Figures and Tables From my Work

All available for download if proper credit is assigned.

Stellar-substellar Multiplicity Fraction

This figure from Dieterich et al. 2012 illustrates the concept of the "brown dwarf desert", which is the lack of brown dwarfs orbiting stellar primaries. The plots indicate the sensitivity to companions in HST/NICMOS images of 126 M dwarfs within 10 parsecs. The small dots represent the sensitivity achieved in PSF planting and recovery. The plus signs indicate the absolute magnitudes and spectral types for which 90% of putative companions are recovered. The numbers indicate known companions. With the exception of number 10, a T7 brown dwarf, all other companions are in the M dwarf range despite our ability to detect fainter companions. The blank space in the center of the plot is a good analogy for the desert.

This figure also from Dieterich et al. 2012 illustrates the mass ratio for binaries as the masses for the primary component approach the hydrogen burning minimal mass. The upper symbols (plus signs) represent the masses of the primary components. The lower symbols (x) represent the masses of the secondary components. Curiously, the mass ratios approach 1 as the primary masses approach the hydrogen burning minimal mass so that with one exception the secondaries do not cross the stellar-substellar boundary. These data prove that the brown dwarf desert is not a function of mass ratio but rather that Nature seems to avoid brown dwarf companions to stars no matter what the mass of the star. The reason for this is a mystery.

The table of multiplicity fractions summarizing the results of Dieterich et al. 2012. To summarize it in one sentence, "the multiplicity fraction for stellar-substellar systems is on the order of a few percent." As discussed in a meta-analysis in the paper this result largely holds true for more massive stellar primaries and other separation ranges.

The Stellar-substellar Boundary

The HR diagram from Dieterich et al. 2014. This is the first HR diagram to clearly distinguish a stellar and substellar population by identifying two radius regimes. The break happens at temperatures immediately cooler than the L2 dwarf 2MASS J0523-1403, which is the smallest known hydrogen burning star.
BELOWThe same HR diagram with radius plotted as an explicit variable. The gap and reversal in the radius trend then become more apparent after spectral type L2. The upper trend at spectral types earlier (hotter) than L2 is likely due to unresolved binaries or very young substellar objects.

The modified HR diagram of Dieterich et al. 2014 superimposed with evolutionary tracks from two model families. The discrepancy between the location of the smallest star at Log(luminosity) = -3.9 and the model predicted end of the stellar main sequence (last circle on dashed line) is clear. See the paper for other model families and plots in temperature space.

The table summarizing the predictions for the stellar/substellar boundary from several theoretical as well as observational studies. Epsilon Indi B and C are known to be substellar because they are T dwarfs. Their properties are not meant to be predictions of the stellar/substellar boundary but rather values with which to test the values predicted by the other studies. This latest version is from Dieterich et al. 2018.

Astrometric Dynamical Masses

The orbit of the combined center of light of Epsilon Indi B and C, deconvolved from proper motion and trigonometric parallax. Blue squares indicate astrometric measurements from the Cerro Tololo Inter-American Observatory Parallax Investigation (CTIOPI) and red triangles indicate data from the Carnegie Astrometric Planet Search (CAPS). The shaded contours indicate 1 sigma (green) and 3 sigma (purple) uncertainties in the orbital solution. The projection of the major axis is indicated by the dash-dot line. Black dots indicate time intervals of approximately 40 days. From Dieterich et al. 2018.

The physical orbits of the B and C components of Epsilon Indi about their mutual center of mass are traced with blue (C) and red (B) squares. The small black squares trace the photocenter's orbit, which was the orbit that was actually observed and is shown in the previous figure. Once the photocentric orbit is obtained a single high resolution observation showing the separation and flux ratios of the components is all that is needed to obtain the physical orbits. Multiple resolved observations can be used to diminish uncertainties. The separations obtained from six high resolution AO observations are shown with solid black lines. The purple dashed line indicates the projection of the major axis. Dieterich et al. 2018.

Same as previous figure, but with projection effects removed. From Dieterich et al. 2018.

Examples of the evolution of Markov chains from the MCMC algorithm used to simultaneously infer the seven orbital parameters, proper motion, and trigonometric parallax. To assure convergence only the last hundred thousand steps were used. Interestingly, some chains show an "inertia" effect in the sense that they slightly overshoot the equilibrium value before converging. The published MCMC code for astrometry and its documentation are available here. From Dieterich et al. 2018.