ISSN 1063-7737, Astronomy Letters, 2008, Vol. 34, No. 5, pp. 353–356. c© Pleiades Publishing, Inc., 2008.Original Russian Text c© I.A. Maslov, A.E. Nadzhip, V.I. Shenavrin, 2008, published in Pis’ma v Astronomicheskiı Zhurnal, 2008, Vol. 34, No. 5, pp. 387–391.

Near-Infrared Observations of Comet C/2004 Q2 (Machholz)

I. A. Maslov1, 2*, A. E. Nadzhip1, and V. I. Shenavrin1

1Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, 119992 Russia2Space Research Institute, Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow, 117997 Russia

Received June 6, 2007

Abstract—Our observations of Comet C/2004 Q2 (Machholz) in the range from 1.2 to 4.8 µm indicatethat the material outflowed from the cometary surface in the form of fragments that separated into gas anddust under sublimation on time scales of the order of days. The albedo of these fragments in the range understudy was wavelength independent, while the dust was heated by the Sun to an equilibrium temperature ata cross section Qλ inversely proportional to the wavelength.

PACS numbers : 96.25.-fDOI: 10.1134/S1063773708050083

Key words: Solar system, comet, dust, infrared radiation.

OBSERVATIONS

From December 2004 through April 2005, weperformed photometric observations of CometC/2004 Q2 (Machholz) in five standard near-infraredbands (J , H , K, L, M ) with the 1.25-m telescope atthe Crimean Laboratory of the Sternberg Astronom-ical Institute. The observations were performed witha chopping InSb photometer (Nadzhip et al. 1986),which measured the flux difference between two skyfields 12′′ in diameter spaced 20′′–40′′ apart in rightascension. Bright stars with measured infrared fluxeswere used for calibration.

We determined the brightness of the central partof the visible coma in comparison with the areas oneand two chopping amplitudes away by making mea-surements for four viewing directions relative to thecoma center, as shown in Fig. 1. We calculated themean (symmetrically in right ascension) differentialbrightnesses for single and double chopping ampli-tudes from a series of such measurements, therebyeliminating the background and its temporal drift.The results of our measurements are presented inTable 1. Its columns give the dates (and Julian dates)of observations, ephemeris data for the comet (thedistance to the Earth, the distance to the Sun, andthe angle between the directions of the Earth and theSun), the angular separation between the measuredsky areas, the linear separation between these areasnear the comet, and the measured J , H , K, L, andM brightnesses. Table 1 also lists the values of ∆AJ ,

*E-mail: imaslov@iki.rssi.ru

∆AH , and ∆AK (∆ indicates that the difference be-tween the central part of the coma and its peripherywas measured) — the brightness coefficients (Moroz1967) derived from observations for the J , H , and Kbands in which the intrinsic thermal radiation of thecometary material is negligible and only the scatteredsolar radiation is recorded (Makarova and Kharitonov1972).

RESULTS

We see from Table 1 that the scattering in the comain the range from 1.2 to 2.2 µm is essentially wave-length independent and that the coma color does notchange with phase angle (see Fig. 2). This suggeststhat the scattering takes place on bodies with sizesmuch larger than the wavelength of 2 µm. At thesame time, the high M-band brightness of the cometis indicative of the presence of particles heated to hightemperatures in the coma.

We fitted our observational data by the expression

∆Bλ =Eλ�π

∆A1.65

(1.65λ

)α

+ Pλ(λ, T#)∆Q4.7

(4.7λ

)β

,

where λ is the wavelength in µm; Eλ� is the spectralflux from the Sun near the comet; Pλ(λ, T ) is thePlanck function for blackbody radiation; T# is theequilibrium temperature to which the dust grains areheated by solar radiation for a power-law wavelength

353

354 MASLOV et al.

Tabl

e1.

Obs

erva

tion

sof

Com

etC

/200

4Q

2

Dat

eD

ista

nce

toE

arth

,A

U

Dis

tanc

eto

Sun

,A

UP

hase

Cho

ppin

gB

righ

tnes

s,∆

AJ

∆A

H∆

AK

T#

,K

α=

−0.

15,β

=0.

78

JDµ

Wm

−2

sr−

1µ

m−

1α

β∆

A1.6

5∆

Q4.7

T#

,K

arcs

ec10

3km

JH

KL

M10

−7

10−

7

Dec

.18,

2004

0.43

91.

341

29◦ .7

3210

.262

723

493

4660

7960

65+

0.93

1.41

550

7720

404

2453

358.

4

Dec

.25,

2004

0.38

61.

298

30.2

329.

059

132

713

052

8670

7885

−0.

390.

6036

974

2640

924

5336

5.4

Feb

.4,2

005

0.52

41.

215

52.3

3212

.231

118

369

3369

3238

40−

0.51

0.45

346

3517

421

2453

406.

2

Feb

.5,2

005

0.53

41.

217

52.3

3212

.470

2042

024

5340

7.3

Feb

.7,2

005

0.55

31.

222

52.3

3212

.943

016

268

2852

4534

40+

0.76

0.79

422

4412

420

2453

409.

3

Feb

.8,2

005

0.56

31.

225

52.3

3213

.130

517

060

3268

3236

35−

0.32

0.50

356

3417

419

2453

410.

264

26.2

328

182

3179

3539

3719

Feb

.9,2

005

0.57

31.

228

52.2

3213

.339

220

772

4369

4145

42−

0.15

0.72

405

4318

419

2453

411.

2

Feb

.10,

2005

0.58

31.

231

52.2

3213

.633

144

3835

3712

418

2453

412.

264

27.1

322

5520

3436

9

Mar

.14,

2005

0.90

61.

415

44.3

3926

.217

174

267

1624

2120

+0.

420.

5133

624

639

524

5344

4.3

7852

.425

891

2713

1436

2621

+1.

231.

3853

235

5

Mar

.15,

2005

0.91

61.

423

44.0

3926

.511

359

260

−2

1617

21−

0.33

1.26

503

17−

239

424

5344

5.3

7853

.012

264

303

−12

1718

23−

0.39

0.78

394

18−

1

Mar

.16,

2005

0.92

61.

431

43.7

3926

.813

561

2610

019

1821

+0.

652.

5080

020

639

324

5344

6.4

7853

.514

137

Apr

.20,

2005

1.30

01.

759

34.4

3734

.814

4−

183

43

−17

360

2453

481.

474

69.7

−4

1−

46−

11

−1

−43

Apr

.25,

2005

1.36

01.

811

33.3

3736

.47

−22

−18

356

2453

486.

374

72.9

811

010

6

Apr

.26,

2005

1.37

21.

822

33.1

3736

.8−

52

035

524

5348

7.3

7473

.5−

61

−1

ASTRONOMY LETTERS Vol. 34 No. 5 2008

NEAR-INFRARED OBSERVATIONS OF COMET 355

1

2

3

4

R.A.

Fig. 1. Positions of the photometer aperture relative to the coma in four measurements. Two sensitivity zones arise from internalchopping in the photometer, with the signal from the right sky area being subtracted from that from the left one.

dependence of their effective cross section (Bochkarev1992):

4T 4+β# R2

# = T 4+β� R2

�,

where T� = 5770 K is the effective temperature of theSun; R� is the radius of the solar photosphere; andR# is the heliocentric distance of the comet.

For the nights when the observations were per-formed in all five bands, we determined the con-stants α and β, along with the coefficients ∆A1.65

and ∆Q4.7 characterizing the scattering and emissivepowers of the coma, by the least-squares method. Thederived α and β together with the equilibrium temper-atures T# are listed in Table 1. Formally, the statis-tical means of these 11 observations are α = 0.17 ±0.20 and β = 0.99 ± 0.19. Given the large scatter,we assumed for our subsequent analysis that theseparameters did not vary over the observing period andwere close to their median values, α = −0.15 and β =0.78, consistent with the above means. Under thisassumption, we estimated the coefficients ∆A1.65 and∆Q4.7 and the dust grain equilibrium temperature T#

for all our observations (see the last three columns inTable 1).

Note that the presence of negative differentialbrightnesses in Table 1 suggests that the coma inthe central part may be fainter than on its periphery,implying that most of the fine hot grains appearat distances of the order of tens of thousands ofkilometers. A similar effect was also observed inHalley’s Comet (Taranova, 1987). Since fine dustis heated very rapidly and the grain velocity in the

coma is ∼1 km s−1 (Krasnopolskii, 1987), we findthe disintegration time scale for coarse grains to beseveral days.

Our observations can be explained in terms ofa model in which the material outflows from thecometary surface in the form of relatively large par-ticles with the sublimation temperature of the icesthat are incorporated into them. At the completion ofthe sublimation, these particles break up into smallerones and are heated to a high temperature. Based onthis model, we can assume that a correlation shouldbe observed between the coma brightness variationsat the center for scattered solar radiation and those onthe periphery for thermal dust radiation with a delayof a day or more. Thus, for our chopping observations

0.7

0.6

0.5

0.4

0.3

0.2

0.1

025 30 35 40 45 50 55°

Phase angle

J

–

H

,

J

–

K

Fig. 2. J–H (squares) and J–K (triangles) colors of thecomet versus phase angle.

ASTRONOMY LETTERS Vol. 34 No. 5 2008

356 MASLOV et al.

Table 2. Correlation between the brightness variations at the center and on the periphery of the coma for CometC/2004 Q2

Dateδ∆A1.65 δ∆Q4.7 s, δ∆Q4.7

δ∆A1.65

δ∆Q4.7(∆t = 0)/δ∆A1.65(∆t = −s/v)

10−7 103 km v = 0.08 km s−1 v = 0.15 km s−1 v = 0.30 km s−1 v = 0.60 km s−1

Feb. 8, 2005 −10 +5 13 −0.5

Feb. 9, 2005 +9 +1 13 +0.1 −0.1

Feb. 10, 2005 −6 −6 14 +1.0 +0.6 −0.7

−9 27 +0.9 −1.0

Mar. 15, 2005 −12 −7 26 +0.6

Mar. 16, 2005 +3 +8 26 +2.7 −0.7 −1.3

+8 52 −0.7

Mean +0.8 +0.6 −0.2 −1.2 −0.7

(center–periphery), one should expect the observedbrightness in the M band to decrease some timeafter the increase in the observed brightness in theJ , H , and K bands. Table 2 gives daily changes incoefficients ∆A1.65 and ∆Q4.7; the change in ∆Q4.7 isgiven for both single and double chopping amplitudes,which yields the spatial separation s between themeasured areas near the comet. Table 2 also givesthe ratio of the observed change in thermal radiationto the change in scattered radiation and the ratio ofthe change in thermal radiation at a given time to thechange in scattered radiation at an earlier time withthe time shift ∆t = −s/v, where v is the velocity ofthe particles of the cometary material that allows itto traverse the distance s in time ∆t and to becomeobservable in the comparison beam of the photometer.

Despite the small amount of data, it can be con-cluded from Table 2 that there is a positive correla-tion between the changes in scattered and thermalradiations and an anticorrelation between the changein thermal radiation and the change in scattered ra-diation at an earlier time. This means that a certainnumber of “hot” particles appear immediately nearthe cometary nucleus. However, given the dispersalof the material in space, the bulk of such particlesappear a day or more later and their velocity exceeds0.3 km s−1.

CONCLUSIONSThus, we have established that the material out-

flowed from the surface of the nucleus of C/2004 Q2(Machholz) in the form of cold fragments whose near-infrared albedo was wavelength independent, to with-in the error limits of our measurements. These frag-

ments separated into gas and fine dust during subli-mation on a time scale of the order of days; the latterwas heated by the Sun to an equilibrium temperaturewith a wavelength dependence of the cross sectionclose to Qλ ∝ 1/λ.

ACKNOWLEDGMENTS

This study was supported by the Russian Foun-dation for Basic Research (project no. 08-02-90485-Ukr-a).

REFERENCES

1. N. G. Bochkarev, Fundamentals of the Physics ofInterstellar Medium (Mosk. Gos. Univ., Moscow,1992), p. 302 [in Russian].

2. V. A. Krasnopolskii, Physics of the Planetary andCometary Airglow (Nauka, Moscow, 1987), p. 239 [inRussian].

3. E. A. Makarova and A. V. Kharitonov, Spectral EnergyDistribution of the Sun and the Solar Constant(Nauka, Moscow, 1972) [in Russian].

4. V. I. Moroz, Physics of Planets (Nauka, Moscow,1967), p. 73 [in Russian].

5. A. E. Nadzhip, V. I. Shenavrin, and V. G. Tikhonov, Tr.Gos. Astron. Inst. im. P.K. Shternberga 58, 119 (1986).

6. O. G. Taranova, Pis’ma Astron. Zh. 13, 149 (1987)[Sov. Astron. Lett. 13, 61 (1987)].

Translated by N. Samus’

ASTRONOMY LETTERS Vol. 34 No. 5 2008