Constraints on Magnetic FieldsConstraints on Magnetic Fieldsfrom Large Scale Structurefrom Large Scale Structure

Tina KahniashviliTina KahniashviliAbastumani Astrophysical Observatory, Abastumani Astrophysical Observatory,

Ilia State University, GeorgiaIlia State University, Georgia&&

McWilliams Center for Cosmology, McWilliams Center for Cosmology, Carnegie Mellon University, USACarnegie Mellon University, USA

NORDITA July 6 2015NORDITA July 6 2015

Outline

Observable Effects on LSS Observable Effects on LSS Lyman-alpha forestLyman-alpha forest Other cosmological testsOther cosmological tests

LimitsLimits

Based on: Kahniashvili, Maravin, Natarajan, Battaglia, Tevzadze, ApJ 2013Kahniashvili, Tevzadze, Sethi, Pandey, RatraPRD 2010

Magnetic Field in the UniverseMagnetic Field in the Universe Must be small Must be small

enough to preserve enough to preserve the isotropy of the the isotropy of the UniverseUniverse

BBN bound: BBN bound: Additional 10% to Additional 10% to the radiation the radiation energy density energy density Limits order of Limits order of

microGaussmicroGauss

Frozen-in conditionFrozen-in condition magnetic flux magnetic flux

conservation conservation

Coupling with Coupling with plasmaplasma MHD in the MHD in the

expanding Universe expanding Universe

Magnetic Field StatisticsMagnetic Field Statistics Spectral shapeSpectral shape

P(k) ~ k at large P(k) ~ k at large scales for causally scales for causally generated fieldsgenerated fields

P(k) ~ k at large P(k) ~ k at large scales for inflation scales for inflation generated fieldsgenerated fields

P(k) ~ k or P(k) P(k) ~ k or P(k) ~ k at small ~ k at small scalesscales

Correlation length Correlation length Limitation for Limitation for

causal fieldscausal fields Evolution (free Evolution (free

decay) during the decay) during the expansion expansion Faster growth for Faster growth for

helical fieldshelical fields

2

-3

-11/3-2

Magnetized Cosmological Magnetized Cosmological Perturbations Perturbations

Density perturbations - scalar mode Density perturbations - scalar mode Fast and slow magnetosound wavesFast and slow magnetosound waves

Vorticity perturbations - vector mode Vorticity perturbations - vector mode Alfven wavesAlfven waves

Gravitational waves - tensor ModeGravitational waves - tensor Mode

Scalar Magnetized Mode Scalar Magnetized Mode

Adams, et al.1996

Linear Magnetized Density Linear Magnetized Density Perturbations Perturbations

Ordinary adiabatic Ordinary adiabatic perturbations perturbations Harrison-ZelHarrison-Zeldovich dovich spectrum spectrum P(k) ~ k P(k) ~ k

Magnetized density Magnetized density perturbations (linear) perturbations (linear) P(k) ~ k P(k) ~ k white noise white noise

Kim, Olinto, Rosner 1996 Kim, Olinto, Rosner 1996

P(k) ~ k P(k) ~ k scale-scale-invariant (inflation)invariant (inflation)

Gopal & Sethi 2003Gopal & Sethi 2003 Gopal & Sethi 2003Gopal & Sethi 2003

4

Non-linear EffectsNon-linear Effects

Magnetized Jeans Magnetized Jeans effect effect Additional magnetic Additional magnetic

pressurepressure Fast-magneto-sound Fast-magneto-sound

waves waves Sound speed Sound speed

rescalling rescalling

Adams et al. 1996Adams et al. 1996

Damping Damping Diffusion (Alfven Diffusion (Alfven

waves) waves) MHD MHD Shaw and Lewis 2012Shaw and Lewis 2012

Kahniashvili, Tevzadze, Sethi, Pandey, Ratra 2010

Magnetized Matter Power SpectrumMagnetized Matter Power Spectrum

Kahniashvili et al. ApJ 2013Kahniashvili et al. ApJ 2013

CAMBCAMB modification by modification by

Shaw & Lewis Shaw & Lewis 20102010

Density Perturbations Amplitude Density Perturbations Amplitude

Jenkins et al. 2001Jenkins et al. 2001

Kahniashvili et al. ApJ 2013Kahniashvili et al. ApJ 2013

Halos AbundanceHalos Abundance Press-SchechterPress-Schechter

Modification by Sheth & Modification by Sheth & Tolmen 1999Tolmen 1999

Kahniashvili et al. ApJ 2013

Lyman-alpha DataLyman-alpha Data P(k) sensitive at P(k) sensitive at

k~0.1-100Mpck~0.1-100Mpc -1

Kahniashvili et al. ApJ 2013

Data: Data: Croft et al. 2002 Croft et al. 2002

LimitsLimits

Strongest limits from Strongest limits from Lyman-alpha dataLyman-alpha data

Planck 2015 Results Planck 2015 Results (XVI cosmological (XVI cosmological parameters)parameters)BBLL at 1Mpc < nG for at 1Mpc < nG for nnBB ~ -3 ~ -3

CMB Faraday RotationCMB Faraday Rotation Homogeneous Homogeneous

magnetic field magnetic field Kosowsky & Loeb 1996Kosowsky & Loeb 1996

Stochastic Magnetic Stochastic Magnetic Field Field

Kahniashvili et al. 2010Kahniashvili et al. 2010

Thermal SZ EffectThermal SZ Effect

Kahniashvili et al. ApJ 2013

THANKS!THANKS!

Constraints on Magnetic Fields from Large Scale StructureOutlineMagnetic Field in the UniverseMagnetic Field StatisticsMagnetized Cosmological PerturbationsScalar Magnetized ModeLinear Magnetized Density PerturbationsNon-linear EffectsPowerPoint PresentationSlide 10Magnetized Matter Power SpectrumDensity Perturbations AmplitudeHalos AbundanceLyman-alpha DataLimitsCMB Faraday RotationSlide 17Thermal SZ EffectTHANKS!