1992^{2}. In order to list them, e.g. on June 9, 1991 UT,

IDL> norp pr evx,’1991-06-09’ <CR> From June 5, 1991 UT to June 8, IDL> st day=’1991-06-05’ <CR>

IDL> ed day=’1991-06-08’ <CR>

IDL> norp pr evx,st day,ed day <CR> For only strong events which have 1000 SFU peak flux in 17GHz,

IDL> norp pr evx,st day,ed day,criterion=1000 <CR>

3.2.2 Daily Averaged Flux

Daily averaged flux values after choosing non-flaring-time data are installed in the database (after November 1987). These data can be used for obtaining pre-flare flux or for studying the long-term variation.

Toyokawa (1, 2, 3.75, 9.4 GHz) : Nov 1987 – Feb 1994 Toyokawa (3.75 GHz only) : Mar 1994 – Apr 1994 Nobeyama (17, 35, 80 GHz) : Mar 1990 – Feb 1994 Nobeyama (1, 2, 3.75, 9.4, 17, 35, 80 GHz) : May 1994 – Present date Note that the data for quiet Sun are fixed for 35 GHz (2400 SFU) and 80 GHz (9000 SFU) due to their instrumental limits.

In order to read the data, e.g. from Jan 1, 1999 to Jun 30, IDL> st day=’1999-01-01’ <CR> IDL> ed day=’1999-06-30’ <CR> IDL> norp rd avg,st day,ed day,timavg,fiavg,fvavg <CR>

for plot, e.g. of 1GHz

IDL> utplot,timavg,fiavg(0,*) <CR> of 2GHz

IDL> utplot,timavg,fiavg(1,*) <CR>

3.3 Where is the Data ?

3.3.1 Calibrated Data in XDR (IDL save) format

Some already-calibrated NoRP data are put in the NSRO archive (see section A). You can obtain them by anonymous FTP. Before synthesizing by yourself, try them first. They are loaded into the IDL session by using the IDL command restore. There are 1-sec resolution data for steady observatin and 0.1-sec resolution data for events.

IDL> file=getenv(’NORP XDR’)+’/1999/08/norp19990828 0056.xdr’ <CR> IDL> restore,file <CR> IDL> help <CR>

2For the events after June 1992, see the event list of Nobeyama Radioheliograph

    DAY             STRING    = '1999-08-28'
    FI              FLOAT     = Array[7, 7590]
    FIAVG           FLOAT     = Array[7]
    FREQ            FLOAT     = Array[7]
    FV              FLOAT     = Array[7, 7590]
    FVAVG           FLOAT     = Array[7]
    MVD             BYTE      = Array[7, 7590]
    TIM             STRUCT    = -> ANYTIM2INTS Array[7590]

freq is observing frequencies in units of GHz (in this example, 1, 2, 3.75, 9.4, 17, 3, 80 GHz), tim is observing time, fi,fv are I (R+L), V (R–L) comonents of flux density and fiavg, fvavg are daily average, respectively. mvd is an array including the values of unity (1) for valid data or zero (0) for non-valid data.

3.3.2 Raw Data

Some raw NoRP data are put in the NSRO archive (see section A). You can obtain them by anonymous FTP.

3.4 Read the Data — Nobeyama Radio Polarimeters

There are two kinds of formats for Nobeyama Radio Polarimeters (NoRP). One is before unifing with Toyokawa Radio Polarimeters and the other is after that. For older format, the files include only 1, 2, 3.75 9.4 GHz data.

In order to read the data into IDL session, give the date (JST) as follows:

IDL> day=’1992-4-23’

IDL> norp rd dat,day,mvd,tim,fi,fv,freq <CR> or give the file name as follows:

IDL> file=’pl920423’

IDL> norp rd dat,file,mvd,tim,fi,fv,freq <CR> freq is observing frequencies in units of GHz (in this example, 1, 2, 3.75, 9.4, 17, 3, 80 GHz), tim is observing time, fi,fv are I (R+L), V (R–L) comonents of flux density, respectively. mvd is an array including the values of unity (1) for valid data or zero (0) for non-valid data. In order to read the data in specified duration:

IDL> timerange=[’1992-4-23 2:00’,’1992-4-23 4:00’] <CR>

IDL> norp rd dat,day,mvd,tim,fi,fv,freq,timerange=timerange <CR> In order to read the data of specified frequency, e.g. for 17 GHz,

IDL> rdfreq=[0,0,0,0,1,0,0] <CR>

IDL> norp rd dat,day,mvd,tim,fi,fv,rdfreq=rdfreq <CR> For 1GHz and 9.4GHz,

IDL> rdfreq=[1,0,0,1,0,0,0] <CR>

IDL> norp rd dat,day,mvd,tim,fi,fv,rdfreq=rdfreq <CR> Each element in the array rdfreq corresponds to the data of one frequency among 1, 2, 3.75, 9.4, 17, 35 and 80 GHz.

3.5 Read the Data — Toyokawa Radio Polarimeters

The Toyokawa Radio Polarimeters were observing in 4 frequencies, namely , 2, 3.75, and 9.4 GHz. In order to read the data into IDL session, give the date (JST) as follows: IDL> day=’2000-4-8’ IDL> tykw rd dat,day,mvd,tim,fi,fv,freq <CR>

or give the file name as follows:

IDL> file=’ty921102.01i’ <CR> ; 1GHz I-component

IDL> file0pa=’ty921102.0pa’ <CR> ; 0PA calibration data

IDL> filestt=’ty921102.stt’ <CR> ; status data

IDL> tykw rd dat,file,file0pa,filestt,mvd,tim,data <CR> freq is observing frequencies in units of GHz, tim is observing time, fi,fv are I (R+L), V (R–L) comonents of flux density, respectively. mvd is an array including the values of unity (1) for valid data or zero (0) for non-valid data.

In order to read the data in specified duration:

IDL> timerange=’1992-11-2 ’+[’2:00’,’4:00’] <CR>

IDL> tykw rd dat,day,mvd,tim,fi,fv,freq,timerange=timerange <CR> In order to read the data of specified frequency, e.g. for 9 GHz,

IDL> rdfreq=[0,0,0,1] <CR>

IDL> tykw rd dat,day,mvd,tim,fi,fv,rdfreq=rdfreq <CR> For 1GHz and 9.4 GHz,

IDL> rdfreq=[1,0,0,1] <CR>

IDL> tykw rd dat,day,mvd,tim,fi,fv,rdfreq=rdfreq <CR> Each element in the array rdfreq corresponds to the data of one frequency among 1, 2, 3.75, and 9.4 GHz.

3.6 Plot

For plotting, IDL> mfreq=0 <CR> IDL> norp plot,mfreq,file,mvd,tim,fi <CR>

where mfreq is the index number of the plotting frequency in the array freq. To overlay another plot

IDL> mfreq1=1 <CR>

IDL> norp plot,mfreq1,file,mvd,tim,fi,/over <CR> Or by directly; IDL> utplot,tim(where(mvd(mfreq,*))),fi(mfreq,where(mvd(mfreq,*))) <CR>

3.7 Spectrum Analysis

By coordinating multiple frequency observation, we may dervive the spectrum of the emission. The obtained variable is α whose definition is

F_{ν} ∝ ν^{α}.

In real, α is not uniform over the frequencies. But the spectrum in microwave range is approximately fitted by the fucntion in the form :

F_{ν} = F̂_{ν} (\frac{ν}{ν̂})^{α_{tk}} \{1 − exp [− (\frac{ν}{ν̂})^{α_{tn}−α_{tk}}]\} ≈ \{ \begin{matrix}F̂_{ν} (ν/ν̂)^{α_{tk}} & for ν ≪ ν̂ \\ F̂_{ν} (ν/ν̂)^{α_{tn}} & for ν ≫ ν̂ \end{matrix}  (1)

Here are 4 fitting parameters: ν̂ is turn-over frequency, F̂_{ν} is turn-over flux density, α_{tk} is power index of low frequency side (optically thick side) and α_{tn} is power index of high frequency side (optically thin side), respectively. The procedures are as follows: IDL> day=’2000-4-8’

IDL> norp rd dat,day,mvd,tim,fi,fv,freq <CR>

IDL> norp rd avg,day,timavg,fiavg,fvavg <CR>

IDL> for m=0,6 do fi(m,*)=fi(m,*)-fiavg(m) <CR>

IDL> norp alpha,freq,fi,mvd,mvdfit,alpha tk,alpha tn,freqpk,fluxpk <CR> After subtracting the pre-flare flux levels (here daily averages are used), the flare fluxes are given to the IDL procedure norp alpha. mvdfit is an array including the values of unity (1) for valid data or zero (0) for non-valid data.

Note: The fitting will usually fail in the simple manner shown here. We need (1) to take longer intergation time for getting better S/N ratio and (2) to remove the inadequate data for fitting (because, say, the emission in that frequency is not due to gyrosynchrotron). See 3.8.3 for better procedures.

3.7.1 Optically-Thin Non-Thermal Gyrosynchrotron Emission (Preliminary)

Note: The procedures described in this subsection are under testing. Comments are welcome for improvement.

Based on approximation models, the relation between the physical variables of emitting region and the emission can be derived. The electron distribution function is assumed to be the power law.

\frac{dNV (E)}{dE} = K (\frac{E}{E_{0}} )^{−δ}

where E is electron energy (keV), NV (E) is number of electrons (particles) that has larger energy than E. This distribution is described with parameters δ, E_{0}, and K. But it is usual to use NV (E_{0}) = K/(δ − 1)/E_{0}^{δ−1} instead of K. And we fix E_{0} = 10 keV after Dulk (1985).

(a) From Physical Variables to Emission Inputs; power-law index δ, magnetic field strength (G), angle between magnetic field and line of sight

(degree), and NV — total number (particles) of non-thermal electron (of E > 10 keV): Outputs; flux density (SFU), circular polarization degree: By Dulk’s (1985) method:

IDL> dulk gysy,delta,bb,theta,nv,freq,fi,rc <CR> If the size of emitting source (by solid angle in unit of sterad) is given additionally, optical depth is also obtained

IDL> dulk gysy,delta,bb,theta,nv,freq,fi,rc,omega,tau <CR> By Ramaty’s (1969) method:

IDL> ramaty gysy,delta,bb,theta,nv,freq,fi,rc <CR>

IDL> ramaty gysy,delta,bb,theta,nv,freq,fi,rc,omega,tau <CR>

(b) From Emission to Physical Variables Based on Dulk’s (1985) model we may derive the physical variables from emission. After deriving α

(see 3.7), power law index of non-thermal electron distribution function is IDL> norp alpha,freq,fi,mvd,mvdfit,alpha tk,alpha tn,freqpk,fluxpk <CR> IDL> norp alpha2delta,alpha tn,delta <CR>

3.7.2 Optically-Thin Thermal Free-Free Emission (Preliminary)

Note: The procedures described in this subsection are under testing. Comments are welcome for improvement.

(a) From Physical Variables to Emission Based on Dulk’s (1985) approximation models, the relation between the physical variables of emitting

region and the emission can be derived. Inputs; electron temperature (K), line-of-site component of magnetic field (G), and volume emission measure (cm^{−3}) Outputs; flux density (SFU), circular polarization degree:

IDL> dulk frfr,te,b loc,vem,freq,fi,rc <CR> If the size of emitting source (by solid angle in unit of sterad) is given additionally, optical depth is also obtained

IDL> dulk frfr,te,b loc,vem,freq,fi,rc,omega,tau <CR>

3.8 Example of Analysis Session

3.8.1 Choose an Event

Many interesting events are introduced in NoRP web site. It is recommended to access first to these pages. The URL is

     http://solar.nro.nao.ac.jp/norp/

3.8.2 Light Curves

After choosing an event for analysis, see the light curves. Calibrated data is already prepared in XDR (IDL save) format for important events. So restore it first,

IDL> file=getenv(’NORP XDR’)+’/1999/08/norp19990828 0056.xdr’ <CR> IDL> restore,file <CR>

For plots, IDL> mfreq=0 <CR> IDL> norp plot,mfreq,mvd,tim,fi <CR>

Here mfreq is the number of the data identifying the frequency. For overplotting another frequency data, IDL> mfreq1=1 <CR> IDL> norp plot,mfreq1,mvd,tim,fi,/over <CR> 3.8.3 Spectrum Analysis

For deriving spectrum, it is better to integrate longer than default for getting better S/N ratio. In case integrating 300 points (30 sec),

IDL> mint=300 <CR>

IDL> norp mkint,mint,mvd,tim,fi,fv,mvdav,timav,fiav,fvav <CR> Next subtract pre-flare flux

IDL> for m=0,6 do fiav(m,*)=fiav(m,*)-fiavg(m) <CR> Using this flux, fit the spectrum

IDL> norp alpha,freq,fiav,mvdav,mvdfit,alpha tk,alpha tn,freqpk,fluxpk <CR> Assuming gyrosynchrotron emission, the power-law index of non-thermal electrons is obtained

IDL> norp alpha2delta,alpha tn,delta <CR>

Sometimes fitting will fail if the observation data include some points extremely out of the fitting function. One reason is that the emission mechanism is different in the low frequency range ( not gyrosynchrotron but plasma emission ). Another reason is bad S/N ratio in high frequency observation, especially in 80 GHz. In this case, remove such data points from fitting as follwos:

IDL> mvfreq=[2,3,4,5,6] <CR>

IDL> norp alpha,freq(mvfreq),fiav(mvfreq,*),mvdav(mvfreq,*) $ <CR> IDL> ,mvdfit,alpha tk,alpha tn,freqpk,fluxpk <CR>

In order to confirm that the fitting is well-done, plot the fitting function over the observation data. For example, for n-th data

IDL> norp funcp,alpha tk(n),alpha tn(n),freqpk(n) ,fluxpk(n),freqfit,fifit <CR> IDL> plot,freq,fiav(*,n),/xlog,/ylog,psym=5 <CR> IDL> oplot,freqfit,fifit <CR>

3.9 Others

3.9.1 Read Raw Data Directly

In order to read raw data directly, for Nobeyama data

IDL> norp rd rdt,file,rdata,date,version <CR> for Toyokawa data

IDL> tykw rd rdt,file,rdata <CR> For obtaining observing time (JST)

IDL> timej=norp rdt2timej(rdata) <CR>

A NoRP data archive: anonymous FTP

The Nobeyama Solar Radio Observatory (NSRO/NAOJ) has prepared the anonymous FTP server for the NoRP data archive. The URL is

   ftp://nsro-archive.nro.nao.ac.jp/pub/norp

If you need to transfer a large amount of data , please contact

   nsro-service@solar.nro.nao.ac.jp

We will make and mail a CD-ROM for you. The network capability in Nobeyama is limited.

B Acknowledgement

We thank the following people. SolarSoftware is a software package for analysis of Solar Data on IDL. That is supported under various NASA contracts (SXT/EIT/MDI/TRACE/YPOP etc.) and is all in the public domain. IDL is a product by Research System Inc.

References

Dulk, G. A., 1985, ARAA, 23, 169 Nakajima et al. ”The Radiometer and Polarimeters at 80, 35, and 17 GHz for Solar Observations at Nobeyama”, PASJ, 37, 163 (1985) Ramaty, 1969, ApJ, 158, 753 Shibasaki et al. ”Solar Radio Data Acquisition and Communication System (SORDACS) of Toyokawa Observatory”, Proc. of the Res. Inst. of Atmospherics, Nagoya Univ., 26, 117 (1979) Torii et al. ”Full-Automatic Radiopolarimeters for Solar Patrol at Microwave Frequencies”, Proc. of the Res. Inst. of Atmospherics, Nagoya Univ., 26, 129 (1979)