1. Pluto’s thermal lightcurve: SPITZER/MIPS observations
E. Lellouch, J . Stansberry,
D. Cruikshank, W. Grundy

2. Introduction
Pluto has strong albedo contrasts and a well-marked visible lightcurve  a thermal lightcurve is expected
IRAS and ISO observations of Pluto-Charon have detected the lightcurve at 60 and 100 micron
ISO: the thermal lightcurve is roughly anticorrelated with the visible lightcurve, but shifted by ~ 25°
Modelling of ISO observations at 60,100,150 and 200 µm indicates (Lellouch et al. 2000)
A measurable thermal inertia  = (1.5-10)x104 cgs
Relatively high bolometric emissivities (e.g for CH4)

3. SPITZER/MIPS Observations
Sept , 2004
Sub-earth latitude = 32°
8 longitudes
24, 70, 160 µm
Data reduction steps
MIPS Instrument Team reduction tools (see J. Stansberry’s talk)
160um data was time-filtered to increase SNR                
Increase in calibration uncertainty  
 Color corrected fluxes

4. 24 micron
70 micron
160 micron

5. Lightcurve clearly detected at 24 micron Amplitude (max/min) ~50 %
First detection of Pluto-Charon at 24 micron
Lightcurve clearly detected at 24 micron
Amplitude (max/min) ~50 %
Lightcurve more noisy at 70 micron
Amplitude (max/min) ~30 %
Lightcurve not detected at 160 micron
Min = 5.4 mJy

6. Pluto-Charon brightness temperatures:
Decrease with increasing wavelengths
Lower than ISO at 70 and 160 micron
SPITZER 70 micron lightcurve has lower amplitude than ISO 60 micron lightcurve

7. Thermophysical modelling
Thermophysical model (from Lellouch et al. 2000), including:
Sub-surface conduction (thermal inertia , thermal parameter )
 = subsurface heat radiative timescale / diurnal timescale
Bolometric albedos (Ab) and emissivity (b), spectral emissivities ()
Beaming (surface roughness – nominal =20°)
Proper geometry (e = s = 32°)
Surface distribution of terrains
Charon
3 units on Pluto N2
CH4
Tholins+H2O

8. Charon’s emission
Charon has ~no visible lightcurve (Ag ~ 0.375)  constant thermal flux
Maximum Charon 24 µm flux = Minimum of 24 µm lightcurve = 5.4 mJy max. Charon brightness temperature : TB < 59 K
This maximum flux can be obtained from TPM with
b =  = 1 (water ice)
Ab = 0.22,  = 2, slope = 20°
NOTE: Even if no beaming, and assuming instantaneous equilibrium with solar insolation ( = 0), flux < 5.4 mJy flux implies Ab > 0.33, i.e. a phase integral
q > 0.88 : unlikely… - Charon has non-zero thermal inertia
Minimum Charon 24 µm flux
Obtained by assuming Charon in equilibrium with diurnally-averaged insolation ( = ). Ab = Ag = No beaming. Gives TB > 49.5 K F(24 mic)=0.7 mJy
Note: Charon’s temperature measured from SMA = 56+/-14 K (Gurwell et al. 2005). Very nice but far too imprecise…

9. Phase integral vs. albedo for planetary surfaces

10. Charon’s emission
Charon has ~no visible lightcurve (Ag ~ 0.375)  constant thermal flux
Maximum Charon 24 µm flux = Minimum of 24 µm lightcurve = 5.4 mJy max. Charon brightness temperature : TB < 59 K
This maximum flux can be obtained from TPM with
b =  = 1 (water ice)
Ab = 0.22,  = 2, slope = 20°
NOTE: Even if no beaming, and assuming instantaneous equilibrium with solar insolation ( = 0), flux < 5.4 mJy flux implies Ab > 0.33, i.e. a phase integral
q > 0.88 : unlikely… - Charon has non-zero thermal inertia
Minimum Charon 24 µm flux
Obtained by assuming Charon in equilibrium with diurnally-averaged insolation ( = ). Ab = Ag = No beaming. Gives TB > 49.5 K F(24 mic)=0.7 mJy
Note: Charon’s temperature measured from SMA = 56+/-14 K (Gurwell et al. 2005). Very nice but far too imprecise…

11. Charon-corrected Pluto brightness temperatures
Decrease with increasing wavelengths
for nominal Charon model
<TB (24 mic)> ~ 50 K
<TB (70 mic)> ~ 42 K
<TB (160 mic)> ~ 35 K

12. Pluto-only TB Decreases with increasing wavelengths from 24 to 160 mic
Mixing of multiple temperatures?
Possible in theory, but does not work quantitatively (at least for simple 2-temperature model)
Emissivity effect?
Can be technically fit with single temperature and spectrally constant emissivity, but solution seems implausible: T ~ 55 K,  ~ 0.3
More likely solution: a spectrally-variable surface emissivity (decreasing with wavelength)

13. Pluto: thermal inertia from lightcurve phase
24-mic lightcurve almost anticorrelated with visible lightcurve, but anticorrelation maximum if 24-mic lightcurve shifted by 14-17°
Elementary modelling of 24-mic data
Includes Charon + 2 types of Pluto terrains (« cold » and « hot » regions)
Fix temperatures of Charon and Pluto cold regions
(TCH = 57 +/-2 K, Tcold = 40 +/- 5 K)
Take Cold / Hot relative proportions from visible lightcurve
Fit thermal lightcurve by solving for Thot and a global shift of thermal lightcurve

14. Pluto/Charon lightcurve: elementary fit
Solution: Th = K and shift = 15-18°
Suggests thermal parameter  ~2-3
As expected, does not match 70 and 160-mic data

15. Physical models CH4 N2 Tholin-H2O Grundy and Fink 96
Lellouch et al 2000
Modified G & F
HST
Modified HST
Physical models
Includes Charon and three-unit models of Pluto – from Grundy et al. 2001
Estimate geometric albedos of each unit from visible lightcurve fit and deduce bolometric albedos
Additional assumptions
-- T (N2) = 35 K
-- Emissivities
Tholin-H2O:  = b = 1
CH4: b = 0.85, 24 mic = 0.35 , 0.7, 1
Focus first on 24-mic lightcurve : solve for thermal parameter  of Pluto and for Charon emission « background »
Then model 70 and 160-mic data

16. CH4 N2
EMISSIVITY OF ICES
(Stansberry et al. 1996)

17. Physical models CH4 N2 Tholin-H2O Grundy and Fink 96
Lellouch et al 2000
Modified G & F
HST
Modified HST
Physical models
Includes Charon and three-unit models of Pluto – from Grundy et al. 2001
Estimate geometric albedos of each unit from visible lightcurve fit and deduce bolometric albedos
Additional assumptions
-- T (N2) = 35 K
-- Emissivities
Tholin-H2O:  = b = 1
CH4: b = 0.85, 24 mic = 0.35 , 0.7, 1
Focus first on 24-mic lightcurve : solve for thermal parameter  of Pluto and for Charon emission « background »
Then model 70 and 160-mic data

18. Fit of 24-mic lightcurve
Need for better
measurements here!

19. 24 micron fit: solution parameters
24 micron fit: solution parameters
Input parameters ! Fitted parameters
Ag(N2)
Ag(CH4)
Ag(thol
CH4
tholin
PL
CH (mJy)
<T>CH (K)
CH GF
0.76
0.53
0.10 1 7
3.9
57.2
3.5
.35 10
5.4 59 2
Lellouch
0.74
0.62
0.25
4.1
57.4 3
5.1
58.6
2.3
Mod. GF
0.69
0.32
4.45
57.9
2.5
0.7
4.6
58.1
HST
0.78
0.83 (!?)
0.20
4.2
57.6
Mod. HST
0.91 8
2.35
54.5
2.15
54.1
PL = 7 – 10
CH = 2 – 10 (generally 2-3.5)
<TCHARON > = K

20.  Calibration problem at 70 micron?
EMISSIVITY RESULTS
CH4: 24 mic = give better fits than 24 mic = 0.35
Models with spectrally-constant emissivities overestimate MIPS-measured TB at 70 and 160 mic (but would almost fit ISO 60 and 150 mic…)
Decrease of spectral emissivities of tholin-H2O regions at long wavelengths? Or
 Calibration problem at 70 micron?

21. Conclusions
Pluto’s thermal parameter  = 7-10, i.e. thermal inertia  = (3-5)x104 cgs: consistent and more accurate than ISO
Newest result: <T>CHARON = K, i.e.  = 2-10 ( = range favored, i.e.  = (1-2)x104 cgs)
Charon is not in instantaneous equilibrium with Sun, but probably has lower thermal inertia than Pluto.
Charon’s TI comparable to Saturn’s icy satellites, and Pluto’s to Galilean satellites.
Pluto’s TI enhanced by atmospheric conduction in porous regolith?
CH4 ice 24-mic emissivity not small (0.7-1)
Tholin-H2O emissivity decreases from 24 to 70 and 160 mic., but possible calibration error ?

22. Charon’s emission
Charon has ~no visible lightcurve (Ag ~ 0.375)  constant thermal flux
Min. 24 µm flux = 5.4 mJy = max. Charon flux TB < 59 K
This maximum flux can be obtained from TPM with
b =  = 1 (water ice)
Ab = 0.22,  = 2, slope = 20°
NOTE: Even if no beaming, and assuming instantaneous equilibrium with solar insolation ( = 0), flux < 5.4 mJy flux implies Ab > 0.33, i.e. a phase integral
q > 0.88 : unlikely… - Charon has non-zero thermal inertia

23. Range of Charon’s emission
Maximum model
<TB> = 59 K; obtained from thermophysical model (TPM) with Ab = 0.22,  = 2, slope = 20°, F(24 mic)=5.4 mJy
Minimum model:
Charon in equilibrium with diurnally-averaged insolation ( = ).
Ab = Ag = No beaming. Gives <TB> = 49.5 K, F(24 mic)=0.7 mJy
Nominal model:
<TB> = 57 K; obtained from thermophysical model (TPM) with Ab = 0.22,  = 3.5, slope = 20°, F(24 mic)=3.75 mJy
Note: Charon’s temperature measured from SMA = 56+/-14 K (Gurwell et al. 2005). Very nice but far too imprecise…

24. Fitting Pluto 24:70 mic. color temperature
___ TB (70 mic)
….. TB (24 mic) X 
X =Charon min
X =Charon nom
X =Charon max
Fitting Pluto 24:70 mic. color temperature
TB (70 mic) ~ 42 K
TB (24 mic) ~ 50 K
No solution for 2-temperature model
An (unlikely?) solution for Tsurf ~55 K and spectrally constant emissivity ~ 0.3
More likely solution: spectrally variable surface emissivity
___ TB (70 mic)
….. TB (24 mic)

25. Fit of visible lightcurve