A study of low-metallicity DLAs at high redshift and C II* as a probe of
  their physical conditions
  We present a detailed high spectral resolution (R $\sim$ 40000) study of five
high-z damped Lyman $\alpha$ systems (DLAs) and one sub-DLA detected along four
QSO sightlines. Four of these DLAs are very metal-poor with [Fe/H] $\le$ $-$2.
One of them, at z$_{abs}$ = 4.20287 towards J0953$-$0504, is the most
metal-poor DLA at z $>$ 4 known till date. This system shows no enhancement of
C over Fe and O, and standard Population II star yields can explain its
relative abundance pattern. The DLA at z$_{abs}$ = 2.34006 towards J0035$-$0918
has been claimed to be the most carbon-enhanced metal-poor DLA. However, we
show that thermal broadening is dominant in this system and, when this effect
is taken into account, the measured carbon enhancement ([C/Fe] = 0.45 $\pm$
0.19) becomes $\sim$ 10 times less than what was reported previously. The gas
temperature in this DLA is estimated to be in the range of 5000 $-$ 8000 K,
consistent with a warm neutral medium phase. From photoionization modelling of
two of the DLAs showing C II* absorption, we find that the metagalactic
background radiation alone is not sufficient to explain the observed C II*
cooling rate, and local heating sources, probably produced by in-situ star
formation, are needed. Cosmic ray heating is found to contribute $\gtrsim$ 60%
to the total heating in these systems. Using a sample of metal-poor DLAs with C
II* measurements, we conclude that the cosmic ray ionization rate is equal to
or greater than that seen in the Milky Way in $\sim$ 33% of the systems with C
II* detections.
