MAGELLAN ADAPTIVE OPTICS FIRST-LIGHT OBSERVATIONS OF THE EXOPLANET β PIC b. II. 3–5 μm DIRECT IMAGING WITH MagAO+Clio, AND THE EMPIRICAL BOLOMETRIC LUMINOSITY OF A SELF-LUMINOUS GIANT PLANET

MagAO (P.I. Laird Close) is a new facility instrument at the Magellan "Clay" telescope at Las Campanas Observatory, Chile (Close et al. 2012a, 2013; Morzinski et al. 2014). The 6.5-m primary mirror was fabricated at the Richard F. Caris Mirror Lab, Steward Observatory, Tucson, Arizona. The 85-cm MagAO adaptive secondary mirror (ASM) glass shell was fabricated in Arizona, integrated with the electronics and mechanics by MicroGate, Bolzano, and A.D.S. International, Lecco, Italy, and integrated and tested with the wavefront sensor (WFS) with our partners at INAF-Arcetri Observatory, Florence, Italy. The AO system updates at up to 1000 Hz and corrects turbulence via the 585-actuator ASM. The WFS is a modulated pyramid (Ragazzoni & Farinato 1999; Tozzi et al. 2008; Esposito et al. 2010). On bright stars such as β Pic A, MagAO flattens the wavefront to ∼100–150 nm rms, depending on seeing and wind.

There are two science cameras behind MagAO: VisAO and Clio. VisAO (P.I. Jared Males) is a new diffraction-limited visible-light camera, taking full advantage of the pyramid WFS. Clio (P.I. Phil Hinz) has been relocated to Magellan from its initial home at the MMT at Mt. Hopkins, Arizona, where it was developed for imaging low-mass companions at 3–5 μm (Heinze et al. 2003; Freed et al. 2004; Sivanandam et al. 2006; Hinz et al. 2010). Clio uses a prototype Hawaii-I HgCdTe array (one of the first MBE arrays) sensitive out to 5 μm, with the following filters as of first light at MagAO in 2012: J, H, K_s, [3.1], [3.3], [3.4], L', [3.9], Barr M, and ${M}^{\prime }.$ Clio has two pixel scales: the Narrow camera has 15.9 mas pixels and a 16 × 8'' field of view (FOV) while the Wide camera has 28 mas pixels and a 28 × 14'' FOV (see Appendix C for the plate scale calculation). Further information is given at our "Information for Observers" website.⁹

Light is collected at the 6.5-m primary mirror of the Magellan Clay telescope, continues to the f/16 secondary, and is folded by the tertiary onto the Nasmyth platform. A mounting ring encloses the compact optical table where both VisAO and the WFS are mounted (the "W-unit"), while Clio is mounted to the Nasmyth ring. The two science cameras are illuminated simultaneously by way of the dichroic window of Clio, for simultaneous observations in the optical and infrared. MagAO was commissioned from 2012 November to 2013 April.

We observed β Pic on the nights of UT 2012 December 1, 2, 4, and 7. Table 1 lists the observing conditions and parameters, including precipital water vapor (PWV) from the forecaster at nearby La Silla Observatory.¹⁰ Seeing ranged from 05–15. We corrected 120–250 modes at a frame rate of 990 Hz, and residual wavefront error was ∼150 nm rms according to the VisAO focal plane measurement on December 4. Since first light, higher-order corrections at 100–130 nm are typical on a bright star when correcting 300 modes.

Table 1.  Observing Conditions and AO Parameters

UT Date	Seeing	PWV	No. of	Freq.	Filter
		/mm	Modes	/Hz
2012 Dec 01	05–07	3	250	990	[3.3]
2012 Dec 02	05–1''	a	250	990	L'
2012 Dec 04	05–1''	8.5	200	990	Ys, M'
2012 Dec 07	1''–15	4.6–5.7	200	990	[3.1]

Note.

^aNot recorded.

Download table as:  ASCIITypeset image

VisAO observations were limited by commissioning of the atmospheric dispersion compensator (ADC), seeing, and other issues to one good night of December 4. With Clio, we observed β Pic in a different filter each night, always with the rotator off so that we were observing in angular differential imaging (ADI) mode (Marois et al. 2006).

Table 2 summarizes the exposure time and field rotation obtained for each filter. Only the deep (usually where the star is saturated) integrations are tabulated for Clio, as these are the frames that are combined via ADI processing to reveal the planet. Shallow (unsaturated) integrations of β Pic A are used to calibrate the photometry.

[3.3]—On UT 2012 December 1 (local night of 2012 November 30–December 1), we used the 3.3 μm filter and the Narrow camera (8'' × 16'' FOV). Unsaturated exposures were 43 ms and taken in the "stamp" mode (400 × 200-pixel subarray), and deep exposures were 280 ms taken in full frame mode (1024 × 512 pixels) with no co-adding. We obtained 1081 frames total, nodding from side to side with the star always on the chip. To trouble-shoot vibrations, we would occasionally shut off the solid nitrogen pump inside Clio, which was on the Nasmyth platform at the time. However, these occasions did not affect the detector temperature: it stayed within 1 K of the set point at 55 K. (The solid nitrogen pump is now located in the basement of the telescope, in order to avoid any vibration issues.) Furthermore, the peak flux of the unsaturated star images (taken four times, about every 45 minutes over the course of the 2.5 hr observation) have a standard deviation of 4% that is dominated by Strehl/sky/flat variation within a sequence rather than over time or temperature variation. The point-spread function (PSF) was extremely stable in the core and inner halo. The final median saturated and unsaturated PSFs are shown in in Figure 1.

Zoom In Zoom Out Reset image size

L'—On UT 2012 December 2, we observed in the L' filter and the Narrow camera. Unsaturated exposures were 43 ms and taken in stamp mode, and deep exposures were 600 ms taken in full frame mode with no co-adding. We obtained 641 frames total, nodding from side to side with the star always on the chip. Thirty seven of the frames were bad, often at the start of a new nod position when the loop was not yet closed again. The PSF was extremely stable in the core and inner halo.

M'—On UT 2012 December 4, we observed β Pic in ${M}^{\prime }.$M' and Y_s were obtained simultaneously (see Paper I). We nodded ∼8'' across the chip by hand, taking four images per nod position. This was so that we could manually start an integration when the AO loop re-closed. All images were obtained in "strip" mode (1024 × 300-pixel subarray) at 400 ms integration with no co-adding—the star was not saturated at this integration time. We obtained 556 images with the Narrow camera (highly over-sampled, to avoid saturation and to better smooth over bad pixels). The PSF was extremely stable in the core and inner halo.

[3.1]—On UT 2012 December 7 we switched to the Wide camera (14'' × 28'' FOV) to attempt to simultaneously image the disk in the ice line at 3.1 μm. Unsaturated exposures were 280 ms and taken in full frame, and deep exposures were 2.5–3 s, also in full frame, all with no co-adding. We obtained 602 frames total. However, the seeing was poor and worsening, the PSF was less stable, and the saturation radius is angularly larger in the Wide camera (see the extreme saturation in Figure 1), all reducing the quality of these data. Finally, we discovered later that the Wide camera was out of focus during the first commissioning run, affecting these data.

2.3.1. Data Reduction

2.3.2. PSF Estimation

2.3.3. Photometric and Astrometric Measurement

The PSF subtraction process described above reveals the planet against a background of residual speckle error as seen in Figure 1 (right-most column). To determine the contrast ratio and position of the planet, we conduct a grid search using simulated planets. We model the planet as the unsaturated PSF, scaled. For the case of M' where none of the images are saturated, each individual image is its own simulated planet. For all other cases, the simulated planet is scaled from the mean of the unsaturated PSFs. We scale the model planet to a particular flux and position it at a particular location; we then subtract this simulated planet from each reduced frame before running KLIP; finally, we run KLIP to determine the residuals with the model planet subtracted out. The modeled flux and position of the planet are iterated via a grid search, until we find the minimum KLIP residuals with the best-fit planet subtracted out (described in further detail in Appendix E).

Photometric Error Budget—The measurement error for the photometry of the planet is given by the signal-to-noise ratio (S/N) of the planet in the residual images. We calculate the S/N of the planet by determining the Gaussian-smoothed peak height over the standard deviation in an annulus 2 × FWHM wide, centered on the final planet location. We also verify this via inspection in the grid-search residual images, in that a two-sigma change in modeled flux is enough to make the too-bright or too-faint simulated planet visible against the noise background of the grid-search KLIP residuals. The next photometric error term is the uncertainty in our measurement of the star's flux, used for calibration of the final contrast ratio. We attribute this uncertainty to Strehl variation, sky-subtraction errors, telluric transmission, and flatfielding errors, as measured on the unsaturated images which were interspersed throughout the saturated images. We measure this term as the standard deviation in the peak height of the set of unsaturated PSFs, divided by the square root of the number of unsaturated PSFs. The number of unsaturated images is N = 81, 65, 36, and 534, for [3.1], [3.3], L', and ${M}^{\prime },$ respectively. Although there is no Strehl variation error in the case of M' (because all the images were unsaturated; therefore, the simulated planet is always an exact copy of the PSF in each image), we include this error for M' to encompass the flat-field variation error (see Appendix B). The photometry error budget is determined by combining the S/N-based error in the photometry with the calibration error due to Strehl/sky/flat variation. The measured photometry, given as contrast ratios in each bandpass with respect to the star, is given in Table 3.

Table 3.  Photometry Error Budget and Final Adopted Contrast

	Contrast	Planet	Star	Total	Final
	Meas.	Meas.	Cal.	Meas.	Meas.
Filter	[Δmag]	Errora	Errorb	Error	Δmag
[3.1]	8.14	0.2410	0.0104	0.2412	8.14 ± 0.24
[3.3]	8.34	0.1256	0.0057	0.1257	8.34 ± 0.13
L'	8.02	0.1116	0.0060	0.1118	8.02 ± 0.11
M'	7.45	0.0587	0.0035	0.0588	7.45 ± 0.06

Notes. All units in magnitudes.

^aPlanet measurement error based on S/N in the KLIP residuals. Details are given in Table 19. ^bStar calibration error due to Strehl/sky/flat error based on standard deviation in peak flux of unsaturated images throughout the observation sequence, divided by the square root of the number of unsaturated images.

Download table as:  ASCIITypeset image

Astrometric Error Budget—The mean astrometry for the Clio data were summarized in Paper I and Nielsen et al. (2014). Here we give the details, shown in Table 4. We find the best separation and PA according to the best parabola fits in the grid search (see Appendix E). We find the errors in separation and PA using the Gaussian fits to the grid search for each filter separately, based on assuming random errors. We propagate the errors in platescale to errors in astrometry by multiplying astrometric separation platescale error over the platescale. Then we combine the 4 filters as follows: The best-fit separation and PA are the weighted mean of all the measurements, as they are independent measurements. We find the total measurement error in the star–planet separation by adding the errors in quadrature for each filter and camera. We calculate the measurement error in finding the platescale (see Appendix C) for each filter and camera by a simple mean. Finally, we determine the total astrometric error by combining the star–planet separation errors in a weighted-mean-error, added in quadrature to the platescale errors. Our final determination of the position of the planet in 2012 December is a separation of 461 ± 14 mas and a position angle of 2119 ± 12.

Table 4.  $[3.1],$ $[3.3],$ L', and M' Astrometry Error Budget for UT (Average) 2012 December 4

				Planet	Star	Star–planet	Platescale	Platescale		Planet	NorthClio	NorthClio
		UT Epoch	Best	Meas.	Centroid	Total Meas.	Meas.	Fiducial	Best	Meas.	Meas.	Fiducial
			Sep.${}^{{\rm{a}}}$	Error	Error	Error${}^{{\rm{a}},{\rm{b}}}$	Error${}^{{\rm{c}}}$	Error${}^{{\rm{d}}}$	PA	Error${}^{{\rm{a}}}$	Error${}^{{\rm{c}}}$	Error${}^{{\rm{d}}}$
Camera	Filter		/mas	/mas	/mas	/mas	/mas	/mas	/deg.	/deg.	/deg.	/deg.
Wide	[3.1]	2012 Dec 07	466.1	74.0	0.14	74.0001	1.20	0.80	212.62	6.26	0.16	0.3
Narrow	[3.3]	2012 Dec 01	463.0	19.9	0.08	19.9002	1.26	1.37	211.92	1.65	0.16	0.3
Narrow	L'	2012 Dec 02	456.9	28.0	0.08	28.0001	1.24	1.36	211.65	2.31	0.16	0.3
Narrow	M'	2012 Dec 04	460.6	33.8	0.08	33.8001	1.25	1.37	212.10	2.84	0.16	0.3
Weighted mean${}^{{\rm{a}}}$			461.1						211.91
Weighted errors${}^{{\rm{a}}}$						14.347				1.19
Averaged errors${}^{{\rm{c}},{\rm{d}}}$							1.238	1.225			0.16	0.3
Combined final${}^{{\rm{e}}}$			461 ± 14 mas						2119 ± 12

Notes. The final measurement is given in Paper I, their Table 2 (p. 8), but the Date should have read "2012 December 1–7."

^aValues and errors from measuring the position of the planet for each data set are combined with a weighted mean. ^bPlanet Gaussian-fit and star centroiding error are added in quadrature to obtain total star–planet measurement error for each data set. ^cClio measurement errors of the Trapezium are simply averaged. ^dFiducial Trapezium errors from Close et al. (2012b) are simply averaged. ^eErrors from previous two lines added in quadrature to get the final astrometry error budget. Final astrometry measurement also reported in Paper I and Nielsen et al. (2014).

Download table as:  ASCIITypeset image

The raw quantity measured in high-contrast photometry is the contrast ratio between the star and planet. The flux of the planet is derived from the contrast measurement, and must include assumptions about the flux of the star, the instrument system, and the distance. Different works employ different calibrations for both the apparent magnitude of β Pic A and the distance to the system. Furthermore, there is a lack of consistency in photometric systems when combining different data sets. Therefore, here we place all available star–planet contrast measurements on a uniform system.

β Pic b has been imaged with the following instruments and cameras, as reported in the literature: VLT UT4/NaCo at L', [4.05], and M' with the L27 camera; NaCo at K_s with the S27 camera; NaCo at J, H, and K_s with the S13 camera; Gemini South/NICI at CH${}_{4s,1\%},$ H, K_s, and K_cont; Gemini South/GPI spectra at J and H; Magellan Clay/MagAO+VisAO at Y_s; and MagAO+Clio at [3.1] in the wide camera and [3.3], L', and M' in the narrow camera. Works with reported photometry of β Pic b at the time of this writing are Lagrange et al. (2009, 2010), Quanz et al. (2010), Bonnefoy et al. (2011, 2013, 2014), Currie et al. (2011, 2013), Boccaletti et al. (2013), Absil et al. (2013), Paper I, Chilcote et al. (2015), and This Work. We compile the contrast ratios measured in these works in Table 5. For completeness, we note not only the bandpass, but also the telescope, instrument, and camera.

Table 5.  Compilation of All β Pic b Photometry to Date

Epoch UT (yyyy Mon dd)	Telescope, Instrument, Camera, Filter	Delta Mag.	Duplicate	Ref.	Ref. Note
2003 Nov 10, 13	VLT UT4 NaCo L27 L'	7.7 ± 0.3	⋯	1	⋯
2009 Oct 25, Nov 24–25, Dec 17, 26, 29	VLT UT4 NaCo L27 L'	(7.8 ± 0.3)	${}^{\dagger 1}$	2	⋯
2010 Apr 03	VLT UT4 NaCo L27 APP [4.05]	7.75 ± 0.23	⋯	3	⋯
2010 Mar 20, Apr 10	VLT UT4 NaCo S13, S27 Ks	9.2 ± 0.1	⋯	4	⋯
2008 Nov 11	VLT UT4 NaCo L27 M'	(∼8.02 ± 0.50)	⋯	5	${5}^{*}$
2009 Dec 29	VLT UT4 NaCo L27 L'	7.71 ± 0.06	${}^{\dagger 1}$	5	⋯
2011 Dec 16	VLT UT4 NaCo S13 J	(10.5 ± 0.3)	${}^{\dagger 2}$	6	⋯
2011 Dec 18, 2012 Jan 11	VLT UT4 NaCo S13 H	(10.0 ± 0.2)	${}^{\dagger 3}$	6	⋯
2012 Nov 26	VLT UT4 NaCo L27 M'	7.5 ± 0.2	⋯	6	⋯
2010 Dec 25	Gemini South NICI Ks	(∼8.8 ± 0.6)	${}^{\dagger 4}$	7	${7}^{*}$
2011 Dec 16	VLT UT4 NaCo S13 J	10.59 ± 0.21	${}^{\dagger 2}$	8	${8}^{*}$
2012 Jan 11	VLT UT4 NaCo S13 H	9.83 ± 0.14	${}^{\dagger 3}$	8	${8}^{*}$
2013 Jan 09	Gemini South NICI H	9.76 ± 0.18	⋯	8	${8}^{*}$
2013 Jan 09	Gemini South NICI Ks	9.02 ± 0.13	⋯	8	${8}^{*}$
2012 Dec 23	Gemini South NICI $[3.09]$	8.26 ± 0.27	⋯	8	${8}^{*}$
2012 Dec 16	VLT UT4 NaCo L27 L'	7.79 ± 0.08	⋯	8	${8}^{*}$
2012 Dec 16	VLT UT4 NaCo L27 $[4.05]$	7.59 ± 0.08	⋯	8	${8}^{*}$
2012 Dec 15	VLT UT4 NaCo L27 M'	7.50 ± 0.13	⋯	8	${8}^{*}$
2013 Jan 31	VLT UT4 NaCo L27 AGPM L'	8.01 ± 0.16	⋯	9	⋯
2012 Dec 04	Magellan II MagAO VisAO Ys	${11.97}_{-0.33}^{+0.34}$	⋯	10	⋯
2011 Oct 20	Gemini South NICI [CH${}_{4\;{\rm{s}},1\%}]$	9.65 ± 0.14	⋯	10	⋯
2010 Dec 25	Gemini South NICI Ks	8.92 ± 0.13	${}^{\dagger 4}$	10	⋯
2011 Oct 20	Gemini South NICI Kcont	8.23 ± 0.14	⋯	10	⋯
2013 Dec 10	Gemini South GPI IFS J	Spectrum	⋯	11	${11}^{*}$
2013 Nov 18, Dec 10	Gemini South GPI IFS H	Spectrum	⋯	12	${12}^{*}$
2012 Dec 07	Magellan II MagAO Clio Wide [3.1]	8.14 ± 0.24	⋯	13	⋯
2012 Dec 01	Magellan II MagAO Clio Narrow [3.3]	8.34 ± 0.13	⋯	13	⋯
2012 Dec 02	Magellan II MagAO Clio Narrow L'	8.02 ± 0.11	⋯	13	⋯
2012 Dec 04	Magellan II MagAO Clio Narrow M'	7.45 ± 0.06	⋯	13	⋯

Notes.  Contrast ratios in parentheses are not included in our SED (see notes).

References.  (1) Lagrange et al. (2009), (2) Lagrange et al. (2010), (3) Quanz et al. (2010), (4) Bonnefoy et al. (2011), (5) Currie et al. (2011), (6) Bonnefoy et al. (2013), (7) Boccaletti et al. (2013), (8) Personal communication (Currie et al. 2014) and Currie et al. (2013), (9) Absil et al. (2013), (10) Paper I, (11) Bonnefoy et al. (2014), (12) Chilcote et al. (2015), (13) This work.

^†Duplications: in cases where the same data are re-reduced, we use the more recent result, which in all cases has smaller error bars: ${}^{\dagger 1}$While Lagrange et al. (2010) present L' NaCo data from the various epochs listed above, the final quoted value in the text of the paper is that of 2009 December 29, which is the data set re-reduced in Currie et al. (2011). ${}^{\dagger 2}$Currie et al. (2013) present a re-reduction of the 2011 December 16 J NaCo point first presented in Bonnefoy et al. (2013). ${}^{\dagger 3}$While Bonnefoy et al. (2013) present H NaCo data from two epochs listed above, the final quoted value in the text of the paper is consistent with the RADI photometry of 2012 January 11 only, which is the data set re-reduced in Currie et al. (2013). ${}^{\dagger 4}$Paper I presents an independent reduction of the 2010 December 25 K_s NICI point also presented in Boccaletti et al. (2013) (without a quoted value in the text). ^* ${}^{*}$Notes on the References: 5${}^{*}$ Not used due to lack of unsaturated calibration data. 7${}^{*}$ The contrast we give here is an average of values in a table in the paper. 8${}^{*}$ Contrast values were determined via personal communication (Currie et al. 2014). 11${}^{*}$–12${}^{*}$ Each author sent us their calibrated spectrum in table format (M. Bonnefoy 2014, private communication and J. Chilcote 2014, private communication). In order to use the valuable information in the shape of the spectrum, and to maintain our self-consistent photometric system, we independently normalize the spectra to the broadband NaCo photomety of Currie et al. (2013) for J and H (10.59 ± 0.21 and 9.83 ± 0.14, respectively).

Download table as:  ASCIITypeset image

In more detail, to create Table 5 we first compile the contrast ratios by inspecting each paper; when multiple values for the contrast ratio are given for a single set of data, we take the value quoted in the text. However, the following caveats apply:

• 1.  
  Currie et al. (2011) quote an approximate (≈) contrast ratio in ${M}^{\prime },$ but no unsaturated calibration data were obtained concurrent with the observations. Therefore, we do not use this value.
• 2.  
  Currie et al. (2013) give the apparent magnitudes of b but do not give the contrast ratios they measured; the apparent magnitudes used for A were determined via personal communication (Currie et al. 2014) and used to calculate the contrast ratios.
• 3.  
  Boccaletti et al. (2013) report a number of contrast ratios measured in various trials in a table, but they do not quote any value in the text, as the mask transmission was not known. Therefore, we do not use their photometry.
• 4.  
  Bonnefoy et al. (2014) and Chilcote et al. (2015) report GPI spectra. The focus of these papers is the shape of the spectrum, and per-channel-contrast-ratios have correlated errors that are difficult to compare directly to the photometric measurements. Therefore, we use these spectra as a check on our model fits but do not combine them with the photometry when calculating the best-fitting model.
• 5.  
  In order to enforce independence of the photometric measurements, duplicates are avoided by using the most recent value in all cases of re-reductions of the same data set (see details in Table 5).

We calculate the resultant flux on our uniform photometric system, via a method similar to that used in Paper I, as follows. First to determine the flux of β Pic A (given as an A6V star in Gray et al. 2006), we interpolate an Hubble Space Telescope (HST) CalSpec spectrum¹¹ of the A6V star TYC 4207-219-1 (which is noted to be variable at the ±1% level (Pancino et al. 2012)). As a check on the applicability of this spectrum we normalized this to the V-band photometry from Cousins (1980a, 1980b), and compared it to the photometry from Mitchell & Johnson (1969), Johnson & Mitchell (1975), Glass (1974), and van der Bliek et al. (1996). This comparison is shown in Figure 2. The A6V spectrum is a good match to the shape of the measured SED to at least 5 μm. This demonstrates that, within the 0.5–5 μm regime, there is no significant attenuation of the starlight of β Pic A, neither from interstellar extinction (at a distance of 19 pc) nor from its edge-on disk. Due to this good match, we also conclude that the 10-mmag-variability of the CalSpec star is negligible, and that β Pic A itself lacks significant variability.

Zoom In Zoom Out Reset image size

The filter curve for each instrument was obtained from its respective website. We then multiplied these curves by an atmosphere appropriate for the site. For both MagAO and Gemini/NICI we use the transmission provided by Gemini for Cerro Pachon¹² based on the ATRAN code (Lord 1992). For VLT/NACO we used the "Paranal-like" atmosphere available on the ESO website.¹³ We perform all calculations at airmass 1.0 since it has only a minor effect. The key parameter is precipitable water vapor (PWV), which is not typically documented for these observations. It is not currently routinely measured at LCO. In Table 6 we list the PWV assumed for each observation. In the case of Paranal this is the only option provided. For LCO we used a slightly higher value based on historical measurements (Thomas-Osip et al. 2010) and forecasts made for nearby La Silla Observatory. As shown in the table, in some filters including the atmosphere in the transmission changes the zero-magnitude flux in that filter by $\gt 2\%,$ which is a systematic bias. While this is smaller than the typical precision in any single high-contrast imaging measurement, there are now enough measurements on this object in some filters that combined precision could be approaching this level if we controlled all systematic effects. Based on this exercise we advocate that observers pay greater attention to atmopheric conditions at the time of such observations, and that capabilities to make coincident PWV measurements should be standard.

Table 6.  Uniform Photometric System and Flux of β Pic A

					No Atm.		With Atm.				β Pic A
Filter	Inst.	Atm.	A.M.a	PWVb	${\lambda }_{0}$	${F}_{\lambda }(0)$ c	${\lambda }_{0}$	${F}_{\lambda }(0)$ c	Base	Color	mag	Fλc
				/mm	/μm	${\rm{(}}\times {10}^{-8}{\rm{)}}$	/μm	(×10−8)	Filt.d			(×10−9)
Ys	VisAO	C.P.	1.00	4.3	0.983	679.0	0.985	674.0	9913col	0.000	3.561 ± 0.035	253.7 ± 9.6
J	NaCo	Paranal	1.00	2.3	1.270	292.1	1.255	302.3	JESO	−0.017	3.564 ± 0.013	113.5 ± 1.6
CH4	NICI	C.P.	1.00	2.3	1.584	127.9	1.584	127.9	HESO	0.023	3.525 ± 0.007	49.74 ± 0.38
H	NaCo	Paranal	1.00	2.3	1.665	112.5	1.655	114.5	HESO	−0.003	3.499 ± 0.007	45.62 ± 0.34
H	NICI	C.P.	1.00	2.3	1.665	113.9	1.658	114.6	HESO	−0.003	3.499 ± 0.007	45.69 ± 0.35
KS	NaCo	Paranal	1.00	2.3	2.150	44.59	2.159	43.81	KESO	−0.033	3.462 ± 0.008	18.07 ± 0.16
KS	NICI	C.P.	1.00	2.3	2.174	42.68	2.175	42.48	KESO	−0.025	3.470 ± 0.008	17.39 ± 0.15
Kcont	NICI	C.P.	1.00	2.3	2.272	35.64	2.272	35.64	KESO	0.068	3.563 ± 0.008	13.39 ± 0.12
$3.09\;\mu {\rm{m}}$	NICI	C.P.	1.00	2.3	3.085	11.22	3.090	11.18	${L}_{\mathrm{ESO}}^{\prime }$	0.002	3.483 ± 0.010	4.518 ± 0.049
$3.1\mu {\rm{m}}$	Clio	C.P.	1.00	4.3	3.096	11.11	3.102	11.04	${L}_{\mathrm{ESO}}^{\prime }$	0.002	3.483 ± 0.010	4.464 ± 0.048
$3.3\mu {\rm{m}}$	Clio	C.P.	1.00	2.3	3.329	8.543	3.345	8.406	${L}_{\mathrm{ESO}}^{\prime }$	0.003	3.484 ± 0.010	3.395 ± 0.037
L'	Clio	C.P.	1.00	4.3	3.785	5.289	3.761	5.408	${L}_{\mathrm{ESO}}^{\prime }$	0.000	3.481 ± 0.010	2.190 ± 0.024
L'	NaCo	Paranal	1.00	2.3	3.814	5.103	3.813	5.106	${L}_{\mathrm{ESO}}^{\prime }$	−0.000	3.481 ± 0.010	2.069 ± 0.022
$4.05\mu {\rm{m}}$	NaCo	Paranal	1.00	2.3	4.056	3.884	4.056	3.883	${L}_{\mathrm{ESO}}^{\prime }$	−0.008	3.473 ± 0.010	1.585 ± 0.017
M'	Clio	C.P.	1.00	7.6	4.687	2.253	4.687	2.250	MESO	−0.002	3.420 ± 0.017	0.9643 ± 0.0177
M'	NaCo	Paranal	1.00	2.3	4.789	2.105	4.818	2.048	MESO	−0.001	3.421 ± 0.017	0.8766 ± 0.0161

Notes.

^aWe perform all calculations at airmass 1.0 since AM has only a minor effect compared to PWV. ^bThe key parameter is precipitable water vapor (PWV), which is not typically documented for these observations. ^cFlux densities in erg s⁻¹ cm${}^{-2}\;\mu$m⁻¹. ^dMeasurement to which the template spectrum color was applied.

Download table as:  ASCIITypeset image

We then use the Vega spectrum of Bohlin (2007) to determine the zero-magnitude flux density in each filter. We use the A6V spectrum to calculate corrections from the measured photometry of β Pic A to the filters used for imaging the planet, from which we derive flux density of the star. We show these in Table 6, along with the primary measurement on which each was based.

Next we combine the photometric system with the contrast measurements listed in Table 5 to determine the planet's flux density in each filter. The absolute magnitudes of β Pic b are found by subtracting the contrast ratio, then applying the distance modulus, using the distance 19.44 ± 0.05 pc (van Leeuwen 2007). We now have the 0.99–4.8 μm SED of β Pic b based on a consistent SED for β Pic A. Table 7 lists the resultant fluxes we determine for the planet. The final resultant SED of β Pic b is shown in Figure 3.

Zoom In Zoom Out Reset image size

Table 7.  Our Determination of the Bandpasses and Flux Densities of the Photometric Measurements of β Pic b to Date

Instrument and Filter	Epoch	${\lambda }_{0}/$μma	${\rm{\Delta }}\lambda /$μmb	Fλ ($\times {10}^{-12}$)c
MagAO/VisAO Ys	2012 Dec 04	0.985	0.084	4.1 ± 1.5
NaCo J	2011 Dec 16	1.255	0.193	6.6 ± 1.5
NICI CH4	2011 Oct 20	1.584	0.017	6.9 ± 1.0
NICI H	2013 Jan 09	1.650	0.268	5.7 ± 1.1
NaCo H	2012 Jan 01	1.655	0.307	5.33 ± 0.81
NaCo Ks	2010 Mar 20, Apr 10	2.159	0.324	3.77 ± 0.41
NICI Ks	2013 Jan 09	2.174	0.269	4.29 ± 0.61
NICI Ks	2010 Dec 25	2.174	0.269	4.70 ± 0.66
NICI Kcont	2011 Oct 20	2.272	0.037	6.8 ± 1.0
NICI $[3.09]$	2012 Dec 23	3.090	0.093	2.24 ± 0.66
MagAO/Clio [3.1]	2012 Dec 07	3.102	0.090	2.48 ± 0.65
MagAO/Clio [3.3]	2012 Dec 01	3.345	0.300	1.57 ± 0.22
MagAO/Clio L'	2012 Dec 02	3.761	0.619	1.36 ± 0.16
NaCo L'	2003 Nov 10, 13	3.813	0.573	1.72 ± 0.56
NaCo L'	2009 Dec 29	3.813	0.573	1.70 ± 0.11
NaCo L'	2012 Dec 16	3.813	0.573	1.58 ± 0.14
NaCo L'	2013 Jan 31	3.813	0.573	1.29 ± 0.23
NaCo $[4.05]$	2010 Apr 03	4.056	0.060	1.26 ± 0.31
NaCo $[4.05]$	2012 Dec 16	4.056	0.060	1.46 ± 0.13
MagAO/Clio M'	2012 Dec 04	4.687	0.185	1.010 ± 0.068
NaCo M'	2012 Nov 26	4.818	0.416	0.88 ± 0.19
NaCo M'	2012 Dec 15	4.818	0.416	0.88 ± 0.12

Notes.

^aFlux-weighted central wavelength. ^bEffective flux-weighted filter width. ^cFlux densities in erg s⁻¹ cm${}^{-2}\;\mu$m⁻¹.

Download table as:  ASCIITypeset image

For this analysis, we choose to fit publicly available models to the data. These are: Speigel & Burrows (Spiegel & Burrows 2012), and the PHOENIX models: AMES "Cond" and "Dusty" (Chabrier et al. 2000; Allard et al. 2001; Baraffe et al. 2003) and "BT Settl" (Allard et al. 2012a). The Spiegel & Burrows models provide a constraint on formation mode by fitting for initial specific entropy. The PHOENIX models provide a constraint on current physical properties, such as effective temperature and surface gravity.

We find the best-fit parameters for each model with a chi-squared-minimization process over all the photometry in Table 7. The GPI spectra are not independent measurements, as we normalize the J- and H-band fluxes with broadband photometry. Therefore, the GPI spectra are not fit, but are overplotted for visual inspection. For each model in each grid we calculate the reduced ${\chi }^{2}$ statistic, using the photometry and uncertainties. For the PHOENIX models we scale the overall luminosity, which amounts to choosing the best-fit radius, to minimize ${\chi }^{2}$ for any given model. The parameters (gravity, temperature, etc.) of the model with minimum ${\chi }^{2}$ are adopted as the best-fit parameters for that grid.

4.1.1. Spiegel & Burrows Models

We first describe the Spiegel & Burrows models (Spiegel & Burrows 2012).¹⁴ These models take as input the accretion efficiency during formation. A range of evolutionary models are calculated with varying initial entropies, including their own version of the "hot-start" and "cold-start" models of Marley et al. (2007), as well as intermediate "warm-start" models and higher-entropy "hotter-start" models.

The initial entropies after formation vary because of varying treatments of the energy radiated away during accretion. Gravitational contraction rather than disk accretion results in a much higher initial entropy, and this is the extreme "hottest-start" case considered by Spiegel & Burrows (2012). The evolutionary models are then combined with boundary conditions and radiative transfer (COOLTLUSTY; Hubeny et al. 2003; Burrows et al. 2006) to create synthetic spectra and magnitudes. For the atmosphere models, they then consider different atmospheric compositions: 1 or 3x Solar metallicity, and hybrid clouds or cloud-free. Hybrid clouds are a linear combination of cloud-free and cloudy atmospheres to represent patchy or partial clouds (Burrows et al. 2011). We select the 25-Myr old models as the closest in age to the β Pic system, and independently fit each of the four cases for cloud-free or hybrid clouds and 1x or 3x Solar metallicity.

The model fits are shown in Figure 4, and Table 8 summarizes the best-fit parameters. The parameters determined in the fit are initial specific entropy, mass, and initial radius. The best-fit mass (14 ${{\mathcal{M}}}_{\mathrm{Jup}}$) is high compared to the upper-limit set by the HARPS radial velocity data (<12 ${{\mathcal{M}}}_{\mathrm{Jup}}$ for a = 9 AU, Lagrange et al. 2012). The initial radius of 1.45 ${{\mathcal{R}}}_{\mathrm{Jup}}$ does not allow room for contraction to the large radii needed to fit the PHOENIX models (below). The two best-fitting models, at ${\chi }_{\nu }^{2}$ = 6.5–6.7, are the hybrid cloud models with 1x and 3x Solar metallicity. Other works have found that β Pic b most likely formed with a high initial entropy, as indicated by its brightness (Bonnefoy et al. 2014; Chilcote et al. 2015) for a planet-mass object at a young age. However, all four best-fit models have an initial specific entropy of 9.75 ${k}_{B}/\mathrm{baryon},$ which is an intermediate "warm-start" value.

Zoom In Zoom Out Reset image size

Table 8.  Best Fits of 25-Myr Old Spiegel & Burrows (2012) Models, Plotted in Figure 4

	Init. Specific		Init.
	Entropy	Mass	Rad.
Model	/kB baryon−1	/${{\mathcal{M}}}_{\mathrm{Jup}}$	/${{\mathcal{R}}}_{\mathrm{Jup}}$	${\chi }_{\nu }^{2}$
Cloud-free, 1x Solar	9.75	14.00	1.45	14.71
Cloud-free, 3x Solar	9.75	14.00	1.45	13.60
Hybrid clouds, 1x''	9.75	14.00	1.45	6.48
Hybrid clouds, 3x''	9.75	14.00	1.45	6.72

Note. The formation is constrained as "warm-start."

Download table as:  ASCIITypeset image

4.1.2. PHOENIX Models

We also use a suite of publicly available models based on the PHOENIX atmosphere simulator.¹⁵ The AMES Cond (Allard et al. 2001; Baraffe et al. 2003) and Dusty (Chabrier et al. 2000; Allard et al. 2001) models represent limiting cases of dust in the atmosphere: Cond models do not include dust opacity; Dusty models treat dust opacity in equilibrium with the gas phase. Note that the effective temperature of β Pic b found by previous studies (∼1600 K) is between the expected valid temperature ranges of the Cond (T_eff < 1400 K) and Dusty (T_eff > 1700 K) models. We might expect better results with the BT-Settl (Allard et al. 2012b) models, which include a cloud model and are valid across the T_eff range of interest. We test both the "CIFIST2011" and "CIFIST2011bc" model grids, which differ in details of how the mixing length is calibrated.¹⁶

The fits to the PHOENIX models are shown in Figure 5. The parameters determined in the fit are T_eff, log(g), radius, and sometimes [Fe/H]. Each spectrum in the grid corresponds to a gravity, temperature, and metallicity (which is Solar for all but BT Settl where it varies, and the best-fit metallicity is shown). We find the scale factor for each spectrum by minimizing ${\chi }^{2}$ over the photometry. This scale factor is (radius/distance) squared, and thus gives the best-fit radius. We then calculate the bolometric luminosity by integrating the scaled spectrum out to 10 μm where we had truncated the models to facilitate the minimization algorithm; we then add 2% for the contribution of flux from 10 to 100 μm to determine the total ${{\mathcal{L}}}_{\mathrm{bol}}$. The T_effs, surface gravities, radii, and luminosities determined from the models are listed in Table 9.

Zoom In Zoom Out Reset image size

Table 9.  Best Fits of the PHOENIX Models (Shown in Figure 5)

		log		log(	Calc.
	Teff	$(g)$	Rad.	${{\mathcal{L}}}_{\mathrm{bol}}$	Mass${}^{{\rm{b}}}$
Model	/K	(cgs)	/${{\mathcal{R}}}_{\mathrm{Jup}}$	/${{\mathcal{L}}}_{\odot }$)${}^{{\rm{d}}}$	/${{\mathcal{M}}}_{\mathrm{Jup}}$	${\chi }_{\nu }^{2}$
AMES-Dusty	1700	3.5	1.31	−3.86	2.2	2.59
AMES-Cond	1400	2.5	1.87	−3.89	0.4	4.82
BT Settl 11bc	1500	3.0	1.88	−3.80	1.4	1.52
BT Settl ${11}^{{\rm{a}}}$	1700	5.0	1.60	−3.77	103${}^{{\rm{c}}}$	1.56

Notes.

^aBest-fit metallicity is [Fe/H] = 0.5. ^bCalculated mass, using model log(g) and best-fit radius. ^cMass >20 ${{\mathcal{M}}}_{\mathrm{Jup}}$ is ruled out by Lagrange et al. (2012). ^dAdded 2% for the 10–100 μm flux region (see the text).

Download table as:  ASCIITypeset image

In addition, we calculate what the mass of the planet would be, given the model gravity and best-fit radius. We include this quantity in Table 9 to help give intuition for the gravities and radii determined via the models, with the caveat that mass is not an explicit output of the model atmospheres, as they do not include evolutionary tracks. Nevertheless, it shows that the high gravity of the best-fit BT Settl 11 model is likely unphysical, because the calculated mass of ∼100 ${{\mathcal{M}}}_{\mathrm{Jup}}$ has been definitively ruled out by radial velocity observations (Lagrange et al. 2012; Bonnefoy et al. 2014).

The results of the model fits show some general trends.

4.2.1. Thick Clouds

Cloud-free models are poor fits to the broadband photometry. AMES-Cond and the cloud-free models of Spiegel & Burrows are faint at 3 and 5 μm, where the planet is bright. Molecular gas opacity modeled in this region includes H₂, He, H₂O, CO, and CH₄ (Sharp & Burrows 2007), which provide some of the absorption features seen in Figure 4 (top), but provide too much absorption at 3 μm and too much flux particularly in the J and H bands. The hybrid cloud models of Spiegel & Burrows are somewhat better, but are still too faint at 5 μm compared to the planet.

The best fits are provided by AMES-Dusty and the BT Settl models. These include the most dust and cloud opacity, particularly in the 3- and 5-μm regions. Therefore, β Pic b's atmosphere is dominated by thick clouds.

Blackbody—An object dominated by thick clouds, as the atmosphere models demonstrate for β Pic b, will predominantly exhibit thermal radiation rather than molecular emission/absorption features. We therefore explore fitting a blackbody curve to the visible through mid-IR photometry. Figure 6 shows the best-fit blackbody curve. Its physical parameters are T_eff = 1750 K and R = 1.34 ${{\mathcal{R}}}_{\mathrm{Jup}}$, giving a bolometric luminosity of log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$) = $-3.79.$ As with the atmosphere models, the GPI spectra are not included in the ${\chi }^{2}$-minimization but are overplotted for visual inspection.

Zoom In Zoom Out Reset image size

The blackbody is the third-best-performing fit to the photometry, after the two BT Settl models. While the broad wavelength coverage for β Pic b is an asset for determining its overall luminosity, its cloudy atmosphere means that spectral features are flattened as compared to cloud-free atmospheres. This underscores the importance of spectra and narrow-band photometry, as well as broad wavelength coverage, to fitting atmosphere models.

4.2.2. Possiblity of Methane

4.2.3. Luminosity, Temperature, and Radius

The two best-fit BT Settl models, with nearly identical reduced ${\chi }^{2}$ s, have different temperatures (1500 and 1700 K, respectively) and radii (1.88 and 1.60 ${{\mathcal{R}}}_{\mathrm{Jup}}$, respectively) but similar luminosities (log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$) of −3.80 and −3.77, respectively). Taking these two models as the envelope of best fits, the radius is determined to 16% and the T_eff to 13%, yet the ${{\mathcal{L}}}_{\mathrm{bol}}$ is determined to 7%. That is, temperature and radius are dually fit by the models, whereas luminosity is well-constrained.

We see this same trend with the best-fit models of other works, listed in Table 10. T_eff and radius are inversely correlated in all cases, whereas ${{\mathcal{L}}}_{\mathrm{bol}}$ is almost unchanged. For all best-fit models, T_eff and radius are constrained to 7% and 14%, respectively, while ${{\mathcal{L}}}_{\mathrm{bol}}$ is constrained to within 4%. We conclude that the models are best providing a constraint on the luminosity rather than the temperature or radius. Therefore, in the next section we extend the SED with blackbody curves to understand the fundamentals of the planet's energy budget.

Table 10.  Best-fit Modeled Parameters for β Pic b^a

		log		log(
	Teff	$(g)$	Rad.	${{\mathcal{L}}}_{\mathrm{bol}}$
Work	/K	(cgs)	/${{\mathcal{R}}}_{\mathrm{Jup}}$	/${{\mathcal{L}}}_{\odot }$)
BT Settl 11bc (this work)	1500	3.0	1.88	−3.80
Baudino et al. (2015)	1550	3.5	1.76	$-{3.77}^{}$ b
Chilcote et al. (2015)	1650	4.0	⋯	⋯
Bonnefoy et al. (2014)	1650	<4.7	1.5	$-{3.80}^{}$ b
BT Settl 11 (this work)	1700	5.0	1.60	−3.77
Blackbody (this work)	1750	⋯	1.34	−3.79

Notes. Atmosphere models fit to the photometry are constraining ${{\mathcal{L}}}_{\mathrm{bol}}$, not T_eff. 

^aPresented without error bars for brief inspection of the trends compared to the best model fits in this work. (See Table 15 for a fuller listing, including the best determination from this work.) ^bThis ${{\mathcal{L}}}_{\mathrm{bol}}$ is calculated from the modeled T_eff and radius.

Download table as:  ASCIITypeset image

Fitting atmospheric models (above) demonstrated that β Pic b has a cloudy/dusty atmosphere. However, because of the correlation between temperature and gravity in fitting the spectra, the excercise of fitting the models points more clearly toward a luminosity than an effective temperature. Given the simplicity and relative success of the blackbody fit (Figure 6), we next determine the full SED of β Pic b by extending the spectrum with a blackbody, and empirically calculating the bolometric luminosity. See Table 11 for the units we use in this work.

Table 11.  Nominal Units and Measures Used in this Work

Quantity${}^{{\rm{a}}}$	Value	Unit	References
Solar Luminosity ${{\mathcal{L}}}_{\odot }$	$3.827\times {10}^{33}$	erg s−1	(1, 2)${}^{{\rm{b}}}$
Jupiter Radius ${{\mathcal{R}}}_{\mathrm{Jup}}$	$7.1492\times {10}^{9}$	cm	(3, 4, 5)${}^{{\rm{c}}}$
Jupiter Mass ${{\mathcal{M}}}_{\mathrm{Jup}}$	$1.8983\times {10}^{30}$	g	(4, 5)
Distance to β Pic A	19.44 ± 0.05	pc	(6)

Notes.

^aScript letters for nominal Solar and Jovian values (${\mathcal{L}},{\mathcal{M}},{\mathcal{R}}$) are used according to the recommendation given in [5], to emphasize that these quantities are used as constants. ^bUpdated to $3.828\times {10}^{33}$ erg s⁻¹ in IAU Resolutions (2015a). ^cEquatorial radius at 1 bar.

References. (1) Mamajek (2012), (2) Mamajek (2014), (3) Fortney et al. (2007), (4) Williams (2015), (5) IAU Resolutions (2015b), (6) van Leeuwen (2007) (Parallax of 51.44 ± 0.12 mas).

Download table as:  ASCIITypeset image

To extend the spectrum with a blackbody, we use the best-fitting blackbody for a selection of T_effs in 100-K increments, listed in Table 12. Figure 7 shows the best-fitting blackbodies for temperatures 1550–1850 K. The long-wavelength data have more measurements and smaller error bars, so these curves are tightly correlated in the Rayleigh–Jeans tail, crossing over near the middle wavelengths of the sample.

Zoom In Zoom Out Reset image size

Table 12.  Best-fit Blackbodies at Each T_eff

Teff/K	Rad./${{\mathcal{R}}}_{\mathrm{Jup}}$	log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$)	${\chi }_{\nu }^{2}$
1550	1.60	−3.85	2.46
1650	1.46	−3.82	1.88
1750	1.34	−3.79	1.66
1850	1.24	−3.77	1.78
1950	1.15	−3.74	2.19

Download table as:  ASCIITypeset image

Next we use these blackbodies to extend the SED. To combine the spectrophotometry, we find the weighted mean at each broad bandpass. At the J and H bands we use the GPI spectra which have been normalized by the broadband photometry. We use the effective filter widths to determine the mean wavelength for the various filters Y_s, K, 3.1 μm, 3.3 μm, L', 4.1 μm, and ${M}^{\prime }.$ The mean photometric points are shown in Figure 8 and listed in Table 13.

Zoom In Zoom Out Reset image size

Table 13.  Weighted-mean Broadband Photometry used to Calculate the Empirical Bolometric Luminosity

λ/μm	Fλ ($\times {10}^{-12}$)${}^{{\rm{a}}}$
Ys 0.985	4.13 ± 1.51
J-band	GPI spectrum
H-band	GPI spectrum
K 2.27	4.31 ± 0.29
3.10	2.35 ± 0.46
3.34	1.57 ± 0.22
L' 3.80	1.56 ± 0.07
4.10	1.43 ± 0.12
M' 4.72	0.97 ± 0.06

Note.

^aFlux densities in erg s⁻¹ cm${}^{-2}\;\mu$m⁻¹

Download table as:  ASCIITypeset image

To find the bolometric luminosity, we integrate the total SED (data + blackbody extension) from 0.001 to 100 μm. To determine the error bars in the bolometric luminosity, we include three error sources. Photometric errors from the data lead to error in the trapezoidal integration of the weighted mean photometric points listed in Table 13, contributing 2.0% to the total ${{\mathcal{L}}}_{\mathrm{bol}}$ error. Error from the unknown blackbody extension is found by the bounds of the various T_eff and radius selections in Table 14, contributing 4.7% (error based on the range). Finally, the unsampled region around 2.7 μm could have a deep absorption feature such as that seen in the AMES-Dusty models (Figure 5), so we insert the modeled value here and repeat the integral—the luminosity drops by 3.9%, which we take as the error (error also based on the range) due to the unsampled region between K and [3.1]. Summing these errors in quadrature gives a total error in the integrated luminosity of 6.4%. Therefore, we find log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$) = $-3.78\pm 0.03.$

Table 14.  Empirical Bolometric Luminosity, Integrating the Data and Extending with a Blackbody Curve

SED	Rad./${{\mathcal{R}}}_{\mathrm{Jup}}$	log(L/${{\mathcal{L}}}_{\odot }$)
Data only (0.985–4.77 μm)	⋯	$-3.86$
Best-fit b.b., 0.985–4.77 μm only	1.34	−3.85
		log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$)
Data + 1550-K best-fit b.b.	1.60	−3.78
Data + 1650-K best-fit b.b.	1.46	−3.78
Data + 1750-K best-fit b.b.	1.34	−3.78
Data + 1850-K best-fit b.b.	1.24	−3.78

Download table as:  ASCIITypeset image

Given the luminosity and age, evolutionary models determine the mass, radius, and temperature as the planet cools and contracts. We use our empirically determined ${{\mathcal{L}}}_{\mathrm{bol}}$ and age 23 ± 3-Myr (Mamajek & Bell 2014), with the same method as in Paper I. The results of a 10,000-trial Monte Carlo experiment are shown in Figure 9. Luminosity and age are assumed to be described by Gaussian statistics with the mean and width specified. A value was chosen from each distribution, and then the mass, T_eff, and radius were found in the AMES-Cond hot-start evolutionary models (Chabrier et al. 2000; Baraffe et al. 2003). The negative skewness of the mass distribution is because of the extreme luminosity increase for deuterium-burning objects above ∼13 ${{\mathcal{M}}}_{\mathrm{Jup}}$. The median physical parameters from the distribution are mass = 12.7 ± 0.3 ${{\mathcal{M}}}_{\mathrm{Jup}}$, T_eff = 1708 ± 23 K, and radius = 1.45 ± 0.02 ${{\mathcal{R}}}_{\mathrm{Jup}}$. The error bars represent the uncertainty from the Monte Carlo trials, but do not include systematic errors of the evolutionary tracks themselves.

Zoom In Zoom Out Reset image size

Table 15 compares our results to recent papers on this planet. We have separated the luminosities determined in each work by method—Bonnefoy et al. (2013, 2014) and Paper I used bolometric corrections to determine the luminosity, whereas Currie et al. (2013) quoted a value from the models. We also calculate the ${{\mathcal{L}}}_{\mathrm{bol}}$ from the model-derived T_eff and radius in cases where it is not presented in the paper.

Table 15.  Physical Parameters of β Pic b

	Teff	log(g)	Radius	log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$)			Mass	Init. Spec. Entropy
Reference	/K	(cgs)	/${{\mathcal{R}}}_{\mathrm{Jup}}$	Modeled	B.C.	Empirical	/${{\mathcal{M}}}_{\mathrm{Jup}}$	/kB baryon−1
Currie et al. (2013)	${1575}^{{\rm{a}}}$	3.8 ± 0.2	1.65 ± 0.06	$-3.80\pm 0.02$	⋯	⋯	${6.9}^{{\rm{a}}}$	⋯
Bonnefoy et al. (2013)	1700 ± 100	4.0 ± 0.5	1.5–1.6${}^{{\rm{a}}}$	$-{3.72}^{{\rm{a}}}$	$-3.87\pm 0.08$	⋯	9–10	$\geqslant 9.3$
Bonnefoy et al. (2014)	1650 ± 150	<4.7	1.5 ± 0.2	$-{3.80}^{{\rm{a}}}$	$-3.90\pm 0.07$	⋯	<20	>10.5
Chilcote et al. (2015)	1600–1700	3.5–4.5	⋯	⋯	⋯	⋯	⋯	⋯
Baudino et al. (2015)	1550 ± 150	3.5 ± 1	1.76 ± 0.24	$-{3.77}^{{\rm{a}}}$	⋯	⋯	${4.0}^{{\rm{a}}}$	⋯
Paper I	1643 ± 32	${4.2}^{{\rm{a}}}$	1.43 ± 0.02	⋯	$-3.86\pm 0.04$	⋯	11.9 ± 0.7	⋯
This Work	1708 ± 23	${4.2}^{{\rm{a}}}$	1.45 ± 0.02	⋯	⋯	−3.78 ± 0.03	12.7 ± 0.3	9.75

Notes. Other works use either the luminosity determined from atmosphere models or via a bolometric correction applied to the K-band photometry. Here we determine the luminosity empirically for the first time, and use the ${{\mathcal{L}}}_{\mathrm{bol}}$ and age to determine the T_eff, radius, and mass.

^aValue calculated based on other parameters.

Download table as:  ASCIITypeset image

Fascinatingly, the luminosities from modeling are typically around log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$) = $-3.8,$ while $-3.9$ dex is the typical value for bolometric-correction-determined values. The empirical value we measured is in agreement with the luminosities determined by modeling. This result confirms that the atmosphere models we and others have used for β Pic b are pointing most strongly to a luminosity but not necessarily a temperature. The radius is unknown and the thick clouds prevent strong molecular absorption features from dominating the broad SED, so the emergent flux is dominated by blackbody-like opacity, thus giving a good measurement of the overall luminosity yet obscuring the gravity and T_eff.

We have integrated the combined spectrophotometry from 0.985 to 4.7 μm to determine the energy output that has been empirically measured. We find that >80% of the total energy has been measured in the data (Table 14). We have sampled the SED across the peak of the blackbody, with the combination of data points yielding photometric errors as small as 0.06–0.07 erg s⁻¹ cm${}^{-2}\;\mu$m⁻¹ at the L and M bands (Table 13).

Because of its brightness and proximity, many different types of observations have led to a wealth of information about this exoplanet. Astrometric monitoring of its orbit show that its semimajor axis is ${9.1}_{-0.2}^{+0.7}$ AU (Macintosh et al. 2014; Nielsen et al. 2014; Millar-Blanchaer et al. 2015). For this orbital separation, radial velocity observations place an upper limit on its mass of <15 ${{\mathcal{M}}}_{\mathrm{Jup}}$ (Lagrange et al. 2012). Comparison with models demonstrate that the planet's SED is dominated by thick clouds (this work). We have constrained its luminosity to log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$) = $-3.78\pm 0.03.$ Our method of empirically determining ${{\mathcal{L}}}_{\mathrm{bol}}$ is a unique approach enabled by the broad wavelength coverage of MagAO.

Although J and H spectra are available thanks to GPI, β Pic b's atmosphere is not dominated by molecular absorption in the way that a cloud-free atmosphere is. Instead the overall brightness is constrained by the models.

Many exoplanet atmospheres are characterized by transmission spectroscopy as the planet transits its star. These exoplanets are necessarily on extremely close orbits (of order 0.1 AU) and are thus so highly irradiated that their energy budgets are predominantly due to stellar insolation. Jupiter, on the other hand, is still glowing from its formation (e.g. Ingersoll & Porco 1978; Young 2003), and is thus "self-luminous." To determine whether a planet is self-luminous, the energy input from its star must be compared to its total energy output.

First we consider the energy input from the star. The spectral type, surface gravity, and effective temperature of β Pic A are determined in Gray et al. (2006) via moderate-resolution (R ∼ 1300) optical spectroscopy to be A6V, log(g) = 4.15, and T_eff = 8052 K, respectively. The mass of β Pic A is determined via astrometric measurements of β Pic b to be 1.60 ± 0.05 ${{\mathcal{M}}}_{\odot }$ (Millar-Blanchaer et al. 2015). Given this mass and surface gravity, the radius and luminosity can be calculated; these values are summarized in Table 16.

Table 16.  Empirical Measures of β Pic A Physical Parameters

Parameter	Value	Reference
Teff/K	8052	Gray et al. (2006)
log(g)[cgs]	4.15	Gray et al. (2006)
Mass/${{\mathcal{M}}}_{\odot }$	1.60 ± 0.05	Millar-Blanchaer et al. (2015)
Radius/${{\mathcal{R}}}_{\odot }$	1.78 ± 0.24	Di Folco et al. (2004)
log(${{\mathcal{L}}}_{\mathrm{bol}}$/${{\mathcal{L}}}_{\odot }$)	1.07	Calculation using above values

Download table as:  ASCIITypeset image

Next we consider the total energy output. The ratio of emitted to absorbed energy is

$$\begin{eqnarray}&&E\;=\;\displaystyle \frac{4}{1-A}{\left(\displaystyle \frac{r}{{R}_{*}}\right)}^{2}{\left(\displaystyle \frac{{T}_{p}}{{T}_{*}}\right)}^{4}\end{eqnarray} \tag{ 1 }$$

(Ingersoll & Porco 1978) where A is the Bond albedo of the planet. Cahoy et al. (2010) find that the Bond albedo can vary from 0.3 to 0.9 for directly imaged Jupiter analogs depending on temperature. The snow line in the β Pic system (the radius where the equlibrium temperature is 170 K) is around ∼10 AU, in agreement with de Vries et al. (2012). The "naive snow line" (Lecar et al. 2006) in the Solar System is ∼2.7 AU (e.g., Hayashi 1981, Podolak 2010). Therefore, we choose the albedo value near 2.7 AU in Cahoy et al. (2010) to give a Bond albedo near the snow line of A = 0.7. For the size of the orbit of β Pic b we use the mean semimajor axis of ${9.1}_{-0.2}^{+0.7}$ AU (Macintosh et al. 2014; Chilcote et al. 2015; Millar-Blanchaer et al. 2015). Thus we find that $E\approx {10}^{4}:$ β Pic b is highly self-luminous.

The equilibrium temperature of a planet is given by

$$\begin{eqnarray}&&{T}_{\mathrm{eq}}\;=\;{T}_{*}\sqrt{\displaystyle \frac{{R}_{*}}{r}}{\left(\displaystyle \frac{1-A}{4}\right)}^{1/4}\end{eqnarray} \tag{ 2 }$$

(e.g., Ingersoll et al. 1975, Guillot et al. 1996). For β Pic b we calculate ${T}_{\mathrm{eq}}\;\sim$ 130 K, while the planet is much hotter at T_eff ∼ 1700 K. This is in contrast to hot Jupiters which have effective temperatures close to their equilibrium temperatures (Cowan & Agol 2011). A planet at equilibrium temperature has lost memory of its formation; a self-luminous planet like β Pic b, on the other hand, is hot enough to point toward its initial entropy—which provides the "warm-start" constraint on its formation for β Pic b.

We calibrated the detector linearity during the second commissioning run (2013 March 30th, UT), with the same detector temperature to within a milli-Kelvin (β Pic data: 54.994 K; Linearity data: 54.999 K) and identical bias voltage (VOS voltage = 2.5 V in both cases) to the first commissioning run. We obtained data in the 3.4-μm filter with the rectangle field stop in the wide camera, illuminating a large fraction of the detector while keeping a small fraction un-illuminated for reference. We stepped up the integration time and recorded the median counts within the illuminated rectangle, for 5 images taken at each integration time. We average the count rate for each integration time, and the standard deviation is found to be <0.5%. Figure 10 plots the measured counts rate in data numbers (DN) against the integration time in ms. The data are not linear, and need to be corrected.

Zoom In Zoom Out Reset image size

"True" counts are the count rate that give a linear relationship with integration time. Departure from linearity is determined by subtracting true from measured counts, normalized by true counts—plotted in Figure 11. A series of polynomials are fit to this line, from 2nd order to 4th order, and the best fit is determined to be a 3rd-order polynomial above 27,000 counts.

Zoom In Zoom Out Reset image size

Based on this fit, the linearity correction formula is:

$$\begin{eqnarray}&&y\;=\;A+{Bx}+{{Cx}}^{2}+{{Dx}}^{3}\end{eqnarray} \tag{ 3 }$$

where y is the true counts and x is the measured counts, where the coefficients are: A = 112.575; B = 1.00273; C = −1.40776e-06; and D = 4.59015e-11, and where x must be >27,000 counts. FITS files with coadded data must first be divided by the number of coadds before applying the linearity correction. Figure 12 shows the result of the linearity correction. The data have been linearized up to ∼46,000 DN.

Zoom In Zoom Out Reset image size

The Clio2 detector is a Hawaii-I HgCdTe with a deep well depth (∼56,000 DN), and is thus ideal for high-contrast imaging. The physical array has 1024 pixels on a side, but only two readout amplifiers are usable, bringing the array size to $1024\times 512.$ Although the chip has poor cosmetics (see Figure 13), we compensate in high-contrast imaging by greatly oversampling the PSF in the Narrow camera, allowing for better averaging over the bad pixels while also increasing the dynamic range.

Zoom In Zoom Out Reset image size

We create the bad pixel map as follows. Several short-exposure darks are averaged; pixels that are bright in these images are flagged as hot pixels. Several long-exposure flats are averaged; pixels that are dark in these images are flagged as dead pixels. The flagging threshold is a sigma-clipping chosen by inspection. The hot and dead pixel maps are combined to make the bad pixel map, with a resultant 7% of the pixels being flagged as bad. Note that a high fraction of those are in two lower corners, which we avoid—see Figure 13. The bad pixel map is available as a FITS file on the web in the Clio manual,¹⁷ in full frame and subarray versions.

Flat Fielding—We have put significant effort into attempting to acquire a flat illumination of the Clio detector. There is no flat-field screen in the dome that works with MagAO, so we took twilight flats, either at dusk or dawn. We took flats with a constant integration time as the sun was setting or rising, to vary the illumination level. We tried different integration times. We tried subtracting darks at the same integration time, as well as flats with less solar illumination at the same integration time. We tried all the different filters and both cameras. In all cases, we are not able to remove the "glow" in the top center of the images (see Figure 14). This photometric variation is on the order of 10% across the field for the wide camera. It looks like an out-of-focus image of the pupil, and we posit that it is either caused by a pinhole of light leaking through, or an imperfect anti-reflective coating allowing the last concave optic to focus a glow onto the detector.

Zoom In Zoom Out Reset image size

In any case, this image is not usable as a flat, because the pixels that are bright in the pupil-glow portion of the "flat" are not more sensitive to light, and therefore the raw data should not be divided by this image. Therefore, rather than flat-fielding our data, we depend on the sky subtraction to remove pixel-to-pixel variation in the sky images. Furthermore, the [3.1], [3.3], and L' images were all saturated, so the variation in the unsaturated PSF (after nodding and dithering around the detector) folds in the flat-fielding errors. However, we must add a "flat-fielding" error term for the M' images, because all the images were unsaturated; thus, the simulated planet is unique to each image and has no variation that could include a flat-fielding error. We find this by the variation in the peak of the nodded and dithered PSFs throughout the data set.

Crosstalk—There is electronic cross-talk between the two amplifiers, that manifests as a negative image of the star, located exactly 512 pixels away, with a flux of 0.7% that of the original image. We avoid this crosstalk with our nod pattern; because β Pic b is only <50 pixels from the star, it was not a problem.

Persistence—Persistence was observed in dark images taken at the end of a long night including hours of β Pic observations, an extremely bright star that was saturated for most of the observations. However, we do not typically record or correct for this effect, which was negligibly small.

We observed the Trapezium Cluster in the Orion Nebula as a reference for our platescale, instrument angle, and distortion. Over the nights of 2012 December 3rd, 4th, 6th, and 8th, we observed various Trapezium fields. We locked the AO loop on either ${\theta }^{1}$ Ori B or C. Stars ${\theta }^{1}$ Ori A and E were also in the fields, as were many fainter Trapezium stars, as listed in Table 17.

Table 17.  Trapezium Observations, 2012 December

Filter	Camera	Epoch	Frame #s	${\theta }^{1}$ Ori Stars in Field${}^{{\rm{a}},{\rm{b}}}$
J	Narrow	2012 Dec 03	472–491	C only (100-pixel stamp subarray)
			492–596	A1, E, 43, 48, 59, 63, (A2)
Ks	Wide	2012 Dec 03	1–140	A1, B1, C, E, 43, 48, 49, 59, 63, 70, 73, (A2, B2, B3, B4, 72)
		2012 Dec 06	1–20	B1, E, 48, 49, 78, 81, (B2, B3, B4)
		2012 Dec 08	1–10	A1, C, E, (A2, ...)
	Narrow	2012 Dec 03	141–471	A1, E, 43, 48, 59, 63, (A2)
		2012 Dec 04	1–40	B1, 49, (B2, B3, B4, 35)
		2012 Dec 08	91–124	A1, E, 38, 43, 59, 63, (A2)
		2012 Dec 08	B 1–10	B1, E, (B2, B3, B4, ...)
[3.1]	Wide	2012 Dec 08	1–20	A1, C, 39, 46, 59, 63, 70, 73, (A2, 72)
[3.3]	Narrow	2012 Dec 08	21–40	A1, E, 43, 48, 59, 63, (A2)
L'	Narrow	2012 Dec 08	41–60	A1, E, 43, 48, 59, 63, (A2)
M'	Narrow	2012 Dec 08	61–90	A1, E, 63, (A2)

Notes.

^aSee McCaughrean & Stauffer (1994) for star identification (A1 = 45, B1 = 60, B2 = 56, C = 68, and E = 40). ^bC is not resolved in the Clio images and is listed singly; A1–A2 and B1–B2–B3–B4 are resolved as listed. Stars in parantheses were not used as part of the astrometric solution, due to either having a known high proper motion (72), being too faint to centroid well on (35), being a non-round proplyd (74), or being a close companion with contamination and/or orbital motion creating centroiding and positional uncertainty (A2, B2, B3, B4).

Download table as:  ASCIITypeset image

McCaughrean & Stauffer (1994) produced a comprehensive work on absolute astrometry of the Trapezium cluster, including tying the infrared observations to their radio counterparts, and resulting in an absolute precision of 30 mas rms. This work is often used as a fiducial for referencing the positions of Trapezium stars, but it is now two decades out of date. Nevertheless, we attempt an astrometric calibration referenced to McCaughrean & Stauffer (1994), as a cross-check to another method.

We start with the K_s Wide-camera images of 2012 December 03 (with the most stars in a single frame) and measure the separations of each pair. After reducing the data in the standard way, we find the centroids for each of the stars listed excluding A2, B2, B3, and B4, giving a total of 12 stars. (We exclude the companions to A1 and B1 because, while they are well-resolved, they show the most orbital motion and have the least certain positions.) Comparing these measurements to those of McCaughrean & Stauffer (1994) gives a platescale and instrument angle estimate for each pair of stars.

We also use the fiducial separations in a more recent work: that of Close et al. (2012b), who measured Trapezium positions with near-IR first-light LBT AO with the Pisces camera in Nov. 2011. We find discrepancies in separations at the 10-mas level over 2'' between these two fiducials. To determine whether the discrepancy is due to proper motion or to distortion in Clio, we take the 12 stars as tie points to de-warp the images using IDL's warp_tri. Repeating the process on the undistorted images still results in separation discrepancies of up to 5 mas over 2''. We attribute the difference to true astrophysical variation such as orbital and proper motion in the intervening two decades, and find that the McCaughrean & Stauffer (1994) positions are now out-of-date for mas-level astrometry. Therefore, we use the Close et al. (2012b) positions as fiducials for the distortion correction that follows, in which we use all our Trapezium observations of 2012 December.

Close et al. (2012b) used a pinhole grid to calibrate distortion on LBT/Pisces, and used HST images of the Trapezium (Ricci et al. 2008) for calibrating the instrument angle and platescale. Therefore, tying our distortion correction to Close et al. (2012b) is one step away from tying it to a pinhole calibration.

To compute the distortion solution, we compare our Trapezium observations to the first-light LBTAO/Pisces observations (Close et al. 2012b). We group our data sets by camera and filter (see Table 17). For each set of (camera, filter) we have a series of frames dithered around the Trapezium cluster. A single frame does not have sufficient numbers of stars to get a good astrometric calibration. Therefore, we solve an inverse problem using MPFIT in IDL (Markwardt 2009) to determine the shifts, scales, and rotations that transform the Pisces coordinates to Clio coordinates for each image. The output are x and y shifts $[{dx},{dy}]$ for each position on the array that imaged a star. While we perform the fit for each set of camera and filter, the distortion is not significantly different for the various filters, so in the end we combine the data into one group for each camera. The distortions are shown as red vectors in Figure 15.

Zoom In Zoom Out Reset image size

These shifts $[{dx},{dy}]$ are fit to a three-dimensional polynomial to create a smooth surface using MPFIT2DFUN (Markwardt 2009). These are shown in Figures 16–17. These images are saved as FITS files for input into the IRAF Drizzle package (Fruchter & Hook 2002).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Finally, we use the distortion correction to get a best value for the platescale and instrument angle. We correct the distortion in the images and determine the platescale and instrument angle by comparing pairs of stars to the fiducial separations and position angles. After correcting the Trapezium data for distortion, the resulting platescale and instrument angle are reported in Table 18.

Table 18.  Astrometric Calibrations, 2012 December

			Meas.	Fid.	Total
Quantity	Value	Unit	Error	Error	Error
Platescale, Narrow	15.846	mas/pix.	0.043	0.047	± 0.064
Platescale, Wide	27.477	mas/pix.	0.071	0.047	± 0.085
${{\rm{NORTH}}}_{{\rm{Clio}}}^{{\rm{a}}}$	−1.797	°	0.159	0.3	± 0.34

Note.

^aDerotation Angle: ${{\rm{DEROT}}}_{{\rm{Clio}}}\;=\;{\rm{ROTOFF}}-180+{{\rm{NORTH}}}_{{\rm{Clio}}}$ A positive angle is counterclockwise to get north up and east left.

Download table as:  ASCIITypeset image

Measurement error is the sample standard deviation of our 10 to 16 frames with 6 to 12 stars per frame. Fiducial error is the uncertainty in the reference positions, as given in Close et al. (2012b). Errors are added in quadrature with measurement error to obtain the total astrometric calibration error. The instrument angle "NORTH Clio" is used to derotate the images counter-clockwise as given in the table.