We present ISO observations of several \mathrm { H } _ { 2 } pure-rotational lines ( from S ( 0 ) to S ( 5 ) ) towards a sample of 16 molecular clouds distributed along the central \sim 500 pc of the Galaxy .
We also present \mathrm { C } ^ { 18 } \mathrm { O } and ^ { 13 } \mathrm { CO } J = 1 \rightarrow 0 and J = 2 \rightarrow 1 observations of these sources made with the IRAM-30m telescope .
With the CO data we derive \mathrm { H } _ { 2 } densities of 10 ^ { 3.5 - 4.0 } cm ^ { -3 } and \mathrm { H } _ { 2 } column densities of a few 10 ^ { 22 } cm ^ { -2 } .
We have corrected the \mathrm { H } _ { 2 } data for \sim 30 magnitudes of visual extinction using a self-consistent method .
In every source , we find that the \mathrm { H } _ { 2 } emission exhibits a large temperature gradient .
The S ( 0 ) and S ( 1 ) lines trace temperatures ( T ) of \sim 150 K while the S ( 4 ) and S ( 5 ) lines indicate temperatures of \sim 600 K. The warm \mathrm { H } _ { 2 } column density is typically \sim 1 - 2 \times 10 ^ { 22 } cm ^ { -2 } , and is predominantly gas with T =150 K. This is the first direct estimate of the total column density of the warm molecular gas in the Galactic center region .
These warm \mathrm { H } _ { 2 } column densities represent a fraction of \sim 30 \% of the gas traced by the CO isotopes emission .
The cooling by \mathrm { H } _ { 2 } in the warm component is comparable to that by CO .
Comparing our \mathrm { H } _ { 2 } and CO data with available ammonia ( NH _ { 3 } ) observations from literature one obtains relatively high NH _ { 3 } abundances of a few 10 ^ { -7 } in both the warm and the cold gas .
A single shock or Photo-Dissociation Region ( PDR ) can not explain all the observed \mathrm { H } _ { 2 } lines .
Alternatives for the heating mechanisms are discussed .