Detection of dark energy near the Local Group with the Hubble Space Telescope
A.D. Chernin, I.D. Karachentsev, P. Teerikorpi, M.J. Valtonen, G.G. Byrd, Yu.N. Efremov, V.P. Dolgachev, L.M. Domozhilova, D.I. Makarov, Yu.V. Baryshev
aa r X i v : . [ a s t r o - ph ] J un Dete tion of dark energy near the Lo al Groupwith the Hubble Spa e Teles opeA.D. Chernin , , I.D. Kara hentsev , P. Teerikorpi , M.J. Valtonen , G.G. Byrd ,Yu.N. Efremov , V.P. Dolga hev , L.M. Domozhilova , D.I. Makarov , Yu.V. Baryshev Sternberg Astronomi al Institute, Mos ow University,Mos ow, 119899, Russia, Tuorla Observatory, Turku University, Piikki(cid:4)o, 21 500, Finland, Spe ial Astrophysi al Observatory, Nizhnii Arkhys, 369167, Russia, University of Alabama, Tus aloosa, USA, Astronomi al Institute, St.Petersburg University, 198504, RussiaWe report the dete tion of dark energy near the Milky Way madewith pre ision observations of the lo al Hubble (cid:29)ow of expansion. Weestimate the lo al density of dark energy and (cid:28)nd that it is near, ifnot exa tly equal to, the global dark energy density. The result isindependent of, ompatible with, and omplementary to the horizon-s ale observations in whi h dark energy was (cid:28)rst dis overed. Togetherwith the osmologi al on ordan e data, our result forms dire t observationaleviden e for the Einstein antigravity as a universal phenomenon (cid:21) in thesame sense as the Newtonian universal gravity.Dark energy is the mysterious form of osmi energy that produ es antigravityand a elerates the global expansion of the universe. It was (cid:28)rst dis overed (1,2)in 1998-99 in observations of the Hubble expansion (cid:29)ow with the use of typeIa supernovae at horizon-size distan es of more than 1000 megaparse (Mp ) (1Mp is equal to 3.26 million light-years). These and other studies, espe ially the1bservations of the osmi mi rowave ba kground (CMB) anisotropy (3,4), indi atethat the global dark energy density is (0 . ± . × − kilograms per ubi meter (kg/m ). It ontributes nearly 3/4 the total energy of the universe (1-4).A ording to the simplest, straightforward and quite likely interpretation, darkenergy is des ribed by the Einstein osmologi al onstant. If this is so, dark energyis the energy of the osmi va uum (5) with the equation of state p V = − ρ V . Here ρ V , p V are the dark energy density and pressure whi h are both onstant in timeand uniform in spa e (the speed of light c = 1 hereafter). The interpretation impliesthat although dark energy betrayed it existen e through its e(cid:27)e t on the universeas a whole, it exists everywhere in spa e with the same density and pressure. Howto examine this in dire t observations on smaller spatial s ales?We have sear hed for dark energy in our losest gala ti neighborhood. Thelo al spa e volume is dominated by our Milky Way and its sister galaxy, M31,lo ated at about 0.7 Mp from us, moving toward ea h other with a relative velo ity ∼
100 km/s. Together with the Magellani Clouds, the Triangulum galaxy andabout four dozen other dwarf galaxies, these two major galaxies form the Lo alGroup. Around the group,two dozen dwarf galaxies are seen whi h all move apartof the group. This is the lo al expansion (cid:29)ow dis overed in the late 1920s byHubble.Systemati observations of distan es and motions of galaxies in the Lo alGroup and in the (cid:29)ow around it have been arried out over the last eight yearswith the Hubble Spa e Teles ope during more than 200 orbital periods(6-12). Highpre ision measurements were made of the radial velo ities (with 1-2 km/s a ura y)and distan es (8-10 % a ura y) for about 200 galaxies of the Lo al Group andneighbors from 0 to 7 Mp from the group bary enter.We have fo used on the shortest distan es less than 3 Mp from the Lo alGroup bary enter. This is the very beginning of the Hubble (cid:29)ow of expansion. The(cid:29)ow is represented in Fig.1 by the plot of radial velo ities versus distan e, and this2s the most omplete version of the Hubble diagram for these s ales up to date. Thevelo ities and distan es are given in the referen e frame of the bary enter of theLo al Group. At less than 1 Mp , one sees the internal, gravitationally-dominatedmotions of galaxies within the group. Most of the galaxies are gathered in twofamilies around the major members of the group. The total mass of the group isestimated as M = 1 . ± . × M ⊙ (10).It is seen from Fig.1 that the expansion (cid:29)ow takes over at a distan e ≃ V ∝ R ,known as the Hubble law, emerges at about 2 Mp distan e. The measured valueof the lo al expansion rate (the Hubble parameter) is H = 72 ± km/s/Mp (11).The (cid:29)ow is rather regular and (cid:16) ool(cid:17): its radial one-dimensional velo ity dispersionis remarkably low, 17 km/s (9).Like in the largest-s ale studies (1,2), we use the observed expansion (cid:29)owas a natural tool for probing dark energy. The dwarf galaxies of the (cid:29)ow aregood (cid:16)test parti les(cid:17) whi h may reveal for us the dynami s behind the observed(cid:29)ow motion. Ea h parti le is a(cid:27)e ted by the gravitational attra tion of the Lo alGroup. Considering only the most important dynami al fa tors, we may take thegravity (cid:28)eld of the group as nearly entrally-symmetri and stati ; this is a goodapproximation to reality, as exa t omputer simulations prove (13,14). A ordingto Newtonian gravity law, this for e gives a parti le a eleration (for e per unitmass) F N = − GM/R , (1)at its distan e R from the group bary enter.We onsider a pi ture in whi h the Lo al Group and the expansion (cid:29)ow aroundit are all embedded in the dark energy with a uniform lo al density ¯ ρ V whi h is,generally, not ne essarily equal to the global density ρ V . Respe tively, ea h parti leof the (cid:29)ow is also a(cid:27)e ted by the repulsive antigravity for e produ ed by thelo al dark energy ba kground. This for e an be des ribed in terms of Newtonian3e hani s as well, and a ording to the `Einstein antigravity law', the dark energygives a eleration F E = G ρ V ( 4 π R ) /R = 8 π Gρ V R, (2)where − ρ V = ¯ ρ V + 3¯ p V is the lo al e(cid:27)e tive (General Relativity) gravitatingdensity of dark energy (for details see (15 ) where a General Relativity treatmentis also given). The lo al pressure of dark energy is negative, ¯ p V , and so the e(cid:27)e tivegravitating density is negative as well. Be ause of this the a eleration is positive,and it speeds up the parti le motion apart from the enter.It is seen from Eqs.1 and 2 that the gravity for e ( ∝ /R ) dominates overthe antigravity for e ( ∝ R ) at small distan es, and here the total a eleration isnegative. At large distan es, antigravity dominates, and the a eleration is positivethere. Gravity and antigravity balan e ea h other, and so the a eleration is zero,at the (cid:16)zero-gravity surfa e(cid:17) whi h has a radius R V = ( 3 M π ¯ ρ V ) / . (3)If one takes into a ount the real stru ture of the Lo al Group, it may beseen (13,14) that the zero-gravity surfa e is not exa tly spheri al and not exa tlystati ; but it is nearly spheri al and remains almost un hanged (within the 15-20%a ura y) sin e the formation of the Lo al group some 12 Gyr ago, as the omputersimulations indi ate.The model des ribed by Eqs.1-3 is obviously very di(cid:27)erent from the Friedmann osmologi al model of a uniform and isotropi universe. And this must be so,be ause there is no uniformity or isotropy on the spatial s ale of a few Mp .Moreover, the for e (cid:28)eld of the universe as a whole is non-stationary and hangingwith time, while the lo al for e (cid:28)eld (given by Eqs.1-2) is stati . Consequently, themotion of the lo al (cid:29)ow galaxies hardly originated in the global initial isotropi Big Bang; its nature is rather essentially lo al and aused by the lo al pro esses.One may imagine that the (cid:29)ow galaxies gained their initial velo ities in the early4ays of the Lo al Group when its major and minor galaxies parti ipated in violentnon-linear dynami s with multiple ollisions and mergers. In this pro ess, some ofdwarf galaxies managed to es ape from the gravitational pool of the Lo al Groupafter having gained es ape velo ity from the non-stationary gravity (cid:28)eld of theforming group. This pro ess is suggested by the on ept of the (cid:16)Little Bang(cid:17)(16)and supported by the omputer simulations (13,14).When es aped parti les o ur beyond the zero-gravity surfa e ( R > R V ),their motion is ontrolled mainly by the dark energy antigravity. The generaltrend of the dynami al evolution of the (cid:29)ow may be seen from Eqs.1-3. At largeenough distan es where antigravity dominates over gravity almost ompletely, thevelo ities of the (cid:29)ow are a elerated and (cid:28)nally they grow with time exponentially: V ∝ exp[ H V t ] . At this limit, the distan es grow exponentially as well. As a result,the expansion (cid:29)ow a quires the linear velo ity-distan e relation asymptoti ally: V → H V R . Here the value H V = ( 8 πG ρ V ) / (4)is the expansion rate whi h is onstant and determined by the lo al dark energydensity alone.The zero-gravity radius R V is obviously the key physi al quantity in thispi ture. How to (cid:28)nd its value in the observed expansion (cid:29)ow? Basing on thedynami s onsiderations above, we may robustly restri t the value of R V withthe use of the diagram of Fig.1. Indeed, sin e the zero-gravity surfa e lies outsidethe Lo al Group volume, it should be that R V > Mp . On the other hand, thefa t that the linear velo ity-distan e relation is seen from a distan e of about 2Mp suggests that R V < Mp . If so, Eq.3 leads dire tly to the robust upper(from
R > Mp ) and lower (
R < Mp ) limits to the lo al dark energy density: (0 . ± . < ¯ ρ V < (1 ± . × − kg/m . (5)(Here the measured value of the Lo al Group mass is also used.)5he lower limit in Eq.5 is most signi(cid:28) ant. It means that the dark energydoes exist in the nearby universe. In ombination, both limits imply that thevalue of the lo al dark energy density is near the value of the global dark energydensity, ¯ ρ V ∼ ρ V , or may be exa tly equal to it. Anyway, the global (cid:28)gure for ρ V ( (0 . ± . × − kg/m (cid:21) see above) lies omfortably in the range given byEq.5.It seems amazing that su h a fundamental physi al quantity as the density of osmi va uum, omes from a simple ombination ¯ ρ V = M πR V of rather modestastronomi al quantities whi h are the Lo al Group mass and the starting distan eof the Hubble (cid:29)ow of expansion.Thus, the observations of the lo al expansion (cid:29)ow enable us to dis over lo aldark energy in the nearby universe and estimate its density at a distan e of afew Mp from the Milky Way galaxy. The result is ompletely independent ofthe largest-s ale osmologi al observations (1,2) in whi h dark energy was (cid:28)rstdis overed; it is also ompatible with and omplementary to them.Now we dis uss the result and its impli ations.1. As we already mentioned, the dark energy (cid:28)rst revealed itself in the Hubble(cid:29)ow at very large distan es. It was found (1,2) that the global osmologi al expansionwas de elerated by gravity at times earlier than at the redshift z = z V ≃ . (whi h orresponds to a distan e ∼ Mp ) and a elerated by antigravity at timeslater than z = z V . At the redshift z = z V , the antigravity of dark energy and thegravity of matter (baryons and dark matter) balan e ea h other for a moment. Thebalan e ondition is ρ M ( z V ) − ρ V = 0 , where ρ M ( z ) is the osmologi al matterdensity. Sin e the matter density s ales with redshift as (1+ z ) and the present-daymatter density is known, ρ M ( z = 0) ≃ . × − kg/m , the estimate of the globaldark energy density omes from the balan e relation: ρ V = ρ M ( z = 0)(1 + z V ) (see its numeri al value in the beginning of the paper).In our sear h for the lo al dark energy, we have followed exa tly the same6ogi . Indeed, the zero-gravity radius of Eq.3 is an exa t lo al ounterpart of the(cid:16)global(cid:17) redshift z V : they both indi ate the gravity-antigravity balan e. But whatis temporal globally proves to be spatial lo ally: the balan e takes pla e only atone proper-time moment (at z = z V ) in the Universe as a whole, while it exists allthe time sin e the formation of the Lo al Group at only one distan e ( R = R V )from the group enter. Unfortunately, the a ura y of the determination of R V isstill onsiderably lower than in the ase of z V ; this is mainly be ause of a relativelysmall number of galaxies (cid:21) only two dozens (cid:21) in the observed lo al (cid:29)ow.The global studies (1,2) are reasonably treated as dire t probe of dark energy (cid:21) ontrary, for instan e, to impli ations from CMB studies (3,4) whi h are onsideredindire t. In the same sense, our lo al method is the dire t one.2. Our model leads to an important spe i(cid:28) predi tion. It follows from Eqs.1-3that at distan es R > R V , the velo ities of the lo al expansion (cid:29)ow must be not lessthan a minimal velo ity V esc . The minimal velo ity omes from the minimal totalme hani al energy needed for a parti le to es ape from the gravitational potentialwell of the Lo al Group. A tually, this predi tion may serve as a riti al test forthe model.In Fig.1, the minimal velo ity V esc is shown by a bold urve; it turns to zeroat R = R V and grows nearly linearly at R > R V . This is one urve of a bun h ofthe urves that ross the distan e segment from 2.1 to 2.3 Mp orresponding tothe observed position of the galaxy I5152 on the diagram. At R > R V , the bun hleaves all the 20 other galaxies above the riti al urves. The bun h parameters arethe mass of the Lo al Group M and the dark energy density ¯ ρ V , and if the massis taken to be M = 1 . ± . × M ⊙ (see above), then the lo al dark matterdensity must be ¯ ρ V = (0 . ± . × − kg/m . (6)Thus, the model passes the test with these parameters, and in this way, the diagramof Fig.1 leads to a new independent estimate of the dark energy density. The value7f Eq.6 is ompatible with the interval of Eq.5.As is seen in Fig.1, the velo ity-distan e stru ture of the (cid:29)ow follows the trendof the minimal velo ity: the linear regression line of the (cid:29)ow (the thin line) isnearly parallel to the minimal velo ity urve, at R > R V .A stronger ondition may also be he ked whi h requires that all the 21 galaxiesat R > R V (in luding the galaxy I5152) are above the riti al lines. In this ase,the value of Eq.6 gives an upper limit for the lo al dark energy density.Note that the test is rather sensible: for instan e, with a higher value of thelo al dark energy density, say, . × − kg/m , over half of the galaxies wouldlie below the urve of the minimal velo ity.For a omparison, a similar minimal es ape velo ity is shown also for a (cid:16)no-va uum model(cid:17) with zero dark energy density (cid:21) dashed line in Fig.1. The real (cid:29)owignores obviously the trend of the minimal velo ity in this ase: the velo ities of the(cid:29)ow grow with distan e, while the minimal velo ity de reases. It is seen also thattwo galaxies of the (cid:29)ow violate obviously the no-va uum model: they are lo atedbelow the dashed line. This omparison is learly in favor of the va uum energymodel and against the model with no dark energy.3. Another independent test of the model involves the measured value of thelo al expansion rate H = 72 ± km/s/Mp (11). Indeed, the model predi ts thatthe expansion rate must be near the value of H V (see Eq.4), at distan es largerthan, say, 2 Mp . So putting roughly H = H V , we get from this equality a newestimate for the lo al dark energy density: ¯ ρ V = 38 πG H = (1 ± . × − kg/m . (7)The result is ompatible with Eqs.5,6, hen e the model passes this test as well.Interesting enough, the three seemingly unrelated quantities (cid:21) the Lo al Groupmass M , the starting distan e of the expansion (cid:29)ow R V and the expansion rate H (cid:21) prove to be essentially linked, so that H R V / ( GM ) ∼ . In this fa t, theself- onsisten y of the model manifests itself.8. A ording to re ent studies by Sandage and his olleagues (see a summarizingpaper (17) and referen es therein), a regular Hubble (cid:29)ow of expansion is observedover a very large distan e range from 4 to 200 Mp . The (cid:29)ow exhibits the Hubblevelo ity-distan e law, and its expansion rate H = 62 . ± . km/s/Mp is pra ti allythe same over the whole s ale range. The simple model of Eqs.1-5 annot beapplied in this ase dire tly. But our dynami s analysis above (see also papers(18-21)) suggests that the kinemati regularity of the (cid:29)ow is possible only due tothe smoothing e(cid:27)e t of the perfe tly uniform dark energy on the otherwise lumpygravitational for e (cid:28)eld of the haoti and non-uniform distribution of the galaxies.In this ase, the rate of expansion must be near the universal value H V of Eq.4.With this new understanding, the data (17) may be used to estimate the lo aldark energy density on the s ales 4-200 Mp . Using the equality H = H V , wehave: ¯ ρ V = 38 πG H ≃ (0 . ± . × − kg/m . (8)This value is pra ti ally equal to the global dark energy density ρ V .5. Beyond the Lo al Group's neighboring expanding population whi h we examinedhere, small galaxy groups have long been known to be quite ommon; re ent studiesdemonstrate this de(cid:28)nitely (22,23). Computer identi(cid:28)ed groups from observationalgalaxy atalogs (24) have been shown to have an expanding population via aDoppler shift number asymmetry relative to the brightest member. Large N-body Λ CDM osmologi al simulations (25-28) show that a stru ture with a massivegroup in its enter and a ool expansion out(cid:29)ow outside is rather typi al for s alesof a few Mp and more. The relative numbers of simulated groups of di(cid:27)erentkinds (29) are near the observed ones, if the lo al dark energy density is assumedat the level of Eq.8. Su h studies of other galaxy groups omplement usefully ourapproa h to the dark energy dete tion around the Lo al Group.9eferen es1. Riess A.G., Filippenko A.V., Challis P. et al. AJ, 116, 1009 (1998)2. Perlmuter S., Aldering G., Goldhaber G. et al. ApJ, 517, 565 (1999)3. Spergel D.N. et al. ApJS 148, 175 (2003)4. Spergel D.N. et al. astro-ph/0603449 (2006)5. Gliner E.B. Sov.Phys. JETP 22, 378 (1966)6. Kara hentsev I.D., Sharina M.E., Makarov D.I., et al. A&A, 389, 812 (2002)7. Kara hentsev I.D., Makarov D.I., Sharina M.E., et al. A&A, 398, 479 (2003)8. Kara hentsev I.D., Kashibadze O.G. Astro(cid:28)zika 49, 5 (2006)9. Kara hentsev I.D., Tully B., Dolphin A.E., et al. AJ 133, 504 (2007)10. Kara hentsev I.D. AJ 129, 178 (2005)11. Kara hentsev I.D. , Dolphin A.E., Tully, R.B. AJ 131, 1361 (2006)12. Kara hentsev I.D., Kara hentseva V.E., Hu htmeier W.K., Makarov D.I., 2004,AJ, 127, 203113. Chernin A.D., Kara hentsev I.D., Valtonen M.J.et al. A&A 415, 19 (2004)14. Chernin A.D., Kara hentsev I.D., Valtonen M.J. et al. A&A (2007 (cid:21) in press)15. Chernin A.D., Teerikorpi P., Baryshev Yu.V. A& A 456, 13 (2006)16. Byrd G.G., Valtonen M.J., M Call M., Innanen K. AJ 107, 2055 (1994)17. Sandage, A., Tamman, G.A., Saha, A., et al. ApJ 653, 843 (2006)18. Chernin A.D., Teerikorpi P., Baryshev Yu.V. (astro-ph//0012021) = Adv.Spa e Res. 31, 459 (2003)19. Kara hentsev, I.D., Chernin, A.D., Teerikorpi, P. Astro(cid:28)zika 46, 491 (2003)20. Teerikorpi, P. Chernin, A., Baryshev, Yu., , A&A 440, 791 (2005)21. Thim, F., Tammann, G., Saha, A., et al. ApJ, 590, 256 (2003)22. van den Bergh, S. AJ 124, 782 (2002)23. van den Bergh, S. ApJ 559, L113 (2001)24. Valtonen, M. J. and Byrd, G. G. ApJ 303, 523 (1986)25. Nagamine, K., Cen, R., Ostriker, J. P. Bul. Amer. Astron. So . 31, 1393 (1999)106. Ostriker, J. P., Suto, Y. ApJ 348, 378 (1990)27. Strauss, M. A., Cen, R., Ostriker, J.P. ApJ 408, 389 (1993)28. Ma i(cid:0)o, A.V., Governato, F. Horellou, C. MNRAS 359, 941 (2005)29. Niemi, S.-M. et al. (to be published)30. A.C., Yu.E., V.D. and L.D. were partly supported by a RFBR grant 06-02-16366.Figure aptionFig.1. The Hubble diagram for the very lo al (distan e