[Abdriged] The origin of the diffuse hard X-ray (2 - 10 keV) emission from starburst galaxies is a long-standing problem. We suggest that synchrotron emission of 10 - 100 TeV electrons and positrons (e+/-) can contribute to this emission, because starbursts have strong magnetic fields. We consider three sources of e+/- at these energies: (1) primary electrons directly accelerated by supernova remnants; (2) pionic secondary e+/- created by inelastic collisions between CR protons and gas nuclei in the dense ISMs of starbursts; (3) pair e+/- produced between the interactions between 10 - 100 TeV gamma-rays and the intense far-infrared (FIR) radiation fields of starbursts. We create one-zone steady-state models of the CR population in the Galactic Center (R <= 112 pc), NGC 253, M82, and Arp 220's nuclei, assuming a power law injection spectrum for electrons and protons. We compare these models to extant radio and GeV and TeV gamma-ray data for these starbursts, and calculate the diffuse synchrotron X-ray and Inverse Compton (IC) luminosities of these starbursts. If the primary electron spectrum extends to ~PeV energies and has a proton/electron injection ratio similar to the Galactic value, we find that synchrotron contributes 2 - 20% of their unresolved, diffuse hard X-ray emission. Inverse Compton emission is likewise a minority of the unresolved X-ray emission in these starbursts, from 0.1% in the Galactic Center to 10% in Arp 220's nuclei. We also model generic starbursts, including submillimeter galaxies, in the context of the FIR--X-ray relation, finding that up to 2% in the densest starbursts with our fiducial assumptions. Neutrino and TeV gamma-ray data can further constrain the synchrotron X-ray emission of starbursts. Our models do not constrain hard synchrotron X-ray emission from any additional hard components of primary e+/- from sources like pulsars in starbursts.
Starburst galaxies are intense generators of cosmic rays (CRs), which are accelerated by supernova remnants or other star-formation processes. CR protons in starbursts can produce γ-rays, neutrinos, and secondary electrons and positrons. Whatever their origin, CR electrons and positrons can produce emission across the electromagnetic spectrum: bremsstrahlung losses produce γ-rays; Inverse Compton scattering of ambient photons produces a broadband spectrum extending into γ-rays; synchrotron emission is responsible for the non-thermal GHz radio emission.
Starburst galaxies are observed to be luminous in hard Xrays (here defined as ∼ 2 -10 keV) as well. The total hard X-ray emission from star-formation typically has a luminosity that is 10 -4 times that of the bolometric luminosity of the starburst, and is sometimes used as a star-formation indicator (Franceschini et al. 2003;Ranalli et al. 2003;Grimm et al. 2003;Persic et al. 2004). Most of these X-rays are from point sources, but diffuse emission also is apparent. The diffuse hard X-ray emission is best studied in the nearby starburst M82 (Strickland & Heckman 2007), but a similar diffuse hard component is observed in NGC 253 (Strickland et al. 2000;Weaver et al. 2002). The diffuse hard X-ray emission bears some superficial resemblance to the Galactic Ridge emission of the Milky Way (Strickland & Heckman 2007), although that has recently been resolved into stellar sources by Chandra (Revnivtsev et al. 2009). At the other extreme, unresolved hard X-ray emission is also observed in brighter starbursts including the Luminous Infrared Galaxy (LIRG) NGC 3256 (Moran et al. 1999;Lira et al. 2002) and the prototypical Ultraluminous Infrared Galaxy (ULIRG) Arp 220 (e.g., Clements et al. 2002;McDowell et al. 2003). Especially in these more distant galaxies, it is unclear whether these components are truly diffuse or simply unresolved sources (e.g., Lira et al. 2002).
The diffuse hard X-ray emission typically has a powerlaw continuum spectrum, with the possible addition of softer thermal emission components and spectral lines (Persic & Rephaeli 2002;Strickland & Heckman 2007;Lehmer et al. 2010). Thermal emission from hot plasma is one possible source of the hard X-rays: hot gas is predicted by superwind theories (e.g., Chevalier & Clegg 1985;Strickland & Heckman 2009), and thermal emission is clearly detected in soft X-rays (e.g., Ptak et al. 1997;Dahlem et al. 1998;Strickland & Stevens 2000), although Strickland & Stevens (2000) argue that the soft X-rays come from a cooler phase of gas than the bulk of the superwind (see also the discussion in Strickland & Heckman 2009). The detection of 6.7 keV iron K lines implies the existence of hot plasma that could be a source of the hard X-rays (Persic et al. 1998;Cappi et al. 1999;Iwasawa et al. 2005Iwasawa et al. , 2009)), although it is not clear that such emission could explain all of the hard continuum (Strickland & Heckman 2007). The hard X-ray emission is often attributed to unresolved X-ray binaries, particularly high-mass X-ray binaries (HMXBs) (e.g., Fabbiano et al. 1982;Fabbiano 1989;Griffiths & Padovani 1990;David et al. 1992;Persic & Rephaeli 2002;Grimm et al. 2003;Persic et al. 2004).
HMXBs in the Milky Way and Magellanic Clouds have a power law continuum (photon spectra of dN/dE ∝ E -Γ ) with a spectral slope of Γ ≈ 1.2 (White et al. 1983). Many starburst galaxies have total hard X-ray emission with Γ ≈ 1 -1.5 (e.g., Rephaeli et al. 1991Rephaeli et al. , 1995)), which makes HMXBs an attractive candidate for the source of most of the hard X-ray emission. However, in M82, diffuse hard X-ray emission remains even after subtracting point sources and extrapolating the luminosity function to faint luminosities, and the diffuse emission is softer (Γ 2-8 ≈ 2 -3) than expected from HMXBs (Strickland & Heckman 2007), unless the HMXB spectrum cuts off at energies 10 keV.
Another possible explanation for this X-ray emission is Inverse Compton emission (Hargrave 1974;Schaaf et al. 1989;Moran & Lehnert 1997;Moran et al. 1999;Persic & Rephaeli 2003). CR electrons and positrons (e ± ) are known to be present in starbursts from their synchrotron radio emission, and the intense infrared emission of starbursts provides many target photons to be upscattered to higher energies. The IC spectrum is expected to extend down to the X-rays and even lower energies. However, recent estimates generally suggest that IC emission is too weak by a factor of 10 in M82 and NGC 253 to explain the hard X-ray emission (e.g., Weaver et al. 2002;Strickland & Heckman 2007). As with HMXBs, the spectral slope of the diffuse X-ray emission in some starbursts may be difficult to explain with IC. The CR e ± spectrum around ∼ 100 MeV and the resultant IC spectrum at keV energies is expected to be hard (Γ ≈ 1.0 -1.5), whereas the diffuse X-ray emission is often softer, as is the case for M82 (Strickland & Heckman 2007).
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