What a surprise: SPACE.com: "
Astronomers Doubt Giant Planet 'Tyche' Exists in Our Solar System"
The two have had the Tyche idea since 1999.
The idea that stars could have gas giants orbiting very close in, is at least forty years old. The skepticism of that idea was natural, a gas giant orbiting inside of the orbit of Mercury, should lose its atmosphere. Let alone, how did it form in the first place in that orbit. Now we know of course that there are lots of solar systems where this happens, and the debate is on about the hows and whys of it.
A ten year old theory is not a great problem but the journalist in that last article has stated it and given the reader a message. Note that he hasn't been explicit and came right out and said these two astronomers are nut cases. It rather looks as though he's gone and got a couple of juicy quotes and then went on to write a smarty pants article.
The smart thing to do, is to sit on the fence. To be totally disinterested; a word that is often misunderstood to mean indifferent.
Is this planet possible? The answer is yes. Is it probable? The answer has to be that we simply don't have enough information on "dark companion" stars to give odds. Again, it makes sense to sit on the fence.
Let's look at that scaled down version of the solar System. The Sun is a billiard ball, the Earth is at about 7.6 metres, Jupiter at forty metres and this planet x at about 1.5 kilometres. The nearest star is going to be 2000 kilometres away, and just for a little bit more idea of the scale of this model, the Earth will have a diameter of 0.5 mm.
This planet x is not going to have a wildly eccentric orbit. It's not going to be dangerous. Though it may have been during the formation of the Solar System. At about 200 a.u. it's just on the "edge" of the Oort cloud but the Oort cloud is thought to have originated closer in and has been flung out. Actually, it would tend to circularize the orbits of Oort cloud icy lumps, so it may be a good thing; even if it did throw the odd one in toward the sun. Even that would create a Sedna type orbit, which could of course be altered by one of the inner gas giants. Pretty rare in any case.
Okay, it's going to be about twentieth mag and the very devil to find. If these two guys want to look for it they'll need telescope time, on at least a metre telescope. Best of luck to them I say.
One last point, this planet x doesn't screw up the theories of planetary formation. Think of it as not so much a planet but a failed star. The cloud from which Sol formed may have broken up into two gas clouds. This is very common. It's one of the ways that the collapsing proto sun loses angular momentum. It would be an interesting question as to whether our planetary system is pulled out as far as it is, by this secondary cloud of dust and gas, being of too low a mass.