View source for M51 at z = 0.1 and z = 0.3 (CASA 4.0)

{{Simulations Intro}}
[[Category: Simulations]] [[Category:ALMA]]
* '''This guide is applicable to CASA version 4.0.  For older versions of CASA see [[M51 at z = 0.1 and z = 0.3 (CASA 3.4)]].'''
* '''To create a script of the Python code on this page see [[Extracting scripts from these tutorials]].'''
* '''Notice that this page uses global Python variables (e.g. fluxScale), not to be confused with task inputs (e.g. inbright).'''

== Overview ==

[[File:M51sim-5and6.png|thumb|CO 1-0 Moment maps of the original BIMA SONG measurements of M51. ''Left'': Moment 0 (integrated intensity). ''Right'': Moment 1 (velocity field).]]

This tutorial presents a simulation of ALMA observations of the well-known galaxy M51 in the CO 1-0 transition. This galaxy is located relatively nearby (luminosity distance = 9 Mpc), but, in this simulation, we will model how it would appear at redshift z = 0.1 (luminosity distance = 460 Mpc). 

The goal of this tutorial is to provide a ''complete'' run-through of a relatively simple simulation. The simulation will include effects of (''u'', ''v'') sampling of a 50-antenna ALMA, the primary beam of the ALMA, and thermal noise. Neither calibration overheads nor errors are included, and so this simulation should be viewed as optimistic.  The CASA task '''simobserve''' will generate simulated visibility measurements from an input model.  The task '''simanalyze''' will image the visibilities and generate diagnostic plots.

For this tutorial, we'll use the [http://nedwww.ipac.caltech.edu/level5/March02/SONG/SONG.html BIMA SONG] ([http://adsabs.harvard.edu//abs/2003ApJS..145..259H Helfer et al. 2003]) observations of M51 as the basis for the model. Grab the file [http://nedwww.ipac.caltech.edu/level5/March02/SONG/NGC5194.bima12m.cm.fits.gz NGC5194.bima12m.cm.fits.gz] and uncompress it in a working directory.

<source lang="bash">
# in bash (or other unix shell)
gunzip NGC5194.bima.12m.cm.fits.gz
</source>

== Initializing the Data and Tasks ==

Task simobserve takes an input model in the form of a CASA image.  So, we begin by converting the BIMA SONG FITS cube into a CASA image using task '''importfits'''. Here we invoke importfits as a function, where the task inputs are set as function input parameters. For convenience, we store the name of the resulting image into the Python variable <tt>cubeName</tt>. The task will produce the new image (which is actually a directory) in the current working directory.

<source lang="python">
# in CASA
cubeName = 'm51-song.image'
# If m51-song.image exists, it needs to be removed for importfits to work as set
os.system('rm -rf '+cubeName)
importfits(fitsimage='NGC5194.bima12m.cm.fits', imagename=cubeName)
</source>

We initialize the simulation tasks by setting their parameters to the default values.  We then make the new CASA image the input model to simobserve by setting parameter '''skymodel'''.
 
<source lang="python">
# in CASA
default("simobserve")
default("simanalyze")
skymodel = cubeName
</source>

== Noise in the Input Model ==

The input model is actually an observation and, as such, certainly contains noise. We're OK as long as the noise in the model falls below the expected thermal noise of the ALMA observation. Here's a quick, back-of-the-envelope calculation.

The noise on the BIMA SONG channels measures roughly 0.1 Jy/beam, which scales to 0.04 mJy/beam at z = 0.1 (to within factors of powers of 1+z for cosmology and root-small-integer for the to-be-degraded beam; see below). For comparison, the expected thermal noise of the ALMA observation is 0.1 mJy / beam (using the [https://almascience.nrao.edu/call-for-proposals/sensitivity-calculator ALMA Sensitivity Calculator], assuming 8 hrs integration, and, to match roughly the BIMA SONG observation, a 4 MHz channel width), a factor of 2.5 greater than the anticipated contribution of noise from the model. Added in quadrature, the noise components total 0.108 mJy, and so we can expect that the input model noise degrades the simulation noise by about 8%.

== Cosmology Calculations ==

Next we'll set up some python globals to handle the scaling of the model coordinates and flux densities appropriate for new redshift. We'll primarily need the angular size and luminosity distances for a given cosmology. To keep things simple, we'll use [http://www.astro.ucla.edu/~wright/CosmoCalc.html Ned Wright's CosmoCalc] ([http://adsabs.harvard.edu/abs/2006PASP..118.1711W 2006]) with the default cosmology; redshifts were collected from [http://nedwww.ipac.caltech.edu/cgi-bin/nph-objsearch?objname=NGC5194&extend=no&hconst=73&omegam=0.27&omegav=0.73&corr_z=1&out_csys=Equatorial&out_equinox=J2000.0&obj_sort=RA+or+Longitude&of=pre_text&zv_breaker=30000.0&list_limit=5&img_stamp=YES NED].

<source lang="python">
# in CASA
# Distinguish between z_lsrk, which sets the observed frequency for scaling, 
# and z_cmb, which is needed to get cosmological distances.
z_old_cmb = 0.002122 # CMB-referenced z for cosmological distances from NED
z_old_lsrk = 0.001544 # from NED
z_new = 0.1
#
# angular size distances from CosmoCalc
da_old = 9.0
da_new = 375.9
#
# luminosity distances from CosmoCalc
dl_old = 8.937
dl_new = 454.8
</source>

We will use the convention where ''old'' refers to M51 as observed at its proper redshift, and ''new'' refers to the new, higher redshift for our model.

== Preparing the Model ==

The next step is to scale the M51 data cube into a model cube appropriate for simobserve. First, we establish the file naming convention by setting the task parameter '''project'''.  Thinking ahead, we might want to rerun this simulation for other redshifts.  So, to make this easy we will include the redshift in the '''project''' name: we'll write 0.1 as <tt>p1</tt> (or "point one") and assign it to Python variable <tt>suffix</tt>.  Then we'll use <tt>suffix</tt> to define '''project'''.

<source lang="python">
# in CASA
suffix = "-p1"
project = "M51-AtZ" + suffix  
</source>

=== Flux Density Scaling ===

Our goal in this step is to set the '''inbright''' parameter of simobserve, which will scale the data cube appropriately for its new luminosity distance.  The task wants models in units of Jy / pixel, but the BIMA SONG cube has units of Jy / beam. We'll use the task <tt>imhead</tt> to get the BIMA SONG clean beam dimensions and we'll use the <tt>qa</tt> tool to convert the dimensions from radians to arcseconds.

<source lang="python">
# in CASA
# Get the major and minor axes of the model clean beam
bmaj = imhead(imagename=cubeName,mode='get',hdkey='beammajor')
bmin = imhead(imagename=cubeName,mode='get',hdkey='beamminor')
# Convert radians to 1-arcsecond pixels using the qa tool
bmaj = qa.convert(bmaj,'arcsec')['value']
bmin = qa.convert(bmin,'arcsec')['value']
# Gaussian beam conversion = beams / pixel
toJyPerPix = 1.0 / (1.1331 * bmaj * bmin)
</source>

Next, scale the flux for the new luminosity distance. Make the approximation that each pixel is a point source, and use the inverse square law to scale.  We then set '''inbright''' to the newly scaled peak flux.

<source lang="python">
# in CASA
# Correct flux density for luminosity distance
fluxScale = (dl_old/dl_new)**2 * (1.0 + z_new) / (1.0 + z_old_cmb)
# Current peak flux (Jy / pixel)
peak = imstat(cubeName)['max'][0] * toJyPerPix
# Desired peak flux (using Python formatting convention)
inbright = "%fJy/pixel" % (peak*fluxScale)
</source>

Notice that there is an additional (1+z) correction because we are scaling flux densities rather than bolometric fluxes.

=== Angular Size Scaling ===

The sky coordinates axes of the model need to be adjusted (1) to place M51 in the southern hemisphere and (2) to correct for the new angular size distance. These tasks can be accomplished by the simobserve parameters '''indirection''' (to change the location of M51 on the sky) and '''incell''' (to change the angular scale of an input pixel). 
To perform task (1), we'll just flip the sign of the declination using [[imhead]]. We'll use the [http://casa.nrao.edu/docs/casaref/quanta-Module.html#x409-4100001.4 qa] tool to convert radians to sexagesimal units.

<source lang="python">
# in CASA
# For clarity, build up "indirection" string one term at a time.
indirection = "J2000 " # Epoch
# RA
crval1 = imhead(imagename=cubeName,mode='get',hdkey='crval1')['value']
indirection += qa.formxxx(str(crval1)+'rad',format='hms') + " " 
# Dec * -1
crval2 = imhead(imagename=cubeName,mode='get',hdkey='crval2')['value']
indirection += qa.formxxx('%frad' % (-1*float(crval2)),format='dms')
</source>

Next, adjust the pixel scale for the new angular size distance. To perform this adjustment, we'll use [[imhead]] with '''mode = "get"''' to read in the original pixel scale, then use the simobserve input parameter '''incell''' to designate the new pixel size.

<source lang="python">
# in CASA
# Scale pixel size: imhead returns radians; convert to arcsec
cdelt2 = imhead(imagename=cubeName,mode='get',hdkey='cdelt2')['value']
oldCell = cdelt2 * 206265
# Scale for new angular size distance
newCell = oldCell * da_old / da_new 
# Format the new pixel size for input to simobserve
incell = "%farcsec" % (newCell)
</source>

=== Adjusting the Frequency Axis ===

Changing the frequency axis of the model header is just a straightforward (1+''z'') correction. simobserve adjusts the channelwidth using the '''inwidth''' parameter and the observing frequency using '''incenter'''. 

Notice that the absolute value of the BIMA SONG channel width is used. The noise calculation in simobserve needs positive channel widths, but the input cube is ordered in increasing velocity rather than increasing frequency. We could transpose the cube; on the other hand, the only penalty of changing the sign is that the sense of rotation will be flipped. Since this simulation is a simple detection experiment, the rotation sense is irrelevant, and so we'll take the easy way out.

<source lang="python">
# in CASA
# Move freq to z_new
oldFreq = imhead(imagename=cubeName,mode='get',hdkey='crval3')['value']
newFreq = oldFreq * (1.0 + z_old_lsrk) / (1.0 + z_new)
nchan = imstat("NGC5194.bima12m.cm.fits")['trc'][2]
# Adjust frequency channelwidth for new z
oldDnu = imhead(imagename=cubeName,mode='get',hdkey='cdelt3')['value']
newDnu = abs((1.0+z_old_lsrk) /(1.0+z_new)*oldDnu) # make channel widths positive
inwidth = "%fHz" % newDnu
# Specify the observing frequency at the center of the observing band:
incenter = "%fHz" % (newFreq + 0.5*nchan*newDnu)
</source>

== Map Size and Mosaicking ==

The original BIMA SONG image is about 480 arcseconds across; scale this image size to the new redshift and assign to parameter '''mapsize'''.  We will also use this value later.

<source lang="python">
# in CASA
imSize = 480.0 * (da_old / da_new) # arcseconds
mapsize = "%farcsec" % imSize
</source>

For relatively high redshifts, there should be no need to mosaic the observations. We'll nevertheless allow for mosaicking in case we want to repeat the simulation for lower redshift.  simobserve needs the spacing between pointings in the mosaic; we'll require pointings spaced by half of the primary beam.  The ALMA primary beam is 17 arcseconds at 300 GHz.

<source lang="python">
# in CASA
primaryBeam = 17.0 * (300e9 / newFreq) # arcseconds
pointingspacing = "%farcsec" % (primaryBeam / 2.0) 
</source>

== Array Configuration ==

We want to set '''antennalist''' such that simobserve will decide on an appropriate ALMA configuration based on the desired beam size.   Thus, we first must estimate the desired output "clean" beam size.  We don't want the new beam to be so large so that we cannot resolve a rotation curve, but we also don't want it to be so small that we effectively resolve out the BIMA SONG data. The BIMA SONG beam was 5 arcsec, and so as a reasonable guess we'll adopt the equivalent of a 15" beam at its true distance (3 times coarser than the BIMA SONG beam) and then scale appropriately to z = 0.1.  

Looking ahead to imaging our simulated data, it's important to sample the beam at least 3 times for stable deconvolution.  We'll sample the beam by 4 times, rounded off to the nearest milliacsecond.  

<source lang="python">
# in CASA
beamNew = 15.0 * (da_old / da_new)
pixelSize = round(beamNew * 1000.0 / 4.0) / 1000.0
</source>

Now, to guard against undersampling the beam as a result of rounding error, reset the desired beam to 4 times the pixel size.

<source lang="python">
# in CASA
beamNew = 4.0 * pixelSize
</source>

Now we can set parameter '''antennalist''' using the beam size (but see [[#Aside: Antenna Configurations|Aside: Antenna Configurations]] below).

<source lang="python">
# in CASA
antennalist = "alma;%farcsec" % beamNew
</source>

== Integration and Total Time ==

We will set the integration time to 100 seconds and the total integration time to 8 hours.  For a real observation, 10 seconds will be a more appropriate integration time.  However, we can decrease the simulation CPU time by increasing the integration interval (See [[Etime study]] for details).  Whenever simulating a new data set, we recommend beginning with a large integration time for initial testing and then lowering the integration time to generate a more realistic measurement set.  

<source lang="python">
# in CASA
integration = '100s'
# 8 hours of total integration
totaltime = '28800s'
</source>

== Noise ==

We will add thermal noise to the simulated data by setting parameter '''thermalnoise''' to <tt>tsys-atm</tt>.  We keep the default values of precipitable water vapor (1 mm) and ambient temperature (269 K).

<source lang="python">
# in CASA
thermalnoise="tsys-atm"
</source>

== simobserve Execution ==

Finally, we set '''graphics''' to <tt>"both"</tt> to send plots to the screen and disk; we set '''verbose''' to <tt>True</tt> to print additional information to the logger and terminal; and we set '''overwrite''' to <tt>True</tt> to overwrite existing files in the '''project''' subdirectory.  Now we are ready to run simobserve.

<source lang="python">
# in CASA
graphics="both"
verbose = True
overwrite = True
simobserve()
</source>

== Aside: Antenna Configurations ==

[[file:Beamsummary.png|thumb|ALMA clean beam size as a function of array configuration number]]

In this tutorial the selection of the {{ALMA}} antenna configuration is automated to produce a decent cube of M51 as viewed at z = 0.1, but, for other simulations (or this one, for that matter), it will be worth playing with the configurations, or perhaps evaluating the possibility of detections in CSV or early science.  CASA comes with stock antenna configurations in the directory <tt>$CASAPATH/data/alma/simmos/</tt>.  Use the Python <tt>os</tt> module to resolve the CASA path.  For example:

<source lang="python">
# In CASA
os.getenv('CASAPATH').split(' ')[0] + '/data/alma/simmos/'
</source>

 CASA <99>: ls /usr/lib64/casapy/stable/data/alma/simmos/
 aca_cycle1.cfg            alma.out05.cfg  alma.out21.cfg  pdbi-c.cfg
 aca.i.cfg                 alma.out06.cfg  alma.out22.cfg  pdbi-d.cfg
 aca.ns.cfg                alma.out07.cfg  alma.out23.cfg  sma.compact.cfg
 aca.tp.cfg                alma.out08.cfg  alma.out24.cfg  sma.compact.n.cfg
 alma.cycle0.compact.cfg   alma.out09.cfg  alma.out25.cfg  sma.extended.cfg
 alma.cycle0.extended.cfg  alma.out10.cfg  alma.out26.cfg  sma.subcompact.cfg
 alma_cycle1_1.cfg         alma.out11.cfg  alma.out27.cfg  sma.vextended.cfg
 alma_cycle1_2.cfg         alma.out12.cfg  alma.out28.cfg  vla.a.cfg
 alma_cycle1_3.cfg         alma.out13.cfg  carma.a.cfg     vla.b.cfg
 alma_cycle1_4.cfg         alma.out14.cfg  carma.b.cfg     vla.bna.cfg
 alma_cycle1_5.cfg         alma.out15.cfg  carma.c.cfg     vla.c.cfg
 alma_cycle1_6.cfg         alma.out16.cfg  carma.d.cfg     vla.cnb.cfg
 alma.out01.cfg            alma.out17.cfg  carma.e.cfg     vla.d.cfg
 alma.out02.cfg            alma.out18.cfg  meerkat.cfg     vla.dnc.cfg
 alma.out03.cfg            alma.out19.cfg  pdbi-a.cfg      WSRT.cfg
 alma.out04.cfg            alma.out20.cfg  pdbi-b.cfg

Note that when setting the '''antennalist''' parameter, it is not necessary to provide the full path.  simobserve will search the standard CASA directory and your current working automatically.

The version of CASA 3.4 contains 36 array configurations for ALMA, as well as configuration files for [http://almascience.nao.ac.jp/ ACA], {{EVLA}}, [http://www.cfa.harvard.edu/sma/ SMA], and other interferometers.

== simobserve Output ==

[[File:M51-ATZ-p1.alma_0.360000arcsec.observe.png|thumb|right|Summary plot output by simobserve (M51-ATZ-p1.alma_0.360000arcsec.observe.png).]]

Outputs from simobserve will be written to a directory specified by the '''project''' parameter, in this case <tt>M51-AtZ-p1</tt>.  simobserve will generate these files:

{| border="1"
! Filename
! Description
|-
| M51-AtZ-p1.alma_0.360000arcsec.ms
| Model measurement set ''sans'' noise
|- 
| M51-AtZ-p1.alma_0.360000arcsec.noisy.ms
| Model measurement set with thermal noise
|-
| M51-AtZ-p1.alma_0.360000arcsec.quick.psf
| CASA image of the point spread function
|-
| M51-AtZ-p1.alma_0.360000arcsec.skymodel
| CASA image of the input sky model rescaled according to the skymodel sub-parameters
|-
| M51-AtZ-p1.alma_0.360000arcsec.skymodel.flat
| flattened CASA image of the input sky model rescaled
|- 
| M51-AtZ-p1.alma_0.360000arcsec.skymodel.png
| flattened PNG image of the input sky model rescaled and overlaid with the mosaic pattern specified by the setpointings sub-parameters
|-
| M51-AtZ-p1.alma_0.360000arcsec.observe.png
| 2x2 PNG summary plot showing: source elevation vs. time, antenna position, uv coverage, and the point spread function
|-
| M51-AtZ-p1.alma_0.360000arcsec.ptg.txt
| ASCII text listing of mosaic pointings
|}

== simanalyze Execution ==

After running simobserve and producing a simulated measurement set, the task '''simanalyze''' will quickly and easily image the simulated data and produce diagnostic plots and images.  (Remember that simanalyze is a convenience task.  You can also use other CASA tasks, like <tt>clean</tt>, directly on the simulated data.)

To setup the simanalyze parameters we will keep the values of '''project''' and '''verbose''' that we set for simobserve.  We set '''vis''' to image the noisy measurement set by concatenating '''project''', '''antennalist''' with ";" replaced by "_", and ".noisy.ms".   We set '''modelimage = cubeName''' so simanalyze will use the model image when cleaning the simulated data.  We then set the clean threshold to 1 mJy.

<source lang="python">
# in CASA
modelimage = cubeName
vis = project +'.'+ antennalist.replace(';','_') +'.noisy.ms'
threshold = "1.0mJy"
</source>

We now set '''cell''' to the pixel size calculated above.

<source lang="python">
cell = "%farcsec" % pixelSize  
</source>

Now we have both the image size and pixel size in arcseconds, but the simanalyze parameter '''imsize''' wants the ratio: the number of pixels along the RA or Dec axis. To keep the image from becoming too small, set the minimum image size to be 256 pixels.

<source lang="python">
# in CASA
imSizePix = int(round(imSize / pixelSize))
if imSizePix < 256: imSizePix = 256
imsize = [imSizePix,imSizePix]
</source>

Now we are ready to execute the task.

<source lang="python">
simanalyze()
</source>

== simanalyze Output ==

[[File:M51-ATZ-p1.alma 0.360000arcsec.analysis.png|thumb|simanalyze summary plot displayed in the CASA plotter.]]

The simanalyze output files will appear in the CASA plotter and in subdirectory <tt>M51-AtZ-p1</tt>.

{| border="1"
! Filename
! Description
|-
| M51-AtZ-p1.alma_0.360000arcsec.noisy.image
| CLEAN-deconvolved cube of M51-AtZ-p1.alma_0.360000arcsec.noisy.ms
|-
| M51-AtZ-p1.alma_0.360000arcsec.noisy.residual
| Residual image after cleaning
|- 
| M51-AtZ-p1.alma_0.360000arcsec.skymodel.flat.regrid
| Input model image regridded to match the output image
|-
| M51-AtZ-p1.alma_0.360000arcsec.skymodel.flat.regrid.conv
| Input model image regridded to match the output image and convolved with the output clean beam
|}

[[File:M51sim-09.png|thumb|Channel 16 of the M51 at z=0.1 simulation. The rms noise is about 0.25 mJy/beam, and the peak flux density on this channel is about 2 mJy/beam.]]

Additional (or fewer) outputs can be produced by simanalyze by setting the '''analyze''' subparameters.  The image at the right can be displayed by running the task viewer and loading the appropriate image file, e.g. <tt>viewer(infile = 'M51-AtZ-p1/M51-AtZ-p1.image', channel = 16)</tt>.

The rest frequency will have been lost in the simulation, and it's worth restoring to the header.

<source lang="python">
# in CASA
imhead(imagename="M51-AtZ-p1/M51-AtZ-p1.alma_0.360000arcsec.noisy.image", 
       mode="put", hdkey="restfreq", hdvalue="115.27120180GHz")
</source>

The simulated data cube can be analyzed just like any other CASA image -- examples are given in the [[Imaging a Mosaicked Spectral Line Dataset|CARMA tutorial]] and the [[NGC 5921: red-shifted HI emission#Cube Moments|VLA 21cm tutorial]].

== Moment Maps ==

[[File:M51simnew.png|thumb|Moment maps of the M51 CO 1-0 at z=0.1 simulation. ''Left'': Moment 0 (integrated intensity) map. ''Right'': Moment 1 (velocity field) map. Note that the rotation sense has been flipped, exactly [[#Adjusting the Frequency Axis | as expected]].]]

Use [[immoments]] to calculate the integrated intensity and velocity field maps from the simulated cube. The '''excludepix''' option applies a 3&sigma; cut.

<source lang="python">
# Must remove this file before immoments is run, if this has been run previously in the directory
os.system('rm -rf M51-AtZ-p1/M51-AtZ-p1.alma_0.360000arcsec.noisy.moments.*')
immoments(imagename='M51-AtZ-p1/M51-AtZ-p1.alma_0.360000arcsec.noisy.image',
          moments=[0,1],axis='spectral', excludepix=[-100,0.0006],
          outfile='M51-AtZ-p1/M51-AtZ-p1.alma_0.360000arcsec.noisy.moments')
</source>

The results are shown at right.

You can view these results by running the task viewer, then selecting the moments maps found in the directory <tt>M51-AtZ-p1</tt>.

== Pushing M51 out to z = 0.3 ==

We'll leave as an exercise for the reader the tuning of this simulation to push M51 all the way out to z = 0.3 (luminosity distance = 1540 Mpc). simobserve produces a reasonable detection in 8 hrs integration, but you'll need to consider more carefully the antenna configuration needed to produce the requisite sensitivity. To conclude, here are the moment maps for the z = 0.3 simulation.

[[File:M51sim78.png|400px|Simulation of M51 CO 1-0 at z = 0.3. ''Left'': integrated intensity map. ''Right'': (marginally resolved) velocity field.]]

{{Simulations Intro}}
{{Checked 4.0.0}}