HAT-P-26 - A transiting hot Jupiter with TTVs

HAT-P-26b: A Low-Density Neptune-Mass Planet Transiting a K Star (emphasis mine)
http://arxiv.org/abs/1010.1008

Quote :

We report the discovery of HAT-P-26b, a transiting extrasolar planet orbiting the moderately bright V=11.744 K1 dwarf star GSC 0320-01027, with a period P = 4.234516 +- 0.000015 d, transit epoch Tc = 2455304.65122 +- 0.00035 (BJD), and transit duration 0.1023 +- 0.0010 d. The host star has a mass of 0.82 +- 0.03 Msun, radius of 0.79 + 0.10 - 0.04 Rsun, effective temperature 5079 +- 88 K, and metallicity [Fe/H] = -0.04 +- 0.08. The planetary companion has a mass of 0.059 +- 0.007 MJ, and radius of 0.565 + 0.072 - 0.032 RJ yielding a mean density of 0.40 +- 0.10 g cm-3. HAT-P-26b is the fourth Neptune-mass transiting planet discovered to date. It has a mass that is comparable to those of Neptune and Uranus, and slightly smaller than those of the other transiting Super-Neptunes, but a radius that is ~65% larger than those of Neptune and Uranus, and also larger than those of the other transiting Super-Neptunes. HAT-P-26b is consistent with theoretical models of an irradiated Neptune-mass planet with a 10 Mearth heavy element core that comprises >~ 50% of its mass with the remainder contained in a significant hydrogen-helium envelope, though the exact composition is uncertain as there are significant differences between various theoretical models at the Neptune-mass regime. The equatorial declination of the star makes it easily accessible to both Northern and Southern ground-based facilities for follow-up observations.

Cool! HAT-net is striking for its efficiency - has two transit Neptune!

So the Neptune-mass planets also have substantial variations in radii. Nice, they were starting to get predictable

Now among all the transiting planets HAT-P-26b has 3-position at the lower mass and the 6-position of the smallest radius.

Since it's discovery, we've had additional transit ephemeres provided by Stevenson (2016) and Wakeford (2017). Now new transit timing observations provided by Essen, et al. show a clear sinusoidal pattern to the transit O-C times, though they don't try to put any serious constraints on the nature of the perturbing body.

Indications for transit timing variations in the exo-Neptune HAT-P-26b
https://arxiv.org/abs/1904.06360

Quote :

From its discovery, the low density transiting Neptune HAT-P-26b showed a 2.1-sigma detection drift in its spectroscopic data, while photometric data showed a weak curvature in the timing residuals that required further follow-up observations to be confirmed. To investigate this suspected variability, we observed 11 primary transits of HAT-P-26b between March, 2015 and July, 2018. For this, we used the 2.15 meter Jorge Sahade Telescope placed in San Juan, Argentina, and the 1.2 meter STELLA and the 2.5 meter Nordic Optical Telescope, both located in the Canary Islands, Spain. To add upon valuable information on the transmission spectrum of HAT-P-26b, we focused our observations in the R-band only. To contrast the observed timing variability with possible stellar activity, we carried out a photometric follow-up of the host star along three years. We carried out a global fit to the data and determined the individual mid-transit times focusing specifically on the light curves that showed complete transit coverage. Using bibliographic data corresponding to both ground and space-based facilities, plus our new characterized mid-transit times derived from parts-per-thousand precise photometry, we observed indications of transit timing variations in the system, with an amplitude of ~4 minutes and a periodicity of ~270 epochs. The photometric and spectroscopic follow-up observations of this system will be continued in order to rule out any aliasing effects caused by poor sampling and the long-term periodicity.

If we assume the simple case of an outer companion causing the star to wobble around a centre of mass (and consequently, the TTV's representing changing light travel delay times rather than intrinsic changes to the b planet's orbit), then the perturber is causing the star to wobble around a barycentre with a radius of at least ~2 light-minutes (~0.24 AU) over a 1,150 day period. That would seem to imply a rather hefty companion, if my math is right, about 0.1 solar masses. I suspect we would have seen that in the RV data though.