The shortest detected intra-day variability of active galactic nuclei in the TESS survey

Open Access

Table 1.

List of various timescales associated with AGN variability.

Category	Formula	Timescale for 10⁷ M_⊙
Light-crossing¹	$t_{lc} ≃ 0.011 (\frac{M_{BH}}{10^{7} M_{⊙}}) (\frac{R}{10 R_{S}})$ $Mathematical equation: $ t_{\mathrm{lc}}\simeq0.011\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right) $$ days	0.18 day
Free-fall²	$t_{ff} ≃ 0.046 (\frac{M_{BH}}{10^{7} M_{⊙}}) {(\frac{R}{10 R_{S}})}^{3 / 2}$ $Mathematical equation: $ t_{\mathrm{ff}}\simeq0.046\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right)^{3/2} $$ days	2.9 days
Orbital¹	$t_{orb} ≃ 0.33 (\frac{M_{BH}}{10^{7} M_{⊙}}) {(\frac{R}{10 R_{S}})}^{3 / 2}$ $Mathematical equation: $ t_{\mathrm{orb}}\simeq0.33\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right)^{3/2} $$ days	21 days
Hydrostatic equilibrium³	same order as the orbital timescale
Sound-crossing in vertical direction³	same order as the orbital timescale
Thermal¹	$t_{th} ≃ 0.53 {(\frac{γ}{0.1})}^{- 1} (\frac{M_{BH}}{10^{7} M_{⊙}}) {(\frac{R}{10 R_{S}})}^{3 / 2}$ $Mathematical equation: $ t_{\mathrm{th}}\simeq0.53\left(\frac{\gamma}{0.1}\right)^{-1}\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right)^{3/2} $$ days	34 days
Sound-crossing in the radial direction⁴	$t_{sound, R} ≃ 0.53 (\frac{R}{10 H}) (\frac{M_{BH}}{10^{7} M_{⊙}}) {(\frac{R}{10 R_{S}})}^{3 / 2}$ $Mathematical equation: $ t_{\mathrm{sound,R}}\simeq0.53\left(\frac{R}{10H}\right)\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right)^{3/2} $$ days	1.7 × 10² days
Viscous⁴	$t_{visc} ≃ 53 {(\frac{R}{10 H})}^{2} {(\frac{γ}{0.1})}^{- 1} (\frac{M_{BH}}{10^{7} M_{⊙}}) {(\frac{R}{10 R_{S}})}^{3 / 2}$ $Mathematical equation: $ t_{\mathrm{visc}}\simeq53\left(\frac{R}{10H}\right)^2\left(\frac{\gamma}{0.1}\right)^{-1}\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right)^{3/2} $$ days	8.2 × 10⁴ days
Cold disc removal³	$t_{evap} ≃ 3.7 \times 10^{2} (\frac{L}{0.1 L_{E}}) (\frac{M_{BH}}{10^{7} M_{⊙}}) {(\frac{R}{10 R_{S}})}^{2}$ $Mathematical equation: $ t_{\mathrm{evap}}\simeq3.7\times10^2\left(\frac{L}{0.1L_E}\right)\left(\frac{M_{\mathrm{BH}}}{10^7\,M_{\odot}}\right)\left(\frac{R}{10R_S}\right)^2 $$ days	2.8 × 10⁵ days

Notes. ¹ Edelson & Nandra (1999); ²Smith et al. (2018); ³ Czerny (2006); ⁴ Paolillo & Papadakis (2025). We use the thin disc model accretion disc size by Shakura & Sunyaev (1973) for R and estimate the ratio of thickness to radius of the accretion disc as $\frac{H}{R} ≃ 12.5 {(\frac{R}{R_{S}})}^{- 1} (\frac{L}{L_{E}}) (1 - \sqrt{\frac{3 R_{S}}{R}})$ $Mathematical equation: $ \frac{H}{R}\simeq12.5\left(\frac{R}{R_S}\right)^{-1}\left(\frac{L}{L_E}\right)\left(1-\sqrt{\frac{3R_S}{R}}\right) $$ and the viscosity parameter as γ = 0.1.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.