Distance Determination of the Hubble Constant Ho by the use of Parallax and Cepheid Variable Stars

presented by Michael McElwain and G. Richard Murphy

Why do we want to know Ho?

• The Hubble constant is one of the most important parameters in Big Bang cosmology.

– The square of the Hubble constant relates the total energy density of the Universe to its geometry.

– It sets the age of the Universe.

– It sets the size of the observable Universe (Robs = ct)

– Determines the Universe’s radius of curvature (Rcurv = c/Ho((-1/k1/2))

– The density of light elements synethesized after the Big Bang depends on the expansion rate.

Ways of Determining Ho

• Ho is determined by comparing the recessional velocity of galaxies, determined from their redshift, and the distance to that galaxy.

• Ho = v/d

• The main difficulties lie in getting accurate distances to galaxies, since the velocities of galaxies can be accurately measured using Doppler measurments.

• Distances to galaxies have been measured using various standard candles, such as Cepheid variables and Supernovae.

What is parallax?

• Parallax is a measure how much a star’s position changes compared to background stars over the course of a year.

• The ‘wobbling’ of the star is caused by the Earth’s motion around the sun.

• The best measurements of parallax possible are to the order of miliarcseconds, this corresponds to a physical distance of 1000 pc.

• However, parallax is only highly accurate (within a few %) to distances out to a few hundred parsecs.

History of Parallax

• The first Parallax of the star 61 Cygni was measured by F. Bessel in 1838.

• Since that time, parallax has been considered the most direct and accurate way to measure the distances to stars.

What are Cepheid Variable Stars?

• These are bright stars that vary in Mv between -2 and -7.

• Relatively few in number in the galaxy

• An evolutionary step that some red giants move to.

• A very good ‘standard candle’ because the relationship between the Period of variation to the Luminosity is well known.

• Cepheid’s Phase period typically run between 2 and 100 days.

• The nearest Cepheid is ~ 200 parsecs away.

• There are two populations of cepheids.

• Type one is the classical type, they are about 4 times brighter than type 2 and have a high metallicity.

• Type two are older stars with a low metallicity.

• With available instrumentation, Cepheids can be used to measure distances as far as 20 Mpc.

Physics of Cepheid Variables• The variation in the luminosity of Cepheids is caused by

variations of surface temperature of the star as well as radius.

• The variation in the star is driven by the strength of the gravitational forces of the star and the radiative pressure of the star being out of sync with each other.

• Normally a star is in hydrostatic equilibrium where, dP/dr = -GM( r )( r )/r2

• This unbalance of forces causes the radius of the star to oscillate, sometimes as much as 10% about it’s average R.

• The gas on the surface of the star must obey Kepler’s Law, so the pulsation period P R3/M

• And M <> R3 so P2 R3/ <> 3 1/ <>

• This shows that a stars pulsation period is related to the square root of its average density.

History of Cepheid Variables

• Cepheid Variable stars are named after Delta Cephei, which was the first star that astronomer’s noticed changed in brightness over a period of about 5 days.

• The Period- Luminosity relation of cepheids was first discovered by Henrietta Leavitt at Harvard in 1912.

• She studied 25 Cepheids in the Small Megallanic Cloud and assuming that all the stars where about the same distance away, found that the brighter stars had longer periods.

• In 1924 Edwin Hubble used this relation to measure the distance to a number of other galaxies and discovered that the universe is expanding.

• Hubble underestimated Luminosities of several of the Cepheids he looked at, and consequently the distances to the galaxies they were in, because he was only aware of one population of Cepheid and the second population hadn't been discovered yet.

The Distance Ladder

• Trigonometric parallax

• Statistical parallax

• Cluster main-sequence fitting

• Cepheids variable stars

• Type-1a Supernovae

• Tully-Fisher Relation

• Planetary Nebulae

Present Observations

• Determining absolute distances requires absolute luminosities for individual calibrators. Therefore, the accuracy with which one can measure Ho is dependent on the accuracy which which one can measure distances within the Galaxy to calibrate the various distance indicators.

• The Hipparcos satellite provided the means for measuring 118,000 star’s positions, proper motions, parallax, and BV photometry.– The location of the main-sequence as a function of age and

chemical abundance.– Direct distance measurements of primary distance indicators. 200

Cepheid variable stars were studied with Hipparcos.

Present Observations 2

• HST Ho Key Project

– Establish an accurate local extragalactic distance scale based on the primary calibration of Cepheid variables.

– Determine Ho by applying the Cepheid calibration.

– Cepheid distances were determined for 17 galaxies which lie from 3 to 25 Mpc.

– Calibration of secondary indicators such as supernovae, Tully-Fisher Relation, etc.

Main Sources of Error 1

• Dust grains live in the region between stars, and are known to lead to reddening and extinction. If the dust is not accounted for, the objects will appear farther away than they really are.– This can be accounted for by studying different wavelengths. It is

difficult; however, to understand the deviation from the P-L relation.

• The chemical composition or metallicity of the star.– Metals in the atomospheres of stars act as an opacity source to the

radiation emerging from the nuclear burning. The radiation is re-emitted at longer wavelenghts.

Main Sources of Error 2

• The number of Cepheid calibrators per method.

• Inhomogeneities in the galaxy distribution.

• Photometric calibration of HST – known to be +/- .09 mag.

Future Experiments 1

• Double Interferometer for Visual Astrometry (DIVA), which is an extension of the Hipparcos project. DIVA will determine positions to .5 mas and probe as deep as 15th magnitude. Planned launch time is 2003.

Future Experiments 2

• The Advanced Camera for Surveys (ACS) on HST will improve the photometric calibrations of Cepheid measurements.

Future Experiments 3• NASA’s Space Interferometry Mission (SIM). Planned to

launch in 2005. – They will be capable of making 2-3 orders of magnitude more

accurate parallaxes than Hipparcos, a few microseconds. This means that the fainter limits will be increased by ~ 1000.

– Accurate measurments of many Cepheids and RR Lyrae variables will be obtained.

– Improved distance to the LMC, and it will be possible to measure the rotational parallaxes of nearby spiral galaxies.

– Measurements will be taken for 10 yrs.

Future Experiments 4

• European Space Agency’s Global Astrometric Interferometer for Astrophysics (GAIA). Planned to launch in 2009.

Future Experiments 5

Conclusions

• Recent results on the determination of Ho are encouraging.

• Contemporary published Cepheid distances to galaxies and values of Ho have rms differences of only 10%.

• Better telescopes and detectors will decrease the uncertainty in the measurement of Ho.

• Parallax and Cepheid variables are two of the most important factors in our present calculations of Ho.

Our Sources

• Freedman, Wendy L. “The Hubble constant and expansion age of the Universe.” Physics Reports, 333-334 (2000) 13-31.

• Jacoby et al. “A Critical Review of Selected Techniques for Measuring Extragalactic Distances.” Publications of the Astronomical Society of the Pacific, 104 (1992)

• Reid, I. Neill. “The HR Diagram and the Galactic Distance Scale After Hipparcos.” Annual Review in Astronomy & Astrophysics, 37:191-237 (1999)