The photometric functions of Phobos and Deimos. II. Surface photometry of Deimos

ICARUS 30, 200--211 (1977)

The Photometric Functions of Phobos and Deimos. II. Surface Photometry of Deimos M. N O L A N D AND J. V E V E R K A

Laboratory for Planetary Studies, Cornell University, Ithaca, New York 14853 Received November 18, 1975; February 4, 1976 To a good approximation the face of Deimos observed by Mariner 9 is covered uniformly by a dark, texturally complex material obeying a Hapke-Irvine scattering law. The intrinsic 20 ° to 80 ° phase coefficient of this material is f~l = 0.017 __+ 0.001mag/deg, corresponding to a disc-integrated value of fl--O.030mag/deg. There is also evidence of a slightly brighter (by ~30%) unit near some craters which may have been produced by the cratering events. Its texture appears to be identical to that of the average material. No evidence of quasi-specular reflection has been found, suggesting that large-scale exposures of unpulverized rock are absent. 1. INTRODUCTION N o l a n d a n d V e v e r k a (1976; h e r e a f t e r referred to as P a p e r I) d e t e r m i n e d t h e m e a n " e q u i v a l e n t s p h e r e " p h a s e curves of P h o b o s a n d D e i m o s b e t w e e n p h a s e angles of 20 ° a n d 80 ° using d i s c - i n t e g r a t e d brightnesses m e a s u r e d f r o m Mariner 9 Bc a m e r a television frames. T h e p h a s e curves of t h e satellites were f o u n d to be similar to t h e p h a s e c u r v e of t h e Moon, a n d characteristic of objects whose surface layers are d a r k a n d i n t r i c a t e in t e x t u r e . As n o t e d in P a p e r I, for such surfaces a good a p p r o x i m a t i o n to the p h o t o m e t r i c s c a t t e r i n g law is g i v e n b y t h e H a p k e - I r v i n e relation (Veverka, 1971) ( c o s / ) I(i'E'°O=C c o s i T c o s ¢

f(~)'

C . f ( a ) o v e r t h e satellites' surfaces. Since t h e Mariner 9 R e d u c e d D a t a R e c o r d (see P a p e r I) gives the relative intensity, I , a t each pixel, we need o n l y calculate i a n d E a t a n y g i v e n p o i n t to d e t e r m i n e C.f(a) f r o m (1). As in P a p e r I, we a s s u m e t h a t D e i m o s is a triaxial ellipsoid. The m e t h o d of d e t e r m i n i n g i a n d E has been described in detail b y N o l a n d (1975). The picture scales ( n u m b e r pixe]s/km) for D e i m o s used in this d e t e r m i n a t i o n are given in T a b l e I, along w i t h t h e i r e s t i m a t e d uncertainties. A t a c o n s t a n t p h a s e angle ~, v a r i a t i o n s in the o b s e r v e d v a l u e of C . f ( a ) could be due to t h r e e m a i n causes: 1. E q u a t i o n (1) is n o t a valid a p p r o x i m a tion to t h e t r u e s c a t t e r i n g law. 2. T h e calculated values o f i a n d ¢ are

(1)

w h e r e C is a c o n s t a n t related to albedo; a is t h e p h a s e angle; i a n d ~ are t h e angles of incidence a n d s c a t t e r i n g r e s p e c t i v e l y ; a n d f ( a ) is a f u n c t i o n which in this a p p r o x i m a t i o n d e p e n d s on a only, a n d n o t on i a n d s e p a r a t e l y . E q u a t i o n (1) a m o u n t s to a simple generalization o f t h e L o m m e l Seeliger s c a t t e r i n g law. I n this a n d in a c o m p a n i o n p a p e r (Noland a n d V e v e r k a , 1977; P a p e r I I I ) we will use t h e Mariner 9 television d a t a to s t u d y the u n i f o r m i t y of the p a r a m e t e r 2oo Copyright ~) 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

TABLE I SCALE OF DEIMOS PICTURES

Spacecraft orbit 1)73 Dill D159 D149 I)25 D63

Scale (pixels/km) 4.3 5.7 4.3 7.8 4.6 5.3

_ 0.1 _ 0.1 __+0.2 + 0.1 + 0.1 +_ 0.1

SURFACE PHOTOMETRY OF DEIMOS n o t close to t h e t r u e values due to signific a n t local slopes. 3. The t e x t u r e a n d / o r albedo of t h e surface material is n o t uniform o v e r t h e disc. Variations in surface t e x t u r e will result in changes in the d e p e n d e n c e of f ( a ) on a. Variations in surface albedo with no a c c o m p a n y i n g changes in surface t e x t u r e will manifest themselves as changes in C. Additionally, if erratic values of C.f(o~) are o b t a i n e d the p h o t o m e t r i c a c c u r a c y of the d a t a could be in doubt. I n P a p e r I we h a v e s t a t e d our reasons for believing t h a t t h e p h o t o m e t r i c a c c u r a c y of the d a t a is a d e q u a t e for our purposes. A l t h o u g h T h o r p e (1975) feels t h a t some correction to the relative p h o t o m e t r y m a y be necessary, t h e suggested correction is < 5 % for 70~
201

t h e causes m e n t i o n e d above is responsible for the variation. 2. A TEST FOR RECIPROCITY Before we investigate the v a l i d i t y of Eq. (1) as an a p p r o x i m a t i o n to the t r u e scattering law of Deimos' surface, we will show t h a t our p h o t o m e t r i c d a t a satisfy the reciprocity principle (Minnaert, 1941; Chandrasekhar, 1960). According to this v e r y general principle, scattering from a n y surface with uniform p h o t o m e t r i c properties m u s t o b e y the relation

I(i, ~) cosE = I*(i*, ~*) cos E*, where ~* = i and i* = E. I n w h a t follows, we refer to points whose incident a n d scattering angles are i n t e r c h a n g e d as conjugate points. W e now consider the d a t a for two pairs of conjugate points on f r a m e D73 a n d t h r e e on D149. These points are chosen a t r a n d o m , e x c e p t t h a t areas which clearly lie within craters are avoided. (In particular, we avoid the p h o t o m e t r i c e q u a t o r s of these two frames, since t h e y contain several craters. See Section 3.) To m a k e the t e s t as stringent as possible we pick points which are far a p a r t on the surface. Table I I gives the l a t i t u d e and longitude, i and E, intensity, and I . cose for t h e chosen pairs. (Note t h a t due to the finite size of t h e pixels, not all of the points are precisely

TABLE II R E C I P R O C I T Y C H E C K F O R ~)EIMOS

Conjugate points Spacecraft orbit

Latitude (deg)

73

30.0 0.0 30.0 10.0

73

149 149 149

20.0 10.0 10.0 0.0 20.0 --10.0

West -longitude (deg)

i (deg)

(deg)

I (DN)

/ COS E

51 55 62 64

+22.5 +112.5 +52.5

66 49 56

49 64 48

78 129 93

%97.5 +15.0 +37.5 +67.5 +345.0 +52.5 +352.5

47 51 26 33 73 39 60

56 24 52 75 32 60 45

116 86 132 120 35 108 83

77 79 30 30 54 58

202

NOLANI)

AND VEVERKA

conjugate.) The reciprocity relation is seen to hold quite well, and we conclude t h a t (i) the relative photometry of the B-camera across the satellite disc is sufficiently accurate for our purposes, (ii) our method of determining i and e is reliable, and (iii) to a first approximation the surface of Deimos is photometrically homogeneous. We now proceed to demonstrate t h a t Eq. (1) provides an adequate description of the scattering law for the surface of Deimos.

3. S T U D Y

OF SCANS A L O N G T H E PHOTOMETRIC E Q U A T O R

Equation (I) predicts that for a homogeneous satellite surface the intensity, I, should increase from terminator to limb, while the "F-function", F(a) _=f(a), should remain constant. This predicted behavior can be tested by studying the values of I and F(a) along the satellite's photometric equator. The approximate path of the photometric equator in each of the six pictures for which we have data is shown in Fig. 1. Since the paths are all located in the same general region of the Mars-facing side

50

I

I

I

I

I

I

I

I

I

~ ~

4C 3C 2O

g

o

J

-20

wift

- -

25

~/.,

[_~<,~.(__._..¢5z

I

I

_

-3O -40 -50

t

t

I

I

I

140 120 I00 80 60 40 20 Longitude (deg)

I

I

i

0 340 320 300

FIG. 1. A p p r o x i m a t e l o c a t i o n o f t h e p h o t o metric equator in each of the pictures studied. The number beside each curve denotes the spacecraft orbit number on which the frame was t a k e n (see T a b l e I). T h e l o c a t i o n s o f a f e w p r o m i nent craters have been sketched in for reference.

of Deimos, our conclusions will pertain only to this region. I and F(a) are plotted against photometric longitude, oJ, for the six Deimos pictures in Figs. 2 to 7. The points shown were obtained by averaging three scan lines centered on the photometric equator. (The Mariner 9 B-camera orientation is such t h a t the scan lines are parallel to the photometric equator.) The error bars represent the variance in the three values averaged to obtain each point shown. Note t h a t since the photometric longitude, ~o, is defined as a spherical coordinate, the limb (E = 90 °) and terminator (i = 90 °) on the satellite do not occur precisely at co = 90 ° and co = - 9 0 ° + a, respectively. Also note t h a t a 3-4 pixel smear, probably due to a combination of camera effects and relative satellite/spacecraft motion during exposures, is evident near the limbs. In the cases of D159, D25, and D63, the behavior is in excellent agreement with Eq. (1): I increases from terminator to limb and F(a) is constant, except in the vicinity of one obvious crater, which causes the calculated i and e to deviate from their true values. We conclude t h a t Eq. (1) provides a good description of the surface scattering function of Deimos. The departure of the other three scans from the expected behavior can be understood by examining the pictures given in Veverka et al. (1974). The two peaks in F(a) which occur near oJ = 0 ° in D73 and D111 and near co = 40 ° in D149 correspond to a small bright patch associated with two or more craters. The enhancement m a y represent either crater highlights, i.e., an apparent brightening of raised rims tilted toward the Sun, or perhaps material of different albedo and/or texture ejected by the impacts which formed the craters. To obtain an intrinsic phase function for Deimos, we wish to avoid this anomalously bright region. The photographs suggest t h a t the section of the photometric equator between the bright area and the limb (i.e., at larger ~o) should be more representative of the average disc. Looking at the line scans again, we can see t h a t F(a) is indeed fairly constant in this region for D l l l and D73. Only a small section of

SURFACE PHOTOMETRY OF DEIMOS

203

Z~,C

- DEIMOS Sev 73

18C

16C 14C

..'t I

12C i

~

8C

t

6C

J

4C 2C

c

r''

Sun

i:(

I.

t-4b-

r

_2qO

II

i

'

0

2O Omega (deg)

40

8O

T£3 DEIMOS Rev 73 520 280 •

i

24O o

200

120

t

80

'

t

.

!

4O 0 -61

i=ff "'

-,b

'

-~o

'

o

Sun

,~o

'

Omega (deg)

,io

'

do

~o

[

FIo. 2. Top : I n t e n s i t y s c a n s across t h e p h o t o m e t r i c e q u a t o r for f r a m e D73. T h e p o i n t s s h o w n were o b t a i n e d b y a v e r a g i n g t h r e e s c a n lines c e n t e r e d o n t h e p h o t o m e t r i c e q u a t o r . T h e e r r o r b a r s r e p r e s e n t t h e v a r i a n c e i n t h e t h r e e v a l u e s a v e r a g e d t o o b t a i n e a c h p o i n t s h o w n . T h e p h o t o m e t r i c l o n g i t u d e is d e n o t e d b y m a n d is defined so t h a t o n a s p h e r e t h e l i m b occurs a t oJ = + 9 0 ° a n d t h e t e r m i n a t o r a t w = - - 9 0 ° + ~, w h e r e c¢ is t h e p h a s e angle. O n D e i m o s t h e s e e x a c t v a l u e s do n o t hold. T h e s u b s o l a r p o i n t a n d t h e s p e c u l a r p o i n t s are i n d i c a t e d . C a m e r a o p t i c s r e s u l t i n s o m e s m e a r i n g a t t h e l i m b . P h a s e a n g l e = 22 °. Bottom: F - f u n c t i o n (see t e x t ) for t h e i n t e n s i t y d a t a a b o v e . T h e p o s i t i o n s o f p r o m i n e n t a l b e d o a n d t o p o g r a p h i c f e a t u r e s are i n d i c a t e d .

this region is visible in D149 (indicated by an arrow in Fig. 4), but we still consider the F(a) corresponding to this area as most representative of Deimos at this phase angle. The F(a) thus obtained is in good agreement with that obtained from D25, which corresponds to a similar phase angle,

and which does not show any effects of local slope or albedo variations (Fig. 6). For each of the Figs. 2 to 7 we estimate the average F(a) and the likely variation in this average. Table I I I gives the raw 2'(a) with their associated error bars, and the corrected F(a), derived from the raw

204

NOLAND AND VEVERKA 500 F DE HvlOS i Rev III I

2s°I

,t~t~#÷{ti+++,~d+"'

(

+

200 i

+

,

150i=

+"

i , !

4

•,.+

I00 i

50

"

1

i I

+

[

i

=E

Sun I

t '

Omega (deg)

8'o

c

o

600 -DEIMOS Rev I~[

--

i--t

50O +

400 °°° • °

LL.

i

300

'

i

°

800

+

.

I00

{ i=~

!

0 -60

-40

-20

0

Sun

20 Or=e~ ( d e g )

40

60

80

:FIG. 3. Same as Fig. 2, but for frame D l l l . Phase angle = 31 °.

.F(o:), by applying the first two correction factors of Table III Paper I. The intrinsic phase function of the surface material of Deimos is now readily obtained since

L~(ao)J

where s 0 is a reference p h a s e angle: in our case, s 0 = 2 2 ° . This p h a s e f u n c t i o n is p l o t t e d in Fig. 8. A least-squares fit yields /3i = 0.019 3= 0.001 m a g / d e g for the m e a n 20 ° to 80 ° intrinsic p h a s e coefficient of the surface, in fairly good a g r e e m e n t w i t h the value 0.017 m a g / d e g p r e d i c t e d in P a p e r I. As in P a p e r I, the values of fli a n d M 0 shown in Fig. 8 (and all s u b s e q u e n t figures) ignore a n y small p h a s e angle opposition effect.

SURFACE PHOTOMETRY OF DEIMOS

205

2OO "DEIMOS Rev 149 180 160

140 (20

0 I00

....

80

6O 40

~Sun

20

0 -so

~lb

'-~o

J

J

,

0

20 Omega ( ,leg )

t

L

,

40

80

60

._c

~F~ omoc

3 6 0 - DE I MOS Rev 149

3ZO

11~"

280

240

~ ° 2OO

A

~ 160

120 8O i=~

0

-6o

t

-4~

1

-io

...A

1

o

_[

2~

Sun L

40

i

6o

e~-,

~o

On,ego (deg)

Fro. 4. Same as FiB. 2, b u t for I)149. Phase angle ----65%

TABLE III DEIMOS

PHASE

FUNCTIO~

Satellite/ spacecraft orbit

l~hase angle m (deg)

]:)73 I)lll D159 ]:)149 ]:)25 D63

22 31 51 65 68 73

~)ETERMINED

FRO~I PKOTO~IETRIC

Average F(~) ( R D R DN) 243 415 285 220 117 210

+ 3 + 4 + 5 + 10 -I- 3 + 10

EQUkTOR

Average/~(~) corrected a 250 219 157 121 115 106

+_ 3 ± 2 + 3 + 5 _____3 ± 5

SCANS

Normalized magnitude 0.00 0.14 0.51 0.79 0.85 0.94

+ 0.02 + 0.01 + 0.02 + 0.05 __ 0 . 0 3 ± 0.05

° F(~) corrected = F(~) (RDR) x shutter speed factor x Sun-Mars distance factor. See P ap er I.

206

NOLANI) AND VEVERKA

200 - DEIMOS Rev 159 180

,}~,} {' ' ;~

160

°t¢

140

,

{

{

120 I00

{{{{

-- 80

,{{

60 {

40 i:E

2O -60

'

-40

Sun

i

-20

0

20 Omega [deg)

i

40

60

80

36C - DE I MOS Rev 159 32C li"P}liiti%--,

t, o

28C

.poll.

240 20C 16C r20

i:E

-60

...........

-40

-20

•

0

......... 20 Omega (deg)

Sun

40

F I O . 5. S a m e a s F i g . 2, b u t f o r D 1 5 9 . P h a s e

4. PHOTOMETRIC BEHAVIOR OF SELECTED AREAS ON DEIMOS

The line scans provide an effective means of demonstrating the applicability of Eq. (1) to the surface material of Deimos, but t h e y cover only a small portion of the satellite's disc. To study the variation of F(a) over the disc more completely, we have to consider areas other than the photometric equator. Since calculation of the F-function for every pixel in a given picture would be prohibitive, we average the intensity over 5 × 5 pixel areas and use the i and E of the center pixel to determine

i. . . . 60

80

a n g l e = 51 °.

F(a). A typical result is shown in Fig. 9, with the picture shown for comparison. An examination of this figure reveals t h a t the surface of Deimos is not quite as uniform as the photometric equator scans would indicate. Two areas have been circled which seem to represent the brightest and darkest areas on the disc. The bright region is located within about 20 ° of latitude 0°S, longitude 30°W, while the dark region is just below the bright area at about latitude 20°S, longitude 20°W. The bright region is readily identified with the two peaks noted in the photometric equator line scans (Figs. 2 to 4).

SURFACE

PHOTOMETRY

207

OF DEIMOS

IOO -DEIMOS Re',' 25 90 80

TO 60 .°e

~ 50 ~

40

3O i"

20 .°

I0 0

i

-60

-4C)

Surl

i=~

-20

0

-4'o

20 Omego(deg)

'

6b I,

eb

?-CO., DEIMOS Rev 25 180 160 140 12C

"''"'""i~""

...... " ""

'~'"

"

~~ ~ ~

Joc 80 6C 40 i=E: o

oo

,

4b

"'2-F - ~

1

,

o

L

20

Sun ,

~

,

6b

,

~o

Omego ( deg )

FIG. 6. S a m e a s F i g , 2, b u t f o r D 2 5 . P h a s e a n g l e = 68 °.

TABLE

IV

DEII~IOS : PHASE FUNCTION FOR BRIGHTEST REGION

Spacecraft orbit

Phase angle a (deg)

D73 Dlll D159 D149 D25

22 31 51 65 68

a See

Table

III.

A v e r a g e lv(~¢) (RDR DN)

280 490 320 280 130

+ + _ -t+

10 20 15 10 10

A v e r a g e F(~¢) (corrected) =

288 259 176 154 128

+ 10 ___ 10 ___ 08 + 05 __ 10

Normalized magnitudes

0.00 0.12 0.53 0.68 0.88

+ 0.05 ___0.05 + .005 __+0.05 __ 0 . 1 0

208

NOLANI) AND VEVERKA

2OO- DE IMOS Rev 65 180 160 140

{~*

120

g ~

tO0

).

813

~"

.... '

6O , e•

4C

i

oI

•"

i=E

ts]°

20 i

0 -60

i

I

-40

I •_1

I

20

0

I

i___l

2~0 Omega (deg)

i

40

810 J

6O

360 DEI MOS Rev 65 520 280 240

o

.-,

u

• ..

200 tL

•

,o- "..o"

""',.0.P,l

.t ~'I°"

*,(

160 120 80 i=E

40

Sun r

t

0 --J -60

. . . . -4'0

-2o

. . . . .

o

20

II

~o

6'0

,

"-

80

Omega (deg)

FIG. 7. S a m e a s F i g . 2, b u t for D63. P h a s e a n g l e = 73 °.

TABLE DEIMOS : P H A S E Spacecraft orbit

Phase angle ~ (deg)

D73 Dlll D159 D149 D25

22 31 51 65 68

a See T a b l e I I I .

V

FUNCTION FOR DARKEST REGION Average F(~) (RDR DN) 210 370 260 205 110

+ 10 _+ 10 ± 10 ± 10 ± l0

Average F(~) (corrected) a 216 195 143 113 108

_ _ ± ± ±

10 05 05 05 l0

Normalized magnitudes 0.00 0.11 0.45 0.70 0.75

+ ± ± ± ±

0.05 0.05 0.05 0.05 0.10

209

S U R F A C E P I t O T O ~ I E T R Y OF I ) E I M O S

Fortunately, both the bright and dark regions can be located approximately on each of the six Deimos pictures. Tables IV 0.2 and V list the estimated F(a) for the bright ~ 0.4 and dark areas, respectively, while Figs. ~ o.6 10 and 11 show the resulting phase curves. ~ 02 Both regions have identical intrinsic phase ~- I0 coefficients, fit = 0.017 ± 0.001 mag/deg, 1.2 f;4 corresponding to equivalent sphere disc1.6 integrated values of fl=0.030mag/deg I0 20 50 40 50 60 70 80 90 (see Paper I). These phase coefficients are a (deg) in general agreement with the values derived from the line scans, and in exact Fro. 8. D e i m o s : A v e r a g e i n t r i n s i c p h a s e c u r v e agreement with the values obtained indeof t h e surface m a t e r i a l d e t e r m i n e d f r o m s c a n s pendently in Paper I. We adopt these a l o n g t h e p h o t o m e t r i c e q u a t o r . T h e d a t a are values as our formal estimate of the phase n o r m a l i z e d t o t h e v a l u e o f F ( ~ ) a t ct = 22 ° (see T a b l e I I I ) . A s t r a i g h t l i n e fit is s h o w n ; fl~ is t h e coefficients of Deimos. slope a n d M o t h e ~ = 0 ° i n t e r c e p t . The identical photometric behavior of

DEIMOS / /3p0.019+0.~[mog.d:legJ

-02- ~ O.C-

O 0 11 75 180 194 148 83 16 o 0 o 0 o

0 31 178 3O9 384 418 386 335 276 59 o 0 o o

0 152 318 34o 405 446 425 380 365 290 23 o i o

30 66 272 298 321 32o 347 358 427 419 441 456 420 431 402 3~9 291~63 348~67 197 3~5 3 126 0 0 0 0

D iii 82 0 o 0 0 3o7 346 374 497 o 321 338 36q 393 476 362 371 385 ~ 388 425 4 2 6 4 ~ / ~ 6 3 ~ 4 2 9 465~'~83~I~1 475 ~21 443~,~08 ~97 48Q-/408 401 ~ 7 44 2 ~ 374 3 6 5 ~ 3 6 2 376 .369 366 369/3~1 426 413 411 403 355 387 457 462 436 379 71 317 ~51 442 369 0 0 72 0 0

0 o 0 488 412 366 363 349 334 311 264 155 0

0 o 0 0 604 425 332 273 263 250 190 75 0 o

FIG. 9. Top: F - v a l u e s d e r i v e d for f r a m e D111. T h e n u m b e r s s h o w n are v a l u e s a v e r a g e d o v e r 5 × 5 pixel areas. N e a r t h e edges o f t h e p i c t u r e t h e v a l u e s are u n r e l i a b l e . T w o regions h a v e b e e n circled : one b r i g h t e r t h a n a v e r a g e (top), t h e o t h e r d a r k e r t h a n a v e r a g e ( b o t t o m ) . T h e p h a s e f u n c t i o n s for t h e s e regions are g i v e n in T a b l e s I V a n d V, a n d in Figs. 10 a n d 11. Bottom: P h o t o g r a p h of f r a m e D111. T h e b r i g h t a n d d a r k regions are a g a i n circled. T h e d a r k " h o l e s " e v i d e n t in t h e d a r k a r e a a r e n o i s e e n l a r g e d b y m a g n i f i c a t i o n (3×). All s u c h noise h a s b e e n r e m o v e d f r o m t h e R D R .

210

NOLAND AND VEVERKA I

I

"3----

,

I

I

I

I

DEIMOS BRIGHT AREA ~1" 0 . 0 i 7 + 0.002 mag/deg -0.2

_

=-

.

-

0,0 Q2 04 E OE OS "B-- LO 12 1.4 16

I I0

I 20

I 30

L 40

I 50

I 60 (deg)

I 70

I 80

90

F I G . 1 0 . Intrinsic phase curve for the bright material identified in Fig. 9. The data are normalized to the value of F(a) at a = 22 ° (see Table IV).

DEIMOS DARK AREA /~i= 0.017 ±0,001 mag/deg _

=o

_

-0.2 0.0 0.2 0.4 "~

O.6

~

0.{3

1.4 1.6

[

I

I

I0

20

30

4O

5O ct (deg)

[ 60

I 70

I 80

90

Fro. 11. Intrinsic phase curve for the dark material identified in Fig. 9. The data are normalized to the value of F(~) at ~ = 22 ° (see Table V).

the two regions reveals the n a t u r e of the bright area. I f the brightening were caused b y crater highlights or b y an albedo a n d / o r t e x t u r a l difference, the degree of brightening would change with aspect and phase angle. If, on the o t h e r hand, the brightening represents only intrinsically brighter material, t h e i n t e n s i t y ratio of the b r i g h t to d a r k regions should be identical in all pictures. Since the i n t e n s i t y ratio is a p p r o x i m a t e l y constant, ~1.3, we conclude

t h a t intrinsically brighter material is present. This brighter unit m a y have been p r o d u c e d b y cratering events. N o t e t h a t since the d a r k material is only 6 - 7 % reflective (Zellner and Capen, 1974) a material 30% brighter is still only 8-9% reflective; i.e., it is still v e r y dark. I f b o t h materials are o f the same t e x t u r e , we would t h u s e x p e c t t h e m to h a v e essentially the same phase function, as is observed.

SURFACE PHOTOMETRY OF DEIMOS 5. SEARCH FOR EVIDENCE OF SOLID ROCK

Large-scale exposures of solid rock seem to be absent. There are two strong indications of this: A solid rock surface usually does not scatter according to Eq. (1), and we find no evidence on Deimos of quasispecular reflection. In Figs. 2 to 7 the locations of the specular points on the photometric equator are indicated. Clearly in Figs. 4 to 7 no brightness enhancement occurs at the specular points. In Figs. 2 and 3 the brightness does increase near the specular points, but this brightening is due to the patches of bright material discussed above, and not quasi-specular reflection. 6. CONCLUSION

To a good approximation the surface of Deimos visible from Mariner 9 is covered uniformly b y a dark, texturally complex material whose photometric behavior is well represented b y the H a p k e - I r v i n e scattering law [Eq. (1)]. The average 20 ° to 80 ° intrinsic phase coefficient of the material is fix = 0.017 ~: 0.001 mag/deg. The corresponding disc-integrated value for a sphere would be fl = 0.030mag/deg. These values are identical to those found independently in Paper I. There is also evidence of a slightly brighter (by ~30%) unit near some craters. This material m a y have been produced b y the cratering events. Photometrically its texture is indistinguishable from that of the average material. Enhanced brightening does not occur at the specular point of the photometric equator for any of the six pictures studied. The implication is that large exposures of solid rock are absent from the Mars-facing side of Deimos.

211

ACKNOWLEDGMENT We are grateful to William Green and to the staff of the Image Processing Laboratory at

J P L for reducing the Mariner 9 B-frame images to photometric form, and to T. D u x b u r y for providing latitude/longitude grids for each satellite frame. We wish to t h a n k especially T. Thorpe, J. B. Pollack, and C. Sagan for helpful comments. This work was supported in part by Grants NGR 33-010-220 and NSG 7156, Planetology Program Office, NASA Headquarters.

REFERENCES ~HANI)RASEKHAR, S. (1960). Radiative Transfer. Dover, New York. MINNAERT, M. (1941). The reciprocity principle in lunar photometry. Astrophys. J. 93, 403410. NOLAND, M. (1975). Photometric studies of Phobos, Deimos and the satellites of Saturn. Ph.D. Thesis, Cornell University. NOLAND, M., AND VEVERKA, J. (1976). The photometric functions of Phobos and Deimos. I. Disc-integrated photometry. Icarus 28, 405-414 (Paper I). NOLAND, M., AND VEVERKA, J. (1977). The photometric functions of Phobos and Deimos. I I I . Surface photometry of Phobos. Icarus. 36 (Paper III). THORPE, T. (1975). Private communication. VEVERKA, J. (1971). The physical meaning of phase coefficients. In Physical Studies of Minor Planets (T. Gehrels, Ed.), pp. 79-90. NASA SP-267. VEVERKA, J., NOLAND, M., SAGAN,C., POLLACK, J. B., QuxM, L., TUCKER, R. B., EROSS, B., DUXBURY, T. C., AND GREEN, W. (1974). A Mariner 9 atlas of the moons of Mars. Icarus 23, 260-289. ZELLNER, B. H., AND CAPEN, R. C. (1974). Photometric properties of the Martian satellites. Icarus. 23, 437-444.