Astronomical Astronomical DistancesDistances

or or Measuring the UniverseMeasuring the Universe

(Chapters 7, 8 & 9)(Chapters 7, 8 & 9)

by by Rastorguev Alexey,Rastorguev Alexey,professor of the Moscow State professor of the Moscow State

University and Sternberg University and Sternberg Astronomical Institute, RussiaAstronomical Institute, Russia

Sternberg AstronomicalSternberg Astronomical InstituteInstitute

Moscow UniversityMoscow University

ContentContent

• Chapter Seven:Chapter Seven: BBWB: Moving Photospheres (Baade-Becker-Wesselink-Balone technique)

• Chapter Eight:Chapter Eight: Cepheid parallaxes and Period – Luminosity relations

• Chapter Nine:Chapter Nine: RR Lyrae distance scale

Chapter SevenChapter Seven

BBWB: Moving Photospheres BBWB: Moving Photospheres (Baade-Becker-Wesselink-(Baade-Becker-Wesselink-

Balone technique)Balone technique)

Astronomical BackgroundAstronomical Background• W.Baade-W.Becker-A.Wesselink-L.BalonaW.Baade-W.Becker-A.Wesselink-L.Balona

technique (BBWBBBWB) is applicable to pulsating stars (Cepheids and RR Lyrae variables) or stars with expanding envelopes (SuperNovae)

• W.BaadeW.Baade (Mittel.Hamburg.Sternw. V.6, P.85, 1931); W.BeckerW.Becker (ZAph V.19, P.289, 1940); A.Wesselink A.Wesselink (Bull.Astr.Inst.Netherl. V.10, P.468, 1946):

• photometry and radial velocities give rise to radius measurement and independent calculation of star’s luminosity

(a) For a pair of phasespair of phases with the same temperature and color (say, B-V), the Cepheid’s apparent magnitudes V differ due only to the ratio of stellar radii:

(b) Radii difference

(R1-R2) can be calculated by integrating the

radial velocity curve, due to VR ~ dR/dt

22

21lg5.2

R

Rm

R1 R2

B-V

Pulsation Phase

• A number of pairs

• (R1 – R2) ~∫VR·dt and R1/R2 ≈ 10-0.2m

give rise to the calculation of mean

radius, <R> = (Rmax + Rmin)/2

I. BBW Surface-brightness technique (SB)I. BBW Surface-brightness technique (SB)

• θLD is “limb-darkened” angular diameter

• Flux incident, EEλλ ≈ ≈ ΦΦλλ··θθLDLD22, where ΦΦλλ being

surface brightness (do not depending on the star’s distance!)

• Apparent magnitude, mmλλ ~ -2.5 lg E ~ -2.5 lg Eλλ , so

• θθLDLD ~ -0.2·m ~ -0.2·mλλ + F + Fλλ + c + c ,

with FFλλ as the “surface-brightness parameter”

θLDEλ

• The surface-brightness parameter is shown to relate with the color CI (due to surface brightness dependence on the effective temperature Φλ ~ Teff

4 and CI-Teff relations)

• FFλλ ≈≈ a·CIa·CIλλ + b + b

• Example relation is shown; interferometriccalibrations (Nordgrenet al. AJ V.123, P.3380,2002)

• The calibrations for surface brightness parameter, Fλ, can be also derived from the photometric data for normal stars (dwarfs, giants and supergiants) with the distances determined, say, by precise trigonometric technique or other data

• See, for example, M.GroenewegenM.Groenewegen “Improved Baade-Wesselink surface brightness relations” (MNRAS V.353, P.903, 2004)

• From both relations,

• θθLDLD ~ -0.2·m ~ -0.2·mλλ + F + Fλλ + c + c

• FFλλ ≈≈ a + a·CIa + a·CIλλ + b+ b

• θθLDLD ~ -0.2·m ~ -0.2·mλλ + a·CI + a·CIλλ + const + const

• Direct calculation of star’s angular Direct calculation of star’s angular diameter vs timediameter vs time

Light-curve Color-curve

• Radial velocity curve integration gives absolute radius change, and being relate to apparent angular diameter change, distance to the pulsating star follows

II. Maximum Likelyhood technique by II. Maximum Likelyhood technique by L.BalonaL.Balona (MNRAS V.178, P.231-(MNRAS V.178, P.231-

243,1977)243,1977) uses all light curve and uses all light curve and precise radial velocity curveprecise radial velocity curve

• Background:

• (a) Stefan-Boltzmann low: Lbol ~ σT4

• (b) Effective temperature and bolometric correction are connected with normal color (see examples)

• (c) Radius change comes from the integration of the radial velocity curve

lg Teff – (B-V)0 relation by P.Flower (1996)relation by P.Flower (1996)

Luminosity classes:

Working interval

ΔMbol – (B-V)0 relation by P.Flower (ApJ, V469, P.355, 1996)relation by P.Flower (ApJ, V469, P.355, 1996)

Luminosity classes

ΔM

bol

Working interval

Quadratic approximations can be written for

lgTeff, ΔMbol by (B-V)0

(and by other normal colors) in the range

0.2 < (B-V)0 < 1.6

)()()(

)()(

)()(lg

0

02

0

02

0

VBEVBVB

VBVBM

VBVBT

bol

eff

Basic equations of the Balone Basic equations of the Balone approachapproach

bolVbol

SunSuneff

Sunbol

bolSunbolbol

SunSun

eff

bolSun

bol

effbol

MMM

R

RTT

L

LMM

R

R

T

T

L

L

RTL

ngSubstituti

lg5lg10lg10

lg5.2

law)Boltzmann -(Stefan42

4

4

24

From the distance modulus expression,

RtrRR

CBA

CBA

VBV

R

RVBVBV

Ad

VM

Sun

VV

valuemean withradiuscurrent is

and,curvescolor andlight are

)(and,constants theare where

,lg5)()(

as MODELcurvelight e wright th we values

all of onsubstitutiafter ,5)pc1(

lg5

)(,,

2

Here constants A, B and C:

2)()10()()10()10(

lg10)(5)pc1(

lg5

),10(

),10()()10(2

VBEVBE

TMVBERd

C

B

VBEA

SunSunbolV

These constants enclose information on colorexcess E(B-V) and the star’s distance d

How to calculate the radius How to calculate the radius change?change?

(to the observer)

Contribution of theContribution of thecircular ring to thecircular ring to theobserved radial velocityobserved radial velocity

-V-V00: photosphere velocity: photosphere velocity

dS: ring areadS: ring area

Mov

ing

phot

osph

ere

Mov

ing

phot

osph

ere

Calculating R(t)=<R>+r (t): integrating radial velocity curve VVrr

Ring contribution to the measured radial velocity:

)cos1(cossin2)(

:"weight" Ring

darkening limb)cos1()4

;fluxlight effect to projectioncos)3

;area ringsin2sin2)2

; on tocontributi ringcos)()1

2

2

rW

drdrr

VrV r

Mean radial velocity weighted along star’s limb = observed VVrr

rp

d

d

r

dW

dWV

Vr 1

)cos1(cossin

)cos1(cossin

)(

)()(

2/

0

2/

0

2

2/

0

2/

0

pp is the projection factor connectingradial velocity and the photosphere speed

Projection factor values:Projection factor values:

• In the absence of limb darkening p=3/2 • In most studies p=1.31 accepted

• But:But: projection factor depend on projection factor depend on– Limb darkening coefficientLimb darkening coefficient– Velocity of the photosphereVelocity of the photosphere– Instrumental line profile used to measure Instrumental line profile used to measure

radial velocityradial velocity

rVpr

Theoretical spectral line will be distorted due to instrumental profile

2

212/1

00

02

0

20

2

)v(exp)2(),v(

:rofileGaussian p alInstrument

) v 0 , cosv

here(

,v

1v2

)v(

: profileline lTheoretica

VVI

VV

VV

rF

N

Line profile calculation enables to derive theoretical value of the projection factor, p

Observed line profile (with taking into account line broadening due to instrumental effects) can be calculated as the convolution

v),v()v()(0

0

dVIFVfV

N

Some examples of the line profiles for different Some examples of the line profiles for different line broadening due to instrumental effectsline broadening due to instrumental effects

Theoretical profile

Observed profile

Instrumental width

Smallvelocity

Good Gaussian fit

Solid: normal

Some examples of the line profiles for different Some examples of the line profiles for different line broadening due to instrumental effectsline broadening due to instrumental effects

Observed profile

Instrumental width

Largevelocity

Theoretical profile

Normal curve (blue line)

Bad Gaussian fit

Normal curve

• Modern calculations confirm the variation of pp by at least ~5-7% due to different effects

• (Nardetto et al., 2004; Groenewegen, 2007; Rastorguev & Fokin, 2009)

Example:Example: projection factor and line projection factor and line width vs photosphere velocity, Vwidth vs photosphere velocity, V00

From Gauss tipFrom line tip

• Projection factor pp and its variation with the velocity VV00 , limb darkening coefficient εε and instrumental width σσ should be “adjusted” to proper spectroscopic technique used for radial velocity measurements

• Example:Example: More than 20000 VR measurements have been performed by Moscow team for ~165 northern Cepheids with characteristic accuracy ~0.5 km/s and σσ ~ 15 km/s ~ 15 km/s

t

r

t

dtVpdtdt

drtr

00

~~)(

Radius change, r(t), can be calculatedby integrating the radial-velocity curve,Vr (t), from some t=0 (where R(0)=<R>)

Example:Example: TT Aql radial velocity curve TT Aql radial velocity curve (upper panel) and radius change (bottom (upper panel) and radius change (bottom

panel)panel)Δ

R,

Sola

r u

nit

sV

r, k

m/s

Pulsation phase

Fitting the light curve for TT Aql Fitting the light curve for TT Aql Cepheid (+) with the model (solid line)Cepheid (+) with the model (solid line)

Sun

Sun

R

R

rVBVBV

RCBA

CRBA

)6.182(15.009.14

08.018.020.069.1

lg5)()()(2

V

Pulsation phase

Steps to luminosity calibrationSteps to luminosity calibration• <R>, A, B, C enable:

– To calculate mean bolometric and visual luminosity of the star and its distance

– To refine transformations of Teff to normal colors and bolometric corrections (additionally)

• BBWB technique has been applied to Cepheid and RR Lyrae variables and turned out to be very effective and very effective and independent tool for P-L calibrationsindependent tool for P-L calibrations (see later)

• For Fundamental tone Cepheids:

• log R/Rlog R/RSunSun = 1.23 ( = 1.23 (±0.03) + (0.62 ±0.03) log ±0.03) + (0.62 ±0.03) log PP

by M.Sachkov (2005)Cepheid radii canbe used to classi-fy Cepheids bythe pulsationmode (first-over-tone pulsatorshave shorter peri-ods at equal radii)

1st

FU

• Well known possibility to measure the distances to some SuperNova remnants via their angular sizes and the envelope expansion velocities is also can be considered as the modification of the moving photospheres technique

• Possible explosion asymmetry can induce large errors to estimated parameters

t1

t2

2

1

)(~t

t

R dttVD

VR

Δφ D

SN

• Optical and NIR interferometric direct observations of the radii changes of nearest Cepheid are of great importance and very promising tool to measure their distances and correct the distance scale

• B.LaneB.Lane et al. (ApJ V.573, P.330, 2002):• Palomar PTI 85-m base length optical interferometer

Distance within10% error

Phase

• P.KervellaP.Kervella et al. (ApJ V.604, L113, 2004): interferometric (ESO VLT) apparent diameter measurements (filled circles) as compared

to BW SB technique (crosses)

D ~ 566 ±20 pc

Very goodagreement

Chapter EightChapter Eight

Cepheid parallaxes andCepheid parallaxes andPeriod – Luminosity relationsPeriod – Luminosity relations

• Astrophysical backgroundAstrophysical background• Overtone pulsatorsOvertone pulsators• Use of Wesenheit indexUse of Wesenheit index• Luminosity calibrationsLuminosity calibrations• P-L or P-L-C ?P-L or P-L-C ?

pc

Cepheids “econiche”Cepheids “econiche”

100 pc … 50 Mpc

Cepheids ascalibratorsfor thesemethods

• Cepheids and RR Lyrae variable stars populate Instability StripInstability Strip on the HRD (see blue strip) where most stars become unstable with respect to radial pulsations

• Instability StripInstability Strip crosses all branches, from supergiants to white dwarfs

• Instability strip for galactic Cepheids (members of open clusters and with BBWB radii) in more details:

• MV-(B-V) and MI-(V-I) CMDs

G.TammannG.Tammann et al. (A&A V.404, P.423, 2003)

• Comprehensive review of the problem by:

Alan Sandage & Gustav TammannAlan Sandage & Gustav Tammann “Absolute magnitude calibrations of Populations I and II Cepheids and Other Pulsating Variables in the Instability Strip of the Hertzsprung-Russell Diagram” (ARAA V.44, P.93-140, 2006)

Cepheids:Cepheids: named after named after δδ Cepheus Cepheus star, the first recognized star of this star, the first recognized star of this

classclass• Young (< 100 Myr) and massive (3-8 Young (< 100 Myr) and massive (3-8

MMSunSun) bright (M) bright (MVV up to -7 up to -7mm)) radially pulsating variable stars with strongly regular brightness change (light curves)

• Typical Periods of the pulsations: from ~1-3 to ~100 days (follow from P ~ (GP ~ (Gρρ))--

1/21/2 expression for free oscillations of the gaseous sphere: mean mass density of huge supergiants, ρ, is very small as compared to the Sun)

• Luminosities:

from ~100 to 30 000 that of the Sun

• Evolution status: yellow and red supergiants, fast evolution to/from red (super)giants while crossing the instability strip (solid lines)

Evolution tracks for1-25MSun stars on the HRD

• Relative fraction of Cepheids population depends on the evolution rate while crossing the instability strip:

• slower evolution means more stars at the appropriate stage

IS

• (a) Tracks are not parallel to the lines of constant periods

• Evolutional period change happens

• (b) Evolution rate during 2nd & 3rd crossings is slower than for 1st crossing, defining the IS population fraction

• (c) Luminosity depend on the crossing number

Cepheids evolution tracks,the instability strip and P=const lines (red)P=const lines (red)

An extra source of P-L scatter

lg L

The differences in the evolutionrates at different crossings giverise to the questions on therelative contribution of brightand faint Cepeids for the sameperiod value

• dP/dt is visible when observing on long time interval (~100 yr)

• At equal periods: Cepheids with different masses but with different crossing number

• lg (dP/dt) vs lg Plg (dP/dt) vs lg P: crossing number diagnostics (as compared to the theory)

• Perspective tool to identify crossing number and to refine the P-L relation…

+P increase

P decrease

… but it requires long time monitoringImpossible to use forextragalactic Cepheids,

Maybe, any spectroscopicfeatures will be foundresponsible for crossing

• The duration of the Cepheids stage is

typically less than 0.5 Myr and, taking also in consideration the rarity of massive stars at all, we guess that Cepheids form very poor galactic populationvery poor galactic population

• Statistics of Cepheids discovered: ~3000 proven and suspected in the

Galaxy, ~2500 in the LMC, ~1500 in the SMC, ~Thousands are found and, ~50 000 are

expected to populate the Andromeda Galaxy (M31)

• Easily recognized by its high brightness and periodic magnitude change among other stars, even in distant galaxies (up to 50 Mpc)

• Typical population of young clusters, spiral and irregular galaxies

• Luminosity increases with the Period (P-L Luminosity increases with the Period (P-L relation)relation)

• Cepheids are still among most important Cepheids are still among most important “standard candles”“standard candles”

Hertzsprung Sequence of Cepheids Hertzsprung Sequence of Cepheids (normalized) light curves. Bump (normalized) light curves. Bump

position.position.(from P.Wils)(from P.Wils)

A.UdalskiA.Udalski et al. “The Optical Gravitational et al. “The Optical Gravitational Lensing Experiment. Cepheids in the LMC. IV. Lensing Experiment. Cepheids in the LMC. IV.

Catalog…” (Acta Astronomica V.49, P.223, Catalog…” (Acta Astronomica V.49, P.223, 1999)1999)

• Apparent mean I magnitude corrected for differential absorption inside LMC vs log P(days) for fundamental fundamental tone (FU)tone (FU) and first overtone first overtone (FO) (FO) cepheids:

• <I> ≈ a + b·lg <I> ≈ a + b·lg PP

• PFO / PFU ≈ 0.71• (Δ lg P ≈ 0.15)

W(I)

Distances are the same:absolute magnitudes <MI>are also linear on log P !

Brightest Cepheids

• Linearity of log P-log Llog P-log L relation retains also for Cepheids absolute magnitudes

• Simple estimate:Simple estimate:

• Brightest LMC Cepheids reach <M<MVV> ≈ -7> ≈ -7mm

• These “standard candles” can be seen from the distance ~50 Mpk~50 Mpk (with ~27m limiting magnitude accessible to HST)

• Brightest Cepheids can be widely used as secondary sources of distance calibrationssecondary sources of distance calibrations to spiral galaxies hosted by SN Ia etc.

We can see Cepheidseven in distant galaxies

• Overtone Cepheids are clearly seen on the “apparent magnitude – period” diagrams of nearby galaxies as having smaller periods for the same brightness

• Problem with Milky Way Cepheids: due to Problem with Milky Way Cepheids: due to distance differences, how to identify distance differences, how to identify overtone pulsators among Cepheids with overtone pulsators among Cepheids with different distances ?different distances ?

• Milky Way Cepheids sample is supposed to Milky Way Cepheids sample is supposed to be contaminated by unidentified first-be contaminated by unidentified first-overtone pulsatorsovertone pulsators

• This problem greatly complicates the extraction of the P-L relation directly from observations of Milky Way cepheids

Sources of calibrations of the Sources of calibrations of the Cepheids absolute magnitudesCepheids absolute magnitudes

• (a) Trigonometric parallaxes (HIPPARCOS and HST FGS)

• (b) Membership of Cepheids in open clusters and associations

• (c) BBWB mean radii• (d) Luminosity refinement by the

statistical parallax technique

(a) Cepheids trigonometric parallaxes

• P-L relation <M<MVV> ≈ a + b·lg P> ≈ a + b·lg P from van Leeuwen (2007) data for 45 parallaxes (σp/p < 0.5). Total of 87 Cepheids shown. Good slope, bad zero-point: ~0.7-0.8m fainter as compared to conventional P-L relations.

Lutz-KelkerBias: shiftsto top butis toouncerntainfor ~50%errors

• To separate the correction to P-L slope from the correction to zero-point, we can rewrite P-L relation in the equivalent form

•<M<MVV > = (a + b) + b·(lg P – 1), > = (a + b) + b·(lg P – 1),

where (a + b)(a + b) is <M<MVV> (at P=10> (at P=10dd)) with the “conventional” values for• (a + b) ≈ -3.9 … –4.2(a + b) ≈ -3.9 … –4.2• (a + b)(a + b) can be considered as zero-point

“substitute”• Common way to refine the constants

• <MV> (at P=10d) vs lg P (from new HIPPARCOS reduction by van Leeuwen, 2007, and extinction data).

• Red:Red: 45 Cepheids with σp/p < 0.5

• Blue:Blue: all Cepheids HIPPARCOSparallaxes alonedisable to derivefine P-L relation!

Partly,overtonepulsators?

(a + b)st

• ““How to deal with the Lutz-Kelker bias?How to deal with the Lutz-Kelker bias?”” – That’s the question not yet finally solved (M.Groenewegen M.Groenewegen & & R.OudmaijerR.Oudmaijer, A&A V.356, P.849, 2000)

• Should the Lutz-Kelker correction be Should the Lutz-Kelker correction be added to each star of the sample (or the added to each star of the sample (or the selection by the parallax is always selection by the parallax is always biased) ?biased) ?

• Some authors use “reduced parallax” approach instead of distances approach (see C.Turon Lacarrieu & M.CrezeC.Turon Lacarrieu & M.Creze “On the statistical use of trigonometric parallaxes”, A&A V.56, P.373, 1977):

VM.~p 2010

• P-L relation: P-L relation: <M> = a + b·lg P<M> = a + b·lg P• (a) zero-point (a) zero-point • (b) slope(b) slope

• Why not to estimate the slope of Why not to estimate the slope of the P-L relation directly from LMC the P-L relation directly from LMC Cepheids ? –Cepheids ? –

• The slopes of the P-L relations in other galaxies maymay differ due to systematic systematic differences in the metal abundancesdifferences in the metal abundances and Cepheids ages (A.Sandage & A.Sandage & G.TammannG.Tammann, 2006)

• Before ~2003, most astronomers used the slope of LMC Cepheids to refine zero-point of Milky Way Cepheids

• If metallicity effects are really important, application of single P-L relation to other galaxies populated by Cepheids can introduce additional systematic errors (see detailed discussion in A.SandageA.Sandage et al., 2006)

Problems with the interstellar Problems with the interstellar extinctionextinction

• Cepheids color excess are uncertain because of:– Finite width of the instability strip

(~0.2m) due to evolution effects– Uncertainty of cepheids “normal colors”

• • Wesenheit index (Wesenheit Wesenheit index (Wesenheit

function)function) is often used to reduce the effects of the interstellar extinction (B.MadoreB.Madore in “Reddening-independent formulation of the P-L relation: Wesenheit function”; ROB No.182, P.153, 1976)

Example:Example: Wesenheit index for (V-I) Wesenheit index for (V-I) colorcolor

• From true distance modulus we have:

• Wesenheit index definition:

VV AplgVM (mas)510

)IV()IV(E

AplgV)VI(W V

(mas)510

Constant!

Wesenheit indexWesenheit index

• Substituting apparent color

we derive:

where const β = AV/E(V-I) ≈ 2.45±

follows from the extinction law

)IV(E)IV()IV( 0

00

0(mas)510

)IV(M)VI(W)IV()IV(E

AM

)IV()IV(E

AAplgV)VI(W

VV

V

VV

Wesenheit index do not dependon the extincton but onlyon the normal color

Normal color as well as <MV> is linear on lg P(see instability strip picture!),so W(VI) is also linear on lg P

• Wesenheit Index can be introduced for any color: W(BV), W(VK)W(BV), W(VK) etc.

• WW incorporates intrinsic color (and Period – Color relation)

• The advantage of using the Wesenheit index WW instead of the absolute magnitude MM is that– (a) Wesenheit index is almost free of

any assumptions on cepheids individual color excess, particularly in our Milky Way, and

– (b) it reduces the scatterreduces the scatter of the P-L relations

Use of the Wesenheit indexUse of the Wesenheit index

• M.Groenewegen M.Groenewegen & & R.OudmaijerR.Oudmaijer, “Multi-colour PL-relations of Cepheids in the HIPPARCOS catalogue and the distance to the LMC” (A&A V.356, P.849, 2000)

• A.SandageA.Sandage et al. “The Hubble constant: a summary of the HST program for the luminosity calibration of type Ia SuperNovae by means of Cepheids” (ApJ V.653, P.843, 2006)

• FF..van Leeuwenvan Leeuwen et al. “Cepheid parallaxes and the Hubble constant” (MNRAS V.379, P.723, 2007)

• FF..van Leeuwenvan Leeuwen et al. “Cepheid parallaxes and the Hubble constant” (MNRAS V.379, P.723, 2007)

W(V

I)

Wesenheit indexW(VI) for 14Cepheids with mostreliable parallaxesfrom HIPPARCOSand HST FGS:Route to P-L relation

W(VI) = α·lg P + γ

W(VI)

• To derive P-L relation:

• MMVV ≈ W(VI) + ≈ W(VI) + ββ·(V-I)·(V-I)00

• Normal colors are also linearly dependent on the period: CICI00 ≈ ≈ δδ·lg P ·lg P + + εε

Example:Example:Period – Color (P-C)relation for galacticCepheids from

G.TammannG.Tammann et al. (A&A V.404, P.423,2003). Wide strip (σCI≈0.07m)

(V-I)0 vs lg P

• To derive P-L relation: W MV:

• MV ≈ W(VI) + β·(V-I)0

• MV ≈ (α + β·δ) ·lg P + (γ + β· ε)

• Serious problem: effects of [Fe/H]Serious problem: effects of [Fe/H]• Theoretical approach:

• A.SandageA.Sandage et al. “On the sensitivity of the Cepheid P-L relation to variations of metallicity” (ApJ V.522, P.250, 1999)

• I.Baraffe & Y.AlibertI.Baraffe & Y.Alibert “P-M relationships in BV IJHK-bands for fundamental mode and 1st overtone Cepheids” (A&A V.371, P.592, 2001)

• G.Tammann et al. (A&A V.404, G.Tammann et al. (A&A V.404, P.423,2003):P.423,2003):

• P-C relations for Galaxy, LMC & SMC• L/SMC aremetal-defici-metal-defici-entent relativeto the Galaxy

LMC/SMCCepheids arebluerbluer than inthe MilkyWay

• Overall impression: [Fe/H] differences affect also P-L relations (slope & zero-point)

• Key question:Key question: Systematic error induced to P-L based distances when we neglect metallicity differences

• From A.Sandage et al.A.Sandage et al. new stellar atmospheres models and synthetic spectra (ApJ V.522, P.250, 1999):

• At P = 10d: bol B V IdM/d[Fe/H] (mag/dex) 0.00 +0.03 -0.08 -

0.10

“…The agreement of the RR Lyraedistance to the LMC, the SMC, andIC 1613 with the Cepheid distancedetermined on the basis of only aof only amildmild (if any) metallicity(if any) metallicity dependencedependenceofof the P-L relation forthe P-L relation for classicalclassicalCepheidsCepheids is our principal conclusion”.

• M.Groenewegen M.Groenewegen & & R.OudmaijerR.Oudmaijer (A&A V.356, P.849, 2000):

• ΔM = MGal – MLMC for VIK bands (LMC is ~0.3-0.4 dex metal-deficient as LMC is ~0.3-0.4 dex metal-deficient as

compared to MWcompared to MW: W.RollestonW.Rolleston et al., A&A V.396, P.53, 2002)

• Corrections disagree due to the differences in the theoretical models

• M.GroenewegenM.Groenewegen “Baade-Wesselink distances and the effect of metallicity in classical Cepheids” (A&A V.488, P.25, 2008)

• Problem was investigated by P-L relations based on BBWB Cepheids radii …

• “Obtaining accurate distances to stars is a non-trivial matter (Yes! – A.R.)(Yes! – A.R.)… The metallicity dependence of the PL-relation is investigated and no significant dependence is found. A firm A firm result is not possibleresult is not possible as the range in as the range in metallicity spanned by the current metallicity spanned by the current sample ofsample of galactic Cepheids is 0.3–0.4 galactic Cepheids is 0.3–0.4 dexdex, while previous work suggested a small dependence on metallicity only (typically −0.2mag/dex).”

• There is no common agreement in the reality of significant differences in the slopes of the P-L relations in different galaxies due to differences in [Fe/H]

• (F.van LeeuwenF.van Leeuwen et al. (2007): “…The main conclusion … is that within current within current uncertaintiesuncertainties <the P-L slope - A.R.> is the same in the Galaxy as in the LMC…”)

• As a consequence, some ambiguity remains in the calibrations of other standard candles based on the Cepheids distance scale

(b) Cepheids in open clusters and (b) Cepheids in open clusters and associationsassociations

• Another way to derive independently the slope and zero-point of the P-L relations of galactic Cepheids comes from open clusters and associations (young stellar groups hosted by the Cepheid variables)

• Their distances calculated by the MS-fitting are good to about few per cent

• Approximately 30-50 galactic Cepheids are Approximately 30-50 galactic Cepheids are considered as possible cluster membersconsidered as possible cluster members

L.Berdnikov et al.L.Berdnikov et al. “ “The BVRIJHK period-luminosity The BVRIJHK period-luminosity relations for Galactic classical Cepheidsrelations for Galactic classical Cepheids” (AstL V.22, ” (AstL V.22,

P.838, 1996) – 9 Cepheids in 5 open clusters:P.838, 1996) – 9 Cepheids in 5 open clusters:

Multicolor (BVRCRICIJHK) P-L relations for galactic Cepheids

days days

days days

Zero-points Slope

Very poor statistics!

Metallicity differences have beentaken into account empirically, by adding the term proportional tothe difference of the galactocentricdistances (due to “mean” [Fe/H]gradient across the galactic disk, Δ[Fe/H] / ΔRG)

P-L slopes as compared to the LMC Cepheids

m

LMC

Optics | NIR

• D.Turner & J.BurkeD.Turner & J.Burke “The distance scale for classical cepheid variables” (AJ V.124, P.2931, 2002)

• The list of 46 Cepheids as possible members of young stellar groups (clusters and associations)

• (Future (Future prospects)prospects)

• D.An et al.D.An et al. “The distances to open clusters from main- sequence fitting. IV. Galactic Cepheids, the LMC, and the local distance scale” (ApJ V.671, P.1640, 2007)

New P-Lfor thegalacticCepheids:

Newdistances

• (c) Distance scale from BBWB radii(c) Distance scale from BBWB radii Comparing Cepheids P-L derived from 23 cluster Cepheids (red) with that from Wesselink radii (blue)

(D.Turner & J.Burke, 2002)(D.Turner & J.Burke, 2002)

Insignificant slopdifference ~0.19

Mean: <MV>≈-1.20m-2.84m·lg P

• A.Sandage et al. A.Sandage et al. (A&A V.424, P.43, (A&A V.424, P.43, 2004)2004)

BBWB P-L (circles) for 36 galactic Cepheids

P-L for 33 cluster members (dots)

P-L are very close within errors

• Rms scatter: Rms scatter: σσ ~ 0.19…0.27 ~ 0.19…0.27mm

MB0 Galaxy

• A.Sandage A.Sandage et al. (A&A V.424, P.43, 2004)

• LMC Cepheids: Instability Strip break on MV

0-(B-V)0 CMD

• Hint on P-L Hint on P-L break at break at P=10P=10dd ? ?

• Complicates the use of P-L for distance measurements

Constantlg P lines

• Nonlinear calculations of the Cepheids models also seem to support an idea on two Cepheids families divided by the period value Plim ~ 9-10d

• Theory:Theory: large fraction of the Cepheids with P < Plim are suspected to be 1st overtone pulsators

• “Broken” at P=10d P-L relations for LMC Cepheids (A.Sandage et al., 2004, 2006)(A.Sandage et al., 2004, 2006)• (a) Flatter P-L for P > 10d can introduce systematic distance errors to distant

galaxies where only brightest Cepheids are observed• (b) Poor statistics (~ 2 dozens) of brightest Cepheids introduces extra scatter

0.5 1.0 1.5 2.0 lg P

For

A.Sandage et al. (2004, A.Sandage et al. (2004, 2006):2006):

• Comparing “broken” P-L (BVI bands) for LMC (solid line) with conventional P-L for the Milky Way Galaxy (BBWB & cluster cepheids: dots & circles)

• Close at P ~ 10d (after reducing LMC zero-points by ~0.15m)

Systematic differences !Systematic differences !

<MB>

<MV>

<MI>

• A.Sandage et al. (2004) “closing speech”:A.Sandage et al. (2004) “closing speech”:

• “…The consequences of the differences in the slopes of the P-L relations for the Galaxy, LMC, and SMC weakens weakens the hope of usingthe hope of using Cepheids to obtain precision galaxy Cepheids to obtain precision galaxy distances.distances. Until we understand the reasons for the differences in the P-L relations and the shifts in the period−color relations, (after applying blanketing corrections for metallicity differences), we are presentlywe are presently at a loss to choose which of the several P-L relations to at a loss to choose which of the several P-L relations to useuse (Galaxy, LMC, and SMC) for other galaxies.

• Although we can still hope that the differences may yetwe can still hope that the differences may yet be caused only by variations in metallicitybe caused only by variations in metallicity, which can be measured, this can only be decided by future researchthis can only be decided by future research such as survey programs to determine the properties of Cepheids in galaxies such as M33 and M101 where metallicity gradients exist across the image. But until we can prove or disprove that metallicity difference is the key parameter, we must provisionallyprovisionally assumeassume that this is the case, and use either the Galaxyand use either the Galaxy P-L relations, P-L relations, or the LMC P-Lor the LMC P-L relations, or those in the SMCrelations, or those in the SMC.”

The use of Cepheids P-L-CThe use of Cepheids P-L-C (Period – Luminosity - Color) relations (Period – Luminosity - Color) relations

• Cepheids P-L-C manifold in

lg T – lg P – lg Llg T – lg P – lg L coordinates

• Projections give P-L & P-C relations and the Instability Strip

P-L-C manifold is the “cousin” of the Fundamental Plane for elliptical galaxies

• Constructing the P-L-C “plane”:Constructing the P-L-C “plane”:• The intrinsic scatter of the P-L relation

is due to the finite widthfinite width of the instability strip and the sloping of the sloping of the constant-periodconstant-period lineslines.

• The scatter can be reduced by introducing a P-L-C relation of the form

• MMλλ = = ααλλ··lg P lg P -- β βλλ·CI·CIλλ + γ+ γλλ ,, CICIλλ is color index (λ)

where βλ is the slope of the constant-period lines on the appropriate CMD

βλ=ΔMλ / ΔCIλ taken for P=const

• A.Sandage et al. (2004)

• CMDs and the constant period lines (red)(red) for LMC Cepheids

• The slopes vary with P

P-L-C relation translatestranslates the magnitude to the value an unreddened Cepheid would have if it were lying on the ridgewould have if it were lying on the ridge lineline of the P-C of the P-C and P-L and P-L relationrelationss (except for observational errors)

• Earlier, the use of P-L-C relation instead of P-L, gave unsatisfactory results because constant slope ΔΔMMVV//ΔΔ(B-V)(B-V) have been supposed for all P, L and colors

• A.Sandage A.Sandage et al. et al. (2004, (2004, 2006):2006):

• P-L-C constants

αα, , ββ, , γγ depend on the period and vary from galaxy to galaxy

• A.Sandage et al. A.Sandage et al. (2004)(2004)

• LMC CepheidsLMC Cepheids Mλ-βλ(B-V) and Mλ-βλ(B-V)

vs lg P relations: reduced scatter (σ ≈ 0.07…0.17m)

• Very attractive idea!

• Least squares solutions for lg P>1 (lower) & lg P<1 (upper) are shown

I

I

V

V

lg P>1

lg P>1

lg P>1

lg P>1

lg P<1

lg P<1

lg P<1

lg P<1

• Note:Note:• Reduced scatter of the P-L-C Reduced scatter of the P-L-C

relation may seem attractive, but relation may seem attractive, but in the absence of independent data in the absence of independent data on the intrinsic color differences on the intrinsic color differences (say, due to metallicity or (say, due to metallicity or extinction differences), this extinction differences), this technique can give rise to artificial technique can give rise to artificial errors in the absolute magnitudeerrors in the absolute magnitude

• A.SandageA.Sandage explains: explains:

• A.Sandage et al. (2004):A.Sandage et al. (2004): “TThe P-L-C he P-L-C relation can onlyrelation can only be used if it can be be used if it can be proven that the Cepheids under proven that the Cepheids under considerationconsideration follow the same P-L follow the same P-L andand P-C P-C relations.relations. Otherwise any intrinsic intrinsic color difference is multiplied by the constant-period slope ββ and erroneously forced upon the magnitudes with detrimentalwith detrimental effects on any derived distanceseffects on any derived distances.”

• It would be wrong idea to apply the LMC P-L-C relation to Milky Way Cepheids which have different P-L (BVIBVI ) relations and (necessarily !) also different P-C relations (for B−V,B−V, B−IB−I ). – Clear as day! (A.R.)– Clear as day! (A.R.)

(d) Luminosity refinement by the statistical parallax technique

• The applicability of the statistical parallax technique to the Milky Way Cepheids requires requires very accurate radial and tangential velocitiesvery accurate radial and tangential velocities. Observational errors obviously should not exceed the intrinsic scatter of space residual velocities. HIPPARCOS proper motions joined with the extensive set (~20000) of CORAVEL radial velocity measurements made by the Moscow group (N.Gorynya et al.N.Gorynya et al., VizieR Cat. III/229, 2002) became real base to Cepheids statistical parallaxes, and enabled to A.Rastorguev et al.A.Rastorguev et al. (AstL V.25, P.595, 1999) to derive the corrections to the Cepheids distance scale (L.Berdnikov et al.L.Berdnikov et al., 1996): extension by ~10% ((ΔΔMMV V ≈≈ -0.2 -0.2mm))

• An example of the Cepheid light curve (SU Cyg) in UBVRIJK bands (top-down):

• The amplitude decreases The amplitude decreases with wavelength, as well as with wavelength, as well as the scatter of multicolor P-the scatter of multicolor P-L relationsL relations

• Few brightness estimates Few brightness estimates in NIR (>2.2 in NIR (>2.2 μμm) suffice to m) suffice to estimate mean magnitude estimate mean magnitude and the distanceand the distance

• NIR/MIR data are of great NIR/MIR data are of great importance for distance importance for distance scale refinement and scale refinement and luminosity calibrationsluminosity calibrations

Rela

tive m

agn

itu

de

NIR/MIR prospectsNIR/MIR prospects

• W.Freedman et al.W.Freedman et al. “The Cepheid P-L relation at mid-infrared wavelengths. I.” (ApJ V.679, P.71, 2008)

• Single-epoch observations for 70 LMC Cepheids from SPITZER (1 point at each light curve!)

• Slope steeper in MIR (>3.3 mμ) than in NIR and optics

• W.Freedman et al.W.Freedman et al. “The Cepheid P-L relation at mid-infrared wavelengths. I.” (ApJ V.679, P.71, 2008)

• P-L relations in MIR (>3.3 mμ) are nearly the same:

• RMS scatter of MIR P-L relations is RMS scatter of MIR P-L relations is ~0.07~0.07mm, so even single MIR observation , so even single MIR observation can give the distance precise to ~8%can give the distance precise to ~8%

• Very promising tool to measure large extragalactic distances

Addendum to Cepheids discussion:Addendum to Cepheids discussion:LMC as the touchstone of the distance LMC as the touchstone of the distance

scale adjustmentscale adjustment• LMC is hosted by a wide variety of stellar

populations, from very young to old ones; as a consequence, LMC with its ~50 kpc distance, is very “suitable” stellar system to apply different tools of distance measurements used different “standard candles”, such as Cepheids, RR Lyrae, RCG, Tip Red Giants, MS-fitting, binaries, Miras etc.

• Ideally, all distances to LMC should agree Ideally, all distances to LMC should agree within appropriate errors of methods usedwithin appropriate errors of methods used

• In the mid-1980’s, measurement of H0 with the goal of 10% accuracy was designated as one of three “Key “Key Projects”Projects” of the HST (M.Aaronson & M.Aaronson & J.MouldJ.Mould, ApJ, V.303, P.1, 1986), with LMC as the central object

• Real HST observations began in the 1991• Results in:Results in: W.FreedmanW.Freedman et al. “Final

Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant” (ApJ V.553, P.47, 2001)

• LMC weighted “mean” distance:LMC weighted “mean” distance:

• (m-M)(m-M)00 ≈ 18.50 ± 0.10 ≈ 18.50 ± 0.10mm

LMC distances from Cepheids: LMC distances from Cepheids: ΔΔM M ≈≈ 0.60.6mm

(m-M)(m-M)00

• Most reliable conventional Cepheids distance scales derived by different approaches, differ from each other at the 0.2-0.3m level (10-15% in the distance)

• Their systematic errors are unknown • Which one is true?

• Concluding remark of A.Sandage & Concluding remark of A.Sandage & G.Tammann (2006):G.Tammann (2006):

• “Clearly, much work lies ahead. We are only at the beginning of a new era in distance determinations using Cepheids. It can be expected that much will be discovered and illuminated in the years to come”.

Chapter NineChapter Nine

RR Lyrae distance scaleRR Lyrae distance scale

RR Lyr starRR Lyr star is an archetype of old halo is an archetype of old halo population (Horizontal Branch) short-period population (Horizontal Branch) short-period variable starsvariable stars

RR LyrRR Lyr is the brightest and nearest star of this is the brightest and nearest star of this type with its type with its <M<MVV> ≈ 9.03 ± 0.02> ≈ 9.03 ± 0.02mm, <B-V> ≈ , <B-V> ≈ 0.44 ± 0.040.44 ± 0.04mm, D ≈ 260 pc, D ≈ 260 pc , (HIPPARCOS, 2007) , (HIPPARCOS, 2007)

• M.Marcony & G.ClementiniM.Marcony & G.Clementini (ApJ V.129, P.2257, 2005)

• Periods < 1Periods < 1dd

• Examples ofLMC RR Lyraelight curves inBV bands

Observations vsObservations vs

theorytheory

Large amplitude,Large amplitude,

ΔΔm ~ 1m ~ 1mm

• Examples of the LMC RR Lyrae light curves in I band (OGLE program, I.SoszynskiI.Soszynski et al., Acta Astr. V.53, P.93, 2003)

• RR are simply RR are simply discernible discernible among field among field stars in stellar stars in stellar systemssystems

•<M<MVV> ≈ +1> ≈ +1mm

T.Brown T.Brown et al. (AJet al. (AJ

V.127, V.127, P.2738,2004)P.2738,2004)

• HST ACS• M31 RR Lyrae light

curves example

• <[Fe/H]> ≈ -1.6 from periods distribution

• NIR light curve of RR Lyr star: look at small amplitude. RR Lyr: nearest star of this type.RR Lyr: nearest star of this type.

Not so brightas Cepheidsbut very important fordistance scalesubject in the galactic halos,bulges and thickdisk populations

• RR Lyrae variable stars in the Instability StripInstability Strip on the HRD

• In contrast to Cepheids, RR Lyrae variables are among oldest oldest starsstars of our Milky Way

• Evolution status:Evolution status: horizontal branch (HB) stars

• RR Lyrae variables RR Lyrae variables populate galactic halos (H)(H) and thick disks (TD)(TD) (as single stars), and globular clusters of different [Fe/H]

• Evolution stage:Evolution stage: Helium core burning• Age:Age: ≥ 10 Gyr• LifeTime:LifeTime: ~100 Myr

RR LyraeRR Lyrae

BHBBHB((EHB)EHB)

TPTP

M2

H TD

V const ?

Close luminosities for thesame [Fe/H] (rms ~ 0.15m)

• The duration of RR Lyrae stage (and HB stage at all) is negligible as compared to the age of stars, ≤100 Myr vs ~10-13 Gyr (<1%), but comparable with lifetime of Red Giants

• Therefore, HB population is comparable with RG population in size, but RR Lyrae form only a small fraction of all stars above Turn-Off point on the CMD

• Thousands of RR LyraeThousands of RR Lyrae are found and catalogued in the Milky Way halo and in its globular clusters

• Post-ZAHB tracks for low-mass stars (by B.Dorman (ApJS V.81, P.221, 1992) with [Fe/H]=-1.66 and Blue & Red edges of the Instability Strip (IS)

• MassesMasses

on ZAHBon ZAHB

are labelledare labelled

StarsStars

evolve fromevolve from

ZAHB toZAHB to

second RGsecond RG

tiptip

IS

Zero-Age Horizontal Branch (ZAHB)

Stellar evolution for low-mass Stellar evolution for low-mass starsstars

HF

IS

• Dots are separated by 10 Myr time interval

• HB position is almost HB position is almost the same for clusters the same for clusters of different ageof different age

• Universality of RR Universality of RR Lyrae population Lyrae population luminosityluminosity

Gyr age

• D.VandenBergD.VandenBerg et al. (ApJ V.532, P.430, 2000) theoretical ZAHB levels for different [Fe/H] and [α/Fe] values

• [Fe/H] seems [Fe/H] seems to be the key to be the key parameter parameter responsible for responsible for RR Lyrae RR Lyrae optical optical luminosityluminosity

• The slopes of P - LP - L and [Fe/H] - L[Fe/H] - L relations seems to be definitely found from the theory as well as from observations in globular clusters and nearby galaxies differ by [Fe/H]

• Zero-point refinement is Main Zero-point refinement is Main problem in RR Lyrae distance problem in RR Lyrae distance scale studiesscale studies

• From late 1980th, it became customary to assume a linear relation between RR Lyrae optical absolute magnitude and metallicity of the form

• <<MMoptopt>> = a + b = a + b··[Fe/H][Fe/H]• The calibration problem reduced to finding

aa and bb by whatever calibration method was used. The three most popular have been:

• (a) theory(a) theory• ((bb) the BBW) the BBWBB moving moving atmosphere methodatmosphere method• ((cc) ) distances of globular clusters; HST & distances of globular clusters; HST &

HIPPARCOS parallaxesHIPPARCOS parallaxes• ((dd) statistical parallaxe) statistical parallaxe technique technique

(a) P.Demarque et al.(a) P.Demarque et al. (AJ V.119, P.1398, 2000)

• Is there universal slop of the <MV> - [Fe/H] relation?

• Theoretical

slopes μμ

(a) G.Bono “(a) G.Bono “RR Lyrae distance scale: theory andRR Lyrae distance scale: theory andobservations”observations” (arXiv:astro-ph/0305102v1, 2003)(arXiv:astro-ph/0305102v1, 2003)

• RR Lyrae models in NIR do obey to a well-defined PLZK relation:

•

• <MK> ≈ -0.775 − 2.07·lg P + 0.167·[Fe/H]

with an intrinsic scatter of ~0.04m

(with small contribution from [Fe/H] term)

(a) M.Catelan et al.(a) M.Catelan et al. “T“The he RRRR LLyrae yrae P-LP-L relation. relation. II. . TTheoretical calibrationheoretical calibration”” (ApJSS V.154, P.633,

2004)• <MI> ≈ +0.109 – 1.132·lg P + 0.205·[Fe/H]

• <MJ> ≈ -0.476 – 1.773·lg P + 0.190·[Fe/H]

• <MH> ≈ -0.865 – 2.313·lg P + 0.178·[Fe/H]

• <MK> ≈ -0.906 – 2.353·lg P + 0.175·[Fe/H]

• <MV> ≈ +1.258 + 0.578·[Fe/H] + 0.108·[Fe/H]2

• (this nonlinear function of [Fe/H] do not depend on lg P:

• <M<MVV> ≈ +0.63> ≈ +0.63mm at [Fe/H]=-1.5 at [Fe/H]=-1.5 )

• Two important RR Lyrae features:Two important RR Lyrae features:

• (a) <MV> depend on [Fe/H] and practically does not depend on period

• (b) <M> in NIR (JHK bands) depend on the period and practically do not depend on [Fe/H]

• [M/H] = [Fe/H] +[M/H] = [Fe/H] +

+ lg (0.638·10+ lg (0.638·10[[αα/Fe]/Fe] + 0.362) + 0.362)

Takes into accountTakes into account

differences in [differences in [αα/Fe]/Fe](from theory: M.Catelan et al., 2004)

• Usually, RR Lyrae distance scales are characterized by the mean absolute magnitude referred to [Fe/H] = -1.5[Fe/H] = -1.5, the maximum of [Fe/H] distribution function of RR Lyrae field stars and GGC (galactic globular clusters)

• (b) BBWB technique(b) BBWB technique rewiev: C.Cacciari & C.Cacciari & G.ClementiniG.Clementini in: Stellar Candles for the Extragalactic Distance Scale ( Ed. D.Alloin & W.Gieren, Lecture Notes in Physics, V.635, P.105-122, 2003):

• <<MMVV>>RRRR = (0.20±0.04)[Fe/H] = (0.20±0.04)[Fe/H] + (0.98±0.05)+ (0.98±0.05)

• C.CacciariC.Cacciari et al. (ApJ V.396, P.219, 1992):

<MV>RR vs [Fe/H] <MV>RR vs lg P

<M<MVV>>RRRR ≈ 0.20·[Fe/H] + 1.04 ≈ 0.20·[Fe/H] + 1.04 <M<MVV>>RRRR ≈ -2.79·lg P -1.08 ≈ -2.79·lg P -1.08

• Notes to BBWB technique applied to Notes to BBWB technique applied to RR Lyrae variables:RR Lyrae variables:

• (a) Zero-points and slopes are in general agreement with the theory

• (b) Interstellar absorption problems seem to be not so important for RR Lyrae (halo stars with small color excess) as compared to the Cepheids

(c) RR Lyr – nearest RR-type variable - HST (c) RR Lyr – nearest RR-type variable - HST trigonometric parallaxtrigonometric parallax

• G.Fritz Benedict et al. (AJ V.123, P.473, 2002) – HST FGS3 parallax for RR Lyr

• • For RR Lyr star itself:

• MMVV(RR) ≈ +0.61 ± (RR) ≈ +0.61 ± 0.10.1mm

• with [Fe/H] ≈ -1.39• <V> ≈ +9.0m

• HIP: old HIPPARCOS• data (1997)

pRR

(c) RR Lyr HIPPARCOS trigonometric (c) RR Lyr HIPPARCOS trigonometric parallaxparallax

• F.van Leeuwen “HIPPARCOS, the new reduction of the raw data” (Springer: 2007)

• – new RR Lyr parallax:

• pRR ≈ (3.88 ± 0.39) mas

• means

• MMVV(RR) ≈0.61±0.09(RR) ≈0.61±0.09mm

• in ideal accord with• HST FGS3 estimate

pRR

• Taking into account <MV>RR variation with [Fe/H], we can extrapolate <MV>RR to RR Lyrae with [Fe/H] ≈ -1.50 (at the maximum of the metallicity distribution function) by using the slope d<Md<MVV>>RRRR/d[Fe/H] ≈ 0.2/d[Fe/H] ≈ 0.2 as

• <M<MVV>>RRRR ([Fe/H] = -1.50) ≈ +0.59 ([Fe/H] = -1.50) ≈ +0.59mm

~ 0.15m brighter than its conventional value, ~0.72-0.75m

Archetype - RR Lyr starArchetype - RR Lyr staris not the best is not the best ““standard candle” !standard candle” !

Notes:Notes:

• (a)(a) Estimated <MV> for individual stars can differ from “mean” absolute magnitude by ~0.15m, intrinsic scatter for the HB stars

• (b)(b) All RR Lyrae calibrations used the trigonometric parallaxes (MS-fitting of globular clusters populated by RR Lyrae based on subdwarf stars, direct RR Lyrae distances) suffer from Lutz-Kelker biassuffer from Lutz-Kelker bias

• There is no common consensus in the statement that the Lutz-Kelker correction really should be applied to individual stars…

(c) M.Frolov & N.Samus (AstL V.24, P.174, 1998)(c) M.Frolov & N.Samus (AstL V.24, P.174, 1998)

• K-band P-L RR Lyrae relation for 173 RR in 9 globular clusters of different [Fe/H]

• <M<MKK> ≈ -2.338 (±0.067) lg P – 0.88 (±0.06)> ≈ -2.338 (±0.067) lg P – 0.88 (±0.06) (with rms scatter ~0.06m)

• Synthetic P-L diagram

• P-L slope is very reliableP-L slope is very reliable, but zero-point can differ from this because it depends on clusters distances adopted

(c) F.Fusi-Pecci et al. (AJ V.112, P.1461, (c) F.Fusi-Pecci et al. (AJ V.112, P.1461, 1996)1996)

• <MV>HB calibration (<MV>HB ≈ >MV>RR)

• HST data for 9 M31 Globular clusters

• <M<MVV>>HBHB ≈ (0.13 ± 0.07) [Fe/H] +(0.95 ± ≈ (0.13 ± 0.07) [Fe/H] +(0.95 ± 0.09)0.09)

• Zero-point depends on M31 distance adopted

(d) RR Lyrae statistical parallaxes(d) RR Lyrae statistical parallaxes

• Comprehensive rewiev of the problem in: A.Gould & P.PopovskyA.Gould & P.Popovsky “Systematics in RR Lyrae statistical parallax. III” (ApJ V.508, P.844, 1998)

• <MV>RR ≈ 0.77±0.13m at [Fe/H]=–1.6 from 147

RR Lyrae 3D velocity field and

• <MV>RR ≈ 0.80±0.11m at [Fe/H]=–1.71 from

865 RR Lyrae 2D velocity field

• Fainter than from other data sources

(d) RR Lyrae statistical parallaxes(d) RR Lyrae statistical parallaxes

• A.Dambis & A.RastorguevA.Dambis & A.Rastorguev “Absolute Magnitudes and Kinematic Parameters of the Subsystem of RR Lyrae Variables” (AstL V.27, P.108, 2001)

• <MV>RR ≈ 0.76±0.12m for “halo” RR population

at [Fe/H]=–1.6

• <MV>RR ≈ 1.01+0.15·[Fe/H] from RR Lyrae

subdivided into 5 independent groups by [Fe/H]

<MV>RR ≈ 0.79m ([Fe/H]=–1.5)

Notes to (d):Notes to (d):• Statistical parallax technique seem to

underestimate RR Lyrae luminosity (and the distance scale)

• C.CacciariC.Cacciari et al. (2003) note two main sources of the systematical errors:– (a) Contamination of halo RR Lyrae sample

by thick disk stars (with differential rotation in the Milky Way)

– (b) Inhomogeneity of the galactic halo that can include considerable fraction of stars came from “accreting” Milky Way satellites“accreting” Milky Way satellites identified in SDSS in recent years

• Two halo subsystems would have different dynamical characteristics and origins, the slowly rotating subsystem being associated to the Galactic thick disk, and the fast rotating (possibly with retrograde motion) subsystem belonging to the accreted outer halo

• From new paper of E.Bell et al. (ApJ E.Bell et al. (ApJ V.680, P.295, 2008):V.680, P.295, 2008): “…“… a a dominant dominant fraction of the stellar halo of the Milky fraction of the stellar halo of the Milky Way is composedWay is composed of the accumulated of the accumulated debris from the disruption of dwarfdebris from the disruption of dwarf galaxiesgalaxies””

• Any kinematical inhomogeneity of the sample used can introduce unpredictable systematical errors to the distance scale

• The statistical parallax technique, very powerful in itself, need more adequate kinematical models for halo populations and more extended RR Lyrae samples, with good radial velocities and proper motions

• Comparing RR Lyrae <M<MVV> vs [Fe/H]> vs [Fe/H] theoretical relation (solid line) with the statistical and trigonometric parallaxes calibrations (A.SandageA.Sandage et al., 2006): systematical differences

Dambis & Rastorguev (2001)

LMC distances from RR Lyrae: LMC distances from RR Lyrae: ΔΔM M ≈≈ 0.50.5mm

(m-M)(m-M)00

• G.Fritz BenedictG.Fritz Benedict et al. (AJ V.123, P.472, 2002) gave a summary of all the distance of all the distance measurements to measurements to LMC galaxyLMC galaxy, performed by 21 different methods, with “mean” value close to (m-(m-M)M)00≈18.50≈18.50mm

• Ranking by value

B.Schaefer (2008) test ofB.Schaefer (2008) test ofLMS distance measurementsLMS distance measurements

• Main goal was to check if: – (a) All measurements are really independent (a) All measurements are really independent

and unbiasedand unbiased– (b) All random errors are correctly reported (b) All random errors are correctly reported

Consider therelative deviationparameter: D = (D = (μμ-<-<μμ>) / >) / σσ

• K-S (Kolmogorov-Smirnov) statistical testK-S (Kolmogorov-Smirnov) statistical test of cumulative |D| distribution: theory (smooth) vs published measurements (step function)

• An excess of small |D| is seen after 2002: ~68% are within 0.5 σ instead of 68% within 1 σ as it

follows from the theory, or too muchtoo much

too presisetoo presise

estimatesestimates

• An excess of large |D| is seen among the results before 2001 (year of publication the results of HST Key Project – HST KP), or too much too inaccurate too much too inaccurate estimatesestimates

• (I) (I) Before the year 2001, the many measuresBefore the year 2001, the many measures spanned a wide range (spanned a wide range (fromfrom 18.1 18.1mm to to 18.818.8mm)),, with with the quoted error bars beingthe quoted error bars being substantially smaller substantially smaller than the spread, and hence the consensus than the spread, and hence the consensus conclusion being thatconclusion being that many of the measures many of the measures had their uncertainties being dominated by had their uncertainties being dominated by unrecognizedunrecognized systematic problemssystematic problems

• (II) After (II) After 20012001 (HST(HST KPKP results results)),, community has community has generally accepted generally accepted and and widely popularized value widely popularized value μ≈μ≈18.50±0.1018.50±0.10mm,, and “and “independentindependent”” measures measures clusterclustereded tightly around tightly around it, i it, indeed,ndeed, too tightly.too tightly. This concentration is a symptom of a worrisome This concentration is a symptom of a worrisome problemproblem:: (a) (a) correlations between papers, correlations between papers, (b) (b) widespread overestimationwidespread overestimation of error of error bars,bars, (c) (c) band-wagon effect band-wagon effect

Summary to Cepheids and RR Summary to Cepheids and RR LyraeLyrae

• Cepheids as very bright and uniquely identified stars are among most “popular” standard candles in the distant galaxies, but their distance scale is still uncertain by ~10% (systematic + random error)

• RR Lyrae are good standard candles used to refine the distances to the “beacon” galaxies (such as LMC/SMC, M31/33 etc.) in the Local Volume (up to ~10 Mpc), and to calibrate other secondary standard candles (SN Ia, Tulli-Fisher & Faber-Jackson relations etc.)

• Much work has to be done with Cepheids and RR Lyrae variables in recent years and in the future, in the context of GAIA and SIM observatories