Deciphering the JWST spectrum of a 'little red dot' at $z \sim 4.53$: An obscured AGN and its star-forming host

JWST has revealed a class of numerous, extremely compact sources, with rest-frame red optical/near-infrared (NIR) and blue ultraviolet (UV) colours, nicknamed "little red dots". We present one of the highest signal-to-noise ratio JWST NIRSpec/PRISM spectra of a little red dot, J0647_1045 at $z = 4.5321 \pm 0.0001$, and examine its NIRCam morphology, to differentiate the origin of the UV and optical/NIR emission, and elucidate the nature of the little red dot phenomenon. J0647_1045 is unresolved ($r_e < 0.17$ kpc) in the three NIRCam long-wavelength filters, but significantly extended ($r_e = 0.45 \pm 0.06$ kpc) in the three short-wavelength filters, indicating a red compact source in a blue star-forming galaxy. The spectral continuum shows a clear change in slope, from blue in the optical/UV, to red in the restframe optical/NIR, consistent with two distinct components, fit by power-laws with different attenuation: $A_V = 0.54 \pm 0.01$ (UV) and $A_V = 5.7 \pm 0.2$ (optical/NIR). Fitting the H$\alpha$ line requires both broad (full width at half-maximum $\sim 4300 \pm 300 km s^{-1}$) and narrow components, but none of the other emission lines, including H$\beta$, show evidence of broadness. We calculate $A_V = 1.1 \pm 0.2$ from the Balmer decrement using narrow H$\alpha$ and H$\beta$, and $A_V > 4.1 \pm 0.2$ from broad H$\alpha$ and upper limit on broad H$\beta$, consistent with the blue and red continuum attenuation respectively. Based on single-epoch H$\alpha$ linewidth, the mass of the central black hole is $8 \pm 1 \times 10^8 M_\odot$. Our findings are consistent with a multi-component model, where the optical/NIR and broad lines arise from a highly obscured, spatially unresolved region, likely a relatively massive active galactic nucleus, while the less obscured UV continuum and narrow lines arise, at least partly, from a small but spatially resolved star-forming host galaxy.