Observations of 0957+561 with the Einstein High Resolution Imager (HRI
) in 1979 May and 1979 November and with the ROSAT HRI in 1991 May and
1992 October reveal large variations in the X-ray fluxes for images A
and B which significantly differ from simultaneously observed changes
of the corresponding optical continuum emission. Most striking was th
e apparent increase by over fivefold in the flux of image B from the l
ate 1970's to the early 1990's. Further, in the 1990's the X-ray flux
for image A increased by a factor of 1.7 +/- 0.3 and that of B by a fa
ctor of 1.9 +/- 0.2 between the two ROSAT observations (separated by 5
40 days), whereas optical measurements showed nearly no changes for A
and B between these epochs. No significant changes in X-ray emission w
ere observed on timescales of hours to days. If we adopt 1.5 yr as the
difference between the propagation times from the quasar to us via th
e two images (''time delay''), then the ratio of the X-ray flux of ima
ge B for the 1992 October epoch to that of A for the 1991 May epoch is
2.7 +/- 0.4. This ratio is significantly greater than the ratio of 1.
05 +/- 0.03 observed in the optical R band, 0.75 in the broad line reg
ion (BLR), and 0.76 +/- 0.03 in the radio (VLBI lambda 13 cm core) for
approximately the same epoch. The wavelength dependence in the ratio
of the fluxes of the two images suggests that either microlensing may
be significant for the X-ray band or the time delay is substantially d
ifferent from 1.5 yr (and the intrinsic variation of the quasar emissi
on were significant within an interval comparable to the uncertainty o
f the time delay), or both. A ROSAT Position Sensitive Proportional Co
unter (PSPC) spectrum of 0957+561 is fitted well with a power law of e
nergy index 1.1 +/- 0.2 plus a Raymond-Smith thermal plasma model with
a temperature of 0.22 +/- 0.17 keV in the source frame. The estimated
unmagnified X-ray luminosity of the thermal component is 3 x 10(44) e
rgs s(-1) (if the magnification of the thermal component by the lens i
s 14). This thermal emission may be a result of a strong cooling flow
in the vicinity of the quasar. There is no evidence for excess absorpt
ion above that attributed to our galaxy for the relatively high-redshi
ft quasar. We place an upper limit of 6(-4)(+3) x 10(20) atoms cm(-2)
(90% confidence) on absorption at the redshift z = 1.391 of a known da
mped Lyman-alpha absorber and provide upper and lower bounds of 30 h(5
0)(-1) kpc and 0.2 h(50)(-1) kpc, respectively, for the spatial extent
of this H I region. For the cluster of galaxies around the primary le
nsing galaxy, G1, the 3 sigma upper limit on the X-ray luminosity with
in a 0.5 Mpc radius over the energy range 2-10 keV (PSPC frame) is 4.1
x 10(44) ergs s(-1) for a cluster core radius of 0.1 Mpc and 1.7 x 10
(44) ergs s(-1) for a core radius of 0.25 Mpc. Similarly the limit on
the X-ray luminosity of a cluster around the galaxy G5 is found to be
2.8 x 10(43) ergs s(-1). Based on the relation of cluster X-ray lumino
sity to gas temperature and system mass, we estimate the 3 sigma upper
limits on the mass of the clusters that contain the galaxies G1 and G
5 within 1 Mpc to be 1.5 x 10(14) and 1 x 10(14) M., respectively.