Hubble’s Law and Hubble Constant James Cox Longwood University – PHYS 223 Introduction Theory, cont. Results, cont. Hubble’s Law relates the distance and velocity of receding 1 galaxies using a constant known as the Hubble Constant. × 1000 = age of universe in billions of years 퐻0 Hubble Constant 퐻0 was found to be This lab activity calculated the Hubble Constant and Methodology 61.0 ± 4.7 km∙s−1∙Mpc−1 (kilometers per second- approximated the age of the universe using publicly megaparsec), with a universe 16.4 ± 1.3 billion years available data, using Edwin Hubble’s original principles.1 Galaxy images were evaluated for angular size and light spectrographs analyzed for the shifted wavelengths of three old. Uncertainty was calculated in Excel by the least- Theory spectral lines, Ca H and Ca K (calcium) absorption lines and H count-squares method. The Hubble Law relates a galaxy’s velocity 푣 with its II II α (hydrogen) emission lines. Visual point-and-click analysis tools distance 푑 and the Hubble Constant 퐻0. This makes the Discussion and Conclusion Hubble Constant the slope of the graph of distance plotted were built into the webpage, provided by the University of against velocity. Washington’s Astronomy Education Department. The galaxy was Results are consistent with the currently understood measured along the long edge, and the wavelength values taken range of the Hubble Constant2 (upper 60s to lower 푣 = 퐻0푑 for the appropriate peaks on the spectrographs. Below is a −1 −1 To determine the Hubble Constant, “standard candles” 70s of km∙s ∙Mpc ). The estimate for the age of such as a type of galaxy, supernova, or other event with sample of the images analyzed for galaxy NGC 3627. the universe is reasonable, as the oldest stars known well-understood size and magnitude is used. This study are 12.5 billion years old. used galaxies approximated to be 22 kiloparsecs across. Additional systematic error may be present due to Assuming galaxies of size 22 kiloparsecs (1 kpc = 3.26 × the analysis method, which involved the observer 103 light years), trigonometry with the small angle clicking on the edges of each galaxy. As the galaxies approximation can be used to calculate distance of galaxies have no hard edge, this necessitates interpretation. 휃 radians in angular size: Galaxies may also not all be 22 kpc across. Note that a high degree of variability exists in modern determinations of the Hubble Constant using different standard candles and methodologies. 표푝푝 0.022 Mpc sin 휃 = ֜ 휃 = Despite the limitations of this study, this mirrors the ℎ푦푝 푑 Results theoretical methodology of Edwin Hubble. His 푑 Rearranging for distance , this gives: discovery of an expanding universe helped affirm 0.022 Mpc Galaxy Velocity vs. Distance 푑 = Einstein’s theory of general relativity and drastically 휃 milliradians changed cosmology by disproving the widely-held Velocity 푣 can be determined by examining the redshift 푧 notion that the universe was static. of spectral lines—places on the light spectrum where common elements like hydrogen and calcium absorb or Sources and Acknowledgements emit light. This gives 푣 as a factor of the speed of light 푐: 1Neta A. Bahcall, PNAS, 11, 112 (2015); 푣 = 푧푐, where doi: 10.1073/pnas.1424299112 2 휆푚푒푎푠푢푟푒푑 − 휆푡푟푢푒 NASA, ”Hubble Constant, H_0,” LAMDA Education, 푧 = https://lambda.gsfc.nasa.gov/education/graphic_history/hubb 휆푡푟푢푒 _const.cfm. where 휆 is the measured wavelength of some 푚푒푎푠푢푟푒푑 Data sourced from the University of Washington at spectral line from a moving galaxy and 휆 is the 푡푟푢푒 https://depts.washington.edu/astroed/HubbleLaw/galaxies.html stationary, lab-determined value for that spectral line’s I would like to thank the University of Washington for providing wavelength. data publicly for students such as myself to use, and Longwood The age of the universe is inversely proportional to the University for helping facilitate this lab. Hubble Constant: Background: Hubble/ESA.