Simultaneous visible and near-infrared time resolved observations of the outer Solar System object (29981) 1999 TD10

The outer Solar System object (29981) 1999 TD₁₀ was observed simultaneously in the R, and J and H bands in September 2001, and in B, V, R, and I in October 2002. We derive B−V=0.80±0.05 mag, V−R=0.48±0.05 mag, R−I=0.44±0.05 mag, R−J=1.24±0.05 mag, and J−H=0.61±0.07 mag. Combining our data with the data from Rousselot et al. (2003, Astron. Astrophys. 407, 1139) we derive a synodic period of 15.382±0.001 hr in agreement with the period from Rousselot et al. Our observations at the same time, with better S/N and seeing, show no evidence of a coma, contrary to the claim by Choi et al. (2003, Icarus 165, 101).     

The rotational and physical properties of the Centaur (32532) 2001 PT13

We present observations of the Centaur (32532) 2001 PT₁₃ taken between September 2000 and December 2000. A multi-wavelength lightcurve was assembled from V-, R- and J-band photometry measurements. Analysis of the lightcurve indicates that there are two peaks of slightly different brightness, a rotation period of 0.34741±0.00005 day, and a maximum photometric range of 0.18 mag. We obtained VRJHK colors (V-R=0.50±0.01, V-J=1.69±0.02, V-H=2.19±0.04, and V-K=2.30±0.04) that are consistent with the grey KBO/Centaur population. The V-R color shows no variation as a function of rotational phase; however, we cannot exclude the possibility that rotational variations are present in the R-J color. Assuming a 4% albedo, we estimate that 2001 PT₁₃ has an effective diameter of 90 km and a minimum axial ratio a/b of 1.18. We find no evidence of a coma and place an upper limit of 15 g s⁻¹ on the dust production rate.     

Water production and release in Comet 153P/Ikeya-Zhang (C/2002 C1): accurate rotational temperature retrievals from hot-band lines near 2.9-μm

Multiple non-resonance fluorescence lines of water (H₂O) were detected in Comet 153/P Ikeya-Zhang (2002 C1) between UT 2002 March 21.9 (R_h=0.51 AU) and April 13.9 (R_h=0.78 AU), using the Cryogenic Echelle Spectrometer (CSHELL) at the NASA Infrared Telescope Facility. Analysis of 2.9-μm water lines enabled accurate determination of rotational temperatures on three dates. The derived H₂O rotational temperatures were 138⁺⁶₋₅, 141⁺¹⁰₋₉, and 94±3 K on UT 2002 March 22.0, March 23.0, and April 13.8, respectively. Water production rates were retrieved from spectral lines measured in nineteen separate grating settings over seven observing periods. The derived heliocentric dependence of the water production rate was Q=(9.2±1.1)×10²⁸[R_h^{(−3.21±0.26)}] molecules s⁻¹. The spatial distribution of H₂O in the coma was consistent with its release directly from the nucleus (as a native source) on all dates.     

Photometric study of Centaur (60558) 2000 EC98 and trans-neptunian object (55637) 2002 UX25 at different phase angles

We present photometric observations of Centaur (60558) 2000 EC₉₈ and trans-neptunian object (55637) 2002 UX₂₅ at different phase angles and with different filters (mainly R but also V and B for some data). Results for 2000 EC₉₈ are: (i) a rotation period of 26.802±0.042 h if a double-peaked lightcurve is assumed, (ii) a lightcurve amplitude of 0.24±0.06 for the R band, (iii) a phase curve with H=9.03±0.01 and G=−0.39±0.08 (R filter) and H=9.55±0.04 and G=−0.50±0.35 (V filter) or a slope of (R filter) and 0.22±0.06 (V filter), (iv) the color indices B-V=0.76±0.15 and V-R=0.51±0.09 (for α=0.1-0.5°) and 0.55±0.08 (for α=1.4-1.5°). The rotation period is amongst the longest ever measured for Centaurs and TNOs. We also show that our photometry was not contaminated by any cometary activity down to magnitude ?27/arcsec². For 2002 UX₂₅ the results are: (i) a rotation period of 14.382±0.001 h or 16.782±0.003 h (if a double-peaked lightcurve is assumed) (ii) a lightcurve amplitude of 0.21±0.06 for the R band (and the 16.782 h period), (iii) a phase curve with H=3.32±0.01 and G=+0.16±0.18 or a slope of (R filter), (iv) the color indices B-V=1.12±0.26 and V-R=0.61±0.12. The phase curve reveals also a possible very narrow and bright opposition surge. Because such a narrow surge appears only for one point it needs to be confirmed.     

Radar and infrared observations of binary near-Earth Asteroid 2002 CE26

We observed near-Earth Asteroid (NEA) 2002 CE26 in August and September 2004 using the Arecibo S-band (2380-MHz, 12.6-cm) radar and NASA's Infrared Telescope Facility (IRTF). Shape models obtained based on inversion of our delay-Doppler images show the asteroid to be 3.5±0.4 km in diameter and spheroidal; our corresponding nominal estimates of its visual and radar albedos are 0.07 and 0.24, respectively. Our IRTF spectrum shows the asteroid to be C-class with no evidence of hydration. Thermal models from the IRTF data provide a size and visual albedo consistent with the radar-derived estimate. We estimate the spin-pole to be within a few tens of degrees of λ=317°, β=−20°. Our radar observations reveal a secondary approximately 0.3 km in diameter, giving this binary one of the largest size differentials of any known NEA. The secondary is in a near-circular orbit with period 15.6±0.1 h and a semi-major axis of 4.7±0.2 km. Estimates of the binary orbital pole and secondary rotation rate are consistent with the secondary being in a spin-locked equatorial orbit. The orbit corresponds to a primary mass of M=1.95±0.25×¹⁰¹³ kg, leading to a primary bulk density of , one of the lowest values yet measured for a main-belt or near-Earth asteroid.     

Physical characterization of the potentially hazardous high-albedo Asteroid (33342) 1998 WT24 from thermal-infrared observations

The potentially hazardous Asteroid (33342) 1998 WT₂₄ approached the Earth within 0.0125 AU on 2001 December 16 and was the target of a number of optical, infrared, and radar observing campaigns. Interest in 1998 WT₂₄ stems from its having an orbit with an unusually low perihelion distance, which causes it to cross the orbits of the Earth, Venus, and Mercury, and its possibly being a member of the E spectral class, which is rare amongst near-Earth asteroids (NEAs). We present the results of extensive thermal-infrared observations of 1998 WT₂₄ obtained in December 2001 with the 3-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea, Hawaii and the ESO 3.6-m telescope in Chile. A number of thermal models have been applied to the data, including thermophysical models that give best-fit values of 0.35±0.04 km for the effective diameter, 0.56±0.2 for the geometric albedo, pv, and 100-300 J m⁻² s^−0.5 K⁻¹ for the thermal inertia. Our values for the diameter and albedo are consistent with results derived from radar and polarimetric observations. The albedo is one of the highest values obtained for any asteroid and, since no other taxonomic type is associated with albedos above 0.5, supports the suggested rare E-type classification for 1998 WT₂₄. The thermal inertia is an order of magnitude higher than values derived for large main-belt asteroids but consistent with the relatively high values found for other near-Earth asteroids. A crude pole solution inferred from a combination of our observations and published radar results is β=−52°, λ=355° (J2000), but we caution that this is uncertain by several tens of degrees.     

Impact of aerosols present in Titan's atmosphere on the CASSINI radar experiment

Simulations of Titan's atmospheric transmission and surface reflectivity have been developed in order to estimate how Titan's atmosphere and surface properties could affect performances of the Cassini radar experiment. In this paper we present a selection of models for Titan's haze, vertical rain distribution, and surface composition implemented in our simulations. We collected dielectric constant values for the Cassini radar wavelength (∼2.2 cm) for materials of interest for Titan: liquid methane, liquid mixture of methane-ethane, water ice, and light hydrocarbon ices. Due to the lack of permittivity values for Titan's haze particles in the microwave range, we performed dielectric constant (ε_r) measurements around 2.2 cm on tholins synthesized in laboratory. We obtained a real part of ε_r in the range of 2-2.5 and a loss tangent between 10⁻³ and 5×10⁻². By combining aerosol distribution models (with hypothetical condensation at low altitudes) to surface models, we find the following results: (1) Aerosol-only atmospheres should cause no loss and are essentially transparent for Cassini radar, as expected by former analysis. (2) However, if clouds are present, some atmospheric models generate significant attenuation that can reach −50 dB, well below the sensitivity threshold of the receiver. In such cases, a 13.78 GHz radar would not be able to measure echoes coming from the surface. We thus warn about possible risks of misinterpretation if a “wet atmosphere” is not taken into account. (3) Rough surface scattering leads to a typical response of ∼−17 dB. These results will have important implications on future Cassini radar data analysis.     

Kinematics of stellar populations with RAVE data

We study the kinematics of the Galactic thin and thick disk populations using stars from the RAVE survey’s second data release together with distance estimates from Breddels et al. (2010). The velocity distribution exhibits the expected moving groups present in the solar neighborhood. We separate thick and thin disk stars by applying the X (stellar-population) criterion of Schuster et al. (1993), which takes into account both kinematic and metallicity information. For 1906 thin disk and 110 thick disk stars classified in this way, we find a vertical velocity dispersion, mean rotational velocity and mean orbital eccentricity of (σ_W, 〈V_Φ〉, 〈e〉)_thin = (18 ± 0.3 km s⁻¹, 223 ± 0.4 km s⁻¹, 0.07 ± 0.07) and (σ_W, 〈V_Φ〉, 〈e〉)_thick = (35 ± 2 km s⁻¹, 163 ± 3 km s⁻¹, 0.31 ± 0.16), respectively. From the radial Jeans equation, we derive a thick disk scale length in the range 1.5-2.2 kpc, whose greatest uncertainty lies in the adopted form of the underlying potential. The shape of the orbital eccentricity distribution indicates that the thick disk stars in our sample most likely formed in situ with minor gas-rich mergers and/or radial migration being the most likely cause for their orbits. We further obtain mean metal abundances of 〈[M/H]〉_thin = +0.03 ± 0.17, and 〈[M/H]〉_thick = −0.51 ± 0.23, in good agreement with previous estimates. We estimate a radial metallicity gradient in the thin disk of −0.07 dex kpc⁻¹, which is larger than predicted by chemical evolution models where the disk grows inside-out from infalling gas. It is, however, consistent with models where significant migration of stars shapes the chemical signature of the disk, implying that radial migration might play at least part of a role in the thick disk’s formation.     

The orbital period and negative superhumps of the nova-like cataclysmic variable V378 Pegasi

A radial velocity study is presented of the cataclysmic variable V378 Pegasi (PG 2337 + 300). It is found to have an orbital period of 0.13858 ± 0.00004 d (3.32592 ± 0.00096 h). Its spectrum and long-term light curve suggest that V378 Peg is a nova-like variable, with no outbursts. We use the approximate distance and position in the Galaxy of V378 Peg to estimate E(B − V) = 0.095, and use near-infrared magnitudes to calculate a distance of 680 ± 90 pc and M_V = 4.68 ± 0.70, consistent with V378 Peg being a nova-like. Time-resolved photometry taken between 2001 and 2009 reveals a period of 0.1346 ± 0.0004 d (3.23 ± 0.01 h). We identify this photometric variability to be negative superhumps, from a precessing, tilted accretion disk. Our repeated measurements of the photometric period of V378 Peg are consistent with this period having been stable between 2001 and 2009, with its negative superhumps showing coherence over as many as hundreds or even thousands of cycles.     

The outgassing and composition of Comet 19P/Borrelly from radio observations

Radio spectroscopic observations of Comet 19P/Borrelly were performed during the 1994 apparition and at, and near, the time of the Deep Space 1 flyby in 2001. HCN, CS, CH₃OH, and H₂CO were detected using the 30-m telescope of the Institut de Radioastronomie Millimétrique and the James Clerk Maxwell Telescope, and their production rates relative to water are estimated to be 0.06-0.11, 0.07, 1.7, and 0.4%, respectively. Only upper limits are derived for H₂S and CO. The upper limit for CO/H₂O (<15%) is not very constraining, while the upper limit for the H₂S/H₂O ratio of 0.45% is near the bottom of the range of values measured for other comets. Observations of the OH radical at the Nançay radio telescope provide water production rates a few weeks before the 1994 and 2001 perihelia. Observations of the 1₁₀-1₀₁ water line at 557 GHz with the Odin satellite yield a water production rate of (2.5±0.5)×10²⁸ s⁻¹ on September 22, 2001, at the time of the Deep Space 1 encounter, and (3.3±0.6)×10²⁸ s⁻¹ averaged over the September 22-24, 2001 period. The line shapes are asymmetric and blueshifted by V₀∼−0.18 km s⁻¹ for the best observed HCN lines recorded one week after perihelion. The HCN line shapes, and the similar OH and HCN velocity shifts over the September-November 1994 and August-September 2001 periods, favor anisotropic outgassing towards the Sun. Strong outgassing directed along the primary dust jet seen on visible images is not excluded by the HCN line shapes, but unrealistically high gas expansion velocities are required to explain the line shapes in that case.     

Secular light curve of Comet 9P/Tempel 1

In support of the Deep Impact Mission, we have updated the secular light curve of 9P/Tempel 1 presented in Paper I [Ferrín, I., 2005. Icarus 178, 493-516], with new data sets. The secular light curves (SLC) of the comet are presented in the log and time plots (Figs. 1 and 2) and provide a clear profile of the overall shape of the envelope. We arrive at the following conclusions: (1) Improved values of 18 photometric parameters are derived including the turn on and turn off points, RON=−3.47±0.05 AU, ROFF=+4.20±0.05 AU, and TON=−410±25 d, TOFF=+555±25 d. (2) The improved SLC shows a most interesting and peculiar shape, with a linear power law of slope n=7.7±0.1 from RON=−3.47 AU to RBP=−2.08±0.05 AU, and then converts to a law with curvature. The break point of the power law at RBP=−2.08 AU, mV(1,R)=14.0±0.1 mag, is interpreted as a change in sublimating something more volatile than water ice (most probably CO₂), to water ice sublimation. In other words, the comet's sublimation is controlled by two different substances. (3) The photometric-age (defined in Paper I) and the time-age of the comet [Ferrín, I., 2006. Icarus. In press] are recomputed, and results in a value P-AGE=21±2 and T-AGE=11±2 comet years. Thus 9P is a young comet. (4) The comet is active almost up to aphelion since the turn off point has been determined at ROFF=+4.20±0.05 AU while aphelion takes place at Q=+4.74 AU. (5) The comet exhibits activity post-aphelion which is not understood. Two hypothesis are advanced to explain this behavior.     

The period of rotation, shape, density, and homogeneous surface color of the Centaur 5145 Pholus

We present optical photometry of the Centaur 5145 Pholus during 2003 May and 2004 April using the facility CCD camera on the 1.8-m Vatican Advanced Technology Telescope on Mt. Graham, Arizona. We derive a double-peaked lightcurve and a rotation period of 9.980±0.002 h for Pholus, consistent with periods of 9.9825±0.004 and 9.9823±0.0012 h by Buie and Bus (1992, Icarus 100, 288-294) and Farnham (2001, Icarus 152, 238-245). We find a lightcurve peak-to-peak amplitude of 0.60 mag, significantly larger than peak-to-peak amplitude determinations of 0.15 and 0.39 mag by Buie and Bus and Farnham. We use the three observed amplitudes and an amplitude-aspect model to derive four possible rotational pole positions as well as axial ratios of a/b=1.9 and c/b=0.9. If we assume an albedo of 0.04, we find Pholus has dimensions of 310×160×150 km. If we assume Pholus is a strengthless rubble-pile and its non-spherical shape is due to rotational distortion, our axial ratios and period measurements indicate Pholus has a density of 0.5 g cm⁻³, suggestive of an ice-rich, porous interior. By combining B-band and R-band lightcurves, we find B−R=1.94±0.01 and any B−R color variation over the surface of Pholus must be smaller than 0.06 mag (i.e., much smaller than the 1.0<B−R<2.0 range seen among the Centaur and Kuiper belt object populations). By combining our V−R measurements with values in the literature, we find no evidence for any color variegation between the northern and southern hemispheres of Pholus. Observations of the Kuiper belt object 2004 DW (90482) over a time interval of seven hours show no color variation Our observations add to the growing body of evidence that individual Centaurs and KBOs exhibit homogeneous surface colors and hence gray impact craters on radiation reddened crusts are probably not responsible for the surprising range of colors seen among the Centaur and Kuiper belt object populations.     

Photometry of Mercury from SOHO/LASCO and Earth: The Phase Function from 2 to 170°

CCD observations of Mercury were obtained with the large angle spectrometric coronograph (LASCO) on the solar and heliospheric observatory spacecraft, near superior and inferior solar conjunctions. Whole disk photometry was extracted from the orange and blue filter images and transformed to V magnitudes on the UBV system. The LASCO data were combined with ground-based, V-filter photometry acquired at larger elongation angles. The resulting photometric phase function covers the greatest span of angles to date and is the first wide-range function to be obtained since the era of visual observation. We analyzed the data using a polynomial fit and a Hapke function fit, and derived the following photometric results. Mercury's fully lit brightness, adjusted to a distance of 1.0 AU from the Sun and observer, was found to be V=−0.694(±0.030), which is more luminous than previously measured. The corresponding geometric albedo is 0.142(±0.005). The phase integral is 0.478(±0.005) and resulting spherical albedo is 0.068(±0.003). The upper limit of a possible rotational brightness variation is about 0.05 magnitude. Mercury's brightness surges by more than 40% between phase angles 10 and 2°, while the illuminated fraction of the disk increases by less than 1%. A set of coefficients for Hapke's function that fit most of the phase curve includes h=0.065±0.002 indicating that Mercury and the Moon have similar regolith compaction states and particle size distributions, and θ-bar=16°±1° implying a macroscopically smoother surface than the Moon. However, we found other solutions that fit the observations nearly as well with significantly smaller and larger values of h, and with values of θ-bar around 25°. The wide range for θ-bar is due to the inability of the model to fit the photometry obtained at large phase angles.     

Flowing afterglow studies of temperature dependencies for electron dissociative recombination of HCNH, CH3CNH and CH3CH2CNH and their symmetrical proton-bound dimers

A study has been made using a variable temperature flowing afterglow Langmuir probe technique (VT-FALP) to determine the equilibrium temperature dependencies of the dissociative electron-ion recombination of the protonated cyanide ions (RCNH⁺, where R=H, CH₃ and C₂H₅) and their symmetrical proton-bound dimers (RCNH⁺NCR). The power law temperature dependencies of the recombination coefficients, α_e, over the temperature range 180 to 600 K for the protonated ions are α_e(T)(cm³ s⁻¹)=3.5±0.5×10⁻⁷ (300/T)^1.38 for HCNH⁺, α_e(T)=3.4±0.5×10⁻⁷ (300/T)^1.03 for CH₃CNH⁺, and α_e(T)=4.6±0.7×10⁻⁷ (300/T)^0.81 for CH₃CH₂CNH⁺. The equivalent values for the proton-bound dimers are α_e(T)(cm³ s⁻¹)=2.4±0.4×10⁻⁶(300/T)^0.5 for (HCN)₂H⁺ to α_e(T)=2.8±0.4×10⁻⁶(300/T)^0.5 for (CH₃CN)₂H⁺, and α_e(T)=2.3±0.3×10⁻⁶(300/T)^0.5 for (CH₃CH₂CN)₂H⁺. The relevance of these data to molecular synthesis in the interstellar medium and the Titan ionosphere are discussed.     

The cosmic distance scale

Summary The status of the cosmic distance scale problem in early 1989 is reviewed. Internally consistent distances to Local Group galaxies are given in Tables 5 and 6. Within the Local Group the distance scale is found to be 11±5% smaller than that previously adopted by Sandage and Tammann. Distances to nearby galaxies are used as stepping stones to the Virgo cluster. The interpretation of the Tully-Fisher observations of Virgo spirals is found to be ambiguous because it is not yet clear which spirals are cluster members and which are background objects. Distance estimates of the Virgo cluster obtained by different techniques are listed in Table 11. The distance modulus of the Virgo cluster is found to be 31.5±0.2, corresponding to a distance of 20±2 Mpc. The elliptical galaxies in the core of the Virgo cluster haveV ₀=1200±46 kms^–1, which corresponds toV _LG=1082±48 km s^–1. With an infall velocity of 250±50 km s^–1 this yields a cosmological redshiftV=1332±69 km s^–1, from which a Hubble parameter H₀=67±8 km s^–1 Mpc^–1 is obtained. Space Telescope observations of distant Cepheids, Tully-Fisher observations of spirals in the Hercules eluster, and interference filter observations of Virgo planetary nebulae in the light of [O_III], should soon result in a major improvement in the accuracy with which H₀ is known.     

New optical measurements of planetary diameters— Part IV: Planet Mars

Optical measurements of the diameter of Mars were made using a double-image micrometer with large refractors from 1952 to 1971. Discussion of the 90 independent series of measurements gives nine determinations of radius with an accuracy of ±7–8km for different latitudes from pole to equator. The Mariner 4, 6 and 7 occultation results and the radar results availble in 1970 added seven further determinations of comparable accuracy. All these values, within the accuracy of measurement, fit an ellipsoid with R_eq=3398±3km and R_po1=3371±4km. The mean density of Mars is thus 3940±0.012g cm⁻³. The resulting optical oblateness of 0.0079, larger than the dynamical value of 0.0052, results in an equatorial radius excess of 9±5 km which presumably comes about by internal stresses.     

HCN fluorescence on Titan

The HCN emission features near 3 μm recently detected by Geballe et al. (2003, Astrophys. J. 583, L39) are analyzed with a model for fluorescence of sunlight in the ν₃ band of HCN. The emission spectrum is consistent with current knowledge of the atmospheric temperature profile and the HCN distribution inferred from millimeter-wave observations. The spectrum is insensitive to the abundance of HCN in the thermosphere and the thousand-fold enhancement relative to photochemical models suggested by Geballe et al. (2003, Astrophys. J. 583, L39) is not required to explain the observations. We find that the spectrum can be matched with temperatures from 130 to 200 K, with slightly better fits at high temperature, contrary to the temperature determination of 130±10 K of Geballe et al. (2003, Astrophys. J. 583, L39). The HCN emission spectrum is sensitive to the collisional de-excitation probability, P₁₀, for the ν₃ state and we determine a value of 10⁻⁵ with an accuracy of about a factor of two. Analysis of absorption lines in the C₂H₂ν₃ band near 3 μm, detected in the same spectrum, indicate a C₂H₂ mole fraction near 0.01 μbar of 10⁻⁵ for P₁₀=10⁻⁴. The derived mole fraction, however, is dependent upon the value adopted for P₁₀ and lower values are required if P₁₀ at Titan temperatures is less than its room temperature value.     

A comprehensive photometric study of the marginal-contact binary BE Cephei

New photometry for the eclipsing binary BE Cephei was performed from 2008 to 2011. The light-curve synthesis indicates that it is a marginal-contact binary with a mass ratio of q = 2.340(±0.009) and a degree of contact of f = 6.9%(±2.3%). From the O − C curve, it is discovered that the orbital period changes show a sinusoidal curve superimposed on a downward parabola. The period and semi-amplitude of the cyclic variation are P_mod = 59.26(±0.52) yr and A = 0.^d0067(±0.^d0010), which may be possibly attributed to light-time effect via the presence of an unseen third body. The long-term period decreases at a rate of dP/dt = −4.84(±0.31) × 10⁻⁸ d yr⁻¹, which may result from mass transfer from the more massive component to the less massive one, accompanied by angular momentum loss. With the period decreasing, the degree of contact will increase. Finally, the marginal-contact binary BE Cep may be evolving into a deep-contact configuration.     

Detection of new hydrocarbons in Uranus' atmosphere by infrared spectroscopy

Ethane (C₂H₆), methylacetylene (CH₃C₂H or C₃H₄) and diacetylene (C₄H₂) have been discovered in Spitzer 10-20 μm spectra of Uranus, with 0.1-mbar volume mixing ratios of (1.0±0.1)×¹⁰⁻⁸, (2.5±0.3)×¹⁰⁻¹⁰, and (1.6±0.2)×¹⁰⁻¹⁰, respectively. These hydrocarbons complement previously detected methane (CH₄) and acetylene (C₂H₂). Carbon dioxide (CO₂) was also detected at the 7-σ level with a 0.1-mbar volume mixing ratio of (4±0.5)×¹⁰⁻¹¹. Although the reactions producing hydrocarbons in the atmospheres of giant planets start from radicals, the methyl radical (CH₃) was not found in the spectra, implying much lower abundances than in the atmospheres of Saturn or Neptune where it has been detected. This finding underlines the fact that Uranus' atmosphere occupies a special position among the giant planets, and our results shed light on the chemical reactions happening in the absence of a substantial internal energy source.