ABSTRACTWe present a detailed investigation of atmospheres around accreting neutron stars with high magnetic—eld G) and low luminosity ergs s(BZ1012 (L [1033 ~1). We compute the atmospheric structure, inten-sity, and emergent spectrum for a plane-parallel, pure hydrogen medium by solving the transfer equa-tions for the normal modes coupled to the hydrostatic and energy balance equations. The hard tailfound in previous investigations for accreting, nonmagnetic neutron stars with comparable luminosity issuppressed, and the X-ray spectrum, although still harder than a blackbody at the star eƒective tem-perature, is nearly Planckian in shape. Spectra from accreting atmospheres, both with high and low—elds, are found to exhibit a signi—cant excess at optical wavelengths above the Rayleigh-Jeans tail of theX-ray continuum.Subject headings: accretion, accretion disks ¨ radiative transfer ¨ stars: magnetic —elds ¨stars: neutron ¨ X-rays: stars 1 . INTRODUCTION The problem of investigating the properties of radiationemitted by neutron stars (NSs) accreting at low rates, M0B1010¨1014gs~1,becameofinterestafteritwasrealizedthatthe Galaxy may contain a large population of low-luminosity magnetic accretors (see, e.g., Nelson et al. 1995).TheGalaxyshouldharbormorethan103Be/X-raybinarieswith an accreting NS shining at B1032¨1034 ergs s~1(Rappaport & van den Heuvel 1982; van den Heuvel RBlaesMseeTrevesetal.1999forareview).At variance with neutron stars accreting at high rates,e.g., in X-ray pulsators, in low-luminosity sources the inter-action of the escaping radiation with the inNowing materialis of little importance, so they provide a much simpler casefor investigating the physics of accretion in a strongly mag-netized environment. For luminosities far below theEddington limit, the accretion problem becomes germaneto that of calculating the spectrum emerging from staticatmospheres around cooling NSs. Spectra from coolingNSs have been widely investigated by a number of authorsin connection with the X-ray emission from young, milli-second pulsars and isolated NSs, both for low and highmagnetic—eldsandfordiƒerentchemicalcompositions(see,e.g., Romani 1987; Shibanov et al. 1992; Rajagopal R Pavlov et al. 1996b). Emerging spectra arenot very diƒerent from a blackbody at the star eƒectivetemperature, the distinctive hardening present at low —elds(B[109 G) becoming less pronounced when the magnetic—eldisD1012¨1013G.Similarconclusionswerereachedforthespectrumemittedbylow-luminosity,low-—eld,accretingNSs by Zampieri et al. (1995, hereafter ZTZT) for a purehydrogenatmosphericcomposition.The search of isolated neutron stars with ROSAT pro-duced in recent years half a dozen promising candidates(Walter, Wolk, & 1996; Haberl et al. 1997;Neu”hauserHaberl, Motch, & Pietsch 1998; Schwope et al. 1999;Motch et al. 1999; Haberl, Pietsch, & Motch 1999). All ofthem show a soft, thermal X-ray spectrum, with typicalenergies D100 eV, and have an exceedingly large X-ray tooptical Nux ratio, Although their association withZ104.isolated neutron stars is —rmly established, their interpreta-tion in terms of an accreting or a cooling object is still amatter of lively debate. Present models predict rathersimilar spectral distributions in both cases, especially in theX-ray band. It is therefore of particular importance toimprove our theoretical understanding of these two classesofsources,looking,inparticular,forspectralsignaturesthatcanenableustodiscriminatebetweenthem.In this paper we present a —rst detailed calculation ofspectra emitted by strongly magnetized G), ac-(BZ1012creting neutron stars, focusing our attention on low lumi-nosities, L D1030¨1033 ergs s~1, such as those expectedfrom old neutron stars accreting the interstellar medium.Spectral distributions are computed by solving the transferequations for the normal modes coupled to the hydrostaticequilibrium and the energy balance for diƒerent values oftheaccretionrateandthemagnetic—eld.We—ndthatspectraemergingfrommagnetizedaccretionatmospheres are blackbody-like in the X-ray band, in closeagreement with the known results for cooling, magnetizedatmospheres. However, accretion spectra show a new anddistinctivefeatureatlowenergies,beingcharacterizedbyanexcess over the Raleigh-Jeans tail of the X-ray continuum387