Studies of X-ray bursters with BATSE as well as studies of individual systems (e.g., 4U 0614+09 and 4U 1915-05) have suggested common characteristics of the hard spectra from neutron stars and the likely differences between neutron star and black hole hard X-ray spectral components. These suggest many observational follow-up studies for future missions with much higher sensitivity and resolution.

Accreting high magnetic field neutron stars are observed as X-ray pulsars. The detection and detailed study of cyclotron lines in their hard X-ray spectra are the best and most direct method of determining neutron star magnetic fields. Indirect arguments invoking spin-up or spin-down near the equilibrium spin period often indicate rather high magnetic fields (~10¹⁴ G in the case of GX1+4). Recent measurements of a cyclotron feature at 110 keV and a possible feature at 55 keV in A0535+26, implying B ~10¹³ G, have strengthened the case for high magnetic fields for some accreting pulsars. High fields are similarly inferred for other Be binaries. Magnetic dipole spin-down remains a possibility although the implied fields approach 10¹⁴ G in several cases. Because of the rapid spin-down to the radio pulsar death line, such ultra-high field neutron stars may be best observed in the X-ray regime. Cyclotron line features and high quality continuum spectra of such sources would probe the strongest magnetic fields in nature and should give important evidence of new quantum effects expected near 10¹⁴ G. The persistence of such high fields may be related to the accretion history of these objects. If so, relatively low average accretion rates may be important such as seen in the Be systems, implying either transient X-ray sources or low steady luminosities. Accordingly, studying these unique high field sources presents several observational challenges: the sources will be transient or faint and the need to obtain high sensitivity, high resolution spectra covering two cyclotron harmonics requires sensitivity to energies as high as 500 keV-1 MeV. The INTEGRAL should give important results on some brighter systems, but future large area imaging experiments will be needed to probe the physics of ultra high-field accreting neutron stars.

2.2.3 WHITE DWARFS

Since the proton accretion free-fall energy onto a white dwarf is ~200 keV, accreting white dwarfs, or cataclysmic variables (CVs), are natural hard X-ray emitters. The magnetic CVs, or AM-Her and DQ Her systems (strong and moderate magnetic fields, respectively) may have accretion flows closest to free-fall since their disks are nonexistent or marginal (respectively). Much more sensitive hard X-ray observations would allow the first broad comparison with the ROSAT Survey, which has greatly extended (to more than 40) the known sample of AM Her systems. These are "ultra-soft."The higher spectral resolution of future hard X-ray missions would allow (for example) a systematic search for the expected change in hard X-ray cutoff energy vs. mass of the white dwarf (due to changing M/R) as might be observable in "new" >200 MG AM Her systems.

2.2.4 SPIN-DOWN PULSARS

Isolated pulsars have been known since their discovery to be neutron stars with spin-powered magnetospheric emission. Not long after their radio detection, the Crab and Vela pulsars were found to be pulsing at optical, X-ray and gamma-ray energies. Despite this well established identification, fundamental questions about these objects remain unanswered, including the basic radiation mechanism, the nature of the particle acceleration, the pulsar birthrate, and the relationship to supernova remnants. An examination of a power spectrum of the pulsed emission shows that the peak energy output for pulsars such as Vela lies at several GeV. The solution to the pulsar problem is thus most likely to be extracted from high-energy gamma-ray observations although it is clear that careful ties with other wave bands provides important information from across the spectrum.