NGC 2403
Bresolin et al.

The metallicity and distance of NGC 2403 from blue supergiants

Fabio Bresolin
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
0000-0002-5068-9833]Fabio Bresolin
Institute for Astronomy, University of Hawaii

2680 Woodlawn Drive

Honolulu, HI 96822, USA

Rolf-Peter Kudritzki
Institute for Astronomy, University of Hawaii

2680 Woodlawn Drive

Honolulu, HI 96822, USA
University Observatory Munich, Scheinerstr. 1, D-81679 Munich, Germany

0000-0002-9424-0501]Miguel A. Urbaneja
Institut für Astro- und Teilchenphysik, Universität Innsbruck

Technikerstr. 25/8, 6020 Innsbruck, Austria

We present the first quantitative spectral analysis of blue supergiant stars in the nearby galaxy NGC 2403. Out of a sample of 47 targets observed with the LRIS spectrograph at the Keck I telescope we have extracted 16 B- and A-type supergiants for which we have data of sufficient quality to carry out a comparison with model spectra of evolved massive stars and infer the stellar parameters.
The radial metallicity gradient of NGC 2403 that we derive has a slope of
$-0.14\, (\pm 0.05)$ dex $r_e^{-1}$, and is in accordance with the analysis of  region oxygen abundances. We present evidence that the stellar metallicities that we obtain in extragalactic systems in general agree with the nebular abundances based on the analysis of the auroral lines, over more than one order of magnitude in metallicity.
Adopting the known relation between stellar parameters and intrinsic luminosity we find a distance modulus $\mu = 27.38 \pm 0.08$ mag. While this can be brought into agreement with Cepheid-based determinations, it is 0.14 mag short of the value measured from the tip of the red giant branch.
We update the mass-metallicity relation secured from chemical abundance studies of stars in resolved star-forming galaxies.

§ INTRODUCTION

Massive evolved stars, known as blue supergiants, can be used to trace the distribution of metals in nearby ($D$ $<$ 10 Mpc) galaxies, by probing their surface chemical composition. The spectroscopy of individual massive stars thus affords a valuable and indispensable alternative to the emission-line analysis of the ionized gas, the long-established, standard technique used in countless studies of the near and distant universe, which unfortunately is still affected by significant and  poorly understood  systematic uncertainties (). The major drawback is represented by the relatively time-consuming observations needed to acquire high-quality stellar spectra, suitable for the quantitative analysis. On the other hand, the same spectroscopic data can yield information on the parent galaxy distances ().

A complementary approach to obtaining present-day chemical abundances, that involves the derivation of both gas-phase and stellar values, is essential in order to untangle the difficulties in establishing the metallicity scale of star-forming galaxies, with repercussions in our understanding of the complex evolutionary processes (such as chemical mixing and galactic flows) that are at work in such systems.

Following a series of papers dealing with the quantitative analysis of stellar spectra in nearly a dozen nearby galaxies presented by our team
over the course of the past two decades  (see , , , , and references therein), covering a wide range of galactic properties (stellar mass, metallicity), we focus here on the spiral galaxy NGC 2403.

Given its small distance ($D=3.19$ Mpc, ) and the relative ease of acquiring the photometry of individual luminous stars, NGC 2403 has appeared prominently in early studies of the bright stellar content of galaxies (), playing an important role in establishing the extragalactic distance scale ladder since the outset ().

Stellar candidates in NGC 2403 were among the first extragalactic supergiant stars to be confirmed spectroscopically in a pioneering effort by <cit.>.
More recently, <cit.> published a spectroscopic study of luminous stars in NGC 2403 and M81, aimed at the characterization of variable stars in the upper H-R diagram of these two galaxies.

In this paper we carry out the first quantitative analysis of blue supergiant () stars in NGC 2403. Our objectives are to measure the stellar metallicities, which we use to trace the radial metallicity gradient of the system, comparing it with the result obtained from  regions,
and to derive a spectroscopic distance to the galaxy. Our sample is
composed of 47 targets. We discuss the observations and the data reduction in Sect. 2, and characterize the stellar targets in Sect. 3, by estimating their spectral classification. In Sect. 4 we present the quantitative analysis of a subsample of 16 stars, which leads to the discussion of the galactocentric metallicity gradient and the comparison between stars and ionized gas (Sect. 5), the updated stellar mass-metallicity relation of nearby galaxies (Sect. 6) and the spectroscopic distance to NGC 2403 (Sect. 7). We conclude by summarizing our findings in Sect. 8.

§ OBSERVATIONS AND DATA REDUCTION

§.§ Target selection

Our targets are generally fainter than the more extreme, high-luminosity objects included in the work by <cit.> and other spectroscopic surveys of luminous and variable stars in NGC 2403 (). These investigations focus on stars that are typically brighter than , while approximately 80% of our targets are fainter than this limit. The brightest blue stars in NGC 2403 are spectroscopically confirmed late-type A supergiants, appearing around  (),  $M_B \simeq -9.2$. Our visually brightest spectroscopic target is also a late A supergiant star, at , and is not included in previous spectroscopic surveys of the stellar content of this galaxy.

Position of the spectroscopic targets in a $g$-band image of NGC 2403 taken from the Sloan Digital Sky Survey. The boxes represent the footprints of the ACS observations, source of the HST photometry. The different colors of the markers and labels are only used to enhance their visibility. The outer ring represents the projected circle having a radius equal to the isophotal radius .

Our target selection was carried out by identifying visually bright, blue candidates from two independent sources of optical photometry. For the central region of NGC 2403 we relied on Hubble Space Telescope (HST) data obtained with the Advanced Camera for Surveys (ACS), as analyzed by the ACS Nearby Galaxy Survey Treasury (ANGST) project ().
Two separate ACS Wide Field Camera pointings (see footprints in Fig. <ref>) yielded magnitudes in the filters F475W, F606W, F814W (Program 10182) and F435W, F606W (Program 10579). We adopted the Johnson-Cousins $B$ and $V$ magnitudes reported by the ANGST project. These values are included in Table <ref> (columns 7 and 8), where we summarize the positional, photometric and spectral class information of our spectroscopic targets.

At larger galactocentric distances, not covered by the HST programs, we adopted $ugi$ photometric measurements of stellar objects we obtained from observations carried out with the MegaPrime camera at the Canada-France-Hawaii Telescope (CFHT) on Mauna Kea in September 2007 under 1-arcsec seeing conditions.
The $g$ magnitudes and $g-i$ colors we measured are shown in Table <ref> (columns 7 and 8), using italicized numerals, to distinguish them from the published HST photometry.
We note that during the target selection process a few late-type stellar candidates were included in order to fill the spectroscopic multi-object masks, despite their red color indices.

Fig. <ref> shows the location of the 47 targets that were selected for the spectroscopic followup, using a publicly available Sloan Digital Sky Survey (SDSS) $g$-filter image. Their celestial coordinates, measured from this image, are presented in Table <ref>. Adopting the geometric parameters of the NGC 2403 disk
summarized in the footnote to Table <ref>, we calculated the galactocentric distances of the targets. In the Table these are reported normalized to both the isophotal (Column 4) and effective (Column 5) radii ( and , respectively), as well as in linear units (kpc, Column 6). Our targets sit well inside the isophotal radius of NGC 2403 (partially displayed in Fig. <ref>), extending radially between 0.05  and 0.72 .

Properties of the spectroscopic targets.

01        07  36  03.25        65  36  26.5        0.64        2.38        6.52      $\mathit{20.98}$      $\mathit{-0.36}$        B1        B17

02 $\ast$        07  36  07.44        65  37  51.8        0.49        1.80        4.93      $\mathit{20.41}$      $\mathit{-0.10}$        B9-A0        B20

03 $\ast$        07  36  11.48        65  38  00.3        0.44        1.61        4.41      $\mathit{20.21}$      $\mathit{-0.29}$        B7-B8        B19

04        07  36  15.73        65  37  25.8        0.40        1.47        4.04      $\mathit{20.99}$      $\mathit{-0.71}$        B4-B5        B16

05 $\ast$        07  36  18.76        65  39  27.4        0.46        1.69        4.63      $\mathit{20.86}$      $\mathit{-0.14}$        B3        B21

06        07  36  20.30        65  37  04.1        0.36        1.32        3.62              20.69               $-0.20$         HII region        B15

07        07  36  22.57        65  38  54.4        0.39        1.43        3.91      $\mathit{20.32}$      $\mathit{ 0.81}$        composite        B18

08 $\ast$        07  36  25.11        65  37  04.6        0.29        1.09        2.98              21.04               $ 0.09$         B0 Ib        B14

09        07  36  26.14        65  36  03.7        0.36        1.34        3.69              19.86               $-0.07$         B1        B11

10 $\ast$        07  36  29.30        65  36  45.0        0.26        0.95        2.60              20.60               $ 0.10$         B9        B12

11        07  36  30.56        65  37  19.6        0.23        0.84        2.31      $\mathit{20.96}$      $\mathit{-0.23}$        B2        B13

12        07  36  37.41        65  36  38.1        0.16        0.58        1.59              21.40               $ 0.16$         composite        B10

13        07  36  42.52        65  35  50.2        0.16        0.61        1.67              21.52               $ 0.21$         composite        B07

14        07  36  44.16        65  36  49.0        0.09        0.35        0.95              20.17               $ 0.01$         B2-B3        B09

15        07  36  46.47        65  35  58.4        0.09        0.34        0.93              21.36               $-0.07$         B1 Ib        B06

16 $\ast$        07  36  47.88        65  35  45.6        0.11        0.39        1.08              20.15               $ 0.24$         B4        A28

17        07  36  47.93        65  36  47.1        0.09        0.32        0.89              21.55               $ 0.10$         indeterminate        B08

18 $\ast$        07  36  48.02        65  35  36.2        0.13        0.48        1.33      $\mathit{18.38}$      $\mathit{ 0.21}$        A7-F0        A27

19        07  36  48.26        65  35  35.0        0.13        0.49        1.33              20.27               $ 0.14$         B7+WC        B05

20 $\ast$        07  36  48.67        65  36  45.0        0.09        0.31        0.86              20.07               $ 0.18$         B8-B9        A31

21        07  36  49.08        65  36  03.4        0.05        0.17        0.46              21.27               $ 0.16$         B3 Ib        A29

22        07  36  51.38        65  34  56.2        0.21        0.78        2.15              20.50               $ 0.31$         B4        B04

23 $\ast$        07  36  54.99        65  36  54.2        0.17        0.62        1.69              20.19               $-0.01$         B2        A30

24        07  36  55.80        65  34  10.5        0.31        1.14        3.14              20.63               $ 0.19$         B+WNL        A20

25 $\ast$        07  36  56.70        65  35  21.1        0.11        0.40        1.11              20.13               $ 0.23$         A3        A24

26        07  36  58.00        65  35  46.0        0.07        0.27        0.73              20.70               $-0.11$         O8-O9        A25

27        07  37  00.12        65  35  22.6        0.11        0.41        1.13              20.80               $-0.05$         B0        A23

28 $\ast$        07  37  00.40        65  34  41.4        0.20        0.74        2.04              20.55               $ 0.16$         A2        B02

29 $\ast$        07  37  01.38        65  34  26.2        0.24        0.88        2.41              20.03               $ 0.13$         B8        A19

30        07  37  01.77        65  35  21.1        0.12        0.45        1.24              21.02               $ 0.13$         B9-A0 Ib        B03

31        07  37  02.08        65  34  24.6        0.24        0.89        2.43              20.76               $-0.02$         B1-B2        B01

32        07  37  06.32        65  35  32.2        0.16        0.61        1.66              21.14               $ 0.28$         A1-A2        A22

33        07  37  06.70        65  35  20.3        0.17        0.61        1.69              20.83               $-0.02$         B0-B1        A21

34        07  37  07.57        65  32  44.5        0.49        1.79        4.92      $\mathit{20.91}$      $\mathit{-0.54}$        B1-B2 Ib        A12

35        07  37  13.86        65  34  59.4        0.24        0.90        2.47      $\mathit{20.94}$      $\mathit{-0.37}$        indeterminate        A17

36        07  37  15.36        65  32  09.9        0.55        2.03        5.57      $\mathit{20.92}$      $\mathit{ 1.22}$        indeterminate        A08

37        07  37  16.91        65  33  18.8        0.39        1.43        3.92      $\mathit{19.57}$      $\mathit{-0.31}$        B3+WN        A11

38 $\ast$        07  37  17.40        65  34  13.9        0.30        1.11        3.06      $\mathit{20.86}$      $\mathit{-0.30}$        A1-A2        A14

39        07  37  17.57        65  33  59.8        0.32        1.18        3.24      $\mathit{20.73}$      $\mathit{ 0.26}$        B7-B8        A13

40        07  37  17.98        65  35  33.5        0.32        1.17        3.21              20.53               $ 0.05$         B1 Ib        A18

41 $\ast$        07  37  18.34        65  34  56.4        0.29        1.09        2.98      $\mathit{20.67}$      $\mathit{-0.23}$        B7        A15

42        07  37  18.55        65  31  49.7        0.59        2.19        6.01      $\mathit{20.18}$      $\mathit{-0.17}$        B0        A06

43 $\ast$        07  37  20.74        65  32  50.6        0.45        1.66        4.57      $\mathit{20.01}$      $\mathit{-0.35}$        B1        A09

44        07  37  21.41        65  31  27.7        0.64        2.37        6.51      $\mathit{20.39}$      $\mathit{ 0.00}$        A0 III        A04

45        07  37  22.36        65  30  55.8        0.72        2.66        7.31      $\mathit{20.91}$      $\mathit{ 0.65}$        indeterminate        A03

46        07  37  27.46        65  31  05.2        0.69        2.54        6.97      $\mathit{20.64}$      $\mathit{-0.04}$        B3 Ib        A02

47 $\ast$        07  37  30.19        65  31  01.5        0.70        2.57        7.04      $\mathit{20.90}$      $\mathit{ 0.09}$        B8-B9 Ib        A01

Normalized galactocentric distances adopt the following disk geometry: i = 63 deg, PA = 124 deg (),  = 657 arcsec () and  = 178 arcsec (). Stars identified with the $\ast$ symbol are those analyzed in Sect. <ref>. Unless the luminosity class is specified, the spectra are consistent with the Ia class. Columns 7 and 8 report either the HST (non italicized) or the CFHT (italicized) photometry.

§.§ Spectroscopy

Spectra of the 47 targets were acquired with the Low Resolution Imaging Spectrometer (LRIS, ) at the Keck I telescope on 2010 Dec 31 – 2011 Jan 02. While both blue and red channel multi-object data were gathered, our paper only presents results based on the blue channel data, obtained with the 600/4000 grism, and covering the approximate wavelength range 3300–5600 Å. We took advantage of an identical setup earlier in 2010 for the spectroscopy of s in M81 (), a galaxy placed at a comparable distance to NGC 2403.

Two separate masks (A and B) were cut with 1.2 arcsec-wide slits, yielding a spectral resolution of $\sim$5 Å. The seeing conditions varied considerably throughout the course of the observing run, from 0.8 to 1.8 arcsec. In the course of the data analysis we decided to utilize only the images with the best image quality, around 1 arcsec , which limited the total effective integration time to 3 h (mask A) and 3.5 h (mask B), respectively.

The data reduction, carried out with iraf[iraf is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.], included the standard procedures of bias subtraction, flat field correction and wavelength calibration. Individual frames were registered and combined. The spectral extractions were finally normalized to unity for the subsequent steps: spectral classification and, when feasible, quantitative analysis. For convenience, Table <ref> (which is ordered by increasing RA) retains in its last column  the original nomenclature of the extracted spectra, which indicates the parent mask (A or B) and the running number of the slit.

At the wavelength of  (4340 Å) the signal-to-noise ratio of the final spectra peaks around S/N = 70  for the brightest target 18[For the remainder of the paper we will indicate our targets using the ID number in column 1 of Table <ref>, prepended by the hash symbol.] at $B=18.4$, decreasing to S/N $\simeq$ 40 at $B=20$ and S/N $\simeq$ 20 at $B=21$.

§ SPECTRAL CLASSIFICATION

For the MK classification of our targets we relied on the monograph by <cit.> and the associated digital spectral standard library (see ). Column 9 of Table <ref> summarizes our results, and shows that for several targets we could not successfully assign a spectral classification. We describe these cases as either `composite', where we can identify specific lines from multiple types, or `indeterminate', where such identification could not be carried out, possibly as a result of an inferior signal-to-noise ratio.
For targets that are considered to be bona fide stars the classification is often provided in terms of a range of types in Table <ref>, reflecting the intrinsic uncertainty in unequivocally assigning a spectral class ( due to weak lines and poor signal-to-noise ratio) and the independent assessment by two of the authors.

Nebular emission (either from localized  regions or diffuse ionized gas) is present in virtually all cases (the 3727 emission line is detected in all spectra), and heavy contamination of the low-order stellar Balmer lines (, ) is therefore common. One target 06 is an  region whose spectrum does not display stellar lines.

Examples of the stellar classification analysis. Each subpanel includes both the identification from Table <ref> (column 1) and the spectral type. The spectra are smoothed to a  resolution of 5 Å.
The main spectral features used for the classification are identified.

The comparison with the spectral standards, in particular the information contained in the line widths, yielded a Ia luminosity classification for the majority of the targets. The exceptions are represented by eight objects of class Ib and a single (foreground) class III star 44.

Three emission line stars (two type N and one type C Wolf-Rayet stars) are included in our target list – in all cases we can discern absorption lines arising from the presence of a companion.
The spectral class exhibited by the remaining bona fide stars ranges from O8-O9 26 to A7-F0 18: the photometric, color-based selection procedure we adopted proved quite effective in providing a sample of about 35 early-type, BA-type supergiants in NGC 2403 (more than 70% of the full spectroscopic sample). In Fig. <ref> we display a selection of spectra spanning the full range of spectral classes, and include the identification of the features used during the classification procedure.

We have two objects in common with <cit.>: their targets 10579-x1-3 (corresponding to our target 20) and 10182-pr-16 (our target 29). In the case of the former <cit.> indicate the presence of nebular emission superposed on top of stellar absorption, but do not provide an estimate of the  spectral class. We classify 20 as a B8-B9 supergiant.
We confirm the B8 supergiant classification assigned by <cit.> to the second star in common.
Both stars are included in the quantitative analysis that follows.

§ QUANTITATIVE ANALYSIS

For 16 of our targets (identified by the asterisk symbols in column 1 of Table <ref>) we were able to carry out a quantitative spectral analysis, aimed at deriving stellar parameters ( and ) and metallicities. The stellar metallicities, measured for supergiant stars in NGC 2403 for the first time, are compared in Sect. <ref> with the gas-phase metallicity of  regions in the same galaxy. In addition, the stellar parameters are employed in Sect. <ref> to obtain the distance to NGC 2403.

The technique we adopt to analyze the spectra of extragalactic s has been covered in detail in previous papers ( ). Here we provide a concise description of our method, which relies on comparing the observed, normalized stellar spectra to synthetic spectra of s.
Different grids of stellar models and line formation calculations are used for early B-type (B0–B4 for the stars in Table <ref>) and A-type (B7 and later) stars. Following <cit.>, we refer to these two groups as OB and BA supergiants, respectively.

OB supergiants – The model spectra of the early-type stars are calculated with the fastwind code (), which accounts for the presence of stellar winds in the expanding atmospheres of these hot objects.
We calculated a grid of non-LTE, line blanketed atmosphere models covering a large parameter space, namely effective temperatures () from 15,000 to 30,000 K,
surface gravities () corresponding to evolutionary stages extending from the main sequence to the Eddington limit,
and surface chemical compositions where the metallicity [Z] ranges from $-1.0$ to 0.3
dex. The line formation is also calculated by fastwind.

BA supergiants – In this case the grid of hydrostatic, line-blanketed model atmospheres described by <cit.> is adopted, covering wide ranges in  (7900–16,000 K),  (0.8–3.0 dex, cgs) and metallicity [$Z$] ($-$1.3 to 0.5 dex). We scale the abundance of the metals to the solar ratios, adopting the solar composition by <cit.>, except for oxygen, for which we refer to <cit.>.
The synthetic spectra are calculated in non-LTE, following <cit.>.

A $\chi^2$ minimization technique is used inside strategically selected wavelength ranges across the supergiant spectra in order to find the best-fitting values of ,  and [$Z$]. The Balmer lines (H4 to H10 are usable, given the observed wavelength range and spectral resolution)
provide the surface gravity diagnostic, once the stellar temperature value is established. As stated earlier, these lines are often contaminated by ionized gas emission, but thanks to the decreasing equivalent width of the emission component with increasing order of the line, we can generally make satisfactory model fits to  (H5) and higher-order lines. An example of Balmer line fitting is shown in Fig. <ref>.

1.15f3af3bFits of the model (red curve) to the observed (black curve) Balmer lines H4 to H10 for the A2 Ia star 28 (left) and the B1 Ia star 43 (right). The abscissa reports the distance in Å from the line center. Some moderate nebular line  contamination can be noticed in the case of the  (H4) line for 28, while for 43 the contamination is much stronger, affecting also  (H5).

Due to the relatively low spectral resolution and limited signal-to-noise ratio of our data, in order to measure the stellar metallicity we do not rely on individual spectral lines, but rather on the simultaneous
fit of various spectral features that are due to metals, as shown in Fig. <ref>.
It should be noted that in the case of the OB stars the metal lines found in the observed spectral range refer mostly to C, N and the $\alpha$ elements O, Mg and Si. For the BA stars the elements responsible for most of the metal lines are the $\alpha$ elements Mg, Si, Ti and the iron peak elements Cr and Fe. The overlap in atomic species represented in the spectra of OB and BA supergiants increases our confidence that the metallicities we assign to our targets are on the same absolute scale between the two groups, despite the differences in generating the models.

In order to complete the characterization of our targets, the
interstellar reddening value for each star is evaluated by comparing
the broad-band colors at our disposal ($B-V$, $u-g$, $g-i$) to the
spectral energy distribution of the best-fitting model. We adopt the
<cit.> extinction law with a total-to-selective
absorption coefficient $R_V$ = $A_V/$ = 3.2 and $R_g$ = $A_g/$E($u-g$) = 3.89 .
The best-fitting solution also provides the bolometric correction (BC), used to calculate the apparent bolometric magnitude .

In the case of the targets with CFHT photometry, we make use of the information from both color indices available to us. The adopted reddening is the average E*($u-g$) = 0.5 E($u-g$) + 0.6 E($g-i$), where the coefficient for the second term proceeds from simulations involving our model spectra and the Cardelli reddening law.
We only use either E($u-g$) or E($g-i$) in those cases where the photometry yields negative E($g-i$)
(41 and 05) or E($u-g$) (18) values, respectively.

Some of our targets are located inside  regions and, as a consequence, their photometry could be affected by line emission. However, in order to avoid severe nebular contamination of the stellar spectra, we have restricted our analysis to objects where this impact is minimal. For the most extreme cases we use the strengths of the emission lines relative to the stellar continuum in conjunction with the filter functions and estimate the potential effects on the broad-band photometry to be smaller than 0.01 mag.

Table <ref> summarizes the stellar parameters we have calculated for the 16 targets. The value of the flux-weighted gravity  = $\,-\, 4\log$(/10$^4$ K) in column 4 is used in Sect. <ref> for the derivation of the spectroscopic distance to NGC 2403. The errors quoted in the Table are obtained from the $\chi^2$ minimization technique () and, in the case of , the sensitivity of the model Balmer lines to variations in surface gravity.

The location of the s in the spectroscopic Hertzsprung-Russell diagram (reporting the distance-independent   log  – see ) is displayed in Fig. <ref>. Stellar tracks that allow for the effects of rotation, taken from <cit.>, are included in the diagram as a reference. From these evolutionary tracks we can infer stellar masses of our sample stars in the approximate range 15-40 , in line with findings from our previous investigations in nearby galaxies ( ).

1.15f4Fits of the model (red curve) to the observed (black curve) metal lines of stars 28 (type A2 Ia; at the top in each panel) and 38 (A1-A2 Ia; bottom) inside three wavelength windows. Lines from the main atomic species used to calculate the synthetic spectra are identified.

1.15f5Fits of the model (red curve) to the observed (black curve) metal lines of star 43 (type B1 Ia) inside five wavelength windows. Lines from the main atomic species used to calculate the synthetic spectra are identified.

Stellar parameters.

BC$_{\rm V}$

E(u $-$ g)

02         $10400\pm250$        $1.54\pm0.05$        $1.47\pm0.06$        $-0.37\pm0.10$        $19.56\pm0.14$      $\mathit{0.15\pm0.03}$      $\mathit{-0.27\pm0.05}$        B20

03         $12400\pm200$        $1.69\pm0.05$        $1.31\pm0.05$        $-0.29\pm0.06$        $18.84\pm0.07$      $\mathit{0.19\pm0.01}$      $\mathit{-0.64\pm0.05}$       B19

05         $18000\pm500$        $2.27\pm0.10$        $1.25\pm0.10$        $-0.21\pm0.10$        $18.34\pm0.13$      $\mathit{0.27\pm0.03}$      $\mathit{-1.48\pm0.05}$        B21

08         $28000\pm1000$       $2.94\pm0.10$        $1.15\pm0.10$        $-0.24\pm0.10$        $17.35\pm0.10$      $0.30\pm0.02$      $-2.72\pm0.05$        B14

10         $11000\pm150$        $1.65\pm0.05$        $1.48\pm0.05$        $-0.15\pm0.10$        $19.52\pm0.04$      $0.15\pm0.01$      $-0.48\pm0.03$        B12

16         $18000\pm500$        $2.12\pm0.10$        $1.10\pm0.10$        $0.02\pm0.10$       $17.06\pm0.13$      $0.38\pm0.03$      $-1.65\pm0.05$        A28

18         $7900\pm30$  	      $0.65\pm0.05$        $1.06\pm0.07$        $-0.22\pm0.10$        $17.45\pm0.11$      $\mathit{0.25\pm0.02}$      $\mathit{0.48\pm0.05}$        A27

20         $10250\pm250$        $1.45\pm0.05$        $1.41\pm0.06$        $-0.10\pm0.10$        $18.88\pm0.06$      $0.20\pm0.01$      $-0.34\pm0.05$        A31

23         $20000\pm500$        $2.25\pm0.10$        $1.05\pm0.10$        $-0.15\pm0.10$        $17.76\pm0.10$      $0.15\pm0.02$      $-1.97\pm0.05$      A30

25         $8750\pm100$  	      $1.17\pm0.05$        $1.41\pm0.08$        $0.00\pm0.10$       $19.23\pm0.05$      $0.19\pm0.01$      $-0.05\pm0.03$        A24

28         $8750\pm100$  	      $1.27\pm0.05$        $1.51\pm0.08$        $-0.15\pm0.10$        $19.88\pm0.05$      $0.14\pm0.01$      $-0.05\pm0.02$       B02

29         $10250\pm300$        $1.50\pm0.05$        $1.46\pm0.06$        $-0.05\pm0.15$        $19.05\pm0.07$      $0.16\pm0.01$      $-0.33\pm0.06$       A19

38         $9750\pm250$  	      $1.47\pm0.05$        $1.54\pm0.07$        $-0.22\pm0.10$        $20.23\pm0.14$      $\mathit{0.13\pm0.03}$      $\mathit{-0.14\pm0.05}$        A14

41         $13500\pm250$        $1.90\pm0.05$        $1.38\pm0.05$        $-0.33\pm0.10$        $18.95\pm0.07$      $\mathit{0.23\pm0.02}$      $\mathit{-0.82\pm0.03}$        A15

43         $23000\pm500$        $2.55\pm0.10$        $1.10\pm0.10$        $-0.25\pm0.10$        $17.03\pm0.13$      $\mathit{0.23\pm0.03}$      $\mathit{-2.10\pm0.05}$        A09

47         $10450\pm300$        $1.84\pm0.05$        $1.76\pm0.07$        $-0.35\pm0.10$        $19.52\pm0.17$      $\mathit{0.29\pm0.04}$      $\mathit{-0.26\pm0.06}$        A01

Columns 7 and 8 report the reddening and bolometric correction, respectively, based either on
the HST (non italicized) or the CFHT (italicized) photometry.

1.15f6Spectroscopic Hertzsprung-Russell diagram for the blue supergiant sample of Table <ref>. A selection of intermediate-mass evolutionary tracks with rotation from <cit.> is included.

§ METALLICITIES: STARS  IONIZED GAS

One of our primary aims in carrying out the spectroscopy of extragalactic s is to evaluate the present-day
chemical abundance of galaxies, independent of, and complementary to, other methods, in particular the study of the emission lines of  regions. This bears on the study of both radial abundance gradients in spiral galaxies and the galaxy mass-metallicity relation.

In order to compare nebular and stellar chemical abundances in NGC 2403 we examine the radial abundance gradients obtained independently from  regions and s. The main caveat in this approach is that the nebular abundances typically refer only to oxygen, while, as explained in Sect. <ref>, the stellar abundances are calculated using stellar features originating from several chemical elements. We assume solar metal abundance ratios and express the metallicity of the ionized gas by adopting the solar oxygen abundance value,  =  8.69 ().

The most comprehensive study of the  region chemical abundances in NGC 2403 todate is the work published by <cit.>. These authors used direct ( based on the detection of auroral lines) abundances of 27 nebulae to calculate the exponential oxygen abundance gradient in this galaxy. In order to facilitate the comparison with their results, we adopt the same deprojection parameters for the computation of the galactocentric distances of our targets (see footnote to Table <ref>).
<cit.> carried out a regression (linear since dealing with logarithmic abundances)
accounting for uncertainties in both  and the galactocentric distances, assuming a 5% error in $r/$. We follow the same approach, and adopt the linmix[<https://github.com/jmeyers314/linmix>] package, a Python port of the Bayesian method described by <cit.>, for calculating the linear regression. Finally, we perform the analysis using galactocentric distances normalized to the galactic effective radius , as done by <cit.>.

The galactocentric metallicity radial gradient of NGC 2403 from both blue supergiants and  regions. Blue continuous line: regression determined using the 16 blue supergiants of Table <ref>, represented by closed (BA) and open (OB) circles. Red dashed line: regression determined using the oxygen abundances of the  regions (), represented by small red dots. For the sake of clarity we omit the errorbars of the  region data points. The shaded areas represent the 95% confidence intervals of the fits.

In Fig. <ref> we display the stellar metallicity gradient, determined from 16 data points, using circle symbols for the  measurements (Sect. <ref>, and Table <ref>). The equation of the linear regression, shown by the continuous blue line, is:

\begin{equation}
[Z] = -0.04\, (\pm 0.06) - 0.14\, (\pm 0.05)~ r/r_e
\end{equation}

while for the  regions (dashed red line – 27 data points) we obtain

\begin{equation}
[Z] = -0.14\, (\pm 0.04) - 0.09\, (\pm 0.03)~ r/r_e
\end{equation}

which replicates Eq. (9) of <cit.>, once  is expressed in terms of metallicity [Z].
The intrinsic scatter about the regression lines for s ($\sigma_i = 0.05\pm0.03$ dex) and ionized nebulae ($\sigma_i = 0.04\pm0.02$ dex) is comparable, as is the standard error of the regression (0.07 dex).

We tested the agreement between the regressions derived for s and  regions
with a bootstrap approach (). We found that the differences in the slope and intercept values between the two regressions both fall inside the corresponding 95% confidence intervals.
In order to test the null hyphoteses that slopes and intercepts are equal, we considered the studentized, bootstrap-$t$ interval
(; see example in ) and found $p$-values $p$ = 0.13 (slopes) and $p$ = 0.08 (intercepts). Adopting the typical critical value $\alpha=0.05$, we conclude that both the slopes and the intercepts of the two regressions are not significantly different.

We should add, however, that the conclusion concerning the intercepts should be considered with some caution, since it depends on both the solar  value we adopt and, arguably more importantly, on how oxygen depletion on dust grains affects the nebular abundances. A correction to the nebular metallicities of approximately +0.1 dex should be expected from empirical results in the literature

Utilizing the bootstrap method we also verified  that the regressions to the OB and BA supergiants, taken separately, can be considered statistical equivalent. This result lends further support to our combining these two groups of stars, which are analyzed with different techniques and with different metal line diagnostics (Sect. <ref>).

If we merge the stellar and nebular data sets, we obtain the linear gradient

\begin{equation}
[Z] = -0.11\, (\pm 0.03) - 0.11\, (\pm 0.03)~ r/r_e.
\end{equation}

For completeness, we express the slope of the stellar abundance gradient in units of dex  $^{-1}$,  dex  kpc$^{-1}$ and dex  $^{-1}$ ( is the disk scale length, with  = 1.678 ) as follows:

\begin{equation}
\nabla_{r_{25}} =  -0.53 \pm 0.18
\end{equation}

\begin{equation}
\nabla_{kpc} =  -0.05 \pm 0.02
\end{equation}

\begin{equation}
\nabla_{r_{d}} =  -0.09 \pm 0.03
\end{equation}

§.§ Stellar and gaseous metallicities: review of literature data

In <cit.> we presented a comparison between  and ionized gas metallicities obtained for 14 galaxies (the Orion nebula representing the Milky Way). The nebular chemical abundances were obtained utilizing the direct method, which is based on the fluxes of auroral lines and of stronger collisionally excited lines (s). For seven systems the nebular abundances were evaluated also from the strengths of  recombination lines (s), whose analysis typically leads to $\sim$0.2 dex higher abundances compared to the  analysis (the abundance discrepancy factor ADF, ).

We update  the comparison presented by <cit.> by including the results obtained here for NGC 2403,
as well as taking into account more recent stellar metallicities for s in M31 and M33, recently studied by <cit.>. The outcome is shown in Fig. <ref>, where we follow our original procedure: (a) for irregular galaxies we adopt mean abundances; (b) for spirals we adopt the central abundances inferred from the abundance gradients (except for the Milky Way, since we only use M42 as representative of the solar neighborhood); (c) we add 0.1 dex to the nebular metallicities in order to approximately correct for the depletion of oxygen onto dust grains.

The addition of NGC 2403 to the diagram in Fig. <ref> is based on the stellar metallicities we present here, the  region  abundances of <cit.> and the  detection of <cit.> in a single  region (VS44 in their paper, equivalent to NGC 2403+96+30 in ). <cit.> and <cit.> report
the same  abundance for this nebula, thus we apply ADF() = 0.30 from <cit.> to augment the
<cit.> total O/H abundance by 0.17 dex. We finally apply this correction to the  region regression intercept in order to obtain the NGC 2403  data point in Fig. <ref>.

Difference in the metallicities derived from blue supergiants and  regions as a function of stellar metallicity
for a galaxy sample drawn from the literature (after ) and NGC 2403. The nebular metallicities are increased by 0.1 dex, in order to account for oxygen depletion onto dust grains. The  region chemical abundances are obtained either from collisionally excited lines (s) with the direct method (blue dots) or from  recombination lines (s, red squares).

Looking at Fig. <ref> we cannot but confirm the conclusions drawn by <cit.>: on average the stellar and the direct nebular metallicities are in good agreement across the whole $[Z]$ range, even though at high metallicities the former tend to be  $\sim$ 0.1-0.2 dex higher for the two objects with the smallest error bars (M42 and M33). In the high-metallicity regime the stellar metallicities are in agreement with the -based nebular abundances. On the other hand, we observe a  discrepancy of the -based metallicities with decreasing $[Z]$ relative to the stellar metallicities. The new data points that refer to NGC 2403 are in line with our initial interpretation. We should add that the apparent trend seen for the -based nebular metallicities could simply be reflecting a similar trend for the -based metallicities, since the ADF is roughly constant. Attempts by the first author to detect  s at the low-metallicity end (WLM, IC 1613) have proved unsuccessful so far. However, we remark that below the solar value the direct nebular metallicities are in good agreement with the s across approximately one order of magnitude in $[Z]$, while the  nebular metallicities based on s are not. For further discussion we refer to

§ THE STELLAR MASS-METALLICITY RELATION

In our previous work ()
we presented the stellar mass-metallicity relation () of local galaxies based on stellar abundance determinations, in place of the more commonly adopted nebular abundances. Following the same spirit that motivated the comparison carried out in Sect. <ref>, it is critical to validate the results found through the emission line analysis of extragalactic  regions with independent determinations of galaxy metallicities secured via the absorption line analysis of the stellar component.

In Fig. <ref> we update the stellar  with our new NGC 2403  data, as well as with the
results of the study of M31 and M33 by <cit.>. Because of the presence of abundance gradients in spiral galaxies, we, somewhat arbitrarily, select the metallicity at a galactocentric distance of 0.4  as representative for the whole galaxies. For NGC 2403 we adopt the stellar mass value  = 9.57, from <cit.>. The location of NGC 2403 in our diagram (stellar symbol) is in line with the trend outlined by the additional galaxies where s have already been investigated (blue dots).

Fig. <ref> includes two additional sets of independent data points. First, those proceeding from the chemical abundance analysis of near-IR spectra of individual red supergiants (s) and super star clusters (s), whose light output is dominated by s (red dots). Both the s and the s are representative of the young population in galaxies, similarly to the s and the  regions, and can therefore be displayed together in the diagram. In Appendix A we provide the details of the stellar abundances and masses used to produce Fig. <ref>, together with the references to the original abundance work.
In addition, in the figure we display the empirical relation obtained by <cit.> from the population synthesis of the stacked SDSS spectra of $2\times10^5$ local star-forming galaxies ($0.027 < z < 0.25$). The  delineated by the SDSS galaxies is in accordance with the relation defined by the supergiant and  data.

Finally, the green curve in Fig. <ref> represents the  resulting from the chemical look-back evolution models by <cit.>. Despite not being a fit to the observed data, the model curve
is compatible with the empirical  we observe from stellar metallicities.

1.15f9The stellar mass-metallicity relation of local galaxies based on abundance data derived from the analysis of stellar spectral features: blue supergiants (), red supergiants (), super star clusters () and SDSS galaxies. Predictions from the look-back models of <cit.> are included for comparison (green curve).

§ THE SPECTROSCOPIC DISTANCE TO NGC 2403

Having obtained the stellar parameters as described in Sect. <ref>, we can measure the spectroscopic distance to NGC 2403 via the flux-weighted gravity–luminosity relationship (; ) and the stellar mass-luminosity relationship.
The existence of a correlation between the flux-weighted gravity  $\equiv$ $g$/ and the bolometric magnitude   stems from the virtually constant luminosities and masses of s as they evolve.

We adopt the calibration of the  by <cit.>, established from the analysis of 90 s in the Large Magellanic Cloud, but reformulated in order to account for the slightly smaller distance modulus to this galaxy reported by <cit.>, $(m-M)_{LMC} = 18.477 \pm 0.004\ {\rm (statistical)} \pm 0.026\ {\rm (systematic)}$. The relationship presented by <cit.> is a piecewise linear fit to the stellar parameters, characterized by a single break point.
With the modified distance to the LMC, the  is:

\begin{equation}\label{eq:fglr1}
M_{bol} = 3.20\, (\log\,g_{\mbox{\tiny\it F}} - 1.5) - 7.878
\end{equation}

for  $>$ 1.30, and

\begin{equation}\label{eq:fglr2}
M_{bol} = 8.34\, (\log\,g_{\mbox{\tiny\it F}} - 1.3) - 8.518
\end{equation}

for  $<$ 1.30.

The empirical  traced by the NGC 2403 s is illustrated in Fig. <ref>, where
we excluded 47 since it is a bright outlier, most likely a blend. There are no obvious differences in the distribution of the data points, whether the source of the photometry is either HST (markers with inner triangles) or CFHT (no triangles), so we believe that in general blending is not a major issue for the ground-based data.

The distance modulus can be assessed by the vertical shift of the fiducial relation (Eq. <ref> and <ref>) that produces the best fit (green line) to the observed distribution of points in Fig. <ref>.
An orthogonal distance regression fit, accounting for errors in both coordinates and computed with the scipy.odr Python package, yields

$$\mu = m-M = 27.38 \pm 0.08$$
which corresponds to a distance
of $2.99^{+0.10}_{-0.12}$ Mpc.

1.15f10The  in NGC 2403. The data points (stars from Table <ref>, except for 47)
are fitted with the fiducial relation (Eq. <ref>-<ref>), vertically shifted by an amount equivalent to the distance modulus. The fitting relation is represented by the green line.

§.§ Comparison to other stellar distance indicators

NGC 2403 was among the first galaxies outside the Local Group where Cepheid variables were identified and studied by Hubble and collaborators ().
The period-luminosity relation of 10 Cepheids in NGC 2403 has been investigated from ground-based CCD observations by <cit.>. The distance modulus they derived, $\mu = 27.51 \pm 0.24$, was revised by <cit.> to $\mu = 27.48 \pm 0.10$. We report the result they obtained without correction for metallicity effects, because the metallicity relative to the LMC that <cit.> adopt, $\Delta Z = 0.3$ dex, is quite large and not consistent with the measurements we show in Fig. <ref>.
It should be noted that only $I$-band data were used, and that a reddening value $E(V-I)=0.20\pm0.10$ was adopted, not measured. From our sample in Table <ref> we transformed the reddening values to $E(V-I)$ using our models, and determined an average $E(V-I)=0.27\pm0.09$. This higher reddening would decrease the <cit.> distance modulus by 0.1 magnitudes. In addition, the zero point of the Cepheid period-luminosity relation used by these authors is defined by
the distance modulus of the LMC, which they adopted to be 18.5. The  distance is instead tied to a $\sim$0.02 mag smaller value from <cit.>. Overall, these effects would lead to an excellent agreement between a `corrected' Cepheid distance ($\mu = 27.36\pm0.10$) and our  determination.

In addition to the $I$-band data, <cit.> included $B$-band photometry from <cit.> and obtained
$\mu = 27.44 \pm 0.15$. The definition of their zero point contains a distance modulus of the LMC of 18.54, which is 0.06 mag larger than the value we adopt.
Our  measurement is again fully consistent with their Cepheid distance.

More accurate distance determinations have been published using the F814W magnitude of the Tip of the Red Giant Branch () measured in various HST fields of NGC 2403. A weighted mean of the distance moduli determined from one WFPC2 and two ACS fields by <cit.> yields $\mu = 27.51 \pm 0.03$.
Similarly, from three ACS fields analyzed by <cit.> we obtain
$\mu = 27.51 \pm 0.05$. The analysis presented by the Extragalactic Distance Database (EDD: ) yields $\mu = 27.52 \pm 0.05$ using F814W magnitudes, as well as values of $27.56\pm0.02$ (F110W) and $27.53\pm0.01$ (F160W).
Therefore, there is an offset $\Delta\mu = \mu_{TRGB} - \mu_{FGLR}$ relative to our  result, which is highly significant if we consider only the near-IR  work.
In Fig. <ref> we follow <cit.> and plot $\Delta\mu$, adopting the EDD F814W-based values for the  distances[<cit.> use the mean of the EED and ANGST values for four of the galaxies, while we only use the EDD.], as a function of the  distances we have determined in our previous work on 10 galaxies[The published  distances have been adjusted, when needed, to account for the <cit.> calibration and the  <cit.> LMC distance.], as well as for NGC 2403. Table <ref>
summarizes the distance moduli we adopt.

The offset we find in the case of NGC 2403, $\Delta\mu = 0.14\pm0.09$, is significant at the  $\sim$1.5$\sigma$ level.
We find comparable or larger offsets for other galaxies (NGC 300, M81, NGC 3621), and the mean difference is $\overline{\Delta\mu} = 0.067 \pm\ 0.044$. The data points in Fig. <ref> may visually suggest a potential trend with distance, but a correlation analysis based on
both the Pearson and Spearman correlation coefficients rules this out (Pearson's $r=0.47$; $p$-value for the null hypothesis that there is no correlation $p=0.14$).

1.15f11Distance modulus offset between  and  determinations as a function of the  distance modulus for 11 galaxies.

and  distance moduli.

2cdistance modulus

IC 1613    	      24.37 $\pm$ 0.11a         24.39 $^{+0.07}_{-0.04}$

M31			   	24.51 $\pm$ 0.13b         24.58 $^{+0.06}_{-0.13}$

M33        	      24.93 $\pm$ 0.07b         24.85 $^{+0.10}_{-0.05}$

WLM			   	25.05 $\pm$	0.06c	   	24.96 $^{+0.05}_{-0.09}$

NGC 3109	   	25.57 $\pm$	0.07d	   	25.63 $^{+0.10}_{-0.08}$

NGC 300		   	26.34 $\pm$	0.06e	   	26.60 $^{+0.06}_{-0.05}$

NGC 55		   	26.79 $\pm$	0.08f	   	26.62 $^{+0.03}_{-0.03}$

NGC 2403	   	27.38 $\pm$	0.08g	   	27.52 $^{+0.05}_{-0.05}$

M81			   	27.62 $\pm$	0.08h	   	27.84 $^{+0.09}_{-0.09}$

M83			   	28.41 $\pm$	0.11i	   	28.45 $^{+0.04}_{-0.03}$

NGC 3621	   	28.95 $\pm$	0.11j	   	29.22 $^{+0.09}_{-0.09}$

The references to the original  data are given below. The  distances are homogenized to the
same calibration and zero point. The  distances are extracted from the Extragalactic Distance Database ().
$^a$<cit.>; $^b$<cit.>; $^c$<cit.>; $^d$<cit.>;
$^e$<cit.>; $^f$<cit.>; $^g$This paper; $^h$<cit.>;
$^i$<cit.>; $^j$<cit.>.

§ SUMMARY

We have carried out the first quantitative spectral analysis of blue supergiant stars in the nearby galaxy NGC 2403. Out of a sample of 47 targets observed with the LRIS spectrograph at the Keck I telescope we have extracted 16 BA stars for which we have spectra of sufficient quality to carry out a comparison with model spectra of evolved massive stars in order to derive the stellar parameters.
There are two main outcomes from our study:

* We measured the galactocentric radial metallicity gradient of NGC 2403 based on our stellar observations, finding that it agrees well with the results obtained from  regions,  both in slope and intercept, especially if we account for a $\sim$0.1 dex depletion of the nebular oxygen due to dust grains. This lends further evidence that the extragalactic stellar metallicities we obtain from our technique are in general agreement with the nebular abundances based on the analysis of the auroral lines over more than one order of magnitude in metallicity.

* Adopting the known relation between stellar parameters and intrinsic luminosity () we derived a distance to NGC 2403 of $2.99^{+0.10}_{-0.12}$ Mpc ($\mu = 27.38 \pm 0.08$ mag). While this can be brought into agreement with Cepheid-based determinations, once we account for differences in reddening and LMC distance between the separate studies,
it is 0.14 mag short of the  value. We have no current explanation for this discrepancy, but note a similar behavior in a handful of spiral galaxies.

We are indebted to Zach Gazak for his contributions in the early phases of this project and to
Richard Gray for sharing the spectra from his digital spectral classification atlas.
This research has made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the National Aeronautics and Space Administration.
RPK acknowledges support by the Munich Excellence Cluster Origins funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC-2094 390783311.

Keck:I (LRIS)

APLpy (), LINMIX (Meyers 2015, <https://github.com/jmeyers314/linmix>), SciPy (), NumPy (), Matplotlib (), PyRAF ().

§ VALUES AND SOURCES OF THE STELLAR MASS-METALLICITY RELATION

We list here the galaxy stellar masses and metallicities that are used to construct the stellar mass-metallicity relation shown in Fig. <ref>. As explained in the text, the stellar metallicity data refer to blue supergiants (), red supergiants () and super star clusters (). In Table <ref> we divide our  and [Z] values into these three categories. The table also reports the literature sources for the measurements.

Stellar mass-metallicity relation.

M31              10.98        0.07         <cit.>        <cit.>

M81              10.68        0.11         <cit.>        <cit.>

Milky Way        10.81        0.11         <cit.>        <cit.>

M83              10.41        0.16         <cit.>        <cit.>

NGC 3621         9.91         $-$0.01      <cit.>        <cit.>

NGC 2403         9.57         $-$0.25      <cit.>         this work

M33              9.55         $-$0.20      <cit.>        <cit.>

NGC 55           9.29         $-$0.46      <cit.>       <cit.>

LMC              9.19         $-$0.36      <cit.>        <cit.>

NGC 300          9.33         $-$0.27      <cit.>        <cit.>

SMC              8.67         $-$0.65      <cit.>       <cit.>

NGC 6822         8.23         $-$0.52      <cit.>        <cit.>

NGC 3109         8.13         $-$0.67      <cit.>        <cit.>

IC 1613          8.03         $-$0.69      <cit.>        <cit.>

WLM              7.65         $-$0.87      <cit.>        <cit.>

Sextans A        7.43         $-$1.00      <cit.>        <cit.>

Milky Way        10.81        0.11         <cit.>        <cit.>

NGC 55           9.29         $-$0.52      <cit.>       <cit.>

LMC              9.19         $-$0.45      <cit.>        <cit.>

NGC 300          9.33         $-$0.31      <cit.>        <cit.>

SMC              8.67         $-$0.61      <cit.>       <cit.>

NGC 6822         8.23         $-$0.60      <cit.>        <cit.>

M83              10.41        0.21         <cit.>        <cit.>

NGC 4038         10.54        $-$0.01         <cit.>        <cit.>

(1) The [Z] values refer to galactocentric distances of 0.4  in those cases where there is a chemical abundance gradient,  for the spiral galaxies.
(2) In order to account for the different solar abundance patterns adopted in the BSG and RSG spectral analysis, the RSG metallicities are rescaled as explained in Appendix A of <cit.>.

§ STRONG-LINE METHODS NEBULAR ABUNDANCES

In our study of the metal-rich galaxy M83 presented in <cit.> we compared the radial abundance gradient obtained from 14 blue supergiants with the gradients obtained from  regions, whose abundances were derived using eight different strong-line abundance diagnostics. We repeat the procedure here for the case of NGC 2403, by using the
same set of nebular abundance diagnostics, for the sake of simplicity and consistency.
Details about these diagnostics are discussed in B16.

The results of the comparison are shown in Fig. <ref>, where the diagnostics used for the panels a–h are summarized below:

[ ](),a;

*  = (3727 + 4959, 5007)/:

* O2N2 = 6584/3727: <cit.>

* O3N2 = 5007/ $\cdot$ /6584: <cit.>

* N2 = /: <cit.>

* O3N2: <cit.>

* O2N2: <cit.>

* ONS: <cit.>

* $R$: <cit.>

[, ](),a;

Metallicity gradients of the  regions determined using various strong line abundance diagnostics, as labeled. For the blue supergiants (Sect. <ref>) and the  regions auroral line analysis () we only show the  gradient regression lines and the confidence intervals, displayed in Fig. <ref>, for clarity. In each panel we report the slope (sl) and intercept (in) values determined from a linear fit to the strong line abundances, and their errors.


11institutetext: Laboratoire d’Optique Appliquée, ENSTA Paris, École
Polytechnique, CNRS-UMR7639, Institut Polytechnique de Paris, 91762 Palaiseau
cedex, France 22institutetext: SFRO - RadioTransNet, Centre Antoine Béclère,
47 rue de la Colonie, 75013 Paris 33institutetext: INSERM 1030, Univ Paris-
Sud, Univ Paris-Saclay, Department of Radiation Oncology, Gustave Roussy
Cancer Campus, Villejuif, France 44institutetext: Univ. Grenoble Alpes, CNRS,
Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France 55institutetext: Institute of
Radiation Physics, Lausanne University Hospital, Lausanne, Switzerland

# Dosimetric characterisation and application to radiation biology of a kHz
laser-driven electron beam

Marco Cavallone 11 Lucas Rovige 11 Julius Huijts 11 Émilie Bayart 1122 Rachel
Delorme 44 Aline Vernier 11 Patrik Gonçalves Jorge 55 Raphaël Moeckli 55 Eric
Deutsch 33 Jérôme Faure 11 Alessandro Flacco _Corresponding author:_
<EMAIL_ADDRESS>
(Received: date / Revised version: date)

###### Abstract

Laser-plasma accelerators can produce ultra short electron bunches in the
femtosecond to picosecond duration range, resulting in high peak dose rates in
comparison with clinical accelerators. This peculiar characteristic motivates
their application to radiation biology studies to elucidate the effect of the
high peak dose rate on the biological response of living cells, which is still
being debated. Electron beams driven by kHz laser systems may represent an
attractive option for such applications, since the high repetition rate can
boost the mean dose rate and improve the stability of the delivered dose in
comparison with J-class laser accelerators running at
$10\text{\,}\mathrm{H}\mathrm{z}$. In this work, we present the dosimetric
characterisation of a kHz, low energy laser-driven electron source and
preliminary results on in-vitro irradiation of cancer cells. A shot-to-shot
dosimetry protocol enabled to monitor the beam stability and the irradiation
conditions for each cell sample. Results of survival assays on HCT116
colorectal cancer cells are in good agreement with previous findings reported
in literature and validate the robustness of the dosimetry and irradiation
protocol.

††journal: myjournal††offprints:

##  1 Introduction

Laser-plasma accelerators can produce ultra short electron bunches with
duration in the range from femtosecond to picosecond. Both quasi-monoenergetic
high-energy electrons (hundreds of MeV) mirzaie_effect_2018 ;
faure_experiments_2008 ; thaury_shock_2015  and high-charge, low-energy (few
MeV) electrons with broadband spectrum guillaume_physics_2015  have been
obtained with 100 TW class lasers. The peculiarity of these sources is the
ultra-high peak dose rate in the pulse (up to
${10}^{10}\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{s}$) that is orders
of magnitude higher than conventional Linac
(${\sim${10}^{2}\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{s}$}$)
ashraf_dosimetry_2020 . The impact of electrons delivered in such short pulses
of ultra-high dose rates on living cells or tissues still need to be
extensively explored. Recent results obtained with FLASH-RT
favaudon_ultrahigh_2014 ; vozenin_advantage_2019 ; vozenin_biological_2019
and laser-accelerated protons raschke_ultra-short_2016 ; bayart_fast_2019
indicate that the temporal structure of high dose rate, pulsed irradiation may
have an impact on the radiobiological response and ask for a deeper
understanding of the phenomena triggered by high dose rate irradiation.
To date, Laser-Accelerated Electrons (LAEs) produced by commercially available
J-class lasers running at 10 Hz have been used for radiation biology studies
andreassi_radiobiological_2016 ; laschinsky_radiobiological_2012 ;
oppelt_comparison_2015 . The main limit of these beams is the shot-to-shot
pointing fluctuation in the order of the beam divergence, that hinders the
reach of the stability standards required in clinics. In this context, low-
energy electrons (few MeV) driven by kHz lasers may represent an interesting
alternative for radiobiology applications. Such laser-plasma accelerators have
been developed in recent years he_high_2013 ; salehi_mev_2017 ;
guenot_relativistic_2017 ; faure_review_2019  and, to our knowledge, no
radiobiology study in these conditions is reported in literature at the time
of writing. The key asset of these beams is the high repetition rate, which
boosts the mean beam current and allows averaging of the shot-to-shot
fluctuations by integration of a large number of shots. From a dosimetric
point of view, this translates into higher mean dose rates (Gy/s), compared to
those obtained with J-class lasers (Gy/min), and into a higher stability of
the dose distribution at the sample.
In this article we present the dosimetric characterisation of a low-energy kHz
laser-driven electron beam for radiation biology applications and report
preliminary results on in-vitro irradiation of HCT116 colorectal cancer cells.
The dose distribution at the irradiated sample was measured at each
irradiation with absolutely calibrated radiochromic films, which have been
shown to be dose-rate independent over a wide range of dose rate up to
${10}^{12}\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{s}$ karsch_dose_2012
; jaccard_high_2017 ; bazalova-carter_comparison_2015 . The use of an IBA
Razor Nano Chamber provided a real time dose monitoring during irradiations
and evaluation of the dose uncertainty in the post-processing analysis.

##  2 Electron source and set-up

The experiment was performed with the Salle Noire laser system of the
Laboratoire d’Optique Appliquée, delivering 3.5 fs pulses at 1 kHz repetition
rate with $3\text{\,}\mathrm{m}\mathrm{J}$ on target. The laser can generate
low energy electrons in a reproducible way in a range from sub-MeV up to few
MeV with charges of $\sim$$10\text{\,}\mathrm{p}\mathrm{C}$ and few pC
respectively, depending on the gas density and profile gustas_high-charge_2018
. In the experiment, the laser pulse was focused with a parabola
($50\text{\,}\mathrm{m}\mathrm{m}$ focal length) onto an N2 gas-jet. The gas-
jet density was optimised so as to maximise the accelerated charge per bunch,
which corresponds to the production of an electron beam featuring a low-energy
quasi-thermal spectrum up to $\sim$$2\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$
and a divergence of $70\text{\,}\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$.

Figure 1: Schematic draft (horizontal cut, top view) of the experimental set-
up.

Fig. 2 shows the electron spectrum taken in four different days. As shown, the
spectral shape can be reproduced from one day to another with good precision.
The measured charge (total charge at the source) was $9.8$ pC/shot with an
instability of $\pm 0.7$ pC/shot (standard deviation).
A draft of the experimental setup is shown in Fig. 1. A tube was inserted in
the vacuum chamber to place the irradiation site (in air) closer to the
electron source, compatibly with the beam diagnostics. A
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick vacuum-air Mylar window was
placed $38\text{\,}\mathrm{cm}$ far from the source. At this location, the
transverse dimension of the beam was $3\text{\,}\mathrm{cm}$ (FWHM), which
allowed to irradiate a circular spot of $1\text{\,}\mathrm{cm}$ diameter with
a sufficiently homogeneous dose. The cell sample was positioned vertically in
air, $2\text{\,}\mathrm{cm}$ after the Mylar window, with a
$800\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick plastic holder aligned to
the beam-axis.

Figure 2: Spectrum of the electron beam taken in four different days, obtained
by integrating 15 shots. The lower limit of the spectrometer is
$400\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$.

A customised metallic support allowed to hold in place the cell holder and to
place it at the same depth in the tube at each irradiation. The support was
also designed to house an IBA Razor Nano Chamber (RNC), which was inserted
behind the cell sample. The chamber ($2\text{\,}\mathrm{mm}$ outer electrode
diameter, $0.003\text{\,}{\mathrm{cm}}^{2}$ active volume) was used as on-line
dose monitor during irradiations and as day-to-day dose reference during the
optimisation of the interaction conditions between the laser and the gas-jet
prior to an experimental run. A radiochromic EBT3 film was placed on the front
side (in beam’s view) of the cell holder at each irradiation for dosimetry. A
motorised set-up, located in the vacuum chamber between the source and the
Mylar window, was used for beam imaging and spectroscopy and was removed
during irradiations. It contains a removable dipole
($0.058\text{\,}\mathrm{T}$) and a phosphor screen coupled with a CCD camera.
Imaging of the beam transverse section, performed by removing the dipole
magnet from the beam axis, allowed to align the electron beam to the cell
sample and to measure the total accelerated charge per bunch. The details of
these diagnostics can be found in D. Gustas (2019) gustas_high-charge_2018 .

##  3 Dosimetry

The dose was measured with an EBT3 radiochromic film placed on the cell
plastic support at each irradiation. The films were scanned 24 hours after
irradiation, as recommended by Devic et al. (2016) devic_reference_2016 , with
an EPSON V800 flatbed scanner and a resolution of 300 DPI. The dose was
measured within a circular ROI of $10\text{\,}\mathrm{m}\mathrm{m}$ diameter
aligned with the cell sample. The EBT3 film batch was calibrated at the Elekta
Synergy linear accelerator of the University Hospital of Lausanne (CHUV,
Switzerland) with $4\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ electrons at a
dose rate of
$6\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{m}\mathrm{i}\mathrm{n}$. The
calibration curve is shown in Fig. 3, together with the five degree polynomial
expression used to fit the experimental points.

Figure 3: Calibration of the EBT3 film batch (red channel) with the
$4\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ electron beam generated by the
Synergy Elekta LINAC available at the University Hospital of Lausanne (CHUV,
Switzerland). The experimental values (blue points) are fitted with a five
degree polynomial (black curve), whose expression is reported in the image.

The film dose was corrected to obtain the dose delivered in the cells by
measuring the attenuation caused by the
$800\text{\,}\mathrm{\SIUnitSymbolMicro m}$ cell plastic holder and the air
gap. Precisely, the dose delivered to the cell is related to the dose absorbed
by the film according to:

$D_{cells}=D_{EBT3}\cdot R_{cells/EBT3}$ (1)

where $R_{cells/EBT3}$ is the ratio between the dose absorbed by the cells and
by the EBT3. This factor was measured with a double film arrangement, as shown
in the insert of Fig. 4. A film was placed on the plastic holder surface, as
during irradiations, and a second film was placed inside the plastic holder at
the cell position. Since the ratio depends on the spectral shape of the beam,
which varied slightly during the day and between days (see Fig. 2), the double
film measurement was carried out before each irradiation series. The results
of the double film measurements, performed in five different days, are
reported in Fig. 4. We measured a factor $R_{cells/EBT3}$ of 0.71 with good
reproducibility during the day and between days (5.8% standard deviation). A
mean dose rate of 1.1 Gy/s and 0.78 Gy/s was measured on the holder surface
and at the cell position, respectively, with an instability of 8% (standard
deviation). As anticipated in the introduction, the mean dose rate achieved
with such a kHz laser-driven electron source is higher than typical dose rates
reported in literature with J-class lasers running at
$10\text{\,}\mathrm{H}\mathrm{z}$ ($\sim$Gy/min) gizzi_laserplasma_2015 ;
andreassi_radiobiological_2016 ; laschinsky_radiobiological_2012 ;
oppelt_comparison_2015 ; beyreuther_establishment_2010 ;
nicolai_realizing_2014 . A rough estimate of the peak dose rate in the pulse
can be obtained by considering the temporal stretch of the beam energy
components between $0.5\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ and
$1\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ at the cell position. The
calculation leads to a pulse duration of $120\text{\,}\mathrm{p}\mathrm{s}$
and a peak dose rate in the order of
${10}^{7}\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{s}$.

Figure 4: Dose rate measured at the surface of the plastic holder and at the
cell position with the double film arrangement shown in the insert.

###  3.1 Dose homogeneity and uncertainty

Since the position of the irradiation site inserted in the tube was fixed, the
electron beam pointing needed to be carefully aligned by adjusting the
incidence angle of the laser on the gas-jet before the beginning of the
irradiations. Once the beam pointing was aligned with the cell holder, the
beam showed a remarkably good stability in terms of dose distribution between
irradiations, as shown in Fig. 5.

Figure 5: Dose distribution measured with the EBT3 film placed on the cell
plastic support in six consecutive irradiations consisting in a dose
escalation performed for the survival essay. The colormap interval is set
between the maximum value and the 50% percent level in all images. The red
circles represent the ROI of $1\text{\,}\mathrm{c}\mathrm{m}$ diameter used to
measure the dose as well as the surface where the cell response was studied.

The figure shows typical dose distributions measured with the EBT3 during a
dose escalation performed for the survival assay. We were able to precisely
align the electron beam with the cell sample and keep the dose inhomogeneity
below $\pm 7$% in most of the irradiations (85%).
The uncertainty on the dose delivered at the cell sample was evaluated by
cross correlation between the dose measured by the EBT3 film and by the RNC
placed behind the sample. In particular, the instability of the ratio between
the two measured doses is an indicator of the spectrum stability between
irradiations and of the uncertainty on the ratio $R_{cells/EBT3}$ used to
quantify the dose delivered at cell sample. Fig. 6 shows the typical behaviour
of the ratio between the dose absorbed by the film and by the RNC during three
dose escalation series performed for the survival assay.

Figure 6: Ratio between the dose meaured by the EBT3 film and by the Razor
Nano Chamber as a function of the exposure time, i.e. the shutter opening
time.

As it is shown, we observed an increase of the ratio with the exposure time. A
similar trend was also observed for the dose rate, which turned out to
slightly decrease with the exposure time. It is possible that the observed
patterns are due to the shutter used to block the laser and control the
irradiation time. Opening the shutter, placed before the last four optics,
after it is kept closed to block the laser during the sample replacement might
generate a transient thermal phenomenon in the optics and affect the laser
properties at the gas-jet. This effect will be verified and solved in future
experiment by placing the laser shutter after the last focusing optics. The
variation of the ratio between irradiations, typically below $\pm 10\%$,
results in a comparable uncertainty on the $R_{cells/EBT3}$ factor measured
with the double film arrangement and, as a consequence, on the dose delivered
to the cell sample.

##  4 Radiation biology experiment

###  4.1 Methods

We performed irradiation of in-vitro cancer cells with the Salle Noire
electron source both to investigate the biological response to kHz laser-
accelerated electrons and to validate the dosimetry. To this aim, we
irradiated colorectal cancer cells HCT116, both the wild type (HCT116 WT) and
its radioresistant counterpart (HCT116 p53-/-) mutated for the tumour
suppressor gene p53. The use of both the wild type and the radioresistant
counterpart allowed to verify the quality of the dosimetry protocol and of the
radiobiology analysis. The colorectal cancer cells HCT116, wild type (WT) or
mutated for the tumour suppressor gene p53 (p53-/-), were cultured and grown
as monolayers in plastic tissue culture disposable flasks (TPP) in McCoy’s 5A
(Modified) Medium with GlutaMAXTM (ThermoFisher Scientific), supplemented with
10% fetal calf serum (PAA) and 1% penicillin and streptomycin (ThermoFisher
Scientific).
All cell lineages were grown at 37° C in a humidified atmosphere of 5% CO2 in
air. Based on the transverse dose homogeneity deducted from radiochromic
films, a $1\text{\,}\mathrm{c}\mathrm{m}$ diameter circular region was
delimited on the inside face of the culture dishes with Creamy Color long
lasting lip pencil (Kiko) in which
$4\text{\times}{10}^{4}\text{\,}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{s}$
were seeded in $100\text{\,}\mathrm{\SIUnitSymbolMicro L}$ of medium. The
culture dish was positioned vertically behind the exit window. After exposure
to the laser-driven electron beam, 1 mL of medium was added and the cell
monolayers were incubated for 4 hours in standard conditions. Cells were
harvested with Accutase (Merck), dispatched into 3 different wells of 12-well
plate (TPP) in $2.5\text{\,}\mathrm{mL}$ of medium and grown for five
generations corresponding to five days (replication time below 20 h).
Appropriate control samples were treated under the same conditions, including
bringing the cell culture dish in a vertical position as for irradiation.
After this period, cells were harvested with
$250\text{\,}\mathrm{\SIUnitSymbolMicro L}$ of Accutase inactivated with
$250\text{\,}\mathrm{\SIUnitSymbolMicro L}$ of 1X PBS (ThermoFisher
Scientific) supplemented with 10% fetal calf serum. The final volume was
adjusted to $1\text{\,}\mathrm{mL}$ with 1X PBS and
$200\text{\,}\mathrm{\SIUnitSymbolMicro L}$ of each well were dispatched into
a non-sterile Ubottom 96-well plate (TPP). In each well,
$2\text{\,}\mathrm{\SIUnitSymbolMicro L}$ of a propidium iodide solution
(Sigma,
$100\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{g}\mathrm{/}\mathrm{m}\mathrm{L}$
in 1X PBS) were added just before counting by flow cytometry technology. Cell
acquisition was performed using Guava® and the data analysis carried out with
GuavaSoft (Merck Millipore).

###  4.2 Survival assay results

Figure 7: Survival curves for the HCT116 WT and HCT116 p53-/- cell lines
obtained in two independent experiments. In both graphs the points represent
the mean of three radiobiological analysis carried out on the same irradiated
sample and the vertical error bar corresponds to the standard deviation of the
survival fraction obtained in the three analysis. The horizontal error bars
represent the sum of the dose error due to the inhomogeneity within the
analysed surface of the sample (circular surface of
$1\text{\,}\mathrm{c}\mathrm{m}$ diameter) and of the uncertainty on the
dosimetry.

The survival curves obtained for the HCT116 WT and HCT116 p53-/- cell lines
grown as monolayers are reported in Fig.7. Both the error due to the dose
homogeneity and to the dosimetry uncertainty are included in the horizontal
error bars. The experimental results were fitted with the Linear-Quadratic
(LQ) model: $\ln S=\alpha D-\beta D^{2}$, where D is the delivered dose and
$\alpha$ and $\beta$ are adjustable parameters. The surviving fraction
decreases with the delivered dose and the curves exhibit the typical shoulder
shape of low LET radiations. Furthermore, the curve of the WT cell line lies
well below the curve of the more radioresistant counterpart p53-/-, which
confirms the quality of both the dosimetry and the biological analysis.

Table 1: D10 values for in-vitro HCT116 cell lines, grown as monolayers, obtained with laser-accelerated electrons (from the survival curves of Fig. 7) and with $662\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$ photons of a 137Cs source at a conventional dose-rate, taken from Pommarel et al. (2017)pommarel_spectral_2017 . Cell line | LAE | Photons 137Cs 662 keV
---|---|---
HCCT116 WT |  $4.34\pm 0.73$ Gy |  $3.8\pm 0.4$ Gy
HCCT116 p53 |  $5.05\pm 0.66$ Gy |  $5\pm 0.4$ Gy

It is relevant to compare the 10% survival dose D10 obtained with the LAE beam
with those previously obtained with low-LET
$662\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$ photons at a conventional dose
rate of
$1.4\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{m}\mathrm{i}\mathrm{n}$
produced by a 137Cs source (integrated in an IBL 637 n∘9418 device
manufactured by CIS Bio)pommarel_spectral_2017 . The D10 values, determined
from the LQ fitting curves (Kaleidagraph software) for the two cell types (WT
and p53-/-) are reported in Table 1. The D10 obtained with LAEs are close to
the values obtained with the 137Cs source, which is in line with the results
reported in literature showing no remarkable difference in the RBE of LAEs in
comparison with conventional sources of comparable LET
laschinsky_radiobiological_2012 .

##  5 Conclusions and outlook

We presented the first dosimetric characterisation and application to
radiation biology of a kHz laser-driven electron beam. The use of both
radiochromic films and an on-line Razor Nano Chamber allowed evaluation of the
dose distribution delivered at the sample at each irradiation and to evaluate
the uncertainty on the delivered dose. We showed good day-to-day
reproducibility of the irradiation conditions in terms of dose rate and beam
quality. A dose rate of $1\text{\,}\mathrm{G}\mathrm{y}\mathrm{/}\mathrm{s}$
was achieved, which is higher than typical dose rates reported in literature
with J-class lasers running at $10\text{\,}\mathrm{H}\mathrm{z}$. Besides the
increase of the mean dose rate, the high repetition rate ensured a remarkably
good stability of the dose distribution at the sample and indicates that such
LAE source can be a promising alternative to electrons produced by
$10\text{\,}\mathrm{H}\mathrm{z}$ lasers for radiation biology applications.
During the dose escalation sequence, we observed an impact of the exposure
time on the beam spectrum, which introduced an uncertainty on dosimetry. The
observed trends are likely to be due to the use of a beam shutter in the laser
chain generating transient thermal phenomena in the optics. This phenomenon,
which is not attributable to inherent source instability, can be significantly
reduced in future studies by placing the shutter at the end of the laser
chain. In addition, an ongoing upgrade of the Salle Noire facility will lead
to an increase of the laser energy up to
$45\text{\,}\mathrm{m}\mathrm{J}\mathrm{/}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{e}$.
This would allow to generate more energetic electrons (with a comparable
charge per bunch) and to reduce the sensitivity of the dosimetry protocol to
spectral instabilities thanks to the higher penetration depth.
Regarding the radiobiological outcome, the survival curves obtained with
HCT116 monolayer samples indicate no significant difference between the
radiobiological effectiveness of kHz laser-driven electrons and conventional
sources with similar LET, in line with previous findings reported in
literature. This result further validates both the dosimetry and the
biological analysis. Future experiments should explore the response of healthy
cells and of spheroids samples as well as the impact of different
fractionation modalities on the biological response bayart_fast_2019  to
provide a more complete indication of the therapeutic potential of such high
peak dose rate sources. Moreover, boosting the energies up to few MeV without
a significant decrease of the charge per bunch would allow to irradiate in
vivo biological targets, such as mice, and would increase the peak dose rate
in the pulse by reducing the pulse temporal stretch to few picoseconds.

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