Friday, January 25, 2013

IDL # operator

I'm playing around with my old MSc code, as I have an idea where it might be useful. Here's something I forgot:
The # operator computes array elements by multiplying the columns of the first array by the rows of the second array. The second array must have the same number of columns as the first array has rows. The resulting array has the same number of columns as the first array and the same number of rows as the second array.

Thursday, January 24, 2013

lit: Galactic Dynamics

I'm reading Binney & Tremaine's section on LSR, asymmetric drift and its correction, as I plan to do the corrections for my stellar velocity fields. Some definitions:
LSR is the hypotetical local standard of rest: velocity of some imaginary stars in precisely circular orbits at the Solar radius.
Characteristic thickness is the ratio of surface density to its volume density at the galactic plane: it's different for different stellar populations (like their vertical scale lengths), arising due to interactions w/ molecular clouds and/or spiral arms.
The collisionless Boltzmann equation states that the flow of stellar phase points through phase space is incompressible: phase space density around a phase point of a given star remains constant. A nice example of such incompressible flow is a marathon race where all participants run at constant speeds: at the begining the density of runners is large, but their speed distribution is wide. At the end of the race the density is low, but the speeds of all runners passing a point are very similar. The coordinates of stars in phase space are (x, v).
Asymmetric drift is the difference between the LSR (local circular speed) and the mean rotation velocity of a population. Velocity dispersion and asymmetric drift: see eq. 4.32-4.34 for the correction formulae; also Neistein, Maoz, Rix et al. for their application.

python: catch multiple exceptions in one line

lit: Asymmetric Drift and the Stellar Velocity ellipsoid

Asymmetric Drift and the Stellar Veloocity ellipsoid by Westfall, Bershady et al.:
The shape of the stellar velocity ellipsoid, defined by \sigma_R, \sigma_{phi}, and \sigma_z, provides key insights into the dynamical state of a galactic disk: \sigm_z:\sigma_R provides a measure of disk heating and  \sigma_{phi}:\sigma_R yields a check on the validity of the epicycle approximation (EA). Additionally, \sigma_R is a key component in measuring the stability criterion and in correcting rotation curves for asymmetric drift (AD), while \sigma_z is required for measuring the disk mass-to-light ratio.
See also p.2 on asymmetric drift corrections for stellar velocities.

Monday, January 21, 2013

Wednesday, January 16, 2013

Probability vs. likelihood

Probability -- a function of the outcome given a fixed parameter value. (What's the probability that 50 heads will come up, given that I toss a fair coin (--> parameters) 50 times?)
Likelihood -- a function of the parameters given a fixed outcome. (What's the likelihood a coin is fair if 50 heads came up out of 100 (--> outcome)?)
The likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values.

Monday, January 14, 2013

Jerusalem WS lecture notes: 16. Signatures of Inflows and Outflows

By R. Dave, slides here.
  • metals in diffuse IGM -- outflows!
  • at high z, SF can't keep up with inflow: the gas accumulation phase: gas can even turn into molecular phase, but due to low efficiency it won't all be processed into stars (equilibrium breaks down), RD 2012
  • eta scaling ~ M_{halo} ^{-1/3} -- z_{equil} ~ 5 for massive galaxies
  • equilibrium model code at
  • 'thesis back in the stone age'
  • constraining outflow parameters: direct observation and direct modelling are challenging
  • direct observation of preventive feedback:
    • mass in CGM: gas in absorption, X-ray emission, soft X-ray bg: COS (Cosmic Origins Spectrograph): OVI high ionisation line, 2 components: photo- and collisional excitation: SF galaxies are probing 300 000 K gas:, Anderson 2012
    • direct observations of ejective feedback: outflowing ISM lines: LBG tomography
    • direct observations of wind recycling: _metallicity_ of inflowing gas. Disk outskirts: \alpha_z ~ 0.3
  • indirect constraints:
    • counting statistics are not as good as scaling relations
    • galaxies to 0th order are a 1-parameter family (stellar or halo mass) --> good scaling parameters
    • conversion efficiency peaks at 10^{12} M_{\odot}
    • if you don't have winds, you have overcooling problems
    • cosmic SFR efficiency: SFR vs. Halo mass infall rate: a simple combination of model parameters (Behroozi et al), simulations are hard
    • SFR vs. M_{\odot}: galaxy MS is the parameter to compare SF galaxies across redshifts, not SFR -- present starbursts and past normal SF galaxies have identical SFRs
    • MS evolution is currently difficult to model
    • SFR -- metallicity relation
    • M_{star} -- feedback relation
    • M_{star} function -- Baldry 2008 simulations -- reproduces the lower mass GSMF well, arbitrary quenching at logM > 11, governed by differential recycling which flattens the relation at intermediate masses --> inflection
    • gas fractions and X_{co}
  • DLAs: kinematics favor ejection, not prevention, CDM has many low-mass halos, if they have many HI, too many narrow DLAs result

Jerusalem WS lecture notes: 15. Star-Forming Galaxies

By R. Genzel, slides here
  • ways to look back in time:
    • look-back imaging surveys
    • local stellar archaeology
    • detailed, resolved in situ observations
    • pathologies: Hanny's Voorwerp: radiation echo --> timescales of AGN evolution
  • SF in MW:
    • shielded regions, pressure comparable to diffuse ISM, density far above MW mean
    • highly structured, velocity dispersion ~5 km/s (supersonic motions), increases with scale
    • unstable to fragmentation
    • in large scales -- virialised, in small scales -- not --> inefficient SF:
    • MW SFR ~ 3 M_{\odot}/yr
    • Krumholz 2005
    • gas depletion time way smaller than Hubble time -- why stars are still forming: MHD pressure (Alfven) prevents collapse, GMCs are magnetically supercritical, but highly supersonic --> theory and observations tend to support the second explanation
  • SF occurs in clusters (70-90%, Lada & Lada 1993), super star clusters with M ~ 10^6 M_{\odot} -- from the collapse of the whole MC
  • SF tracers: Kennicutt 1998
    • H\alpha: traces Lyman continuum, issues w/ extinction correction
    • UV continuum: IR fine structure lines, C+ --> easily collisionally excited, in areas that are exposed to UV, OI line
    • mid and far IR: calorimetric method: UV heats dust, reprocessing: FIR is currently the best, esp. due to Herschel
    • radio: FIR-radio relation, works if there is no AGN, evolutionary changes
    • SFH uncertainties: SF tracers are no better than 0.3 dex
  • pictures of extinction:
    • 'screen' of dust and gas surrounding SF region
    • 'mixed' -- dust and stars are mixed, high and low exctinction regions: you can observe short and high wavelengths together, Calzetti 2000
  • dust extinction: 'greyer' -- less dependent on wavelength
  • mass tracers (see the slides):
    • SED fitting: live stellar mass
    • rotcurves: dynamical mass: HI not detectable beyond z = 0.1-0.2 until at least SKA
    • velocity dispersion
    • CO -- variation of X
    • lensing
    • submm dust luminosity (ALMA)
    • uncertain up to at least factor of 2: SFH, IMF, extinction, spatial distribution, kinematics, conversion factors
  • gas-SF formation:
    • K-S relation (empirical, simple physical motivation (see slides)), Kennicutt & Evans 2012 review
    • conversion factor: MW factor not appropriate for metal poor galaxies
    • classic papers on SF: 'very good papers were written beyond our event horizon': Kenicutt 1983: infall required for SF over cosmic time
    • spatially resolved SF relation: KS law between H_2 and SFR is more linear -- can we ignore HI?
    • HCN traces very dense regions
    • detection thresholds: stellar surface density
    • KS relation breaks down in scales < 500 pc -- CO and H\alpha are not correlated, due to local evolutionary effects: larger areas are necessary to 'smear out'
    • 'J. Gunn in suit'
  • VLT: very thin, large mirror supported by adaptive optics pads
  • LBT: thin faceplate on light honeycomb ceramic structure
  • Concepts for > 20 m telescopes:
    • aplanatic Gregorian optics
    • 30 m telescope (TMT), EELT (10" FoV, 5 mirrors)
  • JWST: 6m, 'Keck in space'
  • AO:
    • wavefront sensor
    • deformable mirror
    • guide star | artificial guide stars
    • feedback w/ computer
  • IFUs: KMOS
  • mm interferometry of cold gas:
    • IRAM Plateau de Bure -- exploration of molecular gas in high redshift
    • ALMA: 0.005" resolution, R = 30 000000

Jerusalem WS notes: first part of student talks

A few notes, without credits.
  • supersonic movement of DM and baryons at z > 10 -- effect on 21cm background, global history of 21 cm signal
  • sSFR was surprisingly const b/ween 2 < z < 7 -- find rising sSFR with z
  • a new generation of submm galaxies: Redhift survey of Herschel-selected starbursts: dusty super-luminous starbursts at z=2
  • submm counts: flat IMF in bursts is required to match them, galaxy pairs contribution: look blended in SCUBA, resolved in ALMA: counts can be matched with standart IMF
  • halo quenching -- high masses and z, bulge-related quenching: low z, low masses
  • R_{vir} much smaller (2-3 times) than the extent of intercluster gas -- it's not the end of a cluster
  • red-sequence fast track
  • mass threshold of outflows

Jerusalem WS lecture notes: 14. Observed galaxies from high to low redshift

By Simon Lilly. Slides here.
  • individual & population observations
  • evolving population: looks simple
  • tracers at EM spectrum
  • small FOVs of high-z surveys
  • young stars: star formation | old stars: stellar mass
  • relative sizes of HST surveys
  • cosmic variance in high-z surveys -- zCOSMOS is completely dominated by LSS, related to CF
  • larger fields: cosmic variance becomes larger relative to Poisson variance: 10% for COSMOS field
  • CV fundamental limitation of high-z statistics
  • beam sizes are non-negligible, sensitivity is limited by confusion noise
  • lensing bias: amplification, esp. faint sources: change LFs
  • the success of photo z's (R = 5 'spectroscopy'):
    • empirical approaches
    • template fitting approaches
    • quite good agreement with spectro z's: why do they work? galaxies occupy a small section of parameter space [eigenspectra]
    • spectroscopic surveys: Baldry picture, density vs. area: SDSS-like survey is impossible in high z
    • sample selection
    • H-R diagram: cool & dim | hot & dim | cool & bright | hot & bright
    • SFR estimates:
      • UV luminosity is best at high z
      • reddening can be estimated from the UV spectrum shape: it does not depend on the IMF, however, mass does, because it is dominated by low mass stars
      • dust absorption: UV is strongly absorbed by dust, estimation from re-radiated emission at IR
      • other UV proxies: H\alpha, [OII] 3727, radio continuum [empirical!], soft X-ray luminosity -- derived at local z
    • how do we define stellar mass?
    • how do we estimate stellar mass?
      • NIR is dominated by RGs, not tracing stellar mass as such. If SFR is constant, it will be dominated by younger populations. If SFR rises with time, SED becomes dominated by younger stars even in NIR.
      • SED fitting output depends on assumed SFR history, exponentially decaying SFR is not valid for higher redshifts, Lee et al, 2010, ApJ: stellar masses are the most robust, then Zs, ages.
    • FMR -- fundamental metallicity relation, Yates et al., 2 methods of SDSS Z estimation
    • sizes, structures and morphologies:
      • ZEST: introduced ellipticity, allows selecting spirals: we can now do automated morph classification
    • environment:
      • overdensity field in high z Universe
    • halo masses aredifficult to get for lower mass haloes (M < 10^{14})
    • galaxy mergers, see Lotz 2011:
      • a key quantity: for a given galaxy, what part of the stars was brought by mergers, what part formed in situ?
      • observational bias when visually looking for disturbed objects
      • pairs of objects
    • gas content: limited information at high z
    • gas inflows, gas outflows:
      • spectra stacking -- very high S/N spectra of galaxy population
    • incomplete observations:
      • high z gas
      • DM haloes
      • systematic uncertainties in many key quantities: SFRs, M_{st}, Zs, etc.

Jerusalem WS lecture notes: 13. Galaxy Formation with Inflows and Outflows

By R. Dave, slides here.
  • 4 phases of baryons:
    • diffuse
    • unbound shock-heated
    • virial shock-heated (condensed)
    • cool halo gas (condensed)
    • low mas haloes cannot keep their gas
  • how gas gets into galaxies:
    • hot mode (shock heating at virial radius, cooling onto disk. slower, limited by cooling time, more spherical)
    • cool mode: more rapid, line emission cooled, filamentary: cold streams (dominant: cold accretion dominates globally, mergers are a small contribution to gas supply: SF is supply-limited)
    • mergers: DM grows by mergers (mass fn is steep), mergers contribute little to gas supply
    • mass dependence of accretion mode: large halos: hot mode, small halos: cold mode, separation at roughly ~10^{11.5} M_{\odot}, with metal cooling -- 10^{12} M_{\odot} -- connection with galaxy bimodality
  • shock stability: shocks form up from a certain mass, that's why cold mode dominates (virial shocks cannot form)
  • simulations
  • accretion w/out feedback overpredicts cold baryon mass (overcooling): conversion efficiency peaks at 10 ^{12}
  • red and dead: AGN feedback as the power source, blue: SNe, YSOs
  • abundance matching: equate nr density of haloes and galaxies with a given mass -- halo occupation distribution -- galaxies and satellites. Procedure assigns galaxies to haloes, matching halo masses to stellar masses, Behroozi +13 -- peak of conversion efficiency constant at all redshifts.
  • galaxies are gas processing factories: raw materials from IGM (infall rate due to gravity)
    • not all infall material ends up in the galaxy -- some gas is prevented from getting into the galaxy, outflow of hot and polluted gas from SF regions (just like in a factory), some outflow material is recaptured -- infall metallicity (\alpha_z in the diagram)
    • resulting SF: mass balance: infall = formed stars + Outflow + gas reservoir change
    • equilibrium condition: reservoir gas is constant over time (from hydro and obs, not true for dwarfs, just for L_{\star}) --> high z galaxies have higher ISM gas fractions
  • Inflow: primordial and recycled gas: recycling metallicity vs. SN ejecta metallicity
  • SFR: set by 3 baryon cycling parameters:
    • feedback preventing parameter (inflow)
    • outflow mass loading factor (outflow)
    • recycled wind metallicity ratio
  • SFH does not depend on (it's expressed in correlations):
    • SF law
    • merger history
    • environment or clustering
    • morphology
    • gas content
  • MS of galaxy evolution: SFR vs. M_{\star}:
    • relation should be close to linear, D. Elbaz
    • SFR should grow with z rapidly --> feeding rate change
  • feedback parameters:
    • quenching at high mass (AGN?)
    • gravitational heating transition to hot mode (\zeta_{grav}, RD 2012) -- power law all the way to high masses, weak dependence on z
    • wind heating suppress accretion
    • specific SFR: feedback effects
    • gas metallicity relation, its evolution -- gas phase metallicities
  • gas content, M_{gas} -- cold gas in the ISM:
    • H_2 gas fraction ~= t_{dep} \cdot sSFR (how much gas is in the ISM that waits to become stars)
    • depletion time t_{dep}
    • t_{dep}: depends on Schmidt law, Kennicutt relation
    • SF law sets t_{dep}, which sets f_{gas} ~ t_{dep}
  • the role of merging: second order effect (like environment), sets scatter (e.g. M_{star}-Z relation)
    • first order: smooth accretion
    • second order: stochasticity: clumps (mergers) --> lower Z, higher SFR (signals recent accretion event) --> high star formation points lie below MZ relation
    • dilution time -- explains scatter

Jerusalem WS lecture notes: 12. Galactic dynamics II

By R. Sari, slides of both talks here.
  • stability: dispersion relation
  • spiral density waves: leading and trailing, pattern speed
  • resonances: co-rotation, Lindblad resonances: drift through arms: epicyclic motion of particles in the disk. Pressure: away from CR, gravity: towards the center. Each epicyclic period a particle drifts one potential peak
  • migration: dynamical friction, one-sided torques from the outer disk and the inner disks: push from inner side stronger than pull from the outer (? shouldn't it be the inverse?)
  • marginally stable galaxies
  • centrifugal barrier: disk stability
  • 18 \pi^2: overdensity
    • final semi-major axis of the overdense region:
    • Keplerian elliptical orbit: t_{vir} = 2\pi/(sqrt(GM/a^3))
    • density ratio: \rho_0(r_0/a)^3/\rho_0*(t_{vir}/t0) = r_0^3/a^3 \cdot 4\pi^2/GMt^2_0 = 9/4 \cdot v_0^2 \cdot 4 \pi^2/1/2 v_0^2 = 18 \pi^2
  • virial theorem:
    • relaxation: two-body, resonant (in almost Keplerian systems), violent. two-body relaxation time t_{rd} = R/V\cdot N/lnN
    • tidal breakup: binaries (interaction with BH), stars, extended objects: 'black hole worshipping' - BH destroys objects, relaxation brings them back
    • binaries destruction: r_{tidal}: when the rotation period of the binary is equal to rotation around the BH (forces are equal)
    • differential force for the binary system: r_{tidal} = a(M_{BH}/m)^{1/3}
    • density: spread out the masses
    • largest orbital velocity for a binary member: v_{esc}, few hundred km/s for MS stars. BHs enhance the velocity by orders of magnitude -> hypervelocity stars
  • loss cone
  • filling rates

Jerusalem WS lecture notes: 11. The physics of stellar feedback

By M. Krumholz, the slides.
  • 'conservative weed'
  • Bate 2009 simulation -- SC formation. SF too efficient and fast -- SF efficiency close to 100%
  • what inhibits SF? feedback:
  • hot gas or photons push material away from the star, kinetic energy in the material shell = star energy output | radius set by momentum conservation (energy or momentum driven cases, radiation or winds). Mass in the shell way larger than the wind mass
  • feedback budgets:
    • Q -- radiant energy, wind energy, number of ionising photons
    • IMF-averaged production rate: luminosity per unit mass (~M/L ratio)
    • lifetime-weighted production rate -- energy out of unit mass (e.g. ergs/g)
    • stochastic IMF sampling in dwarfs -- SLUG code
    • galactic wind: at least as much mass as went into stars
    • what feedbacks are interesting? those that can cause velocities higher than escape velocities --> lower limt
    • losses: gravity, collisions (loss of momentum)
  • ISM feedback taxonomy:
    • ionising radiation: not important for galactic winds formation (sound speed ~10 km/s, so can influence in smaller MCs, Krumholz 2006, 2009, Dale 2012), probably the most important SF regulator today
    • radiation pressure (photon momentum, Thompson scattering) -- ~200 km/s -- cannot be responsible for galactic winds, unless radiation enhancing fraction f_{trap} >> 1. Can be important for subgalactic objects, dwarf galaxies, can blow up gas clouds.
    • the important question: what is the f_{trap}?:
    • 30 Dor: dust grain temperature can help infer the IR radiation field, Lopez 2011
    • simulations: 2D, high resoluton: RT instability -- similar to oil floating on water, right panel: no gravity, 2 different optical depths[surface densities]: RP may affect sub-galactic objects, but cannot produce galactic winds, Krumholz & Thompson 2013
    • stellar winds: Solar wind is a wimpy old thing, O stars. Momentum driven
    • 30 Dor -- most massive binary star system, each ~83 M_{\odot}, still on the MS
    • supernovae: energy budget in stars of 8-10 M_{\odot}
      • N_{SN}/M = 0.01 M_{odot}
      • less energy and momentum than radiation feedback
      • more energy, less momentum than winds
      • SN are most important because they are much closer to energy conserving feedback -- large velocities, post-schock ejecta temperatures are ~10^{10} K --> cooling time is ~ 60 Myr, whereas time required to escape the galaxy is << 1 Myr, so gas cannot cool
      • Sedov-Taylor similarity solution -- first developed for nuclear tests, open literature only in 1995 --> energy of Trinity blast from Time pictures (R_blast as a fn of time, Sedov),
      • trapping factor ~30-40, momentum goes up by this factor during the energy conserving phase, density dependent: SNe explode in low density environments due to star radiation --> f_{trap} is elevated
      • SNs can dominate momentum budget --> proper simulation should take other feedbacks into accounts
    • metallicity feedback
    • metallicity changes SF law (makes difference in dwarfs, high z galaxies) --> metallicity regulated SF (Kuhlen 2012 simulation), interactions wih other feedbacks

Jerusalem WS lecture notes: 10. Formation and Mergers of Massive black Holes

By Avi Loeb, slides here.
  • why most of the matter is not BHs? Due to angular momentum of collapsing matter <- tidal torques from neighbours near turnaround <- non-spherical collapse
  • you can check in, you can't check out
  • fill the orbit of Earth w/ water -> black hole from a huge swimming pool in space
  • pathological point in space-time
  • 'string theorists still get paid, get prizes, they give prizes to each other'
  • no hair theorem: charge is not important in astrophysics, only mass and spin
  • cosmic censorship conjecture (no naked singularities)
  • Beckenstein-Hawking radiation: negligible in astrophysics
  • whenever there is a horizon, there are quantum fluctuations
  • SgrA* 3D star orbits
  • horizon commercial
  • Broderick & Loeb 2006 - imaging SgrA*, cosmological beaming due to lensing
  • BH spin parameter - max value is c, a = 1, normalisation (spin matters!)
  • shadow of the BH: the region behind it has its light obscured
  • gas is optically thin for wavelengths < 1mm
  • ISM does not blur the image due to free e- scattering (turbulence), blurring is smaller than horizon scale
  • VLBA can resolve SgrA* and M87 (~10 u-arcsecs)
  • the Event-Horizon Telescope
  • radio: Fourier space imaging, Broderick, Loeb 2010
  • M87: huge BH, jet base images, Doeleman 2012
  • feeding BH: MR instabilities, funnel (empty region for outflow, collimated by outflowing jet)
  • Eddington limit: Thompson scattering due to luminosity of BH accretion -> outward force, momentum flux, Thompson cross-section. Protons are pulled by gravity create inward force, they are balanced at Eddington luminosity L_E = 1.3x 10^{38} erg/s (M/M_{\odot})
  • BH luminosity: L_E x \eta: mass of BH grows exponentially
  • Eddington timescale: short, we can grow a small seed to large value quickly. By trapping radiation, timescales shorten
  • hot haloes collapse to supermassive stars -> BHs
  • 1% of galaxies are quasars, BH mass is way lower than the total mass of the host: why are quasars short-lived? Because they are suicidal, self-regulating their growth, unbinding the gas that is feeding them.
  • 10% quasars have jets (are radio loud)
  • Binary AGN (Shen 2011)
  • BL regions: characteristic speeds ~0.01c, UV radiation is converted into broad line emission
  • NL regions: ~1kpc distance, gass is illuminated by quasar
  • merger: at some stage, it can have 1 NL region and 2 BL region. Blech, Loeb 2012
  • reverberation mapping, Koessis, Heiman, Loeb
  • residence time of BHB - types of migration, shrinks the orbit differently from GWs
  • Kulkarni & Loeb: excursion set formalism, multiple BHs: 3 body system is unstable (like human beings)
  • SF in outer regions of accretion disk - you're likely to make stars - it may explain why quasar spectra have metal lines!
  • extreme mass ratio inspiral stellar mass BH or NS [LISA]
  • gravitational waves - time-dependent quadrupoles, BH/NS binaries, LIGO, eLISA (detects virtual GWs, generated by people playing WoW) -> precision: 1/1000th diameter of proton
  • BH recoils: if the BHs have different masses, they recoil at hundreds km/s - they get out of the galaxy or move away from the center. GW emission is beamed at one direction, momentum is conserved
  • > kick, candidate CID-42
  • Star clusters around recoiled BHs in the MW halo: ~100 BHs ejected during assembly of MW halo, carrying SCs from cusp of host dwarf galaxy - there should be some unusual clusters in halo clusters, O'Leary & Loeb 2008. Stars are moving around BH Keplerian potential, BH gets a kick, stars may remain bound by E = -1/2 v^2 - GM/r^2 = 0.5(v - v_{kick} - GM/r^2) (vector addition), if E remains negative
  • tidal disruption of stars by BHs ('this is an illustration from NASA, so it has no scientific value')
  • loss cone: tidal disruption 1/10^{-5}
  • BHs larger than 10^8 M_{\odot} swallow the whole stars - Hayasaki, Stone, Loeb 2012
  • for binaries: loss cone filled by GW recoil, star disruption once every 10-100 years
  • miniquasar 2013 - cloud falling into SgrA*, pericenter of highly elliptical, almost radial orbit with T == 200 yr, imsged in Br\gamma -- Burkert 2012 simulation
  • is the cloud pressure-confined? There seems to be no evidence of ambient ram pressure? Maybe this cloud is produced by low mass star with protoplanetary disk - Murray-Clay & Loeb 2012
  • hypervelocity planets from tidal disruption of stellar binaries

lit: face-on TF relation

Andersen and Bershady 2003:
Hence there is a triple penalty at low inclinations for TF studies: (1) erroneously large inclinations lead to undercorrecting the velocity projection, (2) random errors diverge since photometric disk axis ratio measurements have constant errors as a function of axis ratio, and (3) for long-slit studies, P.A. mismatch will always yield systematic underestimates of the projected rotation speed.

Wednesday, January 2, 2013

Jerusalem WS lecture notes: 09. the IMF and the SFR

By M. Krumholz, slides here. I especially liked Mark's lectures, because he wades into murky, difficult topics of the ISM physics that many researchers like to leave out and assume something.
  • THE 2 problems
  • IMF:
    • determines stellar feedback (more at top-heavy IMF, etc), abundances, stellar masses
    • Observations:
    • Bastian 2010 -- MW MF plot -- universal IMF in different regions
    • Why a typical star is a few 10ths M_{\odot}? Insensitive to SF environment, metallicity, dwarf/spiral galaxy type
    • Andersen 2009: IMF in MCs (brightest HII region in the Local Group). Sabbi 2008: in SMC (0.2 Z_{\odot})
    • Variation in cDs? van Dokkum & Conroy 2010 (unresolved stars, red & dead galaxies, stars formed at z = 2) -- "The direct detection of the light of low-mass stars implies that they are very abundant in elliptical galaxies, making up over 80% of the total number of stars and contributing more than 60% of the total stellar mass. We infer that the IMF in massive star-forming galaxies in the early Universe produced many more low-mass stars than the IMF in the Milky Way disk, and was probably slightly steeper than the Salpeter form in the mass range 0.1M_{\odot} to 1M_{\odot}"
    • Peak location: non-isothermality is required, comes either from:
    • galactic properties, e.g. Hopkins 2012
    • local non-isothermality approximation:
    • isothermality broken by star formation: accreting star is brighter than non-accreting star --> Krumholz 2012: the characteristic mass is set by deviation from isothermality due to SF, the characteristic mass (peak location) depends on pressure of the core (lower mass at higher p). Pressure is set by balance vs. gravity (surface density)
    • Slope: universal, probably due to turbulence
  • SFR:
    • bathtub model (gas in, gas out) when t_{SF} << t_H
    • Correlation b/ween molecular gas SD and SF on galactic scales
    • sub-galactic scales: cloud mass vs. no of YSOs, IR luminosity vs. amount of gas (Wu 2005)
    • Galaxy metallicity dependence
    • phase dependence
    • SFR is a function of Toomre Q in galaxy. Dobbs 2011 simulation: self-regulation
    • Top-down model is not sufficient
    • Bottom-up model: what matters is the small scales (local SF law)
    • Why is \epsilon_{eff} (gas conversion to stars ratio) so low, ~1%? Federrath & Klessen 2012 --> few % efficiency for turbulent, virialised objects.
    • l_s -- sound length, size scaling
    • metallicity-phase dependence:
    • why most of the gas is atomic? Dissociation by UV, except in areas where UV is shielded by dust or H_2, 'magic number' -- surface density that shields, ~10M_{\odot}/pc^2
    • why SF follows H_2? Photons that are responsible for dissociation of H_2, are the same that heat the gas, so if the gas is shielded, it cools --> H_2
    • extragalactic phase dependence (SMC has a different SF law because of different metallicity). SF is not only self-regulating process, it depends on global galaxy properties

Jerusalem WS lecture notes: 08. Extended Press-Schechter formalism formalism

by F. van den Bosch, slides here.
  • Press - Schechter theory:
    • filters of density fields: Gaussian, top-hat, sharp k-space filter (same, as top-hat, except we end up having a nice box in Fourier space)
    • mass variance
    • halo mass function: how can we assign halo mass to a collapsed region?
    • PS: only half of the mass of the Universe can become collapsed (overdense), but due to smoothing, this is not entirely correct. fudge factor of 2
    • halo mass function: many more small haloes than higher, exponential suppression
  • Excursion set (EPS) formalism (Bond et al, ~1991, statistics of peak heights):
    • excursion: locations of space
    • sharp k-space filter: Markovian trajectory
    • all mass elements will eventually sit in a halo of arbitrarily low mass
    • works in a statistical sense, not necessarily correct on a per-halo basis
    • the sharp k-space filter looks ugly in real space (sinc-like)
    • the Spherical Cow
    • simulations: underpredicts number of high-mass haloes, over-predicts low-mass haloes
    • halo finding: how we define the haloes? It changes the halo mass function!
  • Ellipsoidal collapse EPS theory:
    • moving barrier up-crossing, mcmc simulations
    • much better agreement w/ simulations
  • Halo merger trees:
    • accurately sampling progenitor mass f-n
    • mass conservation
    • impossible to do properly: conditional probabilities, many ways to draw from the distribution
    • tests on the accuracy of merger trees: consistency test, comparison w/ numerical simulation
      mass assembly history:
    • main central galaxy accretes lower mass haloes (subhaloes, which may survive or not)
    • satellite
    • assembly time: main progenitor reaches 1/2 the final mass (more massive haloes assemble later)

Jerusalem WS lecture notes: 07. Guest lecture on cosmology with the CMB

By C. Bennett, the PI of WMAP, among many other things. Slides not (yet) available.
  • COBE:
    • anisotropy
    • shape of the CMB spectrum: precision cosmology
    • CDM: anisotropy low -- from Silk damping?
    • still only sampling superhorizon scales
    • spinning dust
    • polarisation maps
    • average subtraction: foreground removal
    • foreground modelling: spectral differences, power law spectral indices
    • n_s -- inflation tilt, \tau -- optical depth of scattering, \Delta -- amplitude of fluctuation predicted by inflation
    • E, B modes: gradient, curl
    • 1st acoustic peak: horizon size at decoupling: super-horizon correlation from polarization (inflation)
    • rarefaction/compression peaks, BAO
    • 1st and 2nd peak heights ratio: baryon density --> time of decoupling, sound speed, horizon scale (145.7 Mpc), d_A = 14Gpc
    • geometric degeneracy of CMB measurements
    • constraining inflation: primordial tilt, flatness, tensor to scalar ratio, energy scale -- only from polarization data
    • is the anisotropy Gaussian? 3PCF
    • "Last stand before WMAP" article
    • the 6 parameter space volume was reduced 68k times
    • LAMBDA @Heasarc -- data
    • CLASS experiment
    • WMAP9 -- optimal weighting of the power spectrum

Jerusalem WS lecture notes: 06. The First Galaxies and Reionisation

By A. Loeb, with a short, but brilliant skit on adventure and creativity in science, slides uploaded here.
  • spectrum of the sky:
  • dip: Ly\alpha photons keep the gas coupled to its kinetic temperature
  • most of the comoving volume of the Universe is at high redshifts:
  • SDSS LRGs: 0.001 of the observable volume of the Universe (Loeb &Wyithe 2008)
  • What is the best time to be a cosmologist? At early time, Hubble scale grows, but due to expansion the comoving distance starts to shrink: objects enter and exit the horizon. The optimal cosmic epoch for precision cosmology was at z = 10 (
  • LF at various redshifts -- DM haloes mass slope
  • H, He cooling curve: no excitation at lower energies (T < 10^4), H_2 becomes important at lower T
  • Pop. 3.1 stars -- the very first stars, ~10^8 Myr after BB, SF conditions were differented, higher T: ~200K
  • Pop 3.2 stars: UV photons ionize surrounding gas --> much more efficient cooling by forming H_2, HD, HD radiative cooling --> gravitational instabilities
  • galaxies much more clustered on scales ~100 comoving Mpc than at present -- not many regions exceed the collapse threshold: bias, numerical bottleneck (need large dynamic range)
  • at higher redshifts (~8) you need to produce more photons per baryons to keep the IGM reionized
  • Pop3 observables:
    • stellar remnants:
    • Pair instability supernovae: best-understood SNe, Cooke et al. 2012. Lasts for years: long duration, luminosity comparable to SN II. 160-240 M_sol progenitors: if you start with a few hundredths M_sol progenitor, winds don't reduce the mass enough to avoid the PI SN. Collisionally-formed stars.
    • Long GRBs: seen to the edge of the obs. Universe, jets are drilling a hole in the star, followed by SN. Cosmological stretch of time: longer observation time
  • Ly\alpha forest: probing ISM by QSO spectra
  • Spin transition: Harward connection: horn antenna, snowballs, spin temperature, 21 cm tomography, cosmological evolution of the 21cm signal, X-ray heating (stellar mass BHs? X-ray binaries? AGNs?), LOS anisotropy: Kaiser effects, Pritchard & Loeb 2011, 'CMB is old', EDGES experiment: reionisation was not abrupt, EOR signal
  • extension to other lines: emission (CO, C, C II) by groups of galaxies: unresolved galaxy survey

Tuesday, January 1, 2013

Jerusalem WS lecture notes: 04. Physics of Star-Forming Clouds

By Mark Krumholz, 'the only obstacle between you and the exciting opportunity to combine drinking with jet lag'. Here are the slides.
  • SF gas is cold: observations in radio, mm, far-IR
  • Diffuse gas: emission lines, dust
  • SF ISM is mostly molecular
  • H_2: proof that nature has a cruel sense of humour:
    no electronic excitation in cold gas, vibration: mid-IR energy, too high. Rotations: H2 has no dipole mode, no J1 -> J0 transitions, the lowest transition is J2 --> J0. J2 state -- 511 K off ground: no H2 molecules emission.
  • CO: proof that astronomers are stubborn bastards:
    • If density is high, radiation doesn't change energy distribution (Boltzmann, collisions). Else: way fewer excited molecules than excpected, because collisions don't happen often.
    • Brightness temperature
    • Integrated CO intensity is measure of velocity dispersion (=total gravitating mass), if T = const.
    • Intensity --> directly tells the column density (\Sigma) of CO and H2
    • Motion in gas: bulk, non-thermal, highly supersonic
  • Gas properties:
    • cold (10K, 100K in starbursts): adiabatic compression, viscous dissipation, EUV ionisation/FUV photoelectric heating, CR/X ray heating, cooling processes: adiabatic expansion, lines. Dynamical timescales. CRs and X rays can penetrate high columns.
    • Isothermal gas -- efficient cooling if the gas is compressed. Equilibrium T ~ 10K, hard to change. CR -- main source of heating.
    • dense (n > 100cm^{-3})
    • very supersonic: magnetic forces are important, extremely turbulent (Re ~ 10^9).
    • linewidth-size relation (\sigma ~ size of the region), power spectrum
    • VT: thermal motion/thermal pressure prevent collapse, Bonnor-Ebert mass: for a given pressure, there is a maximum mass that can be stable against collapse.
    • for GMCs: M_{BE} ~= 10^7 M_{\odot}: that's why stars form in MCs.

Jerusalem WS lecture notes: 03. Structure Formation: From Linear to Non-Linear

Given by Frank van den Bosch, slides here.
  • cosmological [over]density field: moments of the PDF
  • the ergodic hypothesis: ensemble average is equal to spatial average taken over one realisation of the random field (we only have one Universe, but it consists of many random subvolumes). Basically, spatial correlations decay rapidly w/ separation, so the subvolumes are statistically independent.
  • random Gaussian field: distribution of arbitrary set of N points is an N-variate Gaussian. covariance matrix is the 2nd moment: 2-point correlation function. We only need this one moment to specify the N-point probability function.
  • 2PCF: 0 for Poisson distribution, != 0 for clustered distribution. Gravity makes things cluster, so we get positive CF for small radii, negative for large radii, then turns towards zero.
  • Higher-order CFs: irreducible CFs cannot be obtained from lower order reduced CFs. Connected moments of all higher order CFs are 0 for a Gaussian field: one can use this to test for Gaussianity.
  • the matter field in Fourier space: V is volume over which the Universe is assumed to be periodic. k -- modes.
  • power spectrum (Z-H)
  • Linear perturbation growth: Silk damping: e- and photons are no longer coupled, photons move away, structure starts growing. Jeans length for DM is very low: free streaming. When perturbations become of order unity, growth becomes non-linear.
  • Non-linear regime: perturbation theory (and Gaussianity assumption) is no longer valid. Modes couple to each other: no analytic solutions, higher order moments are required for complete specification of the density field: higher-order perturbation theory.
  • Numerical simulation, the Halo Model
  • Over-simplified model: top-hat spherical collapse. No shell crossing, mass conservation. Evolution depends only on the mass inside the shell. parametric form: implies maximum radius before turnaround. Collapse -- shell crossing, after it mass is not conserved.
  • By using linear theory, we can identify regions that had already collapsed.
  • Beyond shell crossing: collapse is not spherical, hence BHs don't form. Virialization: halo is in equillibrium as a result. We can compute overdensity of the virialised DM halo: 178: haloes finding at 200.
  • Zel'dovich approximation:
    • Lagrangian picture: works in mildly non-linear regime, calculated displacement of particles from the initial conditions.
    • no spherical symmetry is required, mass-conservation is valid until shell crossing.
    • deformation tensor in the initial density field, eigenvalues: positive: contracting coordinate, neg: expansion. No over-simplified geometry, works in qusi-linear regime. Collapse happens first in one direction (largest eigenvalue) --> pancake.
    • ellipsoidal overdensity --> sheet (pancake) -- > filament --> halo (longest axis 'halo formation')
  • Relaxation and virialisation:
    • 2 body-relaxation time: time required for a particle to change its E_k by about its initial amount due to 2 body interactions. How can galaxies appear relaxed, if galaxies and haloes have 2body relaxation times larger than t_H. 4 mechanisms:
    • Phase mixing: different phases, same energies: mixing in phase space, goes linearly with time. Completely reversible: no information is lost.
    • chaotic mixing --> the book [MBW]
    • violent relaxation: potential is time-dependent, particles gain or lose energy. Overall, energy distribution is broadened by the process. No segregation by mass, quite opposite to collisional (2-body) relaxation. e.g. stars don't sink to the center. Mixing on coarse-grained level. Self-limiting: no all knowledge of initial conditions is erased.
    • Landau damping --> the book

Jerusalem WS lecture notes: 02. Structure Formation in the Universe

By A. Loeb. I didn't take notes for some reason, so I'll only point to the slides.

Jerusalem WS lecture notes: 01. Introduction to LCDM Cosmology

I'll be posting my lecture notes from Jerusalem winter school during the next several days. It's easier to link things up here.
Introduction to LCDM Cosmology by J. Primack, .pdf here.
J. Primack, with collaborators, created the LCDM model as we know it -- and gave an amazing historical account of the topic.
  • dark matter particle discovery in the next few years
  • Zwicky 1937, 'on the masses of nebulae and clusters of nebulae' -- huge amount of mass is necessary to bind galaxy clusters together
  • Rubin 1970: M31 rotation curve
  • Einasto 1974
  • Faber 1979
  • Zeldovich HDM: light neutrinos make up the DM, galaxy formation is top-down, from fragmentation
  • mixmaster Universe [Misner], explosions [Ostriker]
  • 'Giant voids in the Universe', Zeldovich, Einasto
  • Pagel, Primack 1982, R-parity, gravitino, SUSY DM
  • 'if you're looking for a good problem, understand galaxies' -- R. Feynman
  • Cooling theory: groups & clusters can't cool, because cooling is too inefficient
  • Zeldovich spectrum
  • "The Seven Samurai"
  • 1997: start of precision cosmology (WMAP, etc)
  • 46 Gly
  • Double dark theory
  • 1st CMB peak at 1 deg: space is flat
  • 5 independent measures show that 4% of the Universe is made of baryons
  • 'imagine that the entire Universe is an ocean of dark energy. on that ocean sail billions of ghostly ships made of dark matter. we only see the beacons on the tops of the highest ships'
  • Millenium simulation parameters are 4-5\sigma away from observations, due to WMAP1 parameters
  • Bolshoi, BigBolshoi, AREPO simulations
  • Baryonic mass-velocity relation
  • how is the mass assembly related to star formation?
  • Most-efficient star formation mass range [cooling]:
    • Massive galaxies: started SF early, shut down early, are red today, live in dark haloes that are much more massive than their stellar mass.
    • Small galaxies: started SF late, are blue, DH masses are comparable to stellar masses.
    • "Downsizing": star formation is a wave that started in the largest galaxies and swept down to smaller masses later.
  • DM detection: catch it, infer it, make it, weigh it [CDMS, LHC, Fermi, cluster X-ray observation, Planck/Hershel]
  • detector sensitivity increased by 3 orders of magnitude in 5 years, XENON 1000
  • Donation of an unused US spy satellite might allow restarting WFIRST