Erratum: Eccentric tidal disruption event discs around supermassive black holes: dynamics and thermal emission

In the original paper (Zanazzi & Ogilvie 2020), we used an incorrect expression for the area element of an eccentric disc. Here, we rectify this error and discuss how this correction affects the thermal emission from eccentric tidal disruption event (TDE) discs. Fig. 1 shows how the corrected area element affects the flux per unit area. Here, we use the same disc model as Zanazzi & Ogilvie (2020). Comparing with fig. 8 of Zanazzi & Ogilvie (2020), we see that the bolometric luminosity per unit area is significantly less near pericentre, and typically does not exceed the luminosity near apocentre (E ≈ |$\pi$|⁠). Same as fig. 8 of Zanazzi & Ogilvie (2020), except we use the Jacobian for the eccentric coordinates (a, E) [equation (6)], instead of the Jacobian for Delaunay variables (Λ, λ) [equation (2)]. The correct Jacobian gives significantly less bolometric flux per unit area near pericentre (E ≈ 0), especially for large eccentricities. Fig. 2 shows the thermal emission from a disc with a constant eccentricity. Comparing with fig. 9 of Zanazzi & Ogilvie (2020), using the correct Jacobian in equation (7) can lead up to an order of magnitude reduction of the disc’s X-ray and far-UV flux for appreciable eccentricities (e ≳ 0.7). Same as fig. 9 of Zanazzi & Ogilvie (2020), except we use the Jacobian for the eccentric coordinates (a, E) [equation (6)], instead of the Jacobian for Delaunay variables (Λ, λ) [equation (2)]. The correct Jacobian leads to less X-ray flux for highly eccentric discs. In this section, we recalculate the spectral energy distributions (SEDs) from section 3.3 of Zanazzi & Ogilvie (2020), using the correct area element [equation (5)]. We use the same underlying disc models, as well as the same non-linear eccentric disc eigenmode solutions, as Zanazzi & Ogilvie (2020). Fig. 3 displays the SEDs, while Fig. 4 shows the UV/optical and X-ray luminosities, from our eccentric disc solutions. The dependence of the thermal emission on all parameters is identical to that discussed in Zanazzi & Ogilvie (2020), but the X-ray and far-UV luminosity are significantly reduced. In particular, the X-ray and UV/optical luminosity predictions from our model are now in a better agreement with those observed from TDE candidates (Fig. 4). Same as fig. 10 of Zanazzi & Ogilvie (2020), except we use the Jacobian for the eccentric coordinates (a, E) [equation (6)], instead of the Jacobian for Delaunay variables (Λ, λ) [equation (2)]. The correct Jacobian leads to less X-ray and far-UV flux from highly eccentric regions of the disc. Same as fig. 11 of Zanazzi & Ogilvie (2020), except we use the Jacobian for the eccentric coordinates (a, E) [equation (6)], instead of the Jacobian for Delaunay variables (Λ, λ) [equation (2)]. The correct Jacobian leads to less X-ray and far-UV flux from highly eccentric regions of the disc. JZ thanks Elliot Lynch for pointing out that we were using the wrong Jacobian for the eccentric disc coordinates. JZ was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under the funding reference #CITA 490888-16, and a David Crighton Fellowship from DAMTP. GIO acknowledges the support of STFC through grant ST/P000673/1.

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