# Hubble Constant

Now that you have learned how to measure the brightness of a Type 1a supernova, you can proceed to use a collection of these “standard candles” to derive your own measurement of the Hubble Constant: the rate at which the Universe is expanding. In order to do this, you will analyze two types of data from each supernova: the lightcurve and the spectrum. For each plot of a supernova lightcurve, you will choose the brightest point and click on it. The value of the brightness you select will be entered into the answer box in magnitudes. Magnitudes are special units typically used by professional astronomers that get larger as objects become fainter. For example, a 14th magnitude star is about 2.5 times brighter than a 15th magnitude star.

Each supernova also has a second chart that shows its spectrum: how much energy is emitted as a function of the wavelength of light. After clicking the button labeled “Spectrum” click on the wavelength that corresponds to the lowest point in a Silicon absorption line near 6150 Angstroms. (One Angstrom is equal to 10^-10 m.) The wavelength that you measure will be greater than 6150 Angstroms, because the expansion of the Universe will shift the absorption line towards longer wavelengths (“redshift”). You can zoom in to part of the graph by holding the left mouse button down and dragging a box around the spot you would like to see more clearly, zoom back out by clicking the right mouse button. You can zoom in to part of the graph by holding the left mouse button down and dragging a box around the spot you would like to see more clearly, zoom back out by clicking the right mouse button.

Now that you have selected the peak brightness (in magnitudes) and wavelength (in Angstroms), for each supernova, the numbers have been automatically filled in the table below. This table also does the rest of the calculations for you. First, the peak magnitudes are converted into distances by assuming the peak brightness of each supernova is the same. Then the wavelengths of the line minima are converted into recession velocities by measuring the redshift of the line. When the recession velocities (y-axis) are plotted against the distances (x-axis) , the slope of the best fit line in the plot is the measured Hubble constant. Hubble constants are typically measured in km s^-1 Mpc^-1 . For each Megaparsec traveled, the expansion velocity of the Universe increases in km/sec. For example, a Hubble constant of 70 km s^-1 Mpc^-1 means that at a distance of 1 Mpc, objects are moving away from us at 70 km/sec. At 2 Mpc, the recession velocity would be 140 km/sec, and so on.

Magnitude Wavelength D Dist., Mpc Dist., km Redshift Speed

The equation that is written above is the best fit line from the table of measurements that you created. The slope of the line is the Hubble constant.
The age of the Universe is related to the inverse of the Hubble Constant. Note that 1 Mpc = 10^6 pc, 1 pc = 3.26156 light years, and 1 light year = 9.46 x 10^12 km. Therefore, with proper conversion of units, the Hubble constant can be converted into units of s^-1 . The inverse Hubble constant therefore provides the approximate age of the Universe in seconds, which can then be converted into years (1 year = 3.154 x 10^7 seconds). Click the Calculate button and enter your value of the Hubble constant to calculate the age of the Universe from your measurements.