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THE CMB DIPOLE: THE MOST RECENT MEASUREMENT AND SOME HISTORY
astro-ph/9609034 5 Sep 1996
Charles H. Lineweaver Universite Louis Pasteur Observatoire Astronomique de Strasbourg 11 rue de l'Universite, 67000 Strasbourg, France charley@cdsxb6.u-strasbg.fr

ABSTRACT
The largest anisotropy in the cosmic microwave background (CMB) is the 3 mK dipole assumed to be due to our velocity with respect to the CMB. Over the past ten years the precision of our knowledge of the dipole has increased by a factor of ten. We discuss the most recent measurement of this dipole obtained from the four year COBE Di erential Microwave Radiometers (DMR) as reported by Lineweaver et al. (1996). The best- t dipole is 3:358 0:001 0:023 mK in the direction (`; b) = (264 :31 0 :04 0 :16; +48 :05 0 :02 0 :09), where the rst uncertainties are statistical and the second include calibration and systematic uncertainties. The inferred velocity of the Local Group is vLG = 627 22 km/s in the direction ` = 276 3, b = 30 2. We compare this most recent measurement to a compilation of more than 30 years of dipole observations.


1 Introduction
The Sun's motion with respect to the rest frame of the cosmic microwave background (CMB) is believed to be responsible for the largest anisotropy seen in the COBE DMR maps: the 3 mK dipole in the direction of the constellation Leo. A high precision measurement of this Doppler dipole is important because it tells us our velocity with respect to the rest frame of the CMB. will be used as the primary calibrator for an increasing number of ground, balloon and satellite anisotropy experiments (Bersanelli et al. 1996). Small scale experiments are becoming sensitive enough to use the dipole to calibrate (Richards 1996). Thus the typical 10-20% absolute calibration accuracy of ground and balloon-borne experiments can be improved by more than an order of magnitude to the 0.7% absolute calibration accuracy of the DMR dipole. permits the accurate removal of the Doppler dipole and Doppler quadrupole from anisotropy maps thus improving the precision of the anisotropy results. calibrates bulk ow observations which yield independent but much less precise dipole values. permits an eventual test of the Doppler origin of the CMB dipole in which it is compared to the dipoles in other background radiations (Lineweaver et al. 1995). In this paper we discuss the most recent determination of the precise direction and the amplitude of the dipole observed in the DMR four-year data. We discuss contamination from Galactic emission as well as other factors contributing to the error budget (see Lineweaver et al. (1996) for details). We then compare our results to a compilation of more than 30 years of dipole results.

We estimate the in uence of Galactic emission on the measurement by solving for the dipoles for a series of Galactic plane latitude cuts. The dipole amplitude and direction results from each channel and each Galactic cut are shown in Figure 1. Galactic emission produces a dipole which pulls the solutions towards it. This is easily seen in Figure 1 from the locations of the 0 and 5 cut solutions relative to the cluster of higher cut results on the right. Since the Galactic dipole vector is nearly orthogonal to the CMB dipole vector, it is almost maximally e ective in in uencing the CMB dipole direction and almost minimally e ective in in uencing the CMB dipole amplitude. In Figure 1, the general increase of the dipole amplitudes seen in the top panel as the Galactic cut increases from 0 to 5 to 10 can be explained by the fact that the Galactic dipole vector contains a component in the direction opposite to the CMB dipole (the Galactic center is 94 away) and thus reduces the total dipole in the maps. Figure 1 clearly shows the in uence of the Galaxy for the 0 and 5 cuts as well as the relative agreement of the independent channel results for both amplitude and direction. It

2.1 Galactic Plane Cuts

2 Minimizing the Error Due to Galactic Foreground, CMB Background and Instrument Noise


The results for each channel and Galactic plane cut (from left to right in the top panel), jbj > 0 ; 5 ; 10 ; 15 ; 20 ; 25 ; 30 are shown. Channels and cuts are denoted with the same point type and size in both panels. Solutions for the dipole where no e ort has been made to eliminate Galactic emission (i.e., 0 Galactic cuts) are labeled with the channel names \53A", \53B", \90A" and \90B". The 31 GHz labels indicate the 5 cut solutions since their 0 cut solutions are o the plot at longitude 271 . For each channel, the successive Galactic cuts are connected by lines (31: long dashes, 53: dots, 90: short dashes, Average: solid). The direction of the Galactic center is toward higher latitudes for the same reason that one ies north-west from London to arrive at New York. The latitude and longitude ranges were chosen to display an approximately square piece of the sky. For each channel, the direction error bars on the 15 Galactic cut solutions are shown. Our nal dipole amplitude, including the calibration uncertainty is the point in the far right of the top panel. The grey box in the bottom panel denotes the 68% con dence levels of our nal dipole direction (cf. Fig. 1, Lineweaver et al. (1996)).

Figure 1. Dipole Amplitudes (top) and Directions (bottom)

is also apparent that to rst approximation a 10 cut is su cient to remove the e ect of the Galaxy on the direction of the best- t dipole; increases of the cut from 10 to 15 and so on, do not push the directions away from the Galactic center or in any other particular direction. The results tend to cluster together. The directional precision of the various channels and Galactic cuts is seen to be 0 :3 and it is perhaps reassuring to note that at the bottom and the top of the cluster are the least sensitive 31A and 31B solutions. Galactic emission signi cant enough to a ect the dipole results will tend to pull the three channels in approximately the same direction and favor a spectral behavior typical of synchrotron or free-free emission. This is easily seen for the 0 and 5 cuts (cf. Figure 2, Lineweaver et al. 1996). The absence of this behavior for the 10 and 15 cuts and larger is evidence that the Galaxy is no longer the ma jor contributor to the directional uncertainty of the dipole. For the purposes of determining the dipole there are two sources of noise; instrument noise with a power law spectral index n 3 and the n 1 CMB signal. At 10 scales the CMB signal to noise ratio in the maps is 2 (Bennett et al. 1996). Thus on larger scales the CMB

2.2 Higher Multipole CMB as Unwanted Contamination


signal dominates the instrument noise and correspondingly, the uncertainties on the dipole from the CMB signal are larger than those from the instrument noise. The uncertainties from both are reduced by lowering the Galactic plane cut. This is further supported by the fact that for jbj > 20 , the combined free-free and dust emission from the Galaxy at 53 and 90 GHz produces only 10 K rms (Kogut et al. 1996a) while the CMB signal rms is 35 K (Banday et al. 1996). To estimate the uncertainty in the dipole results due to the CMB signal we simulate n = 1:2, Qrms P S = 15:3 K CMB skies for 2 ` 25. We superimpose these maps on a known dipole and solve for the dipole using a 15 Galactic plane cut. No bias is detected and the rms's of the results around the input values are 3:3 K in amplitude, 0 :127 in longitude and 0 :062 in latitude. We include these CMB contamination uncertainties in our estimate of the systematic errors. We have found that Galactic cuts greater than 15 are not useful corrections which eliminate more and more Galactic contamination; they introduce systematic errors associated with large Galactic cuts due to the increasingly non-orthogonal basis functions Y`m ( ; ), over the increasingly limited and thus noisier input data. We conclude that the Galactic cuts of 10 and 15 are the best compromise to minimize the combined e ect of CMB aliasing, Galactic contamination and noise. The high precision of our dipole direction results depend on this conclusion. Note that this choice for the optimal Galactic cut is smaller than the 20 cut used when one is trying to compute the correlation function or determine the ` 2 components of the power spectrum of the CMB signal which are smaller than the dipole by a factor of 200. For such determinations, the similar compromise for simultaneously minimizing Galactic contamination, instrument noise and other procedural/systematic e ects demands a larger cut.

3 Results
Taking the averages of the 10 and 15 cuts and the weighted average of all six channels we obtain a best- t dipole amplitude 3:358 0:001 0:023 mK in the direction (`; b) = (264 :31 0 :04 0 :16; +48 :05 0 :02 0 :09), where the rst uncertainties are statistical and the second are estimations of the combined systematics. In celestial coordinates the direction is ( ; ) = (11h 11m 57s 23s ; 7 :22 0 :08) (J2000). The uncertainty in the dipole amplitude is dominated by the absolute calibration of the DMR instrument (Kogut et al. 1996b). This is easily seen in Figure 1 by comparing the large error bars on our nal result (far right) with the noise-only error bars on the channel results. The calibration uncertainty plays no role in the directional uncertainty for the same reason that the directions of vectors ~ and a~ (where a is any positive x x constant) are the same. Under the assumption that the Doppler e ect is responsible for the entire CMB dipole, the velocity of the Sun with respect to the rest frame of the CMB is v = 369:0 2:5 km/s, which corresponds to the dimensionless velocity = v =c = 1:231 0:008 10 3 . The associated rms Doppler quadrupole1 is Qrms = 1:23 0:02 K with components Q1; Q2; Q3; Q4; Q5] = 0:91 0:02; 0:20 0:01; 2:04 0:03; 0:91 0:02; 0:18 0:01] K. The velocity of the Local Group with respect to the CMB can be inferred; following Kogut et al. (1993) we obtain vLG = 627 22 km/s in the direction ` = 276 3, b = 30 2.
Q2ms r Q1(3sin2 b
1

the components are de ned by To 2 (2cos2 (2=3)) = + Q4cos2 b cos2` + Q5cos2 b sin2`, where To is the mean CMB temperature and is the angle between the dipole direction and the direction of observation: (`; b). =
43 15 4
2

2 Q2 + Q2 + Q3 + Q2 + Q2 ] where 1 2 4 5 1)=2 + Q2sin2b cos` + Q3sin2b sin`


4 Historical Discussion
We have compiled more than 30 years of dipole measurements in Table 1 and these numbers were used to make Figure 2. This plot may a good example of scienti c progress. We acknowledge support from the French Ministere des A aires Etrangeres.

These results and the number labels in the bottom panel correspond to the references in Table 1. To see how realistically the dipole community has estimated its errors we have calculated the 2 per degree of freedom for the amplitudes, galactic longitudes and latitudes of the reported results. They are respectively 1.6, 5.7 and 1.5 (approximately correct error estimates yield 2=dof 1). Thus, the amplitude and latitude estimates are believable while the reported errors on longitude have been underestimated. This can probably be attributed to the various ways in which Galactic emission has (or has not) been accounted for since a line t to the set of dipole directions passes through the Galactic center (` = 360 ; b = 0). This plot may be a good example of scienti c progress.

Figure 2. 30 Years of CMB Dipole Measurements


# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Amplitude D(mK) Penzias & Wilson(1965) < 270 Partridge & Wilkinson(1967) 0:8 2:2 Wilkinson & Partridge(1969) 1:1 1:6 Conklin(1969) 1:6 0:8 Boughn et al. (1971) 7:6 11:6 Henry(1971) 3:3 0:7 Conklin(1972) > 2:28 0:92 Corey & Wilkinson(1976) 2:4 0:6 Muehler(1976) 2:0 1:8 Smoot et al. (1977) 3:5 0:6 Corey(1978) 3:0 0:7 Gorenstein(1978) 3:60 0:5 Cheng et al. (1979) 2:99 0:34 Smoot & Lubin(1979) 3:1 0:4 Fabbri et al. (1980) 2:9 0:95 Boughn et al. (1981) 3:78 0:30 Cheng(1983) 3:8 0:3 Fixsen et al. (1983) 3:18 0:17 Lubin (1983) 3:4 0:2 Strukov et al. (1984) 2:4 0:5 Lubin et al. (1985) 3:44 0:17 Cottingham(1987) 3:52 0:08 Strukov et al. (1987) 3:16 0:07 Halpern et al. (1988) 3:4 0:42 Meyer et al. (1991) Smoot et al. (1991) 3:3 0:1 Smoot et al. (1992) 3:36 0:1 Ganga et al. (1993) Kogut et al. (1993) 3:365 0:027 Fixsen et al. (1994) 3:347 0:008 Bennett et al. (1994) 3:363 0:024 Bennett et al. (1996) 3:353 0:024 Fixsen et al. (1996) 3:372 0:005 Lineweaver et al. (1996) 3:358 0:023

Reference

Table 1: CMB Dipole Measurements a
Longitude `(deg) 96 270 195 306 207 248 288 229 287 250:6 256:7 275:4 265:7 264: 272: 266: 289: 249: 265 264: 267: 264: 265: 264: 264: 264: 264: 3 2 4 5 9 7 0 4 6 4 26 14 31 30 30 30 28 15 26 11 9 9 13:8 3:9 3:0 1: 2: 2: 4: 4: 1 0: 1: 0: 0: 0: 0: 0: 0: 9 3 3 1 5 8 0 3 75 2 33 17 17

Latitudea b(deg)

Freq (GHz) 4 9 9 85 30 8 37 24 25 10 66 10 8 38 20 19 11 150 56 10 33 43 19 19 67 8 33 61 6 30 63:2 6 33 57:4 7:7 300 46:8 4:5 46 30 47:3 1:5 25 90 67 49:2 1:3 90 49:9 1:5 19 48:5 1:6 67 38:4 4:8 150 47:7 3:0 170 48 1 53 48:2 0:5 53 49:0 0:7 170 48:4 0:5 53 48:3 0:5 300 48:1 0:4 53 48:22 0:13 53 48:26 0:16 300 48:05 0:10 53

a

Galactic coordinates


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