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The measurement of neutron star mass and radius is one of the most direct wayto distinguish between various dense matter equations of state. The mass andradius of accreting neutron stars hosted in low mass X-ray binaries can beconstrained by several methods, including photospheric radius expansion fromtype-I X-ray bursts and from quiescent spectra. In this paper, we apply for thefirst time these two methods simultaneously to constrain the mass and radius ofAql X-1, as a reliable distance estimation, high signal-to-noise ratioquiescent spectra from Chandra and XMM-Newton, and photospheric radiusexpansion bursts from RXTE are available. This is also used to verify theconsistency between the two methods, and to narrow down the uncertainties ofthe neutron star mass and radius. It is found that the distance to Aql X-1should be in the range of $4.0-5.75$ kpc, based on the overlapping confidenceregions between photospheric radius expansion burst and quiescent spectramethods. In addition, we show that the mass and radius determined for thecompact star in Aql X-1 are compatible with strange star equations of state andconventional neutron star models.

Simultaneous constraints on the mass and radius of Aql X-1 from quiescence and X-ray burst observations