# V471 Tauri's circumbinary brown dwarf non-observation; Applegate, or over-restrictive assumptions?

tl;dr Has the brown dwarf observation been disproven?

I have just started reading about the interesting object V471 Tauri. The first two sentences of the introduction to The V471 Tauri System: A Multi-datatype Probe Vaccaro et al. (2015):

V471 Tau, a white dwarf-red dwarf eclipsing binary (EB) in the Hyades with orbit period $0^d.52118$, is primarily known for its unique historical role as a stimulus to common envelope evolution theory (Chau et al. 1974; Refsdal 1974; Sparks & Stecher 1974; Ostriker 1976; Paczynski 1976; Alexander et al. 1976; Taam et al. 1978). Other properties include a likely brown dwarf companion to the EB, measured white dwarf spin, mass loss and exchange in a detached binary, differential rotation measured via magnetic spots, spot distributions, accurate white dwarf parameters, and photometric-spectroscopic distance measures that help to pin down the binary’s location within the Hyades.

It's the "likely brown dwarf companion" I'd like to ask about. The paper with the catchy title "The First Science Results from SPHERE: Disproving the Predicted Brown Dwarf around V471 Tau" Hardy et al. (2015) SPHERE is a new, advanced adaptive optics system at the Very Large Telescope (VLT). The image below (figure 3) is part of the argument, and the suggestion is that if there is no brown dwarf seen in the band between the two white circles, then the predicted brown dwarf does not exist.

This would be interesting, because an alternative explanation for the slow, periodic drift in the eclipse timing would have to be found. One possibility is the Applegate Mechanism which I don't understand, but may ask a separate question after this.

Back to Vaccaro 2015, section 9, titled "On the Reality of the Third Star" is over six pages of discussion of the underlying assumptions, and if I understand it correctly provides several possible ways in which a suitable brown dwarf could exist but not show up in the SPHERE image. In essence disproving the existence disproof.

I would like to know: Is my understanding of the current situation correct? Have there been more recent developments?

above: Left panel of Fig. 3 of Hardy et al. 2015: "Figure 3. H-band image of V471 Tau obtained on the SPHERE IRDIS instrument at the VLT. Left panel: Resulting image after angular differential imaging (ADI). The area in-between the white circles denotes the 5 sigma predicted position of the brown dwarf..."

above: The monster currently known as SPHERE from here.

• What a great question. SPHERE looks amazing! – Fattie Sep 23 '16 at 15:57

For all of these direct imaging results, the critical parameter is the contrast as a function of separation. This lets you know how much fainter an object you can see around the much brighter primary object whose light has been suppressed by the coronograph (the black circle in the center of the star).

From the change in eclipse timings (Figure 1 in their paper) you can predict the expected mass and separation of the third object (proposed brown dwarf) using their equation 1 since you know the mass of the binary. From evolutionary models of brown dwarfs, you can make predictions of how bright the proposed brown dwarf should be for its predicted mass.

You can then look for an object at the right separation in the SPHERE images. This is shown in their Figure 3 (right hand figure of the 2) where they show how bright an object they could see as a function of separation from the primary star; everything above the solid curve is something they should see. The vertical dotted lines show the boundary on the separation of the brown dwarf, predicted from the eclipse timings. The diamond symbol is the predicted brightness of the brown dwarf from the evolutionary models given its mass.

Since this is well above the contrast curve (by a factor of about 15x) and nothing is seen in the images at that separation, this strongly suggests that the proposed brown dwarf does not exist. The only "get-outs" are if the SPHERE team have measured their contrast curve incorrectly (unlikely at the level needed) or our models of how bright brown dwarfs should be are also wrong by about a factor of 15x and the brown dwarf is much, much fainter than predicted.

The Applegate mechanism is a bit weird. The idea is that as the star goes through magnetic activity cycles (as the Sun and a lot of other stars do) and the magnetic field strength grows and shrinks, this causes the shape of the star to change, bulging more or less at the star's equator as the cycle progresses. This changes the amount of angular momentum in the star, which has to couple into the binary orbit as the angular momentum has to be conserved, causing the binary orbit to shrink or expand. This would then explain the change in timings of the eclipses without the need for the third body brown dwarf tugging on binary. Unfortunately the Applegate mechanism, although it may work in V471 Tau, can't explain the variations in a bunch of other binary systems (magnetic field strength not strong enough) so it can't be the only solution for eclipse time variations.

The latest paper I could find that references the Vaccaero et al. 2015 paper, is Vanderbosch et al. 2017. They argue that because of the timing of the eclipses change but the spin period of the white dwarf secondary doesn't change, a third body such as a brown dwarf can't explain the changes as it should change the timing of both "clocks".

• Thank you for posting this nicely-written answer! It's great when someone revives an older question and posts a well-sourced and thoughtful answer. I'll give Vanderbosch et al. 2017 a read today. – uhoh Jul 22 '18 at 1:29
• Why must the brown dwarf be at that separation and in the plane of the sky? – Rob Jeffries Jul 22 '18 at 17:56
• This is a good point. The SPHERE authors have performed Markov Chain Monte Carlo simulations to model the eclipse time variations. i3, the inclination of the 3rd body (brown dwarf) is in the formula but they don't show the range or correlation parameters for this parameter in the fits. I assume the uncertainty on i3 is included in their error bars for the separation. Presumably the allowed range of 3rd body semi-major axes from the eclipse timings, coupled with the close distance, produces a narrow range of possible separations. – astrosnapper Jul 22 '18 at 19:13
• Thanks again for the excellent answer. The two-clock method (i.stack.imgur.com/LXSqR.png) is a nice complement to the non-observation with SPHERE. I don't completely understand Applegate yet, (a body changing it's moment of inertia can conserve angular momentum by just changing its own rotation rate rather than exchanging with orbital angular momentum, no?) but I'll read up on that a bit and perhaps ask a new question about it. – uhoh Jul 28 '18 at 9:25