2 transistors in solar charging circuit
It's a constant current charger for the battery.



The lower transistor receives base current through the LED and 33k. I estimate it will be about 400 uA and this is probably shared mainly by the 1N400 diode - so let's say the NPN base current is about 100uA when the solar panel produces 12V. At lower voltages the current will be roughly proportionately less.

100uA x NPN current gain means the base current through the PNP is going to be in the region of 10mA (please double check the data sheets for the devices and remember this is an explanation not a definitive simulation!).

With 10mA base current it's likely that the PNP could be providing anything up to 1A for the battery and as the solar panel voltage drops this current will fall proportionately.