Distances luminosities and_temperatures_of_the_coldest_known_substelar_objects

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  • 1. Reports  One major goal in astrophysics is to extend previous successes in the characterization and modeling of stellar atmospheres to the much cooler atmospheres of extrasolar planets. A key pathway is the identification of free-floating objects that not only share common temperatures with exoplanets but that also share common masses and thus surface gravities. In recent years, searches for ever colder free-floating brown dwarfs- objects with masses below the hydrogen-fusing mass limit-have steadily pushed the census of the solar neighborhood to ever lower masses and finally perhaps into the planetary-mass regime ( 13 Jupiter masses).< The detection of large samples of brown dwarfs at the beginning of the last decade ushered in two, now widely accepted, spectral types de- noted by the letters “L” and “T” that extend the canonical OBAFGKM scheme for classifying stars that had stood untouched for nearly a centu- ry. Over the last two years, candidates for a “Y” spectral class have been uncovered in binary surveys (1, 2) and in all-sky imaging data from WISE, the Wide-field Infrared Survey Explorer (3). The primary criterion adopted to trigger this class has been the appearance of ammonia (NH3) absorption in near-infrared (1-2.5 μm) spectra. Y dwarfs probe colder atmospheric physics than before, with puta- tive effective temperatures as low as Teff 300 K and masses of ≈ 5-20 Jupiter masses (3). If found orbiting a star, a Y dwarf would likely be considered a gas-giant planet. However, these estimated properties of Y dwarfs are speculative given the uncertainty in their temperatures, ages, and luminosities. Temperatures have only been estimated from model atmospheres that use incomplete molecular line lists and simple prescrip- tions for complex processes like nonequilibrium chemistry and conden- sate formation. An independent approach for determining temperatures is to com- bine bolometric luminosities (Lbol) with evolutionary model-predicted radii (R ) and apply the Stefan-Boltzmann Law, Teff ≡ (4πσR 2 /Lbol)−1/4 . Recent observations of transiting substellar objects generally support evolutionary model radius predictions over a wide range of masses (4– 6). Although many may not be ideal test cases, since they may have formed via core accretion or have been intensely irradiated, variations in radii are expected to be relatively small and not strongly influence our resulting temperatures given the weak dependence on radius (Teff R −1/2 ). Therefore, the key measurements need- ed to determine temperatures via lumi- nosity are accurate distances to Y dwarfs, along with a method for com- puting Lbol from multi-wavelength pho- tometry. Trigonometric parallaxes provide the only direct means of measuring distances to stars. A star’s distance is inversely proportional to the amplitude of its apparent periodic motion on the sky relative to more distant background stars, which is due to the Earth’s orbital motion around the Sun. The amplitude of this effect is small, 0.1 arcseconds for a star at 10 parsec, and thus measur- ing parallaxes requires long-term, pre- cise position measurements. We have been using the Infrared Array Camera (IRAC) on board the Spitzer Space Telescope to obtain such astrometry of late-T and Y dwarfs from 2011-2012. Spitzer currently trails the Earth by ≈ 2 months in its solar orbit, and keeping its solar shield directed at the Sun forces the telescope to observe stars near par- allax maximum. By maintaining a cold temperature Spitzer can obtain sensitive images in the thermal mid-infrared, where Y dwarfs emit most of their flux, giving it an advantage over ground-based near-infrared observations of Y dwarfs. We also use an improved correction for the nonlinear optical distortion of Spitzer/IRAC that enables 10× smaller residual errors than the correction used by the standard data pipeline, allowing us to unlock the precision astrometric capabilities of Spitzer. Distances, Luminosities, and Temperatures of the Coldest Known Substellar Objects Trent J. Dupuy1 and Adam L. Kraus1,2 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA. 2 Astronomy epartment, University of Texas at Austin, 1 University Station C1400, Austin, TX 78712, USA.D Corresponding author. E-mail: tdupuy@cfa.harvard.edu The coolest known brown dwarfs are our best analogs to extrasolar gas-giant planets. The prolific detections of such cold substellar objects in the past two years has spurred intensive followup, but the lack of accurate distances is a key gap in our understanding. We present a large sample of precise distances based on homogeneous mid-infrared astrometry that robustly establish absolute fluxes, luminosities, and temperatures. The coolest brown dwarfs have temperatures of 400 to 450 kelvin and masses ≈5 to 20× that of Jupiter, showing they bridge the gap between hotter brown dwarfs and gas-giant planets. At these extremes, spectral energy distributions no longer follow a simple correspondence with temperature, suggesting an increasing role of other physical parameters such as surface gravity, vertical mixing, clouds, and metallicity. By combining our parallaxes (Table S1, Fig. S1) with photometry from the literature (7–9), we have determined absolute magnitudes in the near-infrared YJHK bands (≈ 1.0-2.4 μm) and Spitzer’s mid-infrared bands at 3.6 μm and 4.5 μm (Table S2, Fig. 1, Fig. 2). For each spectral type bin, we computed the weighted mean absolute magnitude as well as upper/lower limits on the amount of intrinsic scatter in the magnitudes (Table S3). Objects classified as normal Y0 dwarfs are ≈2 magnitudes (≈6×) fainter in the near-infrared compared to the latest type T dwarfs, yet they generally share very similar colors. The most notable exception is that the Y−J colors become much bluer for Y dwarfs (9), which we find is due to flux at ≈1.25 μm dropping by 5× while flux at ≈ 1.05 μm only drops by 2.5×. This behavior is consistent with prior speculation that Y dwarfs may be so cool that the alkali atoms that dominate absorption at blue wavelengths for warmer brown dwarfs finally become locked into molecules like Na2S and KCl, thereby reducing the opacity at 1.05 μm relative to 1.25 μm (10). The appearance of such molecules could result in the return of substantial condensate clouds (11) and corresponding variability/weather. In contrast to their near-infrared behavior, Y dwarfs show remarka- ble diversity in their mid-infrared colors. Even though they are only ≈2× fainter than the latest T dwarfs at these wavelengths, they range from the same color as late-T dwarfs to much redder (≈0.8 magnitudes). One of the reddest objects is WISEP J1405+5534, which has been typed as “Y0 peculiar?” because its H-band spectral peak is shifted 60 Å redder than the Y0 standard WISEP J1738+2732 (3). We find that WISEP J1405+5534 in fact has a very similar temperature to other Y0 dwarfs (Table S5) indicating that its unusual spectrum is due to another physical / http://www.sciencemag.org/content/early/recent / 5 September 2013 / Page 1/ 10.1126/science.1241917 onSeptember9,2013www.sciencemag.orgDownloadedfrom
  • 2. property. Both the mid-infrared color and peculiar spectrum may be explained by a reduced level of nonequilibrium chemistry in the photo- sphere, perhaps due to reduced vertical mixing. This would produce enhanced NH3 absorption at H-band as compared to other Y0 dwarfs and enhanced CH4 absorption relative to CO driving WISEP J1405+5534 to redder [3.6]−[4.5] colors. The coldest brown dwarfs also demonstrate unusual behavior in their absolute fluxes as a function of spectral type. Despite the plummeting near-infrared flux-normal Y0 dwarfs are ≈6× fainter than the latest T dwarfs-Y0 dwarfs have indistinguishable fluxes compared to each other to within 15%-25%. This is very unusual compared to warmer brown dwarfs, which do not show such step-function behavior at any spectral type transition and also show much larger intrinsic scatter (≈30%-50%) in absolute fluxes for a given spectral type (12). This homogeneity among the Y0 dwarfs is further unexpected because it reverses the trend observed for the late-T dwarfs that the scatter increases substantially with later type, cooler objects (Fig. 3). For example, here we double the sample of T9 dwarfs with accurate distances and find that their near- infrared fluxes typically have a scatter of 130%-210%. Another unexpected result is that T9.5 dwarfs appear to be brighter at all bandpasses than the mean for T9 dwarfs and the T9 standard UGPS J0722−0540. Given the smaller sample of T9.5 dwarfs (three objects) and their more uncertain distances, this brightening is currently a 2σ result, i.e., the weighted means in Table S3 are consistent with being equal at a p-value of 0.05. Such a brightening is reminiscent of the change in near-infrared fluxes from late-L to early-T dwarfs (13, 14), however we note that the brightening at the L/T transition only occurs at blue near-infrared wavelengths whereas we see brightening at all bands for the T9.5 dwarfs. To derive bolometric luminosities from the absolute fluxes, we com- puted “super-magnitudes” by summing the fluxes in near- and mid- infrared bandpasses. This is an approximation to the standard method of integrating the observed spectral energy distribution as a function of wavelength, which is not possible for Y dwarfs given the current lack of sensitive mid-infrared spectrographs. We derive a multiplicative correc- tion to account for the remaining flux not captured in these bands from a large grid of model atmospheres (11, 15). The weak dependence on these models is highlighted by the 8% fractional uncertainty in this correction factor (Fig. S4). We used the Cond evolutionary models (16) to estimate radii and thereby temperatures, masses, and surface gravities from the bolometric luminosities of our sample (Fig. 4, Table S5). We assumed fiducial ages of 1 Gyr and 5 Gyr as expected for the field population (17, 18). The tangential velocities for our sample are consistent with having such typi- cal ages. We find that the fractional change in temperature over this narrow range of spectral types is remarkably large: the mean temperature of T8 dwarfs is 685-745 K (for 1-5 Gyr), and this drops to 410-440 K for Y0 dwarfs (Table S6). Thus, these two subtypes alone span the same fractional range in temperature as the entire sequence of FGK stars (7300-4400 K) that are 10× hotter. Although much cooler than their late-T counterparts, Y0 dwarfs turn out to be significantly warmer than previously suggested from model atmosphere fitting (Fig. S5). The most common best-fit models of Y0 dwarfs in previous work have Teff = 350 K, with plausible model fits of 400 K in some cases (3). Thus, model fits are typically 60-90 K (≈15%- 25%) cooler than we find from our distances combined with evolution- ary model radii. If the fault lies with our assumed radii, they would need to be 30%-50% larger than expected because Teff R −1/2 . This would require very young ages ( 100 Myr) or very large systematic errors in the evolutionary models that are not likely given the aforementioned empirical validation from transiting brown dwarfs. Rather, we suggest that parameters derived from fitting model atmospheres to near-infrared spectra, where < 5% of the flux emerges, are less likely to be accurate because current atmospheres imperfectly reproduce observed spectra. < Using our luminosity measurements, we find that the coldest brown dwarfs would be 6-10 Jupiter masses given an age of 1 Gyr. An older age of 5 Gyr implies 16-25 Jupiter masses. These masses therefore straddle the current demarcation of “planetary mass” set by the deuteri- um-fusing mass limit of ≈ 13 Jupiter masses (19–21). Thus, it is possible that the atmospheres of our objects harbor deuterated molecules such as HDO or CH3D that have not yet been detected because of the observa- tional challenges (22). Given the interest in both identifying the coldest atmospheric benchmarks and searching for the bottom of the initial mass function we briefly consider the most extreme objects in our sample in terms of tem- perature and mass. WISEP J1828+2650 has been dubbed the archetypal Y dwarf with a model-atmosphere temperature of < 300 K, i.e., room temperature, based on extremely red colors implying that the Wien tail of its underlying blackbody distribution has moved into the near-infrared (3). Our luminosity for this object is inconsistent with such a low tem- perature, and we find it must be at least 420 K at 2σ; our calculations give K at an age of 1 Gyr. (If WISEP J1828+2650 is a binary as proposed by (9) the 2σ limit at 1 Gyr only drops to 360 K and 340 K for the hypothetical two components.) Its atypical properties compared to other Y dwarfs may simply be due to a slightly lower surface gravity, i.e., slightly younger age, which qualitatively agrees with model predic- tions that the collapse in near-infrared flux happens at warmer tempera- tures for lower surface gravity (23). Ross 458C is a contender for the lowest mass object, at 7 Jupiter masses, if its age is near the 150 Myr lower limit of its proposed age range (24). However, WD 0806−661B is the most secure case for both lowest temperature (330-375 K) and lowest mass (6-10 Jupiter masses) object known, given that it has a precise age of 2.0 ± 0.5 Gyr (25). 60 50520+ − Overall, our results strengthen the connection between the coolest brown dwarfs and gas-giant exoplanets. We validate that they probe an extreme physical regime that bridges the gap between previously known, hotter brown dwarfs and Jupiter-like planets. We find that objects of very similar temperatures can have widely varying spectral energy dis- tributions and absorption features, e.g., a range of 0.8 magnitudes in mid-IR colors for the same Teff. Along with the fact that the ≥Y2 dwarf is warmer than the Y0 dwarfs, this implies that temperature is not the prin- cipal determinant in shaping spectra but rather seems to be on compara- ble footing with other physical properties such as surface gravity, vertical mixing, clouds, and perhaps metallicity. Consequently, the cur- rent spectral classification scheme used to identify Y dwarfs may not strongly correlate with temperature as it generally does for L and T dwarfs. This could explain the unusually homogeneous fluxes for Y0 dwarfs, unusually heterogeneous fluxes for T9 dwarfs, and plateau or brightening of flux from T9 to T9.5. 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  • 6. Fig. 1. Color-magnitude diagrams for all objects with spectral types T8 and later that have direct distance measurements. Data points are color coded according to spectral type, with open/white points indicating that no spectra are available. Small gray points are earlier type field brown dwarfs. Near-infrared photometry is on the Mauna Kea Observatory (MKO) system. Fig. 2. Absolute magnitude as a function of spectral type for near-infrared and mid-infrared bandpasses. Objects typed as peculiar are shown as open white symbols. Objects with very uncertain distances are plotted with smaller gray symbols. Error bars for spectral types are not plotted, and small x-axis offsets have been added to the spectral types for clarity. / http://www.sciencemag.org/content/early/recent / 5 September 2013 / Page 6/ 10.1126/science.1241917 onSeptember9,2013www.sciencemag.orgDownloadedfrom
  • 7. Fig. 4. Bolometric luminosities (Lbol) and effective temperatures for objects of spectral type T8 and later; spectrally peculiar objects are denoted by white symbols. Objects with Lbol uncertainties larger than 0.2 dex are shown as smaller, gray symbols. These are either objects with very uncertain distances or the components of tight binaries where the lack of resolved mid-infrared photometry results in a very uncertain bolometric flux. Error bars for spectral types are not plotted, and small x- axis offsets have been added to the spectral types for clarity. Effective temperatures are derived from our Lbol measurements and Cond evolutionary model radii. Upward and downward pointing triangles correspond to the median Lbol and lower and upper age limits used (see Table S5). Error bars show the range of temperatures corresponding to the ±1σ range of Lbol over the same age range. Fig. 3. Intrinsic photometric scatter among objects at each spectral type; unfilled symbols are upper limits where no scatter is detected. Y0 dwarfs show remarkably low intrinsic scatter in the near-infrared, reversing the trend observed at the end of the T dwarf sequence that later type T dwarfs show increasing dispersion in their near-infrared absolute magnitudes. The much smaller sample of T9.5 dwarfs are also suggestive of this reversal at J and H bands. There is no evidence for such a reversal in the mid-infrared where both late-T and Y dwarfs show much less intrinsic scatter and distance uncertainties for Y dwarfs do not permit strong enough upper limits. / http://www.sciencemag.org/content/early/recent / 5 September 2013 / Page 7/ 10.1126/science.1241917 onSeptember9,2013www.sciencemag.orgDownloadedfrom