Stellar Lunch

Blue Supergiants as distance andstellar metallicity measuresin the Local Volume

David Nicholls24 November 2009

Abstract

Rolf Kudritzki and co-workers at the IfA, University of Hawaii (and elsewhere) have, over the past14 years, been developing techniques to use low resolution spectroscopy of distant B-A supergiantsto measure stellar metallicity, surface gravities, reddening and extinction, absolute bolometric mag-nitudes and distances. With the current 8-10 metre class telescopes the technique permits these mea-surements out to distances approaching 10Mpc. This talk will be about their latest methods and theirbasis.

1 November 24, 2009

L84 EXTRAGALACTIC DISTANCE DETERMINATION METHOD Vol. 582

TABLE 1Adopted Temperature

Scale

Spectral TypeTeff

(K)

B8 . . . . . . . . . . . . . . 12000B9 . . . . . . . . . . . . . . 10500A0 . . . . . . . . . . . . . . 9500A1 . . . . . . . . . . . . . . 9250A2 . . . . . . . . . . . . . . 9000A3 . . . . . . . . . . . . . . 8500A4 . . . . . . . . . . . . . . 8350

Fig. 1.—Fit of the Balmer lines Hg,d and H8 to H11 of the NGC 300 A0 Iasupergiant C6 (see Bresolin et al. 2002) using atmospheric models withT peff

K and (thick line) and 1.65 (thin line) (gravities given in cgs9500 logg p 1.60units). Note that the use of information from many Balmer lines enhances theaccuracy of the determination significantly. The FWHM of the instrumentallog gprofile is∼5 A, which is larger than the intrinsic width of the Balmer lines andthe line broadening through rotation (typically≤50 km s�1 for A supergiants).Therefore, the calculations are convolved with the instrumental profile. Thisexplains why gravity effects cannot be seen in the line wings but only in thecores. These effects in the line cores reflect the changes of the integrated ab-sorption-line strength (equivalent width) as a function of gravity.

Fig. 2.—Absolute bolometric magnitude vs. logarithm of flux-weightedgravity of B8 to A4 supergiants in NGC 300 and NGC 3621. Note thatTeff

is used in units of 104 K.

early A supergiants based on the recent quantitative spectro-scopic work cited above. We conclude that spectral classifi-cation allows for a temperature determination with a relativeaccuracy of about 4%. Then, for a given spectral type (andeffective temperature) the higher Balmer lines as typical pho-tospheric absorption lines allow for a rather precise determi-nation of the gravity even for only medium-resolution spectraof faint and distant objects (see Fig. 1). Assuming a typicalrelative uncertainty of 0.05 for , we estimate the uncer-log gtainty in from equation (1) to be about 0.3 mag for a singleMbol

object. This is a very encouraging estimate. Note that at thispoint we do not have to worry about absolute errors in thedetermination ofg and , as long as we calibrate the methodTeff

with a stellar sample at a known distance and apply the methodstrictly differentially.

3. SUPERGIANTS IN NGC 300 AND NGC 3621

Recently, Bresolin et al. (2002) studied the population of bluesupergiants in the Sculptor group spiral galaxy NGC 300 at adistance of∼2.0 Mpc ( ; Freedman et al. 2001).m � M p 26.53Using FORS1 at the Very Large Telescope (VLT), medium-resolution (∼5 A) spectra of 70 blue supergiant candidates wereobtained and spectral types, magnitudes, and colors (the latterbased on the work by Pietrzyn´ski et al. 2001) for 62 objectswere presented. These observations provide the ideal data for acareful test of the new method.

In our analysis, we restrict ourselves to objects where wecan be sure that the higher Balmer lines (Hg, Hd, etc.) are notcontaminated by Hii region emission; i.e., we avoid objectswith a clear indication of nebular Ha emission or with a hintof nebular emission at Hg above or below the two-dimensionalstellar spectrum. In addition, we select only spectral typeswithin a narrow range between B8 and A4, where we knowfrom our recent work (Przybilla et al. 2001; Przybilla & Butler2001; Przybilla 2002) that our model atmosphere analysis toolsare very reliable, in particular with regard to the relative ac-curacy of a strictly differential study. For the given spectraltypes, we adopt effective temperatures according to Table 1and determine gravities from the higher Balmer lines as dis-played in Figure 1. We then calculate intrinsic colors with ourmodel atmosphere code to determine reddening and extinctionand use the calculated bolometric correction and the distancemodulus to obtain bolometric magnitudes.

The data set for NGC 300 is not the only one available tous. In a similar way, Bresolin et al. (2001) have used FORS1at the VLT to study 17 objects in the spiral galaxy NGC 3621at a distance of 6.7 Mpc ( ; Freedman et al.m � M p 29.082001). Applying the same selection criteria as above, we canadd four more objects to the sample and apply the same spectralanalysis.

The result of the test is displayed in Figure 2, which showsa surprisingly tight correlation, as predicted by equation (1).The linear regression coefficients are anda p �3.85 b p

, the standard deviation of the residual bolometric mag-13.73nitude from this regression being mag. The objectsj p 0.26in NGC 3621 seem to indicate a somewhat smaller distancemodulus (by 0.2 mag) than adopted. However, we prefer towait for forthcoming stellar photometry of both NGC 300 andNGC 3621 with the Advanced Camera on board theHubbleSpace Telescope before we follow up on the relative distanceof these two galaxies.

4. OBJECTS FROM LOCAL GROUP GALAXIES

The small standard deviation obtained in Figure 2 might bean artifact resulting from the relatively low number of objects

Figure 1: from Kudritzki et al. (2003)

L83

The Astrophysical Journal, 582:L83–L86, 2003 January 10� 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.

A NEW EXTRAGALACTIC DISTANCE DETERMINATION METHOD USING THE FLUX-WEIGHTED GRAVITYOF LATE B AND EARLY A SUPERGIANTS1

Rolf P. Kudritzki, Fabio Bresolin, and Norbert PrzybillaInstitute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822;

kud@ifa.hawaii.edu; bresolin@ifa.hawaii.edu; norbert@ifa.hawaii.eduReceived 2002 October 16; accepted 2002 December 2; published 2002 December 6

ABSTRACT

Stellar evolution calculations predict the flux-weighted gravity and absolute bolometric magnitude of4g/Teff

blue supergiants to be strongly correlated. We use medium-resolution multiobject spectroscopy of late B andearly A supergiants in two spiral galaxies, NGC 300 and NGC 3621, to demonstrate the existence of such arelationship, which proves to be surprisingly tight. An analysis of high-resolution spectra of blue supergiants inLocal Group galaxies confirms this detection. We discuss the application of the relationship for extragalacticdistance determinations and conservatively conclude that once properly calibrated it has the potential to allowfor measurements of distance moduli out to 30.5 mag with an accuracy of 0.1 mag or better.

Subject headings: galaxies: distances and redshifts — galaxies: stellar content — stars: early-type

1. INTRODUCTION

Bright supergiants in external galaxies have been recognizedas valuable extragalactic distance indicators for a long time,since the pioneering work of Hubble (1936). A number ofworks have attempted to calibrate photometric and/or spectro-scopic signatures of blue supergiants (those of spectral typeOBA) for this purpose, but the uncertainty in the derived dis-tances (typically 0.4 mag or larger in distance modulus) hasalways been a major drawback for these techniques (Hum-phreys 1988; Tully & Wolff 1984).

The discovery of a wind momentum–luminosity relationship(WLR) for blue supergiants (Kudritzki & Puls 2000) exploitsthe dependency of the strength of the radiation-driven winds ofmassive stars on stellar luminosity, offering a potentially moreaccurate distance indicator. While hot O stars provide so far thebest calibration of the WLR (Puls et al. 1996, 2002), it is thevisually brightest late B and early A supergiants ( ) thatM � �9V

offer the largest potential as extragalactic standard candles (Ku-dritzki 1998; Kudritzki et al. 1999). This can now be investigatedfor the nearby galaxies ( Mpc) with multiobject spec-D ! 10troscopy at 8 m class telescopes, as the exploratory work ofBresolin et al. (2001, 2002) has shown. Quantitativespectroscopyof individual BA supergiants leads to the determination of grav-ities, temperatures, metallicities, and stellar wind parameters(based on the wind emission in Ha), which are then combinedto provide distances.

In this Letter, we suggest a novel method, based on theabsorption strengths of the higher Balmer lines formed in thephotosphere. The concept is not entirely new, since a relation-ship between the equivalent width of Hg and for GalacticMV

and Magellanic Cloud BA supergiants, together with a tem-perature dependence, has already been discussed by severalauthors (Petrie 1965; Crampton 1979; Tully & Wolff 1984;Hill, Walker, & Yang 1986). The recent improvements in themodeling of A supergiant atmospheres in non-LTE and thedevelopment of new diagnostic tools (Venn 1995a, 1995b,1999; Venn et al. 2000; Przybilla et al. 2001; Przybilla & Butler2001; Przybilla 2002) allow us to determine stellar parameterswith unprecedented accuracy and reliability. Based on theseachievements, we discuss here a promising application on a

1 Based on observations obtained at the ESO Very Large Telescope.

set of high- to intermediate-resolution spectra obtained for asample of A supergiants in the Milky Way, the MagellanicClouds, NGC 300, NGC 3621, and few additional objects ina handful of nearby galaxies. The theoretical concept is ex-plained in § 2, and we present the observational tests in §§ 3and 4. Future work on supergiants in nearby galaxies is brieflysummarized in § 5.

2. BASIC CONCEPT

Massive stars during their evolution toward the red super-giant stage pass through the phase of late B and early A su-pergiants quickly and with roughly constant mass and lumi-nosity (Meynet & Maeder 2000; Meynet et al. 1994; Heger &Langer 2000). This means that in this phase the stellar gravityg and effective temperature are coupled through the con-Teff

dition . We call the “flux-weighted gravity.”4 4g/T p const g/Teff eff

Assuming that mass and luminosity follow the usual relation( ), we derive a relationship between absoluteaL ∝ M a ∼ 3

bolometric magnitude and the flux-weighted gravity of theMbol

form

4�M p a log (g/T ) � b, (1)bol eff

with a of the order of�3.75. This means that for these spectraltypes the fundamental stellar parameters of effective temper-ature and gravity are tightly coupled to the absolute magnituderendering the possibility of purely spectroscopic distance de-termination. In the following, we refer to equation (1) as the“flux-weighted gravity–luminosity relationship” (FGLR).

Assuming constant luminosity and, in particular, a simple(one exponent) power law for the mass-luminosity relationshipis, of course, a simplification. One might argue that the mass-loss history of supergiants and its dependence on stellar angularmomentum and metallicity will complicate the situation. How-ever, we are encouraged by detailed evolutionary calculations(Meynet & Maeder 2000; Meynet et al. 1994), which indicatefor the luminosity and mass range of late B and early A su-pergiants that the amount of mass lost on the way from themain sequence is still relatively small and that differences inmass loss caused by stellar rotation and metallicity have nosubstantial effects on the theoretical FGLRs derived.

Table 1 lists the effective temperature scale for late B and

Figure 2: from Kudritzki et al. (2003)

2 November 24, 2009

L84 EXTRAGALACTIC DISTANCE DETERMINATION METHOD Vol. 582

TABLE 1Adopted Temperature

Scale

Spectral TypeTeff

(K)

B8 . . . . . . . . . . . . . . 12000B9 . . . . . . . . . . . . . . 10500A0 . . . . . . . . . . . . . . 9500A1 . . . . . . . . . . . . . . 9250A2 . . . . . . . . . . . . . . 9000A3 . . . . . . . . . . . . . . 8500A4 . . . . . . . . . . . . . . 8350

Fig. 1.—Fit of the Balmer lines Hg,d and H8 to H11 of the NGC 300 A0 Iasupergiant C6 (see Bresolin et al. 2002) using atmospheric models withT peff

K and (thick line) and 1.65 (thin line) (gravities given in cgs9500 logg p 1.60units). Note that the use of information from many Balmer lines enhances theaccuracy of the determination significantly. The FWHM of the instrumentallog gprofile is∼5 A, which is larger than the intrinsic width of the Balmer lines andthe line broadening through rotation (typically≤50 km s�1 for A supergiants).Therefore, the calculations are convolved with the instrumental profile. Thisexplains why gravity effects cannot be seen in the line wings but only in thecores. These effects in the line cores reflect the changes of the integrated ab-sorption-line strength (equivalent width) as a function of gravity.

Fig. 2.—Absolute bolometric magnitude vs. logarithm of flux-weightedgravity of B8 to A4 supergiants in NGC 300 and NGC 3621. Note thatTeff

is used in units of 104 K.

early A supergiants based on the recent quantitative spectro-scopic work cited above. We conclude that spectral classifi-cation allows for a temperature determination with a relativeaccuracy of about 4%. Then, for a given spectral type (andeffective temperature) the higher Balmer lines as typical pho-tospheric absorption lines allow for a rather precise determi-nation of the gravity even for only medium-resolution spectraof faint and distant objects (see Fig. 1). Assuming a typicalrelative uncertainty of 0.05 for , we estimate the uncer-log gtainty in from equation (1) to be about 0.3 mag for a singleMbol

object. This is a very encouraging estimate. Note that at thispoint we do not have to worry about absolute errors in thedetermination ofg and , as long as we calibrate the methodTeff

with a stellar sample at a known distance and apply the methodstrictly differentially.

3. SUPERGIANTS IN NGC 300 AND NGC 3621

Recently, Bresolin et al. (2002) studied the population of bluesupergiants in the Sculptor group spiral galaxy NGC 300 at adistance of∼2.0 Mpc ( ; Freedman et al. 2001).m � M p 26.53Using FORS1 at the Very Large Telescope (VLT), medium-resolution (∼5 A) spectra of 70 blue supergiant candidates wereobtained and spectral types, magnitudes, and colors (the latterbased on the work by Pietrzyn´ski et al. 2001) for 62 objectswere presented. These observations provide the ideal data for acareful test of the new method.

In our analysis, we restrict ourselves to objects where wecan be sure that the higher Balmer lines (Hg, Hd, etc.) are notcontaminated by Hii region emission; i.e., we avoid objectswith a clear indication of nebular Ha emission or with a hintof nebular emission at Hg above or below the two-dimensionalstellar spectrum. In addition, we select only spectral typeswithin a narrow range between B8 and A4, where we knowfrom our recent work (Przybilla et al. 2001; Przybilla & Butler2001; Przybilla 2002) that our model atmosphere analysis toolsare very reliable, in particular with regard to the relative ac-curacy of a strictly differential study. For the given spectraltypes, we adopt effective temperatures according to Table 1and determine gravities from the higher Balmer lines as dis-played in Figure 1. We then calculate intrinsic colors with ourmodel atmosphere code to determine reddening and extinctionand use the calculated bolometric correction and the distancemodulus to obtain bolometric magnitudes.

The data set for NGC 300 is not the only one available tous. In a similar way, Bresolin et al. (2001) have used FORS1at the VLT to study 17 objects in the spiral galaxy NGC 3621at a distance of 6.7 Mpc ( ; Freedman et al.m � M p 29.082001). Applying the same selection criteria as above, we canadd four more objects to the sample and apply the same spectralanalysis.

The result of the test is displayed in Figure 2, which showsa surprisingly tight correlation, as predicted by equation (1).The linear regression coefficients are anda p �3.85 b p

, the standard deviation of the residual bolometric mag-13.73nitude from this regression being mag. The objectsj p 0.26in NGC 3621 seem to indicate a somewhat smaller distancemodulus (by 0.2 mag) than adopted. However, we prefer towait for forthcoming stellar photometry of both NGC 300 andNGC 3621 with the Advanced Camera on board theHubbleSpace Telescope before we follow up on the relative distanceof these two galaxies.

4. OBJECTS FROM LOCAL GROUP GALAXIES

The small standard deviation obtained in Figure 2 might bean artifact resulting from the relatively low number of objects

Figure 3: from Kudritzki et al. (2003)

L84 EXTRAGALACTIC DISTANCE DETERMINATION METHOD Vol. 582

TABLE 1Adopted Temperature

Scale

Spectral TypeTeff

(K)

B8 . . . . . . . . . . . . . . 12000B9 . . . . . . . . . . . . . . 10500A0 . . . . . . . . . . . . . . 9500A1 . . . . . . . . . . . . . . 9250A2 . . . . . . . . . . . . . . 9000A3 . . . . . . . . . . . . . . 8500A4 . . . . . . . . . . . . . . 8350

Fig. 1.—Fit of the Balmer lines Hg,d and H8 to H11 of the NGC 300 A0 Iasupergiant C6 (see Bresolin et al. 2002) using atmospheric models withT peff

K and (thick line) and 1.65 (thin line) (gravities given in cgs9500 logg p 1.60units). Note that the use of information from many Balmer lines enhances theaccuracy of the determination significantly. The FWHM of the instrumentallog gprofile is∼5 A, which is larger than the intrinsic width of the Balmer lines andthe line broadening through rotation (typically≤50 km s�1 for A supergiants).Therefore, the calculations are convolved with the instrumental profile. Thisexplains why gravity effects cannot be seen in the line wings but only in thecores. These effects in the line cores reflect the changes of the integrated ab-sorption-line strength (equivalent width) as a function of gravity.

Fig. 2.—Absolute bolometric magnitude vs. logarithm of flux-weightedgravity of B8 to A4 supergiants in NGC 300 and NGC 3621. Note thatTeff

is used in units of 104 K.

early A supergiants based on the recent quantitative spectro-scopic work cited above. We conclude that spectral classifi-cation allows for a temperature determination with a relativeaccuracy of about 4%. Then, for a given spectral type (andeffective temperature) the higher Balmer lines as typical pho-tospheric absorption lines allow for a rather precise determi-nation of the gravity even for only medium-resolution spectraof faint and distant objects (see Fig. 1). Assuming a typicalrelative uncertainty of 0.05 for , we estimate the uncer-log gtainty in from equation (1) to be about 0.3 mag for a singleMbol

object. This is a very encouraging estimate. Note that at thispoint we do not have to worry about absolute errors in thedetermination ofg and , as long as we calibrate the methodTeff

with a stellar sample at a known distance and apply the methodstrictly differentially.

3. SUPERGIANTS IN NGC 300 AND NGC 3621

Recently, Bresolin et al. (2002) studied the population of bluesupergiants in the Sculptor group spiral galaxy NGC 300 at adistance of∼2.0 Mpc ( ; Freedman et al. 2001).m � M p 26.53Using FORS1 at the Very Large Telescope (VLT), medium-resolution (∼5 A) spectra of 70 blue supergiant candidates wereobtained and spectral types, magnitudes, and colors (the latterbased on the work by Pietrzyn´ski et al. 2001) for 62 objectswere presented. These observations provide the ideal data for acareful test of the new method.

In our analysis, we restrict ourselves to objects where wecan be sure that the higher Balmer lines (Hg, Hd, etc.) are notcontaminated by Hii region emission; i.e., we avoid objectswith a clear indication of nebular Ha emission or with a hintof nebular emission at Hg above or below the two-dimensionalstellar spectrum. In addition, we select only spectral typeswithin a narrow range between B8 and A4, where we knowfrom our recent work (Przybilla et al. 2001; Przybilla & Butler2001; Przybilla 2002) that our model atmosphere analysis toolsare very reliable, in particular with regard to the relative ac-curacy of a strictly differential study. For the given spectraltypes, we adopt effective temperatures according to Table 1and determine gravities from the higher Balmer lines as dis-played in Figure 1. We then calculate intrinsic colors with ourmodel atmosphere code to determine reddening and extinctionand use the calculated bolometric correction and the distancemodulus to obtain bolometric magnitudes.

The data set for NGC 300 is not the only one available tous. In a similar way, Bresolin et al. (2001) have used FORS1at the VLT to study 17 objects in the spiral galaxy NGC 3621at a distance of 6.7 Mpc ( ; Freedman et al.m � M p 29.082001). Applying the same selection criteria as above, we canadd four more objects to the sample and apply the same spectralanalysis.

The result of the test is displayed in Figure 2, which showsa surprisingly tight correlation, as predicted by equation (1).The linear regression coefficients are anda p �3.85 b p

, the standard deviation of the residual bolometric mag-13.73nitude from this regression being mag. The objectsj p 0.26in NGC 3621 seem to indicate a somewhat smaller distancemodulus (by 0.2 mag) than adopted. However, we prefer towait for forthcoming stellar photometry of both NGC 300 andNGC 3621 with the Advanced Camera on board theHubbleSpace Telescope before we follow up on the relative distanceof these two galaxies.

4. OBJECTS FROM LOCAL GROUP GALAXIES

The small standard deviation obtained in Figure 2 might bean artifact resulting from the relatively low number of objects

Figure 4: from Kudritzki et al. (2003)

3 November 24, 2009

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Figure 5: from Kudritzki et al. (2008a)

4 November 24, 2009

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ed

egen

eracyo

fsu

cha

relation

ship

with

me

tallicity.F

ortu

nately,a

way

ou

to

fth

isd

ilemm

ais

the

use

of

the

spectralen

ergy

distribu

tion

s(S

ED

s)an

dh

ere,in

particu

laro

fth

eB

almer

jum

pDB .W

hile

the

ob

servedp

ho

tom

etryfro

mB

-ban

dto

I-ban

dis

used

toco

nstrain

the

interstellar

redd

enin

g,DB

turn

so

ut

tob

ea

reliable

temp

erature

diag

no

stic,as

isin

di

catedb

yF

ig.1.A

simu

ltaneo

us

fitofth

eB

almer

lines

and

the

Balm

erju

mp

allows

toco

nstrain

effec-tive

temp

erature

and

gravity

ind

epen

den

tofassu

mp

tion

so

nm

etallicity.Fig

.2d

emo

nstrates

the

sensitivity

ofth

eB

almer

lines

and

the

Balm

erju

mp

tog

ravity

and

effectivetem

peratu

re,respec-

tively.A

ta

fixedtem

peratu

reth

eB

almer

lines

allowfo

ra

det

ermin

ation

oflog

gw

ithin

0.0

5d

exu

ncertain

ty,wh

ereasth

eB

almer

jum

pata

fixedg

ravityyi

elds

atem

peratu

reu

ncertain

tyo

f2

percen

t.H

owever,

since

the

isoco

nto

urs

inF

ig.1

aren

ot

or

tho

go

nal,th

em

aximu

merro

rso

fT

eff an

dlog

gare

5p

ercent

and

0.2

dex,

respectively.

Th

eseerro

rsare

sign

ificantly

larger

than

for

the

analysis

of

hig

hreso

lutio

nsp

ectra,bu

tth

eystillallow

for

anaccu

rated

etermin

ation

of

metallicity

and

distan

ces.T

he

accurate

determ

inatio

no

fT

eff an

dlog

gis

crucialfo

rth

eu

seo

fAsu

perg

iants

asd

istance

ind

icators

usin

gth

erelatio

nsh

ipb

etween

abso

lute

bo

lom

etric

mag

nitu

deM

bo

l and

flux

weig

hted

gravity

logg

Fd

efined

as

logg

F=

logg−

4logTe

ff,4(4

.1)

wh

ereTe

ff,4 =T

eff /1

00

00

K(see

Ku

dritzki,B

resolin

&P

rzybilla

20

03).T

he

relatively

large

un

-certain

tieso

btain

edw

ithth

isfit

meth

od

may

castsd

ou

bts

wh

etherlog

gF

canb

eo

btain

edac-

curately

eno

ug

h.

Fo

rtun

ately,th

en

on

-orth

og

on

albeh

aviou

ro

fth

efit

curves

inth

eleft

part

of

Fig

.1lead

sto

errors

inTeff an

dlog

g,wh

ichare

correlated

ina

way

thatred

uces

the

un

certaintie

so

flogg

F .Th

isis

dem

on

stratedin

righ

tparto

fFig

.1,wh

ichsh

ows

the

corresp

on

din

gfitcu

rveso

fth

eB

almer

lines

and

DBin

the

(logg

F,log

Teff )

plan

e.A

sa

con

sequ

ence,m

uch

smaller

un

-certain

tiesare

ob

tained

forlog

gF ,

nam

ely±0

.10

dex.

KU

BG

Pg

ivea

detailed

discu

ssion

of

ph

ysicalreason

beh

ind

this.

Figure

2.Left:

Modelatm

ospherefitof

two

observedB

almer

linesof

NG

C300

target

No.

21of

KU

BG

Pfor

Teff =

10000K

andlogg

=1.55

(solid).Two

additionalmodels

with

same

Teff butlog

g=

1.45and

1.65,respectively,

arealso

shown

(dashed).R

ight:M

odelatm

ospherefit

ofthe

observedB

almer

jump

ofthe

same

targetforTeff =

10000K

andlogg

=1.55

(solid).Two

additionalmodels

with

thesam

elog

gbutTe

ff =9750

K(dashed)

and10500

K(dotted)

arealso

shown.T

hehoriz

ontalbarat3600A

representsthe

averageofthe

fluxlogarithm

overthis

wavelength

interval,which

isused

tom

easureDB .

Figure 6: from Kudritzki et al. (2008a)

5 November 24, 2009

Extrag

ala

cticS

tella

rA

stron

om

y5

Kn

owin

gth

estellaratm

osp

heric

param

etersT

eff an

dlogg

KU

BG

Pare

able

tod

etermin

estellar

metallicities

by

fitting

the

metallin

esw

ithth

eirco

mp

rehe

nsive

grid

of

line

form

ation

calcula-

tion

s.Th

efitp

roced

ure

pro

ceeds

inseveralstep

s.First,spectralw

ind

ows

ared

efined

,for

wh

icha

go

od

defin

ition

of

the

con

tinu

um

isp

ossib

lean

dw

hich

arere

lativelyu

nd

isturb

edb

yflaw

sin

the

spectru

m(fo

rin

stance

caused

by

cosm

iceven

ts)o

rin

terstellar

emissio

nan

dab

sorp

tion

.Atyp

icalspectralw

ind

owu

sedfo

ralltarg

etsis

the

wavelen

gth

interval4

49

7A6

λ6

46

07

A.

Fig

.3sh

ows

the

synth

eticsp

ectrum

calculated

for

the

atmo

psh

ericp

arameters

of

target

No

.2

1(th

ep

reviou

sexam

ple)

and

for

allthe

metallicities

ofth

eg

ridran

gin

gfro

m-1

.306

[Z]6

0.3

0.

Itisvery

obvio

us

thatth

estren

gth

so

fthe

metallin

efeatu

res

area

stron

gfu

nctio

no

fmetallicity.

InF

ig.4

the

ob

servedsp

ectrum

of

targetN

o.2

1in

this

spectr

alregio

nis

show

noverp

lotted

by

the

synth

eticsp

ectrum

for

eachm

etallicity.Sep

aratep

lot

sare

used

for

eachm

etallicity,becau

seth

eo

ptim

alrelativen

orm

alization

ofth

eo

bserved

and

calcu

latedsp

ectrais

obvio

usly

metallicity

dep

end

ent.T

his

pro

blem

isad

dressed

by

reno

rmalizin

gth

eo

bserved

spectru

mfo

reach

metal-

licityso

that

the

synth

eticsp

ectrum

always

intersects

the

ob

servation

sat

the

same

value

atth

etw

oed

ges

of

the

spectral

win

dow

(ind

icatedb

yth

ed

ashed

vertical

lines).

Th

en

extstep

isa

pixel-b

y-pixelco

mp

arison

ofcalcu

latedan

dn

orm

alizedo

bserved

fluxes

foreach

metallicity

and

acalcu

lation

of

a χ2-valu

e.Th

em

inim

umχ

([Z])as

afu

nctio

no

f[Z]is

then

used

tod

etermin

eth

em

etallicity.Th

isis

alsosh

own

inF

ig.4

.A

pp

lication

of

the

same

meth

od

on

differen

tspec-

tralwin

dow

sp

rovides

add

ition

alind

epen

den

tinfo

rmatio

no

nm

etallicityan

dallow

sto

determ

ine

the

average

metallicity

ob

tained

from

allwin

dow

s.A

value

of

is[Z

]=

-0.3

9w

itha

verysm

alld

ispersio

no

fon

ly0

.02

dex.H

owever,o

ne

alson

eedto

con

siderth

eeffects

ofth

estellar

param

e-ter

un

certainties

on

the

metallicity

determ

inatio

n.T

his

is

do

ne

by

app

lying

the

same

correlatio

nm

etho

dfo

r[Z

]for

mo

dels

atth

eextrem

eso

fth

eerro

rb

ox

for

Te

ff and

logg.T

his

increases

the

un

certainty

of[Z

]to±0

.15

dex,stilla

veryreaso

nab

leaccu

racyo

fthe

abun

dan

ced

etermin

ation

.T

he

fito

fth

eo

bserved

ph

oto

metric

fluxes

with

the

mo

delatm

os

ph

ereflu

xesw

asu

sedto

de-

termin

ein

terstellarred

den

ing

E(B

-V)

and

extinctio

nA

V=

3.1

E(B

-V).

Sim

ultan

eou

sly,th

efit

alsoyield

sth

estellaran

gu

lardiam

eter,wh

ichp

rovides

the

stellarradiu

s,ifad

istance

isad

op

ted.

Altern

atively,for

the

stellarp

arameters

(T

eff ,log

g,[Z])

determ

ined

thro

ug

hth

esp

ectralanalysis

the

mo

delatm

osp

heres

alsoyield

bo

lom

etricco

rrection

sB

C,

wh

ichw

eu

seto

determ

ine

bo

lo-

metric

mag

nitu

des.T

hese

bo

lom

etricm

agn

itud

esth

enalso

allow

us

toco

mp

ute

radii.T

he

radii

determ

ined

with

these

two

differen

tmeth

od

sag

reew

ithin

af

ewp

ercent.

Gieren

etal.(2

00

5a)

Figure

3.Synthetic

metalline

spectracalculated

forthe

stellarpar

ameters

oftargetNo.21

asa

functionof

metallicity

inthe

spectralw

indowfrom

4497Ato

4607A

.M

etallicitiesrange

from[Z

]=

-1.30to

0.30,as

describedin

thetext.

The

dashedvertical

linesgive

thee

dgesof

thespectral

window

asused

fora

determination

ofmetallicity.

Figure 7: synthetic spectra vs metallicity from Kudritzki et al. (2008a)

6 November 24, 2009

6R

olfK

ud

ritzki,Mig

uelA

.Urb

aneja,F

abio

Breso

lin&

No

rbertP

rzybilla

inth

eirm

ulti-w

aveleng

thstu

dy

ofa

large

samp

leo

fCep

heid

sin

NG

C3

00

inclu

din

gth

en

ear-IRh

aved

etermin

eda

new

distan

cem

od

ulu

sm

-M=

26

.37

mag

,wh

ichco

rrespo

nd

sto

ad

istance

of

1.8

8M

pc.K

UB

GP

have

ado

pted

these

values

too

btain

the

radii

and

abso

lute

mag

nitu

des.

5.A

Pilot

Studyin

NG

C300

-R

esultsA

sa

firstresu

lt,th

eq

uan

titativesp

ectrosco

pic

meth

od

yield

sin

terstellarred

den

ing

and

ex-tin

ction

asa

by-p

rod

ucto

fthe

analysis

pro

cess.Fo

ro

bject

sem

bed

ded

inth

ed

usty

disk

ofa

starfo

rmin

gsp

iralgalaxy

on

eexp

ectsa

wid

eran

ge

of

interstell

arred

den

ing

E(B

-V)

and

,ind

eed,a

rang

efro

mE

(B-V

)=

0.0

7m

agu

pto

0.2

4m

agw

asfo

un

d.T

he

ind

ivid

ualred

den

ing

values

aresig

nifican

tlylarg

erth

anth

evalu

eo

f0

.03

mag

ado

pted

inth

eH

ST

distan

cescale

keyp

roject

stud

yo

fC

eph

eids

by

Freed

man

etal.(2

00

1)an

dd

emo

nstrate

th

en

eedfo

ra

reliable

redd

en-

ing

determ

inatio

nfo

rstellar

distan

cein

dicato

rs,atleastas

lon

gth

estu

dy

isrestricted

too

ptical

wavelen

gth

s.T

he

average

overth

eo

bserved

samp

leis

〈E(B−

V)〉

=0

.12

mag

inclo

seag

ree-m

entw

ithth

evalu

eo

f0.1

mag

fou

nd

by

Gieren

etal.(2

00

5a)inth

eirop

ticalton

ear-IRstu

dy

of

Cep

heid

sin

NG

C3

00

.Wh

ileC

eph

eids

have

som

ewh

atlower

mass

esth

anth

eA

sup

ergian

tso

fo

ur

stud

yan

dare

con

sequ

ently

som

ewh

atold

er,they

no

neth

eless

belo

ng

toth

esam

ep

op

ulatio

nan

dare

fou

nd

atsimilar

sites.Th

us,o

ne

expects

them

tob

eaf

fectedb

yin

terstellarred

den

ing

inth

esam

ew

ayas

Asu

perg

iants.

Fig

.5sh

ows

the

locatio

no

fall

the

ob

servedtarg

etsin

the

(logg,log

Teff )

plan

ean

din

the

HR

Dco

mp

aredto

the

earlyB

-sup

ergian

tsstu

died

by

Urb

aneja

etal.(2

00

5).T

he

com

pariso

nw

ithevo

lutio

nary

tracksg

ivesa

firstind

ication

ofth

estellar

masses

ina

rang

efro

m1

0M⊙ to

40

M⊙

.T

hree

targets

have

obvio

usly

hig

her

masses

than

the

resto

fth

esam

ple

and

seemto

be

on

asim

ilarevo

lutio

nary

trackas

the

ob

jectsstu

died

by

Urb

aneja

etal.(2

00

5).T

he

evolu

tion

aryin

form

ation

ob

tained

from

the

two

diag

rams

app

earsto

be

con

sistent.

Th

eB

-sup

ergian

tsseem

tob

em

ore

massive

than

mo

sto

fth

eA

sup

ergian

ts.T

he

same

thr

eeA

sup

ergian

tsap

paren

tlym

ore

massive

than

the

restb

ecause

of

their

lower

gravities

are

alsoth

em

ost

lum

ino

us

ob

jects.T

his

con

firms

that

qu

antitative

spectro

scopy

is-at

leastq

ualitatively

-cap

able

toretrieve

the

info

rmatio

nab

ou

tabso

lute

lum

ino

sities.No

teth

atth

efac

tthat

allthe

Bsu

perg

iants

stud

iedb

yU

rban

ejaetal.

(20

05)

arem

ore

massive

issim

ply

aselectio

neffecto

fthe

Vm

agn

itud

elim

itedsp

ectrosco

pic

survey

by

Breso

linetal.

(20

02).

At

similar

Vm

agn

itud

eas

the

Asu

perg

iants

tho

seo

bjects

have

hig

her

bo

lom

etricco

rrection

sb

ecause

of

their

hig

her

effectivetem

peratu

resan

dare,th

erefore,m

ore

lum

ino

us

and

massive.

Fig

.6sh

ows

the

stellarmetallicities

and

the

metallicity

grad

ientas

afu

nctio

no

fang

ularg

alac-

Figure

4.Left:

Observed

spectrumoftargetN

o.21for

thesam

espectralw

indow

asF

ig.3overplotted

bythe

same

syntheticspectra

foreach

metallicity

separately.R

ight: χ([Z

])as

obtainedfrom

thecom

parisonofobserved

andcalculated

spectra.The

solidcurve

isa

third

orderpolynom

ialfit.

Figure 8: Metallicity estimation, from Kudritzki et al. (2008a)

7 November 24, 2009

Model atmospheres

1102 N. Przybilla et al.: Quantitative spectroscopy of BA-type supergiants

Excellent agreement with vrad data from the literature (seeTable 2) was found. Representative parts of the spectra aredisplayed in Fig. 1.

3. Model atmospheres

Model atmospheres are a crucial ingredient for solving the in-verse problem of quantitative spectroscopy. Ideally, BA-SGsshould be described by unified (spherically extended, hydro-dynamical) non-LTE atmospheres, accounting for the effectsof line blanketing. Despite the progress made in the last threedecades, such model atmospheres are still not available for rou-tine applications. In the following we investigate the suitabilityof existing models for our task, their robustness for the applica-tions and their limitations. The criterion applied in the end willbe their ability to reproduce the observations in a consistentway.

3.1. Comparison of contemporary model atmospheres

Two kinds of classical (plane-parallel, hydrostatic and sta-tionary) model atmospheres are typically applied in the con-temporary literature for analyses of BA-SGs: line-blanketedLTE atmospheres and non-LTE H+He models (without line-blanketing) in radiative equilibrium. First, we discuss what ef-fects these different physical assumptions have on the modelstratification and on synthetic profiles of important diagnosticlines. We therefore include also an LTE H+He model with-out line-blanketing and additionally a grey stratification in thecomparison for two limiting cases: the least and the most lu-minous supergiants of our sample, ηLeo and HD 92207, ofluminosity class (LC) Ib and Iae. The focus is on the photo-spheric line-formation depths, where the classical approxima-tions are rather appropriate – the velocities in the plasma re-main sub-sonic, the spatial extension of this region is small(only a few percent) compared to the stellar radius in mostcases, and the BA-SGs photospheres retain their stability overlong time scales, in contrast to their cooler progeny, the yellowsupergiants, which are to be found in the instability strip of theHertzsprung-Russell diagram, or the Luminous Blue Variables.

The non-LTE models are computed using the code Tlusty(Hubeny & Lanz 1995), the LTE models are calculated withAtlas9 (Kurucz 1993), in the version of M. Lemke, asobtained from the CCP7 software library, and with furthermodifications (Przybilla et al. 2001b) where necessary. Lineblanketing is accounted for by using solar metallicity opacitydistribution functions (ODFs) from Kurucz (1992). For the greytemperature structure, T 4 = 3

4 T 4eff [τ+q(τ)], exact Hopf param-

eters q(τ) (Mihalas 1978, p. 72) are used.In Fig. 2 we compare the model atmospheres, represented

by the temperature structure and the run of electron numberdensity ne. For the less-luminous supergiant marked differencesin the line-formation region (for metal lines, typically betweenRosseland optical depth −1 <∼ log τR <∼ 0) occur only be-tween the line-blanketed model, which is heated due to thebackwarming effect by <∼200 K, and the unblanketed models.In particular, it appears that non-LTE effects on the atmosphericstructure are almost negligible, reducing the local temperature

by <∼50 K. The good agreement of the grey stratification andthe unblanketed models indicates that Thomson scattering islargely dominating the opacity in these cases. A temperaturerise occurs in the non-LTE model because of the recombi-nation of hydrogen – it is an artefact from neglecting metallines. The gradient of the density rise with atmospheric depthis slightly flatter in the line-blanketed model. In the case ofthe highly luminous supergiant, line-blanketing effects retaintheir importance (heating by <∼300 K), but non-LTE also be-comes significant (cooling by <∼200 K). From the comparisonwith observation it is found empirically, that a model with themetal opacity reduced by a factor of 2 (despite the fact thatthe line analysis yields near-solar abundances) gives an over-all better agreement. This is slightly cooler than the model forsolar metal abundance and may be interpreted as an empiricalcorrection for unaccounted non-LTE effects on the metal blan-keting in the most luminous objects, i.e. βOri and HD 92207in the present case. The local electron number density in theline-blanketed case is slightly lower than in the unblanketedmodels. We conclude from this comparison that at photosphericline-formation depths the importance of line blanketing out-weighs non-LTE effects, with the rôle of the latter increasingtowards the Eddington limit, as expected. In the outermost re-gions the differences between the individual models becomemore pronounced. However, none of the stratifications can beexpected to give a realistic description of the real stellar at-mosphere there, as spherical extension and velocity fields areneglected in our approach.

The results of spectral line modelling depend on the de-tails of the atmospheric structure and different line strengthsresult from computations based on the different stratifica-tions. Therefore, non-LTE line profiles for important stellarparameter indicators are compared in Fig. 3: Hδ as a rep-resentative for the gravity-sensitive Balmer lines, a typicalHe i line, and features of Mg i/ii, which are commonly usedfor the Teff-determination. In the case of the Balmer and theMg ii lines discrimination is only possible between the line-blanketed and the unblanketed models. Both the LTE and non-LTE H+He model structure without line blanketing result inpractically the same profiles. This changes for the lines of He iand Mg i, which react sensitively to modifications of the atmo-spheric structure: all the different models lead to distinguish-able line profiles. These differences become more pronouncedat higher luminosity.

This comparison of model structures and theoretical lineprofiles is instructive, but the choice of the best suited modelcan only be made from a confrontation with observation. Itis shown later that the physically most sophisticated approachavailable at present, LTE with line blanketing plus non-LTEline formation and appropriately chosen parameters, allowshighly consistent analyses of BA-SGs to be performed. Thisis discussed next.

3.2. Effects of helium abundance and line blanketing

Helium lines become visible in main sequence stars at thetransition between A- and B-types at Teff ∼ 10 000 K.

Figure 9: Details of model atmospheres used, from Przybilla et al. (2006)

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galactic Distances Theoretical Concepts, in Lecture Notes in Physics, Berlin Springer Verlag, Vol.635, Stellar Candles for the Extragalactic Distance Scale, ed. D. Alloin & W. Gieren, 123–148

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