The spatial distribution of the Ly \alpha forest is studied using new HST data for the quasar pair Q 1026–0045 A and B at z _ { em } = 1.438 and 1.520 respectively .
The angular separation is 36 arcsec and corresponds to transverse linear separations between lines of sight of \sim 300 h ^ { -1 } _ { 50 } kpc ( q _ { o } = 0.5 ) over the redshift range 0.833 < z < 1.438 .
From the observed numbers of coincident and anti-coincident Ly \alpha absorption lines , we conclude that , at this redshift , the Ly \alpha structures have typical dimensions of \sim 500 h ^ { -1 } _ { 50 } kpc , larger than the mean separation of the two lines of sight .
The velocity difference , \Delta V , between coincident lines is surprisingly small ( 4 and 8 pairs with \Delta V < 50 and 200 km s ^ { -1 } respectively ) . Metal line systems are present at z _ { abs } = 1.2651 and 1.2969 in A , z _ { abs } = 0.6320 , 0.7090 , 1.2651 and 1.4844 in B .
In addition we tentatively identify a weak Mg ii system at z _ { abs } = 0.11 in B .
It is remarkable that the z _ { abs } = 1.2651 system is common to both lines of sight .
The system at z _ { abs } = 1.4844 has strong O vi absorption . There is a metal-poor associated system at z _ { abs } = 1.4420 along the line of sight to A with complex velocity profile .
We detect a strong Ly \alpha absorption along the line of sight to B redshifted by only 300 km s ^ { -1 } relatively to the associated system .
It is tempting to interpret this as the presence of a disk of radius larger than 300 h ^ { -1 } _ { 50 } kpc surrounding quasar A .