Simulated Observations of Redshifted CO in M51

About M51 (the Whirlpool Galaxy):

M51 (NGC 5194), also known as the Whirlpool Galaxy, is located 10 Mpc away, and thus 1" corresponds to about 50 pc in physical scales. The optical disk of the galaxy is inclinded by about 20 degrees from the line of sight, allowing us to have this nearly face-on view. The diameter of the optical disk is about 6' (about 20 kpc). The total molecular gas content of M51 is about 10^10 solar masses. In comparison, its FIR luminosity is about 2 x 10^10 solar luminosity. Therefore it is a somewhat gas-rich spiral with a moderate level of massive star forming activity -- but not exceptional.

CO (3-2) emission in z=0.1 M51 in 200 hrs with ALMA


Figure: (left) original CO (1-0) image of M51 from Tamara; (middle) simulated CO (3-2) image of M51 at z=0.1 at 1" resolution; (right) first moment (velocity field) derived from the same data cube.

I took the original CO (1-0) data cube provided by Tamara at 6" resolution (300 pc) and 5 km/s velocity resolution and convolved it with a spatial resolution of 2 kpc (1" at z=0.1) and a velocity resolution of 25 km/s. The observed flux should be corrected for the luminosity distance (D), frequency, and spectral contraction (S_new = S_old * J^2 * (1+z) * (10/D)^2, assuming M51 at 10 Mpc). Lastly, expected noise (10 mJy rms in each 25 km/s channel after 200 hrs of integration time) is added in each channel. A constant line brightness is assumed, and this may only be off by a factor two or so -- a conclusion of the HHT CO (3-2) and CO (4-3) measurements of M51 at 20" (1 kpc) resolution. The channel maps can be found here.

I tried this for 0.1" resolution observation first, but we basically do not have enough brightness sensitivity to detect CO at any cosmological distances at that resolution. At z=0.1, the spatial resolution is comparable (200 pc) to the existing data, but the peak flux of the line is only about 10 mJy while the expected noise is also about 10 mJy, i.e. S/N = 1 after 200 hrs. It only gets worse with higher redshifts because (1/D)^2 kills us.

Spatial averaging increases the peak line flux in each channel, so we can start imaging things once we sum up several pixels together. By going from 0.1" to 1" resolution, we are summing over 100 times more pixels, and we gain in peak line flux by (100*f) factor, where "f" is a filling factor. (This is why the detection experiments are best done when the source size and beam size are matching.) Not only we image the CO distribution reasonable well, we recover the kinematical information very well also (right panel).

Problem: 1" resolution at z=1 corresponds to a spatial resolution of 23 kpc -- the whole M51 fits into a single beam. We will still have some sensitivity to the kinematical structure because we are still partially resolving the source. This is not going to be pretty, however. SO, WHAT WOULD BE A REASONABLE NEXT STEP? Imaging CO at z=0.1 is not so stunning. We might do a reasonably interesting job with 0.5" resolution. Any suggestions on the next step?

A "back of the envelope" calculation

ALMA sensitivity for redshift CO. This assumes we are not resolving any structure. To estimate what is needed: the brightest feature in the original M51 map is about 2 Jy/beam at 300 pc scales; Jy/K should be around 50; 25 km/s channels -- thus about 10^5 K km/s pc^2. A 5 sigma sensitivity at z=1 is 10^7, so we need to integrate a lot longer and cannot afford to resolve the structure too much.... We can gain most of it back with 200 hr integration, but we cannot afford to have a beam much smaller than a few kpc.