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**Dark Energy and the Hubble Constant**

Jim Condon DE comprises the majority of the energy density of the universe. DE controls its present and future expansion. More locally, DE is both a mystery for theoretical physics and a huge opportunity for observational astronomy. The two “take home” points from this colloquium are: Measuring the Hubble constant to < 3% rms provides a strong constraint on DE, its energy density and its equation of state (2) The Water Maser Cosmology Project is now measuring the Hubble constant, directly by geometry and not indirectly using standard candles and the “distance ladder”

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**What is dark energy (DE)? **

How does an accurate ( < 3%) local measurement of the Hubble constant H0 plus CMB data constrain DE? How can astrometry determine H0? Bonus: accurate SMBH masses The Megamaser Cosmology Project Jim Braatz, Jim Condon, Fred Lo (NRAO) Mark Reid (CfA) Christian Henkel (MPIfR), Ingyin Zaw (NYU),... Most of what we know about it is summarized in its name! Dark no electromagnetic interaction Energy |pressure| ~ energy density, unlike nonrelativistic matter pressure ~ 0, only quantities in Friedman equation for expansion. Pressure is negative to cause acceleration of universe, unlike radiation. DE accounts for 3/4 of the universe by mass, but very low density and smoothly distributed so very hard to detect (no cold DE halos), has accelerated the expansion of the universe and slowed the formation of large-scale structure in past few billion years. Very big problem (opportunity) for physics, which predicts DE dex(120) too high, like old ultraviolet catastrophe.

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**How can the universe accelerate?**

Only energy density and pressure p are relevant. For each constituent of the Universe, define w p / . For nonrelativistic matter, w = 0; for radiation, w = 1/3. Acceleration requires a sufficiently negative pressure w < -1/3; e.g., the quantum vacuum has constant w = -1 (but wildly wrong energy density). Is DE a variable “quintessence”? H0 plus CMB data constrain w via the expansion history of the universe. As far as cosmologists are concerned, we are all just density and pressure. All nonrelativistic matter has p ~ 0, so we are just density. Energy can have p ~ rho (note: rho is energy density, not mass density). GR needed for this calculation. w < -1/3 implies DE capable of accleration is very relativistic, smoothly distributed, unlike cold, clumped dark matter. Quantum vacuum needed for “spontaneous” emission yields modern “ultraviolet catastrophe” for rho. Big problem = big opportunity. Ex. ultraviolet catastrophe for blackbody radiation solved by Planck in 1905 quantized radiation, ultimately leading to quantum mechanics. Quintessence = “aether” = “fifth element” after earth air fire water, thought to be pure energy filling space above the terrestrial sphere.

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**WMAP 5-year TT power spectrum**

The absolute linear size of the structure producing the first peak can be calculated from physics, providing an absolute standard ruler of comoving size 144 Mpc, whose angular size was measured by WMAP, so WMAP gives the absolute angular-size distance to the surface of last scattering at z ~ Accuracy limited by cosmic variance, won’t be improved significantly. Baryon acoustic oscillations. Absolute angular-size distance to z ~ 1089 = linear size (theory) / angular size (observed)

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The CMB and H0 “While models with ΩDE=0 are not disfavored by the WMAP data only, the combination of WMAP data plus measurements of the Hubble constant strongly constrain the geometry and composition of the universe” Spergel et al. 2006 “The single most important complement to the CMB for measuring the DE equation of state at z ~ 0.5 is a determination of the [local] Hubble constant to better than a few percent.”---Hu, W , “Dark Energy Probes in Light of the CMB,” ASPC 339, 215 WMAP gets only the absolute angular size distance to z = 1089; flat CDM models assume both Omega = 1 (flat universe) and W = -1 to get H0. Note that CMB gets absolute matter densities, need H0 squared to convert to matter; the largest uncertainty is in H0. Spergel et al., 2006

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The Impact of an H0 Prior HST Key Project H0 = (Freedman et al. 2001) Sandage et al. (2006) H0 = 62 Freedman et al. 2001, ApJ, (Cepheids) Sandage et al. 2006, ApJ, 653, 843 (Ia SNe recalibrated by Cephieds) need H_0 to 3% to get “round” error ellipse, much better H_0 is less critical since cosmic variance won’t allow us to narrow the CMB minor axis. These plots are where our 3% goal comes from.

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**Geometric Distances to H2O Megamasers**

NGC 4258 D = r/ a = Vr2/r D = Vr2/(a ) NGC 4258 r rotation-line slope of systemic masers 2Vr Advantages of H2O “parallaxes”: speed ~ 900 km/s >> 30 km/s, period > 1000 years, relative position accuracy ~ 10 microarcsec with phase-coherent interferometry. Also directly measures SMBH masses (use for SMBH M / bulge sigma_v correlation, estimating Eddington ratio), observe accretion disks with sub-pc linear resolution, sub km/s velocity resolution. N4258 M= X10^6 MSun. Also, proper motions ~30 microarcsec/yr for LOS component of N Acceleration ~10 km/s/yr for N Enclosed density > 10^9 MSun/pc^3. satellite-line rotation curve 2 =

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**Megamaser Cosmology Project goals:**

Detect N > 10 suitable H2O megamasers (strong enough for VLBA+GBT, in edge-on disks) at distances D ~ 100 Mpc (in Hubble flow) around the sky and measure their recession speeds Measure their geometric distances to ~10% each via acceleration, mapping, and proper motion. Correct for known velocity fields to determine the average H0 within 3%, assuming random errors. No questionable standard candles, minimal assumptions, minimal systematic errors, systematics uncorrelated from one galaxy to the next. N4258 already Mpc, goal is +-3%.

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**Step 1: Detections and velocities**

10x faster than any other telescope thanks to large area, accurate surface, and low noise. The GBT is at the center of the universe for measuring H0 via H20 masers. Over 1000 AGN observed so far, 10 minutes integration reaches v ~ X 1000 km/s. Note semitrailers. Need more Seyfert 2’s outside SDSS area: 2MASS zcat in north, 2dF and 6dF -30 deg < dec.

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**GBT Spectra of Some Maser Disks**

Note weak fluxes; VLBA sensitivity is a problem, as usual. Phase referencing works sometimes, depending on source availability, but always at the cost of sensitvitiy. Like selfcal is better, but selfcalibrating on a single line with the HAS = GBT + VLBA + sometimes Effelsberg requires ~ 100 mJy in a 2 km/s line. Recently Cheng Yu developed a simultaneous multiline scheme that works down to about 50 mJy, more like what is needed. Sometimes lines also flare up for ~ weeks.

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**Step 2: Measure Accelerations**

UGC 3789 acceleration .

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**Step 3: Imaging GBT + VLBA**

The GBT lets us: Image fainter (more distant) H2O masers Use fainter (closer on the sky) continuum phase calibrators or even line self-calibration (NGC 1194 S > 500 mJy during flares) GBT to scale of VLBA antennas, multiplies baseline sensitivity by 4X. Resolution at 1.3 cm wavelength ~ 300 microarcsec, little “confusion” by multiple masers because of high velocity resolution, so relative positions << 300 microarcsec. Single-line flares in NGC 1194 > 500 mJy at D ~ 55 Mpc!

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**UGC 3789 Results R ~ 0.09 - 0.20 pc (0.40 - 0.87 mas)**

V ~ km/s Mbh ~ 1.2 x 107 Msun a ~ 3.6 km s-1 yr-1 (mean value) D ~ 50 Mpc ± 13% H0 ~ 71 ± 10 km s-1 Mpc-1

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**Direct measurements of SMBH masses**

Galaxy Radius (pc) Mbh (Msun) Mrk – × 106 NGC – × 107 NGC – × 106 NGC – × 107 NGC – × 107 UGC – × 107 Diameter .53 pc ~ 1 mas, so D ~ 110 Mpc, H_0 ~ km/s/Mpc. More in pipeline, will expand search beyond SDSS DR5, e.g., 6DF in south, and 2MASS redshift sample. Time scale for results ~ 5 yr. Note inner radius (pc) ~ M /10^8 so density limits > 10^8 solar masses per pc^3, >> 10 solar masses per pc^3 avg in central bulge . Ties down low-mass end of SMBH/bulge mass ratio.

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Summary An accurate ( < 3%) measurement of H0 independent of the CMB and other techniques (e.g. distance ladder) is critical for characterizing dark energy, testing the flat CDM model, and fixing fundamental cosmological parameters (e.g. deriving m from the CMB observed mh2). Recent observations of megamaser disks support the feasibility of using the GBT and VBLA to measure H0 directly. Astrometry yields accurate masses of SMBHs

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