“TNOs are Cool”: A survey of the trans-Neptunian region

The target sample consists of both dynamically cold and hot classicals (Table 1). We use a cut-off limit of $i=4.5\text{degr}$ in illustrating the two subsamples. Another typical value used in the literature is $i=5\text{degr}$. The inclination limit is lower for large objects (Petit2011 ()) which have a higher probability of belonging to the hot population. Targets 119951 (2002 KX${}_{14}$), 120181 (2003 UR${}_{292}$) and 78799 (2002 XW${}_{93}$) are in the inner classical belt and are therefore considered to belong to the low-inclination tail of the hot population. The latter two would be Centaurs in the DES system and all targets in Table 1 with $i$ $>$ $15\text{degr}$ would belong to the scattered-extended class of DES.

The median absolute V-magnitudes ($H_V$, see Section 2.5) of our sample are 6.1  mag for the cold sub-sample and 5.3  mag for the hot one. Levison2001 () (2001) found that bright classicals have systematically higher inclinations than fainter ones. This trend is seen among our targets (see Section 5.1.3). Another known population characteristics is the lack of a clear color demarcation line at $i\approx 5\text{degr}$ (Peixinho2008 ()), which is absent also from our sample of 10 targets with known colors.

PACS is an imaging dual band photometer with a rectangular field of view of $1.75\text{arcmin}$ $\times$ $3.5\text{arcmin}$ with full sampling of the $3.5m$-telescope’s point spread function (PSF). The two detectors are bolometer arrays, the short-wavelength one has 64 $\times$ 32 pixels and the long-wavelength one 32 $\times$ 16 pixels. In addition, the short-wavelength array has a filter wheel to select between two bands: 60 – $85\mu m$ or 85 – $125\mu m$, whereas the long-wavelength band is 125 – $210\mu m$. In the PACS photometric system these bands have been assigned the reference wavelengths $70.0\mu m$, $100.0\mu m$ and $160.0\mu m$ and they have the names “blue”, “green” and “red”. Both bolometers are read-out at $40Hz$ continuously and binned by a factor of four on-board.

We specified the PACS observation requests (AOR) using the scan-map Astronomical Observation Template (AOT) in HSpot, a tool provided by the Herschel Science Ground Segment Consortium. The scan-map mode was selected due to its better overall performance compared to the point-source mode (Muller2010 () 2010). In this mode the pointing of the telescope is slewed at a constant speed over parallel lines, or “legs”. We used 10 scan legs in each AOR, separated by $4\text{arcsec}$. The length of each leg was $3.0\text{arcmin}$, except for Altjira where it was $2.5\text{arcmin}$, and the slewing speed was $20\text{arcsec}{s}^{-1}$. Each one of these maps was repeated from two to five times.

To choose the number of repetitions, i.e. the duration of observations, for our targets we used the Standard Thermal Model (see Section 3) to predict their flux densities in the PACS bands. Based on earlier Spitzer work (Stansberry2008 (), 2008) we adopted a geometric albedo of 0.08 and a beaming parameter of 1.25 for observation planning purposes. The predicted thermal fluxes depend on the sizes, which are connected to the assumed geometric albedo and the absolute V-magnitudes via Equation (3). In some cases the absolute magnitudes used for planning purposes are quite different (by up to 0.8 mag) from those used for modeling our data as more recent and accurate visible photometry was taken into account (see Section 2.5).

The PACS scan-map AOR allows the selection of either the blue or green channel; the red channel data are taken simultaneously whichever of those is chosen. The sensitivity of the blue channel is usually limited by instrumental noise, while the red channel is confusion-noise limited (PACSrelnote ()). The sensitivity in the green channel can be dominated by either source, depending on the depth and the region of the sky of the observation. For a given channel selection (blue or green) we grouped pairs of AORs, with scan orientations of $70\text{degr}$ and $110\text{degr}$ with respect to the detector array, in order to make optimal use of the rectangular shape of the detector. Thus, during a single visit of a target we grouped 4 AORs to be observed in sequence: two AORs in different scan directions and this repeated for the second channel selection.

The timing of the observations, i.e. the selection of the visibility window, has been optimized to utilize the lowest far-infrared confusion noise circumstances (Kiss2005 ()) such that the estimated signal-to-noise ratio due to confusion noise has its maximum in the green channel. Each target was visited twice with similar AORs repeated in both visits for the purpose of background subtraction. The timing of the second visit was calculated such that the target has moved 30-$50\text{arcsec}$ between the visits so that the target position during the second visit is within the high-coverage area of the map from the first visit. Thus, we can determine the background for the two source positions.

The observational details are listed in Table 2. All of the targets observed had predicted astrometric $3\sigma$ uncertainties less than $10\text{arcsec}$ at the time of the Herschel observations (David Trilling, priv. comm.).

The data reduction from level 0 (raw data) to level 2 (maps) was done using Herschel Interactive Processing Environment (HIPE³³3Data presented in this paper were analysed 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.) with modified scan-map pipeline scripts optimized for the “TNOs are Cool” key program. The individual maps (see Fig. 1 for examples) from the same epoch and channel are mosaicked, and background-matching and source-stacking techniques are applied. The two visits are combined (Fig. 2), in each of the three bands, and the target with a known apparent motion is located at the center region of these maps. The detector pixel sizes are $3.2\text{arcsec}\times 3.2\text{arcsec}$ in the blue and green channels, and $6.4\text{arcsec}\times 6.4\text{arcsec}$ in the red channel whereas the pixel sizes in the maps produced by this data reduction are $1.1\text{arcsec}$ / $1.4\text{arcsec}$ / $2.1\text{arcsec}$ in the blue / green / red maps, respectively. A detailed description of the data reduction in the key program is given in Kiss et al. (in prep.).

Once the target is identified we measure the flux densities at the photocenter position using DAOPHOT routines (Stetson1987 ()) for aperture photometry. We make a correction for the encircled energy fraction of a point source (PSF2010 ()) for each aperture used. We try to choose the optimum aperture radius in the plateau of stability of the growth-curves, which is typically 1.0-1.25 times the full-width-half-maximum of the PSF ($5.2\text{arcsec}$ / $7.7\text{arcsec}$ / $12.0\text{arcsec}$ in the blue / green / red bands, respectively). The median aperture radius for targets in the “TNOs are Cool” program is 5 pixels in the final maps (pixel sizes 1.1”/1.4”/2.1” in the blue / green / red maps). For the uncertainty estimation of the flux density we implant 200 artificial sources in the map in a region close to the source ($<50\text{arcsec}$) excluding the target itself. A detailed description of how aperture photometry is implemented in our program is given in SantosSanz2012 () (2012).

In order to obtain monochromatic flux density values of targets having a spectral energy distribution different from the default one color corrections are needed. In the photometric system of the PACS instrument flux density is defined to be the flux density that a source with a flat spectrum ($\lambda F_{\lambda }=$constant, where $\lambda$ is the wavelength and $F_{\lambda }$ is the monochromatic flux) would have at the PACS reference wavelengths (Poglitsch2010 ()). Instead of the flat default spectrum we use a cool black body distribution to calculate correction coefficients for each PACS band. The filter transmission and bolometer response curves needed for this calculation are available from HIPE, and we take as black body temperature the disk averaged day-side temperature calculated iteratively for each target ($\frac{8}{9}\times T_{SS}$, using STM assumptions from Section 3, the Lambertian emission model and the sub-solar temperature from Eq. 2.) This calculation yields on the average 0.982 / 0.986 / 1.011 (flux densities are divided by color correction factors) for the blue / green / red channels, respectively, with small variation among the targets of our sample.

The absolute flux density calibration of PACS is based on standard stars and large main belt asteroids and has the uncertainties of 3% / 3% / 5% for the blue / green / red bands (PACScal2011 ()). We have taken these uncertainties into account in the PACS flux densities used in the modeling, although their contribution to the total uncertainty is small compared to the signal-to-noise ratio of our observations.

The color corrected flux densities are given in Table 3. They were determined from the combined maps of two visits, in total 4 AORs for the blue and green channels and 8 AORs for the red. The only exceptions are 19521 Chaos and 90568 (2004 GV${}_9$), whose one map was excluded from our analysis due to a problem in obtaining reliable photometry from those observations. The uncertainties in Table 3 include the photometric $1\sigma$ and absolute calibration $1\sigma$ uncertainties. 17 targets were detected in at least one PACS channel. The upper limits are the $1\sigma$ noise levels of the maps, including both the instrumental noise and residuals from the eliminated infrared background confusion noise. 79360 Sila has a flux density which is lower by a factor of three in the red channel than the one published by Muller2010 () (2010). We have re-analyzed this earlier chopped/nodded observation using the latest knowledge on calibration and data reduction and found no significant change in the flux density values. As speculated in Muller2010 () (2010) the 2009 single-visit Herschel observation was most probably contaminated by a background source.

About 75 TNOs and Centaurs in the “TNOs are Cool” program were also observed by the Spitzer Space Telescope (Werner2004 ()) using the Multiband Imaging Photometer for Spitzer (MIPS; Rieke2004 ()). 43 targets were detected at a useful signal-to-noise ratio in both the $24\mu m$ and $70\mu m$ bands of that instrument. As was done for our Herschel program, many of the Spitzer observations utilized multiple AORs for a single target, with the visits timed to allow subtraction of background confusion. The MIPS $24\mu m$ band, when combined with 70-160 $\mu m$ data, can provide very strong constraints on the temperature of the warmest regions of a TNO.

The absolute calibration, photometric methods and color corrections for the MIPS data are described in Gordon et al. (2007), Engelbracht et al. (2007) and Stansberry et al. (2007). Nominal calibration uncertaintes are 2% and 4% in the $24\mu m$ and $70\mu m$ bands respectively. To allow for additional uncertainties that may be caused by the sky-subtraction process, application of color corrections, and the faintness of TNOs relative to the MIPS stellar calibrators, we adopt uncertainties of 3% and 6% as has been done previously for MIPS TNO data (e.g. Stansberry2008 () 2008, Brucker2009 () 2009). The effective monochromatic wavelengths of the two MIPS bands we use are $23.68\mu m$ and $71.42\mu m$. With an aperture of $0.85m$ the telescope-limited spatial resolution is $6\text{arcsec}$ and $18\text{arcsec}$ in the two bands.

Spitzer flux densities of 13 targets overlapping our classical TNO sample are given in Table 4. The new and re-analyzed flux densities are based on re-reduction of the data using updated ephemeris positions. They sometimes differ by $10\text{arcsec}$ or more from those used to point Spitzer. The ephemeris information is used in the reduction of the raw $70\mu m$ data, for generating the sky background images, and for accurate placement of photometric apertures. This is especially important for the Classical TNOs which are among the faintest objects observed by Spitzer. Results for four targets are previously unpublished: 275809 (2001 QY${}_{297}$), 79360 Sila, 88611 Teharonhiawako, and 19521 Chaos. As a result of the reprocessing of the data, the fluxes for 119951 (2002 KX${}_{14}$), 148780 Altjira, 2001 KA${}_{77}$ and 2002 MS${}_4$ differ from those published in Brucker2009 () (2009) and Stansberry2008 () (2008).

The $70\mu m$ bands of PACS and MIPS are overlapping and the flux density values agree typically within $\pm 5\%$ for the six targets observed by both instruments with SNR $\gtrsim 2$.

The averages of V-band or R-band absolute magnitude values available in the literature are given in Table 1. The most reliable way of determining them is to observe a target at multiple phase angles and over a time span enough to determine lightcurve properties, but such complete data are available only for 119951 (2002 KX${}_{14}$) in our sample. For all other targets assumptions about the phase behavior have been made due to the lack of coverage in the range of phase angles.

The IAU (H,G) magnitude system for photometric phase curve corrections (Bowell1989 ()), which has been adopted in some references, is known to fail in the case of many TNOs (Belskaya2008 () 2008). Due to the lack of a better system we prefer linear methods as a first approximation since TNOs have steep phase curves which do not deviate from a linear one in the limited phase angle range usually available for TNO observations. The opposition surge of very small phase angles ($\alpha \lesssim 0.2\text{degr}$, Belskaya2008 () 2008) has not been observed for any of our 19 targets due to the lack of observations at such small phase angles. All of our Herschel and Spitzer observations are limited to the range $1.0\text{degr}<\alpha <2.1\text{degr}$.

We have used the linear method ($H_V=V-5\log \left(r\Delta \right)-\beta \alpha$, where $V$ is the apparent V-magnitude in the Johnson-Coussins or the Bessel V-band, and other symbols are as in Table 2, and $\beta$ is the linearity coefficient) to calculate the $H_V$ values from individual V-magnitudes given in the references (see Table 5) for 2001 XR${}_{254}$, 275809 (2001 QY${}_{297}$), 79360 Sila, 88611 Teharonhiawako, 148780 Altjira and 19521 Chaos. In order to be consistent with most of the $H_V$ values in the literature we have adopted $\beta =0.14\pm 0.03$ calculated from Sheppard2002 () (2002). The effect of slightly different values of $\beta$ or assumptions of its composite value used in previous works is usually negligible compared to uncertainties caused by lightcurve variability (an exception is 90568 (2004 GV${}_9$)).

For five targets with no other sources available we take the absolute magnitudes in the R-band ($H_R$ in Table 5) from the Minor Planet Center and calculate their standard deviation, since the number of V-band observations for these targets is very low, and use the average (V-R) color index for classical TNOs $0.59\pm 0.15$ (Hainaut2002 () 2002) to derive $H_V$. While the MPC is mainly used for astrometry and the magnitudes are considered to be inaccurate by some works (e.g. Benecchi2011 () 2011, Romanishin2005 () 2005), for the five targets we use the average of 9 to 16 R-band observations and adopt the average R-band phase coefficient ${\beta }_R=0.12$ (calculated from Belskaya2008 () 2008).

The absolute V-magnitudes used as input in our analysis (the “Corrected $H_V$” column in Table 5) take into account additional uncertainties from known or assumed variability in $H_V$. The amplitude, the period and the time of zero phase of the lightcurves of three hot classicals (145452 (2005 RN${}_{43}$), 90568 (2004 GV${}_9$) and 120347 Salacia) are available in the literature, but even for these three targets the uncertainty in the lightcurve period is too large to be used for exact phasing with Herschel observations. The lightcurve amplitude or amplitude limit is known for half of our targets and for them we add 88% of the half of the peak-to-peak amplitude ($1\sigma$ i.e. 68% of the values of a sinusoid are within this range) quadratically to the uncertainty of $H_V$. According to a study of a sample of 74 TNOs from various dynamical classes (Duffard2009 ()) 70% of TNOs have a peak-to-peak amplitude $\lesssim 0.2$ mag, thus we quadratically add 0.09 mag to the uncertainty of $H_V$ for those targets in our sample for which lightcurve information is not available.

The error estimates of the geometric albedo, the diameter and the beaming parameter are determined by a Monte Carlo method described in Mueller et al. (2011). We generate 500 sets of synthetic flux densities normally distributed around the observed flux densities with the same standard deviations as the observations. Similarly, a set of normally distributed $H_V$ values is generated. For those targets whose ${\chi }^2>>1$ we do a rescaling of the errorbars of the flux densities before applying the Monte Carlo error estimation as described in SantosSanz2012 () (2012) and illustrated in Mommert2012 () (2012).

The NEATM model gives us the effective diameter of a spherical target. 70-80% of TNOs are known to be MacLaurin spheroids with an axial ratio of 1.15 (Duffard2009 (), Thirouin2010 () 2010). When the projected surface has the shape of an ellipse instead of a circle, then this ellipse will emit more flux than the corresponding circular disk which has the same surface because the Sun is seen at higher elevations from a larger portion of the ellipsoid than on the sphere. Therefore, the NEATM diameters may be slightly overestimated. Based on studies of model accuracy (e.g. Harris2006 ()) we adopt uncertainties of 5% in the diameter estimates and 10% in the $p_V$ estimates to account for systematic model errors when NEATM is applied at small phase angles.