Direct imaging of sub-stellar companions

Introduction:

For a direct detection of a planet close to its host star, one has to overcome the large dynamical range problem: The planet is much fainter than its host star and very close to its bright host star. Normal Jupiter-like planets around low-mass stars (say, 0.1 solar masses) with one to few Gyr age are 6 orders of magnitude fainter than their host stars – unless the planet would have a large albedo and would be very close to the star and, hence, would reflect a significant amount of star light, but then it is too close to the star for direct detection (less than one milli arc sec). Another exception are young planets, which are self-luminous due to ongoing contraction and maybe accretion, so that they are only 2 to 4 orders of magnitude fainter (for 13 to 1 Jup mass planets, respectively) than their (young) host stars, again for stars with 0.1 solar masses. Hence, direct imaging of planets is less difficult around young stars with ages up to a few hundred Myr.

To overcome the problem of dynamical range, one has to use Adaptive Optics (AO) imaging in the near-infrared JHKL bands (1 to 3.5 micro meter), in order to directly detect a planet, i.e. To resolve it from the star. The infrared (IR) is best, because planets are cool and therefore brightest in the near- to mid-IR, while normal stars are brighter in the optical than in the IR. Before any planets or planet candidates became detectable by ground-based AO observations, brown dwarfs as companions to normal stars were detected, because brown dwarfs are more massive and, hence, brighter, Gl 229 B being the first one (Nakajima et al. 1995, Oppenheimer et al. 1995).

Confirmation of candidates:

Once a faint object is directly detected close to a star, one can consider it a planet candidate, which needs to be confirmed. Two common tests can be performed on such candidates:

(a) Common proper motion test: Both the star and the planet have to show the same (or at least very similar) proper motion. The host star in normally a relatively nearby star (up to a few hundred pc, otherwise the planet would be too faint, i.e. Not detectable), so that its proper motion is normally known. If the faint object would be a background star, it would be 1 to several kpc distant, so that its proper motion should be negligible compared to the star. Hence, if both the star and the faint object show the same proper motion, then the companion is not a non-moving background star, but a co-moving companion. Given the orbital motion of the star and its companion, depending on the inclination and eccentricity, one would of course expect that their proper motions are not identical, but the differences (typically few milli arc sec per year, mas/yr) are negligible compared to the typical proper motions. Instead of (or best in addition to) common proper motion, it is also sufficient to show that both objects (primary and companion candidate) show the same radial velocity, and that the secular evolution of the radial velocity is consistent with orbital motion and inconsistent with the background hypothesis.

(b) Spectrum: If the faint object next to the star would be a planet, its mass and temperature should be much smaller than for the star. This can be shown by a spectrum. Once a spectrum is available, one can determine the spectral type and temperature of the companion. If those values are consistent with planetary masses, then the faint object is most certainly a planet orbiting that star. However, it could still be a very low-mass cool background object (very low-mass L-type star or L- or T-type brown dwarf). In cases where the companion is too faint and/or too close to the star, a spectrum might not be possible, yet, so that one should try to detect the companion in different bands to measure color indices, which can also yield (less precise) temperature or spectral type; then, however, one has the problem to distinguish between a reddened background object and the truely red (i.e. Cool, e.g. planetary) companion.

The case of the ScoPMS 214 companion candidate (no. 1 or B) has shown that both tests are neccessary for a convincing case: The young K2 T Tauri star ScoPMS 214, member of the Scorpius T association, shares apparently common proper motion with a faint object nearby (3 arcsec separation) over five years; however, a spectrum of this companion candidate has shown that it is a foreground M dwarf (Metchev & Hillenbrand 2009). Hence, the spectroscopic test is indeed neccessary. Also, red colors alone (even if together with common proper motion) is not convincing, because a faint object near a star could just be reddened by extinction (background) instead of being intrinsically red, i.e. cool.

It is not sufficient to show that a star and a faint object nearby show the same proper motion (or proper motion consistent within 1 to 3 sigma) one also has to show that the data are inconsistent with the background hypothesis. Common proper motion can be shown with two imaging detections with an epoch difference large enough to significantly reject the background hypothesis, namely that the faint object would be an unrelated non-moving background object. The epoch difference needed depends on the astrometric precision of the detector(s) used and the proper motion of the host star. Spectra are usually taken with an infrared spectrograph with a large telescope and AO.

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Mass determination:

The masses of such companions can be determined in different ways, the first two of which are usually used:

(i) Given the direct detection of the companion, its brightness is measured. If the companionship to the star is shown, e.g. by common proper motion, then one can assume that the companion has the same distance and age as its host star. If either a spectrum or color index is also observed, one can estimate the temperature of the companion, so that the bolometric correction can be determined; if neither color nor spectrum is available, one can often roughly estimate the temperature from the brightness difference, assuming companionship. From brightness, bolometric correction, and distance, one can estimate the luminosity. Using theoretical evolutionary models, one can then estimate the mass from luminosity, temperature, and age. However, those models are uncertain due to unknown initial conditions and assumptions. In particular for the youngest systems, below 10 Myr, the values from the models are most uncertain.

(ii) If a good S spectrum with sufficient resolution is obtained, one can also measure the effective temperature and surface gravity of the companion. Then, from temperature and luminosity, one can estimate the companion radius. Then, from radius and gravity, one can estimate the companion mass. This technique is independant of the uncertain models, but needs both distance and gravity with good precision. Since gravities (and sometimes also distances) cannot be measured precisely, yet, the masses derived in this way typically have a very large possible range.

(iii) In the case of the directly imaged planet around the star Fomalhaut,an upper mass limit of 3 Jupiter masses, for the companion could be determined by the fact that a dust debris ring is located just a few AU outside the companion orbit (Kalas et al. 2008). In other planet candidates also orbiting host stars with debris disks, such an upper mass limit estimate should also be possible, e.g. in HR 8799 (Marois et al. Et al. 2008, Reidemeister et al. 2009), or beta Pic (see Freistetter et al. 2007).

(iv) If there are several planets or candidates imaged around the same star, then one can also try to determine masses or limits by stability arguments, see e.g. HR 8799 (Marois et al. 2008, Reidemeister et al. 2009).

(v) If there are other sub-stellar objects with very similar values regarding temperature, luminosity, and age, for which there is also a direct mass estimate, e.g. directly obtained in an eclipsing double-lined binary such as 2M0535 (Stassun et al. 2006) or in a visualy resolved system with full orbit determination such as HD 130948 BC (Dupuy et al. 2009), one can conclude that the sub-stellar companion in question also has a similar mass. If a sub-stellar companion has temperature and luminosity smaller than another sub-stellar object with a direct mass estimate, but the same age, then the sub-stellar companion in question should have a smaller mass. For HD 130948 BC, there is only an estimate for the total mass being 114 Jupiter masses (Dupuy et al. 2009), i.e. Somewhat too large for comparison to planet candidates. The object 2M0535 is an eclipsing double-lined spectroscopic binary comprising of two brown dwarfs, member of the Orion star forming region, hence not older than a few Myr, maybe below 1 Myr. For a double-lined spectroscopic binary, one can determine brigtness, temperatures, luminosities, and lower mass limits m sin i for both objects individually. The orbital inclination i can then be obtained from the eclipse light curve.
Hence, both masses are determined dynamically without model assumptions, e.g. 36±3 Jupiter masses for B (Stassun et al. 2006). Given that several of the sub-stellar companions discussed here have a very similar age, we can compare them with 2M0535 A and B. If all parameters are similar,
than the masses should also be similar. If a companion has lower values (at a similar age), i.e. being cooler and fainter, then it will be lower in mass. Such a comparison should also be done with great care, because also other properties like magnetic field strength, spots on the surface, and chemical composition (metallicity) affect the analysis.

(vi) If one could determine a full orbit of two objects around eachother, one can then estimate the masses of both the host star and the companion using Kepler's 3rd law as generalized by Newton. However, since all planets and planet candidates imaged directly so far have large separations from their host star (otherwise, they would not have been detected directly), the orbital periods are typically tens to hundreds of years, so that full orbits are not yet observed.

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