1. Name of program and authors

Weak lensing using ALMA

Andrew Blain

   2. One short paragraph with science goal(s)

Gravitational lensing by large-scale structure in the Universe
produces systematic distortions in the shapes of galaxies at moderate
and high redshifts (by about 0.1-1% for z>0.2). These distortions can
be used to map the distribution of dark matter along the line of sight
to the lensed object.  Currently, this effect is detected
statistically with samples of over 10,000 galaxies detected in optical
survey fields at least 10 square arcmin in extent.

Although ALMA will have exquisite spatial resolution, it will not be
able to cover large enough fields to match this work. The ALMA archive
would allow this science to be pieced together in field observed for
other deep science investigations.

There is however, a possible unique niche for ALMA to study weak
lensing, along with the astrophysics of gas emission from galaxies at
moderate redshifts. By imaging disk galaxies that are close to each
other on the sky (separated by an arcmin or less), and by measuring
their rotation fields very accurately the distortion can perhaps be
detected (Blain 2002 ApJ 570 L54). The most promising way to probe
this should be to detect the CO(3-2) line from z~0.5, at which there
should be a significant amount of excited gas present, and yet the
distance is such that the galaxy is neither too small nor too
faint. z~0.5 line-emitting galaxies may also be important for galaxy
evolution science. This project may be possible in parallel.

   3. Number of sources

1 trial pair of z~0.5 spiral galaxies separated by up to about 1 arcmin on
sky (perhaps pre-selected from a deep ALMA survey region). Program could
be extended, combining examples in an interconnected web to build up a
map of the distortion 1 arcmin at a time.

   4. Coordinates:

      4.1. Rough RA and DEC No restriction. 
      4.2. Moving target: no 
      4.3. Time critical: no 

   5. Spatial scales:
      5.1. Angular resolution (arcsec): 0.03-0.1" at 230 GHz.
	Best possible resolution is essential to resolve the rotation curve
      5.2. Range of spatial scales/FOV (arcsec): 0.03-10"
		Pair of single fields.
      5.3. Single dish total power data: no
      5.4. ACA: NO
      5.5. Subarrays: no

   6. Frequencies:
      6.1. Receiver band: Band 6
      6.2. Lines and Frequencies (GHz):
		CO(3-2) redshifted to 230GHz
       6.3. Spectral resolution (km/s):
		1-2 km/s
      6.4. Bandwidth or spectral coverage (km/s or GHz):
		>500 km/s

   7. Continuum flux density:

      7.1. Typical value (Jy):	0.1 mJy
      7.2. Required continuum rms (Jy or K):	N/A
      7.3. Dynamic range within image: 
		Not a problem. Bright nearby objects will be avoided

   8. Line intensity:

      8.1. Typical value (K or Jy):
		0.4 Jy km/s integrated over 300 km/s, i.e 1.3 mJy line flux.
		Point by point probably a 10 km/s wide line.
      8.2. Required rms per channel (K or Jy):
	Need accurate central velocity of the resolved CO line, so 2 km/s
		resolution required.
SG : I don't understand that
	[0.4 Jy km/s must be split into >100 independent resolution elements.
	10-sigma per 2 km/s channel in 100 elements implies=20
	need RMS - 400 / ( 10 . 100 . sqrt(5) ) =3D 0.18mJy. ]
SG: my own estimate
	Line flux is 1.3 mJy, so 10 sigma means 0.13 mJy rms noise

      8.3. Spectral dynamic range:             =20
		Not a problem

   9. Polarization:  no  (optional)
      9.1. Required Stokes
      9.2. Total polarized flux density (Jy)
      9.3. Required polarization rms and/or dynamic range
      9.4. Polarization fidelity

   10. Integration time for each observing mode/receiver setting (hr):
	0.13 mJy. RMS in 2 km/s channel in 1 hr is 0.93 mJy, so 51 hours.
	2 pointings, 100 hours.

	Corresponding brightness sensitivity is 1.2 K at 0.05" resolution.

   11. Total integration time for program (hr):

	100 hrs on a carefully considered target pair of z~0.5 galaxies

   12. Comments on observing strategy (e.g. line surveys, Target of
       Opportunity, Sun, ...): (optional)


Review Chris Carilli: OK, integration times checked