X-ray observations with the ROSAT HRI and with ASCA are presented for the nearby radio quasar B2 1028+313 , which is located in the cD galaxy at the center of the Abell cluster A1030 .
We also analyze archival ROSAT PSPC observations .
We find that the X-ray emission is dominated by the quasar .
The flux varied by a factor of about two between the ROSAT HRI and ASCA observations , which were about one year apart .
The X-ray spectrum of the quasar is fit by a single power-law , except at low energies where there is a soft excess .
Although the shape of the soft excess is not strongly constrained , it can be fit by a blackbody with a temperature of about 30 eV .
There was evidence for extended X-ray emission , which contributed about 25 % of the total flux .
However , this emission does not appear to be normal X-ray emission from intracluster gas or a central cooling flow .
The extended X-ray emission appears to be quite soft ; if its spectrum is modeled as thermal emission , the temperature is \sim 0.2 keV , rather than the 5-10 keV expected for ICM emission .
The radial surface distribution of the emission was not fit by either the beta model which usually describes ICM emission , or by a cooling flow model .
The ASCA and ROSAT spectra showed no convincing evidence for a thermal component with a cluster-like temperature , either in the overall spectral shape or in emission lines .
In addition , the ROSAT PSPC image showed that the extended X-ray emission was highly elongated to the NNW and SSE , in the same direction as the extended radio emission from the quasar .
We suggest that the extended emission is inverse Compton emission from the extended radio lobes .