Effects of hair on the image of a rotating black hole illuminated by a thin accretion disk

Abstract In this paper, we investigate the shadow and optical appearance of the hairy Kerr black hole illuminated by a thin accretion disk. The deformation parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and hair parameter $$l_o$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>l</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:math> are found to influence the motions of accretion as well as the redshift effect of the photon, such that they significantly affect the shadow and image of the hairy Kerr black hole. In particular, $$l_o$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>l</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:math> suppresses the shadow size of the black hole while $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> enhances it. We then analyze the widths of the direct, lensed ring and photon ring emission regions for the thin accretion disk. It is found that the widths of the direct emission and lensed ring emission change slightly with the parameters, whereas the width of the photon ring emission increases dramatically as $$l_o$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>l</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:math> decreases. This feature provides more favorable conditions for observing the photon rings of black hole. Finally, we study the redshift of the direct and lensed images, showing that the maximal blueshift point is shifted by the change of the parameters. We argue that our study provides a preliminary theoretical prediction that the image of the hairy Kerr black hole, especially the photon ring structure, may be used to constrain the hair parameters with future high-precision astronomical observation.