Near-infrared spatially resolved spectroscopy of (136108) Haumea’s multiple systemThanks: Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, Program ID: 60.A-9235.

Figure 2.A shows the average spectra obtained in 2007 and 2011 in the 1.4–2.4 $\mu$m range. We also present the spectra corresponding to the different regions (DRS and no-DRS).

These four spectra look broadly similar with no major differences between the DRS and the no-DRS regions, and the main spectral features are that of water ice, with deep absorption bands at 1.5 $\mu$ and 2 $\mu$m. The shapes of these bands, and their relative depths between 1.50 and 1.57 $\mu$m, and around 1.65 $\mu$m, confirm that most of the H₂O ice is in its crystalline state (amorphous ice lacks the 1.57 and 1.65 $\mu$m absorption bands, while the 1.5 and 2.0 $\mu$m band shapes remain; see Grundy & Schmitt 1998). This predominance of crystalline ice is not surprising, since it is the most thermodynamically stable phase of water ice and has been widely reported on the surface of other icy outer solar system objects (e.g., satellites of giant planets and transneptunian objects).

It is important to note that the spectral difference observed in the 1.63-1.8 $\mu$m range is due to a feature of the solar analog (HD142093) used for our 2007 observations. It is clearly visible in Fig. 2.A, between 1.63-1.80 $\mu$m (gray region in Fig. 2.B), where we present the ratio between both dates for Haumea and the solar analog spectra. We decided not to remove this artifact in the spectra to conserve all the observed properties, but we excluded this wavelength region from our analysis of the spectral slope. We could not extract the spectra of the satellites because of their high proximity with Haumea.

As a result of the above analysis, we only considered the spectral ranges between 1.51-1.63 $\mu$m in H and 2.03-2.30 $\mu$m in K (represented in blue in Fig. 2.B) to measure the overall spectral slope. We determined a slope of 0.81 ($\pm$ 0.60) %/100 nm for the ratio between the data acquired in 2007 and in 2011, and a slope of 1.49 ($\pm$ 0.60) %/100 nm for the ratio between the data taken inside and outside the DRS. These values confirm thereby a redder surface for the DRS region. This behavior was so far only known for the visible part of the spectrum; present measurements are the first detection of this redder slope in the near infrared. We refined the measurements by computing the ratio of each spectrum with the average spectrum of the no-DRS region (H11_x observations, with x = [2,3,4,5]). The spectral slopes are presented in Fig. 3 and were obtained from a simple linear fit of our data over the same wavelength range as Fig. 2.

The obtained slope coefficients are presented in Fig. 4, which shows the evolution of the spectral slope versus time. The dispersion of the data points is larger for the DRS region, which is also shown by their larger error bars. Still, the average slope obtained from all DRS measurements point to a redder surface in this region. Similarly, the points with the maximum slope values (3.25 and 3.26 %/100 nm) are located at Haumea’s longitudes 30^∘ and 81^∘, respectively, i.e., within the DRS region. Even though better data are needed to improve our measurements, we can confirm from this analysis that the DRS region is spectrally redder than the rest of the surface of Haumea.

The depth of an absorption feature is computed as

where $f_{\lambda}$ is the normalized reflectance at the wavelength $\lambda$. This formula gives the percentile value of the absorption depth of a given band, which informs us about the relative quantity of the absorber and a possible indication of the path length traveled by the light. To compute this parameter we assume the ratio between the median values of the bottom band [2.00-2.05 $\mu$m] and the top band [2.20-2.25 $\mu$m], where all the spectra were normalized (at 2.225 $\mu$m). The results of the band depth are shown in Figure 5. We see that the values of the absorption band depth are in the range 40% to 60% with no significant difference between DRS and no-DRS. However, the smallest water-ice absorption (41.5%) seems to coincide with the smallest longitude (10^∘, close to the lowest maximum of the light curve). As a result, the surface material present on the DRS region, even though dominated by crystalline water ice, could correspond to a less hydrated mixture than the remaining surface of Haumea.

However, the most unambiguous characterization of the surface properties of the DRS might come from the spectral analysis of the H-band area. For this, we investigated the behavior of all Haumea spectra around the 1.50-1.63 $\mu$m absorption band (sadly, we could not study the crystalline water-ice band at 1.65 microns because of the artifact introduced by the solar analog used in our 2007 data). The integrated areas of the 1.5 $\mu$m water-ice absorption complex were computed by fitting the continuum level on either side of the absorption band (1.50 to 1.63 $\mu$m). Then we determined the value corresponding to "one minus the normalized spectrum" over the band interval, following a method proposed by Grundy et al. (2006). The results are shown in Figure 6 where we see the variations of this integrated area with time (and rotational phase). The shallow 1.56 $\mu$m band, still included in our wavelength range of study, is also of interest to investigate possible differences between amorphous and crystalline ice, as was suggested in the laboratory (Mastrapa et al. 2008). Figure 6 shows that the strongest absorptions in the H-band region are located within the DRS with a band area almost twice larger (at longitude 10^∘) than for the region outside the DRS. Indeed, contrary to the 2.0 $\mu$m band behavior (see previously), the highest absorption seems to coincide with the smallest longitude (10^∘, close to the lowest maximum of the light curve). This result points to the fact that, although the DRS might represent the less hydrated region of the surface, it could still display a higher concentration of crystalline water ice than the rest of the surface. This result itself is confirmed by the analysis of our spectral modeling explained in the next section.

We use the spectral model developed by Hapke (1981, 1993) to investigate the chemical properties of the surface of Haumea. This approach allows us to model the reflectance spectrum and the albedo of a medium, from the physical properties of the different chemical compounds present on the surface. The albedo is approximated using Eq. (44) of Hapke (1981):

where $w$ is the single-scattering albedo and $r_{0}$ the bi-hemispherical reflectance, which is purely single-scattering albedo dependent, i.e.,

where $w$ depends on the optical constants and the size of the particles and is computed for a multicomponent surface that is assumed to be intimately or geographically mixed; see Poulet et al. (2002). The parameter $B_{0}$ is the ratio of the near-surface contribution to the total particle scattering at zero phase angle and $P$ is the phase function. The method follows the instruction provided by Merlin et al. (2010), assuming an albedo approximation model with a phase angle equal to $0$, and $B_{0}$ close to 0.67 for icy objects (Verbiscer & Helfenstein 1998). The surface roughness and interference were neglected in this work.

The free parameters are the asymmetry parameters of the phase function (which is approximated by a single Henyey-Greenstein function), the particle sizes, and the abundances of the various compounds. In order to take the blue component in our model into account, we add two other parameters, $a$ and $b$, to adjust the blue continuum of the spectrum with a second degree polynomial curve. We note $x$ the wavelength, given by $x$ = ($\lambda$[i]-1.75) $\mu$m, to normalize the spectra at 2.24 $\mu$m with an albedo of 0.67. In each case, the model is adjusted to the spectra using this continuum. The result is shown in Figure 7. The normalization at 1.75 $\mu$m was correlated for each date (geometrical albedo: 0.75 and 0.702 for 2007 and 2011, respectively) taking into account the solar analog artifact described earlier and affecting the 2007 data. A previous model for the 2007 observations (Dumas et al. 2011) is also represented with a normalization at 0.60 at 1.75 $\mu$m.

We considered two sets of data: all 2007 observations in a first part (DRS) and all 2011 data (no-DRS, and excluding H11_6, which corresponds to the DRS region) in the second part. For each date, two models are used: one considering only crystalline water ice, and a second including some amorphous water ice. To constrain the free parameters, we use a best-fit model based on the Levenberg-Marquardt algorithm to minimize the reduced $\chi^{2}$. The minimization is applied outside the telluric absorption bands, which can affect the results. Best models are based on an intimate mixture of crystalline water ice (optical constants at 50K from Grundy & Schmitt 1998), amorphous carbon (from Zubko et al. 1996), and amorphous water ice (at low temperature, from Mastrapa et al. 2008). For the 2007 data, the [1.63-1.80] $\mu$m range was considered but with a lower weight than the rest of the spectra to minimize the contamination of the solar analog artifact. All the results are shown in Table 2.
Crystalline water ice with grain sizes smaller than 60 $\mu$m as the major component, with a few percent of amorphous carbon, are sufficient to fit the data. Some improvements of the fit can be obtained by adding $\sim$10% of amorphous water ice. Indeed, we see that, for the 2007 data, the presence of amorphous water ice (with large-size 0.1 mm grains) allows us to better fit the spectrum of the DRS region, as measured by the small difference of the reduced $\chi^{2}$. For the 2011 data, we obtain a nearly similar reduced $\chi^{2}$ between both models (with and without amorphous ice), although we get lower values than for 2007 owing to the analog artifact affecting our older data. If we focus on Model 2 for both epochs, we confirm our earlier result that a higher concentration of crystalline water ice is seen for the DRS region (87.0% for 2007 $vs$ 83.6% for 2011), considering all grain sizes. Finally, we note that the different amounts of amorphous carbon needed to fit the 2011 (more than 10%) and 2007 (less than 2%) also points to differences in composition between the DRS and no-DRS surfaces. It is also important to note that Hershel could not detect any “signature” associated with the DRS in its analysis of Haumea’s light curve (Lellouch et al. 2010), emphasizing the difficulty of quantifying any variation of surface properties at the spot’s location.

Taking advantage of the imaging capabilities of SINFONI, we extracted the relative astrometric position of Haumea and its largest satellite Hi‘iaka from the hyperspectral cubes of 2172 x 64 x 64 pixels. We created a broadband image by stacking the cube along the wavelength, avoiding wavelength ranges affected by telluric absorption. The resulting image, shown in Fig. 8, contains all the slices in the wavelength intervals 1.524–1.764 $\mu$m and 2.077–2.332 $\mu$m.

We used Moffat 2-D functions to determine the coordinates of the photocenters of the components, following the procedure described in Carry et al. (2011). The spatial accuracy of this measurement is about a quarter of a pixel. Owing to the rectangular shape of SINFONI pixels, it is twice as large in the north-south direction (100 mas) than along the east-west direction (50 mas). The relative positions of Hi‘iaka with respect to Haumea photocenter are listed in Table 3, and shown in Fig. 9. The brightness difference between Hi‘iaka and Haumea, which is normalized to the average brightness of Haumea, that is, removing the effect of Haumea’s high-amplitude light curve, is also reported as a magnitude difference ($\Delta$Mag) for each epoch. With the exception of the last epoch, the magnitude difference ranges from 2.6 to 3.1, with an average of 2.76 $\pm$ 0.18, in agreement with the value of 3.0 reported in Lacerda (2009). The estimation of the flux of the components is rather crude, and is reported here only for information. Namaka is not detected in 2011 image (see Fig. 8), although its detection is within SINFONI capabilities (Dumas et al. 2011, see Fig. 8 and). It is likely that Namaka was angularly too close to Haumea at the time of the observations, as suggested by its predicted position at (0″.008, -0″.110), based on the orbit by Ragozzine & Brown (2009) and our own computations below, thus less than 2 pixels from the center of Haumea.

where $n$ is the number of observations, and $x_{i}$ and $y_{i}$ are the relative position between Hi‘iaka and Haumea along the right ascension and declination, respectively. The exponents $o$ and $c$ stand for observed and computed positions, and exponent $e$ stands for measured error. For convenience, in the following text, we express the fitness function as the quadratic mean of the residuals. The main advantage of this fitness function is to provide a link between the quality of the fitted orbit and the uncertainties of the astrometric positions provided by the ephemeris. A definition and discussion about estimating uncertainties in astronomy can be found, for example, in Andrae (2010), Andrae et al. (2010), and references therein.
We used a total of 35 astrometric positions, spread over 2264 days or 46.2 orbital periods, to determine the orbit of Hi‘iaka. The orbit of Namaka is based on 30 observations spread over 1175 days or 64.1 orbital periods. We added to the set of HST observations, the positions measured on SINFONI spectral cubes in 2007 and 2011 (see above) and the set of observations obtained with NIRC2 on the W. K. Keck II telescope (pixel scale of 9.963 mas) between 2005 and 2008 reported by Brown et al. (2005), Brown et al. (2006), and Ragozzine & Brown (2009).
Albeit the intrinsic precision of Keck images is deemed cruder than that of HST, which benefits from highly stable PSF, and the absolute link between HST and Keck astrometry is unknown (pixel scale and field orientation), we favor orbital solutions based on a longer time baseline that are more sensitive to departures from a pure Keplerian motion. Because of these points, however, the goodness of fit is expected to be lower. The addition of Keck data here corresponds to an increase of 350 days of time coverage. Compared to the case using only HST data, as carried out by Ragozzine & Brown (2009), this represents 44% of the temporal baseline. This baseline is longer with the addition of the SINFONI measurements in 2011, the leverage provided by Keck data is of 20% (see Fig. 10).

We run two separate orbital fits: one assuming the central object (Haumea) to be a point-like mass and the satellites to be massless test particles (i.e., Genoid-Kepler), and one considering the zonal harmonic coefficients $J_{2}$ and $J_{4}$ of the central object, its size, and the coordinates of its pole of sidereal rotation (i.e., Genoid-ANIS).

Figure 11 shows the residual positions (between observed and computed) obtained normalized by the positional uncertainty. We list in Table 4 the orbital parameters of Hi‘iaka and Namaka obtained with Genoid-Kepler. They correspond to the same geometry as the orbits presented by Ragozzine & Brown (2009), albeit Namaka eccentricity is found to be lower (0.15 here vs 0.25). We note the existence of a numerical solution with similar residuals ($f_{p}$ =10.7 mas) in which the orbital motion of Hi‘iaka is reversed. We do not consider this solution here.