7.3 Relative Distance 7.3 Relative Distance EstimatorsEstimators

김대원김대원

Absolute distance estimatorAbsolute distance estimator

• Direct method to determine distance Direct method to determine distance to particular objects.to particular objects.

• Simple and powerful.Simple and powerful.

• However most astronomical However most astronomical phenomena is not that simple, no phenomena is not that simple, no such simple modeling is possible such simple modeling is possible anymore when we want to estimate anymore when we want to estimate their distances.their distances.

Empirical relationship after Empirical relationship after calibrationcalibration can be used as can be used as

distance estimator.distance estimator.

Typical features of Typical features of relative distance estimatorsrelative distance estimators

• Distance-independent properties Distance-independent properties which vary with distance.which vary with distance.

• Properties which is empirically based.Properties which is empirically based.

• To calibrate relative distance, we To calibrate relative distance, we MUST obtain, at least, one absolute MUST obtain, at least, one absolute distance to the objects.distance to the objects.

Advantages of R.D.Advantages of R.D.

• Not subject to the systematic Not subject to the systematic uncertainties that arises if our uncertainties that arises if our assumptions are incorrect.assumptions are incorrect.

• Can be estimated using common Can be estimated using common sources sources we can measure the we can measure the distances to many more sources!distances to many more sources!

7.3.1 Luminosities of7.3.1 Luminosities ofvariable starsvariable stars

• Cepehid variable M_v ~ -3, RR Lyrae M_v ~ Cepehid variable M_v ~ -3, RR Lyrae M_v ~ 0.60.6– Excellent standard candles.Excellent standard candles.– Can be observed to reasonably large distances Can be observed to reasonably large distances

because they are bright.because they are bright.– Can be calibrated quite straightforwardly becaCan be calibrated quite straightforwardly beca

use large number of them are found near the use large number of them are found near the Sun.Sun.

– Under optimal conditions, the distances error iUnder optimal conditions, the distances error is ~ 10%.s ~ 10%.

7.3.2 Luminosity functions7.3.2 Luminosity functions

• Globular clustersGlobular clusters– By Shapley, 1953.By Shapley, 1953.

•Average luminosities of GC in the Milky Way, the LAverage luminosities of GC in the Milky Way, the LMC and M31 are similar.MC and M31 are similar.

•For the MW, Mv_GC = -7.4 +- 0.1For the MW, Mv_GC = -7.4 +- 0.1•One caveat : different natures between spiral and eOne caveat : different natures between spiral and e

lliptical galaxies.lliptical galaxies.

]2/))(exp[()( 22_

GCGCGC mmm

• Planetary nebulaePlanetary nebulae– Narrow bandpass filters centered on the 500.Narrow bandpass filters centered on the 500.

7nm, oxygen line, show planetary luminosity fu7nm, oxygen line, show planetary luminosity function with cut-off apparent magnitude, m^cutnction with cut-off apparent magnitude, m^cut_PN._PN.

)])(3exp[1()( 307.0 mmem cutPN

mPN

http://www.noao.edu/jacoby/pnlf/pnlf.html

If we adopt a distance to M31 of 740 +- 40 kpc, we obtain an If we adopt a distance to M31 of 740 +- 40 kpc, we obtain an absolute magnitude for the cut_off = -4.6 +-0.1absolute magnitude for the cut_off = -4.6 +-0.1

7.3.3 Novae and 7.3.3 Novae and supernovaesupernovae

• Novae : propertiesNovae : properties– Explosive ignition of accreted material on the sExplosive ignition of accreted material on the s

urface of WD.urface of WD.– M_v ~ -7 at maximum brightness.M_v ~ -7 at maximum brightness.– Rather independent on the metallicity if their hRather independent on the metallicity if their h

ost systems.ost systems.

• Novae : distance indicator for MW.Novae : distance indicator for MW.– Expansion parallaxExpansion parallax

– cannot be used for extra-galactic novae cannot be used for extra-galactic novae due to their small angular diameters.due to their small angular diameters.

skmvtvD /1000,/ expexp

• Novae : distance indicator in extra-galactic Novae : distance indicator in extra-galactic scale.scale.– M_v : from -4.8 to -8.9 M_v : from -4.8 to -8.9 Only the intrinsic ar Only the intrinsic ar

e not standard candles.e not standard candles.– However, their decline rates of luminosities dHowever, their decline rates of luminosities d

epend on their absolute brightness. (faint novaepend on their absolute brightness. (faint novae decays more slowly)e decays more slowly)

; where t_2 is the time that the nova took to decline in brightness by t; where t_2 is the time that the nova took to decline in brightness by two magnitudes from this maximum. See Figure 7.5.wo magnitudes from this maximum. See Figure 7.5.

)/log(3.27.10(max) 2 daytM v

• Novae : etc.Novae : etc.– Distance uncertainty is ~ 25%Distance uncertainty is ~ 25%– Some novae are fainter or brighter than Some novae are fainter or brighter than

predicted by previous equations.predicted by previous equations.– LF of novae at maximum brightness LF of novae at maximum brightness

shows double-peaked function, which shows double-peaked function, which could be used as standard candle.could be used as standard candle.

• Type Ia supernovae : propertiesType Ia supernovae : properties– All Ia follow remarkably similar evolution. All Ia follow remarkably similar evolution. lu lu

minosities of Ia might also all be very similar. minosities of Ia might also all be very similar. ideal standard candles. ideal standard candles.

– M_v = -19.52 +- 0.07, M_b = -19.48 +- 0.97, M_v = -19.52 +- 0.07, M_b = -19.48 +- 0.97, when adopting Cepheid distance scale.when adopting Cepheid distance scale.

– Theoretically, M_b = -19.4 +- 0.3, consistent Theoretically, M_b = -19.4 +- 0.3, consistent with the empirical calibrations.with the empirical calibrations.

• Type Ia supernovae : etc.Type Ia supernovae : etc.– Maza et al (1994)Maza et al (1994)

•Studied two Ia SN. They should differ by only 0.1 mStudied two Ia SN. They should differ by only 0.1 mag. But they differ 0.8+-0.2 in the B band and 0.4+ag. But they differ 0.8+-0.2 in the B band and 0.4+-0.2 in the I band.-0.2 in the I band.

•Phillips (1995) suggested that their colors vary with Phillips (1995) suggested that their colors vary with luminosity declines.luminosity declines.

– Hoflich & Khokhlov (1996) simulated Ia supernHoflich & Khokhlov (1996) simulated Ia supernovae and found that the peak luminosities and ovae and found that the peak luminosities and light curve shape could be vary from system to light curve shape could be vary from system to system.system.