Photometry

Measuring EnergyPhotometry measures the energy from a source using a narrow range of wavelengths.Visual wavelengths from 400-700 nmNarrower slice of wavelengths

Photometry uses filters to select wavelengths.Spectroscopy measures energy over a wide range of wavelengths.Visual spectrumUV, IR spectraFull EM spectra

Spectroscopy requires instruments to get at each wavelength separately.Interferometer

Luminosity of StarsLuminosity measures how much energy is produced.Absolute brightness L

Relative luminosity is usually based on the Sun.Astronomers measure luminosity relative to the Sun.LSun = 1 L LSirius = 23 L

Stars range from 0.0001 L to 1,000,000 L .

MagnitudeThe observed brightness is related to the energy received.

The magnitude scale was originally 6 classes.Effectively logarithmic

The magnitude (m) was made formal in 1856.Lower numbers brighter6m at the limit of human visionFor 1 unit of magnitude:

Brightness MagnifiedImages from a telescope must fit within the pupil.Brightness proportional to the aperture squaredRatio of observed to natural

No increase for extended objects from magnification.Eg. M31(> moon)Light on more rodsExclusion of other light

Point Source MagnifiedPoint sources are smaller than one pixel (or rod).No increase in image size from magnification

The ratio of brightness increase is the light grasp G.Pupil size 7 mm

The limiting magnitude comes from the aperture.CCD 5 to 10 magnitudes betterin meters8 aperture is 13.3m

Apparent MagnitudeThe observed magnitude depends on the distance to the source.Measured as apparent magnitude.

The scale is calibrated by stars within 2 of the north celestial pole.

Some bright stars (app. mag.):Sun-26.7Sirius-1.4Alpha Centauri-0.3Capella0.1Rigel0.1Betelgeuse0.5Aldebaran0.9

These are all brighter than first magnitude (m = 1.0)

Distance CorrectionBrightness falls off as the square of the distance d.

Absolute magnitude M recalculates the brightness as if the object was 10 pc away.1 pc = 3 x 1016 m = 3.26 ly

The absolute magnitude can be corrected for interstellar absorption AD.

AD = 0.002 m/pc in galactic plane

Absolute MagnitudeDistance is important to determine actual brightness.

Example: 2 identical stars A is 7 pc, B is 70 pc from EarthThe apparent brightness of B is 1/100 that of AThe magnitude of B is 5 larger.Some bright stars (abs. mag.):Sun4.8Sirius1.4Alpha Centauri4.1Capella0.4Rigel-7.1Betelgeuse-5.6Aldebaran-0.3

These are quite different than their apparent magnitudes.

ImagingPhotographic images used the width of an image to determine intensity.Calibrate with known starsFit to curveCCDs can directly integrate the photoelectrons to get the intensity.Sum pixels covered by imageSubtract intensity of nearby dark sky

Data is corrected for reddening due to magnitude and zenith angle.

Solar FactsRadius: R = 7 105 km = 109 RE

Mass : M = 2 1030 kg M = 333,000 ME

Density: r = 1.4 g/cm3(water is 1.0 g/cm3, Earth is 5.6 g/cm3)

Composition:Mostly H and He

Temperature:Surface is 5,770 KCore is 15,600,000 K

Power:4 1026 W

Hydrogen Ionization

Particle equilibrium in a star is dominated by ionized hydrogen.

Equilibrium is a balance of chemical potentials.n = 1n = 2n = 3ep = p2/2m

Saha Equation

The masses in H are related.Small amount en for degeneracy

Protons and electrons each have half spin, gs = 2.H has multiple states.

The concentration relation is the Saha equation.Absorption lines

Spectral TypesThe types of spectra were originally classified only by hydrogen absorption, labeled A, B, C, , P.

Understanding other elements lines allowed the spectra to be ordered by temperature.

O, B, A, F, G, K, MOh, Be A Fine Guy/Girl, Kiss MeOur Brother Andy Found Green Killer Martians. Type TemperatureO35,000 KB20,000 KA10,000 KF 7,000 KG 6,000 KK 4,000 KM 3,000 K

Spectral ClassesSome bright stars (class):SunG2SiriusA1Alpha CentauriG2CapellaG8RigelB8BetelgeuseM1AldebaranK5

Temperature and luminosity are not the same thing.

Detailed measurements of spectra permit detailed classes.

Each type is split into 10 classes from 0 (hot) to 9 (cool).

FiltersFilters are used to select a restricted bandwidth.Wide: Dl ~ 100 nmIntermediate: Dl ~ 10 nmNarrow: Dl < 1 nm

A standard set of optical filters dates to the 1950sU (ultraviolet violet): lp = 365 nm, Dl = 70 nmB (photographic): lp = 440 nm, Dl = 100 nmV (visual): lp = 550 nm, Dl = 90 nm

Filter SetsOther filter sets are based on a specific telescope.HST: 336, 439, 450, 555, 675, 814 nmSDSS: 358, 490, 626, 767, 907 nm

The standard intermediate filter set is by Strmgren.u, b, v, y, b bw: lp =486 nm, Dl=15 nm

CCDs have are good in IR, so filter sets have moved into IR as well.U, B, V, R, I, Z, J, H, K, L, M.Example M : lp = 4750 nm, Dl = 460 nm

Color IndexThe Planck formula at relates the intensity to the temperature.Approximate for T < 104 K

Two magnitude measurements at different temperatures can determine the temperature.Standard with B and V filtersGood from 4,000 to 10,000 K

Stellar RelationsThe luminosity of a star should be related to the temperature.Blackbody formulaDepends on radiusSome bright stars:SunG24.8SiriusA11.4Alpha Centauri G24.1CapellaG80.4RigelB8-7.1Betelgeuse M1-5.6Aldebaran K5-0.3

Luminosity vs. Temperature

Most stars show a relationship between temperature and luminosity.Absolute magnitude can replace luminosity.Spectral type/class can replace temperature.

Sun

Hertzsprung-Russell DiagramThe chart of the stars luminosity vs. temperature is called the Hertzsprung-Russell diagram.

This is the H-R diagram for hundreds of nearby stars.Temperature decreases to the right

Main Sequence

Most stars are on a line called the main sequence.

The size is related to temperature and luminosity:hot = large radiusmedium = medium radiuscool = small radius1 solar radiusSirius

Balmer JumpThe color indexes can be measured for other pairs of filters.

The U-B measurement brackets the Balmer line at 364 nm.Opaque at shorter wavelength

This creates a discontinuity in energy measurement.Greatest at type ADrop off for B and GMichael Richmond, RIT

Photometric ComparisonStellar classification is aided by different response curves.

Bolometric MagnitudeBolometric magnitude measures the total energy emitted at all wavelengths.Modeled from blackbodyStandard filter VZero for main sequence stars at 6500 K

Luminosity is directly related to absolute bolometric magnitude.Flux to apparent bolometric magnitude