Incompatible Gravity Pouria Khalaj Physics Department Sharif University

Incompatible Gravity Pouria Khalaj Physics Department Sharif University of Technology May 11, 2010

Outline Terminology Introduction The Problem Solutions: Modified Newtonian Dynamics (MOND) Dark Matter Compound Theories Modified Gravity (!) Summary Proposal

Terminology Mass to Light Ratio: Surface Brightness: HSB Galaxies: High-Surface Brightness Galaxies LSB Galaxies: Low-Surface Brightness Galaxies Dynamical Mass: Derived from spectroscopy. Luminous Mass: Derived form photometry.

Introduction In the 17 th century Sir Isaac Newton could successfully give a unified description of the motion for celestial and terrestrial objects in one consistent theory. Newton’s universal law of gravitation and its three laws of motion was enough for us to go to the Moon. However precise measurements showed some significant deviations from what is predicted by theory. (Precession of the planetary orbits (esp. Mercury), light deflection, time dilation and gravitational red shift. ) Albert Einstein published Theory of General Relativity in 1915. In contrast to Newtonian gravity, GR was able to solve the above problems. However one big problem still remains unsolved.

The Problem • In 1937 the Swiss astronomer Zwicky measured the velocity dispersion of the Coma cluster. Astronomers got familiar with the idea that the universe is filled by dark matter. • In 1978, flat rotation curves of galaxies posed a serious problem in astronomy. (Using Doppler effect, we can draw rotation curves of spiral galaxies. By doing so we’ll reach unexpected results. Instead of having a descending curve we have a flat curve. It indicates that gravitation must be an stronger than expected. )

Flat Rotation Curves Observed Curve (gives dynamical mass) Expected Curve (from M/L ratio)

Examples

Galaxy Clusters From Virial Theorem we know: By applying Virial Theorem to galaxy clusters we have:

The Problem In both cases we conclude that the dynamical mass is not equal to the luminous mass. There are two possible explanations: 1 - A kind of unseen matter exists in the galaxy. Dark Matter 2 -We are facing a failure of the law of gravitation. MOND

MOND theory was proposed by M. Milgrom in 1983. In this theory the known Newtonian acceleration is replaced by a modified acceleration so that in the case of gravity, it has a 1/r dependency at large distances from the center of the spiral galaxies. Thus it can explain flat rotation curves.

MOND � MOND effects are observed when the gravitational accelerations falls below a certain value so its effects are negligible in the range of ordinary accelerations. • (Begeman et al. 1991)

MOND What is the general form of µ? Bekenstein & Milgrom (1984) There also other forms: Famaey & Binney (2005), Bekenstein (2004), and Zhao et al. (2006).

Example If we model the Galactic disk as a simple, infinitesimally thin Kuzmin disk (Kuzmin 1956), the corresponding Newtonian potential (Binney & Tremaine 1987) is given by:

Dark Matter Does not interact via electromagnetic force. Does interact via gravitational force. Can not be seen by its radiation. (It has no radiation at all) Comes into three types: - Cold Dark Matter (CDM): Non-relativistic - Warm Dark Matter (WDM): Relativistic - Hot Dark Matter (HDM): Ultra-Relativistic

Dark Matter or Missing Mass? Nucleosynthesis Theory constraint on baryonic matter: Primordial black holes (CDM) Neutrinos (HDM, CDM) MACHOs: Massive Compact Halo Objects (CDM) Brown Dwarfs (CDM) Unseen gas and dust (CDM) Non-baryonic dark matter (WIMP)

Examples (CDM halo Models) Power-law potential Logarithmic potential

MOND versus DM Issues for DM: • Does the stuff we call Dark Matter really exist? • Can a dark matter based theory explain the MONDian phenomenology observed in rotation curves? • Why should the mass discrepancy only appear at a particular acceleration scale? Issues for MOND: • Can a modified force law explain all observations? • Can a satisfactory theory encompassing both General Relativity and MOND be found?

Curve Fitting (MOND +1) In contrast to DM, MOND gives very little flexibility in curve fitting which is good!! MOND has one free parameter which is M/L. Sometimes M/L becomes irrelevant. DM has three free parameters which are M/L, the halo core radius and the halo asymptotic velocity.

Example (NGC 6503) Solid curve: Three-parameter dark-halo it Dashed line: Stellar component Dotted line: Gas component Dash-dotted line: Dark halo component

Fake Curve Fitting Data form UGC 128 and NGC 2403

Magellanic Stream

Tully-Fisher Relation (MOND +1) T-F relation (spiral galaxies) in MOND: T-F relation in Newtonian gravity: which is wrong! Since we have HSBs and LSBs.

HSBs and LSBs (left) T-F relation (right) F-J relation

Bullet Cluster (DM +1)

Gravitational Lensing (DM +1) MOND with some approximation can explain gravitational lensing. Modified MOND is not acceptable!

Compound Theories and Modified Gravity There are some situations that one needs to assume that both dark matter and MOND theory are true. In this case we can ask what is the benefit of MOND at all when we still need some dark matter? Is Dark Matter another epi-cycle? How about dark energy? Instead of MOND, one may use other forms of equations for gravity. Asymmetric gravity for example.

Summary Observational Test Dark Matter MOND LSBG Tully-Fisher Relation ? ? + M/L-Surface Brightness Relation X + Stellar Mass to Light Ratios NP + Mass Surface Densities X + Local M/L NP + Galaxy Clusters ? ? ? + NT Gravitational Lensing + = prediction confirmed CMB Geometry X = prediction falsified* ? = uncertain but promising ? ? = uncertain but not promising NP = no prediction NT = no test

Proposal One big question of mine: How Cosmic Rays can be used as a tool to determine whether MOND or Dark Matter is true?

References Hoekstra, H. , Franx, M. , Kuijken, K. , 1999, ar. Xiv: astro- ph/9911106 v 1 Brownstein, J. R. , ar. Xiv: 0908. 0040 v 1 Bekenstein, J. D. 2010, ar. Xiv: 1001. 3876 v 1 Haghi, H. , Rahvar, S. , Hassani-Zanooz, A. 2006, Ap. J, 652, 354 Liddle, Andrew, An Introduction to Modern Cosmology, WILEY, 2003 Haghi, H. , Hassani-Zanooz, A. , Rahvar, S. , Magellanic stream: a possible tool for studying dark halo model www. wikipedia. org

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