The Dark Matter Crisis: Problems with the Current Standard Model of Cosmology and Steps Towards an Improved Model

The dark matter crisis: problems with the current standard model of cosmology and steps towards an improved model

Pavel Kroupa Helmholtz-Institut fuer Strahlen und Kernphysik (HISKP) University of Bonn

AAS Topical Meeting "Probes of Dark Matter on Galaxy Scales" Monterey, CA, 14-19 July 2013

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 1

Standard model of physics :

Computation and prediction of dynamical structures (particles and their excited states).

Until now excellent agreement with experiments (e.g. LHC).

Standard model of cosmology :

Computations and predictions of dynamical structures (galaxies and their satellite galaxies).

This talk.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 2 Standard model of cosmology :

Postulate I : Einstein's ﬁeld equation is valid everywhere

Postulate II : Matter is conserved

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 3

Standard model of cosmology :

Assumptions are immediately falsiﬁed : - Prediction of a highly curved highly inhomogeneous universe - Prediction of falling rotation curves of galaxies and structure formation too slow

Solution: not understood - Postulate a mathematical trick (inﬂation) - Postulate existence of unknown exotic matter (dark matter) not found But this also does not work: - Universe expands today faster, than it should

Solution: not understood - Postulate a mathematical trick (dark energy)

Problem : - Model (=Standard Model of Cosmology = LCDM) does not conserve energy

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 4 The standard model of cosmology (SMoC) : ﬁx its parameters such that it accounts for the observed large-scale structure.

Assume it is a valid description of the universe, then test on intermediate and galactic scales where data are excellent . . .

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 5

Consequence I

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 6 Structures form according to the cosmological merger tree

the beginning Big Bang

Lacey & Cole (1993)

DM substructures form first and coalesce to larger structures

today

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 7

250 kpc

Astrophysics of Galaxies VIII: LG Donnerstag, 18. Juli 13 8 Consequence II

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 9

Structures form according to the cosmological merger tree

the beginning

Lacey & Cole (1993)

galaxies interact and merge

TDGs = tidal dwarf galaxies form

today

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 10 Tidal tails

Miho & Maxwell, web Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 11

(Weilbacher et al. 2000)

NTDG ≈ 14

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 12 (Weilbacher et al. 2000)

bulge Phase-space correlated formation satellites form naturally in the same event as a bulge does.

TDG formation

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 13

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 14 Relevance : The collision of two disks at high redshift

Wetzstein, Naab & Burkert 2007 Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 15

Wetzstein, Naab & Burkert 2007 Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 16 (Weilbacher et al. 2000)

NTDG ≈ 14

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 17

Thus in the Standard Model of Cosmology (SMoC) a galaxy must look as follows: phase-space spheroidal correlated distribution distribution

+ DM satellites + TDG satellites

have different properties

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 18 The Dual Dwarf Galaxy Theorem must be true if the SMoC is true :

The Dual Dwarf Galaxy Theorem :

E V Kroupa 2012 SMoC ⇒ Type A dwarfs Type B dwarfs

with Dark Matter (DM) TDGs w/o DM

spheroidal phase-space distribution correlation

If only one type exists then the Dual Dwarf Galaxy Theorem is falsified.

Is there any evidence for the co-existence of two types of dwarf galaxy ?

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 19

The Gentile et al., 2007 Baryonic Tully -Fisher Relation :

If the SMoC is true the BTFR then the BTFR must be given by the dark matter halo and tidal dwarf galaxies } dark matter cannot objects lie on the same BTFR !

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 20 The Gentile et al., 2007 Baryonic Tully -Fisher Relation :

the BTFR

But TDGs do lie on the same BTFR !? TDGs TDGs

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 21

Types of stellar systems Dabringhausen et al. 2012

only one 4 10 type of dwarf galaxy exists !

103

102

101

projected half-light radius [ pc ] GCs / UCDs elliptical galaxies 100 fit to giant ellipticals fit to dwarf ellipticals

102 104 106 108 1010 1012 stellar mass [ M ] ! Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 22 Types of stellar systems Dabringhausen et al. 2012

104

TDGs coincide with 3 10 dE / dSph satellites

102

101

projected half-light radius [ pc ] GCs / UCDs elliptical galaxies 100 observed TDGs numerical calculations

102 104 106 108 1010 1012 stellar mass [ M ] ! Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 23

Thus: Kroupa 2012; Dabringhausen & Kroupa 2013

The Dual Dwarf Galaxy Theorem : V

SMoC ⇒ E Type A dwarfs Type B dwarfs

only one type of dwarf galaxy is observed.

Dual Dwarf Galaxy Theorem is falsified. ⇔

Type A dwarf = Type B dwarf ⇒ SMoC

has been shown

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 24 Remember :

The Dual Dwarf Galaxy Theorem must be true if the Kroupa 2012; SMoC is true : Dabringhausen & Kroupa 2013

The Dual Dwarf Galaxy Theorem : V

SMoC ⇒ E Type A dwarfs Type B dwarfs

with DM TDGs w/o DM

spheroidal phase-space distribution correlation

consistency check next . . .

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 25

Consistency Check I

the Milky Way satellites are TDGs without dark matter

then

they ought to be in a phase-space correlated distribution.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 26 Vast Polar Structure around the Milky Way Pawlowski et al. 2012

YH globular clusters

dSph satellites

UFD satellites See also YouTube video "The Vast Polar Structure" streams

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 27

Vast Polar Structure around the Milky Way Pawlowski et al. 2012

YH globular clusters

dSph satellites

UFD satellites See also YouTube video "The Vast Polar Structure" streams

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 28 Vast Polar Structure around the MW Pawlowski et al. 2012

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 29

If the MW satelites are DM dominated sub-halos, then

A) they have to have fallen-in recently (z<1) in order to be arranged in the DoS/VPOS Deason et al. (2011)

AND

B) they have to have fallen in a long time ago (z=3-10) in order for them to have lost their gas Nichols & Bland-Hawthorn (2011)

A and B are mutually exclusive.

==> logical inconsistency of the model

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 30 Phase-space-correlated tidal debris Pawlowski et al. 2012

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 31

Fly-by encounter: e.g. Milky Way and Andromeda ? about 10-11 Gyr ago Pawlowski et al. 2011

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 32 Consistency Check II

Other, extra-galactic,

phase-space correlated distributions

of satellite systems.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 33

Bournaud et al. (2007, Science)

observed model

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 34 Bournaud et al. (2007, Science)

observed model

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 35

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 36 Duc et al. (2011 (post-merger 2-3 Gyr) NGC 5557 MNRAS)

200 kpc

dSph dSph Text dSph

(Kroupa et al. 2010) Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 37

Tollerud et al. (2011, Andromeda MNRAS)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 38 Tollerud et al. 2011, Andromeda Ibata et al. 2013, Nature; Conn et al. 2013)

50 % of all satellites are in thin disk (14 : 400kpc).

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 39

The formation of faint dwarf galaxies in the interaction between two spirals (NGC 3169)

Credit: Martinez-Delgado (ZAH) and Adam Block (MtLemmon Obs)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 40 GALEX image (NGC 3169)

From: Martinez-Delgado (ZAH)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 41

Remember :

Kroupa 2012 The Dual Dwarf Galaxy Theorem must be true if the SMoC is true :

The Dual Dwarf Galaxy Theorem : V

SMoC ⇒ E Type A dwarfs Type B dwarfs

with DM TDGs w/o DM

spheroidal phase-space distribution correlation

consistency check next . . .

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 42 Thus: Kroupa 2012

The Dual Dwarf Galaxy Theorem : V

SMoC ⇒ E Type A dwarfs Type B dwarfs

only one type of dwarf galaxy is observed.

Dual Dwarf Galaxy Theorem is falsified. ⇔

Type A dwarf = Type B dwarf ⇒ SMoC

has been shown

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 43

If this falsification is true, then the standard model of cosmology must show other and general discrepancies with data . . .

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 44 The Theory Confidence Graph Kroupa 2012

angular momentum cusp/core

missing satellites down sizing DoS (later VPOS) TDG mass deficit invariant disk galaxies common DM mass scale of satellite galaxies constant surface density

MFn of luminous sub-halos bulgeless disk galaxies isolated massive galaxies Local Void too empty Bullet cluster missing massive satellites thin old disk Train-Wreck cluster missing dark matter massive galaxy clusters

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 45

Kroupa 2012 Failure 14 : 58–74 per cent of all observed disk galaxies are claimed to not have a classical bulge (Kormendy et al. 2010).

This is in conflict with the heavy merging history expected for bright galaxies if the SMoC were true (Hammer et al. 2007).

Failure 21 : Over spatial scales of 100 Mpc the density of matter fluctuates by 10% if the SMoC were valid.

By counting up all matter within the local sphere with a radius of 50 Mpc, Karachentsev (2012) demonstrates the actual density to be too low by a factor of 3–4. Most of the missing mass is DM.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 46 What has been achieved so far ?

The dynamical structures which must form if collisionless dark matter particles exist are not observed.

Compare with success of the standard model of particle physics,

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 47

An important clue follows from the Andromeda satellite system:

The vast thin disk (VTD) of satellites can only be understood if the satellites in the VTD are TDGs (Hammer et al. 2013).

But each has an identical very large dark-matter content as those satellites which are not in the VTD.

TDGs + DM => logical inconsistency

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 48 Cold or warm dark matter particles therefore cannot exist.

==> effective gravity is not Newtonian/Einsteinian (or DM has extremely complicated dynamics -- the "epicycle on epicycle" approach)

Which impact does this have for understanding dynamics in galaxies and on a cosmological scale ?

(Remember: Cold or warm dark matter is postulated as a result of adopting the Einsteinian field equation on galactic and cosmologcial scales)

Do the data on galaxy-scales contain clues ?

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 49

Mass-Discrepancy correlation with acceleration McGaugh 2004 Famaey & McGaugh 2012 Kroupa 2012

galaxy

Vb = theoretical V = (Newtonian) observed rotation rotation speed speed

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 50 Mass-Discrepancy correlation with acceleration McGaugh 2004 Famaey & McGaugh 2012 Kroupa 2012

galaxy 15 17 1pc=31 10 m 1m=3.2 10 pc

Vb = theoretical V = (Newtonian) observed rotation rotation speed speed

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 51

Mass-Discrepancy correlation with acceleration McGaugh 2004 Famaey & McGaugh 2012 Kroupa 2012

galaxy 15 17 1pc=31 10 m 1m=3.2 10 pc

Vb = theoretical V = (Newtonian) observed rotation rotation speed speed

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 52 Mass-Discrepancy correlation with acceleration McGaugh 2004 Famaey & McGaugh 2012 Kroupa 2012

Correlation 15 17 can't be 1pc=31 10 m 1m=3.2 10 pc explained by Dark Matter : DM particle physics is independent of the local acceleration in the SMoC.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 53

Consider space-time scale invariance : (Milgrom 2009; Kroupa, Pawlowski & Milgrom 2012)

If (t, x, y, z) (t, x, y, z) 2 then, the Newtonian gravitational acceleration, g N GM/r , 2 scales as g g N N 1 dx˙ while the kinematical acceleration, g , scales as g g dt 

For gravitational and kinematical acceleration to also be scale invariant we thus need g to scale as 1/2 gN 1/2 2 or 2 i.e. g (a g ) g = aogN a = aogN o N i.e. a a = gN ao

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 54 space-time scale invariance (from above) : a i.e. pGM a = gN , thus a = pa0 ao r

centrifugal acceleration = centripetal acceleration 2 V pGMa0 a = = (V Vc) r r ⌘

1 the Tully-Fisher relation ! V =(GMa ) 4 0 and flat rotation curves !

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 55

The observational Baryonic Tully -Fisher Relation Famaey & McGaugh 2012

No "kink" here.

DDO 210

6 15 km/s; Mb 5 10 M ⇥

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 56 The observational Baryonic Tully -Fisher Relation Famaey & McGaugh 2012

But TDGs are purely should baryonic objects. be here as no So, why are they so dark matter similar in TDGs to the other galaxies ? ✓ in Milgrom Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 57

Consider space-time scale invariance : (Milgrom 2009; Kroupa, Pawlowski & Milgrom 2012)

If (t, x, y, z) (t, x, y, z) 2 or 2 g = aogN a = aogN a i.e. a = gN ao

2 1 Since V =(Ga0M) 2 GM V 2 = b r

2 1 1 1 V (Ga0M) 2 (Ga0M) 2 a0 2 = GM = = Vb r 2 ra a ✓ ◆ r ⇣ ⌘

2 1 V a 2 i.e. = 0 Vb a ✓ ◆ ⇣ ⌘ Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 58 Mass-Discrepancy correlation with acceleration

2 1 V a0 2 from space-time = Vb a scale-invariance ✓ ◆ ⇣ ⌘

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 59

Milgromian Dynamics from quantum mechanical processes in the vacuum

Kroupa et al. (2010), Appendix A:

". . . an accelerated observer in a de Sitter universe (curved with a positive cosmological constant Λ) sees a non-linear combination of the Unruh (1975) vacuum radiation and of the Gibbons & Hawking (1977) radiation due to the cosmological horizon in the presence of a positive Λ. Milgrom (1999) then defines inertia as a force driving such an observer back to equilibrium as regards the vacuum radiation (i.e. experiencing only the Gibbons-Hawking radiation seen by a non-accelerated observer). Observers experiencing a very small acceleration would thus see an Unruh radiation with a low temperature close to the Gibbons-Hawking one, meaning that the inertial resistance defined by the difference between the two radiation temperatures would be smaller than in Newtonian dynamics, and thus the corresponding acceleration would be larger. This is given precisely by the formula of Milgrom (1983) with a well-defined transition-function μ(x), and ao = c (Λ/3)1/2. Unfortunately, no covariant version (if at all possible) of this approach has been developed yet."

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 60 . . . Milgromian Dynamics (current best bet) . . .

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 61

Milgromian Dynamics

Ansatz : (Milgrom 1983, ApJ, 270, 371)

a µ(x)=1if|x| ! 1 −1 µ !a = g!N i.e. !a = g!N µ ≥ g!N !a0 " { µ(x)=x if |x| ! 1

What is the interpretation ? Milgromian dynamics can be understood to be

a different effective Law of Gravity a modification of the Law of Inertia through a different "Poisson" equation through the breaking of the equivalence of inertial and gravitating mass 1 ⌥ ⌅ ⌃ ⇥ ⌥ µ ⇥ ⌥ ⌅ =4⇥ G ⇤ ⌃a = F⌃ mµ ⇥ · ⌅ ⇥ a ⇤ ⇥ ⇧ 0 ⌅ ⇥ a0 ⇤⇧ ⌃ ⌥ ⌃ ⌥ giving the Milgromian potential where F ⌅ = m g ⌅ N for gravity

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 62 From Robert Sanders' Book on "The Dark Matter Problem", Cambridge University Press, 2010

Milgromian dynamics LCDM

Renzo's rule

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 63

In fact, given an observed baryonic matter distribution, the rotation curve

can be precisely predicted using Milgromian dynamics

cannot be predicted using LCDM.

plus in Milgromian dynamics dark matter significantly reduced in galaxy clusters

(e.g. Sanders 2009 (review) : "Modiﬁed Newtonian Dynamics : A Falsiﬁcation of Cold Dark Matter")

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 64 Milgromian dynamics and structure formation

Combes & Tiret 2009, arXiv:0908.3289 :

". . . simulations yield comparable results between [Milgromian dynamics] and the standard model for the large-scale structure, . . . "

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 65

Milgromian dynamics and structure formation

Skordis et al. 2006, PhRvL "We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekenstein’s theory of" Milgromian dynamics.

Angus 2010 on SciLogs: "State-of-the-art cosmology: the current status" Perfect fit to all CMB peaks with 11ev sterile neutrino.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 66 CMB power spectrum in Milgromian dynamics

Angus & Diaferio 201; Kroupa 2012

Data: WMAP (2006), Acbar (2004)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 67

Gary Angus, 2009, MNRAS:

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 68 Thus,

The Concordance Cosmological Modell does not uniquely account for the CMB nor Large Scale Structure.

In fact, with the falsiﬁcation of the SMoC, it has become irrelevant to ask whether any set of data (e.g. large-scale structure or CMB) ﬁt the SMoC.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 69

Conclusions The standard model of cosmology is falsified : Dynamically relevant dark matter cannot exist in galaxies. (The search for it will be fruitless / DM substructures don't exist). Effective dynamics is Milgromian. (i.e. "dark matter" must be mathematically equivalent to Milgromian dynamics).

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 70 The Standard LCDM Model of Cosmology structure formation tree

(Lacey & Cole 1993)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 71

The new baryonic-galaxy structure formation tree within the VBLC

(Metz: PhD 2008; Kroupa et

al. 2010) time

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 72 Conclusions The standard model of cosmology is falsified : Dynamically relevant dark matter cannot exist in galaxies. (The search for it will be fruitless / DM substructures don't exist). Effective dynamics is Milgromian. (i.e. "dark matter" must be mathematically equivalent to Milgromian dynamics).

Matter cycle : galaxies appear to grow slowly in a self-regulated manner :

M˙ bar = HMbar With a new ansatz based on Einstein's field equation a new cosmological model can be suggested: vacuum baryo-leptogenesis cosmology (VBLC) - It fits the supernova Ia data --> no dark energy ! - Inflation is not necessary. - The problem with the vacuum energy density being 120 orders of magnitude may vanish.

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 73

Falsification of LCDM :

Find no evidence whatsoever for dynamical friction affecting satellite galaxy motions. (e.g. Sgr or LMC)

Falsification of Milgromain Dynamics:

Find isolated galaxies w/o a dark matter (e.g. E galaxies - Aaron Romanowski)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 74 Conclusions The standard model of cosmology is falsified : Dynamically relevant dark matter cannot exist in galaxies. (The search for it will be fruitless / DM substructures don't exist). Effective dynamics is Milgromian. (i.e. "dark matter" must be mathematically equivalent to Milgromian dynamics).

Matter cycle : galaxies appear to grow slowly in a self-regulated manner :

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 75

THE END

Donnerstag, 18. Juli 13 76 Evolution of TDGs

The Time

77 Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 77

Evolve dwarf galaxies w/o dark matter in a computer

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 78 Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 79

Star-cluster complex (cf Tadpole)

50 clusters 6 each 10 M!

clusters as fundamental galactic building blocks ⇓ Spheroidal dwarf galaxy ! (Fellhauer et al. 2001, 2002a,b,c, 2005; Bekki et al. 2004) Pavel Kroupa: University of Bonn

Donnerstag, 18. Juli 13 80 1-10% of

population Pavel Kroupa: University of Bonn in remnant

Donnerstag, 18. Juli 13 81

(Kroupa 1997) e =0.74

Remnants have a highly anisotropic f ( R ,V) 5 and mass ≈ 10 M!

R ≈ few 100 pc

M and ≈ 10 2 − 3 ! L e =0.60 Pavel Kroupa: University of Bonn

Donnerstag, 18. Juli 13 82 Hercules D=130kpc (Coleman et al. 2007)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 83

Hercules D=130kpc (Coleman et al. 2007)

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 84 MV = −9 mag (Kroupa 1997) r0.5 =180pc very similar to Hercules ! M =102.3 { L

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 85

This is a real prediction 10 years before the discovery of this type of celestial object !

Pavel Kroupa: University of Bonn Donnerstag, 18. Juli 13 86 THE END

Donnerstag, 18. Juli 13 87