  We present a hard X-ray NuSTAR observation of PSR J0437-4715, the nearest
millisecond pulsar. The known pulsations at the apparent pulse period ~5.76 ms
are detected at energies up to 20 keV. We measure a photon index $\Gamma=
1.65\pm0.24$ (90% confidence) for the power law fit to the non-thermal
emission. It had been shown that spectral models with two or three thermal
components fit the XMM-Newton spectrum of PSR J0437-4715, depending on the
slope of the power-law component, and the amount of absorption of soft X-rays.
The new constraint on the high-energy emission provided by NuSTAR removes
ambiguities regarding the thermal components of the emission below 3 keV. We
performed a simultaneous spectral analysis of the XMM-Newton and NuSTAR data to
confirm that three thermal components and a power law are required to fit the
0.3-20 keV emission of PSR J0437-4715. Adding a ROSAT-PSPC spectrum further
confirmed this result and allowed us to better constrain the temperatures of
the three thermal components. A phase-resolved analysis of the NuSTAR data
revealed no significant change in the photon index of the high-energy emission.
This NuSTAR observation provides further impetus for future observations with
the NICER mission (Neutron Star Interior Composition Explorer) whose
sensitivity will provide much stricter constraints on the equation of state of
nuclear matter by combining model fits to the pulsar's phase-folded lightcurve
with the pulsar's well-defined mass and distance from radio timing
observations.
