# DIISC-V: Variations in H$\alpha$-to-FUV Star Formation Rate Ratios Across
Star-forming Regions in Nearby Galaxies

Mansi Padave School of Earth & Space Exploration, Arizona State University,
Tempe, AZ 85287-1404, USA<EMAIL_ADDRESS>Sanchayeeta Borthakur School of
Earth & Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA
Rolf A. Jansen School of Earth & Space Exploration, Arizona State University,
Tempe, AZ 85287-1404, USA  David A. Thilker Department of Physics & Astronomy,
Johns Hopkins University, Baltimore, MD, 21218, USA  Jacqueline Monkiewicz
School of Earth & Space Exploration, Arizona State University, Tempe, AZ
85287-1404, USA  Rogier A. Windhorst School of Earth & Space Exploration,
Arizona State University, Tempe, AZ 85287-1404, USA

###### Abstract

We present the variations in far-ultraviolet (FUV) and H$\alpha$ star
formation rates (SFR), SFRUV and SFRHα, respectively, at sub-kpc scales in 11
galaxies as part of the Deciphering the Interplay between the Interstellar
Medium, Stars, and the Circumgalactic medium (DIISC) survey. Using archival
GALEX FUV imagery and H$\alpha$+[N II] narrowband images obtained with the
Vatican Advanced Technology Telescope, we detect a total of 1335 (FUV-
selected) and 1474 (H$\alpha$-selected) regions of recent high-mass star
formation, respectively. We find the H$\alpha$-to-FUV SFR ratios tend to be
lower primarily for FUV-selected regions, where SFR${}_{\textrm{H}\alpha}$
generally underestimates the SFR by an average factor of 2–3, for SFR $<$ 10-4
M⊙ yr-1. In contrast, the SFRs are generally observed to be consistent for
H$\alpha$-selected regions. This discrepancy arises from morphological
differences between the two indicators. Extended FUV morphologies and larger
areas covered by FUV-only regions, along with decreasing overlap between FUV
clumps and compact H II regions with $R/R_{25}$ suggest that stochastic
sampling of the initial mass function may be more pronounced in the outer
regions of galaxies. Our observed H$\alpha$-to-FUV SFR ratios are also
consistent with stochastic star formation model predictions. However, using
larger apertures that include diffuse FUV emission results in an offset of 1
dex between SFRHα and SFRUV. This suggests that the observed low H$\alpha$-to-
FUV SFR ratios in galaxies are likely caused by diffuse FUV emission, which
can contribute $\sim$60–90% to the total FUV flux.

Spiral Galaxies (1560) — Star formation(1569) — Star forming regions(1565) — H
II regions(593) — H alpha photometry(691) — Stellar associations(1582) —
Ultraviolet photometry(1740)

††journal: ApJ††facilities: GALEX, VATT, Spitzer, WISE, VLA††software: astropy
(Astropy Collaboration et al., 2013, 2018), Photutils (Bradley et al., 2023),
Source Extractor (Bertin & Arnouts, 1996)

##  1 Introduction

The H$\alpha$ nebular line and far-ultraviolet (FUV) continuum are two of the
most widely used tracers of star formation in galaxies (Kennicutt, 1998a;
Kennicutt & Evans, 2012). The FUV continuum is produced by non-ionizing UV
photons from O-stars as well as B- and A-stars and probes timescales of
$\sim$100 Myr. In contrast, H$\alpha$ emission is a byproduct of gas ionized
by UV photons emanating from the photospheres of short-lived massive O-type
and early B-type stars, tracing a shorter star formation timescale of
$\lesssim$10 Myr. Despite their power to probe recent and current high-mass
star formation, respectively, these indicators have long been scrutinized due
to the discrepancy between the star formation rates (SFR) of galaxies inferred
from them.

Following the standard calibrations from Kennicutt (1998b), consistent values
for the SFR, invariant with time and environment, are expected from the two
indicators. Nonetheless, several observations have revealed a systematic
decline in the H$\alpha$-to-FUV ratios with decreasing luminosities and at low
levels of star formation in galaxies (Buat et al., 1987; Bell & Kennicutt,
2001; Iglesias-Páramo et al., 2004; Meurer et al., 2009; Lee et al., 2009;
Boselli et al., 2009). It is found that while the average ratio remains
constant at SFR $\gtrsim 0.1$ M⊙ yr-1, it varies by a factor of 2 to an order
of magnitude for SFR $\lesssim 10^{-3}$ M⊙ yr-1, also observed for low-mass
dwarf galaxies (Lee et al., 2009, 2016). These observations highlight the
nuances in the production of H$\alpha$ and FUV photons, due to deviations from
the assumptions that are foundational to SFR prescriptions: a constant star
formation history (SFH) over $\sim$1 Gyr, a well-populated initial mass
function (IMF) for solar metallicity, and no loss of Lyman continuum photons
or dust extinction.

Many independent studies have analyzed the variations in H$\alpha$-to-FUV
ratios in galaxies to explore the deviations from the model assumptions. Non-
constant or bursty SFH have been found to have a considerable impact on the
ratios (Iglesias-Páramo et al., 2004; Weisz et al., 2012; Emami et al., 2019;
Kauffmann, 2021). Lower H$\alpha$ emission in galaxies, especially for the low
mass systems ($M<10^{8}M_{\odot}$), can be explained by a lull in star
formation, during which the H$\alpha$ luminosities can drop quickly compared
to the FUV luminosities (Mehta et al., 2023). Moreover, stochastic sampling of
stellar and cluster IMFs means lower-mass systems are likely to have fewer
high-mass clusters and, consequently, fewer high-mass stars (Fumagalli et al.,
2011; Koda et al., 2012). Additionally, the escape of ionizing photons from
HII regions lowers photoionization rates, and excluding the diffuse component
of H$\alpha$ emission in the warm ionized medium can lead to underestimating
H$\alpha$ luminosities (Hoopes et al., 2001; Eldridge & Relaño, 2011; Hunter
et al., 2011; Relaño et al., 2012; Lee et al., 2016; Watkins et al., 2024).
Given the abundance of evidence supporting these factors, they all likely play
a role in the observed variations in H$\alpha$-to-FUV ratios.

On spatially-resolved scales, the H$\alpha$-to-FUV ratios in galaxies provide
interesting insights into star formation in galactic outskirts. In search of a
star formation threshold, Martin & Kennicutt (2001) identified truncated
H$\alpha$ radial profiles in nearby spiral galaxies. However, such sharp
declines were not observed in the UV profiles, and many nearby galaxies showed
UV knots at large galactocentric distances or emitted faint UV, termed Type-I
and Type-II extended ultraviolet (XUV) disks (Thilker et al., 2007). These
differences in the radial profiles have been associated both with the relative
numbers of the detected UV and H$\alpha$ knots as well as the declining fluxes
in the outer disks of galaxies (Zaritsky & Christlein, 2007; Goddard et al.,
2010). H II regions have also been discovered well beyond the optical edge
(R25) of the galaxy disks (Hodge, 1969; Ferguson et al., 1998; van Zee et al.,
1998; Lelièvre & Roy, 2000; Ryan-Weber et al., 2004; Werk et al., 2010),
sometimes as far out as 4R25, as is the case with M83 (Thilker et al., 2005).

So far, H$\alpha$-to-FUV ratios in galaxies have been extensively investigated
with integrated luminosity and SFR measurements. On spatially-resolved scales,
the ratios have been explored mainly for XUV disk galaxies or individual
galaxies (Barnes et al., 2011; Byun et al., 2021; Padave et al., 2021). As
part of the Deciphering the Interplay between Star Formation, Interstellar
Medium, and the Circumgalactic Medium (DIISC) survey, Padave et al. (2021)
investigated H$\alpha$ emission for FUV-selected stellar associations in NGC
3344. They found a considerable scatter in the H$\alpha$-to-FUV SFR ratios in
the XUV region, with SFRUV$\gtrsim$SFRHα for the stellar associations. In this
paper, we delve deeper into the variations between the FUV and H$\alpha$ SFR
indicators on sub-kpc scales for a larger sample and include star-forming
galaxies showing signatures of stellar disk growth (see Padave et al., 2024,
and §2 for details) from the DIISC survey. Our primary goal in this work is to
examine the morphology and spatial distribution of FUV and H$\alpha$ emission
and investigate aperture effects on the connection between SFRUV and SFRHα at
sub-kpc scales. The structure of the paper is as follows. In §2, we present
our sample, observations, and data reduction and calibration procedures. The
source detection on the H$\alpha$ and FUV maps is described in §3. We present
our results on the H$\alpha$-to-FUV SFR ratios of the detected sources and
their spatial overlaps in §4, followed by a discussion on the relation between
SFRHα and SFRUV. Finally, we present our conclusions in §6.

##  2 Sample & Data

We carried out a follow-up H$\alpha$-DIISC program to obtain H$\alpha$+[N II]
imaging of the 34 galaxies from the DIISC survey, intending to map any H II-
regions in the outskirts at a signal-to-noise ratio (SNR) $\gtrsim 5$. Deep
narrow-band H$\alpha$+[N II] and broad-band Sloan-r (henceforth denoted r)
imaging observations of the galaxies were carried out with the 1.8 m Vatican
Advanced Technology Telescope (VATT) operated by the Mt. Graham International
Observatory in Arizona. The observations took place over a total of 19 nights
between 2019 March to 2021 March. The typical seeing for these observations
was between 0$\farcs$8 and 2$\farcs$2, with a pixel scale of
0$\farcs$375/pixel. A set of seven different H$\alpha$ filters of $\sim 70$ Å
FWHM, covering the redshifted H$\alpha$ emission lines within a range of
650–700 nm, were used for these observations. The total integration time
ranges between 60 min and 100 min in the narrow-band H$\alpha$ filters and 20
min in r, the latter used for continuum subtraction. The continuum-subtraction
procedure is described in Section 2.1.

To effectively investigate the H$\alpha$-to-FUV SFR ratios at sub-kpc scales,
our selection criteria prioritized spatial resolution and the number of
detected H II regions in the H$\alpha$+[N II] images. After considering
factors such as distance, angular diameter, availability of deep FUV data from
the Galaxy Evolution Explorer (GALEX; Martin et al., 2005; Morrissey et al.,
2007), and the distribution of H II regions across the disk, we chose 11
galaxies out of the 34 in the DIISC sample for the present study. Salient
features of these galaxies are noted in Table 1. Figure 1 compares the SFRUV
and SFRHα of our sample with the $\sim$300 spirals and dwarf galaxies from the
11 Mpc H$\alpha$ and Ultraviolet Galaxy Survey (11HUGS) investigated by Lee et
al. (2009).

Figure 1: Comparison of SFRUV and SFRHα of the sample plotted over spiral and
dwarf galaxies from 11HUGS investigated in Lee et al. (2009). The solid line
represents the one-to-one correspondence between the SFRs. Most of our
galaxies show SFRUV$>$SFRHα with H$\alpha$-to-FUV SFR ratios ranging from
0.38–1.15.

The continuum-subtracted H$\alpha$+[N II] maps of our sample are shown in
Figure 2 with GALEX FUV contours overlaid on top. The sensitivity limits of
the H$\alpha$+[N II] and FUV maps are noted in Table 1. In addition to the
H$\alpha$+[N II] and FUV imaging, we use 22$\mu$m and 24$\mu$m images from the
Wide-field Infrared Survey Explorer (WISE) All-Sky Data Release (Wright et
al., 2010) and Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al.,
2004), respectively. All galaxies in our sample are also investigated in
Padave et al. (2024), hence, we refer the reader to that paper for details
regarding the data mentioned above and additional sample properties.

Table 1: Properties of Galaxies in the Sample. Galaxy | R.A. | Dec | cz | Distance | Scale | $i$ | Sensitivity Limit | SFR${}_{\text{UV}}$ | SFR${}_{\text{H}\alpha}$
---|---|---|---|---|---|---|---|---|---
FUV | H$\alpha$
(deg) | (deg) | (km s-1) | (Mpc) | (pc/″) | (∘) | ($\times 10^{-19}$) | ($\times 10^{-19}$) | ($M_{\odot}$ yr-1) | ($M_{\odot}$ yr-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
NGC 99 | 5.99747 | 15.77042 | 5313 | 79.4 | 378.17 | 20 | 9.05 | 7.21 | 2.45 | 1.48
NGC 3344 | 160.87951 | 24.92249 | 588 | 8.28 | 40.14 | 6 | 5.73 | 4.08 | 0.47 | 0.27
NGC 3351 | 160.99038 | 11.7038 | 778 | 9.29 | 45.04 | 44 | 4.51 | 2.59 | 0.79 | 0.44
NGC 3433 | 163.01611 | 10.1483 | 2724 | 44.59 | 216.18 | 22 | 4.92 | 6.03 | 1.20 | 0.46
NGC 3485 | 165.00991 | 14.84157 | 1433 | 29.43 | 142.68 | 23 | 4.45 | 4.40 | 0.83 | 0.59
NGC 3666 | 171.10861 | 11.34222 | 1060 | 17.1 | 82.90 | 75 | 15.40 | 11.30 | 0.32 | 0.25
NGC 3810 | 175.24481 | 11.47112 | 993 | 15.3 | 74.18 | 47 | 18.50 | 4.36 | 1.25 | 0.48
NGC 4303 | 185.47894 | 4.47347 | 1567 | 18.7 | 90.66 | 22 | 6.05 | 6.96 | 5.25 | 6.05
NGC 4321 | 185.7289 | 15.82101 | 1576 | 13.93 | 67.53 | 24 | 2.87 | 5.74 | 2.49 | 1.46
NGC 5669 | 218.18311 | 9.8917 | 1369 | 14.5 | 70.30 | 48 | 16.50 | 2.78 | 0.29 | 0.17
NGC 5951 | 233.42933 | 15.00715 | 1778 | 27.1 | 131.38 | 77 | 8.45 | 6.23 | 0.23 | 0.11

###  2.1 Data Reduction & Calibration of H$\alpha$ Images

The VATT H$\alpha$+[N II] and r images were reduced as described in Padave et
al. (2021) and Padave et al. (2024). In brief, we use standard IRAF procedures
to perform overscan correction, bias subtraction, and flat-field correction.
Removal of cosmic rays was carried out using the L.A.COSMIC routine (van
Dokkum, 2001). Science exposure frames were aligned using Astroalign (Beroiz
et al., 2020) before co-adding. The World Coordinate System of the final
stacked images was refined with the http://astormetry.net software (Lang et
al., 2010). The background was estimated using Astropy Photutils (Bradley et
al., 2023) and subsequently removed. Flux calibration of the r maps was
carried out using the Aperture Photometry Tool (Laher et al., 2012) by
matching the instrumental magnitudes to the SDSS DR12 magnitudes of field
stars. For the broad-band r images, we reach 1$\sigma$ depths of surface
brightness of $\sim$25–27 mag arcsec-2.

The H$\alpha$+[N II] images were processed further to remove the stellar
continuum. The r image was appropriately scaled and then subtracted from the
H$\alpha$ image, to produce an emission-line only H$\alpha$+[N II] image. The
scale factor, $F$, defined as the ratio of narrow-to-broad band counts, was
estimated empirically using the field stars under the assumption that they do
not emit H$\alpha$. We iterated the continuum subtraction process for a range
of scale factors until the residual flux of non-saturated foreground stars was
lowest, and the surface brightness of the continuum-dominated regions reached
the the background level. This implicitly assumes the galaxy disk spectral
energy distribution matches the foreground stars and does not vary with
location. For the selected galaxies in our sample, the nominal scale factors
were found to be between 0.031–0.047.

The absolute flux measurements of the emission-only H$\alpha$+[N II] image
were determined using the method outlined in Kennicutt et al. (2008). We
employed the photometric zero point (ZP) of the r-band image, the bandwidth
(FWHM${}_{\text{NB}}$) of the corresponding narrowband H$\alpha$ filter, count
rates (CR${}_{\text{H}\alpha}$) in counts s-1 from the continuum-subtracted
H$\alpha$+[N II] map, and $F$ to compute the total emission-line flux,
$f_{\text{tot}}$:

$f_{\text{tot}}=U\cdot\text{FWHM}_{\text{NB}}\cdot\text{CR}_{\text{H}\alpha}\cdot
T_{\lambda}^{-1}$

Here, $U$ and $T_{\lambda}$ are calculated as follows:

$\displaystyle U$
$\displaystyle=\lambda^{-2}10^{-0.4[\text{ZP}+2.397-\kappa\sec(x)]}$
$\displaystyle T_{\lambda}$
$\displaystyle=T_{NB}(\lambda)-T_{r}(\lambda)\frac{t_{r}}{t_{NB}}F$

We assumed a standard atmospheric extinction coefficient, $\kappa=0.08$ mag
airmass-1 for airmass $x$. The term $T_{\lambda}$ adjusts for the effective
filter transmission at the redshifted H$\alpha$ line, ensuring the recovery of
the H$\alpha$ flux from the r image lost during continuum subtraction.
$T_{NB}(\lambda)$ and $T_{r}(\lambda)$ represent the normalized filter
transmission, while $t_{NB}$ and $t_{r}$ denote the exposure times of the
H$\alpha$ and r maps, respectively. A Galactic (foreground) extinction
correction is also applied based on Schlafly & Finkbeiner (2011), with
A${}_{H\alpha}=2.5\times E(\bv)$. We note that these calculations contain the
contribution from the [N II]$\lambda\lambda 6548,6584$ forbidden lines. All
narrowband H$\alpha$ observations of our sample include [N II] emission and
the process of subtracting the [N II] flux and its implications are discussed
in §3.4.

Figure 2: Continuum-subtracted H$\alpha$ imagery for our galaxies. FUV
contours (blue) at 5$\sigma$ and 10$\sigma$ levels are overlaid on top. A
physical scale of 5 kpc is shown in the bottom left corner of each map. North
is up and East is towards left.

##  3 FUV- & H$\alpha$-bright Stellar Complexes

###  3.1 Source Detection

We created a catalog of both UV- and H$\alpha$-bright objects in our galaxies
using Source Extractor (Bertin & Arnouts, 1996) and its Python library, sep
(Barbary, 2016). UV-bright stellar complexes or star-forming clumps are
detected using the GALEX maps and are referred to as FUV-selected regions. H
II regions, H$\alpha$ knots or H$\alpha$-bright objects detected using the
VATT H$\alpha$+[N II] maps are termed as H$\alpha$-selected regions.

The FUV-selected regions were detected by extracting sources 3$\sigma$ above
the background level of the FUV maps. To optimize source extraction in various
environments, such as the densely populated central regions of galaxies and
the sparser galactic outskirts, we execute separate runs of sep on cutouts of
different regions within each galaxy. Adjustments to the background box and
filter sizes, as well as the deblending threshold and contrast parameter, were
made for each run to ensure efficient object detection and minimize overlap
between detected objects. After a preliminary catalog of objects is created
for a galaxy, the catalog is cleaned for background and foreground
contaminants and overlapping apertures. Apertures at the positions of
foreground stars seen in the optical images were removed. Additionally, manual
adjustments were made to redefine certain apertures to encompass detected
regions effectively.

A similar process is employed for extracting H$\alpha$-selected regions from
the H$\alpha$+[N II] maps. Prior to source extraction, the H$\alpha$+[N II]
maps, with a resolution of $\sim$1$\farcs$5 FWHM, are convolved to match the
resolution of the GALEX FUV map (4$\farcs$2 FWHM). To achieve this, the
H$\alpha$+[N II] maps, which have a pixel scale of 0$\farcs$375/pixel, were
first resampled to 1$\farcs$5/pixel to match the FUV maps and then smoothed.
This process ensures consistent source detection and spatial matching,
facilitating a direct comparison between the FUV-selected and
H$\alpha$-selected regions.

For the final catalog, we also ensure that only regions reliably detected in
both the H$\alpha$ and FUV datasets are considered. For this, a region is
included in the final catalog only if it is detected above the sensitivity
limits of both maps. The final catalog comprises 1335 regions detected in the
FUV and 1474 regions detected in H$\alpha$ across our sample of 11 DIISC
galaxies. In Figure 3, we show histograms depicting the distributions of
various properties of the FUV- and H$\alpha$-selected regions, along with
their radial distribution. Properties of the regions detected in each galaxy
are described in the following sections and summarised in Table 2.

Table 2: Properties of the Detected FUV- and H$\alpha$-selected Sources Galaxy | R25 | Adopted [N II]/H$\alpha$ | FUV-selected Regions | H$\alpha$-selected Regions
---|---|---|---|---
value or Gradient | N | Sizes | Areas | $R_{\text{max}}$ | N | Sizes (kpc) | Areas | $R_{\text{max}}$
| (kpc) |  |  | (kpc) | (kpc2) | ($R_{25}$) |  | (kpc) | (kpc2) | ($R_{25}$)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
NGC 99 | 11.46 | $-0.03R_{25}-0.56$ | 27 | 1.04 – | 2.50 – | 1.56 | 21 | 0.76 – | 1.16 – | 1.50
3.63 | 15.24 | 3.33 | 16.79
NGC 3344 | 7.93 | $-0.91R_{25}+0.77$ | 315 | 0.09 – | 0.02 – | 1.24 | 312 | 0.08 – | 0.02 – | 1.24
0.66 | 0.80 | 0.49 | 0.38
NGC 3351 | 8.15 | $-0.14R_{25}-0.47$ | 230 | 0.09 – | 0.01 – | 1.46 | 261 | 0.07 – | 0.01 – | 1.42
0.55 | 0.47 | 0.37 | 0.28
NGC 3433 | 17.66 | 0.67 ($R\leq R_{25}$) | 102 | 0.53 – | 0.63 – | 1.67 | 105 | 0.42 – | 0.39 – | 1.52
0 ($R>R_{25}$) | 2.36 | 8.25 | 1.64 | 4.38
NGC 3485 | 9.87 | 0.58 ($R\leq R_{25}$) | 62 | 0.37 – | 0.29 – | 1.84 | 78 | 0.25 – | 0.16 – | 1.85
0 ($R>R_{25}$) | 1.26 | 3.18 | 0.86 | 1.36
NGC 3666 | 4.90 | 0.56 ($R\leq R_{25}$) | 29 | 0.23 – | 0.14 – | 1.86 | 33 | 0.20 – | 0.10 – | 2.18
0.13 ($R>R_{25}$) | 0.84 | 1.22 | 0.59 | 0.73
NGC 3810 | 7.54 | 0.73 ($R\leq R_{25}$) | 61 | 0.22 – | 0.10 – | 1.14 | 94 | 0.14 – | 0.04 – | 1.42
0.29 ($R>R_{25}$) | 1.05 | 1.69 | 0.64 | 0.67
NGC 4303 | 17.37 | $-0.74R_{25}-0.53$ | 223 | 0.17 – | 0.08 – | 1.10 | 207 | 0.15 – | 0.06 – | 1.10
1.02 | 1.69 | 0.83 | 1.04
NGC 4321 | 12.85 | $-0.16R_{25}-0.61$ | 219 | 0.14 – | 0.06 – | 1.03 | 270 | 0.11 – | 0.03 – | 1.16
1.07 | 1.29 | 0.53 | 0.68
NGC 5669 | 6.52 | 0.36 ($R\leq R_{25}$) | 53 | 0.21 – | 0.11 – | 1.45 | 72 | 0.13 – | 0.05 – | 1.42
0 ($R>R_{25}$) | 0.60 | 0.73 | 0.67 | 1.05
NGC 5951 | 6.88 | 0.49 ($R\leq R_{25}$) | 15 | 0.37 – | 0.24 – | 1.90 | 22 | 0.32 – | 0.26 – | 1.88
0 ($R>R_{25}$) | 1.49 | 4.81 | 1.10 | 1.84

###  3.2 Source Sizes & Morphologies

The physical sizes of the detected regions vary between 60 pc to 3.6 kpc.
These range from compact, isolated stellar associations or H II-regions to UV-
bright star-forming clumps or conglomerations of H II regions. Approximately
70% of the H$\alpha$-selected regions have sizes ranging from 60–320 pc,
indicating a comparatively more compact size than the FUV-selected regions,
where around 60% of the regions range from 150–500 pc. Consequently, the
morphology of the FUV-selected regions tends to be more elongated than the
H$\alpha$-selected regions, as observed in the top left panel of Figure 3. The
axis ratios, $a/b$, of the elliptical apertures reveal that $\sim$50% of the
FUV-selected regions have $a/b$ $>$ 1.5, while $\sim$70% of the
H$\alpha$-selected regions are compact. The areas of the H$\alpha$-selected
regions are also smaller than those of the FUV-selected regions, as depicted
in the top right panel of Figure 3. Unsurprisingly, the larger regions with
areas $\gtrsim$1 kpc2 in the catalog are predominantly from the more distant
galaxies in our sample: NGC 99, NGC 3433, and NGC 3485, as a direct
consequence of degradation of resolution.

Figure 3: Histograms showing the distribution of (top) axis ratios ($a/b$) for
elliptical apertures, their surface areas, (middle) deprojected $R/R_{25}$,
and the SFRHα/SFRUV ratio of the FUV- and H$\alpha$-selected regions. The
inset in the middle left panel shows a zoom-in of the histogram for
$1.25R_{25}\leq R\leq 2.5R_{25}$. The bottom panels show the locations of the
FUV-selected (left) and H$\alpha$-selected (right) regions on the $R/R_{25}$
plane for a representative galaxy. Each region is color-coded based on its
SFRHα/SFRUV ratio with unique symbols used in Figure 1 to identify the sample
galaxy. The symbols are not displayed on the plot for brevity. The overlaid
larger circles show the average SFRHα/SFRUV in a given azimuthal and radial
bin marked by the dashed lines and solid circles, only shown for bins with
more than one region. The concentric circles show $R=0.5,1,1.5,2,2.5\times
R_{25}$.

###  3.3 Radial Distribution of Sources

We observe an almost identical radial distribution of the FUV- and
H$\alpha$-selected objects across our sample, as illustrated in the middle
left panel of Figure 3. The deprojected galactocentric distances of the
regions, $R$, are normalized by $R_{25}$ of the galaxy, as taken from Padave
et al. (2024). The 2D distribution of detected regions is shown in the bottom
panel. We note that this panel is mainly to illustrate the distribution of
sources beyond $R_{25}$. Approximately 80% of the sources lie within $R_{25}$
and we detect 248/1335 FUV- and 222/1474 H$\alpha$-selected regions beyond the
optical disk. About 22% of these outer objects were detected in the extended
ultraviolet (XUV) disk of NGC 3344. The farthest UV clump in our catalog at
1.9$R_{25}$ in NGC 5951 was also detected in H$\alpha$. The farthest
H$\alpha$-selected region was detected in NGC 3666 at 2.18$R_{25}$ but is not
detected in FUV. We note that these galaxies are highly inclined, and
deprojection issues are unavoidable. However, as we already take into account
the detection thresholds of both the FUV and H$\alpha$ maps, regions that are
undetected by GALEX could be very young, such that these complexes may still
be embedded within their birth cloud and thus highly obscured.

###  3.4 H$\alpha$-to-FUV Ratios of Sources

The H$\alpha$-to-FUV SFR ratios, or SFRHα/SFRUV are estimated for all FUV- and
H$\alpha$-selected regions. Before estimating the SFRs, we attempt to retrieve
the true H$\alpha$ flux from the H$\alpha$+[N II] maps. Corrections for the
contamination from [N II]$\lambda\lambda 6548,6584$ forbidden lines are
implemented using [N II]/H$\alpha$ radial gradients or values sourced from the
literature. These are noted in Table 2 and described below.

Olvera et al. (2024) investigated the optical spectra of H II regions in NGC
99, estimating the metallicity gradient in the galaxy using several emission
lines-selected indicators, including [N II]/H$\alpha$. They found that the [N
II] flux is $\sim$25% of H$\alpha$ in the center, decreasing to $\sim$6% in
the outer zones of the galaxy. Similarly, in NGC 3344, the [N II]/H$\alpha$
ratios range from 0.6 in the inner regions to 0.2 in the outer regions (Moumen
et al., 2019). We make use of the [N II]/H$\alpha$ gradient from Moumen et al.
(2019) to recover the H$\alpha$ flux in NGC 3344 in this study instead of the
integrated [N II]/H$\alpha$ value of 0.52 used in Padave et al. (2021). For
NGC 3351, NGC 4303, and NGC 4321, gas-phase metallicity gradients from
Pilyugin et al. (2023) were used along with calibrations provided in Curti et
al. (2020), to derive the [N II]/H$\alpha$ gradient in these galaxies. [N
II]/H$\alpha$ estimates for other galaxies were obtained from SDSS Data
Release 18 (Almeida et al., 2023), and for NGC 3485, the ratio was sourced
from Ho et al. (1997). Given that [N II] fluxes typically dominate the metal-
rich inner disks of galaxies and decrease with R, we adopt different values
for regions within $R_{25}$ compared to those beyond and reduce systematic
uncertainties. For most galaxies, the [N II]/H$\alpha$ estimate is derived
from the nuclear region spectra in SDSS and is used to remove the contribution
from regions with $R\leq R_{25}$. In cases where estimates for regions with
$R>R_{25}$ were available, those values were used for [N II]/H$\alpha$;
otherwise, no contribution from [N II] was assumed to avoid any discrepancies
due to varying metallicity gradients among galaxies (Pilyugin et al., 2023,
Olvera et al. 2024).

We also account for internal dust extinction of the FUV and H$\alpha$ fluxes,
which have only been corrected for foreground extinction so far. For
extinction correction, a combination of FUV and H$\alpha$ with infrared fluxes
has been widely used and provides both the unobscured and dust-obscured
components of the star formation (Calzetti et al., 2007; Kennicutt et al.,
2007). We use the following calibrations computed in Kennicutt (1998a),
Calzetti et al. (2007) and Leroy et al. (2008) to calculate the inherent SFRUV
and SFRHα of the detected regions:

$\displaystyle SFR_{\rm UV}$ $\displaystyle=0.68\times 10^{-28}~{}{\rm
L}_{\nu,\rm{FUV}}+2.14\times 10^{-42}~{}{\rm L}_{\rm{24}\mu{\rm m}}$
$\displaystyle SFR_{\rm{H}\alpha}$ $\displaystyle=5.3\times
10^{-42}(\rm{L}_{\rm{H}\alpha}+3.1\times 10^{-2}~{}\rm{L}_{\rm{24}\mu{\rm
m}})$

where SFRUV and SFRHα are in M ⊙ yr-1, and the FUV, H$\alpha$, and 24$\mu$m
luminosity, Lν,FUV, LHα, and L24μm are in erg s-1 Hz-1, erg s-1, and erg s-1,
respectively. The SFRUV and SFRHα prescriptions assume a Salpeter (1955) and
Kroupa (2001) initial mass function and a factor of 1.59 is used for the
conversion. While Lν,FUV and LHα take no account of internal extinction, L24μm
is assumed to account for the dust-processed light. Where 24$\mu$m data is not
available, we use 22$\mu$m fluxes.

We only apply a first-order extinction correction from the IR maps to a
detected region when estimating SFRs instead of estimating 22$\mu$m or
24$\mu$m luminosities for individual regions. Firstly, the 22$\mu$m
observations have a resolution of 12″, which is significantly worse than our
FUV and H$\alpha$ maps. As we are mainly interested in investigating UV- and
H$\alpha$-bright star-forming clumps or H II regions, convolving these maps to
12″ would result in missing out on low-surface brightness regions in the
outskirts and other structural details. Secondly, the 24$\mu$m observations,
especially beyond $R_{25}$, have low signal-to-noise ratios. Hence, any
attempt to perform photometry on the IR maps would result in additional
uncertainties in our SFRs. Instead, we make use of the 24$\mu$m and 22$\mu$m
surface brightness profiles from Padave et al. (2024) to estimate the mean IR
value at a given R. This mean value is then incorporated in the second term of
the SFR equations for a region at a given R.

In the middle right panel of Figure 3, we present the histogram of SFRHα/SFRUV
for the regions. We find that the FUV-selected regions exhibit an almost
symmetric and broader distribution, with most ratios falling between 0.34–0.9.
The H$\alpha$-selected regions generally have SFRHα/SFRUV ratios
$\gtrsim$0.45, with more regions showing SFRHα$>$SFRUV. Overall, FUV-selected
regions tend to display lower SFRHα/SFRUV compared to H$\alpha$-selected
regions. In the 2D distribution shown in the bottom panels of Figure 3, the
regions are colored according to $\log_{10}$ SFRHα/SFRUV. The average ratios
per azimuthal and radial bin are over-plotted as large circles for convenience
in bins where the number of regions is more than 1. Not much variation in the
H$\alpha$-to-FUV ratios is observed in the bins. Additionally, we find a
considerable scatter of 0.36 dex and 0.33 dex per annular bin in the ratios in
the FUV- and H$\alpha$-selected H$\alpha$-to-FUV ratios, respectively. We
explore radial trends of the SFRs and the ratios in the following section.

##  4 Results

###  4.1 Radial Trends in SFRs

Figure 4: Radial variation in SFRUV (solid lines) and SFRHα (dashed lines) for
the FUV-selected regions in each galaxy in our sample. The filled and unfilled
symbols denote the average SFRUV and SFRHα respectively, within a radial bin.
The 1$\sigma$ scatter in the SFRs at each radius is denoted by the vertical
bars. The vertical dashed line shows the radii containing 90% of the SFRUV in
the galaxy, taken from Padave et al. (2024).

In Figures 4 and 5, we show the variation in SFRUV and SFRHα as a function of
$R/R_{25}$ for the FUV-selected and H$\alpha$-selected regions, respectively.
In each panel, average SFRUV and SFRHα within a radial bin are estimated from
the detected regions and denoted by filled and unfilled symbols, respectively,
for a galaxy. The scatter in the SFRs in each bin is represented by the
vertical bars. For reference, we show the radii containing 90% of the SFR
estimated from SFRUV distribution in Padave et al. (2024) as the vertical
dashed line.

In Figure 4, we observe a general decline in SFRUV and SFRHα with $R/R_{25}$
in most galaxies for the FUV-selected regions. SFRHα is typically lower
compared to SFRUV, especially at large galactocentric distances. The SFRs are
seen to closely follow each other within $0.5R_{25}$ and then begin to deviate
beyond $0.5R_{25}$. Notably, NGC 3810, and NGC 4303 do not follow these
trends, showing SFRHα surpassing SFRUV. We bring to the reader’s attention
that dust correction for our SFRs was done using annular-averaged 24$\mu$m or
22$\mu$m value. Additionally, the poor resolution and depths of the 22$\mu$m
maps are also causing the IR fluxes to be spread out over areas much larger
than the regions we are probing. This may be affecting these galaxies and some
of the regions, where SFRUV is observed to be lower than SFRHα.

We also note no evidence of truncation in the H$\alpha$ emission. Sharp
turnovers in H$\alpha$ surface density profiles around $R_{25}$ have been
observed in many galaxies and attributed to gravitational, gas-phase, or cloud
fragmentation instabilities and even truncation of the upper-mass end of the
IMF (Martin & Kennicutt, 2001; Schaye, 2004; Krumholz & McKee, 2008; Pflamm-
Altenburg & Kroupa, 2008). The absence of truncation in our sample is likely
because we are not considering surface densities but rather the average SFR of
all detected regions in a given bin.

From the observed offsets in the FUV-selected regions across the sample, we
find that the H$\alpha$-to-FUV SFR ratios generally decline with $R/R_{25}$.
We note $\log_{10}$ SFRHα/SFRUV to decrease by 0.3$\pm 0.03$ dex/$R_{25}$ on
average with Pearson-$r$ value of -0.27. This weak dependence on $R/R_{25}$
highlights the fact that the radial trends for individual galaxies also show
variations and exhibit considerable scatter. As the number of regions per
galaxy shows a large range with the lowest value of only 15 detected FUV-
selected regions in NGC 5951, we refrain from fitting radial trends for
individual galaxies and look at the sample as a whole. The decline in
H$\alpha$-to-FUV ratios, albeit weak, suggests that the SFRHα of individual
regions decreases rapidly compared to SFRUV in the galactic outskirts. If this
scenario is entirely true, then we would expect similar radial trends and
offsets for the H$\alpha$-selected regions.

Figure 5: Same as Figure 4 but for the H$\alpha$-selected regions in each
galaxy in our sample.

Interestingly, the H$\alpha$-selected profiles in Figure 5 present a different
picture. Here, both SFRUV and SFRHα closely follow each other in the inner
parts without significant offsets as those observed in the FUV-selected
profiles. The SFRs begin to deviate around $R_{25}$ but the decline in SFRHα
is still less pronounced compared to the FUV-selected trends. This indicates
that where H$\alpha$ knots are detected with UV counterparts, the H$\alpha$
fluxes are generally comparable to the UV fluxes. Similar observations were
noted by Goddard et al. (2010) in XUV disk galaxies, where H II regions in the
outskirts showed comparable H$\alpha$-to-FUV SFR ratios to those in the inner
disks. Consequently, the H$\alpha$-to-FUV SFR ratios for our
H$\alpha$-selected regions are noted to decrease by only 0.15$\pm$0.02
dex/$R_{25}$ for the entire sample and show no dependence on $R/R_{25}$
(Pearson-$r$ of -0.15). This difference in trends noted between the FUV- and
H$\alpha$-selected regions suggests that the decline in the H$\alpha$ emission
compared to the FUV does not just result from differences in declining fluxes.

The fact that the extent of the discrepancies in the SFRs varies in the two
cases also underscores fundamental differences in the star-forming regions
probed by the two indicators. We perform the Kolmogorov-Smirnov (KS) test on
the distribution of FUV-selected SFRUV and H$\alpha$-selected SFRHα, under the
null hypothesis that the two samples are drawn from the same parent
distribution. We obtain a $p$-value $\lesssim 0.01$ and hence, find that the
two distributions are inherently different. This is expected as UV and
H$\alpha$ complexes represent different physical star-forming phenomena. While
the H$\alpha$ emission arises from H II regions fueled by OB stars, the FUV
complexes can encompass multiple H II-regions, runaway OB stars, and longer-
lived late-type field B- and A-stars. These lead to morphological differences
between the two, where the FUV-selected regions are more elongated and
dispersed than the compact H$\alpha$-complexes, also impacting H$\alpha$-to-
FUV SFR ratios. Hence, differences in the FUV and H$\alpha$ apertures as well
as morphologies of the regions are playing a significant role. We explore this
further in §4.2.

###  4.2 Spatial Distribution & Overlaps of FUV and H$\alpha$ Emission

The observations in the previous section allude to aperture mismatches between
the FUV-selected detections and the morphology of H II regions. The larger
FUV-selected apertures compared to the concentrated morphologies of
H$\alpha$-selected regions, as discussed in §3.2, cause SFRHα to be generally
lower for FUV-selected detections. In larger apertures, H$\alpha$ emission
originates only from the portion of the aperture containing H II regions. The
aperture may include diffuse H$\alpha$ emission, but it is likely picking up
noise in areas where UV emission is dominant. Additionally, UV clumps may also
not have any associated H II regions (Gil de Paz et al., 2005; Thilker et al.,
2005; Zaritsky & Christlein, 2007).

In Figure 6, we present two stacked bar plots for each galaxy: the first bar
shows the number of regions, and the second shows the area associated with the
regions. The bar plots are further subdivided into three categories: only FUV,
both FUV and H$\alpha$, and only H$\alpha$ regions. The number of detected
regions and areas for each category are normalized by their corresponding
totals for each galaxy. A region is considered to be detected in both FUV and
H$\alpha$ if the FUV- and H$\alpha$-selected apertures overlap by at least 5
pixels, and are denoted as overlap in the plot. Otherwise, the regions are
considered only FUV or only H$\alpha$ detections.

Figure 6: Stacked bar plots showing the fraction of detected regions (left)
and their corresponding areas (right) for each galaxy. Each bar is subdivided
into three categories: regions detected only in FUV (bottom), overlapping
regions, i.e., regions detected in both FUV and H$\alpha$ (middle), and
regions detected only in H$\alpha$ (top). The number of regions associated
with each category for each galaxy is noted on the bar on the left.

The areal contrast between the FUV-selected and H$\alpha$-selected detections
is clearly illustrated in Figure 6. FUV regions occupy 55–85% of the total
detected area in our galaxies. Further, a significant number of regions,
roughly 30%, are detected in both FUV and H$\alpha$, covering $\sim$20% of the
total detected area. The H$\alpha$-selected regions cover a lower detected
area of 25–65% than FUV. However, most galaxies have more H$\alpha$-only
regions compared to FUV-only. This is not surprising, as H$\alpha$
distributions are clumpier as they are directly linked to the presence of H II
regions and easily detected. However, it is plausible that the continuum UV
emission associated with the H II region is diffuse and widespread, and
doesn’t necessarily show clumping to be detected. Accordingly, the FUV-only
detections imply that these regions do not contain massive stars capable of
producing H II regions.

The areal impact of FUV-selected detections is even more dramatic with
galactocentric distances as seen in Figure 7. Here, we show the cumulative
detection fraction (DF) of the FUV-selected (DFUV), H$\alpha$-selected (DFHα),
and overlapping (DFUV+Hα) pixels as a function of $R/R_{25}$. We define DF as
the ratio of pixels detected in FUV, H$\alpha$, or both to the total number of
pixels detected as sources. The total number of detected pixels is estimated
as $N_{UV}+N_{H\alpha}-N_{FUV+H\alpha}$, where $N_{UV}$, $N_{H\alpha}$, and
$N_{FUV+H\alpha}$, are pixels detected in FUV, H$\alpha$ and both,
respectively. We subtract $N_{FUV+H\alpha}$ to avoid double counting the
overlapping pixels.

Owing to the extensive areal coverage of the UV continuum distribution, we
observe that DFUV is generally higher at any given radius compared to the
H$\alpha$-selected detections, with the exceptions of NGC 5669 and NGC 5951.
This corroborates our observations in §4.1 of larger offsets between SFRUV and
SFRHα seen at large galactocentric distances for the FUV-selected regions
compared to the H$\alpha$-selected regions. The radial decline in DFHα and
DFUV+Hα is pronounced, especially for the latter, when compared to DFUV. The
low DFUV+Hα suggests that a significant portion of the detections is unique to
FUV and H$\alpha$ emission. However, the decline in DFHα relative to DFUV does
not result from a decline in the overall number of H II regions with radius.
We detect comparable numbers of H$\alpha$\- and FUV-selected regions even at
large galactocentric distances (middle left panel of Figure 3). Thus, the high
DFUV and reduction of overlap with increasing radius indicates that
contributions from UV clumps lacking H II regions are substantial.

Figure 7: Cumulative distribution of FUV-selected (dotted line),
H$\alpha$-selected (dashed line), and overlapping (solid line) pixel detection
fraction (DF) as a function of $R/R_{25}$. For most galaxies, DFUV is higher
at a given radius compared to DFHα. DFUV+Hα is considerably lower than DFUV
and DFHα and declines faster with radius. The vertical line shows the radii
containing 90% of the stellar mass in the galaxy, taken from Padave et al.
(2024).

The significant presence of FUV-only emission at larger galactocentric
distances suggests that stochastic variations in the prevalence of massive
stars, and consequently H II regions, may increase with radius. We discuss
this further in the next section.

##  5 Discussion

We investigate the relation between SFRUV and SFRHα derived from the FUV- and
H$\alpha$-selected regions in Figure 8. In general, we find an agreement
between the two SFRs in both cases. A simple linear regression fit to the FUV-
selected data gives SFRHα $=1.10~{}(\pm~{}0.01)~{}\times$ SFRUV
$+~{}0.29(\pm~{}0.05)$. For these regions, SFRUV and SFRHα estimates strongly
correlate with Pearson-$r=0.92$. The H$\alpha$-selected estimates, on the
other hand, also show a closer accord between the two indicators. We note the
linear fit as SFRHα $=1.06~{}(\pm~{}0.01)~{}\times~{}$SFRUV
$+~{}0.08~{}(\pm~{}0.04)$ with a Pearson-$r$ value of 0.93. The median SFR
values per bin are depicted as black symbols and closely align with the linear
trend. Additionally, we note an average scatter of $\pm$0.40 dex per SFR bin.

For a consistent comparison of the SFRs, we compare SFRUV and SFRHα for the
overlapping pixels that are detected in both FUV and H$\alpha$ in Figure 9.
The distribution of SFRUV and SFRHα for overlapping regions yields a linear
fit of SFRHα $=1.06~{}(\pm~{}0.01)~{}\times$ SFRUV $+~{}0.17(\pm~{}0.05)$ with
Pearson-$r$ of 0.94. Overall, we find consistent SFRs from the two indicators.
At lower star formation levels, the underprediction of SFRHα is less
prominent, comparable to the H$\alpha$-selected distribution. Furthermore, the
scatter in the overall distribution is lower when compared to the FUV- and
H$\alpha$-selected relations. This is expected as contributions from FUV-only
and H$\alpha$-only regions are excluded in this case.

Figure 8: Relation between FUV and H$\alpha$ SFRs derived from FUV-selected
(left) and H$\alpha$-selected (right) regions. The solid line shows the one-
to-one correspondence between the two SFRs. The dashed line shows the line of
best fit. The black symbols represent median SFR values per bin with 1$\sigma$
scatter. We find a general agreement between SFRUV and SFRHα.  Figure 9: Same
as Figure 8 but for overlapping pixels.

To completely alleviate any biases that arise from apertures, we also
investigate the distribution of SFRs estimated using grid-based apertures. For
this, we create 6″$\times$6″(4$\times$4 pixels) grid which is consistent with
the GALEX FUV resolution. We estimate the SFRs only within grids where the FUV
and H$\alpha$ signal-to-noise ratio is above 5$\sigma$. The grid-based
distribution is depicted in Figure 10. We find a larger scatter in the grid
distribution, especially towards the low star formation levels. We note a
linear fit giving SFRHα $=1.07~{}(\pm~{}0.01)~{}\times$ SFRUV
$+~{}0.12(\pm~{}0.02)$ and a Pearson-$r$ of 0.87. Interestingly, we do not
find the linear fit to show any significant change in comparison to the FUV-
and H$\alpha$-selected fits.

Figure 10: Same as Figure 8 but for Grid-based estimates.

Figure 11: H$\alpha$-to-FUV SFR ratios as a function of SFRHα for (left) FUV-
selected and (right) H$\alpha$-selected regions. The solid line marks
SFRUV=SFRHα. The black symbols represent median ratios and SFRHα per bin with
1$\sigma$ scatter. We plot integrated SFRs of star-forming spiral and dwarf
galaxies from Lee et al. (2009) along with outlying H II regions in NGC
1512/10 from (Werk et al., 2010). Best fit lines for grid-based SFRs are
plotted in the left panel. The grid sizes, along with the parameters of the
linear fit—slope and intercept—are noted on the plot.

###  5.1 Factors Influencing H$\alpha$-to-FUV SFR Ratios

Our results so far have highlighted the effect of FUV- and H$\alpha$-selected
apertures on H$\alpha$-to-FUV SFR ratios of star-forming regions. While in
general, FUV and H$\alpha$ closely follow each other, discrepancies in the
FUV-to-H$\alpha$ ratios seem to mainly arise from UV emission contributing
more to star formation due to the inherent nature of their continuum
distribution and production mechanisms. We discuss the different factors
affecting the H$\alpha$-to-FUV ratios in this section.

We present the H$\alpha$-to-FUV SFR ratios of the FUV- and H$\alpha$-selected
detections as a function of SFRHα in Figure 11. For comparison, we include the
integrated estimates for the galaxies investigated in Lee et al. (2009) and
outlying HII regions, dubbed Emission-Line Dots (ELdots), in NGC 1512/10 from
(Werk et al., 2010). We note that in each study, the apertures under
consideration are different. While Lee et al. (2009)’s are integrated SFRs,
Werk et al. (2010) use measurements from spectroscopic observations of H II
regions.

We do not observe a severe decline in the ratios as is seen for integrated
SFRs from Lee et al. (2009) at low star formation levels. This offset between
our observations and the integrated values is not surprising as the latter
encompasses the diffuse component of the UV emission in galaxies. We already
note that UV clumps contribute significantly to star formation compared to
H$\alpha$, however, the UV light associated with star clusters or clumps
constitutes $\sim$20% of the total UV flux, while the rest is dominated by
diffuse light (Meurer et al., 1995; Chandar et al., 2005). This diffuse
component of UV light can arise from B stars that have dispersed throughout
the galaxy over time, isolated massive stars, light scattered off of dust
grains, or unresolved star clusters. For nearby galaxies (z$\sim$0.5), the
clumped fraction of the UV was found to constitute 15–40% of the total UV
light (Guo et al., 2015). For our sample, the FUV-selected regions contribute
to only 8–36% of the total SFRUV, leading to relatively high H$\alpha$-to-FUV
SFR ratios when compared to integrated SFRs. Further, H$\alpha$-selected
regions contribute 10–50%, and the clump fraction is on average
$\sim$1.6$\times$ higher than the UV clump fraction.

To investigate the effect of contributions from the diffuse UV light to the
H$\alpha$-to-FUV ratios, we create grids of 10$\times$10 (15″$\times$15″),
30$\times$30 (45″$\times$45″), and 50$\times$50 (75″$\times$75″) pixels, in
addition to the 4$\times$4 pixel grid. The best-fit lines for the relation
between H$\alpha$-to-FUV SFR ratios and SFRHα for the grids are plotted in the
left panel of Figure 11. The slopes and intercepts of the linear fits are
noted in parentheses for each fit on the plot. The 4$\times$4 grid
distribution aligns with the median ratios for the FUV-selected regions.
However, with increasing grid sizes, the intercept is observed to decrease
without much change in the slope of the distribution. These apertures capture
diffuse UV flux, giving rise to H$\alpha$-to-FUV ratios $\sim$0.56 dex lower
than those seen for FUV-selected regions, clearly illustrating the cause of
offset between our distribution and the one from Lee et al. (2009).

Larger apertures lead to lower H$\alpha$-to-FUV ratios. This is also seen when
comparing the FUV-selected and H$\alpha$-selected distribution of
H$\alpha$-to-FUV SFR ratios in Figure 11. The distribution for our sample
progressively declines for the FUV-selected regions, and tails for the
H$\alpha$-selected estimates. At SFRs below 10-4 M⊙ yr-1, the
H$\alpha$-selected regions, SFRHα are generally lower than SFRUV by a factor
of $\sim$1.2–1.5 on average. However, the FUV-selected shows that SFR from
H$\alpha$ is underpredicted by a factor of $\sim$2–3, and the offset between
the two SFRs can increase to 1 dex for larger grids and integrated fluxes.

Another factor affecting the H$\alpha$-to-FUV SFR ratios is the contribution
from UV-only emission that dominates in galaxy disks (Figure 7), especially in
the outer regions where star formation levels are low and hint at stochastic
effects playing a significant role. In low-SFR environments, the IMF may not
be fully populated leading to a lack of massive stars capable of generating H
II regions (Koda et al., 2012; Fumagalli et al., 2011). Combined with the
FUV’s ability to probe a wider range of stellar types and environments,
stochastic variations in the upper end of the IMF result in an increased
prevalence of UV clumps without corresponding H II regions. To illustrate
stochastic effects, Fumagalli et al. (2011) used models generated from the
fully stochastic stellar population synthesis code, SLUG (Stochastically
Lighting Up Galaxies; da Silva et al., 2012) and showed that that the LHα/LUV
distribution in galaxies can be effectively reproduced by simultaneously
modeling the SFR, cluster mass function (CMF), and IMF.

Drawing from Fumagalli et al. (2011)’s findings, we present the LHα/LUV
distribution for our FUV-selected regions as a function of LUV in Figure 12
and compare it to $\sim$5$\times$106 SLUG models. These models are computed
for SFRs ranging from $0.2\times 10^{-5}$ to $0.02$ M⊙ yr-1, assuming a
universal Kroupa IMF spanning masses from 0.08 to 120 M⊙. We adopt the default
CMF with $\beta=2$ across the mass range of 20 to $10^{7}$ M⊙, under the
assumption that all stars form within clusters. Further details regarding the
models align closely with those presented in Fumagalli et al. (2011).
Theoretical prediction from the Kroupa (2001) IMF is also depicted in Figure
12. We find that our observations overlap with the simulated galaxy regions
and are consistent with the analytical prediction from the IMF. While
Fumagalli et al. (2011)’s investigations were carried out for integrated
luminosities, with LUV$>$26 erg s-1 Hz-1, we note that at sub-kpc scales the
models agree with our observations.

Figure 12: H$\alpha$-to-FUV luminosity ratio for FUV-selected regions as a
function of LUV. Models from SLUG (da Silva et al., 2012) for Kroupa IMF with
a cluster fraction of 1 are plotted in the background for comparison. The
dashed line represents the analytical predictions from a fully sampled Kroupa
IMF.

Scatter in the H$\alpha$-to-FUV ratios also highlights other factors affecting
the FUV and H$\alpha$ emission. Flux losses in H II regions are likely and
result from the leakage of Lyman continuum (LyC) photons. We can infer that
LyC leakage may be contributing to some extent to the underestimation of SFRHα
from the H$\alpha$-selected and overlapping regions. While SFRHα and SFRUV are
generally noted to be consistent for H$\alpha$-selected regions throughout our
study, the H$\alpha$ knots with lower H$\alpha$ flux are likely losing
ionizing photons. The leakage of ionizing photons is generally prominent in
low-mass systems (Hoopes et al., 2001; Relaño et al., 2012) and would
contribute to the diffuse component of ionized gas (van Zee, 2000; Oey et al.,
2007). Deeper imaging surveys like those in Lee et al. (2016); Watkins et al.
(2024) and investigations of forbidden-to-Balmer line ratios (Hoopes &
Walterbos, 2003; Madsen et al., 2006; Wang et al., 2019) can shed light on the
effect of Lyman continuum leakage and the budget of the diffuse ionizing gas
on the H$\alpha$-to-FUV ratios.

Notably, there are H II regions and H$\alpha$ knots that are found to have
SFRHα$>$SFRUV. These are seen in both the FUV-selected and H$\alpha$-selected
regions and throughout the galactic disk. If these regions are shrouded in
dust, then FUV would be affected significantly. In that case, first-order dust
corrections may not suffice. However, dust extinction effects may not be as
significant in the outskirts. Kim et al. (2019) investigated dust-extinction
values, AV as a function of galactocentric distance for 257 nearby galaxies,
and found that spiral galaxies showed steeper AV profiles. It is also likely
that the outer disks have relatively small dust grains, as observed in the
Milky Way and nearby galaxies (Zasowski et al., 2009; Keel et al., 2023). For
our sample, the level of dust emission probed using 22$\mu$m and 24$\mu$m data
is seen to decline with radius as investigated by Padave et al. (2024),
suggesting that regions beyond $R_{25}$ may not be affected by dust unless
these are very young and completely obscured by dust. Deeper observations in
the infrared, mapping the dust and its properties would be essential (Williams
et al., 2024).

Moreover, it is also probable that regions with high SFRHα are going through a
recent burst of star formation. FUV and H$\alpha$ are extensively used to
trace burstiness in galaxies due to the different timescales they probe (Emami
et al., 2019; Mehta et al., 2023; Rezaee et al., 2023). Bursty star formation
histories have been extensively found to impact H$\alpha$-to-FUV SFR ratios in
galaxies (Weisz et al., 2012; Emami et al., 2019). At the scale of star-
forming regions, if a region is undergoing a starburst, the H$\alpha$
luminosity (LHα) would increase due to contributions from new O-stars and
consequently, take $\lesssim$10 Myrs to equilibrate. While LHα adjusts quickly
to reflect this change in SFR, the FUV luminosity (LUV) will lag and take
about $\sim$100 Myrs including contributions from the longer-lived stars. This
would lead to higher H$\alpha$-to-FUV SFR ratios. Subsequently, the latter
stages of the burst would result in a decline in the ratios variation in the
H$\alpha$-to-FUV SFR ratios, as the FUV contribution increases and massive
stars die. In lower mass systems and at low star formation levels, Weisz et
al. (2012) found time-variable star formation histories to be consistent with
their observations of H$\alpha$-to-FUV SFR ratios.

##  6 Conclusion

In this study, we investigate the distribution and variations in the H$\alpha$
and FUV emission and examine H$\alpha$-to-FUV flux ratios across star-forming
regions in 11 nearby star-forming galaxies. We utilize archival GALEX FUV
imaging and our narrowband H$\alpha$+[N II] imaging from the VATT to extract
FUV and H$\alpha$ sources from the respective maps. We note these sources as
FUV-selected and H$\alpha$-selected regions. We investigate the demographics
of these regions, morphologies, and radial distributions and also explore
SFRUV and SFRHα for these regions. We summarize our key findings below:

  * 1.

We detect 1335 FUV-selected and 1474 H$\alpha$-selected regions throughout our
sample of 11 galaxies. The morphology of the FUV-selected regions tends to be
extended and these regions generally occupy 55–85% of the total detected area
in a galaxy. H$\alpha$-selected regions, on the other hand, are generally
compact compared to the FUV-selected regions.

  * 2.

The spatial distribution of the FUV-selected and H$\alpha$-selected regions
are identical, and regions are detected even beyond $R_{25}$. However, the
areal spread of FUV-selected regions is significantly larger than
H$\alpha$-selected regions and increases with $R/R_{25}$. The overlap between
FUV- and H$\alpha$-selected regions also decreases with $R/R_{25}$ pointing
towards a radial increase in the stochastic effects in the production of
massive stars responsible for producing H II regions. Our observed
distribution of H$\alpha$-to-FUV SFR ratios agrees with stochastic star
formation models that simultaneously consider the SFR, CMF, and IMF.

  * 3.

Lower H$\alpha$-to-FUV SFR ratios at low levels of SFRs are primarily observed
for FUV-selected regions. At SFR $\lesssim 10^{-3}$ M⊙ yr-1, SFRHα is
underestimated by a factor of 2–3 for the FUV-selected regions. However, when
larger grids are used to estimate SFRs, this factor consistently increases,
and can be as high as $\sim$10\. This discrepancy is due to the increasing
contribution from diffuse UV flux not fully captured by FUV-selected regions,
which only account for 8–36% of the total UV flux in our sample. On the other
hand, H$\alpha$-to-FUV SFR ratios for H$\alpha$-selected regions do not show
any dependence on $R/R_{25}$ and SFRHα, and are only underestimated by a
factor of 1.2–1.5.

The scatter in the SFRHα and SFRUV also suggests that other factors, such as
dust, LyC leakage, and varying star formation histories are also playing a
role in governing the H$\alpha$-to-FUV ratio. In the future, further modeling
of star formation history, metallicities, and dust effects may improve our
understanding of observed offsets and how best to evaluate SFRs in low-density
media.

## ACKNOWLEDGEMENTS

MP, SB, RJ, and DT are supported by NASA ADAP grant 80NSSC21K0643, SB
acknowledges support from by NSF grants 2009409 and 2108159. MP, SB, RJ, and
JM acknowledge the land and the native people that Arizona State University’s
campuses are located in the Salt River Valley. The ancestral territories of
Indigenous peoples, including the Akimel O’odham (Pima) and Pee Posh
(Maricopa) Indian Communities, whose care and keeping of these lands allow us
to be here today.

We thank the staff at the Steward Observatory and the Vatican Advanced
Technology Telescope for their help and support on this project. All GALEX
data presented in this paper were obtained from the Mikulski Archive for Space
Telescopes (MAST) at the Space Telescope Science Institute. The specific
observations analyzed can be accessed viahttps://doi.org/10.17909/rf6m-3y73
(catalog https://doi.org/10.17909/rf6m-3y73).

GALEX is a NASA Small Explorer, launched in 2003 April. We gratefully
acknowledge NASA’s support for the construction, operation, and science
analysis of the GALEX mission, developed in cooperation with the Centre
National d’´Etudes Spatiales (CNES) of France and the Korean Ministry of
Science and Technology.

Based on observations made with the NASA/ESA Hubble Space Telescope, obtained
from the data archive at the Space Telescope Science Institute. STScI is
operated by the Association of Universities for Research in Astronomy, Inc.
under NASA contract NAS 5-26555.

This work is also partly based on observations with the VATT: the Alice P.
Lennon Telescope and the Thomas J. Bannan Astrophysics Facility.

This work is based [in part] on observations made with the Spitzer Space
Telescope, which was operated by the Jet Propulsion Laboratory, California
Institute of Technology under a contract with NASA.

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,
funded by the National Aeronautics and Space Administration.

This research made use of Photutils, an Astropy package for the detection and
photometry of astronomical sources (Bradley et al., 2023).

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