On the Nature of Ultra-faint Dwarf Galaxy Candidates. II. The Case of Cetus II

For the calibration of the instrumental magnitudes generated by the dolphot photometry, we followed the same steps as those discussed in Paper I. The GMOS-S data were cross-matched with APASS⁹  (Henden et al. 2015) calibrated DECam photometry.¹⁰ We utilized the same technique as that described in Paper I, applying the same color term and then calculating the linear offset (a combination of a zeropoint offset and atmospheric extinction correction) from a generic instrumental zeropoint. The calibration proceeds by first applying the offset directly to the raw magnitudes and then iterating the magnitudes using the color and color term to achieve the final solution, as shown in Equation (1). Apply the offset

$$\begin{eqnarray}&&\mathrm{rawmag}=\mathrm{rawmag}+\mathrm{offset}.\end{eqnarray} \tag{ 1 }$$

Iterate the magnitudes using

$$\begin{eqnarray}&&\mathrm{newmag}=\mathrm{rawmag}+\mathrm{Color}\ \mathrm{Term}\ast (g-r).\end{eqnarray} \tag{ 2 }$$

After each iteration, update rawmag to the new newmag value then repeat until the solution converges. These color terms and offsets, applied to the Cetus II field, are listed in Table 2. The selection criteria for objects to be included in the final catalog consisted of finding objects where

• 1.  
  in either filter, sharpness² ≤0.1;
• 2.  
  in both filters, signal-to-noise ratio ≥3.5;
• 3.  
  and the object type corresponds to "good stars" (Objtype = 1).

Spurious or saturated objects were removed from the catalog through either their extremely large magnitude errors or zero magnitude error respectively.

Table 2.  Photometric Calibration Results

	g band	r band
Color term (g−r)a	$+{0.026}_{-0.046}^{+0.045}$	$-{0.059}_{-0.041}^{+0.042}$
Cetus II offsets	$-{3.018}_{-0.029}^{+0.028}$	$-{2.771}_{-0.027}^{+0.026}$

Note. Color terms and offsets derived from comparison with APASS calibrated DES photometry. All photometry assumed a zeropoint of 30.00 for both filters prior to the offsets being applied. The offset values listed are a combination of the true zeropoint correction and the atmospheric extinction correction.

^aFrom Conn et al. (2018).

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Following the procedure described in Paper I, the photometric completeness of the Cetus II field was determined using the dolphot built-in artificial star experiment by generating a flat luminosity function with around 500,000 stars covering the magnitude interval 20 < m < 29 and subdivided in 0.3 mag bins. The recovery rate in each filter was fitted with a Logistic function:

$$\begin{eqnarray}&&\mathrm{Completeness}={(1+{e}^{(m-{mc})/\lambda })}^{-1},\end{eqnarray} \tag{ 3 }$$

where m is the magnitude, mc is the 50% completeness value, and λ is the width of the rollover. The parameters of the best-fit solutions are listed in Table 3 and Figure 3.

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To explore the impact of the bright stars in the field on both the photometric completeness and any potential overdensity in the field, we show the position of the unrecovered artificial stars sorted by g-band magnitude in Figure 4. Here we can see clearly the effect of the bright stars and their halos in the field. Interestingly, the biggest effect is in the magnitude range 24 < g < 26, whereas at fainter magnitudes (greater than the 50% completeness level) the distribution of unrecovered stars becomes much smoother. In general, the amount of the field lost to the bright stars is quite small as can be seen in Figure 3 where, at the brighter magnitudes, the completeness is very close to 100%. Significant loss of coverage would lower the maximum completeness level proportional to the amount of contamination.

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Figure 5 shows the extinction-corrected (g−r)_◦, g_◦ CMD of the GMOS-S field using all point sources from our photometry analysis found in the vicinity of Cetus II. The window in the brighter section of the CMD highlights the region that was investigated in the discovery paper derived from DES data (Figure 14 in Drlica-Wagner et al. 2015). The Galactic extinction correction is based on the Schlegel et al. (1998) reddening map along with the correction coefficients of Schlafly & Finkbeiner (2011). The Cetus II main sequence is prominently visible and extends from g_◦ ≈ 20.5 mag down to g_◦ = 26.3 over three magnitudes fainter than the discovery data. The limiting magnitude of the data is g_lim ∼ 27.5. Unresolved background galaxies appear as plume below g_◦ = 24.2 and −0.5 < (g−r)_◦ < +0.6. The red stars in the color interval 1.0 < (g−r)_◦ < 2.0 are the population of local Milky Way M dwarfs. The 50% photometric completeness is indicated as a dashed line and reaches g_◦ = 26.08 mag.

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For determining the properties of the Cetus II population, we computed the model isochrone that best describes the main-sequence stars distributed over the entire GMOS-S field (Figure 5) using the maximum-likelihood method introduced in Frayn & Gilmore (2002). This method was employed in our previous studies (Kim & Jerjen 2015a; Kim et al. 2015b, 2016). In brief, we calculated the maximum-likelihood values ${{ \mathcal L }}_{i}$ over a grid of Dartmouth model isochrones (Dotter et al. 2008) as defined by Equations (1) and (2) in Fadely et al. (2011). The grid points cover ages from 7 to 14 Gyr, a broad range of chemical composition −2.5 ≤ [Fe/H] ≤ −0.8 dex, −0.2 ≤ [α/Fe] ≤ +0.6 dex, and a distance interval 16.88 < (m−M) < 17.88, where the central value of 17.38 mag is the reported distance modulus for Cetus II from the discovery paper. Grid steps were 0.5 Gyr, 0.1 dex, 0.2 dex, and 0.05 mag, respectively.

Figure 6 shows the maximum-likelihood density map of the age–metallicity space for Cetus II. The well-defined location that corresponds to the best-fitting isochrone is marked with a cross. Cetus II's stellar population is found to have an age of 11.2 Gyr, an [Fe/H] of −1.28 dex, an [α/Fe] of 0.0 dex and a distance modulus of (m−M)_◦ = 17.10 ± 0.10 (26.3 ± 1.2 kpc). The corresponding isochrone is superimposed on the CMD in Figure 7 together with the associated mask. The mask has an upper and lower magnitude limit of g_o = 19.5 and 27.2, respectively. The color width of the mask for a given magnitude g_o was determined from the photometric uncertainties:

$$\begin{eqnarray*}&&{(2\pi {\sigma }_{\mathrm{tot}}^{2})}^{-1/2}\exp (-{(({g}_{* }-{r}_{* })-{(g \mbox{-} r)}_{\mathrm{iso}})}^{2}/2{\sigma }_{\mathrm{tot}}^{2})\gt 0.5,\end{eqnarray*}$$

where (g−r)_iso is the color of the model isochrone at g_o and ${\sigma }_{\mathrm{tot}}^{2}={\sigma }_{\mathrm{int}}^{2}+{\sigma }_{{g}_{* }}^{2}+{\sigma }_{{r}_{* }}^{2}$. The quantity σ_int = 0.07 mag was chosen as the intrinsic color width of the isochrone mask and ${\sigma }_{{g}_{* }}^{2}$, ${\sigma }_{{r}_{* }}^{2}$ are the photometric uncertainties of a star.

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We apply the isochrone mask to select the most likely Cetus II stars and plot their on-sky distribution in Figure 8. To highlight the positions of bright foreground stars in the field, we also overplotted objects from the AllWISE¹¹ catalog as red circles. The sizes of these circles correlate with the apparent magnitudes of the objects. We further show a large, dashed circle that represents the center and half-light radius of Cetus II as reported in Drlica-Wagner et al. (2015). Although we trace the main-sequence stars over six magnitudes, there is no evidence of any concentration of stars in the Cetus II field that would indicate the presence of an ultra-faint star cluster or dwarf galaxy candidate. We note that the two bright AllWISE stars in the field (see also Figure 2) are not affecting our ability to identify an overdensity of stars at the Cetus II location.

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As seen in Figure 1, Cetus II is projected onto the stellar density contours of the Law & Majewski (2010) model for the Sagittarius (Sgr) tidal stream. The presence of the Sgr stream at this location is observationally confirmed in Figure 1 (bottom panel) from Bernard et al. (2016). In Figure 9, we use the Law & Majewski (2010) model to further explore the possibility that the Cetus II stars are associated with the Sgr tidal stream. In the top panel (d_⊙ versus R.A.), the distance and location of Cetus II is populated by model particles that were stripped on the previous pericentric passage of Sgr (Pcol=1). The Law & Majewski (2010) particles in a 4° × 4° window around the nominal center of Cetus II with a Pcol value of 1 (40 particles in total) have an average heliocentric distance of 23.4 kpc and a scatter of σ = 2.9 kpc. Our derived Cetus II distance is in excellent agreement.

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We further compare the Cetus II distance with the Sgr Stream distance map generated from RR Lyrae stars of type ab identified in the Pan-STARRS1 3π survey (Hernitschek et al. 2017). In their Figure 1, the Cetus II stellar population is at the same distance as the Sgr stream stars cover at $({\tilde{{\rm{\Lambda }}}}_{\odot },\tilde{B})\approx (274^\circ ,-8^\circ )$. In Figure 4 of the same paper, we find that the Cetus II stars reside in the Sagittarius trailing arm.

In terms of age and metallicity, we also find excellent agreement between the Cetus II population ([Fe/H] = −1.28 ± 0.07, age $=\,{11.2}_{-0.4}^{+1.3}$) and the metal-poor Population B of Sgr ([Fe/H] = −1.2 ± 0.1, age = 11 ± 1 Gyr), e.g., Law & Majewski (2010) and Siegel et al. (2007). The final confirmation of these stars belonging to the Sagittarius tidal stream would be a spectroscopic investigation to determine their radial velocities. The Law & Majewski (2010) model prediction for stars in this part of the Milky Way halo is velocities in the range −95 km s⁻¹ < v_GSR < −60 km s⁻¹ with a mean of −78 km s⁻¹ and a standard deviation of 9 km s⁻¹, see Figure 10. At the location and distance of Cetus II, the Population B (Pcol=1) Sgr stars represent approximately 75% of the Sgr stars in the field. The photometry presented here will be used as the basis for future spectroscopic follow-up of the Cetus II region.

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Although we found strong evidence that Cetus II stars are part of the Sgr Stream trailing arm, we briefly want to look into other potential explanations for the Cetus II phenomenon. Is there another stream candidate that might explain the Cetus II stellar population? In their recent study of Milky Way halo substructures from the Pan-STARRS1 3π Survey, Bernard et al. (2016) did not report a new stream nor is there any obvious candidate stream visible in their Figure 1 at the Cetus II location. The next best alternative origin for the Cetus II stars would be the Cetus Polar Stream (CPS) (Newberg et al. 2009).

In Figure 11, we compare the density distribution of particles from the Sgr Stream simulation (Law & Majewski 2010) with five positions along the CPS measured using blue horizontal branch stars by Yam et al. (2013). The width of the CPS stream for each data point (σ_l in Table 1 of Yam et al. 2013) is represented by a horizontal error bar. The (l, b)° coordinates of Cetus II disagree with the N-body simulation of a satellite on the best-fitting CPS orbit (see Figure 18 in Yam et al. (2013). Moreover, the heliocentric distance of the CPS increases systematically from 27.2 kpc at b ∼ −36° to 32.5 kpc at b ∼ −66°. This gradient is suggesting an extrapolated distance of ≈35 kpc at the Galactic latitude of Cetus II. Hence, the measured distance of Cetus II (26.3 ± 1.2 kpc) seems incompatible. Finally, the CPS is reported in Yam et al. (2013) to have a metallicity of −2.5 < [Fe/H] < −2.0 which is significantly more metal-poor than the stellar population in the Cetus II field.

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The Cetus II case, as with Tucana V (Conn et al. 2018), highlights the complication that there are objects within the current set of candidate Milky Way satellites that are potential false-positive detections. Since they consist of a coherent stellar population but with no central overdensity, these detections could be part of tidally disrupted stellar systems, which have either small physical sizes (e.g., Kim 1, Kim & Jerjen 2015a) or are part of a much larger stream (e.g., Sgr tidal Stream). The shallow photometric depth of typical discovery data combined with perhaps the apparent random clustering of stars are driving the discovery of these objects prior to a robust confirmation of their status.

The presence of a coherent stellar population combined with marginal evidence for clustering does not automatically guarantee that they belong to a stellar overdensity as was demonstrated in Jerjen et al. (2013), where multiple stellar populations were detected without being associated with a specific object or overdensity. How then are these stellar populations being identified as overdensities? Can we attribute this to solely the chance clustering of member stars or are they examples of some underlying substructure?

Before the revision of their nature, Tucana V and Cetus II curiously occupied a very similar regime in the size–luminosity plane that we have dubbed the "TUC" in Conn et al. (2018). There were four objects in TUC of which two are now known not to be star clusters or dwarf galaxies.

Of the two remaining objects, Draco II is the brightest TUC object and has been tentatively confirmed as an ultra-faint dwarf galaxy by Martin et al. (2016a) using KECK/DEIMOS spectroscopic data, but without improving on the shallow PanSTARRS1 discovery CMD (g_lim ∼ 22.0, Figure 1, Laevens et al. 2015a). DES J0225+0304 (Luque et al. 2017) has yet to be followed up.

While spectroscopy is a good tool to test the presence of a discrete stellar overdensity, the measured velocity dispersion often used to derive the total mass is not a clean cut indicator of what type of object is being probed. For example, the classical Milky Way dwarf galaxy satellites have velocity dispersions of ∼10 km s⁻¹ (Walker et al. 2007) while the ultra-faint dwarf satellites are in the range 3.3–7.6 km s⁻¹ (Simon & Geha 2007; Kirby et al. 2015; Simon et al. 2015). The Milky Way globular cluster population on the other hand has velocity dispersions of approximately 6 ± 4 km s⁻¹ (Harris 1996). In many cases, the values are broadly consistent with the expected velocity dispersion of stars in a stellar stream, e.g., the Sagittarius tidal stream of ∼9 km s⁻¹ at the location of Cetus II. It is for this reason that confirmation and refinement of the physical properties (e.g., half-light radius, radial profile, ellipticity, and evidence of tidal disruption) of candidate ultra-faint objects are vital if we are to determine what sort of structures we are probing at these scales. However, as has been seen with Tucana V (Conn et al. 2018), scaling relations such as those presented in Forbes et al. (2014) are not applicable if, as with Cetus II, a central overdensity cannot be identified.

The original discovery of Cetus II was made using DECam with its very wide field of view; however, for low surface brightness systems such as these, the question then arises, can deep observations on a smaller field of view adequately describe the system? In Figure 12, we present the expected radial density profile for a Cetus II-like model galaxy assuming the parameters from Drlica-Wagner et al. (2015) and comparing them with the radial density profile as calculated using our data. In each case, the object has a 2D Gaussian profile centered on the Cetus II position published in Drlica-Wagner et al. (2015) and is populated with the 393 stars located in the Cetus II mask (see Figure 7). The three panels correspond to the 1σ range of possible half-light radii reported in the discovery paper: ${r}_{h}={1.9}_{-0.5}^{+1.0}$ arcmin. For each half-light radius, the stellar distribution was drawn 1000 times and a radial density profile was calculated. The lines plotted in each panel represent the properties of the total sample for a given radius. The solid line is the median, the dotted lines delimit the 1st and 3rd Quartiles and the dashed lines show the minimum and maximum values at that radius. The solid circles are the radial profile as generated using our GMOS-S data.

In the top panel of Figure 12, the most compact of the three scenarios, with a half-light radius of 1.4 arcmin, demonstrates that there are significant discrepancies between the data and model. Inside the half-light radius, the model consistently overpredicts the star density per radius compared to the data, while, at larger radii, the data outstrips the model. The middle panel, with r_h = 1.9 arcmin, the model is marginally more consistent at larger radii but the core density is still overpopulated. For the largest half-light radius (r_h = 2.9 arcmin), the median radial profile is very flat, but once again the model predicts at least 20 more stars in the innermost radii, which are not seen in the data. Even with such a flat profile, an extra 20 stars at the center of the field would be easily detected in high-quality data like those presented here.

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