Mid-infrared characterization of the planetary-mass companion ROXs 42B b

TL;DR

This study presents new mid-infrared photometry of the planetary-mass companion ROXS 42B b, compares it with models and other objects, and explores its atmospheric properties, revealing unique features and uncertainties in atmospheric composition.

Contribution

First mid-infrared photometry of ROXS 42B b combined with existing data, providing new insights into its atmospheric characteristics and diversity among young planetary-mass objects.

Findings

ROXS 42B b's spectral energy distribution resembles GSC 06214 B and κ And b.

Models with atmospheric dust/clouds fit the data better than dust-free models.

Atmospheric retrieval limits CO₂ fractional density to log(n_CO2)<-2.7.

Abstract

We present new Keck/NIRC2 3$-$5 $\mu$m infrared photometry of the planetary-mass companion to ROXS 42B in $L^\prime$, and for the first time in Brackett-$\alpha$ (Br$\alpha$) and in $M_\mathrm{s}$-band. We combine our data with existing near-infrared photometry and $K$-band (2$-$2.4 $\mu$m) spectroscopy and compare these with models and other directly imaged planetary-mass objects using forward modeling and retrieval methods in order to characterize the atmosphere of ROXS 42B b. ROXS 42B b's 1.25$-$5 $\mu$m spectral energy distribution most closely resembles that of GSC 06214 B and $\kappa$ And b, although it has a slightly bluer $K_{\rm s}$$-$$M_{\rm s}$ color than GSC 06214 B and thus so far lacks evidence for a circumplanetary disk. We cannot formally exclude the possibility that any of the tested dust-free/dusty/cloudy forward models describe atmosphere of ROXS 42B b well. However, models with substantial atmospheric dust/clouds yield temperatures and gravities that are consistent when fit to photometry and spectra separately, whereas dust-free model fits to photometry predict temperatures/gravities inconsistent with ROXS 42B b's $K$-band spectrum and vice-versa. Atmospheric retrieval on the 1$-$5 $\mu$m photometry places a limit on the fractional number density of CO$_2$ of $\log(n_{\rm CO_2})<-2.7$ but provides no other constraints so far. We conclude that ROXS 42B b has mid-IR photometric features that are systematically different from other previously observed planetary-mass and field objects of similar temperature. It remains unclear whether this is in the range of the natural diversity of targets at the very young ($\sim$2 Myr) age of ROXS 42B b, or unique to its early evolution and environment.

Tables

Table 1. Table 1: Observing Log: 2015-06-15, Keck/NIRC2

Object	Obs. Time	Filter	$t_{\mathrm{int}}$	$N_{\mathrm{images}}$	PA (start)	PA (end)
	UT		(s)		(∘)	(∘)
ROXs 42B	07:20:17	$L^{\prime }$	20	13	$-$42.99	$-$38.96
ROXs 42B	07:44:55	$M_s$	30	18	$-$36.79	$-$32.99
ROXs 42B	08:03:34	Br$\alpha$	30	9	$-$32.16	$-$30.82
HD 141569A	08:16:18	$L^{\prime }$	50	74	$-$27.16	18.75
HD 141569A	09:43:39	$L^{\prime }$	0.075	6	…	…
HD 141569A	09:46:11	Br$\alpha$	1	6	…	…
HD 141569A	09:48:42	$M_s$	0.1	6	…	…
ROXs 42B	09:53:33	$M_s$	30	18	1.87	7.10
ROXs 42B	10:11:16	Br$\alpha$	30	18	7.81	11.74

Table 2. Table 2: Photometry of ROXS 42B and ROXS 42B b

			primary		Companion		apparent		Abs Mag
UT Date	Telescope/Camera	Filter	mag		$\Delta$mag		Mag		(dereddened)		S/Na𝑎aa𝑎a$a$Signal-to-noise ratio as derived in Sect. 3.2	ref.
2011-Jun-22	Keck/NIRC2	$J$	9.906 $\pm$	0.020b𝑏bb𝑏b$b$From the 2MASS catalog (Cutri et al., 2003)	7.00 $\pm$	0.11	16.91 $\pm$	0.11	10.75 $\pm$	0.17	11c	2
2011-Jun-22	Keck/NIRC2	$H$	9.017 $\pm$	0.020b𝑏bb𝑏b$b$From the 2MASS catalog (Cutri et al., 2003)	6.86 $\pm$	0.05	15.88 $\pm$	0.05	9.87 $\pm$	0.14	33c	3
2011-Jun-22	Keck/NIRC2	$K_s$	8.671 $\pm$	0.020b𝑏bb𝑏b$b$From the 2MASS catalog (Cutri et al., 2003)	6.34 $\pm$	0.06	15.01 $\pm$	0.06	9.14 $\pm$	0.14	52c	2
2016-Jun-08	Keck/NIRC2	$L^{\prime }$	8.42 $\pm$	0.05	5.55 $\pm$	0.06	13.97 $\pm$	0.06	8.23 $\pm$	0.10	22.2	1
2016-Jun-08	Keck/NIRC2	Br$\alpha$	8.37 $\pm$	0.06	5.53 $\pm$	0.05	13.90 $\pm$	0.08	8.18 $\pm$	0.12	14.5	1
2016-Jun-08	Keck/NIRC2	$M_s$	…		…		14.01 $\pm$	0.23	8.31 $\pm$	0.24	6	1

Table 3. Table 3: 5 σ 𝜎 \sigma detection limits

	$\Delta$ (mag) at $\rho$ =
Filter	0$\stackrel{\prime \prime }{.}$10	0$\stackrel{\prime \prime }{.}$25	0$\stackrel{\prime \prime }{.}$50	0$\stackrel{\prime \prime }{.}$75	1″	2″
$L^{\prime }$	3.5	6.6	7.2	7.8	8.4	9.2
Br$\alpha$	3.7	6.0	7.4	7.5	7.7	7.7
$M_s$	3.1	5.5	6.6	6.7	7.1	7.0

Table 4. Table 4: Used models and input parameter ranges

Model family	$T_{\mathrm{eff}}$	$\log g$	Ref.
Without dust in the atmosphere
AMES-COND	1500–3000	2.5–5.5	1,2
BT-COND	1500–2500	4.0–5.5	3
	2600–3000	2.5–5.5
With atmospheric dust
AMES-DUSTY	1500–3000	3.5–5.5	1,4
BT-DUSTY	1500–2500	4.5–5.5	3
	2600–3000	2.5–5.5
With a cloud model
BT-SETTL	1500–1900	3.5–5.5	3
	2000–3000	2.5–5.5
BT-SETTL-2015	1500–1900	3.5–5.5	5
	2000–3000	2.5–5.5
Burrows	1900–2400	3.4–4.0	6

Table 5. Table 5: Fitting results

	best fit					rangea𝑎aa𝑎a$a$Parameter range of models that are consistent with the data according to their significance $P$$>$0.05 (see Sect. 3.3). Numbers in italics are at the limit of the probed model parameter space (see Table 4).
Model family	$T_{\mathrm{eff}}$	$\log g$	$R$ ($R_{\mathrm{Jup}}$)	${\chi }_{\min }^2$	$P\left({\chi }_{\min }^2\right)$	$T_{\mathrm{eff}}$	$\log g$	$R$ ($R_{\mathrm{Jup}}$)
$J$$H$$K_s$$L^{\prime }$Br$\alpha$$M_s$ photometry ($N$=6)
AMES-COND	1700	2.5	3.4	10.0	0.07	1700	2.5	3.4
BT-COND	1800	4.0	3.1	14.1	0.01	…	…	…
AMES-DUSTY	2000	5.0	2.5	4.1	0.54	1800–2100	3.5–5.5	2.4–2.8
BT-DUSTY	1900	4.5	3.0	5.5	0.36	1700–2000	4.5–5.5	2.6–3.2
BT-SETTL	2000	3.0	2.4	2.5	0.78	1600	4.5	3.4
						1800–2100	2.5–5.5	2.3–3.2
BT-SETTL-2015	1900	4.5	2.6	2.3	0.81	1700–2100	2.5–5.5	2.4–3.1
Burrows	1900	3.4	2.2	1.5	0.91	1900–2100	3.4–4.0	2.0–2.7
$K$-band spectroscopy ($N$=292)
AMES-COND	2800	4.0	1.5	265	0.86	2700–3000	3.5–4.5	1.3–1.6
BT-COND	2600	3.5	1.6	212	1	2500–2800	2.5–4.5	1.4–1.7
AMES-DUSTY	2700	3.5	1.5	252	0.95	1600–1700	5.5	2.9–3.2
						2600–2900	3.5–4.5	1.3–1.6
BT-DUSTY	2300	4.5	1.8	211	1	1600–2000	4.5–5.0	2.6–4.7
						2300	4.5	1.8
						2600–2800	2.5–4.5	1.4–1.8
BT-SETTL	2400	2.5	1.8	173	1	1500–1800	3.5	2.9–4.1
						1700	3.5–5.0	3.0–3.3
						2000–2800	2.5–4.5	1.4–2.3
BT-SETTL-2015	2700	3.5	1.5	234	1	1500–1600	2.5–3.0	3.7–4.6
						1500–1600	4.0	3.4–3.7
						2400–2900	3.0–4.5	1.3–1.8
Burrows	2100	3.6	1.9	316	0.15	1950–2100	3.4–3.6	1.9
Spectroscopy+photometry ($N$=298)
AMES-COND	2800	4.0	1.5	338	0.05	2800	4.0	1.5
BT-COND	2600	3.5	1.7	259	0.95	2600–2700	2.5–4.5	1.5–1.7
AMES-DUSTY	2700	3.5	1.6	315	0.23	2600–2800	3.5–4.0	1.5–1.7
BT-DUSTY	1800	4.5	3.4	234	1	1600–2000	4.5–5.0	2.6–3.9
						2300	4.5	1.9
						2600–2700	2.5–4.5	1.5–1.7
BT-SETTL	2300	2.5	2.0	196	1	1500–1800	3.5	2.8–3.6
						1700	3.5–5.0	2.8–3.4
						2000–2700	2.5–4.5	1.5–2.4
BT-SETTL-2015	2600	3.5	1.6	294	0.54	1500	3.0	3.8
						2500–2800	3.0–4.0	1.4–1.8
Burrows	2100	3.6	2.0	323	0.14	1950–2100	3.4–3.8	2.0–2.5

Full text

1 Introduction

In the past decade, direct imaging observations of nearby young stars have revealed over a dozen companions with estimated masses between 4 and 13 $M_{\mathrm{Jup}}$ (Bowler, 2016, and references therein). Multiwavelength photometry and/or spectroscopy of the first of these planetary-mass companions (e.g., HR 8799 bcde, 2M 1207 B; Marois et al. 2008, 2010; Chauvin et al. 2004) revealed key differences with field brown dwarfs, with color-magnitude diagram positions following a reddened extension of the L dwarf sequence to fainter magnitudes and cooler temperatures. Compared to field objects of the same effective temperatures (early T dwarfs), their atmospheres are substantially cloudier and exhibit stronger non-equilibrium carbon chemistry (Currie et al., 2011; Galicher et al., 2011). The companions’ low surface gravities drive these two effects, allowing clouds to extend higher up into the atmosphere and enhancing vertical mixing of carbon monoxide. More generally, these objects and other similar ones reveal a gravity/age dependent transition from L type (cloudy and methane poor) to T type (mostly clear and methane rich) (Marley et al., 2012).

More recently, analysis of hotter directly imaged planetary companions ($T_{\rm eff}$ $\sim$ 1500–2500 $K$) like $\beta$ Pictoris b and other young L-type objects have also revealed differences with old field L dwarfs. Typically, these objects lie redward of the field sequence in both near- and mid-infrared color-magnitude diagrams (Currie et al., 2013; Faherty et al., 2016) and are likewise thought to be particularly cloudy and – like the HR 8799 planets – low gravity. Analyzing other directly imaged L-type planetary companions allows us to determine whether they share these characteristics.

While directly imaged planets have typically been analyzed using atmosphere forward modeling (e.g., Currie et al., 2011), some recent studies have instead adopted a “spectral retrieval” method. With retrieval methods, the key features of a planet’s atmosphere – surface gravity, composition, and pressure-temperature profile – are treated as free parameters. Although the input physics is simpler than that of forward models, retrieval allows robust determinations of the uncertainty in individual parameters, such as the abundances of the main molecular constituents, the shape of the pressure-temperature profile, and the surface gravity. Retrieval has been applied toward modeling infrared photometry of transiting planets (e.g., Madhusudhan & Seager, 2009; Line et al., 2012; Barstow et al., 2017) and has now been utilized for the directly imaged planets HR 8799 b and $\kappa$ And b (Lee et al., 2013; Lavie et al., 2016; Todorov et al., 2016), both of which are at least 30 Myr old but cover a wide range of temperatures (800–2000 K; Marois et al., 2008; Currie et al., 2011; Carson et al., 2013; Hinkley et al., 2013).

The wide-separation companion to ROXS 42B (ROXS 42B b, Currie et al., 2014a) provides another insight into the properties of the youngest and highest temperature planetary-mass objects. First identified as a candidate companion by Ratzka et al. (2005) and subsequently confirmed to be a bound companion (Currie et al., 2014a; Kraus et al., 2014), ROXS 42B b orbits a close binary M star (Simon et al., 1995) that is a likely member of the 2–3 Myr-old $\rho$ Ophiuchus star-forming cloud. Given this age, adopting a distance of 135 pc (Mamajek, 2008), and assuming standard planet cooling models (e.g., Baraffe et al., 2003), ROXS 42B b is most likely a $\sim$ 9$\pm$3 $M_{\mathrm{Jup}}$ companion orbiting at $\sim$ 150 au, slightly more massive and at a somewhat wider orbital separation than HR 8799 b (70 au, Marois et al., 2008). Early analysis of ROXS 42B b’s near-infrared colors reveals that it too is redder than the field L dwarf sequence (Currie et al., 2014a); its spectrum shows evidence for a low surface gravity (Currie et al., 2014a; Bowler et al., 2014). The first atmospheric modeling of ROXS 42B b argues in favor of thicker clouds than field L dwarfs of the same temperature and implies a mass broadly consistent with cooling model estimates (Currie et al., 2014b).

New thermal infrared photometry of ROXS 42B b expand the wavelength coverage for this planetary object and allow us to better probe trends found in other young planets. For example, in the case of $\beta$ Pic b, atmospheric forward models fit to the planet’s rather flat spectral energy distribution in the thermal infrared provided evidence not only of thick clouds, but also of small dust grains in its atmosphere (Currie et al., 2013). For the HR 8799 planets, 3–5 $\muup$m imaging probed non-equilibrium carbon chemistry (Galicher et al., 2011). Thermal infrared imaging of GSC 06214 B identified extremely red colors consistent with a circum(sub)stellar disk, corroborating evidence for an accretion disk from spectroscopy (Bowler et al., 2011). While somewhat shallow $L^{\prime}$ imaging of ROXS 42B b has already been published (Kraus et al., 2014; Currie et al., 2014b), deeper $L^{\prime}$ data and photometry obtained at longer wavelengths clarify the object’s overall spectral energy distribution shape and may better point to trends in young hot planet atmospheres. Analyzing ROXS 42B b with spectral retrieval methods may place further quantitative constraints on its molecular abundances.

Here we present new photometry in the $L^{\prime}$ ($\lambda_{\mathrm{c}}$=3.78 $\muup$m), Br$\alphaup$ ($\lambda_{\mathrm{c}}$=4.05 $\muup$m), and $M_{\mathrm{s}}$ filters ($\lambda_{\mathrm{c}}$=4.67 $\muup$m) observed with the NIRC2 instrument on Keck. Section 2 describes the observations and data; Sect. 3 presents our photometry as well as an analysis using spectral fitting and retrieval methods. Results are presented in Sect. 4 and discussed in Sect. 5.

2 Observations and data reduction

Photometry was obtained on June 8, 2015, using the NIRC2 infrared imaging instrument on the Keck telescope. The narrow camera was used in pupil-stabilized mode featuring a pixel scale of 9.952$\pm$0.050 mas/pix (Yelda et al., 2010). Individual exposure times were 0.2, 1.0, and 0.1 seconds in $L^{\prime}$, Br$\alphaup$, and $M_{\mathrm{s}}$, respectively; the number of coadds were adjusted to add up to integration times of 20 ($L^{\prime}$) and 30 seconds (Br$\alphaup$, $M_{\mathrm{s}}$) per exposure and filter. Overall, we obtained total on-source integration times of 13$\times$20 sec=260 sec, 27$\times$30 sec = 810 sec, and 36$\times$30 sec = 1080 sec in $L^{\prime}$, Br$\alphaup$, and $M_{\mathrm{s}}$, respectively. A summary of the observational parameters is presented in Table 1.

Individual images were bad-pixel corrected, flat-fielded, and sky subtracted. Sky frames were composed from on-source science exposures, which were taken in a 3-point dither pattern, through median combination. A distortion correction was applied using the nirc2dewarp.pro IDL routine111http://www2.keck.hawaii.edu/inst/nirc2/dewarp.html. Modest field rotations of \lesssim$$5^{\circ} were achieved in all filters. Accordingly, no high-angular resolution postprocessing algorithms (e.g., LOCI, PCA) were applied, but instead we derotated and stacked all images obtained in a filter to increase the signal-to-noise ratio (S/N). Figure 1 shows our final reduced images in the $L^{\prime}$, Br$\alphaup$, and $M_{\mathrm{s}}$ filters after subtracting a radially averaged profile from the primary to reduce the seeing halo.

3 Analysis

3.1 Photometry

For photometric calibration, we observed HD 141569 close in time. We compensated for the difference in airmass (target am$\approx$1.4–1.6, std am$\approx$1.1) using the corrections described in Tokunaga et al. (2002), subtracting 0.05, 0.075, and 0.1 mag from the calculated apparent $L^{\prime}$, Br$\alphaup$, and $M_{\mathrm{s}}$ magnitudes, respectively. For this B9.5 spectral type star (Merín et al., 2004) we assume intrinsic H$$-$$M_{\mathrm{s}} $\approx$ 0.0 and H$$-Br$\alphaup$ $\approx$ 0.0 colors (we note that both J$$-$$H and H$$-$$K_{\mathrm{s}} are $<$0.05 mag) and thus infer $M_{\mathrm{s}}$ = Br$\alphaup$ = $H$ = $6.86$ mag.

It was discovered during the analysis that the photometric standard shows Br$\alphaup$ in emission (Sean Brittain, private communication). While this has no strong effect on our $L^{\prime}$ photometry (Br$\alphaup$ emission line width $\sim$0.01 $\muup$m $\ll$ filter width $\approx$0.75 $\muup$m), we cannot use HD 141569 to calibrate our 4.05 $\muup$m photometry. Instead, we measure the magnitude difference between ROXS 42B b and its host star using PSF photometry with the primary as PSF reference. The measured $\Delta$Br$\alphaup$=5.53$\pm$0.05 mag is translated into an apparent magnitude of Br$\alphaup$=13.90$\pm$0.08 mag by estimating the primary’s Br$\alphaup$ brightness from its $K_{\mathrm{s}}$-band magnitude and K_{\mathrm{s}}$$-Br$\alphaup$ color. The latter we determine as K_{\mathrm{s}}$$-Br$\alphaup$=0.298 $\pm$ 0.06 mag by linearly interpolating the expected K_{\mathrm{s}}$$-W1=0.11$\pm$0.01 mag and K_{\mathrm{s}}$$-W2=0.17$\pm$0.01 mag colors of a young M0-type star (Pecaut & Mamajek, 2013) at 4.05$\muup$m [(K_{\mathrm{s}}$$-Br$\alphaup$)intrinsic=0.159 mag] and adding a reddening of E(K_{\mathrm{s}}$$-Br$\alphaup$)=0.139 mag using an $R_{\mathrm{V}}$=3.1 extinction law (Mathis, 1990) and the ROXS 42B extinction of $A_{\mathrm{V}}$ = 1.9${}^{+0.3}_{-0.2}$ mag (Currie et al., 2014a). The uncertainty of the K_{\mathrm{s}}$$-Br$\alphaup$ color is calculated from the uncertainty of both the interpolation and the dereddening.

We derive dereddened absolute magnitudes of ROXS 42B b assuming a distance of 135 $\pm$5 pc from Mamajek (2008) and assuming that the extinction is the same as for the primary. Table 2 shows our new $>$3 $\muup$m photometry together with previous observations at shorter wavelengths. The new $L^{\prime}$ photometry is consistent with previous measurements by Currie et al. (2014b).

3.2 Sensitivity and signal-to-noise ratio

To estimate the S/N, we measure the flux in 16 apertures333In the case of $L^{\prime}$, three apertures were too close to the edge of the detector and have been disregarded of radius 0$\aas@@fstack{\prime\prime}$043 ($L^{\prime}$, Br$\alphaup$) and 0$\aas@@fstack{\prime\prime}$060 ($M_{\mathrm{s}}$), distributed along a circle of 0$\aas@@fstack{\prime\prime}$28–0$\aas@@fstack{\prime\prime}$35 radius centered on the companion. Comparing the standard deviation of the noise measurement to the flux in an aperture of the same size centered on the companion, we infer S/N of 22.2, 14.5, and 5.7 for our detections of ROXS 42B b in $L^{\prime}$, Br$\alphaup$, and $M_{\mathrm{s}}$, respectively.

Fig. 2 shows our 5$\sigma$ sensitivity to the detection of any additional companions in the field of view.

Contrast was derived as in the above scheme, but noise apertures were distributed on circles with radii between 0$\aas@@fstack{\prime\prime}$05 and 2$\aas@@fstack{\prime\prime}$5 around the primary star and the number of apertures was set to the maximum possible number fitting on this circle with no overlap between neighboring apertures. The values are listed in Table 3.

3.3 Model fitting

We compare the photometric SED of ROXS 42B, including the new mid-IR photometry, as well as published K-band (1.95–2.45 $\muup$m) spectroscopy (Currie et al., 2014a) to stellar atmosphere models. In order to explore whether any additional constraints can be obtained from the new mid-infrared photometry, we select a similar set of models to those used in Currie et al. (2014b). We compare three types of models, those with dust-free atmospheres (AMES-COND, BT-COND), models with uniformly dusty atmospheres (AMES-DUSTY, BT-DUSTY), and models with a cloud model (for references see Table 4). The third category includes BT-SETTL and our own models, hereafter called Burrows models, which feature a thick cloud layer and small dust grains. Where possible, models were retrieved from the Theoretical spectra server444svo2.cab.inta-csic.es/theory/newov/ for consistent data formats (all except BT-SETTL (2015) and the Burrows models), spanning effective temperatures of $T\!_{\mathrm{eff}}$=1500 K…3000 K in steps of 100 K, surface gravities of $\log g$=2.5…5.5 in steps of 0.5, and keeping metallicity fixed at a solar level. Other metallicity values were not available for most of the models, in particular none in the interesting temperature range of 1500 K–2500 K. Spectra from the BT-SETTL (2015) grid were retrieved directly from the respective web repositories555https://phoenix.ens-lyon.fr/Grids/BT-Settl/ covering the same parameter range. Burrows models span a smaller range from $\log g$=3.4 to 4 and $T\!_{\mathrm{eff}}$=1900…2400, spaced by 50 K ($<$2000 K) and 100 K ($>$2000 K). See Table 4 for a summary of the models and probed parameter space.

For every parameter combination ($T\!_{\mathrm{eff}}$,$\log g$) we calculate $\chi^{2}=\sum_{i}w_{i}((f_{\mathrm{data},i}-c\cdot f_{\mathrm{model},i})/\sigma_{i})^{2}$, where $f_{\mathrm{data},i}$ are the photometric data from Table 2, $\sigma_{i}$ are the measurement uncertainties, and $c=(R/10\,\mathrm{pc})^{2}$ is a dilution factor dependent on the radius $R$ of the object. In the case of photometry, $f_{\mathrm{model},i}$ is obtained by multiplying the model spectrum with the respective filter curves. To compare the models with spectroscopy, we use the $K$-band spectrum of ROXS 42B b as presented by Currie et al. (2014a), i.e., binned to the resolution of the Burrows models of $R\approx 300$. Model spectra of the other families were rebinned to the same resolution. To account for the varying number of resolution elements in each filter, every data point is weighted with $w_{i}$ proportional to the FWHM of the photometric filter or the width of the spectroscopic resolution element, respectively (Cushing et al., 2008). The validity of $\chi^{2}$ is conserved by normalizing the weighting factors so that $\sum w_{i}=N$, identical to the number of data points. In the case of fitting the combined spectroscopy and photometry, weights for the photometric filters are $w_{J}$=18, $w_{H}$=33, $w_{K_{\mathrm{s}}}$=34, $w_{L^{\prime}}$=77, $w_{\mathrm{Br}\alpha}$=7.2, and $w_{M_{\mathrm{s}}}$=28, while a spectroscopic element is weighted with $w_{\mathrm{spec}}$=0.18. Because the spectroscopy was calibrated with the $K$-band photometry, it entered the combined fit as $\chi^{2}=\sum_{i}w_{i}((f_{\mathrm{phot},i}-c\cdot f_{\mathrm{model},i})/\sigma_{i})^{2}+\sum_{j}w_{\rm spec}((f_{\mathrm{spec},j}-c^{*}\cdot f_{\mathrm{model},j})/\sigma_{j})^{2}$ for $i=\{1,\dots,6\}$ photometric and $j=\{1,\dots,292\}$ spectroscopic data points. The scaling factor $c^{*}$ minimizes the second summand and may be different from $c$. This way we avoid giving the $K$-band photometry overproportional weight as it has already been used for absolute calibration of the spectrum.

Prior to fitting, our photometry and spectroscopy were dereddened assuming $A_{\mathrm{V}}$=1.9 mag and an $R_{\mathrm{V}}$=3.1 extinction law (Mathis, 1990) and converted to flux density units using the zero points in Currie et al. (2013). We note that assuming an extinction of $A_{\mathrm{V}}$=1.7 mag as derived by Bowler et al. (2014) does not lead to significantly different fitting results. The K-band spectroscopy was flux calibrated by scaling it so that integration over the 2MASS $K_{\mathrm{s}}$ filter curve reproduces the ROXS 42B b $K_{\mathrm{s}}$ magnitude (Table 2). The uncertainty of the calibration enters our fit as an uncertainty of the derived radius ($\sim$15%).

Best fits for every model in the grid were determined through $\chi^{2}$ minimization using the mpfit.pro procedure in IDL (Markwardt, 2009) with the dilution factor $c$ as the parameter of interest. This implies $n_{\mathrm{dof}}$=N$$-1 degrees of freedom (where $N$ can assume either the number of photometric data points, the number of spectral resolution elements, or their sum, depending on the statistical test we perform), which is used to calculate the statistical significance $P$ for each best-fit model, i.e., the chance to obtain the measured $\chi^{2}_{\rm min}$ assuming that the model represents the data. For $P<0.05$, the hypothesis that the model is an acceptable representation of the data is rejected with 95% confidence.

The ranges of $T\!_{\mathrm{eff}}$ and $\log g$ of all models that are not rejected are listed in Table 5 together with the best-fit parameters for fits of the JH$$K_{\mathrm{s}}$$L^{\prime}Br\alphaup$$M_{\mathrm{s}} photometry, the K-band spectroscopy, and their combination, respectively. Fig. 3 shows the best fits to all available JH$$K_{\mathrm{s}}$$L^{\prime}Br\alphaup$$M_{\mathrm{s}} photometry.

In Fig. 4 we show all best-fit models for the example of the Burrows models to illustrate the diversity of spectra that satisfy $P>0.05$. The panels show all selected models for the following four cases: a) when only near-infrared photometry is fit, b) when using fits to all JH$$K_{\mathrm{s}}$$L^{\prime}Br\alphaup$$M_{\mathrm{s}} photometry, c) when fitting $K$-band spectroscopy alone, and d) when fitting all 1–5 $\muup$m photometry and $K$-band spectroscopy. It can clearly be observed how the choices of input data constrain the range of acceptable model fits.

3.4 Retrieval

To investigate how the mid-IR photometry constrains the atmospheric properties of ROXS 42B b, we adapted the spectral retrieval code described in Todorov et al. (2016) to accept photometric input. We refer to Todorov et al. for a detailed description of the method, and here give a brief summary and describe the adaptions made.

In order to fit the photometric points with a model, we require a computationally cheap approach that takes a very limited number of free parameters as input and produces a model emission spectrum. The approach we take utilizes the plain parallel approximation for the companion’s atmosphere, containing 50 layers spaced equally in the log of pressure. All layers contain the same abundances of the chemical species we consider, at a temperature and pressure specified by a pressure-temperature (P-T) profile. The number densities as a fraction of the total number of CH4, CO, CO2, H2O, C2H2, HCN, and NH3 are free parameters. Additional free parameters include the surface gravity of the object and the temperatures of six layers spaced equally (in $\log(P)$) throughout the atmosphere. The temperatures corresponding to the other layers are interpolated to create a smoothly varying P-T profile. We experiment with sampling the pressure range by dividing it into more layers and fewer layers, but we find no impact on the upper limits we are able to place on the number densities of molecules. For CO, CO2, and H2O we adopt the opacities from the HITEMP data base (Rothman et al., 2010), while those for CH4, C2H2, HCN, and NH3 are adopted from Freedman et al. (2014). Collision-induced opacities for H2-H2 and H2-He are also included (Borysow et al., 2001; Borysow, 2002).

We assume a cloud-free atmosphere. The effect of clouds would be to make the spectrum appear flatter (see, e.g., Lee et al., 2013) because emission from below the cloud deck, i.e., at high temperatures, is being absorbed. The strength of this effect as a function of wavelength depends on the assumed cloud model, e.g., particle material, size distribution, and shape, as well as the horizontal extent of the clouds (patchy versus full coverage), and their vertical extent and particle column density. While degeneracies introduced by clouds, for example between molecular abundances and cloud presence, may be resolved by high signal-to-noise spectroscopy studies (e.g., L-band spectroscopy, see Figure 1 in Lee et al., 2013), the current data set does not constrain enough parameters to justify introducing a complex cloud model.

The fitting approach we employ to match this simple emission model to the observed photometry is a Markov chain Monte Carlo (MCMC) setup, based on the Metropolis-Hastings algorithm using a Gibbs sampler and a Gaussian trial value probability distribution (Ford, 2005, 2006). Our specific implementation is discussed in detail in Todorov et al. (2012). We assume flat priors for all free parameters. We run the chain for $10^{6}$ iterations and in our analysis we discard the initial 10%, where chain convergence occurs, to avoid biasing our results.

4 Results

4.1 Infrared colors of ROXS 42B b

We compare the near- to mid-IR photometry of ROXS 42B b with the photometry of field dwarfs from the compilation by Leggett et al. (2010), spanning spectral types between M7 and T5, equivalent to temperatures between $\sim$2500 K and 700 K. In addition, we include the photometry of young directly imaged planetary mass objects around $\beta$ Pic (Currie et al., 2013), HR 8799 (Marois et al., 2008, 2010; Currie et al., 2011), $\kappa$ And (Carson et al., 2013), GSC 06214 (Ireland et al., 2011; Bailey et al., 2013), and RXS 1609 (Lafrenière et al., 2010) using the photometry compiled by Currie et al. (2013), and the updated HR 8799 near-IR photometry by Zurlo et al. (2016).

Fig. 5 shows color-color diagrams featuring the new mid-IR $L^{\prime}$, Br$\alphaup$, and $M_{\mathrm{s}}$-band photometry of ROXS 42B b.

Like some of the other young low-mass objects (but not, for example, HR 8799bcd), ROXS 42B b takes a rather inconspicuous position with respect to the J$$-$$K_{\mathrm{s}} and K_{\mathrm{s}}$$-$$L^{\prime} colors of field brown dwarfs, on top of the L-type sequence, close to the M-L spectral type transition. Among young low-mass targets with measured K_{\mathrm{s}}$$-$$M_{\mathrm{s}} or L^{\prime}$$-Br$\alphaup$ color, ROXS 42B b appears as one of the bluest. In these colors, which show no color inversion with temperature (unlike L^{\prime}$$-$$M_{\mathrm{s}}, see the right panel of Fig. 6), this is likely due to its comparably high temperature at a young age compared to the other targets with temperatures in the range of $\sim$1000–2200 K.

Its position in infrared color-magnitude diagrams (Fig. 6) reveals a higher luminosity compared to field targets of the same color.

GSC 06214 B is the only other young target in the diagram with a brightness comparable to that of ROXS 42B b. However, it has a slightly redder K_{\mathrm{s}}$$-$$M_{\mathrm{s}} color, which may be due to circumstellar dust (Bailey et al., 2013). In general, the red appearance of young low-mass objects appears to be a frequent phenomenon (Faherty et al., 2016) and has led to suggestions of cloudy atmospheres with vertical mixing and low gravity rather than circumstellar disks, with the caveat that most targets are much older than ROXS 42B ($\sim$2 Myr) and GSC 06214 B ($\sim$10 Myr), i.e., ages where field targets have a lower probability to show significant signs of circumplanetary material.

A comparison of the spectral energy distribution (SED) of ROXS 42B b with directly imaged objects at a similar temperature ($\beta$ Pic b, $\sim$1600 K; 1RXS 1609b, 1800 K; $\kappa$ And b, 2000 K; GSC 06214 B, 2200 K) helps to further assess the diversity of SEDs of young low-mass objects and their circumstellar environments. As in Currie et al. (2013), we scale the comparison SEDs with a factor whose value is the result of a $\chi^{2}$ minimization. Best fits and reduced $\chi^{2}$ values are shown in Fig. 7.

The figure allows us to simultaneously compare all available color information between 1–5 $\muup$m without being biased by the comparably high luminosity of ROXS 42B b.

We find that the hottest targets, GSC 06214 B and $\kappa$ And b, are nominally preferred ($\chi^{2}_{\rm red}=0.82$ and $\chi^{2}_{\rm red}=1.1$, respectively) over the cooler objects ($\chi^{2}_{\rm red}>3$). However, the GSC 06214 B near-IR slope (JH$$K_{\mathrm{s}}) appears to be flatter than that of ROXS 42B b, in contrast to the other three comparison objects, which follow the near-infrared slope closely. This can again be explained by the GSC 06214 B infrared excess from a circumstellar disk and a slightly hotter temperature than ROXS 42B b, giving rise to the flatter JH$$K_{\mathrm{s}} slope.

We conclude that the near- to mid-IR SED of ROXS 42B b does not exhibit any distinctive features which would set it formally apart (in a $\chi^{2}$ test) from other young objects of similar temperature, at least not with the precision of the currently available photometry. However, none of the probed SEDs seems to simultaneously reproduce both the near-IR and mid-IR trends perfectly. A similar conclusion was reached for $\beta$ Pic b (Currie et al., 2013).

4.2 Forward modeling constraints on surface gravity, effective temperature, and radius

Of all the tested models, only BT-COND was not able to return an acceptable fit to the photometric data within the probed parameter range. The lack of fit can be explained by the fact that a smaller parameter range is covered by this model compared to other models wihout atmospheric dust (AMES-COND); low gravities \log g$$<4 were not available in the BT-COND parameter grid for temperatures $<$2600 K. Because AMES-COND and BT-COND both lead to the rejection of all models with \log g$$\geq4 means that we cannot exclude the possibility that dust-free atmospheres in both frameworks are consistent with low-gravity \log g$$\leq3 solutions for the ROXS 42B b atmosphere for temperatures between 1600 and 1800 K.

Based on 1–5 $\muup$m photometry alone, we find that none of the tested dusty or cloudy atmosphere models should be excluded from being considered as representing the spectral energy distribution of ROXS 42B b. As is known from previous fitting attempts (e.g., Currie et al., 2013) and also seen in Table 5, near- to mid-IR photometry alone is only weakly sensitive to surface gravity and our fitting does not strongly constrain this parameter. Effective temperature, however, appears to be better constrained. When assuming that the models describe the atmosphere of ROXS 42B b sufficiently well, we can exclude the lowest ($<$1700 K) and highest temperatures ($>$2100 K) at $>$95% confidence.

With the exception of the Burrows models, the best-fit temperatures to the $K$-band spectroscopy are on average higher than the photometry fits, mostly 2500–2900 K. Higher temperatures from spectroscopy compared to photometrically inferred temperatures were already seen by Currie et al. (2014b). The fact that formal significances of the spectroscopic fits are close to 1 for most best fits may suggest an overestimation of the error bars. We thus flag the current results as conservative, but note that future studies with more precise flux calibrated spectroscopy are expected to provide stronger constraints.

Considering the fits to photometry and spectra separately show a preference for models with substantial atmospheric dust/clouds, similar to the results from Currie et al. (2014b). The best-fit dust-free models for photometry and those for spectra (considered separately, not jointly) are inconsistent. The AMES/BT-COND model fits to photometry prefer temperatures of $\sim$1700–1800 K, while fits to the $K$-band spectrum center on 2500–3000 K. Acceptable fits to the photometry and spectrum for the AMES-DUSTY and BT-SETTL 2015 models are similarly inconsistent. In contrast, a subset of the Burrows, BT-SETTL and BT-DUSTY model fits to photometry also fit the $K$-band spectrum. The union of the Burrows, BT-DUSTY, and BT-Settl model fits cover $T\!_{\mathrm{eff}}$=2000–2100 K/$\log g$=3.4–3.6, and $T\!_{\mathrm{eff}}$=1700–2000 K/$\log g$=4.5–5, $T\!_{\mathrm{eff}}$=1600 K/$\log g$=4.5, $T\!_{\mathrm{eff}}$=1800 K/$\log g$=3.5, respectively.

To assess the influence of mid-infrared photometry on model selection, we compare the best fits that are obtained for the Burrows models when only near-infrared photometry is known to those with 1–5 $\muup$m photometry (top panel of Fig. 4), as well as spectroscopy fits with and without 1–5 $\muup$m photometry (bottom panel). We find that model spectra consistent with near-infrared photometry of T\!_{\mathrm{eff}}$$\sim2000 K objects can vary as much as 50% in the 2–4 $\muup$m range where the SED is the brightest. This translates into a 25% uncertainty of the bolometric luminosity. For comparison, the luminosity of spectra consistent with JH$$K_{\mathrm{s}}$$L^{\prime}Br\alphaup$$M_{\mathrm{s}} photometry varies by only $\sim$6%.

When fit simultaneously with the photometric data, the $K$-band spectroscopy appears to dominate the result. While the smallest parameter range is found to fit the combined spectroscopy and photometry, the bottom right panel of Fig. 4 demonstrates, using the example of the Burrows models, that they do not fit the spectroscopy and photometry equally well. The same conclusions are reached for the other model families. The on average lower significances of the simultaneous fits reinforce the discrepancy between the photometry and spectroscopy for most model families, as discussed above.

The average inferred radii from the photometry fits range between $\sim$2.4 $R_{\mathrm{Jup}}$ and $\sim$3.2 $R_{\mathrm{Jup}}$. Radii consistent with the spectroscopy fits are bimodal (1.3–2.4 $R_{\mathrm{Jup}}$ and 2.6–4.7 $R_{\mathrm{Jup}}$) where the lower bracket is due to on average higher temperatures of the accepted spectroscopic fits. When compared with stellar evolution models, the photometrically derived radii appear larger while the radii derived from the spectroscopic data are consistent with the expectations for a 2 Myr, $M$=9$\pm$3 $M_{\mathrm{Jup}}$ object. For example, isochrones from the AMES models suggest radii of 1.9–2.4 $R_{\mathrm{Jup}}$ for ROXS 42B b, very similar radii are derived from the Burrows models (Burrows et al., 2001).

In the AMES framework this combination of radius and mass is equivalent to a surface gravity value of \log g$$\approx3.7, consistent with all fits except the photometry-only fits of the COND models and BT-DUSTY. A low surface gravity is corroborated by empirical results; based on comparison with other young low-mass objects Currie et al. (2014a) concluded that ROXS 42B b has a surface gravity of $\log g$ = 3.5–4.5.

4.3 Atmospheric retrieval modeling results

Using ground-based photometry to perform retrieval is challenging for several reasons. First, the photometric bands are designed to probe wavelengths with very little absorption from common molecules like water, CO, CO2, and methane. Thus, the retrieval algorithm has very little leverage on the abundances of these molecules in the observed planetary atmosphere. An additional constraint is that broadband photometry in general contains only a small amount of information about the abundances of specific molecules (e.g., Line et al., 2012, 2014). Difficulties in constraining the molecular abundances with broadband photometry also arise from complex degeneracies between molecular absorption, surface gravity, potential clouds, and the pressure-temperature profile of the atmosphere. All of these parameters are strongly correlated or anticorrelated and the degeneracies can very often be broken only by the detection of well-resolved spectral features with a high signal-to-noise ratio (e.g., Line et al., 2012). Despite these difficulties, photometry contains some information about the atmospheric composition. Our simplified, cloud-free plane-parallel framework combined with MCMC retrieval (see Sect. 3.4) can reproduce the observed photometry well (Figure 8), with the caveat that the fit contains more free parameters than photometric data points. Thus, we are unable to determine robust uncertainties, but in principle we are able to exclude certain classes of models. In this way, we are able to place an upper limit on $\log(n_{\rm CO_{2}})$ of $-$2.7 (95% confidence level), within the framework of our retrieval model. The abundances of the remaining major molecular species that we include in our analysis remain unconstrained.

This is not surprising; even when spectroscopy is available, precise determinations of molecular abundances can be difficult. For example Todorov et al. (2016) use low-resolution 1–1.8 $\muup$m spectroscopy to retrieve abundances of the $\kappa$ And b  atmosphere. Using the same fitting parameters as we do (their case 3), they derive an upper limit for methane of $\log(n_{\rm CH_{4}})$ $<$ $-2.4$ for $\kappa$ And b (T\!_{\mathrm{eff}}$$\approx2000 K) and find no constraints for the abundances of $\log(n_{\rm CO})$. Their 95% upper limit for $\log(n_{\rm CO_{2}})$ of $-2.2$, however, is consistent with what we find for ROXS 42B b. Only the water abundance of $\kappa$ And b is fully constrained ($\log(n_{\rm H_{2}O})$ $=$ $-3.5^{+0.4}_{-7.8}$).

We note that our upper limit on $\log(n_{\rm CO_{2}})$ is not strict enough to support or exclude equilibrium chemistry. Equilibrium with other species (such as $\rm H_{2}O$, CO, $\rm CH_{4}$) can be represented with a system of equations involving the abundances of multiple chemical species (Heng & Tsai, 2016). A comparison with equilibrium forward models is difficult without assuming the overall metallicity of the atmosphere and the pressure-temperature structure of the atmosphere (which here are unconstrained). To obtain an estimate, we calculate the equilibrium $\rm CO_{2}$ abundances for an isothermal atmosphere at 2000 K with solar abundances of C, O, and He using the open source VULCAN777https://github.com/exoclime/VULCAN code (Heng & Tsai, 2016). We derive an abundance of $\log(n_{\rm CO_{2}})<-7.0$ at all pressures, lower than our retrieved upper limit of $\log(n_{\rm CO_{2}})<-2.7$. The reported upper limit will nevertheless be useful and will serve as a reference value for future spectroscopic atmospheric retrieval results and studies of other targets.

5 Summary and discussion

We present new 3–5 $\muup$m photometry of the directly imaged exoplanet candidate ROXS 42B b. To analyze the spectra and measure how mid-IR photometry helps to constrain atmospheric parameters, we combine this data with previous near-infrared photometry and spectroscopy, and compare the combined data to atmosphere models and other young low-mass objects.

We find that atmospheric models with either uniformly dusty atmospheres (AMES-DUSTY, BT-DUSTY) or featuring clouds (BT-SETTL, Burrows) are in agreement with the combined 1–5 $\muup$m photometry. As is expected for L-type objects, cloudless models (AMES-COND, BT-COND) generally fit the data less well, according to their $P$-value. Based on photometry alone, we reject temperatures $>$2100 K and $<$1600 K for all models with 95% confidence (explored parameter range: $T\!_{\mathrm{eff}}$=1500–3000 K, $\log g$=2.5–5.5). While this agrees well with results from the previous fitting of near-IR photometry ($J$–$L^{\prime}$ band), which suggested effective temperatures of 1800–2000 K (Currie et al., 2014b), the additional photometry helps to significantly narrow the range of acceptable models. Owing to the weak sensitivity of the photometry to surface gravity, no additional constraints can be placed on the ROXS 42B b gravity beyond the empirical values of \log g$$\approx3.5–4.5 reported by Currie et al. (2014a).

Fits of $K$-band spectroscopy of ROXS 42B b (Currie et al., 2014a) result in average higher best-fit temperatures of mostly 2500–2900 K, as was seen previously (Currie et al., 2014b). Models with dust-free (AMES/BT-COND) atmospheres show a particularly strong discrepancy between the photometric and spectroscopic temperature estimates, whereas the dusty and/or cloudy BT-DUSTY, BT-SETTL, and Burrows models each cover a part of the $T\!_{\mathrm{eff}}$-$\log g$ parameter space where both the spectroscopic and photometric fit can be accepted. Nevertheless, we find that the none of the tested models reproduces all the qualitative features equally well in a weighted simultaneous photometric and spectroscopic fit (e.g., the shape of the K-band spectroscopy continuum and the 1–5 $\muup$m photometry). Our new analysis thus reinforces the notion by Currie et al. (2014b), which was based on 1–3.5 $\muup$m data and a smaller range of atmosphere models, that the ROXS 42B b infrared photometry and spectroscopy cannot be simultaneously fit by most atmosphere models with satisfactory results. This might point to either insufficiently accurate descriptions of the opacities and temperature structure of planetary atmosphere models or nonstandard element abundances in ROXS 42B b. The latter branch has been explored for other directly imaged planets by invoking non-equilibrium carbon abundances (e.g., Skemer et al., 2014) or by changing the overall metallicity (Skemer et al., 2016; Wagner et al., 2016). While the effective temperature of ROXS 42B b is likely too high for non-equilibirum chemistry to have a significant effect on the observed infrared properties (Madhusudhan et al., 2014), an increased metallicity may have a noticeable effect on the intrinsic colors and the spectral signature. Metallicity offsets relative to the star may be a sign of the formation of a companion in a circumstellar disk rather than through cloud fragmentation in a stellar formation channel (Skemer et al., 2016) and thus open an interesting path to distinguish formation scenarios. Dedicated modeling efforts in future studies will help to constrain this possibility for ROXS 42B b.

Comparison of the ROXS 42B b photometric 1–5 $\muup$m SED with previous observations of young low-mass objects in a similar temperature range return acceptable point-wise agreement with GSC 06214B and $\kappa$ And b. Nevertheless, none of the targets is simultaneously consistent in near- to mid-infrared colors and luminosity. One of the distinguishing features of ROXS 42B is its very young age of $\sim$2 Myr (assuming it is a member of the Ophiuchus region). Owing to the currently small number of directly imaged planetary-mass objects, however, it is not clear whether the atmospheric properties of ROXS 42B b  are characteristic of young targets. Furthermore, it is known that young substellar objects, including planetary-mass companions (e.g., GSC 06241 B; Bailey et al., 2013), can exhibit circumstellar disks that can have a strong effect on the measured mid-IR SED. It is possible that circumplanetary material might be present around ROXS 42B b  given that $\sim$1/3 of all Ophiuchus members harbor circumstellar dust (Erickson et al., 2011). However, additional signs of disks, such as strong emission lines indicative of accretion, are not seen in our data.

From our cloudless atmospheric retrieval analysis of the ROXS 42B b 1–5 $\muup$m photometry we infer an upper limit for the abundance of CO2 of $\log n_{\rm CO_{2}}\!<\!-2.7$. Other probed molecular species (e.g., water, methane, carbon monoxide) or properties ($T\!_{\mathrm{eff}}$, $\log g$) are not constrained by the measured filter set. In general, inference of the atmospheric parameters based on six photometric data points make strong constraints on atmospheric properties impossible. An in-depth study will hence require more mid-IR observations as well as infrared spectroscopy over a long wavelength range of reference objects at similar temperatures and ages. In particular, retrieval methods will benefit strongly from new data since parameter constraints are a strong function of the number of data points (Lee et al., 2013). As such an analysis is beyond the scope of the current paper, we defer the analysis of additional photometry and new spectroscopic measurements of ROXS 42B b to future work (Currie et al.  in prep.).

Acknowledgements.

We thank the anonymous referee for a critical review of the manuscript and helpful comments. We thank Mickaël Bonnefoy, Sascha Quanz, and Adam Amara for discussing details of the project. We particularly thank Sean Brittain for sharing with us his spectra of HD 141569. This work has been carried out within the frame of the National Centre for Competence in Research PlanetS supported by the Swiss National Science Foundation. S.D. acknowledges the financial support of the SNSF. This work was supported in part by NSERC grants to R.J. The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.