# Tests of star formation metrics in the low metallicity galaxy NGC 5253 using
ALMA observations of H30$\alpha$ line emission

G. J. Bendo1,2, R. E. Miura3, D. Espada3, K. Nakanishi3,4, R. J. Beswick1,M.
J. D’Cruze1, C. Dickinson1, G. A. Fuller1,2
1 Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The
University of Manchester, Oxford Road,
Manchester M13 9PL, United Kingdom
2 UK ALMA Regional Centre Node
3 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo,
181-8588, Japan
4 The Graduate University for Advanced Studies (Sokendai), 2-21-1 Osawa,
Mitaka, Tokyo 181-0015, Japan

###### Abstract

We use Atacama Large Millimeter/submillimeter Array (ALMA) observations of
H30$\alpha$ (231.90 GHz) emission from the low metallicity dwarf galaxy NGC
5253 to measure the star formation rate (SFR) within the galaxy and to test
the reliability of SFRs derived from other commonly-used metrics. The
H30$\alpha$ emission, which originates mainly from the central starburst,
yields a photoionizing photon production rate of
(1.9$\pm$0.3)$\times$$10^{52}$ s-1 and an SFR of 0.087$\pm$0.013 M⊙ yr-1 based
on conversions that account for the low metallicity of the galaxy and for
stellar rotation. Among the other star formation metrics we examined, the SFR
calculated from the total infrared flux was statistically equivalent to the
values from the H30$\alpha$ data. The SFR based on previously-published
versions of the H$\alpha$ flux that were extinction corrected using Pa$\alpha$
and Pa$\beta$ lines were lower than but also statistically similar to the
H30$\alpha$ value. The mid-infrared (22 $\mu$m) flux density and the composite
star formation tracer based on H$\alpha$ and mid-infrared emission give SFRs
that were significantly higher because the dust emission appears unusually hot
compared to typical spiral galaxies. Conversely, the 70 and 160 $\mu$m flux
densities yielded SFR lower than the H30$\alpha$ value, although the SFRs from
the 70 $\mu$m and H30$\alpha$ data were within 1-2$\sigma$ of each other.
While further analysis on a broader range of galaxies are needed, these
results are instructive of the best and worst methods to use when measuring
SFR in low metallicity dwarf galaxies like NGC 5253.

###### keywords:

galaxies: dwarf - galaxies: individual: NGC 5253 - galaxies: starburst -
galaxies: star formation - radio lines: galaxies

††pagerange: Tests of star formation metrics in the low metallicity galaxy NGC
5253 using ALMA observations of H30$\alpha$ line emission–References

##  1 Introduction

Star formation in other galaxies is typically identified by looking at tracers
of young stellar populations, including either photoionizing stars,
ultraviolet-luminous stars, and supernovae. The most commonly-used star
formation tracers are ultraviolet continuum emission; H$\alpha$ (6563 Å) and
other optical and near-infrared recombination lines; mid- and far-infrared
continuum emission; and radio continuum emission. However, each of these
tracers have disadvantages when used to measure star formation rates (SFRs).
Ultraviolet continuum and optical recombination line emission directly trace
the young stellar populations, but dust obscuration typically affects the SFRs
from these tracers. Near-infrared recombination line emission is less affected
by dust obscuration, but it is still a concern in very dusty starburst
galaxies. Dust continuum emission in the infrared is unaffected by dust
obscuration except in extreme cases, but since this emission is actually a
tracer of bolometric stellar luminosity and not just the younger stellar
population, it may yield an overestimate of the SFR if many evolved stars are
present. Radio continuum emission traces a combination of free-free continuum
emission from photoionized gas and synchrotron emission from supernova
remnants, so proper spectral decomposition is needed to accurately convert
radio emission to SFR. Additionally, the cosmic rays that produce synchrotron
emission will travel significant distances through the ISM, making radio
emission appear diffused relative to star formation on scales of $\sim$100 pc
(Murphy et al., 2006a, b).

Higher-order recombination line emission at millimetre and submillimetre
wavelengths, which is produced by the same photoionized gas that produce
H$\alpha$ and other optical and near-infrared recombination lines, can also be
used to measure SFRs. Unlike ultraviolet, optical, and near-infrared star
formation tracers, these millimetre and submillimetre recombination lines are
not affected by dust extinction, but unlike infrared and radio synchrotron
emission, the recombination lines directly trace the photoionizing stars.
Recombination line emission can also be observed at centimetre and longer
wavelengths, but the line emission at these longer wavelengths is generally
affected by a combination of masing effects and opacity issues in the
photoionized gas, while the millimetre and submillimetre lines are not (Gordon
& Walmsley, 1990).

The primary reason why these millimetre and submillimetre recombination lines
are not used more frequently as star formation tracers is because the emission
is very faint. Before the Atacama Large Millimeter/submillimeter Array (ALMA)
became operational, millimetre and submillimetre recombination line emission
has only been detected within three other galaxies: M82 (Seaquist et al.,
1994, 1996), NGC 253 (Puxley et al., 1997), and Arp 220 (Anantharamaiah et
al., 2000). ALMA, however, has the sensitivity to potentially detect this
emission in many more nearby galaxies, including many nearby luminous infrared
galaxies and other starbursts (Scoville & Murchikova, 2013). Detections of
recombination line emission from the first three cycles of ALMA observations
include measurements of the H40$\alpha$ (99.02 GHz) emission from the centre
of NGC 253 (Meier et al., 2015; Bendo et al., 2015b) and H42$\alpha$ (85.69
GHz) emission from the centre of NGC 4945 (Bendo et al., 2016) as well as a
marginal detection of H26$\alpha$ (353.62 GHz) in Arp 220 (Scoville et al.,
2015).

The NGC 253 and 4945 analyses included comparisons of SFRs from ALMA
recombination line and free-free emission to other star formation tracers in
radio and infrared emission. The results illustrated some of the challenges in
measuring star formation rates in other wavebands. SFRs from radio continuum
emission calculated using one of the conversions given by Condon (1992) or
Murphy et al. (2011) yielded results that differed significantly from the ALMA
data. Recombination line emission at centimetre or longer wavelengths often
produced much less accurate results. For NGC 253 specifically, some of the
SFRs from recombination line emission at these longer wavelengths were
$\sim$3$\times$ lower than what was determined from the ALMA data, which
indicated that the longer wavelength lines may be affected by gas opacity
effects. The SFR from the mid-infrared data for the central starburst in NGC
4945 was $\sim$10$\times$ lower than the SFR from the H42$\alpha$ or free-free
emission, but the SFR from the total infrared flux was consistent with the
ALMA-based SFRs. This suggests that the centre of NGC 4945 is so dusty that
even the mid-infrared light from the dust itself is heavily obscured.

While the results for NGC 253 and 4945 have revealed some of the limitations
of other star formation tracers, the analyses have mainly focused on radio or
infrared data. The dust extinction is so high in the central starbursts in
both galaxies that comparisons of millimetre recombination line emission to
ultraviolet or H$\alpha$ emission is not worthwhile. Such comparisons need to
be performed using a less dusty object.

NGC 5253 is a nearby blue compact dwarf galaxy within the M83/Centaurus A
Group (Karachentsev et al., 2007) that hosts a starburst nucleus. Most
published distances for the galaxy range from 3 to 4 Mpc; we use a distance of
3.15$\pm$0.20 Mpc (Freedman et al., 2001). Because the starburst is both very
strong and relatively nearby, it has been intensely studied at multiple
wavelengths, including H$\alpha$, infrared, and radio emission, making it an
ideal object to use in a comparison of SFRs from millimetre recombination line
data to SFRs from data at other wavelengths. Radio recombination line emission
from NGC 5253 has been detected previously by Mohan et al. (2001) and
Rodríguez-Rico et al. (2007) at lower frequencies, but they indicated that
adjustments for masing and gas opacity would need to be taken into account to
calculate SFR. As millimetre recombination line emission is unaffected by
these issues, it can provide more accurate measurements of the SFR.

We present here ALMA observations of the H30$\alpha$ line at a rest frequency
of 231.90 GHz, with which we derive a SFR that directly traces the
photoionizing stars while not being affected by dust attenuation. We compare
the ALMA-based SFR to SFRs from other wavebands to understand their
effectiveness, and we also examine the efficacy of SFRs based on combining
H$\alpha$ emission (a tracer of unobscured light from star forming regions)
with infrared emission (a tracer of light absorbed and re-radiated by dust).
The ALMA observations and the SFRs derived from the line are presented in
Section 2. SFRs from optical, infrared, and radio emission as well as
composite SFRs based on multiple wavebands are derived and compared to the
H30$\alpha$ values in Section 3. Section 4 provides a summary of the results.

##  2 ALMA data

###  2.1 Observations and data processing

Observations were performed with both the main (12 m) array and the Morita (7
m) Array with baselines ranging from 8 to 1568 m. The observations with both
arrays consist of two pointings centered on positions 13:39:55.9 -31:38:26 and
13:39:56.8 -31:38:32 in J2000 coordinates, which were used to map both
emission from the compact central starburst and more diffuse, extended
emission from gas to the southeast of the centre (see Miura et al. in
preparation). Additional data are also available from ALMA total power
observations, but since the H30$\alpha$ emission is from a very compact
source, the total power data will not substantially improve the detection of
the line emission. Moreover, inclusion of the total power data will complicate
the data processing procedure, and these data currently cannot be used for
continuum imaging. Hence, we did not include the total power data in our
analysis.

General information about each execution block used to construct the
H30$\alpha$ image cube and continuum image is listed in Table 1. Information
about the spectral set-up for each spectral window in each execution block is
given in Table 2.

Table 1: ALMA observation information. Array | Unique | Observing | On-source | Usable | uv | Bandpass | Flux | Phase
---|---|---|---|---|---|---|---|---
| identifier | dates | observing | antennas | coverage | calibrator | calibrator | calibrator
|  |  | time (min) |  | (m) |  |  |
Morita | A002/X8440e0/X29c6 | 15 Jun 2014 | 30.7 | 9 | 8-48 | J1427-4206 | Ceres | J1342-2900
Morita | A002/X9652ea/X5c3 | 10 Dec 2014 | 30.7 | 9 | 9-45 | J1337-1257 | Callisto | J1342-2900
12 m | A002/X966cea/X25de | 11 Dec 2014 | 8.5 | 37 | 13-336 | J1337-1257 | Callisto | J1342-2900
12 m | A002/Xa5df2c/X50ce | 18 Jul 2015 | 13.2 | 39 | 14-1512 | J1337-1257 | J1427-4206 | J1342-2900
12 m | A002/Xa5df2c/X52fa | 18 Jul 2015 | 15.8 | 39 | 14-1568 | J1337-1257 | Titan | J1342-2900
Table 2: ALMA spectral window settings.

Array | Unique | Frequency rangea | Bandwidth | Number of
---|---|---|---|---
| identifier | (GHz) | (GHz) | channels
Morita | A002/X8440e0/X29c6 | 229.216 - 231.208 | 1.992 | 2040
|  | 230.577 - 232.569 | 1.992 | 2040
|  | 243.594 - 245.586 | 1.992 | 2040
Morita | A002/X9652ea/X5c3 | 229.247 - 231.239 | 1.992 | 2040
|  | 230.608 - 232.601 | 1.992 | 2040
|  | 243.627 - 245.619 | 1.992 | 2040
12 m | A002/X966cea/X25de | 229.306 - 231.181 | 1.875 | 1920
|  | 230.667 - 232.542 | 1.875 | 1920
|  | 243.686 - 245.561 | 1.875 | 1920
12 m | A002/Xa5df2c/X50ce | 229.270 - 231.145 | 1.875 | 1920
|  | 230.630 - 232.505 | 1.875 | 1920
|  | 243.647 - 245.522 | 1.875 | 1920
12 m | A002/Xa5df2c/X52fa | 221.269 - 231.144 | 1.875 | 1920
|  | 230.630 - 232.505 | 1.875 | 1920
|  | 243.647 - 245.522 | 1.875 | 1920

a These values are the observed (sky) frequencies and not rest frequencies.

The visibility data for each execution block was calibrated separately using
the Common Astronomy Software Applications (CASA) version 4.7.0. To begin
with, we applied amplitude corrections based on system temperature
measurements to all data, and we applied phase corrections based on water
vapour radiometer measurements to the 12 m data. For the data with baselines
greater than 1000 m, we also applied antenna position corrections. Following
this, we visually inspected the visibility data and flagged data with noisy or
abnormal phase or amplitude values as well as atmospheric lines centered at
231.30 GHz. Next, we derived and applied calibrations for the bandpass, phase,
and amplitude. The Butler-JPL-Horizons 2012 models were used to obtain the
flux densities for Callisto and Titan. J1427-4206 is one of the 43 quasars
routinely monitored for flux calibration purposes as described within the ALMA
Technical Handbook555https://almascience.eso.org/documents-and-
tools/cycle4/alma-technical-handbook (Magnum & Warmels, 2016). The getALMAFlux
task within the Analysis Utilities software package was used to calculate the
flux density of J1427-4206 based on measurement in the ALMA Calibrator Source
Catalogue666https://almascience.eso.org/alma-data/calibrator-catalogue. The
version of the Butler-JPL-Horizons 2012 models implemented in CASA 4.7.0 is
known to produce inaccurate results for Ceres, so the data for the bandpass
calibrator J1427-4206 and the estimated flux density from the getALMAFlux task
were used to flux calibrate the 15 June 2014 observation. The uncertainty in
band 6 flux calibration is specified in the ALMA Proposer’s
Guide777https://almascience.eso.org/documents-and-tools/cycle4/alma-proposers-
guide (Andreani et al., 2016) as 10%, but because the uncertainty in the
estimated flux densities for J1427-4206 was 15%, we used 15% as the final
calibration uncertainty.

The H30$\alpha$ image was created after subtracting the continuum from the
visibility data in the spectral window containing the line. The continuum was
determined by fitting the visibility data at approximately 230.7-231.2 GHz and
231.7-232.5 GHz (in the Barycentric frame of reference) with a linear
function; this frequency range avoids not only the H30$\alpha$ line but also
the atmospheric absorption feature centered at 231.30 GHz. After this, we
concatenated the continuum-subtracted data and then created a spectral cube
using clean within CASA. We used Briggs weighting with a robust parameter of
0.5, which is the standard weighting used when producing ALMA images of
compact sources like the H30$\alpha$ source in NGC 5253. After creating the
image, we applied a primary beam correction. The spectral channels in the cube
have a width of 10 MHz (equivalent to a velocity width of 12.9 km s-1) and
range from sky frequencies of 231.40 to 231.80 GHz in the Barycentric frame.
The pixels have a size of 0.05 arcsec, and the imaged field was 100$\times$100
arcsec. The reconstructed beam has a size of 0.21$\times$0.19 arcsec.

We also created a 231.6 GHz (observed frame) continuum image using the data
from 230.7-231.2 GHz and 231.7-232.5 GHz. We could have used the data from the
spectral windows covering the CO and CS lines. However, the potentially steep
slope of the continuum at these frequencies (see the discussion in Section
2.2), problems with observations on the shortest baselines in the spectral
window covering the 243.6-245.6 GHz frequency range, and the relatively broad
CO line emission made it difficult to create reliable continuum images using
all spectral windows. Because we found evidence for extended continuum
emission, we used natural weighting when creating the final image. The image
dimensions are the same as for the H30$\alpha$ image cube. The beam size is
0.28$\times$0.25 arcsec.

As a test of the flux calibration, we imaged J1427-4206 and J1337-1257
(another quasar monitored by ALMA for flux calibration purposes) using the
same parameters that we used for creating the H30$\alpha$ image cube. The
measured flux densities differ by $<$10% from the getALMAFlux estimates, which
is below our assumed flux calibration uncertainty of 15%.

We also checked the astrometry of each of the two longest-baseline
observations by imaging the astrometry check source (J1339-2620) using the
same parameters as for the continuum image, fitting the peak with a Gaussian
function, and comparing the position to the coordinates in the ALMA Calibrator
Source Catalogue. The positions match to within one pixel, or 0.05 arcsec.
Equations in the ALMA Technical Handbook (Magnum & Warmels, 2016) yield a
smaller value, but we will use 0.05 arcsec as the astrometric uncertainty.

###  2.2 H30$\alpha$ and 231.6 GHz continuum images

Figure 1: Images of the central 8$\times$8 arcsec of NGC 5253 in 231.6 GHz
(sky frequency) continuum emission (top) and H30$\alpha$ line emission
(bottom). The contours in each image show the 2$\sigma$, 3$\sigma$, 5$\sigma$,
10$\sigma$, and 100$\sigma$ detections levels in each image, where $\sigma$ is
1.0 Jy arcsec-2 for the 231.6 GHz image and 0.69 Jy km s1 arcsec-2 for the
H30$\alpha$ image. The red ovals at the bottom right of each panel show the
FWHM of the beam (0.28$\times$0.25 arcsec for the 231.6 GHz image and
0.21$\times$0.19 arcsec for the H30$\alpha$ image).

Figure 1 shows the 231.6 GHz (sky frequency) continuum and H30$\alpha$
spectral line images of the central 8$\times$8 arcsec of NGC 5253. The
H30$\alpha$ image is the integral of the continuum-subtracted flux between sky
frequencies of 231.55 and 231.65 GHz. Both sources show a very bright central
peak at a right ascension of 13:39:55.965 and declination of -31:38:24.36 in
J2000 coordinates. No significant H30$\alpha$ emission is observed outside of
the central peak. The best-fitting Gaussian function to the H30$\alpha$ image
has a FWHM 0.27$\times$0.21 arcsec, indicating that the H30$\alpha$ source may
have a deconvolved angular size of $\sim$0.15 arcsec. In the continuum image,
a second unresolved source to the northeast of the centre is clearly detected
at the 10$\sigma$ level. Several other compact sources are detected in
continuum at the 3-5$\sigma$ level, including a few sources outside the region
shown in Figure 1, and some diffuse emission near the 3$\sigma$ level is seen
around the central peak, most notably immediately to south of the centre.

Figure 2:  A map showing the positions of several sources detected in
different bands in the centre of NGC 5253. The H30$\alpha$ source is
identified in green, and the ellipse represents the FWHM of a Gaussian
function fit to the data, which is 0.27$\times$0.21 arcsec. The blue circles
identify the locations of the two brightest H$\alpha$ and Pa$\alpha$ sources
imaged by Calzetti et al. (2015, ; blue), and the diameters of the circles
represent the 0.20 arcsec astrometric uncertainty in the data. The deconvolved
size (0.099 $\times$ 0.039 arcsec) of the 43 GHz core imaged by Turner & Beck
(2004) is shown in red; this source also corresponds to the central source
imaged at 15 and 23 GHz by Turner et al. (2000). A secondary 23 GHz source
identified by Turner & Beck (2004) is shown in magenta, and the ellipse
diameter matches the 0.22 $\times$ 0.08 arcsec FWHM of the beam.

Figure 2 shows the location of the H30$\alpha$ source (which coincides with
the location of the peak in 231.6 GHz emission) relative to other sources
detected in observations with comparable angular resolutions. The H30$\alpha$
source lies within 0.04 arcsec of the peak in 43 GHz emission measured by
Turner & Beck (2004), which has the same position as the brightest 15 and 23
GHz sources detected in the high angular resolution radio observations
presented by Turner et al. (2000). This offset is smaller than the astrometric
uncertainty of 0.05 arcsec that we are using for the ALMA data. Turner et al.
(2000) also reported the detection of a second 23 GHz source at a location
0.21 arcsec east of the H30$\alpha$ source, although this source is not
detected at 15 GHz, and it also is either a very weak detection or non-
detection in the 43 GHz images shown by Turner & Beck (2004). The difference
between the peak fluxes of the primary and secondary 23 GHz sources is
$\sim$6$\times$. If this secondary source has a corresponding H30$\alpha$
source, it would be difficult to separate the emission of this secondary
source from the brighter H30$\alpha$ source given the small angular separation
between the sources compared to the FWHM of the ALMA beam and the much lower
flux expected from the secondary source relative to the brighter source.
Additional millimetre or radio observations with better angular resolutions
and better sensitivities would be needed to confirm that the secondary source
is present.

The two brightest H$\alpha$ and Pa$\alpha$ (1.876 $\mu$m) sources that were
identified by Calzetti et al. (2015) using Hubble Space Telescope straddle the
H30$\alpha$ source. These sources, which were labelled clusters 5 and 11, have
counterparts to sources identified by Calzetti et al. (1997), Alonso-Herrero
et al. (2004), Harris et al. (2004), and de Grijs et al. (2013). Calzetti et
al. (2015) had suggested that the brightest radio continuum sources actually
corresponded to cluster 11 (as originally suggested by Alonso-Herrero et al.
(2004)), that the secondary 23 GHz source detected by Turner et al. (2000) at
23 GHz corresponds to cluster 5 and that the offset between the radio and
optical/near-infrared data was related to systematic effects in the astrometry
systems used to create the images. It is therefore possible that the
H30$\alpha$ source detected in the ALMA data corresponds to cluster 11.
However, clusters 5 and 11 are separated by a distance of 0.46 arcsec, so they
should have been resolved into two separate components in the H30$\alpha$ map.
The Pa$\alpha$ fluxes measured by Calzetti et al. (2015) differ by only
$\sim$25%, but after they attempt to correct for dust absorption using models
that account for the intermixing of the stars and dust, the line fluxes are
expected to differ by $\sim$6$\times$. The peak of the H30$\alpha$ source is
detected by ALMA at the 18$\sigma$ level, so a second photoionization region
with at least one-sixth the flux of the main source would be detected at the
3$\sigma$ level.

It is possible that the second source is even fainter than expected relative
to the primary H30$\alpha$ source, which could occur if the primary source is
more obscured than expected. Alternately, it is possible that both sources lie
at ends of a larger star forming complex that is heavily obscured in the
optical and near-infrared bands, although the 0.46 arcsec separation between
the two optical/near-infrared sources is larger than the $\sim$0.15 arcsec
size of the H30$\alpha$ source we derived, which makes this second scenario
less likely.

The coincidence of the H30$\alpha$ emission with the 231.6 GHz continuum
emission provides additional support for the possibility that the central star
forming region is very heavily obscured. As discussed below, the 231.6 GHz
continuum emission is expected to contain a combination of dust and free-free
emission, although the relative contributions of each may be very uncertain.
If the 231.6 GHz emission is primarily from dust, then we would expect the
optical and near-infrared light to be heavily obscured where most of the
photoionizing stars are also located and for the Pa$\alpha$ and H$\alpha$
emission to be more easily detected at the fringes of the region. In fact,
Calzetti et al. (2015) noted that the Pa$\alpha$ emission is offset relative
to the H$\alpha$ emission in their cluster 11, which would be consistent with
this interpretation of the millimetre continuum and recombination line
emission. However, if the 231.6 GHz emission includes substantial free-free
emission, then we would expect to easily detect a second photoionization
region, even one that is 20$\times$ fainter than the central photoionizing
region.

Figure 3: Plots of the integrated 231.6 GHz continuum flux density (top) and
integrated H30$\alpha$ flux (bottom) as a function of the radius of the
measurement aperture. The uncertainties in the continuum measurement related
to random noise in the image are smaller than the width of the line.

To understand the distribution of the continuum and H30$\alpha$ emission, we
measured integrated fluxes within apertures with radii varying from 0.1
arcsec, which is equivalent to the radius of the beam, to 9 arcsec, which is
the radius at which we begin to measure artefacts related to the negative
sidelobes of the central source. These curve-of-growth profiles are shown in
Figure 3. Most of the H30$\alpha$ flux from the unresolved central source
falls within a radius of 0.3 arcsec, so we will use the measurements of the
line flux from within that radius as the total flux. The integrated continuum
emission peaks at a radius of $\sim$8.5 arcsec. Emission on angular scales
larger than 17 arcsec is either resolved out, strongly affected by the
negative sidelobes, or affected by the high noise at the edge of the primary
beam. While differences in the signal-to-noise ratio may explain why the
continuum emission is detected at a larger radius than the H30$\alpha$ line,
it is also possible that a significant fraction of the continuum emission may
originate from dust within NGC 5253 that is distributed more broadly than the
photoionized gas.

Table 3: Continuum measurements of NGC 5253 at 230-250 GHz. Reference | Telescope | Frequency | Beam | Flux Density | Aperture
---|---|---|---|---|---
|  | (GHz) | FWHM | (mJy) | Diameter
|  |  | (arcsec) |  | (arcsec)
[this paper] | ALMA | 231.6 | 0.28$\times$0.25 | $104\pm 16$ | 17
Meier et al. (2002) | OVRO | 233.3 | $6.5\times 4.5$ | $46\pm 10$ | 20
Vanzi & Sauvage (2004) | SEST | 250 | 11 | $114\pm 4$ | 11
Miura et al. (2015) | SMA | 230 | $11\times 4$ | $34\pm 9$ | $11\times 4$

The 231.6 GHz continuum flux density within a radius of 8.5 arcsec is
104$\pm$16 mJy. A few other continuum flux densities at comparable frequencies
have been published. These measurements as well as details about the data are
listed in Table 3.

The ALMA measurement is very close to the Swedish-ESO Submillimetre Telescope
(SEST) measurement from Vanzi & Sauvage (2004). While the Vanzi et al. number
is for both a smaller aperture and a higher frequency than the ALMA
measurement, adjustments for both the measurement aperture and spectral slope
should potentially cancel out.

The Meier et al. (2002) flux density from the Owens Valley Radio Observatory
(OVRO)and Miura et al. (2015) flux density from the Submillimeter Array (SMA)
are both lower than the ALMA measurements by 2-3$\times$. Both measurements
have high uncertainties related to either calibration or detection issues,
which could partly explain the mismatch between these data and ours. The Miura
et al. (2015) measurement is also for a smaller area; when we use a similar
aperture to their beam size, we obtain a flux density of 47$\pm$7 mJy, which
is near their measurement. However, it is also likely that the OVRO and SMA
data were insensitive to the faint, extended continuum emission from this
source because of a combination of limited uv coverage and the broader beam
size. The extended emission observed by OVRO and SMA could have been smeared
into the negative sidelobes of the central source or could have been
redistributed on spatial scales larger than the largest angular scales
measurable by the arrays. The ALMA observations, which used both short and
long baselines, can recover structures on the same angular scales as OVRO and
SMA while not spreading the emission onto scales where it is not recoverable
by the interferometer, and since the ALMA data have a smaller beam, any
negative sidelobes will not cover a significant fraction of the diffuse,
extended emission within a radius of 8.5 arcsec of the centre.

We therefore think the ALMA flux density, which is consistent with the SEST
measurement, should be fairly reliable. Having said this, we will emphasize
that much of the continuum emission in our image has a surface brightness at
$<$5$\sigma$; more sensitive measurements would be needed to confirm our
results.

The emission at 231.6 GHz could originate from a variety of sources. The
amount of dust emission at 231.6 GHz can be estimated by extrapolating the
modified blackbody function from Rémy-Ruyer et al. (2013) that was fit to the
100-500 $\mu$m Herschel Space Observatory data. This gives a flux density of
63 mJy, but the uncertainties in the parameters for the best fitting function
indicate that the uncertainty is$\sim$2$\times$. Free-free emission as well as
a few more exotic emission mechanisms could contribute to the emission at
231.6 GHz. While a more in-depth analysis of the SED is beyond the scope of
this paper, we discuss this topic further in Section 3.1.

Figure 4: The continuum-subtracted spectrum of the centre of NGC 5253 showing
the H30$\alpha$ line emission. This spectrum was measured within a region with
a radius of 0.5 arcsec. The green line shows the best-fitting Gaussian
function, which has a mean relativistic velocity in the Barycentric frame of
391$\pm$2 km s-1 and a FWHM of 68$\pm$3 km s-1.

Figure 4 shows the portion of the continuum-subtracted spectrum that includes
the H30$\alpha$ line emission. The line has a mean relativistic velocity in
the Barycentric reference frame of 391$\pm$2 km s-1 and a FWHM of 68$\pm$3 km
s-1. The integral of the line is 0.86 Jy km s-1 with a measurement uncertainty
of 0.04 Jy km s-1 and a calibration uncertainty of 0.13 Jy (15%). The spectral
window covering the H30$\alpha$ line does not include any other detectable
spectral lines. Miura et al. (in preparation) will discuss the CO (2-1) line
emission and any other spectral lines detected in the other spectral window.

###  2.3 SFR from the H30$\alpha$ data

For this analysis, we assume that the nuclear starburst detected in
H30$\alpha$ data contains most of the photoionizing stars in the galaxy and
that a SFR derived from it will be representative of the global SFR. While the
source is near the brightest clusters found in H$\alpha$ and Pa$\alpha$
emission, fainter $<$5 Myr clusters and diffuse emission are found outside the
central starburst (Calzetti et al., 2004, 2015; Harris et al., 2004). Although
most of this emission should fall within the region imaged by ALMA, the lack
of H30$\alpha$ emission detected from these fainter sources could cause the
SFR from the H30$\alpha$ emission to be biased downwards. Given the central
concentration of the H$\alpha$ and Pa$\alpha$ emission, however, the bias may
not be too severe to significantly affect comparisons to other star formation
tracers.

The H30$\alpha$ flux can be converted to a photoionizing photon production
rate $Q$ using

$\begin{split}\frac{\mbox{Q}(\mbox{H30}\alpha)}{\mbox{s}^{-1}}=3.99\times
10^{30}\left[\frac{\alpha_{B}}{\mbox{ cm}^{3}\mbox{ s}^{-1}}\right]\ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\\
\times\left[\frac{\epsilon_{\nu}}{\mbox{erg s}^{-1}\mbox{
cm}^{-3}}\right]^{-1}\left[\frac{\nu}{\mbox{~{}GHz}}\right]\left[\frac{D}{\mbox{
Mpc}}\right]^{2}\left[\frac{\int f_{\nu}(\mbox{line})dv}{\mbox{Jy km
s}^{-1}}\right]\end{split}$ (1)

based on equations from Scoville & Murchikova (2013). The effective
recombination coefficient ($\alpha_{B}$) and emissivity ($\epsilon_{\nu}$)
terms in this equation depend on the electron density and temperature. Both
term varies by less than 15% for electron densities between $10^{2}$ and
$10^{5}$cm-3. The terms do vary significantly with electron temperature
between 3000 and 15000 K, and the resulting $Q$ can change by a factor of
$\sim$2.4 depending on which temperature is selected. In analyses at lower
frequencies, where the continuum emission is dominated by free-free emission,
it is possible to use the line-to-continuum ratio to estimate electron
temperatures. However, thermal dust emission comprises a significant yet
poorly-constrained fraction of the 231.6 GHz continuum emission in the central
starburst, so this method would produce questionable results. Instead, we use
11500 K for the electron temperature, which is based on [OIII] measurements
near the centres of the brightest optical recombination line sources within
NGC 5253 from Kobulnicky et al. (1997), López-Sánchez et al. (2007), Guseva et
al. (2011), and Monreal-Ibero et al. (2012). For the electron density, we use
600 cm-3, which is the mean of electron densities based on measurements of the
[OII] and [SII] from these same regions as given by López-Sánchez et al.
(2007), Guseva et al. (2011), and Monreal-Ibero et al. (2012). Although the
electron density measurements from these three studies vary by a factor of
$\sim$3, probably because of issues related to the position and size of the
measurement apertures as discussed by Monreal-Ibero et al. (2012), the
resulting $Q$ values should be unaffected by the relatively large disagreement
in these measurements. Dust extinction could have affected both the electron
temperature and density estimates, but we do not expect extinction affects to
alter the data to a degree where our calculations are affected. We
interpolated among the $\alpha_{B}$ and $\epsilon_{\nu}$ terms published by
Storey & Hummer (1995) to calculate specific values for these terms based on
our chosen electron temperature and density. Based on these terms and our
H30$\alpha$ flux, we calculated $Q$ to be (1.9$\pm$0.3)$\times$$10^{52}$ s-1.

The $Q$ value can be converted to SFR (in M⊙ yr-1) using a simple scaling
term, but this term depends upon the characteristics of the stellar population
within the star forming regions. Using Starburst99 (Leitherer et al., 1999),
Murphy et al. (2011) derived a scaling term of $7.29\times 10^{-54}$ for solar
metallicity (defined in older versions of Starburst99 as $Z$=0.020) and a
Kroupa (2002) initial mass function (IMF)888The Kroupa IMF used in Starburst99
is defined as having an index of 2.3 between 100 M⊙ (the IMF upper mass
boundary) and 0.5 M⊙ and an index of 1.3 between 0.5 M⊙ and 0.1 M⊙ (the IMF
lower mass boundary).. However, the conversion factor is dependent on
metallicity. Monreal-Ibero et al. (2012) reported that 12+log(O/H) for NGC
5253 is 8.26$\pm$0.04 (on a scale where solar metallicity corresponds to
12+log(O/H)=8.66 and $Z$=0.014), which is consistent with older results
(Kobulnicky et al., 1997; López-Sánchez et al., 2007; Guseva et al., 2011).
Assuming that all other abundances scale with the O/H ratio, this oxygen
abundance is equivalent to $Z$$\cong$0.0056.

The current version (7.0.1) of Starburst99 (Leitherer et al., 2014) provides
the Geneva 2012/13 evolutionary tracks, which include stellar rotation
(Ekström et al., 2012; Georgy et al., 2012), as an option for the simulations.
Stellar rotation enhances convection and also metallicity at the surfaces of
the stars, which makes stars hotter and therefore affects the conversion
between $Q$ and SFR. Currently, Starburst99 includes tracks for no rotation
and rotation at 40% of the break up velocity. These two extremes are expected
to bracket the actual rotation velocities of typical stellar populations. The
current version of Starburst99 also only includes Geneva tracks with rotation
for $Z=0.002$ and $Z=0.014$. We assume that the logarithm of $Q$ scales
linearly with $Z$ when deriving conversion factors. Based on Starburst99
results using the 1994 versions of the Geneva tracks (Shaller et al., 1992;
Charbonnel et al., 1993; Schaerer et al., 1993a, b), this interpolation should
be accurate to within 5%.

We report three versions of the SFR: a version based on solar metallicity and
no rotation using the Murphy et al. (2011) conversion; a version based on the
Geneva 2012/13 tracks for $Z$=0.0056 with no stellar rotation; and a version
based on the Geneva 2012/13 tracks for $Z$=0.0056 where we use the average of
model results for no rotation and 40% of the break up velocity. The last two
numbers are derived from Starburst99 simulations using a Kroupa IMF and should
be applicable to scenarios where star formation has been continuous for $>$10
Myr. The three conversion factors are listed in Table 4, with more general-
purpose correction factors for metallicity and rotation effects listed in
Table 5. The SFRs based on Equation 1 and the conversion factors between $Q$
and SFR are reported in Table 6. Additionally, Figure 5 shows a graphical
comparison between the SFR from the H30$\alpha$ data and the SFRs calculated
from other star formation tracers as described in the following section. In
accounting for metallicity effects (using the new Geneva tracks), the
resulting SFR decreases by $\sim$25%. When rotation is incorporated, the SFR
decreases by an additional $\sim$10% relative to the solar value without
rotation.

Table 4: Conversions between $Q$ and SFR.

Model | Conversion from $Q$ to SFR
---|---
| ( M⊙ yr-1 / (s-1) )
Solar metallicity, no stellar rotation | $7.29\times 10^{-54~{}a}$
$Z$=0.0056b, no stellar rotation | $5.40\times 10^{-54}$
$Z$=0.0056b, with stellar rotation | $4.62\times 10^{-54}$

a This conversion is from Murphy et al. (2011).
b These metallicities are based on a scale where solar metallicity is 0.014.

Table 5: Corrections in SFR relative to solar metallicity scenario with no
stellar rotation.

General | Specific | Correction factora
---|---|---
waveband | star formation |  $Z$=0.0056 |  $Z$=0.0056
| metrics | no stellar rotationb | with stellar rotationb
Recombination lines | H$\alpha$, H30$\alpha$ | 0.74 | 0.63
Infrared | 22 $\mu$m, 70 $\mu$m, 160 $\mu$m, total infrared | $0.90\pm 0.03$ | $0.72\pm 0.03$

a Derived SFRs should be multiplied by these correction factors.

b On this scale, solar metallicity corresponds to $Z$=0.014, and $Z$=0.0056 is
the approximate metallicity of NGC 5253 based on 12+log(O/H) measurements.

Table 6: SFRs calculated for NGC 5253.

Waveband | SFR (M⊙ yr-1)a
---|---
| Solar metallicity |  $Z$=0.0056 |  $Z$=0.0056
| no stellar rotation | no stellar rotation | with stellar rotation
H30$\alpha$ | $0.14\pm 0.02$ | $0.102\pm 0.015$ | $0.087\pm 0.013$
22 $\mu$m | $0.41\pm 0.02$ | $0.37\pm 0.02$ | $0.30\pm 0.02$
70 $\mu$m | $0.095\pm 0.004$ | $0.086\pm 0.005$ | $0.068\pm 0.004$
160 $\mu$m | $0.070\pm 0.003$ | $0.063\pm 0.003$ | $0.050\pm 0.003$
Total infrared | $0.148\pm 0.009$ | $0.133\pm 0.009$ | $0.107\pm 0.008$
H$\alpha$ (corrected using Pa$\alpha$, Pa$\beta$ data)b | $0.11\pm 0.03$ | $0.08\pm 0.02$ | $0.07\pm 0.02$
H$\alpha$ (corrected using 22 $\mu$m data) | $0.221\pm 0.012$ | $0.164\pm 0.009$ | $0.139\pm 0.008$
H$\alpha$ (corrected using total infrared data) | $0.055\pm 0.04$ | $0.041\pm 0.003$ | $0.035\pm 0.003$

a All uncertainties incorporate measurement uncertainties and uncertainties
related to the correction factors in Table 5. The uncertainties do not include
the uncertainties in the multiplicative factos applied when converting from
the fluxes in the individual bands to SFR.

b The extinction corrections for these data were calculate and applied by
Calzetti et al. (2015).

Figure 5: A graphical depiction of the SFRs for NGC 5253. These are values
calculated using corrections to account for the metallicity of NGC 5253
($Z=0.0056$) and stellar rotation effects; they correspond to the values in
the rightmost column in Table 6. Uncertainties for the individual data points
(when they are larger than the symbols in this plot) correspond to the
measurement uncertainties and uncertainties related to the correction factors
in Table 5 but do not include uncertainties in the conversion factors between
the fluxes and SFR. The grey band corresponds to the mean and 1$\sigma$
uncertainties in the SFR from the H30$\alpha$ data.

##  3 Other star formation tracers

Having derived the SFR from the H30$\alpha$ data, we calculated SFRs using
other publicly-available infrared and H$\alpha$ data. While the H30$\alpha$
emission primarily originates from stars younger than 5 Myr, other star
formation tracers may trace stellar populations with different ages, so the
derived SFRs could differ if the rate has changed significantly over time.
SFRs based on most star formation tracers are also affected by IMF,
metallicity, and stellar rotation effects. Most current conversions, including
all of the ones we used, are calibrated for a Kroupa IMF. However, the SFR
equations are usually calibrated for solar metallicities and do not account
for stellar rotation. We therefore report SFRs both using the original
equations for solar metallicity and using conversions modified for the
metallicity of NGC 5253. For the lower metallicity scenario, we include SFRs
with and without incorporating stellar rotation effects. All corrections are
derived using version 7.0.1 of the Starburst99 models and are applicable to
scenarios with a Kroupa IMF and continuous star formation older than 10 Myr.
The corrections for stellar rotation are the average of values for no rotation
and 40% of the break-up velocity.

###  3.1 Comparisons of H30$\alpha$ results to other results from millimetre
and radio data

The H30$\alpha$ results can be compared to some of the published $Q$ based on
other radio data analyses. To start with, two papers have published analyses
based on radio recombination lines. Mohan et al. (2001) published multiple
values of $Q$ based on different models applied to H92$\alpha$ (8.31 GHz)
data; these $Q$ values range from 0.9$\times$$10^{52}$ to 2$\times$$10^{52}$
s-1 when rescaled for a distance of 3.15 Mpc. Rodríguez-Rico et al. (2007)
using H53$\alpha$ (42.95 GHz) data obtained a $Q$ of 1.2$\times$$10^{52}$ s-1.
Most of these measurements are lower than the value of
(1.9$\pm$0.3)$\times$$10^{52}$ s-1 from the H30$\alpha$ data, although Model
IV from Mohan et al. (2001) produced a slightly higher $Q$, and most other
results differ by less than 2$\times$. Both the Mohan et al. (2001) and
Rodríguez-Rico et al. (2007) $Q$ values are based on models that have
attempted to account for masing and gas opacity effects, but it is possible
that they were not always able to correct for these effects accurately.
Nonetheless, some fine-tuning of the models of the lower frequency
recombination line emission may yield more accurate $Q$ and SFR values from
the higher order recombination lines.

A series of analyses of the 23 - 231 GHz continuum emission published by
Turner et al. (2000), Meier et al. (2002), Turner & Beck (2004), and Miura et
al. (2015) treated the emission at these frequencies as originating mainly
from free-free emission. Based on this assumption, these observations gave $Q$
values ranging from 2.4$\times$$10^{52}$ to 4.8$\times$$10^{52}$ s-1 after
being rescaled for a distance of 3.15 Mpc. Some of these values are
significantly higher than the value of (1.9$\pm$0.3)$\times$$10^{52}$ s-1 from
the H30$\alpha$ line emission. As discussed in Section 2.2, thermal dust
emission could produce more than half of the observed emission at 231 GHz, and
this probably resulted in the high $Q$ values calculated by Meier et al.
(2002) and Miura et al. (2015) based on photometry as similar frequencies. The
highest $Q$ from Turner & Beck (2004) is based on 43 GHz emission measured
within a region with a diameter of 1.2 arcsec. Rodríguez-Rico et al. (2007)
determined that only $\sim$20% of the 43 GHz emission originated from a region
with a diameter of 0.4 arcsec, comparable to the region where we detected
H30$\alpha$ emission. If we adjust the value of $Q$ from Turner & Beck (2004)
to account for the aperture effects, the value drops to
$\sim$1.0$\times$$10^{52}$ s-1, which is nearly 2$\times$ lower than what we
measure from the H30$\alpha$ source.

Meier et al. (2002) and Rodríguez-Rico et al. (2007) both indicate that
optical thickness effects could alter the free-free emission, which
complicates the conversion from continuum emission to $Q$. Additionally, it is
possible that other emission sources that are not understood as well from a
physical standpoint, such as the ”submillimetre excess” emission that has been
identified in many other low-metallicity dwarf galaxies (e.g. Galametz et al.,
2011; Rémy-Ruyer et al., 2013) or anomalous microwave emission (e.g. Murphy et
al., 2010; Dickinson et al., 2013), could contribute to the emission in the
millimetre bands. The data from the analysis in our paper are insufficient for
determining how any of these phenomena affect the radio or millimetre emission
from NGC 5253 or affect the calculation of $Q$ from radio or millimetre data.
A deeper analysis of the SED, potentially including the reprocessing and
analysis of ALMA 86 - 345 GHz data acquired in 2014 and later as well as a re-
examination of archival radio data from the Very Large Array, would be needed
to identify the various emission components in the 1-350 GHz regime as well as
to determine how to convert the continuum emission to SFR. However, this is
beyond the scope of our paper.

Aside from the calculations described above, a widely-used conversion between
radio continuum emission and SFR relies upon the empirical correlation between
1.4 GHz emission, which is an easily-observable radio continuum band, and far-
infrared emission. We can only find published 1.4 GHz flux densities
integrated over an area much broader than the aperture used for the
H30$\alpha$ measurement, and the radio emission is very extended compared to
the central starburst (e.g. Turner et al., 1998; Rodríguez-Rico et al., 2007).
Hence, any SFR calculated using the available globally-integrated flux density
will also be affected by aperture effects, so it would be inappropriate to
list it alongside the other SFRs in Table 6. Having said this, if we use

$\frac{\mbox{SFR}(\mbox{1.4 GHz})}{\mbox{M}_{\odot}\mbox{
yr}^{-1}}=0.0760\left[\frac{D}{\mbox{Mpc}}\right]^{2}\left[\frac{f_{\nu}(1.4\mbox{
GHz})}{\mbox{Jy}}\right],$ (2)

which is based on the conversion from Murphy et al. (2011), and the globally-
integrated measurement of $84.7\pm 3.4$ mJy from the 1.4 GHz NRAO VLA Sky
Survey (Condon et al., 1998), we obtain a SFR of $0.064\pm 0.003$ M⊙ yr-1.

The SFR from the 1.4 GHz emission is lower than the SFR from the H30$\alpha$
data even though the 1.4 GHz emission is measured over a much larger area. The
1.4 GHz band has been calibrated as a star formation tracer using data for
solar metallicity galaxies and relies upon a priori assumptions about the
relative contributions of free-free and synchrotron emission to the SED. The
ratio of these forms of emission can vary between spiral and low mass
galaxies, but the relation between infrared and radio emission has been found
to staty linear in low metallicity galaxies in general (e.g. Bell, 2003; Wu et
al., 2007, and references therein). In NGC 5253 specifically, the relative
contribution of synchrotron emission to the 1.4 GHz band is very low
(Rodríguez-Rico et al., 2007), which is probably sufficient to cause the SFR
from the globally-integrated 1.4 GHz measurement to fall below the SFR from
the nuclear H30$\alpha$ measurement as well as the SFR from the total infrared
flux (see Section 3.2).

In any case, it appears that Equation 2 simply is not suitable for NGC 5253,
as it evidently deviates from the empirical relations between radio emission
and either infrared flux or SFR. An SFR based on the spectral decomposition of
the SED and the analysis of its components would potentially yield more
accurate results, but as we stated above, this analysis is beyond the scope of
this paper.

###  3.2 Comparisons of H30$\alpha$ and infrared dust continuum results

####  3.2.1 SFR calculations

For calculating SFRs based on infrared flux densities, we used globally-
integrated values, mainly because the infrared emission appears point-like in
most data and because no data exist with angular resolutions comparable to the
ALMA data. Figures 1 and 3 show that a significant fraction of the cold dust
emission originates from an extended region outside the central starburst.
However, the 8 $\mu$m image from Dale et al. (2009) shows that most of the
emission in that band (a combination of hot dust and polycyclic aromatic
hydrocarbon (PAH) emission as well as a small amount of stellar emission)
originates from a central unresolved source with a diameter smaller than 2
arcsec. The emission at mid-infrared wavelengths should be very compact and
therefore should be directly related to the luminosity of the central
starburst seen in H30$\alpha$ emission. The SFR from the total infrared
emission could be affected by diffuse dust heated by older stellar populations
outside the centre and therefore could be higher. While we do not apply any
corrections for this diffuse dust, we discuss the implications of this more in
Section 3.2.2.

Table 7: Infrared data for NGC 5253. Wavelength | Flux
---|---
($\mu$m) | densitya (Jy)
12 | $1.86\pm 0.08$
22 | $12.4\pm 0.7$
70 | $33.0\pm 1.6$
100 | $33.2\pm 1.6$
160 | $22.4\pm 1.2$
250 | $7.3\pm 0.6$
350 | $3.3\pm 0.3$
500 | $1.04\pm 0.09$

We calculated SFRs based on flux densities measured in individual bands as
well as total infrared fluxes based on integrating the SED between 12 and 500
$\mu$m, which covers most of the dust continuum emission. Table 7 shows the
data we used in this analysis.

For the 12 and 22 $\mu$m bands, we made measurements within Wide-field
Infrared Survey Explorer (WISE; Wright et al., 2010) images from the AllWISE
data release. Although 24 $\mu$m flux densities based on Spitzer data have
been published by Engelbracht et al. (2008) and Dale et al. (2009), the centre
of NGC 5253 is saturated in the 24 $\mu$m image (Bendo et al., 2012). Hence,
we used the WISE 22 $\mu$m data instead and assumed that the conversions from
WISE 22 $\mu$m flux densities to SFR will be the same as for Spitzer 24 $\mu$m
data. The 12 and 22 $\mu$m flux densities were measured within circles with
radii of 150 arcsec; this is large enough to encompass the optical disc of the
galaxy as well as the beam from the central source, which has a FWHM of 12
arcsec at 22 $\mu$m (Wright et al., 2010). The backgrounds were measured
within annuli with radii of 450 and 500 arcsec and subtracted before measuring
the flux densities. Calibration uncertainties are 5% at 12 $\mu$m and 6% at 22
$\mu$m. Colour corrections from Wright et al. (2010), which change the flux
densities by $<$$\sim$10%, are applied based on spectral slopes proportional
to $\nu^{-3}$ at 12 $\mu$m and $\nu^{-2}$ at 22 $\mu$m, which is based on the
spectral slopes between 12 and 22 and between 22 and 70 $\mu$m.

For the 70, 100, 160, 250, 350, and 500 $\mu$m measurements, we used the
globally-integrated flux densities measured from Herschel data by Rémy-Ruyer
et al. (2013). These data include no colour corrections, so we applied
corrections equivalent to that for a point-like modified blackbody with a
temperature of 30 K and an emissivity that scales as $\nu^{2}$, which is
equivalent to the shape of the modified blackbody fit by Rémy-Ruyer et al.
(2013) to the data. The 70, 100, and 160 $\mu$m colour corrections, which
change the flux densities by $<$$\sim$5%, are taken from Müller et al.
(2011)999http://herschel.esac.esa.int/twiki/pub/Public/PacsCalibrationWeb
/cc_report_v1.pdf, and the 250, 350, and 500 $\mu$m colour corrections, which
change the flux densities by $\sim$10%, are taken from Valtchanov
(2017)101010http://herschel.esac.esa.int/Docs/SPIRE/spire_handbook.pdf. These
colour-corrected data are listed in Table 7.

While multiple methods have been derived for calculating the total infrared
flux using a weighted sum of flux densities measured in multiple other
individual bands (e.g. Dale et al., 2002; Boquien et al., 2010; Galametz et
al., 2013; Dale et al., 2014), most of these derivations are calibrated for
galaxies with SEDs similar to those of spiral galaxies. The dust in NGC 5253
is much hotter than in than in most spiral galaxies, and in particular, the
22/70 $\mu$m ratio of 0.38 in NGC 5253 is higher than the 24/70 $\mu$m ratio
of 0.05-0.10 found in many spiral galaxies (e.g. Dale et al., 2007; Bendo et
al., 2012). We therefore calculated the total infrared flux by first linearly
interpolating between the logarithms of the monochromatic flux densities as a
function of the logarithm of the wavelength and then integrating under the
curve. This gave a total infrared flux of (3.2$\pm$0.2)$\times$$10^{14}$ Jy
Hz, with the uncertainties derived using a monte carlo analysis.

Most conversions from infrared emission to SFR work given the assumption that
star forming regions produce most of the observed bolometric luminosity of
galaxies and that dust absorbs and re-radiates virtually all of the emission
from the star forming regions. Additionally, the conversions of measurements
from individual infrared wavebands to SFR is based on the assumption that the
SED does not change shape and that the flux densities in the individual band
scale linearly with the total infrared flux. For this analysis, we used

$\frac{\mbox{SFR}(22\mu\mbox{m})}{\mbox{M}_{\odot}\mbox{ yr}^{-1}}=2.44\times
10^{-16}\left[\frac{D}{\mbox{Mpc}}\right]^{2}\left[\frac{\nu
f_{\nu}(22\mu\mbox{m})}{\mbox{Jy Hz}}\right]$ (3)

from Rieke et al. (2009),

$\frac{\mbox{SFR}(70\mu\mbox{m})}{\mbox{M}_{\odot}\mbox{ yr}^{-1}}=7.04\times
10^{-17}\left[\frac{D}{\mbox{Mpc}}\right]^{2}\left[\frac{\nu
f_{\nu}(70\mu\mbox{m})}{\mbox{Jy Hz}}\right]$ (4)

from Calzetti et al. (2010),

$\frac{\mbox{SFR}(160\mu\mbox{m})}{\mbox{M}_{\odot}\mbox{ yr}^{-1}}=1.71\times
10^{-16}\left[\frac{D}{\mbox{Mpc}}\right]^{2}\left[\frac{\nu
f_{\nu}(160\mu\mbox{m})}{\mbox{Jy Hz}}\right]$ (5)

from Calzetti et al. (2010), and

$\begin{split}\frac{\mbox{SFR}(\mbox{total infrared})}{\mbox{M}_{\odot}\mbox{
yr}^{-1}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\\ =4.66\times
10^{-17}\left[\frac{D}{\mbox{Mpc}}\right]^{2}\left[\frac{f(\mbox{total
infrared})}{\mbox{Jy Hz}}\right]\end{split}$ (6)

from Kennicutt & Evans (2012) based on derivations from Hao et al. (2011) and
Murphy et al. (2011). The SFRs calculation using these equations are listed in
Table 6.

While the conversion for total infrared flux is derived using Starburst99 for
solar metallicity and older (but unspecified) stellar evolutionary tracks, the
conversions for the 22, 70, and 160 $\mu$m bands are based on part upon
empirical relations between the emission in those individual bands and other
star formation tracers. However, all of these conversions are based upon the
assumption that the infrared flux as measured in an individual band or as
integrated over a broad wavelength range will scale with the bolometric
luminosity. Based on both the Geneva 1994 and 2012/13 tracks implemented in
Starburst99 version 7.0.1, the conversions factors in Equations 3-6 should be
multiplied by 0.90 to correct for the lower metallicity in NGC 5253. To
account for metallicity and rotation in the same way as we did for the
recombination lines, the conversions need to be multiplied by 0.72. Versions
of the SFRs with these corrections applied are listed in Table 6 alongside the
value calculated assuming solar metallicity and no stellar rotation.

####  3.2.2 Discussion

The 22 $\mu$m flux density yielded a SFR that was $\sim$3$\times$ higher than
the H30$\alpha$ SFR and is also significantly higher than the SFRs calculated
using most other methods. The aberrant SFR from the mid-infrared data is a
consequence of the low metallicity of NGC 5253. As stated in the previous
section, the conversions from flux densities in individual infrared bands to
SFRs are based upon the key assumptions that the total infrared flux
originates from light absorbed from star forming regions and that the
individual bands will scale linearly with the total infrared flux. When the
second condition is not met, the SFRs from individual infrared bands will be
inaccurate. This problem had been anticipated for low metallicity galaxies
like NGC 5253 (e.g. Calzetti et al., 2010). Low metallicity galaxies contain
less interstellar dust, so the light from star forming regions is not
attenuated as much as it is in larger galaxies. As a result, the dust that is
present is irradiated by a relatively hard and strong radiation field, which
makes the dust warmer than in spiral galaxies (Hunt et al., 2005; Engelbracht
et al., 2008; Rosenberg et al., 2008; Hirashita & Ichikawa, 2009; Rémy-Ruyer
et al., 2013). The resulting change in the shape of the infrared SED results
in biasing the SFR from 22 $\mu$m data upwards.

The 70 $\mu$m flux density yielded a SFR that was 1-2$\sigma$ smaller than the
H30$\alpha$ value (depending on which versions from in Table 6 are compared),
while the SFR from the 160 $\mu$m data was approximately half of the
H30$\alpha$ value. This change in the calculated SFR with increasing
wavelength is clearly a consequence of the unusually hot dust within NGC 5253.
The longer wavelength bands appear low in comparison to the total infrared
flux, which is expected to scale with the bolometric luminosity, and the
resulting SFRs from the 70 and 160 $\mu$m data are also lower. Additionally,
longer wavelength infrared bands are typically expected to include emission
from diffuse dust heated by older stars (e.g. Bendo et al., 2015a), which
should affect the SFRs based on the data from the bands (Calzetti et al.,
2010). However, if diffuse dust (particularly extended cold dust emission from
outside the central starburst) was present, the SFRs should be biased upwards
at longer wavelengths. The low SFRs from the 70 and 160 $\mu$m data indicate
that the 70 and 160 $\mu$m bands contain relatively little cold, diffuse dust,
at least compared to the galaxies used by Calzetti et al. (2010) to derive the
relations between SFR and emission in these bands.

Notably, the difference between the SFRs from the total infrared and
H30$\alpha$ fluxes is less than 1$\sigma$ or 5% before any corrections for
metallicity or stellar rotation are applied. This increases to 1.5-2$\sigma$
or 20-30% when the correction are applied, but given the number of assumptions
behind the corrections as well as the calculation of the SFRs themselves, this
match is actually very good. Aside from the potential calibration issues, the
total infrared flux may also yield a slightly higher SFR because the dust
emission could also include some energy absorbed from an older stellar
population. However, given the low SFRs from the 70 and 160 $\mu$m bands,
which would be more strongly affected by an older stellar population, it seems
very unlikely that any such diffuse dust emission, especially extended dust
emission outside the central starburst, contributes significantly to the total
infrared flux. It is also possible that photoionizing photons are directly
absorbed by dust grains before they are absorbed by the ionized gas, which
could cause a slight difference in the SFRs. None the less, calibration issues
are probably one of the main reasons for any discrepancies between the SFRs
from the H30$\alpha$ and total infrared fluxes.

###  3.3 Optical and near-infrared recombination line data

####  3.3.1 SFR calculations

Table 8: H$\alpha$ fluxes for the centre of NGC 5253a.

Extinction Correction | Flux (erg cm-2 s-1
---|---
No correctionb | $(8.9\times 2.0)\times 10^{-13}$
Correction by Calzetti et al. (2015) | $(1.7\pm 0.5)\times 10^{-11}$
Correction using 24$\mu$m flux densityc | $(3.47\pm 0.19)\times 10^{-11}$
Correction using total infrared fluxc | $(8.6\pm 0.5)\times 10^{-12}$

a All H$\alpha$ fluxes are based on the sum of fluxes from clusters 5 and 13
from Calzetti et al. (2015).
b These data include foreground dust extinction corrections but no corrections
for intrinsic dust extinction.
c Infrared fluxes are based on the globally-integrated measurements, which
primarily originate from a pointlike source; see Section 3.2 for details.

While the two central H$\alpha$ and Pa$\alpha$ sources are the brightest
optical and near-infrared recombination line sources seen in this galaxy,
multiple other fainter sources are also detected by Alonso-Herrero et al.
(2004), Harris et al. (2004), and Calzetti et al. (2015), and diffuse extended
emission is also present in the H$\alpha$ image from Dale et al. (2009). While
a comparison could be made between the global H$\alpha$ and H30$\alpha$
emission, the inclusion of these fainter sources would cause some
inaccuracies. We therefore compared the SFR from the H30$\alpha$ data to the
SFR from the near-infrared and optical line data from Calzetti et al. (2015).
As indicated in Section 2.2, it is possible that the two central clusters
identified by Alonso-Herrero et al. (2004) and Calzetti et al. (2015) are
actually parts of one larger photoionization region, so we will use the sum of
the optical and near-infrared fluxes from these two sources in our analysis.

Calzetti et al. (2015) published H$\alpha$, Pa$\alpha$, and Pa$\beta$ fluxes
that have been corrected for foreground dust extinction but not for intrinsic
dust extinction within the galaxy. Using these data, they then derive the
intrinsic dust extinction for the sources as well as extinction-corrected
H$\alpha$ fluxes. The corrections for cluster 5 assume a simple foreground
dust screen, but cluster 11 is treated as a case where the line emission is
attenuated both by a foreground dust screen and by dust intermixed with the
stars. The sum of these corrected H$\alpha$ fluxes, which are listed in Table
8, are used for computing one version of SFRs.

We also tested SFRs calculated by correcting H$\alpha$ for dust attenuation by
adding together the observed H$\alpha$ emission (representing the unobscured
emission) and infrared emission multiplied by a constant (representing the
obscured H$\alpha$ emission). Such constants have been derived for multiple
individual infrared bands, including the Spitzer 8 and 24 $\mu$m bands and the
WISE 12 and 22 $\mu$m bands, as well as the total infrared flux (e.g. Calzetti
et al., 2005, 2007; Kennicutt et al., 2007; Zhu et al., 2008; Kennicutt et
al., 2009; Lee et al., 2013). To be concise, we restrict our analysis to the
WISE 22 $\mu$m and total infrared flux. The relations we used for these
corrections are

$f(\mbox{H}\alpha)_{corr}=f(\mbox{H}\alpha)_{obs}+0.020\nu
f_{\nu}(22\mu\mbox{m})$ (7)

and

$f(\mbox{H}\alpha)_{corr}=f(\mbox{H}\alpha)_{obs}+0.0024f(\mbox{TIR}),$ (8)

which are from Kennicutt et al. (2009). Based on the dispersions in the data
used to derive these relations, the uncertainty in the result from Equation 7
and 8 are 0.12 dex (32%) and 0.089 dex (23%), respectively. The sum of the
uncorrected H$\alpha$ fluxes for clusters 5 and 11 from Calzetti et al. (2015)
as well as versions of these fluxes corrected using Equations 7 and 8 are
listed in Table 8.

The H$\alpha$ fluxes can be converted to SFR using

$\frac{\mbox{SFR}(\mbox{H}\alpha)}{\mbox{M}_{\odot}\mbox{ yr}^{-1}}=6.43\times
10^{8}\left[\frac{D}{\mbox{
Mpc}}\right]^{2}\left[\frac{f(\mbox{H}\alpha)}{\mbox{erg s}^{-1}\mbox{
cm}^{-2}}\right]$ (9)

from Murphy et al. (2011). This result is based on models from Starburst99
using a Kroupa IMF, solar metallicities, and older but unspecified stellar
evolution tracks. The assumed $T_{e}$ is 10000 K, which is close to the
measured value in NGC 5253, so we will make no modifications to this
conversion. The SFRs can be rescaled to correct for metallicity and stellar
rotation effects in the same way that the SFR from the H30$\alpha$ was
rescaled. The SFRs based on the three different extinction-corrected H$\alpha$
fluxes are listed in Table 6.

####  3.3.2 Discussion

The extinction-corrected H$\alpha$ fluxes calculated by Calzetti et al. (2015)
using Pa$\alpha$ and Pa$\beta$ line data yield SFRs that fall within 25% of
the SFRs from the H30$\alpha$ data. Given that the extinction corrections
changed the H$\alpha$ fluxes by $\sim$20$\times$, that relatively complex dust
geometries were used in calculating the corrections, and that the
uncertainties in the extinction-corrected H$\alpha$ fluxes are relatively
high, this match is reasonably good. However, the fact that the SFR from the
H30$\alpha$ is higher would indicate that the method of correcting the
H$\alpha$ flux could still be improved.

We discussed in Section 2.2 the non-detection of a second H30$\alpha$ source
corresponding to the secondary star forming region seen in optical and near-
infrared bands, which is labelled as cluster 5 by Calzetti et al. (2015). One
possible explanation for this is that the optical/near-infrared sources lie at
the ends of a much larger star forming complex that is heavily obscured in its
centre. If this is the case, then the ratio of the area of the optical/near-
infrared sources to the area of the much larger star forming complex should be
roughly similar to the ratio of the SFR from the extinction-corrected
H$\alpha$ emission to the SFR from the H30$\alpha$ emission. Calzetti et al.
(2015) do not list sizes for their sources, but they do state that they use
measurement apertures with diameters of 0.25 arcsec, which we can treat as an
upper limit on the source sizes. The hypothetical larger star forming complex
would need to be 0.71 arcsec in size to encompass both optical/near-infrared
regions. Based on the ratio of the area of the two smaller optical/near-
infrared sources to the area of the hypothetical larger complex (which we can
assume is spherical), the optical/near-infrared regions should yield a SFR
that is only 25% of that from the H30$\alpha$ emission, not the 75% that we
measure. This indicates that it is unlikely that both optical/near-infrared
sources are part of one larger obscured complex centered on the H30$\alpha$
source.

The other possible reason for the non-detection of a second H30$\alpha$ source
corresponding to cluster 5 from Calzetti et al. (2015) is that the difference
in brightness between it and the brighter source (cluster 11) is higher than
the factor of $\sim$6$\times$ derived from the analysis of the optical and
near-infrared data. The results here indicate that the extinction correction
for the H$\alpha$ data applied by Calzetti et al. (2015) may indeed be too
low, so it is possible that the difference in the extinction-corrected
brightness between the two sources is much greater than implied by their
analysis. In such a scenario, the second source would be too faint in
recombination line emission to detect in the ALMA data at the 3$\sigma$ level.

The SFR based on the composite H$\alpha$ and 22 $\mu$m data yields a SFR that
is highest among the three based on the H$\alpha$ data, and it is also
significantly higher than the SFR from the H30$\alpha$ flux. This is most
likely a result of the unusually hot dust within NGC 5253, and the problem is
similar to the direct conversion of 22 $\mu$m flux density to SFR discussed in
Section 3.2. The extinction correction in Equation 7 was calibrated using
spiral galaxies and, to some degree, relied on a linear relation between the
amount of energy absorbed by dust and mid-infrared emission. Since that
scaling relation does not apply well to NGC 5253, Equation 7 overcorrected the
extinction.

In contrast, the composite H$\alpha$ and total infrared flux yielded a SFR
that was too low compared to the H30$\alpha$ value or most other values listed
in Table 6. Again, this is probably because the relation was calibrated using
spiral galaxies. The emission from cold, diffuse dust heated by evolved stars
seems to be a relatively small fraction of the total infrared emission in NGC
5253 in comparison to what is found in spiral galaxies. If Equation 8 is
effectively calibrated to account for this cold dust, then it may yield an
underestimate of the extinction correction in galaxies like NGC 5253. Also
note that any attempt to correct the total infrared flux for extended emission
outside the central starburst will simply make the SFR from Equation 8 more
discrepant comapred to values calculated from the H30$\alpha$ data or most
other bands.

The relative sizes of the uncorrected H$\alpha$ and infrared components in
Equations 7 and 8 provide some additional insights into these extinction
corrections. In both cases, the infrared component is dominant. In Equation 7,
the observed H$\alpha$ flux is equivalent to 2.6% of the 22 $\mu$m term, so
using Equation 7 and 9 to calculate a SFR is effectively an indirect
conversion of the 22 $\mu$m flux density to SFR. Meanwhile, the uncorrected
H$\alpha$ flux in Equation 8 is equal to 11.5% of the total infrared flux
term, so using the resulting corrected H$\alpha$ flux in Equation 9 is not
quite as much like indirectly converting the total infrared flux to SFR.

Related to this, Kennicutt & Evans (2012) and references therein describe how
infrared flux could be used correct ultraviolet flux densities in the same way
as they correct H$\alpha$ fluxes. However, when we investigated using such
equations with the ultraviolet flux densities measured for the central two
star clusters, we found that the infrared terms were $>$100$\times$ higher
than the ultraviolet terms, which meant that any SFR based on combining
ultraviolet and infrared data would effectively be independent of the
ultraviolet measurements.

##  4 Conclusions

To summarize, we have used ALMA observations of H30$\alpha$ emission from NGC
5253, a low-metallicity blue compact dwarf galaxy, in a comparison with
different methods of calculating SFR for the centre of this galaxy. We measure
a $Q$ (1.9$\pm$0.3)$\times$$10^{52}$ s-1, which is based on using a distance
of 3.15 Mpc. Accounting for the low metallicity of the galaxy and stellar
rotation, we obtain an SFR of 0.087$\pm$0.013 M⊙ yr-1; with only the
correction for metallicity, we obtain 0.102$\pm$0.015 M⊙ yr-1.

In our analysis, we found three SFR measurements that best matched the
H30$\alpha$ measurements and that seemed to be the least affected by the types
of systematic effects that we could identify as causing problems with other
bands.

The total infrared flux (calculated by integrating the SED between 12 and 500
$\mu$m) yielded a SFR that was very similar to the value from the H30$\alpha$
data. In other dusty low-metallicity starbursts like NGC 5253, the total
infrared flux may yield the most accurate star formation rates as long care is
taken to account for the unusual shapes of the SEDs for these galaxies.

The 70 $\mu$m band may be the best monochromatic infrared star formation
tracer available, as it yielded a SFR that was closest to the SFRs from either
the H30$\alpha$ and total infrared flux. However, given how the conversion of
70 $\mu$m flux to SFR depends on a linear relationship between emission in
this band and the total infrared flux, it is not clear how reliable 70 $\mu$m
emission would be for measuring SFR in other low metallicity galaxies where a
relatively large but potentially variable fraction of the dust emission is at
mid-infrared wavelengths.

The SFR from the H$\alpha$ flux that was extinction corrected by Calzetti et
al. (2015) using Pa$\alpha$ and Pa$\beta$ data was 25% lower than but
consistent with the SFR from the H30$\alpha$ data. However, as we noted in
Section 2.2, it is possible that some parts of the central star forming
complex are completely obscured in the optical and near-infrared observations,
which potentially illustrates the issues with examining star formation within
dust starbursts, even at near-infrared wavelengths.

Most other star formation tracers that we examined seemed to be affected by
systematic effects that cause problems when calculating SFRs.

Previously-published versions of the SFR based on millimetre and radio data
yielded star formation rates with a lot of scatter relative to each other and
relative to the SFR from the H30$\alpha$ data. At least some of the SFRs from
radio continuum measurements are affected by incorrect assumptions about the
nature of the emission sources in these bands. A new analysis of broadband
archival radio and millimetre data is needed to produce better models of the
SED and to covert emission from these bands into SFRs more accurately.

The 22 $\mu$m flux density by itself and the combined H$\alpha$ and 22 $\mu$m
metric produced SFRs that were exceptionally high compared to the value from
the H30$\alpha$ data and compared to SFRs from other tracers. The main problem
is that the dust in this low metallicity environment is thinner than in solar
metallicity objects, so the dust that is present is exposed to a brighter and
hotter radiation field. Consequently, the total dust emission is stronger in
low metallicity environments, and the mid-infrared emission is stronger
relative to total infrared emission. Based on these results, we strongly
recommend not using any star formation tracer based on mid-infrared data for
low metallicity galaxies.

Infrared emission at 160 $\mu$m yields a very low SFR. This is probably
because the dust temperatures within NGC 5253 are relatively hot and because
the conversion of emission in this band to SFR accounts for the presence of
diffuse dust heated by older stars that is present in spiral galaxies but not
in NGC 5253 and similar dwarf galaxies.

The composite H$\alpha$ and total infrared star formation metric yielded a SFR
that was too low. Again, this could be because the correction is calibrated
using spiral galaxies that contain relatively higher fractions of diffuse,
cold dust than NGC 5253. If such a metric were to be used for measuring star
formation in low metallicity systems, it would need to be recalibrated.

This analysis represents the first results from using ALMA observations of
hydrogen millimetre recombination line emission to test SFR metrics based on
optical data, and it is also one of the first comparisons of SFR metrics for a
low metallicity galaxy that has involved ALMA data. A more thorough analysis
of star formation tracers observed in low metallicity galaxies is needed to
understand whether the results obtained for NGC 5253 are generally applicable
to similar objects. Further analysis of more ALMA recombination line
observations combined with this and previous works on this subject (Bendo et
al., 2015b, 2016) will allow us to create a broader picture of the reliability
of various tracers of star formation in both nearby starbursts and more
distant galaxies.

## Acknowledgments

We thank the reviewer for the constructive criticisms of this paper. GJB and
GAF acknowledge support from STFC Grant ST/P000827/1. KN acknowledges support
from JSPS KAKENHI Grant Number 15K05035. CD acknowledges funding from an ERC
Starting Consolidator Grant (no. 307209) under FP7 and an STFC Consolidated
Grant (ST/L000768/1). This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2013.1.00210.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. This research has made use of the NASA/ IPAC Infrared Science Archive,
which is operated by the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space
Administration. This publication makes use of data products from the Wide-
field Infrared Survey Explorer, which is a joint project of the University of
California, Los Angeles, and the Jet Propulsion Laboratory/California
Institute of Technology, and NEOWISE, which is a project of the Jet Propulsion
Laboratory/California Institute of Technology. WISE and NEOWISE are funded by
the National Aeronautics and Space Administration.

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