SN2010da/NGC 300 ULX-1 was first detected as a supernova impostor in May 2010 and was recently discovered to be a pulsating ultraluminous X-ray source .
In this letter , we present VLT/X-shooter spectra of this source obtained in October 2018 , covering the wavelength range 350-2300 nm .
The J - and H -bands clearly show the presence of a red supergiant donor star that is best matched by a MARCS stellar atmosphere with T _ { eff } = 3650 - 3900 K and \log ( L _ { bol } / L _ { \odot } ) = 4.25 \pm 0.10 , which yields a stellar radius R = 310 \pm 70 R _ { \odot } .
To fit the full spectrum , two additional components are required : a blue excess that can be fitted either by a hot blackbody ( T \gtrsim 20 , 000 K ) or a power law ( \edit 1spectral index \alpha \approx 4 ) and is likely due to X-ray emission reprocessed in the outer accretion disk or the donor star ; and a red excess that is well fitted by a blackbody with a temperature of \sim 1100 K , and is likely due to warm dust in the vicinity of SN2010da .
The presence of a red supergiant in this system implies an orbital period of at least 0.8-2.1 years , assuming Roche lobe overflow .
Given the large donor-to-compact object mass ratio , orbital modulations of the radial velocity of the red supergiant are likely undetectable .
However , the radial velocity amplitude of the neutron star is large enough ( up to 40-60 km s ^ { -1 } ) to potentially be measured in the future , unless the system is viewed at a very unfavorable inclination .