Our Peculiar Motion Inferred from Number Counts of Mid Infra Red AGNs and the Discordance Seen with the Cosmological Principle
PProceedings
Solar System Peculiar Motion from Mid Infra Red AGNs and its Cosmological Implications
Ashok K. Singal
Astronomy and Astrophysics Division, Physical Research Laboratory, Navrangpura, Ahmedabad - 380 009, India; [email protected] Tel.: +91-942-763-1833
Abstract:
According to the Cosmological Principle, the Universe shouldappear isotropic, without any preferred directions, to a comoving observer.However, a peculiar motion of the observer, or equivalently of the solarsystem, might introduce a dipole anisotropy in some of the observedproperties of the Cosmos. The peculiar motion of the solar system,determined from the dipole anisotropy in the Cosmic Microwave BackgroundRadiation (CMBR), gave a velocity 370 km/s along l=264 ° ,b=48 ° . However,dipoles from number counts, sky brightness or redshift distributions in largesamples of distant active galactic Nuclei (AGNs) have yielded values of thepeculiar velocity many times larger than that from the CMBR, though in allcases the directions agreed with the CMBR dipole. Here we determine ourpeculiar motion from a sample of ~0.28 million AGNs, selected from the MidInfra Red Active Galactic Nuclei (MIRAGN) sample comprising more than amillion sources. We find a peculiar velocity more than four times the CMBRvalue, although the direction seems to be within ~2σ of the CMBR dipole.Since a real solar peculiar velocity should be the same whatever may be thedata or the technique of observations, such discordant dipoles, could implythat the explanation for the genesis of these dipoles, including that of theCMBR, might lie elsewhere. At the same time a common direction for all thesedipoles, determined from completely independent surveys by differentgroups, does indicate that these dipoles are not merely due to somesystematics, and it might instead suggest a preferred direction in the Universeimplying a genuine anisotropy, which would violate the CosmologicalPrinciple, the core of modern cosmology. Keywords: a ctive galactic nuclei surveys; cosmic background radiation; large-scale structure of universe; solar system peculiar motion; cosmologicalprinciple
1. Introduction
According to the Cosmological Principle, the Universe, whenseen on a sufficiently large scale (beyond a few hundred Mpc), shouldappear isotropic, without any preferred directions, to a co-movingobserver in the expanding Universe. Such an observer is at rest withrespect to the Universe at large and the angular distribution of sourcesin sky should appear to be the same in all directions. However, ifrelative to the co-moving coordinates the observer has a motion, called a peculiar motion, then because of the Doppler boosting as wellas aberration, the observer will find the number counts to manifest adipole anisotropy, proportional to the peculiar velocity of theobserver. The Cosmic Microwave Background Radiation (CMBR),shows such a dipole anisotropy, which, when ascribed to the peculiarmotion of the Solar system, yields a peculiar velocity 370 km/s alongl=264 ° , b=48 ° [1-3]. On the other hand, our peculiar velocity has also beendetermined from the anisotropy observed in the sky distribution oflarge samples of discrete radio sources. The NRAO VLA Sky Survey(NVSS), comprising 1.8 million radio sources [4], showed a dipoleasymmetry corresponding to a velocity ~4 times the CMBR value [5],at that time a totally unexpected result, but confirmed subsequentlyby many independent groups [6-9]. Further, in the TIFR GMRT SkySurvey (TGSS) [10], comprising 0.62 million sources [11], a verysignificant (>10σ) dipole anisotropy, amounting to a velocity ~10 timesthe CMBR value, is detected [9,12]. However, the direction of motionin both cases has turned out to be along the CMBR dipole. Recently, ahomogeneously selected DR12Q sample of 103245 distant quasars hasshown a redshift dipole along the CMBR dipole direction, implying avelocity ~6.5 times though in a direction directly opposite to theCMBR dipole [13]. A more recent determination of the peculiarmotion from a sample of quasars derived from the Wide-field InfraredSurvey Explorer (WISE), has shown an amplitude over twice as largethe CMBR value [14]. Now a genuine solar peculiar velocity cannotvary from one set of measurements to another and such discordantdipoles could imply that the explanation for the genesis of thesedipoles, including that of the CMBR, might lie elsewhere. At the sametime a common direction for all these dipoles, determined fromcompletely independent surveys by different groups, usingindependent computational routines, does indicate that thedifferences in the dipoles are not merely random fluctuations or dueto some systematics in data or procedures, otherwise their directionstoo should be different. Instead, it might suggest a preferred directionin the Universe implying a genuine anisotropy, which would violatethe Cosmological Principle, the core of modern cosmology. Because ofthe huge impact on the cosmological models any genuine variations inthe dipole magnitudes may impart, further independentdeterminations of the dipole vectors are warranted. Here wedetermine our peculiar motion from a sample of ~0.28 million AGNs,selected from the Mid Infra Red Active Galactic Nuclei (MIRAGN)sample comprising more than a million sources [17].
2. Dipole Vector Due to the Observer’s Motion
An observer moving with a velocity v , will find a source along anangle θ with respect to the direction of motion, to appear brighter dueto Doppler boosting by a factor δ + α , where δ = 1 + (v/c) cos θ is theDoppler factor and α is the spectral index defined by S ∝ ν − α [15].Here we have used the non-relativistic formula for the Doppler factoras all previous observations indicate that v ≪ c . As the integral sourcecounts of the extragalactic source population usually follow a powerlaw, N(> S) ∝ S − x , the number of sources observed by a telescope of a st Electronic Conference on Gravitation, Cosmology, Field Theory, High Energy Physics, and Astronomy(Universe2021),22–28 February 2021 given sensitivity will be higher by a factor, δ x ( + α ) , due to the Dopplerboosting [15]. Additionally, due to the aberration of light, theapparent position of a source will shift by a small value, ( v/c ) sinθ ,thereby changing the number density by another factor ∝ δ . Thus, asa combined effect of Doppler boosting and aberration, the observednumber counts will vary with direction as ∝ δ + x ( + α ) , which, for v ≪ c , can be expressed as a dipole anisotropy, 1+ Dcosθ , of amplitude D =[2+ x (1+α)]( v/c ) [5,15,16]. Let r i be the position vector of i th source, then a stationary observer,due to the assumed isotropy of the Universe, à la CosmologicalPrinciple, should get Σ r i =0. However, for a moving observer, Σ r i willyield a net vector along the direction of motion [16], and from θ i computed with respect to that vector, the sum Σcos θ i /Σ|cos θ i |=2 D /3[5,12], would then give the peculiar speed v of the observer.Thus, using the angular positions of extragalactic sources in a largesurvey that covers the whole sky and is complete in the sense that itcomprises all sources above a certain flux-density limit, we candetermine our peculiar motion. It should be noted that exclusions ofstrips like the galactic plane, |b| < 15° (Figure 1), which affect theforward and backward measurements identically, do not havesystematic effects on the results [5,15].
3. Our Sample of MIRAGNs
The sample of AGNs used in this study is selected from apublicly made available larger all-sky sample of 1.4 million activegalactic nuclei (AGNs) [17], in turn derived from the Wide-fieldInfrared Survey Explorer final catalog release (AllWISE), thatincorporates data from the WISE Full Cryogenic, 3-Band Cryo, andNEOWISE Post-Cryo survey [18,19]. The WISE survey is an all-skymid-IR survey at 3.4, 4.6, 12, and 22 μm (W1, W2, W3, and W4) withangular resolutions 6.1, 6. 4, 6.5 and 12 arcsec, respectively. AllWISEcomprises data for almost 748 million objects, out of these about 1.4million objects met a two-color infrared photometric selection criteriafor AGNs, that formed the original MIRAGN sample [17]. For our purpose we have restricted the MIRAGN sample to anupper limit of magnitude, W1 <15.0, mainly because of a differentialincrease in the number density for weaker sources in various regionsof the sky, especially near the ecliptic poles, due to deeper WISEcoverage. However, due to the completeness of the basic survey atstrong source levels, the number density distribution in the sky at lowinfrared magnitudes remains unaffected as a deeper coverage addsonly fainter sources, which are at higher infrared magnitudes. From adetailed examination of the original MIRAGN sample data in small-range magnitude slices at different W1 levels, we find that fromW1≈15.5 onward, there is a non-uniform distribution in sky thatincreases rapidly at higher magnitudes, i. e., for weaker sources.Accordingly, we have chosen W1=15.0 to be our upper magnitudelimit. On the lower side, we have restricted our sample to W1>12.0.This is only to minimize the effects of the local bulk flows which willaffect sources at low redshifts, z<0.05, corresponding to W1<12. In anycase, the number of sources for W1<12 is relatively very small andtheir inclusion or exclusion hardly affects the results. Further, we have st Electronic Conference on Gravitation, Cosmology, Field Theory, High Energy Physics, and Astronomy(Universe2021),22–28 February 2021 also excluded all sources in the galactic plane with |b|<15o to avoidcontamination by galactic sources [17]. Our final sample thencomprises 279139 AGNs. Results and Discussion
Figure 1 shows the sky distribution of all ~0.28 million MIRAGNAGNs in our sample, in the Hammer-Aitoff equal-area projectionmap, plotted in equatorial coordinates. The source distribution looksquite uniform over the sky, except for the gap in the galactic planeband, where we have removed a ±15° band about the galactic plane.As mentioned earlier, such exclusions, which affect the forward andbackward measurements identically, do not have systematic effects onthe results.Before proceeding with the actual source sample we made Monte–Carlo simulations with source distributions similar to that in oursample. In each simulation, for the magnitude (W1) distributions wetook the actual values as in our sample, however, the sky position wasallotted randomly for each one of the 0.28 million sources. On thiswere superimposed Doppler boosting and aberration effects of anassumed peculiar motion of the observer, choosing a different velocityvector for each simulation. The resultant artificial sky was then usedto recover back the velocity vector and compared with the valueactually used in that particular simulation. This not only verified ourprocedure and the computation routine, but also allowed us to makean estimate of errors in the dipole direction from the spread observedin 500 independent simulations.
Figure 1.
The sky distribution of ~0.28 million AGNs of our
MIRAGN sample, plotted in equatorial coordinates. The sky position of the pole determined from our MIRAGN sample is indicated by M, along with the error ellipse, while other pole positions for various dipoles shown on the map are: N(NVSS), T(TGSS) and D(DR12Q). The CMBR pole at C has negligible errors. st Electronic Conference on Gravitation, Cosmology, Field Theory, High Energy Physics, and Astronomy(Universe2021),22–28 February 2021
Table 1.
Peculiar velocity estimated from the dipole asymmetry in number counts.
Magnitude Range N D RA Dec SpeedW1 (10 -2 ) (°) (°) (10 km/s) ≥12.0 279139 3.0±0.3 148±19 23±17 1.7±0.2 15.0 >W1≥14.7 102822 4.1±0.5 157±20 23±18 2.3±0.3 14.7 >W1 ≥14.3 086035 2.9±0.6 132±21 32±19 1.6±0.3 14.3 >W1 ≥12.0 090282 2.1±0.6 143±21 11± 19 1.2±0.3 The 1 st column gives the magnitude range, 2 nd column gives the number of sources, 3 rd column gives the dipolemagnitude, 4 th and 5 th columns give the direction of the dipole in terms of Right Ascension and Declination and the last column gives the value of the speed estimated from D. In Table 1, we give the results for the dipole, determined from theanisotropy in number counts in our sample of about 0.28 millionMIRAGNs in the 12 Σcos θ i /2Σ|cos θ i |, with error Δ D =√(3/N) [5,12,16]. Then thepeculiar speed of the observer, or rather of the Solar system, iscomputed from D =[2+ x (1+α)]( v/c ). In order to determine x we havemade a plot of the integrated source counts N( A plot of the integrated source counts N( Although we have restricted our sample to W1>12.0 to minimizethe effect of local bulk flows, still, in order to estimate the influence onour results of any local clustering, like the virgo super-cluster, wedetermined dipole vectors by excluding sources at low super-galacticlatitudes, progressively in steps of five degrees, and from acomparison of these cases (|SGB|>0°,5°,10°,15°,20°; Table 2), nounusually large variations, beyond the statistical uncertainties, wereseen in the computed dipole vectors.A genuine peculiar velocity of the Solar system should not bedependent upon the specific data or the technique used to determineit. The discordant values of the inferred peculiar motion fromobserved dipoles for the AGNs, may imply that we should insteadlook for some other possible cause for the genesis of these dipoles,including that of the CMBR. One could not say that the CMBRprovides a reference frame which is to be considered as morefundamental than the other ones for establishing the peculiar motionof the solar system. While the CMBR refers to the radiation era, AGNsrepresent the much later matter era. A common direction for all thesedipoles (Figure 1), determined from completely independent surveysby different groups, does indicate that these dipole amplitudes differnot because of random statistical fluctuations, or due to somesystematics in the observations or in the data analysis, otherwise eventheir directions should have been different. A not-too-far-fetchedinference drawn could be that a common direction for the dipoles, st Electronic Conference on Gravitation, Cosmology, Field Theory, High Energy Physics, and Astronomy(Universe2021),22–28 February 2021 Table 2. Dipole estimates for various |SGB| limits. |SGB| limit N D RA Dec Speed (°) (10 -2 ) (°) (°) (10 km/s) | SGB| ≥0 279139 3.0±0.3 148±17 23±17 1.7±0.2 | SGB| ≥5 251281 3.1±0.3 145±18 21±18 1.7±0.2 | SGB| ≥10 223230 3.4±0.3 142±18 20±19 1.9±0.2 | SGB| ≥15 195664 3.7±0.3 141±19 12±20 2.0±0.2 | SGB| ≥20 168826 3.7±0.3 136±20 09±20 2.1±0.2 The 1 st column gives the |SGB| limit, 2 nd column gives the number of sources, 3 rd column gives the dipole magnitude, 4 th and 5 th columns give the direction of the dipole in terms of Right Ascension and Declinationand the last column gives the value of the speed estimated from D. including of the CMBR, is a pointer toward the presence of aninherently preferred cosmic direction (axis!), implying perhaps ananisotropic Universe, in conflict with the Cosmological Principle, acornerstone of the modern cosmology. 5. Conclusions From the angular positions in sky of a sample of ~0.28 millionMid Infra Red AGNs, we found an anisotropy in their numberdensities in different directions. Ascribing this anisotropy to thepeculiar motion of the observer, we determined the peculiar velocityof the Solar system that turned out to be, like other earlier AGNdipoles, at least a factor of four larger that that inferred from theCMBR dipole, but along the same direction. Since the peculiar velocityof the Solar system should not depend upon the specific data or thetechnique used to determine it, the question arises about the nature ofthese dipoles seen in the sky and whether the genesis of some or all ofthese dipoles indeed is due to the peculiar motion of the Solar system.A common direction for all these dipoles, including the CMBR one,determined from completely independent surveys by differentgroups, does indicate that the differences in the dipole amplitudes aregenuine and not because of random statistical fluctuations, or due tosome systematics in the observations or in the data analysis, otherwiseeven the dipole directions would be different. An inference that couldpossibly be drawn from a common direction for all the dipoles is thatit might be a pointer toward the presence of an inherently preferredcosmic direction (axis!), implying perhaps an anisotropic Universe, indiscordance with the Cosmological Principle, a cornerstone of themodern cosmology. Conflicts of Interest: The author has no conflicts of interest to declare that arerelevant to the content of this paper. No funds, grants, or other support of anykind was received from anywhere for this research. References 1. Lineweaver, C.H. et al. The dipole observed in the COBE DMR 4 year data Astrophy. J. , , , 38-42.2. Hinshaw, G. et al. Five-year Wilkinson microwave anisotropy probe observations: Data processing, skymaps, and basic results Astrophy. J. Supp. Ser. , , , 225-245.3. Aghanim N. et al. Planck 2018 results I. Overview and the cosmological legacy of Planck. 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