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A&A
Volume 541, May 2012
Article Number L6
Number of page(s) 4
Section Letters
DOI https://doi.org/10.1051/0004-6361/201218874
Published online 04 May 2012

© ESO, 2012

1. Introduction

The Herschel Space Observatory1 (Pilbratt et al. 2010) allows the detection of thermal radiation from several trans-Neptunian objects (TNOs) at the precision level of  <1   mJy. Since the expected fluxes around the peak of the spectral energy distribution (SED) significantly exceed this precision, Herschel provides a great opportunity to characterize TNOs and obtain basic thermophysical information. In this work, we present recent measurements of the prominent objects (90377) Sedna and 2010 EK139 using the Photodetector Array Camera and Spectrometer instrument (PACS, Poglitsch et al. 2010) on board the Herschel Space Observatory. These observations are part of the “TNOs are Cool!: a survey of the trans-Neptunian region” Open Time Key Program (Müller et al. 2009, 2010; Lellouch et al. 2010; Lim et al. 2010).

Sedna is a prominent member of the detached objects, that is often classified as an inner Oort-cloud object. Until now, no accurate measurements of the diameter and albedo have been available for this object. Both direct imaging (Brown 2008) and upper limits to the thermal radiation using the Spitzer Space Telescope (2.4   mJy at 70   μm, see Stansberry et al. 2008) have yielded an upper limit of  ≈1670   km for its diameter (within 97% confidence).

2010 EK139 has been discovered in 2010 by Sheppard et al. (2011) in the course of a southern Galactic plane survey. Prediscovery observations date back to 2002, allowing for a relatively accurate orbit determination. This places 2010 EK139 among the scattered disk objects. 2010 EK139 orbits the Sun on an eccentric orbit (e ≈ 0.53) and has a perihelion distance of q ≈ 32.5   AU. In addition, 2010 EK139 is a suspected member of the 2:7 resonance group2. We note that a more complete sample of SDOs/detached objects observed with Herschel/PACS is presented by Santos-Sanz et al. (2012).

Table 1

Summary of Herschel observations of Sedna and 2010 EK139.

2. Observations, data reduction, and photometry

Sedna was observed by Herschel/PACS in two visits: the first started on 2010 August 6, 10:55:17 UTC and a follow-up started on 2010 August 9, 08:11:37 UTC, both taking place during the Routine Science Phase observation series of the “TNO’s are Cool!” key programme (Müller et al. 2009). 2010 EK139 was also observed by Herschel/PACS in two visits, the first started on 2010 December 23, 07:04:30 UTC, and a follow-up started the same day, 19:58:27 UTC. Herschel/PACS observed Sedna and 2010 EK139 for  ≈3.14 and  ≈1.26 h, respectively. For both objects, we used both the blue/red (70/160   μm) and green/red (100/160   μm) channel combinations. The actual details of these observations are summarized in Table 1.

Raw observational data were reduced using the Herschel Interactive Processing Environment (HIPE3, see also Ott, 2010) and the processing scripts are similar to the ones employed in Mommert et al. (2012), Santos-Sanz et al. (2012), or Vilenius et al. (2012). For each observation, these scripts create a pair of maps, one for the blue or green channel and one for the red channel. The maps have an effective pixel size of 1.″1\hbox{$1\farcs1$}, 1.″4\hbox{$1\farcs4$}, and 2.″1\hbox{$2\farcs1$}, for the blue, green, and red filters, respectively: these pixel sizes are set to sample the respective point spread functions (PSFs) properly. Data frames were selected by the actual scan speed (10′′/s ≤ speed ≤ 25′′/s) of the spacecraft, which maximized the effective usage of the detector and yielded significantly higher signal-to-noise (S/N) ratios than the standard setting (approximately 20′′/s).

Since the apparent motion of Sedna and 2010 EK139 between the two visits (15–35 map pixels, depending on the actual filter) is relatively large compared to the PSF but small compared to the detector size, the location of the target in the first visit can simply be used as a background area on the maps of the second visit and vice versa. Owing to the satellite pointing uncertainty that is about a few arcsec (Poglitsch et al. 2010), we derived the true map-center displacements using the red channel maps – on which the background confusion is the strongest – as follows. By varying the proper motion vector between the two visits, we computed the cross-correlation residuals for each trial vector. By minimizing the residuals, we obtained a more precise value for the shift between the visits and the photometry of combined maps was found to be more reliable. Since simple averaging the registered maps does not cancel the background confusion noise, we employed background removal techniques as it is described in Santos-Sanz et al. (2012) or Mommert et al. (2012). The maps on which the photometry was then performed are shown in Fig. 1.

thumbnail Fig. 1

Image stamps showing the combined maps of Sedna (upper panels) and 2010 EK139 (lower panels) in the 70   μm (blue), 100   μm (green), and 160   μm (red) channels. Each stamp covers an area of 56′′ × 56′′, while the tick marks on the axes show the relative positions in pixels. The effective beam size (i.e. the circle with a diameter corresponding to the full width at half magnitude) is also displayed in the lower-left corners of the stamps.

Table 2

Thermal fluxes of Sedna and 2010 EK139 derived from our Herschel measurements.

Regardless of the background structures, in the subtracted and combined maps the only expected source is the TNO itself and this source can be treated as an isolated point source. We estimated the fluxes and their uncertainties using (1) a single aperture that maximizes the expected S/N ratio; (2) the aperture growth curve method and implanted artificial sources in a Monte Carlo fashion (see e.g. Santos-Sanz et al. 2012); and (3) we also checked the individual (non-combined) maps on which they had sufficient S/N ratio. For a more detailed description, we refer to Mommert et al. (2012) and Santos-Sanz et al. (2012).

Table 3

Orbital and optical data for Sedna and 2010 EK139 at the time of the Herschel observations.

thumbnail Fig. 2

Spectral energy distribution of Sedna (left) and 2010 EK139 (right) in the far-infrared region, based on Herschel/PACS measurements. Superimposed are the best-fit TPM (solid lines) and STM curves with floating beaming parameter (dashed lines).

We found that all three methods yielded the same fluxes and uncertainties for each channel. The individual analysis of maps for 2010 EK139 also showed consistent results. Therefore, we accepted the means of all measurements per object and filter as final fluxes (see Table 2) and used them for thermal modeling. We note here that the color corrections provided in Poglitsch et al. (2010) are negligible: it is nearly or less than 1 per cent for 2010 EK139 and for Sedna, it is 6 per cent in the 70   μm channel and less than 3 per cent in the other longer wavelength channels, so almost less by a magnitude than the relative photometric uncertainties in all of these cases.

3. Thermal properties

The basic physical properties of Sedna and 2010 EK139 were estimated by a hybrid standard thermal model (STM, Lebofsky et al. 1986; Stansberry et al. 2008) in which the beaming parameter is adjustable and the asteroid thermophysical model (TPM, see Lagerros 1996, 1997, 1998). The absolute magnitudes of the reflected sunlight from these TNOs are available from the literature (Rabinowitz et al. 2007; Sheppard et al. 2011). In addition for 2010 EK139, we conservatively increased the formal uncertainty (0.03 mag, based on MPC data) up to 0.10 mag: we took into account the possible omission of the phase angle corrections and also added quadratically an average TNO lightcurve amplitude of 0.088 mag (based on Duffard et al. 2009). The employed geometric parameters and absolute magnitudes are summarized in Table 3.

The hybrid STM predicts thermal fluxes from the geometric albedo, diameter, and beaming parameter and these fluxes can be computed for arbitrary solar and geocentric distances. Hybrid STM provides reliable estimates only for small phase angles (via a simple form of phase angle corrections), although owing to the distances of these objects, this estimate is fairly sufficient in our cases. To estimate the physical parameters and their respective uncertainties, we used a Monte Carlo (MC) approach by varying the fit input around their mean with the standard deviation equal to their respective uncertainty. For both targets, we used the fixed-η approach for the beaming parameter, i.e. taking η = 1.14    ±    0.15 for each MC step. This mean value of and scatter in the beaming factor are taken from Santos-Sanz et al. (2012) and seem to be an acceptable approach for TNOs. To estimate the phase integral q, i.e. the ratio of the Bond to geometric albedo (i.e. A = qpV), we employed an iterative approach. First, the phase integral is computed for unity slope parameter (G = 1, i.e. q = 0.29 + 0.68G), and then refined using eq. 1 of Brucker et al. (2009) until convergence. This procedure applied for hybrid STM yielded the diameter, geometric albedo, and slope parameter of D = 1060    ±    100 km, pV = 0.290    ±    0.061, and G = 0.42    ±    0.04 for Sedna and D = 535    ±    30 km, pV = 0.187    ±    0.027, and G = 0.37    ±    0.03 for 2010 EK139, respectively. We repeated the similar procedure by allowing the beaming parameter η to vary. This analysis yielded η = 0.95    ±    0.43 for Sedna, with the corresponding diameter and albedo of D = 990    ±    95 km and pV = 0.336    ±    0.072. For 2010 EK139, the best-fit value of the beaming parameter is somewhat smaller, 0.70    ±    0.31, while the diameter and albedo values are D = 450    ±    35 km and pV = 0.261    ±    0.047.

In the case of Sedna, we note that the linear phase coefficient β = 0.151    ±    0.033 (Rabinowitz et al. 2007) would imply a phase integral of q=0.89-0.29+0.55\hbox{$q=0.89^{+0.55}_{-0.29}$}, assuming the same phase behavior over the whole phase angle range. Although the phase curve is known for very small domains (α ≲ 0.6°, see also Fig. 2 of Rabinowitz et al. 2007), this value broadly agrees, within a nearly 1-σ difference from the phase integral of q = 0.59    ±    0.03 as implied by the radiometric albedo and the Brucker formula.

The results of the TPM estimates were the following. For Sedna, we used the rotation period of  ≈10.27 h (Gaudi et al. 2005) and assumed an equator-on rotation and the most favorable solution for the thermal inertia was found to be 0.2   J   m-2   K-1   s−1/2, which corresponds to the diameter of D = 995    ±    80   km and the geometric albedo of pV = 0.32    ±    0.06. For 2010 EK139, we assumed a period of 12 h and equator-on rotation and found that this object also requires a very low thermal inertia, 0.1   J   m-2   K-1   s−1/2. This may change slightly if the rotation period and the spin vector orientation were very different, although all feasible solutions put the thermal inertia below 1.0   J   m-2   K-1   s−1/2. Our best fit yielded a diameter of D=470-10+35 km\hbox{$D=470^{+35}_{-10}\,{\rm km}$} and a geometric albedo of pV=0.25-0.05+0.02\hbox{$p_{\rm V}=0.25^{+0.02}_{-0.05}$}, which do not differ significantly from the hybrid STM model results in which the beaming parameter was also varied. We note that here the uncertainties include both the statistical errors and the ambiguities in the rotation parameters (see also Müller et al. 2011, for more details about this modeling).

In Fig. 2, we displayed the far-infrared SEDs for these two objects as it is estimated from the hybrid STM and TPM fitting and our best-fit data and the floating η values. We also note that the rotation period of Sedna found by Gaudi et al. (2005) corresponds to a peak-to-peak amplitude of 0.02 mag. The small amplitude does not change the reliability of the thermal modeling and the corresponding shape effects are not relevant to the size determination.

4. Discussion

We have estimated the sizes and surface albedos for the trans-Neptunian objects Sedna and 2010 EK139 using recent observations of their thermal emission at 70/100/160   μm with Herschel/PACS. On the basis of earlier Spitzer measurements, Sedna had already only an upper limit to its size estimate (Stansberry et al. 2008). Our analysis has shown that for Sedna and 2010 EK139, the respective geometric albedos are pV = 0.32    ±    0.06 and pV=0.25-0.05+0.02\hbox{$p_{\rm V}=0.25^{+0.02}_{-0.05}$}, thus both objects have brighter surfaces than the average TNO population (Stansberry et al. 2008) or SDOs/detached population (Table 5 in Santos-Sanz et al. 2012). We note that the albedos of Sedna and 2010 EK139 closely match those of detached objects in Fig. 4a (pV vs. diameter) in Santos-Sanz et al. (2012). According to Schaller & Brown (2007) and Brown et al. (2011), even with these newly derived parameters, Sedna lies in the region in which volatiles are expected to be retained in the surface (see Fig. 1 in that paper for an equivalent temperature of 20    ±    2 K), hence one can also expect a brighter surface (see also Barucci et al. 2005; Emery et al. 2007). Sedna is currently approaching its perihelion. Thus, if the brightness of the surface were changing owing to the ongoing sublimation of ices, it might be detectable in the variation in the absolute magnitude on a timescale of decades. In contrast, 2010 EK139 falls in the region in which volatiles should have been lost (using 48    ±    3 K for equivalent temperature). However, objects of this size can have such a high albedo if water ice is present on the surface (see e.g. Barkume et al. 2006; Ragozzine & Brown 2009; Dumas et al. 2011). The presence of water could be tested by measuring the intrinsic color to see whether it is bluish (Brown 2008). As they lack known satellites, we do not know the masses and hence the surface gravity and escape velocities of these objects that could place tighter constraints on the surface properties.

1

Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

3

Data presented in this paper were analyzed using “HIPE”, a joint development by the Herschel Science Ground Segment Consortium, consisting of ESA, the NASA Herschel Science Center, and the HIFI, PACS and SPIRE consortia members, see http://herschel.esac.esa.int/DpHipeContributors.shtml

Acknowledgments

We gratefully thank the valuable comments and suggestions of the referee, Josh Emery. The work of A.P., Cs.K., and N.Sz. has been supported by the ESA grant PECS 98073. A.P. and Cs.K. were also supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. Cs.K. thanks the support of the OTKA grant K101393. Part of this work was supported by the German DLR projects number 50 OR 1108, 50 OR 0903, and 50 OR 0904. M.R. acknowledges support from the German Deutsches Zentrum für Luft- und Raumfahrt, DLR project number 50OFO 0903. M.M. acknowledges support through the DFG Special Priority Program 1385. P.S.-S. would like to acknowledge financial support by the Centre National de la Recherche Scientifique (CNRS). J.-L.O. acknowledges the Spanish grants AYA2008-06202-C03-01, AYA2011-30106-C02-01 and 2007-FQM2998.

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All Tables

Table 1

Summary of Herschel observations of Sedna and 2010 EK139.

In the text
Table 2

Thermal fluxes of Sedna and 2010 EK139 derived from our Herschel measurements.

In the text
Table 3

Orbital and optical data for Sedna and 2010 EK139 at the time of the Herschel observations.

In the text

All Figures

thumbnail Fig. 1

Image stamps showing the combined maps of Sedna (upper panels) and 2010 EK139 (lower panels) in the 70   μm (blue), 100   μm (green), and 160   μm (red) channels. Each stamp covers an area of 56′′ × 56′′, while the tick marks on the axes show the relative positions in pixels. The effective beam size (i.e. the circle with a diameter corresponding to the full width at half magnitude) is also displayed in the lower-left corners of the stamps.
In the text
thumbnail Fig. 2

Spectral energy distribution of Sedna (left) and 2010 EK139 (right) in the far-infrared region, based on Herschel/PACS measurements. Superimposed are the best-fit TPM (solid lines) and STM curves with floating beaming parameter (dashed lines).
In the text

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